id sid tid token lemma pos american_scientific_journal-7553 1 1 32 32 NUM american_scientific_journal-7553 1 2 american american ADJ american_scientific_journal-7553 1 3 academic academic ADJ american_scientific_journal-7553 1 4 scientific scientific ADJ american_scientific_journal-7553 1 5 research research NOUN american_scientific_journal-7553 1 6 journal journal NOUN american_scientific_journal-7553 1 7 for for ADP american_scientific_journal-7553 1 8 engineering engineering NOUN american_scientific_journal-7553 1 9 , , PUNCT american_scientific_journal-7553 1 10 technology technology NOUN american_scientific_journal-7553 1 11 , , PUNCT american_scientific_journal-7553 1 12 and and CCONJ american_scientific_journal-7553 1 13 sciences sciences PROPN american_scientific_journal-7553 1 14 issn issn PROPN american_scientific_journal-7553 1 15 ( ( PUNCT american_scientific_journal-7553 1 16 print print NOUN american_scientific_journal-7553 1 17 ) ) PUNCT american_scientific_journal-7553 1 18 2313 2313 NUM american_scientific_journal-7553 1 19 - - SYM american_scientific_journal-7553 1 20 4410 4410 NUM american_scientific_journal-7553 1 21 , , PUNCT american_scientific_journal-7553 1 22 issn issn PROPN american_scientific_journal-7553 1 23 ( ( PUNCT american_scientific_journal-7553 1 24 online online ADJ american_scientific_journal-7553 1 25 ) ) PUNCT american_scientific_journal-7553 1 26 2313 2313 NUM american_scientific_journal-7553 1 27 - - SYM american_scientific_journal-7553 1 28 4402 4402 NUM american_scientific_journal-7553 1 29 http://asrjetsjournal.org/ http://asrjetsjournal.org/ NOUN american_scientific_journal-7553 1 30 calculate calculate VERB american_scientific_journal-7553 1 31 the the DET american_scientific_journal-7553 1 32 ground ground NOUN american_scientific_journal-7553 1 33 state state NOUN american_scientific_journal-7553 1 34 energy energy NOUN american_scientific_journal-7553 1 35 of of ADP american_scientific_journal-7553 1 36 hydro hydro PROPN american_scientific_journal-7553 1 37 helium helium NOUN american_scientific_journal-7553 1 38 cation cation NOUN american_scientific_journal-7553 1 39 ( ( PUNCT american_scientific_journal-7553 1 40 2 2 NUM american_scientific_journal-7553 1 41 + + NOUN american_scientific_journal-7553 1 42 ) ) PUNCT american_scientific_journal-7553 1 43 ( ( PUNCT american_scientific_journal-7553 1 44 he he PRON american_scientific_journal-7553 1 45 + + PROPN american_scientific_journal-7553 1 46 + + NUM american_scientific_journal-7553 1 47 h h NOUN american_scientific_journal-7553 1 48 ) ) PUNCT american_scientific_journal-7553 1 49 ayesha ayesha PROPN american_scientific_journal-7553 1 50 khurshid khurshid PROPN american_scientific_journal-7553 1 51 a a PROPN american_scientific_journal-7553 1 52 * * PROPN american_scientific_journal-7553 1 53 , , PUNCT american_scientific_journal-7553 1 54 zia zia PROPN american_scientific_journal-7553 1 55 khan khan PROPN american_scientific_journal-7553 1 56 b b PROPN american_scientific_journal-7553 1 57 a a DET american_scientific_journal-7553 1 58 ned ned ADJ american_scientific_journal-7553 1 59 university university NOUN american_scientific_journal-7553 1 60 of of ADP american_scientific_journal-7553 1 61 engineering engineering PROPN american_scientific_journal-7553 1 62 & & CCONJ american_scientific_journal-7553 1 63 technology technology NOUN american_scientific_journal-7553 1 64 , , PUNCT american_scientific_journal-7553 1 65 address address NOUN american_scientific_journal-7553 1 66 , , PUNCT american_scientific_journal-7553 1 67 karachi karachi PROPN american_scientific_journal-7553 1 68 sindh sindh PROPN american_scientific_journal-7553 1 69 , , PUNCT american_scientific_journal-7553 1 70 pakistan pakistan PROPN american_scientific_journal-7553 1 71 b b PROPN american_scientific_journal-7553 1 72 department department PROPN american_scientific_journal-7553 1 73 of of ADP american_scientific_journal-7553 1 74 electrical electrical ADJ american_scientific_journal-7553 1 75 and and CCONJ american_scientific_journal-7553 1 76 electronic electronic ADJ american_scientific_journal-7553 1 77 engineering engineering NOUN american_scientific_journal-7553 1 78 , , PUNCT american_scientific_journal-7553 1 79 universiti universiti PROPN american_scientific_journal-7553 1 80 teknologi teknologi PROPN american_scientific_journal-7553 1 81 petronas petronas PROPN american_scientific_journal-7553 1 82 , , PUNCT american_scientific_journal-7553 1 83 malaysia malaysia PROPN american_scientific_journal-7553 1 84 a a DET american_scientific_journal-7553 1 85 email email NOUN american_scientific_journal-7553 1 86 : : PUNCT american_scientific_journal-7553 1 87 aisha.khurshid91@gmail.com aisha.khurshid91@gmail.com PROPN american_scientific_journal-7553 1 88 , , PUNCT american_scientific_journal-7553 1 89 b b X american_scientific_journal-7553 1 90 email email NOUN american_scientific_journal-7553 1 91 : : PUNCT american_scientific_journal-7553 1 92 zia.aseer@gmail.com zia.aseer@gmail.com X american_scientific_journal-7553 1 93 abstract abstract ADJ american_scientific_journal-7553 1 94 the the DET american_scientific_journal-7553 1 95 purpose purpose NOUN american_scientific_journal-7553 1 96 of of ADP american_scientific_journal-7553 1 97 this this DET american_scientific_journal-7553 1 98 work work NOUN american_scientific_journal-7553 1 99 is be AUX american_scientific_journal-7553 1 100 to to PART american_scientific_journal-7553 1 101 calculate calculate VERB american_scientific_journal-7553 1 102 the the DET american_scientific_journal-7553 1 103 ground ground NOUN american_scientific_journal-7553 1 104 energy energy NOUN american_scientific_journal-7553 1 105 of of ADP american_scientific_journal-7553 1 106 hydro hydro PROPN american_scientific_journal-7553 1 107 helium helium NOUN american_scientific_journal-7553 1 108 cation cation NOUN american_scientific_journal-7553 1 109 ( ( PUNCT american_scientific_journal-7553 1 110 2 2 NUM american_scientific_journal-7553 1 111 + + NOUN american_scientific_journal-7553 1 112 ) ) PUNCT american_scientific_journal-7553 1 113 by by ADP american_scientific_journal-7553 1 114 using use VERB american_scientific_journal-7553 1 115 the the DET american_scientific_journal-7553 1 116 quantum quantum PROPN american_scientific_journal-7553 1 117 monte monte PROPN american_scientific_journal-7553 1 118 carlo carlo PROPN american_scientific_journal-7553 1 119 method method NOUN american_scientific_journal-7553 1 120 . . PUNCT american_scientific_journal-7553 2 1 using use VERB american_scientific_journal-7553 2 2 the the DET american_scientific_journal-7553 2 3 diffusion diffusion NOUN american_scientific_journal-7553 2 4 quantum quantum PROPN american_scientific_journal-7553 2 5 monte monte PROPN american_scientific_journal-7553 2 6 method method NOUN american_scientific_journal-7553 2 7 , , PUNCT american_scientific_journal-7553 2 8 we we PRON american_scientific_journal-7553 2 9 have have VERB american_scientific_journal-7553 2 10 to to PART american_scientific_journal-7553 2 11 calculate calculate VERB american_scientific_journal-7553 2 12 the the DET american_scientific_journal-7553 2 13 ground ground NOUN american_scientific_journal-7553 2 14 energy energy NOUN american_scientific_journal-7553 2 15 of of ADP american_scientific_journal-7553 2 16 hydro hydro PROPN american_scientific_journal-7553 2 17 helium helium NOUN american_scientific_journal-7553 2 18 cation cation NOUN american_scientific_journal-7553 2 19 ( ( PUNCT american_scientific_journal-7553 2 20 2 2 NUM american_scientific_journal-7553 2 21 + + NOUN american_scientific_journal-7553 2 22 ) ) PUNCT american_scientific_journal-7553 2 23 . . PUNCT american_scientific_journal-7553 3 1 our our PRON american_scientific_journal-7553 3 2 calculation calculation NOUN american_scientific_journal-7553 3 3 is be AUX american_scientific_journal-7553 3 4 based base VERB american_scientific_journal-7553 3 5 on on ADP american_scientific_journal-7553 3 6 slater slater NOUN american_scientific_journal-7553 3 7 - - PUNCT american_scientific_journal-7553 3 8 jastrow jastrow NOUN american_scientific_journal-7553 3 9 form form NOUN american_scientific_journal-7553 3 10 . . PUNCT american_scientific_journal-7553 4 1 we we PRON american_scientific_journal-7553 4 2 have have AUX american_scientific_journal-7553 4 3 developed develop VERB american_scientific_journal-7553 4 4 python python PROPN american_scientific_journal-7553 4 5 code code NOUN american_scientific_journal-7553 4 6 and and CCONJ american_scientific_journal-7553 4 7 run run VERB american_scientific_journal-7553 4 8 this this PRON american_scientific_journal-7553 4 9 on on ADP american_scientific_journal-7553 4 10 high high ADV american_scientific_journal-7553 4 11 - - PUNCT american_scientific_journal-7553 4 12 performing perform VERB american_scientific_journal-7553 4 13 computers computer NOUN american_scientific_journal-7553 4 14 . . PUNCT american_scientific_journal-7553 5 1 a a DET american_scientific_journal-7553 5 2 very very ADV american_scientific_journal-7553 5 3 large large ADJ american_scientific_journal-7553 5 4 number number NOUN american_scientific_journal-7553 5 5 of of ADP american_scientific_journal-7553 5 6 iterations iteration NOUN american_scientific_journal-7553 5 7 is be AUX american_scientific_journal-7553 5 8 required require VERB american_scientific_journal-7553 5 9 to to PART american_scientific_journal-7553 5 10 find find VERB american_scientific_journal-7553 5 11 the the DET american_scientific_journal-7553 5 12 best good ADJ american_scientific_journal-7553 5 13 result result NOUN american_scientific_journal-7553 5 14 . . PUNCT american_scientific_journal-7553 6 1 we we PRON american_scientific_journal-7553 6 2 have have AUX american_scientific_journal-7553 6 3 used use VERB american_scientific_journal-7553 6 4 the the DET american_scientific_journal-7553 6 5 ‘ ' PUNCT american_scientific_journal-7553 6 6 hartree hartree ADJ american_scientific_journal-7553 6 7 unit unit NOUN american_scientific_journal-7553 6 8 ’ ' PUNCT american_scientific_journal-7553 6 9 in in ADP american_scientific_journal-7553 6 10 the the DET american_scientific_journal-7553 6 11 calculation calculation NOUN american_scientific_journal-7553 6 12 of of ADP american_scientific_journal-7553 6 13 electronic electronic ADJ american_scientific_journal-7553 6 14 wave wave NOUN american_scientific_journal-7553 6 15 functions function NOUN american_scientific_journal-7553 6 16 for for ADP american_scientific_journal-7553 6 17 atoms atom NOUN american_scientific_journal-7553 6 18 and and CCONJ american_scientific_journal-7553 6 19 molecules molecule NOUN american_scientific_journal-7553 6 20 . . PUNCT american_scientific_journal-7553 7 1 keywords keyword NOUN american_scientific_journal-7553 7 2 : : PUNCT american_scientific_journal-7553 7 3 hydro hydro NOUN american_scientific_journal-7553 7 4 helium helium NOUN american_scientific_journal-7553 7 5 cation cation NOUN american_scientific_journal-7553 7 6 ; ; PUNCT american_scientific_journal-7553 7 7 quantum quantum PROPN american_scientific_journal-7553 7 8 monte monte PROPN american_scientific_journal-7553 7 9 carlo carlo PROPN american_scientific_journal-7553 7 10 ; ; PUNCT american_scientific_journal-7553 7 11 slater slater NOUN american_scientific_journal-7553 7 12 - - PUNCT american_scientific_journal-7553 7 13 jastrow jastrow NOUN american_scientific_journal-7553 7 14 . . PUNCT american_scientific_journal-7553 8 1 1 1 X american_scientific_journal-7553 8 2 . . X american_scientific_journal-7553 8 3 introduction introduction NOUN american_scientific_journal-7553 8 4 when when SCONJ american_scientific_journal-7553 8 5 we we PRON american_scientific_journal-7553 8 6 have have VERB american_scientific_journal-7553 8 7 a a DET american_scientific_journal-7553 8 8 single single ADJ american_scientific_journal-7553 8 9 electron electron NOUN american_scientific_journal-7553 8 10 , , PUNCT american_scientific_journal-7553 8 11 we we PRON american_scientific_journal-7553 8 12 use use VERB american_scientific_journal-7553 8 13 schrodinger schrodinger ADJ american_scientific_journal-7553 8 14 equation equation NOUN american_scientific_journal-7553 8 15 . . PUNCT american_scientific_journal-7553 9 1 but but CCONJ american_scientific_journal-7553 9 2 , , PUNCT american_scientific_journal-7553 9 3 for for ADP american_scientific_journal-7553 9 4 a a DET american_scientific_journal-7553 9 5 system system NOUN american_scientific_journal-7553 9 6 containing contain VERB american_scientific_journal-7553 9 7 more more ADJ american_scientific_journal-7553 9 8 than than ADP american_scientific_journal-7553 9 9 one one NUM american_scientific_journal-7553 9 10 electron electron NOUN american_scientific_journal-7553 9 11 , , PUNCT american_scientific_journal-7553 9 12 we we PRON american_scientific_journal-7553 9 13 have have VERB american_scientific_journal-7553 9 14 to to PART american_scientific_journal-7553 9 15 go go VERB american_scientific_journal-7553 9 16 through through ADP american_scientific_journal-7553 9 17 some some DET american_scientific_journal-7553 9 18 approximate approximate ADJ american_scientific_journal-7553 9 19 method method NOUN american_scientific_journal-7553 9 20 to to PART american_scientific_journal-7553 9 21 solve solve VERB american_scientific_journal-7553 9 22 the the DET american_scientific_journal-7553 9 23 equation equation NOUN american_scientific_journal-7553 9 24 . . PUNCT american_scientific_journal-7553 10 1 different different ADJ american_scientific_journal-7553 10 2 approximation approximation NOUN american_scientific_journal-7553 10 3 method method NOUN american_scientific_journal-7553 10 4 is be AUX american_scientific_journal-7553 10 5 used use VERB american_scientific_journal-7553 10 6 to to PART american_scientific_journal-7553 10 7 solve solve VERB american_scientific_journal-7553 10 8 approximately approximately ADV american_scientific_journal-7553 10 9 many many ADJ american_scientific_journal-7553 10 10 - - PUNCT american_scientific_journal-7553 10 11 body body NOUN american_scientific_journal-7553 10 12 problems problem NOUN american_scientific_journal-7553 10 13 . . PUNCT american_scientific_journal-7553 11 1 initially initially ADV american_scientific_journal-7553 11 2 , , PUNCT american_scientific_journal-7553 11 3 one one NUM american_scientific_journal-7553 11 4 of of ADP american_scientific_journal-7553 11 5 the the DET american_scientific_journal-7553 11 6 basic basic ADJ american_scientific_journal-7553 11 7 concepts concept NOUN american_scientific_journal-7553 11 8 and and CCONJ american_scientific_journal-7553 11 9 approximation approximation NOUN american_scientific_journal-7553 11 10 was be AUX american_scientific_journal-7553 11 11 introduced introduce VERB american_scientific_journal-7553 11 12 in in ADP american_scientific_journal-7553 11 13 1927 1927 NUM american_scientific_journal-7553 11 14 by by ADP american_scientific_journal-7553 11 15 max max PROPN american_scientific_journal-7553 11 16 born bear VERB american_scientific_journal-7553 11 17 and and CCONJ american_scientific_journal-7553 11 18 j.robert j.robert PROPN american_scientific_journal-7553 11 19 oppenheimer oppenheimer PROPN american_scientific_journal-7553 11 20 to to PART american_scientific_journal-7553 11 21 separate separate VERB american_scientific_journal-7553 11 22 the the DET american_scientific_journal-7553 11 23 electronic electronic ADJ american_scientific_journal-7553 11 24 and and CCONJ american_scientific_journal-7553 11 25 nuclear nuclear ADJ american_scientific_journal-7553 11 26 wave wave NOUN american_scientific_journal-7553 11 27 function function NOUN american_scientific_journal-7553 11 28 with with ADP american_scientific_journal-7553 11 29 neglecting neglecting NOUN american_scientific_journal-7553 11 30 of of ADP american_scientific_journal-7553 11 31 electron electron NOUN american_scientific_journal-7553 11 32 - - PUNCT american_scientific_journal-7553 11 33 nuclear nuclear NOUN american_scientific_journal-7553 11 34 interaction interaction NOUN american_scientific_journal-7553 11 35 and and CCONJ american_scientific_journal-7553 11 36 obtained obtain VERB american_scientific_journal-7553 11 37 the the DET american_scientific_journal-7553 11 38 wave wave NOUN american_scientific_journal-7553 11 39 function function NOUN american_scientific_journal-7553 11 40 and and CCONJ american_scientific_journal-7553 11 41 energy energy NOUN american_scientific_journal-7553 11 42 by by ADP american_scientific_journal-7553 11 43 solving solve VERB american_scientific_journal-7553 11 44 time time NOUN american_scientific_journal-7553 11 45 independent independent ADJ american_scientific_journal-7553 11 46 schròdinger schròding ADJ american_scientific_journal-7553 11 47 equation equation NOUN american_scientific_journal-7553 11 48 . . PUNCT american_scientific_journal-7553 12 1 first first ADJ american_scientific_journal-7553 12 2 quantum quantum ADJ american_scientific_journal-7553 12 3 mechanical mechanical ADJ american_scientific_journal-7553 12 4 understanding understanding NOUN american_scientific_journal-7553 12 5 of of ADP american_scientific_journal-7553 12 6 chemically chemically ADV american_scientific_journal-7553 12 7 bounded bound VERB american_scientific_journal-7553 12 8 system system NOUN american_scientific_journal-7553 12 9 by by ADP american_scientific_journal-7553 12 10 heitler heitler PROPN american_scientific_journal-7553 12 11 and and CCONJ american_scientific_journal-7553 12 12 london london PROPN american_scientific_journal-7553 12 13 in in ADP american_scientific_journal-7553 12 14 1927 1927 NUM american_scientific_journal-7553 12 15 . . PUNCT american_scientific_journal-7553 13 1 they they PRON american_scientific_journal-7553 13 2 calculate calculate VERB american_scientific_journal-7553 13 3 the the DET american_scientific_journal-7553 13 4 binding bind VERB american_scientific_journal-7553 13 5 energy energy NOUN american_scientific_journal-7553 13 6 and and CCONJ american_scientific_journal-7553 13 7 inter inter ADJ american_scientific_journal-7553 13 8 nuclear nuclear ADJ american_scientific_journal-7553 13 9 separation separation NOUN american_scientific_journal-7553 13 10 of of ADP american_scientific_journal-7553 13 11 hydrogen hydrogen NOUN american_scientific_journal-7553 13 12 molecules molecule NOUN american_scientific_journal-7553 13 13 [ [ X american_scientific_journal-7553 13 14 1 1 NUM american_scientific_journal-7553 13 15 ] ] PUNCT american_scientific_journal-7553 13 16 . . PUNCT american_scientific_journal-7553 14 1 in in ADP american_scientific_journal-7553 14 2 1928 1928 NUM american_scientific_journal-7553 14 3 d.r d.r PRON american_scientific_journal-7553 14 4 hartree hartree NOUN american_scientific_journal-7553 14 5 introduced introduce VERB american_scientific_journal-7553 14 6 a a DET american_scientific_journal-7553 14 7 new new ADJ american_scientific_journal-7553 14 8 method method NOUN american_scientific_journal-7553 14 9 at at ADP american_scientific_journal-7553 14 10 that that DET american_scientific_journal-7553 14 11 time time NOUN american_scientific_journal-7553 14 12 this this DET american_scientific_journal-7553 14 13 method method NOUN american_scientific_journal-7553 14 14 is be AUX american_scientific_journal-7553 14 15 called call VERB american_scientific_journal-7553 14 16 the the DET american_scientific_journal-7553 14 17 self self NOUN american_scientific_journal-7553 14 18 -the -the DET american_scientific_journal-7553 14 19 consistent consistent ADJ american_scientific_journal-7553 14 20 field field NOUN american_scientific_journal-7553 14 21 method method NOUN american_scientific_journal-7553 14 22 . . PUNCT american_scientific_journal-7553 15 1 by by ADP american_scientific_journal-7553 15 2 using use VERB american_scientific_journal-7553 15 3 this this DET american_scientific_journal-7553 15 4 method method NOUN american_scientific_journal-7553 15 5 he he PRON american_scientific_journal-7553 15 6 wanted want VERB american_scientific_journal-7553 15 7 to to PART american_scientific_journal-7553 15 8 solve solve VERB american_scientific_journal-7553 15 9 many many ADJ american_scientific_journal-7553 15 10 - - PUNCT american_scientific_journal-7553 15 11 body body NOUN american_scientific_journal-7553 15 12 complex complex ADJ american_scientific_journal-7553 15 13 problems problem NOUN american_scientific_journal-7553 15 14 . . PUNCT american_scientific_journal-7553 16 1 but but CCONJ american_scientific_journal-7553 16 2 this this DET american_scientific_journal-7553 16 3 method method NOUN american_scientific_journal-7553 16 4 is be AUX american_scientific_journal-7553 16 5 insufficient insufficient ADJ american_scientific_journal-7553 16 6 because because SCONJ american_scientific_journal-7553 16 7 of of ADP american_scientific_journal-7553 16 8 neglecting neglect VERB american_scientific_journal-7553 16 9 the the DET american_scientific_journal-7553 16 10 antisymmetric antisymmetric ADJ american_scientific_journal-7553 16 11 behavior behavior NOUN american_scientific_journal-7553 16 12 of of ADP american_scientific_journal-7553 16 13 wave wave NOUN american_scientific_journal-7553 16 14 function function NOUN american_scientific_journal-7553 16 15 . . PUNCT american_scientific_journal-7553 17 1 this this DET american_scientific_journal-7553 17 2 deficiency deficiency NOUN american_scientific_journal-7553 17 3 was be AUX american_scientific_journal-7553 17 4 overcome overcome VERB american_scientific_journal-7553 17 5 by by ADP american_scientific_journal-7553 17 6 fock fock ADJ american_scientific_journal-7553 17 7 . . PUNCT american_scientific_journal-7553 18 1 then then ADV american_scientific_journal-7553 18 2 this this DET american_scientific_journal-7553 18 3 method method NOUN american_scientific_journal-7553 18 4 is be AUX american_scientific_journal-7553 18 5 called call VERB american_scientific_journal-7553 18 6 the the DET american_scientific_journal-7553 18 7 hartree hartree ADV american_scientific_journal-7553 18 8 - - PUNCT american_scientific_journal-7553 18 9 fock fock ADJ american_scientific_journal-7553 18 10 method method NOUN american_scientific_journal-7553 18 11 [ [ X american_scientific_journal-7553 18 12 2 2 NUM american_scientific_journal-7553 18 13 ] ] PUNCT american_scientific_journal-7553 18 14 . . PUNCT american_scientific_journal-7553 19 1 moreover moreover ADV american_scientific_journal-7553 19 2 , , PUNCT american_scientific_journal-7553 19 3 other other ADJ american_scientific_journal-7553 19 4 approximation approximation NOUN american_scientific_journal-7553 19 5 methods method NOUN american_scientific_journal-7553 19 6 have have AUX american_scientific_journal-7553 19 7 been be AUX american_scientific_journal-7553 19 8 developed develop VERB american_scientific_journal-7553 19 9 in in ADP american_scientific_journal-7553 19 10 which which PRON american_scientific_journal-7553 19 11 many many ADJ american_scientific_journal-7553 19 12 - - PUNCT american_scientific_journal-7553 19 13 electron electron NOUN american_scientific_journal-7553 19 14 theory theory NOUN american_scientific_journal-7553 19 15 ( ( PUNCT american_scientific_journal-7553 19 16 dft dft PROPN american_scientific_journal-7553 19 17 ) ) PUNCT american_scientific_journal-7553 19 18 was be AUX american_scientific_journal-7553 19 19 introduced introduce VERB american_scientific_journal-7553 19 20 in in ADP american_scientific_journal-7553 19 21 1964 1964 NUM american_scientific_journal-7553 19 22 . . PUNCT american_scientific_journal-7553 20 1 ----------------------------------------------------------------------- ----------------------------------------------------------------------- PUNCT american_scientific_journal-7553 21 1 * * PUNCT american_scientific_journal-7553 21 2 corresponding correspond VERB american_scientific_journal-7553 21 3 author author NOUN american_scientific_journal-7553 21 4 . . PUNCT american_scientific_journal-7553 22 1 http://asrjetsjournal.org/ http://asrjetsjournal.org/ PROPN american_scientific_journal-7553 22 2 american american PROPN american_scientific_journal-7553 22 3 academic academic PROPN american_scientific_journal-7553 22 4 scientific scientific ADJ american_scientific_journal-7553 22 5 research research NOUN american_scientific_journal-7553 22 6 journal journal NOUN american_scientific_journal-7553 22 7 for for ADP american_scientific_journal-7553 22 8 engineering engineering NOUN american_scientific_journal-7553 22 9 , , PUNCT american_scientific_journal-7553 22 10 technology technology NOUN american_scientific_journal-7553 22 11 , , PUNCT american_scientific_journal-7553 22 12 and and CCONJ american_scientific_journal-7553 22 13 sciences science NOUN american_scientific_journal-7553 22 14 ( ( PUNCT american_scientific_journal-7553 22 15 asrjets asrjet NOUN american_scientific_journal-7553 22 16 ) ) PUNCT american_scientific_journal-7553 22 17 ( ( PUNCT american_scientific_journal-7553 22 18 2022 2022 NUM american_scientific_journal-7553 22 19 ) ) PUNCT american_scientific_journal-7553 22 20 volume volume NOUN american_scientific_journal-7553 22 21 87 87 NUM american_scientific_journal-7553 22 22 , , PUNCT american_scientific_journal-7553 22 23 no no DET american_scientific_journal-7553 22 24 1 1 NUM american_scientific_journal-7553 22 25 , , PUNCT american_scientific_journal-7553 22 26 pp pp ADV american_scientific_journal-7553 22 27 32 32 NUM american_scientific_journal-7553 22 28 - - SYM american_scientific_journal-7553 22 29 38 38 NUM american_scientific_journal-7553 22 30 33 33 NUM american_scientific_journal-7553 22 31 the the DET american_scientific_journal-7553 22 32 assumption assumption NOUN american_scientific_journal-7553 22 33 made make VERB american_scientific_journal-7553 22 34 in in ADP american_scientific_journal-7553 22 35 this this PRON american_scientific_journal-7553 22 36 is be AUX american_scientific_journal-7553 22 37 that that SCONJ american_scientific_journal-7553 22 38 a a DET american_scientific_journal-7553 22 39 many many ADJ american_scientific_journal-7553 22 40 electron electron NOUN american_scientific_journal-7553 22 41 system system NOUN american_scientific_journal-7553 22 42 is be AUX american_scientific_journal-7553 22 43 reduced reduce VERB american_scientific_journal-7553 22 44 in in ADP american_scientific_journal-7553 22 45 a a DET american_scientific_journal-7553 22 46 single single ADJ american_scientific_journal-7553 22 47 electron electron NOUN american_scientific_journal-7553 22 48 problem problem NOUN american_scientific_journal-7553 22 49 with with ADP american_scientific_journal-7553 22 50 effective effective ADJ american_scientific_journal-7553 22 51 electron electron NOUN american_scientific_journal-7553 22 52 potential potential NOUN american_scientific_journal-7553 22 53 that that PRON american_scientific_journal-7553 22 54 relies rely VERB american_scientific_journal-7553 22 55 on on ADP american_scientific_journal-7553 22 56 electron electron NOUN american_scientific_journal-7553 22 57 density density NOUN american_scientific_journal-7553 22 58 . . PUNCT american_scientific_journal-7553 23 1 in in ADP american_scientific_journal-7553 23 2 1942 1942 NUM american_scientific_journal-7553 23 3 , , PUNCT american_scientific_journal-7553 23 4 frosted frosted ADJ american_scientific_journal-7553 23 5 developed develop VERB american_scientific_journal-7553 23 6 high high ADJ american_scientific_journal-7553 23 7 accuracy accuracy NOUN american_scientific_journal-7553 23 8 approximation approximation NOUN american_scientific_journal-7553 23 9 in in ADP american_scientific_journal-7553 23 10 the the DET american_scientific_journal-7553 23 11 variational variational ADJ american_scientific_journal-7553 23 12 quantum quantum ADJ american_scientific_journal-7553 23 13 monte monte PROPN american_scientific_journal-7553 23 14 carlo carlo PROPN american_scientific_journal-7553 23 15 ( ( PUNCT american_scientific_journal-7553 23 16 qmc qmc PROPN american_scientific_journal-7553 23 17 ) ) PUNCT american_scientific_journal-7553 23 18 method method NOUN american_scientific_journal-7553 23 19 . . PUNCT american_scientific_journal-7553 24 1 other other ADJ american_scientific_journal-7553 24 2 types type NOUN american_scientific_journal-7553 24 3 of of ADP american_scientific_journal-7553 24 4 qmc qmc PROPN american_scientific_journal-7553 24 5 had have AUX american_scientific_journal-7553 24 6 been be AUX american_scientific_journal-7553 24 7 developed develop VERB american_scientific_journal-7553 24 8 later later ADV american_scientific_journal-7553 24 9 . . PUNCT american_scientific_journal-7553 25 1 like like ADP american_scientific_journal-7553 25 2 diffusion diffusion NOUN american_scientific_journal-7553 25 3 qmc qmc PROPN american_scientific_journal-7553 25 4 , , PUNCT american_scientific_journal-7553 25 5 green green ADJ american_scientific_journal-7553 25 6 function function NOUN american_scientific_journal-7553 25 7 qmc qmc PROPN american_scientific_journal-7553 25 8 , , PUNCT american_scientific_journal-7553 25 9 path path NOUN american_scientific_journal-7553 25 10 integral integral ADJ american_scientific_journal-7553 25 11 qmc qmc NOUN american_scientific_journal-7553 25 12 , , PUNCT american_scientific_journal-7553 25 13 and and CCONJ american_scientific_journal-7553 25 14 auxilary auxilary ADJ american_scientific_journal-7553 25 15 -field -field PROPN american_scientific_journal-7553 25 16 qmc qmc PROPN american_scientific_journal-7553 25 17 method method NOUN american_scientific_journal-7553 25 18 . . PUNCT american_scientific_journal-7553 26 1 qmc qmc VERB american_scientific_journal-7553 26 2 method method NOUN american_scientific_journal-7553 26 3 gives give VERB american_scientific_journal-7553 26 4 the the DET american_scientific_journal-7553 26 5 most most ADV american_scientific_journal-7553 26 6 accurate accurate ADJ american_scientific_journal-7553 26 7 wavefunction wavefunction NOUN american_scientific_journal-7553 26 8 including include VERB american_scientific_journal-7553 26 9 co co NOUN american_scientific_journal-7553 26 10 - - NOUN american_scientific_journal-7553 26 11 relation relation NOUN american_scientific_journal-7553 26 12 terms term NOUN american_scientific_journal-7553 26 13 of of ADP american_scientific_journal-7553 26 14 electron electron NOUN american_scientific_journal-7553 26 15 and and CCONJ american_scientific_journal-7553 26 16 finds find VERB american_scientific_journal-7553 26 17 energies energy NOUN american_scientific_journal-7553 26 18 for for ADP american_scientific_journal-7553 26 19 small small ADJ american_scientific_journal-7553 26 20 and and CCONJ american_scientific_journal-7553 26 21 large large ADJ american_scientific_journal-7553 26 22 molecules molecule NOUN american_scientific_journal-7553 26 23 as as ADV american_scientific_journal-7553 26 24 well well ADV american_scientific_journal-7553 26 25 as as ADP american_scientific_journal-7553 26 26 for for ADP american_scientific_journal-7553 26 27 liquid liquid NOUN american_scientific_journal-7553 26 28 , , PUNCT american_scientific_journal-7553 26 29 solids solid NOUN american_scientific_journal-7553 26 30 , , PUNCT american_scientific_journal-7553 26 31 and and CCONJ american_scientific_journal-7553 26 32 clusters cluster NOUN american_scientific_journal-7553 26 33 [ [ X american_scientific_journal-7553 26 34 3 3 NUM american_scientific_journal-7553 26 35 ] ] PUNCT american_scientific_journal-7553 26 36 . . PUNCT american_scientific_journal-7553 27 1 1.1 1.1 NUM american_scientific_journal-7553 27 2 purpose purpose NOUN american_scientific_journal-7553 27 3 of of ADP american_scientific_journal-7553 27 4 study study NOUN american_scientific_journal-7553 27 5 we we PRON american_scientific_journal-7553 27 6 want want VERB american_scientific_journal-7553 27 7 to to PART american_scientific_journal-7553 27 8 calculate calculate VERB american_scientific_journal-7553 27 9 ground ground NOUN american_scientific_journal-7553 27 10 state state NOUN american_scientific_journal-7553 27 11 energy energy NOUN american_scientific_journal-7553 27 12 of of ADP american_scientific_journal-7553 27 13 hydro hydro NOUN american_scientific_journal-7553 27 14 helium helium NOUN american_scientific_journal-7553 27 15 cation cation NOUN american_scientific_journal-7553 27 16 by by ADP american_scientific_journal-7553 27 17 using use VERB american_scientific_journal-7553 27 18 simulation simulation NOUN american_scientific_journal-7553 27 19 of of ADP american_scientific_journal-7553 27 20 diffusion diffusion NOUN american_scientific_journal-7553 27 21 of of ADP american_scientific_journal-7553 27 22 quantum quantum PROPN american_scientific_journal-7553 27 23 montee montee PROPN american_scientific_journal-7553 27 24 carlo carlo PROPN american_scientific_journal-7553 27 25 ( ( PUNCT american_scientific_journal-7553 27 26 dmc dmc PROPN american_scientific_journal-7553 27 27 ) ) PUNCT american_scientific_journal-7553 27 28 . . PUNCT american_scientific_journal-7553 28 1 as as ADP american_scientific_journal-7553 28 2 the the DET american_scientific_journal-7553 28 3 number number NOUN american_scientific_journal-7553 28 4 of of ADP american_scientific_journal-7553 28 5 electrons electron NOUN american_scientific_journal-7553 28 6 increases increase NOUN american_scientific_journal-7553 28 7 , , PUNCT american_scientific_journal-7553 28 8 systems system NOUN american_scientific_journal-7553 28 9 are be AUX american_scientific_journal-7553 28 10 going go VERB american_scientific_journal-7553 28 11 to to ADP american_scientific_journal-7553 28 12 many many ADJ american_scientific_journal-7553 28 13 problems problem NOUN american_scientific_journal-7553 28 14 in in ADP american_scientific_journal-7553 28 15 which which PRON american_scientific_journal-7553 28 16 interaction interaction NOUN american_scientific_journal-7553 28 17 terms term NOUN american_scientific_journal-7553 28 18 are be AUX american_scientific_journal-7553 28 19 increased increase VERB american_scientific_journal-7553 28 20 . . PUNCT american_scientific_journal-7553 29 1 because because SCONJ american_scientific_journal-7553 29 2 , , PUNCT american_scientific_journal-7553 29 3 every every DET american_scientific_journal-7553 29 4 electron electron NOUN american_scientific_journal-7553 29 5 interacts interact VERB american_scientific_journal-7553 29 6 with with ADP american_scientific_journal-7553 29 7 the the DET american_scientific_journal-7553 29 8 nucleus nucleus NOUN american_scientific_journal-7553 29 9 , , PUNCT american_scientific_journal-7553 29 10 proton proton NOUN american_scientific_journal-7553 29 11 , , PUNCT american_scientific_journal-7553 29 12 and and CCONJ american_scientific_journal-7553 29 13 electron electron NOUN american_scientific_journal-7553 29 14 . . PUNCT american_scientific_journal-7553 30 1 for for ADP american_scientific_journal-7553 30 2 many many ADJ american_scientific_journal-7553 30 3 problem problem NOUN american_scientific_journal-7553 30 4 systems system NOUN american_scientific_journal-7553 30 5 , , PUNCT american_scientific_journal-7553 30 6 we we PRON american_scientific_journal-7553 30 7 use use VERB american_scientific_journal-7553 30 8 different different ADJ american_scientific_journal-7553 30 9 approximation approximation NOUN american_scientific_journal-7553 30 10 methods method NOUN american_scientific_journal-7553 30 11 and and CCONJ american_scientific_journal-7553 30 12 simulation simulation NOUN american_scientific_journal-7553 30 13 techniques technique NOUN american_scientific_journal-7553 30 14 . . PUNCT american_scientific_journal-7553 31 1 for for ADP american_scientific_journal-7553 31 2 qmc qmc PROPN american_scientific_journal-7553 31 3 , , PUNCT american_scientific_journal-7553 31 4 our our PRON american_scientific_journal-7553 31 5 result result NOUN american_scientific_journal-7553 31 6 is be AUX american_scientific_journal-7553 31 7 based base VERB american_scientific_journal-7553 31 8 on on ADP american_scientific_journal-7553 31 9 the the DET american_scientific_journal-7553 31 10 trial trial NOUN american_scientific_journal-7553 31 11 wave wave NOUN american_scientific_journal-7553 31 12 function function NOUN american_scientific_journal-7553 31 13 . . PUNCT american_scientific_journal-7553 32 1 1.2 1.2 NUM american_scientific_journal-7553 32 2 literature literature PROPN american_scientific_journal-7553 32 3 review review PROPN american_scientific_journal-7553 32 4   X american_scientific_journal-7553 32 5 calculate calculate NOUN american_scientific_journal-7553 32 6 lattice lattice NOUN american_scientific_journal-7553 32 7 energy energy NOUN american_scientific_journal-7553 32 8 for for ADP american_scientific_journal-7553 32 9 different different ADJ american_scientific_journal-7553 32 10 molecular molecular ADJ american_scientific_journal-7553 32 11 crystals crystal NOUN american_scientific_journal-7553 32 12 using use VERB american_scientific_journal-7553 32 13 the the DET american_scientific_journal-7553 32 14 diffusion diffusion NOUN american_scientific_journal-7553 32 15 quantum quantum PROPN american_scientific_journal-7553 32 16 monte monte PROPN american_scientific_journal-7553 32 17 carlo carlo PROPN american_scientific_journal-7553 32 18 approach approach NOUN american_scientific_journal-7553 32 19 and and CCONJ american_scientific_journal-7553 32 20 compared compare VERB american_scientific_journal-7553 32 21 their their PRON american_scientific_journal-7553 32 22 result result NOUN american_scientific_journal-7553 32 23 with with ADP american_scientific_journal-7553 32 24 experimental experimental ADJ american_scientific_journal-7553 32 25 results result NOUN american_scientific_journal-7553 32 26 . . PUNCT american_scientific_journal-7553 33 1 they they PRON american_scientific_journal-7553 33 2 calculated calculate VERB american_scientific_journal-7553 33 3 lattice lattice NOUN american_scientific_journal-7553 33 4 energy energy NOUN american_scientific_journal-7553 33 5 for for ADP american_scientific_journal-7553 33 6 three three NUM american_scientific_journal-7553 33 7 polymorphs polymorph NOUN american_scientific_journal-7553 33 8 of of ADP american_scientific_journal-7553 33 9 ice ice NOUN american_scientific_journal-7553 33 10 ; ; PUNCT american_scientific_journal-7553 33 11 hexagonal hexagonal ADJ american_scientific_journal-7553 33 12 ice ice NOUN american_scientific_journal-7553 33 13 , , PUNCT american_scientific_journal-7553 33 14 ice ice NOUN american_scientific_journal-7553 33 15 ii ii PROPN american_scientific_journal-7553 33 16 and and CCONJ american_scientific_journal-7553 33 17 ice ice PROPN american_scientific_journal-7553 33 18 iii iii PROPN american_scientific_journal-7553 33 19 , , PUNCT american_scientific_journal-7553 33 20 carbon carbon NOUN american_scientific_journal-7553 33 21 dioxide dioxide NOUN american_scientific_journal-7553 33 22 ( ( PUNCT american_scientific_journal-7553 33 23 co2 co2 NOUN american_scientific_journal-7553 33 24 ) ) PUNCT american_scientific_journal-7553 33 25 , , PUNCT american_scientific_journal-7553 33 26 ammonia ammonia NOUN american_scientific_journal-7553 33 27 ( ( PUNCT american_scientific_journal-7553 33 28 nh3 nh3 NOUN american_scientific_journal-7553 33 29 ) ) PUNCT american_scientific_journal-7553 33 30 naphthalene naphthalene NOUN american_scientific_journal-7553 33 31 ( ( PUNCT american_scientific_journal-7553 33 32 c10h8 c10h8 X american_scientific_journal-7553 33 33 ) ) PUNCT american_scientific_journal-7553 33 34 and and CCONJ american_scientific_journal-7553 33 35 anthracene anthracene VERB american_scientific_journal-7553 33 36 ( ( PUNCT american_scientific_journal-7553 33 37 c14h10 c14h10 NOUN american_scientific_journal-7553 33 38 ) ) PUNCT american_scientific_journal-7553 34 1 [ [ X american_scientific_journal-7553 34 2 4 4 NUM american_scientific_journal-7553 34 3 ] ] SYM american_scientific_journal-7553 34 4 table table NOUN american_scientific_journal-7553 34 5 1 1 NUM american_scientific_journal-7553 34 6 crystal crystal NOUN american_scientific_journal-7553 34 7 dmc(large dmc(large NOUN american_scientific_journal-7553 34 8 supercell supercell NOUN american_scientific_journal-7553 34 9 ) ) PUNCT american_scientific_journal-7553 34 10 dmc dmc PROPN american_scientific_journal-7553 34 11 ( ( PUNCT american_scientific_journal-7553 34 12 small small ADJ american_scientific_journal-7553 34 13 supercell supercell NOUN american_scientific_journal-7553 34 14 ) ) PUNCT american_scientific_journal-7553 34 15 experiment experiment NOUN american_scientific_journal-7553 34 16 ice ice NOUN american_scientific_journal-7553 34 17 ih ih NOUN american_scientific_journal-7553 34 18 59.3±0.5 59.3±0.5 NUM american_scientific_journal-7553 34 19 59.2±0.2 59.2±0.2 NUM american_scientific_journal-7553 34 20 58.8 58.8 NUM american_scientific_journal-7553 34 21 ice ice NOUN american_scientific_journal-7553 34 22 ii ii NOUN american_scientific_journal-7553 34 23 59.1±0.6 59.1±0.6 NUM american_scientific_journal-7553 34 24 59±0.3 59±0.3 NUM american_scientific_journal-7553 34 25 58.8 58.8 NUM american_scientific_journal-7553 34 26 ice ice NOUN american_scientific_journal-7553 34 27 viii viii NOUN american_scientific_journal-7553 34 28 57.3±0.6 57.3±0.6 NUM american_scientific_journal-7553 34 29 57.4±0.1 57.4±0.1 NUM american_scientific_journal-7553 34 30 57.4 57.4 NUM american_scientific_journal-7553 34 31 co2 co2 NOUN american_scientific_journal-7553 34 32 28.2 28.2 NUM american_scientific_journal-7553 34 33 + + NOUN american_scientific_journal-7553 34 34 1.3 1.3 NUM american_scientific_journal-7553 34 35 28.5±0.4 28.5±0.4 NUM american_scientific_journal-7553 34 36 28.4 28.4 NUM american_scientific_journal-7553 34 37 nh3 nh3 NUM american_scientific_journal-7553 34 38 37.1±0.4 37.1±0.4 NUM american_scientific_journal-7553 34 39 51.2 51.2 NUM american_scientific_journal-7553 34 40 + + NOUN american_scientific_journal-7553 34 41 0.2 0.2 NUM american_scientific_journal-7553 34 42 50.6 50.6 NUM american_scientific_journal-7553 34 43 c6h6 c6h6 NOUN american_scientific_journal-7553 34 44 52.1±0.4 52.1±0.4 NUM american_scientific_journal-7553 34 45 51.2±0.2 51.2±0.2 NUM american_scientific_journal-7553 34 46 50.6 50.6 NUM american_scientific_journal-7553 34 47 c10h8 c10h8 NOUN american_scientific_journal-7553 34 48 78.8±8 78.8±8 NUM american_scientific_journal-7553 34 49 78.0±0.6 78.0±0.6 NUM american_scientific_journal-7553 34 50 79.2 79.2 NUM american_scientific_journal-7553 34 51 c14h10 c14h10 NOUN american_scientific_journal-7553 34 52 105.5±1.7 105.5±1.7 PROPN american_scientific_journal-7553 34 53 103.9±1 103.9±1 NUM american_scientific_journal-7553 34 54 105.8 105.8 NUM american_scientific_journal-7553 34 55   NOUN american_scientific_journal-7553 34 56 calculated calculate VERB american_scientific_journal-7553 34 57 the the DET american_scientific_journal-7553 34 58 binding bind VERB american_scientific_journal-7553 34 59 energies energy NOUN american_scientific_journal-7553 34 60 of of ADP american_scientific_journal-7553 34 61 isolated isolate VERB american_scientific_journal-7553 34 62 trions trion NOUN american_scientific_journal-7553 34 63 and and CCONJ american_scientific_journal-7553 34 64 biexcitons biexciton NOUN american_scientific_journal-7553 34 65 using use VERB american_scientific_journal-7553 34 66 the the DET american_scientific_journal-7553 34 67 approach approach NOUN american_scientific_journal-7553 34 68 of of ADP american_scientific_journal-7553 34 69 vmc vmc PROPN american_scientific_journal-7553 34 70 and and CCONJ american_scientific_journal-7553 34 71 dmc dmc NOUN american_scientific_journal-7553 34 72 . . PUNCT american_scientific_journal-7553 35 1 [ [ X american_scientific_journal-7553 35 2 5 5 NUM american_scientific_journal-7553 35 3 ] ] PUNCT american_scientific_journal-7553 35 4   X american_scientific_journal-7553 35 5 studied study VERB american_scientific_journal-7553 35 6 and and CCONJ american_scientific_journal-7553 35 7 calculated calculate VERB american_scientific_journal-7553 35 8 the the DET american_scientific_journal-7553 35 9 ground ground NOUN american_scientific_journal-7553 35 10 state state NOUN american_scientific_journal-7553 35 11 energy energy NOUN american_scientific_journal-7553 35 12 of of ADP american_scientific_journal-7553 35 13 free free ADJ american_scientific_journal-7553 35 14 and and CCONJ american_scientific_journal-7553 35 15 confined confine VERB american_scientific_journal-7553 35 16 hydrogen hydrogen NOUN american_scientific_journal-7553 35 17 atoms atom NOUN american_scientific_journal-7553 35 18 by by ADP american_scientific_journal-7553 35 19 using use VERB american_scientific_journal-7553 35 20 variational variational ADJ american_scientific_journal-7553 35 21 quantum quantum NOUN american_scientific_journal-7553 35 22 montee montee PROPN american_scientific_journal-7553 35 23 carlo carlo PROPN american_scientific_journal-7553 35 24 ( ( PUNCT american_scientific_journal-7553 35 25 vmc vmc PROPN american_scientific_journal-7553 35 26 ) ) PUNCT american_scientific_journal-7553 35 27 . . PUNCT american_scientific_journal-7553 36 1 [ [ X american_scientific_journal-7553 36 2 6 6 NUM american_scientific_journal-7553 36 3 ] ] PUNCT american_scientific_journal-7553 36 4   X american_scientific_journal-7553 36 5 calculated calculate VERB american_scientific_journal-7553 36 6 the the DET american_scientific_journal-7553 36 7 dielectric dielectric ADJ american_scientific_journal-7553 36 8 permittivity permittivity NOUN american_scientific_journal-7553 36 9 of of ADP american_scientific_journal-7553 36 10 suspended suspend VERB american_scientific_journal-7553 36 11 graphene graphene NOUN american_scientific_journal-7553 36 12 by by ADP american_scientific_journal-7553 36 13 using use VERB american_scientific_journal-7553 36 14 the the DET american_scientific_journal-7553 36 15 simulation simulation NOUN american_scientific_journal-7553 36 16 technique technique NOUN american_scientific_journal-7553 36 17 of of ADP american_scientific_journal-7553 36 18 qmc qmc VERB american_scientific_journal-7553 36 19 for for ADP american_scientific_journal-7553 36 20 a a DET american_scientific_journal-7553 36 21 set set NOUN american_scientific_journal-7553 36 22 of of ADP american_scientific_journal-7553 36 23 temperatures temperature NOUN american_scientific_journal-7553 36 24 and and CCONJ american_scientific_journal-7553 36 25 extrapolated extrapolate VERB american_scientific_journal-7553 36 26 to to ADP american_scientific_journal-7553 36 27 zero zero NUM american_scientific_journal-7553 36 28 distance distance NOUN american_scientific_journal-7553 36 29 . . PUNCT american_scientific_journal-7553 37 1 [ [ X american_scientific_journal-7553 37 2 7 7 X american_scientific_journal-7553 37 3 ] ] PUNCT american_scientific_journal-7553 37 4   X american_scientific_journal-7553 37 5 calculate calculate NOUN american_scientific_journal-7553 37 6 the the DET american_scientific_journal-7553 37 7 helmholtz helmholtz NOUN american_scientific_journal-7553 37 8 free free ADJ american_scientific_journal-7553 37 9 energy energy NOUN american_scientific_journal-7553 37 10 ( ( PUNCT american_scientific_journal-7553 37 11 sum sum NOUN american_scientific_journal-7553 37 12 of of ADP american_scientific_journal-7553 37 13 electronic electronic ADJ american_scientific_journal-7553 37 14 energy energy NOUN american_scientific_journal-7553 37 15 and and CCONJ american_scientific_journal-7553 37 16 harmonic harmonic ADJ american_scientific_journal-7553 37 17 vibrational vibrational ADJ american_scientific_journal-7553 37 18 free free ADJ american_scientific_journal-7553 37 19 energy energy NOUN american_scientific_journal-7553 37 20 ) ) PUNCT american_scientific_journal-7553 37 21 of of ADP american_scientific_journal-7553 37 22 tio2 tio2 NOUN american_scientific_journal-7553 37 23 polymorphs polymorph NOUN american_scientific_journal-7553 37 24 using use VERB american_scientific_journal-7553 37 25 diffusion diffusion NOUN american_scientific_journal-7553 37 26 quantum quantum PROPN american_scientific_journal-7553 37 27 monte monte PROPN american_scientific_journal-7553 37 28 carlo carlo PROPN american_scientific_journal-7553 37 29 ( ( PUNCT american_scientific_journal-7553 37 30 dmc dmc PROPN american_scientific_journal-7553 37 31 ) ) PUNCT american_scientific_journal-7553 37 32 method method NOUN american_scientific_journal-7553 37 33 and and CCONJ american_scientific_journal-7553 37 34 density density NOUN american_scientific_journal-7553 37 35 function function NOUN american_scientific_journal-7553 37 36 theory theory NOUN american_scientific_journal-7553 37 37 ( ( PUNCT american_scientific_journal-7553 37 38 dft).[8 dft).[8 PROPN american_scientific_journal-7553 37 39 ] ] PUNCT american_scientific_journal-7553 37 40   X american_scientific_journal-7553 37 41 calculated calculate VERB american_scientific_journal-7553 37 42 the the DET american_scientific_journal-7553 37 43 total total ADJ american_scientific_journal-7553 37 44 energy energy NOUN american_scientific_journal-7553 37 45 of of ADP american_scientific_journal-7553 37 46 lithium lithium NOUN american_scientific_journal-7553 37 47 dime dime NOUN american_scientific_journal-7553 37 48 ( ( PUNCT american_scientific_journal-7553 37 49 li+2 li+2 X american_scientific_journal-7553 37 50 and and CCONJ american_scientific_journal-7553 37 51 li-2 li-2 NOUN american_scientific_journal-7553 37 52 ) ) PUNCT american_scientific_journal-7553 37 53 by by ADP american_scientific_journal-7553 37 54 using use VERB american_scientific_journal-7553 37 55 the the DET american_scientific_journal-7553 37 56 quantum quantum ADJ american_scientific_journal-7553 37 57 monte monte PROPN american_scientific_journal-7553 37 58 carlo(dmc carlo(dmc PROPN american_scientific_journal-7553 37 59 ) ) PUNCT american_scientific_journal-7553 37 60 method.[9 method.[9 PROPN american_scientific_journal-7553 37 61 ] ] PUNCT american_scientific_journal-7553 37 62 american american PROPN american_scientific_journal-7553 37 63 academic academic ADJ american_scientific_journal-7553 37 64 scientific scientific ADJ american_scientific_journal-7553 37 65 research research NOUN american_scientific_journal-7553 37 66 journal journal NOUN american_scientific_journal-7553 37 67 for for ADP american_scientific_journal-7553 37 68 engineering engineering NOUN american_scientific_journal-7553 37 69 , , PUNCT american_scientific_journal-7553 37 70 technology technology NOUN american_scientific_journal-7553 37 71 , , PUNCT american_scientific_journal-7553 37 72 and and CCONJ american_scientific_journal-7553 37 73 sciences science NOUN american_scientific_journal-7553 37 74 ( ( PUNCT american_scientific_journal-7553 37 75 asrjets asrjet NOUN american_scientific_journal-7553 37 76 ) ) PUNCT american_scientific_journal-7553 37 77 ( ( PUNCT american_scientific_journal-7553 37 78 2022 2022 NUM american_scientific_journal-7553 37 79 ) ) PUNCT american_scientific_journal-7553 37 80 volume volume NOUN american_scientific_journal-7553 37 81 87 87 NUM american_scientific_journal-7553 37 82 , , PUNCT american_scientific_journal-7553 37 83 no no DET american_scientific_journal-7553 37 84 1 1 NUM american_scientific_journal-7553 37 85 , , PUNCT american_scientific_journal-7553 37 86 pp pp ADV american_scientific_journal-7553 37 87 32 32 NUM american_scientific_journal-7553 37 88 - - SYM american_scientific_journal-7553 37 89 38 38 NUM american_scientific_journal-7553 37 90 34 34 NUM american_scientific_journal-7553 37 91 2 2 NUM american_scientific_journal-7553 37 92 . . PUNCT american_scientific_journal-7553 37 93 methodology methodology NOUN american_scientific_journal-7553 37 94 we we PRON american_scientific_journal-7553 37 95 use use VERB american_scientific_journal-7553 37 96 the the DET american_scientific_journal-7553 37 97 dmc dmc PROPN american_scientific_journal-7553 37 98 method method NOUN american_scientific_journal-7553 37 99 to to PART american_scientific_journal-7553 37 100 calculate calculate VERB american_scientific_journal-7553 37 101 the the DET american_scientific_journal-7553 37 102 ground ground NOUN american_scientific_journal-7553 37 103 energy energy NOUN american_scientific_journal-7553 37 104 of of ADP american_scientific_journal-7553 37 105 hydro hydro NOUN american_scientific_journal-7553 37 106 helium helium NOUN american_scientific_journal-7553 37 107 cation cation NOUN american_scientific_journal-7553 37 108 . . PUNCT american_scientific_journal-7553 38 1 our our PRON american_scientific_journal-7553 38 2 trial trial NOUN american_scientific_journal-7553 38 3 wave wave NOUN american_scientific_journal-7553 38 4 function function NOUN american_scientific_journal-7553 38 5 is be AUX american_scientific_journal-7553 38 6 based base VERB american_scientific_journal-7553 38 7 on on ADP american_scientific_journal-7553 38 8 slater slater NOUN american_scientific_journal-7553 38 9 - - PUNCT american_scientific_journal-7553 38 10 jastrow jastrow NOUN american_scientific_journal-7553 38 11 type type NOUN american_scientific_journal-7553 38 12 and and CCONJ american_scientific_journal-7553 38 13 used use VERB american_scientific_journal-7553 38 14 importance importance NOUN american_scientific_journal-7553 38 15 sampling sample VERB american_scientific_journal-7553 38 16 technique technique NOUN american_scientific_journal-7553 38 17 to to PART american_scientific_journal-7553 38 18 improve improve VERB american_scientific_journal-7553 38 19 accuracy accuracy NOUN american_scientific_journal-7553 38 20 for for ADP american_scientific_journal-7553 38 21 the the DET american_scientific_journal-7553 38 22 dmc dmc PROPN american_scientific_journal-7553 38 23 method method NOUN american_scientific_journal-7553 38 24 , , PUNCT american_scientific_journal-7553 38 25 trial trial NOUN american_scientific_journal-7553 38 26 wave wave NOUN american_scientific_journal-7553 38 27 function function NOUN american_scientific_journal-7553 38 28 is be AUX american_scientific_journal-7553 38 29 based base VERB american_scientific_journal-7553 38 30 on on ADP american_scientific_journal-7553 38 31 a a DET american_scientific_journal-7553 38 32 basic basic ADJ american_scientific_journal-7553 38 33 set set NOUN american_scientific_journal-7553 38 34 of of ADP american_scientific_journal-7553 38 35 slater slater NOUN american_scientific_journal-7553 38 36 type type NOUN american_scientific_journal-7553 38 37 orbitals orbital NOUN american_scientific_journal-7553 38 38 ( ( PUNCT american_scientific_journal-7553 38 39 stos stos NOUN american_scientific_journal-7553 38 40 ) ) PUNCT american_scientific_journal-7553 38 41 . . PUNCT american_scientific_journal-7553 39 1 we we PRON american_scientific_journal-7553 39 2 have have AUX american_scientific_journal-7553 39 3 developed develop VERB american_scientific_journal-7553 39 4 the the DET american_scientific_journal-7553 39 5 qmc qmc ADJ american_scientific_journal-7553 39 6 code code NOUN american_scientific_journal-7553 39 7 for for ADP american_scientific_journal-7553 39 8 this this DET american_scientific_journal-7553 39 9 cation cation NOUN american_scientific_journal-7553 39 10 and and CCONJ american_scientific_journal-7553 39 11 simulated simulate VERB american_scientific_journal-7553 39 12 it it PRON american_scientific_journal-7553 39 13 as as ADP american_scientific_journal-7553 39 14 a a DET american_scientific_journal-7553 39 15 python python NOUN american_scientific_journal-7553 39 16 programming programming NOUN american_scientific_journal-7553 39 17 language language NOUN american_scientific_journal-7553 39 18 . . PUNCT american_scientific_journal-7553 40 1 dmc dmc PROPN american_scientific_journal-7553 40 2 algorithm algorithm NOUN american_scientific_journal-7553 40 3 the the DET american_scientific_journal-7553 40 4 dmc dmc PROPN american_scientific_journal-7553 40 5 algorithm algorithm NOUN american_scientific_journal-7553 40 6 used use VERB american_scientific_journal-7553 40 7 to to PART american_scientific_journal-7553 40 8 calculate calculate VERB american_scientific_journal-7553 40 9 the the DET american_scientific_journal-7553 40 10 ground ground NOUN american_scientific_journal-7553 40 11 energy energy NOUN american_scientific_journal-7553 40 12 is be AUX american_scientific_journal-7553 40 13 almost almost ADV american_scientific_journal-7553 40 14 similar similar ADJ american_scientific_journal-7553 40 15 to to ADP american_scientific_journal-7553 40 16 those those PRON american_scientific_journal-7553 40 17 in in ADP american_scientific_journal-7553 40 18 reference reference NOUN american_scientific_journal-7553 40 19 [ [ X american_scientific_journal-7553 40 20 10][11 10][11 NUM american_scientific_journal-7553 40 21 ] ] PUNCT american_scientific_journal-7553 40 22 . . PUNCT american_scientific_journal-7553 41 1 i. i. PROPN american_scientific_journal-7553 41 2 at at ADP american_scientific_journal-7553 41 3 the the DET american_scientific_journal-7553 41 4 start start NOUN american_scientific_journal-7553 41 5 of of ADP american_scientific_journal-7553 41 6 the the DET american_scientific_journal-7553 41 7 simulation simulation NOUN american_scientific_journal-7553 41 8 for for ADP american_scientific_journal-7553 41 9 time time NOUN american_scientific_journal-7553 41 10 0 0 NUM american_scientific_journal-7553 41 11 to to ADP american_scientific_journal-7553 41 12 t t PROPN american_scientific_journal-7553 41 13 for for ADP american_scientific_journal-7553 41 14 walker walker PROPN american_scientific_journal-7553 41 15 0 0 PROPN american_scientific_journal-7553 41 16 to to PART american_scientific_journal-7553 41 17 nwalker nwalker VERB american_scientific_journal-7553 41 18 for for ADP american_scientific_journal-7553 41 19 particles particle NOUN american_scientific_journal-7553 41 20 0 0 NUM american_scientific_journal-7553 41 21 to to ADP american_scientific_journal-7553 41 22 n n PROPN american_scientific_journal-7553 41 23 particles particle NOUN american_scientific_journal-7553 41 24 a. a. NOUN american_scientific_journal-7553 41 25 initial initial PROPN american_scientific_journal-7553 41 26 walker walker PROPN american_scientific_journal-7553 41 27 ni ni PROPN american_scientific_journal-7553 41 28 are be AUX american_scientific_journal-7553 41 29 distributed distribute VERB american_scientific_journal-7553 41 30 in in ADP american_scientific_journal-7553 41 31 configuration configuration NOUN american_scientific_journal-7553 41 32 space space NOUN american_scientific_journal-7553 41 33 to to PART american_scientific_journal-7553 41 34 prepare prepare VERB american_scientific_journal-7553 41 35 some some DET american_scientific_journal-7553 41 36 initial initial ADJ american_scientific_journal-7553 41 37 wave wave NOUN american_scientific_journal-7553 41 38 function function NOUN american_scientific_journal-7553 41 39 b. b. PROPN american_scientific_journal-7553 42 1 the the DET american_scientific_journal-7553 42 2 reference reference NOUN american_scientific_journal-7553 42 3 energy energy NOUN american_scientific_journal-7553 42 4 er er INTJ american_scientific_journal-7553 42 5 is be AUX american_scientific_journal-7553 42 6 taken take VERB american_scientific_journal-7553 42 7 as as ADP american_scientific_journal-7553 42 8 an an DET american_scientific_journal-7553 42 9 average average ADJ american_scientific_journal-7553 42 10 potential potential NOUN american_scientific_journal-7553 42 11 of of ADP american_scientific_journal-7553 42 12 walker walker PROPN american_scientific_journal-7553 42 13 ii ii PROPN american_scientific_journal-7553 42 14 . . PUNCT american_scientific_journal-7553 43 1 at at ADP american_scientific_journal-7553 43 2 each each DET american_scientific_journal-7553 43 3 iteration iteration NOUN american_scientific_journal-7553 43 4 of of ADP american_scientific_journal-7553 43 5 the the DET american_scientific_journal-7553 43 6 simulation simulation NOUN american_scientific_journal-7553 43 7 a. a. NOUN american_scientific_journal-7553 43 8 the the DET american_scientific_journal-7553 43 9 time time NOUN american_scientific_journal-7553 43 10 t t PROPN american_scientific_journal-7553 43 11 is be AUX american_scientific_journal-7553 43 12 chosen choose VERB american_scientific_journal-7553 43 13 by by ADP american_scientific_journal-7553 43 14 a a DET american_scientific_journal-7553 43 15 small small ADJ american_scientific_journal-7553 43 16 change change NOUN american_scientific_journal-7553 43 17 . . PUNCT american_scientific_journal-7553 44 1 b. b. VERB american_scientific_journal-7553 45 1 the the DET american_scientific_journal-7553 45 2 position position NOUN american_scientific_journal-7553 45 3 of of ADP american_scientific_journal-7553 45 4 walker walker NOUN american_scientific_journal-7553 45 5 is be AUX american_scientific_journal-7553 45 6 reformed reform VERB american_scientific_journal-7553 45 7 by by ADP american_scientific_journal-7553 45 8 an an DET american_scientific_journal-7553 45 9 arbitrary arbitrary ADJ american_scientific_journal-7553 45 10 variate variate NOUN american_scientific_journal-7553 45 11 from from ADP american_scientific_journal-7553 45 12 a a DET american_scientific_journal-7553 45 13 gaussian gaussian ADJ american_scientific_journal-7553 45 14 distribution distribution NOUN american_scientific_journal-7553 45 15 with with ADP american_scientific_journal-7553 45 16 mean mean PROPN american_scientific_journal-7553 45 17 0 0 NUM american_scientific_journal-7553 45 18 and and CCONJ american_scientific_journal-7553 45 19 standard standard ADJ american_scientific_journal-7553 45 20 deviation deviation NOUN american_scientific_journal-7553 45 21 σ σ NOUN american_scientific_journal-7553 45 22 = = PUNCT american_scientific_journal-7553 45 23 √(ħ∆ʈ/ √(ħ∆ʈ/ PROPN american_scientific_journal-7553 45 24 mn mn PROPN american_scientific_journal-7553 45 25 ) ) PUNCT american_scientific_journal-7553 45 26 c. c. PROPN american_scientific_journal-7553 45 27 reference reference NOUN american_scientific_journal-7553 45 28 energy energy NOUN american_scientific_journal-7553 45 29 is be AUX american_scientific_journal-7553 45 30 calculated calculate VERB american_scientific_journal-7553 45 31 from from ADP american_scientific_journal-7553 45 32 the the DET american_scientific_journal-7553 45 33 new new ADJ american_scientific_journal-7553 45 34 configuration configuration NOUN american_scientific_journal-7553 45 35 of of ADP american_scientific_journal-7553 45 36 walkers walker NOUN american_scientific_journal-7553 45 37 by by ADP american_scientific_journal-7553 45 38 the the DET american_scientific_journal-7553 45 39 function function NOUN american_scientific_journal-7553 45 40 er=+α(1 er=+α(1 NOUN american_scientific_journal-7553 45 41 - - PUNCT american_scientific_journal-7553 45 42 n n CCONJ american_scientific_journal-7553 45 43 / / SYM american_scientific_journal-7553 45 44 ni ni NOUN american_scientific_journal-7553 45 45 ) ) PUNCT american_scientific_journal-7553 45 46 ( ( PUNCT american_scientific_journal-7553 45 47 1 1 X american_scientific_journal-7553 45 48 ) ) PUNCT american_scientific_journal-7553 45 49 where where SCONJ american_scientific_journal-7553 45 50 < < X american_scientific_journal-7553 45 51 v v X american_scientific_journal-7553 45 52 > > X american_scientific_journal-7553 45 53 is be AUX american_scientific_journal-7553 45 54 the the DET american_scientific_journal-7553 45 55 average average ADJ american_scientific_journal-7553 45 56 potential potential NOUN american_scientific_journal-7553 45 57 of of ADP american_scientific_journal-7553 45 58 all all DET american_scientific_journal-7553 45 59 the the DET american_scientific_journal-7553 45 60 walkers walker NOUN american_scientific_journal-7553 45 61 and and CCONJ american_scientific_journal-7553 45 62 n n NOUN american_scientific_journal-7553 45 63 is be AUX american_scientific_journal-7553 45 64 the the DET american_scientific_journal-7553 45 65 present present ADJ american_scientific_journal-7553 45 66 number number NOUN american_scientific_journal-7553 45 67 of of ADP american_scientific_journal-7553 45 68 walkers walker NOUN american_scientific_journal-7553 45 69 . . PUNCT american_scientific_journal-7553 46 1 d. d. PROPN american_scientific_journal-7553 46 2 for for ADP american_scientific_journal-7553 46 3 every every DET american_scientific_journal-7553 46 4 walker walker NOUN american_scientific_journal-7553 46 5 , , PUNCT american_scientific_journal-7553 46 6 a a DET american_scientific_journal-7553 46 7 number number NOUN american_scientific_journal-7553 46 8 mn mn PROPN american_scientific_journal-7553 46 9 is be AUX american_scientific_journal-7553 46 10 calculated calculate VERB american_scientific_journal-7553 46 11 by by ADP american_scientific_journal-7553 46 12 mn=[w(xn)+u mn=[w(xn)+u NOUN american_scientific_journal-7553 46 13 ] ] PUNCT american_scientific_journal-7553 46 14 ( ( PUNCT american_scientific_journal-7553 46 15 2 2 X american_scientific_journal-7553 46 16 ) ) PUNCT american_scientific_journal-7553 46 17 u u NOUN american_scientific_journal-7553 46 18 is be AUX american_scientific_journal-7553 46 19 a a DET american_scientific_journal-7553 46 20 random random ADJ american_scientific_journal-7553 46 21 number number NOUN american_scientific_journal-7553 46 22 that that PRON american_scientific_journal-7553 46 23 is be AUX american_scientific_journal-7553 46 24 equally equally ADV american_scientific_journal-7553 46 25 distributed distribute VERB american_scientific_journal-7553 46 26 from from ADP american_scientific_journal-7553 46 27 0 0 NUM american_scientific_journal-7553 46 28 to to ADP american_scientific_journal-7553 46 29 1 1 NUM american_scientific_journal-7553 46 30 and and CCONJ american_scientific_journal-7553 46 31 w(xn w(xn NOUN american_scientific_journal-7553 46 32 ) ) PUNCT american_scientific_journal-7553 46 33 is be AUX american_scientific_journal-7553 46 34 the the DET american_scientific_journal-7553 46 35 weight weight NOUN american_scientific_journal-7553 46 36 of of ADP american_scientific_journal-7553 46 37 the the DET american_scientific_journal-7553 46 38 walker walker NOUN american_scientific_journal-7553 46 39 with with ADP american_scientific_journal-7553 46 40 xn=1,,2,3 xn=1,,2,3 PROPN american_scientific_journal-7553 46 41 , , PUNCT american_scientific_journal-7553 46 42 … … PUNCT american_scientific_journal-7553 46 43 . . X american_scientific_journal-7553 47 1 defined define VERB american_scientific_journal-7553 47 2 as as ADP american_scientific_journal-7553 47 3 american american PROPN american_scientific_journal-7553 47 4 academic academic PROPN american_scientific_journal-7553 47 5 scientific scientific ADJ american_scientific_journal-7553 47 6 research research NOUN american_scientific_journal-7553 47 7 journal journal NOUN american_scientific_journal-7553 47 8 for for ADP american_scientific_journal-7553 47 9 engineering engineering NOUN american_scientific_journal-7553 47 10 , , PUNCT american_scientific_journal-7553 47 11 technology technology NOUN american_scientific_journal-7553 47 12 , , PUNCT american_scientific_journal-7553 47 13 and and CCONJ american_scientific_journal-7553 47 14 sciences science NOUN american_scientific_journal-7553 47 15 ( ( PUNCT american_scientific_journal-7553 47 16 asrjets asrjet NOUN american_scientific_journal-7553 47 17 ) ) PUNCT american_scientific_journal-7553 47 18 ( ( PUNCT american_scientific_journal-7553 47 19 2022 2022 NUM american_scientific_journal-7553 47 20 ) ) PUNCT american_scientific_journal-7553 47 21 volume volume NOUN american_scientific_journal-7553 47 22 87 87 NUM american_scientific_journal-7553 47 23 , , PUNCT american_scientific_journal-7553 47 24 no no DET american_scientific_journal-7553 47 25 1 1 NUM american_scientific_journal-7553 47 26 , , PUNCT american_scientific_journal-7553 47 27 pp pp ADV american_scientific_journal-7553 47 28 32 32 NUM american_scientific_journal-7553 47 29 - - SYM american_scientific_journal-7553 47 30 38 38 NUM american_scientific_journal-7553 47 31 35 35 NUM american_scientific_journal-7553 47 32 w(xn)= w(xn)= PROPN american_scientific_journal-7553 47 33 ( ( PUNCT american_scientific_journal-7553 47 34 ( ( PUNCT american_scientific_journal-7553 47 35 3 3 X american_scientific_journal-7553 47 36 ) ) PUNCT american_scientific_journal-7553 47 37 if if SCONJ american_scientific_journal-7553 47 38 mn=0 mn=0 PROPN american_scientific_journal-7553 47 39 walker walker NOUN american_scientific_journal-7553 47 40 is be AUX american_scientific_journal-7553 47 41 destroyed destroy VERB american_scientific_journal-7553 47 42 and and CCONJ american_scientific_journal-7553 47 43 diffusion diffusion NOUN american_scientific_journal-7553 47 44 will will AUX american_scientific_journal-7553 47 45 be be AUX american_scientific_journal-7553 47 46 stopped stop VERB american_scientific_journal-7553 47 47 this this PRON american_scientific_journal-7553 47 48 termed term VERB american_scientific_journal-7553 47 49 as as ADP american_scientific_journal-7553 47 50 the the DET american_scientific_journal-7553 47 51 death death NOUN american_scientific_journal-7553 47 52 of of ADP american_scientific_journal-7553 47 53 the the DET american_scientific_journal-7553 47 54 particle particle NOUN american_scientific_journal-7553 47 55 if if SCONJ american_scientific_journal-7553 47 56 mn=1 mn=1 PRON american_scientific_journal-7553 47 57 continues continue VERB american_scientific_journal-7553 47 58 with with ADP american_scientific_journal-7553 47 59 the the DET american_scientific_journal-7553 47 60 next next ADJ american_scientific_journal-7553 47 61 diffusion diffusion NOUN american_scientific_journal-7553 47 62 and and CCONJ american_scientific_journal-7553 47 63 particle particle NOUN american_scientific_journal-7553 47 64 will will AUX american_scientific_journal-7553 47 65 remain remain VERB american_scientific_journal-7553 47 66 unaffected unaffected ADJ american_scientific_journal-7553 47 67 mn>0 mn>0 PROPN american_scientific_journal-7553 47 68 continues continue VERB american_scientific_journal-7553 47 69 with with ADP american_scientific_journal-7553 47 70 diffusion diffusion NOUN american_scientific_journal-7553 47 71 with with ADP american_scientific_journal-7553 47 72 the the DET american_scientific_journal-7553 47 73 birth birth NOUN american_scientific_journal-7553 47 74 of of ADP american_scientific_journal-7553 47 75 particle particle NOUN american_scientific_journal-7553 47 76 3 3 NUM american_scientific_journal-7553 47 77 . . PUNCT american_scientific_journal-7553 48 1 repeat repeat VERB american_scientific_journal-7553 48 2 the the DET american_scientific_journal-7553 48 3 configuration configuration NOUN american_scientific_journal-7553 48 4 moves move NOUN american_scientific_journal-7553 48 5 for for ADP american_scientific_journal-7553 48 6 several several ADJ american_scientific_journal-7553 48 7 steps step NOUN american_scientific_journal-7553 48 8 . . PUNCT american_scientific_journal-7553 49 1 4 4 X american_scientific_journal-7553 49 2 . . PUNCT american_scientific_journal-7553 49 3 to to PART american_scientific_journal-7553 49 4 calculate calculate VERB american_scientific_journal-7553 49 5 the the DET american_scientific_journal-7553 49 6 ground ground NOUN american_scientific_journal-7553 49 7 state state NOUN american_scientific_journal-7553 49 8 energy energy NOUN american_scientific_journal-7553 49 9 , , PUNCT american_scientific_journal-7553 49 10 the the DET american_scientific_journal-7553 49 11 reference reference NOUN american_scientific_journal-7553 49 12 energies energy NOUN american_scientific_journal-7553 49 13 of of ADP american_scientific_journal-7553 49 14 alliteration alliteration NOUN american_scientific_journal-7553 49 15 are be AUX american_scientific_journal-7553 49 16 averaged average VERB american_scientific_journal-7553 49 17 . . PUNCT american_scientific_journal-7553 50 1 5 5 X american_scientific_journal-7553 50 2 . . X american_scientific_journal-7553 50 3 repeat repeat VERB american_scientific_journal-7553 50 4 until until SCONJ american_scientific_journal-7553 50 5 sufficient sufficient ADJ american_scientific_journal-7553 50 6 data datum NOUN american_scientific_journal-7553 50 7 is be AUX american_scientific_journal-7553 50 8 obtained obtain VERB american_scientific_journal-7553 50 9 2.1 2.1 NUM american_scientific_journal-7553 50 10 dmc dmc NOUN american_scientific_journal-7553 50 11 flow flow NOUN american_scientific_journal-7553 50 12 diagram diagram NOUN american_scientific_journal-7553 50 13 the the DET american_scientific_journal-7553 50 14 flow flow NOUN american_scientific_journal-7553 50 15 diagram diagram NOUN american_scientific_journal-7553 50 16 of of ADP american_scientific_journal-7553 50 17 the the DET american_scientific_journal-7553 50 18 dmc dmc PROPN american_scientific_journal-7553 50 19 method method NOUN american_scientific_journal-7553 50 20 for for SCONJ american_scientific_journal-7553 50 21 a a DET american_scientific_journal-7553 50 22 computer computer NOUN american_scientific_journal-7553 50 23 program program NOUN american_scientific_journal-7553 50 24 is be AUX american_scientific_journal-7553 50 25 shown show VERB american_scientific_journal-7553 50 26 in in ADP american_scientific_journal-7553 50 27 figure figure NOUN american_scientific_journal-7553 50 28 1 1 NUM american_scientific_journal-7553 50 29 . . PUNCT american_scientific_journal-7553 51 1 input input NOUN american_scientific_journal-7553 51 2 all all DET american_scientific_journal-7553 51 3 initial initial ADJ american_scientific_journal-7553 51 4 data datum NOUN american_scientific_journal-7553 51 5 to to PART american_scientific_journal-7553 51 6 start start VERB american_scientific_journal-7553 51 7 the the DET american_scientific_journal-7553 51 8 simulation simulation NOUN american_scientific_journal-7553 51 9 which which PRON american_scientific_journal-7553 51 10 consists consist VERB american_scientific_journal-7553 51 11 of of ADP american_scientific_journal-7553 51 12 the the DET american_scientific_journal-7553 51 13 number number NOUN american_scientific_journal-7553 51 14 of of ADP american_scientific_journal-7553 51 15 coordinates coordinate NOUN american_scientific_journal-7553 51 16 , , PUNCT american_scientific_journal-7553 51 17 particles particle NOUN american_scientific_journal-7553 51 18 , , PUNCT american_scientific_journal-7553 51 19 and and CCONJ american_scientific_journal-7553 51 20 iterations iteration NOUN american_scientific_journal-7553 51 21 , , PUNCT american_scientific_journal-7553 51 22 the the DET american_scientific_journal-7553 51 23 number number NOUN american_scientific_journal-7553 51 24 of of ADP american_scientific_journal-7553 51 25 walkers walker NOUN american_scientific_journal-7553 51 26 , , PUNCT american_scientific_journal-7553 51 27 reference reference NOUN american_scientific_journal-7553 51 28 energy energy NOUN american_scientific_journal-7553 51 29 , , PUNCT american_scientific_journal-7553 51 30 value value NOUN american_scientific_journal-7553 51 31 of of ADP american_scientific_journal-7553 51 32 time time NOUN american_scientific_journal-7553 51 33 step step NOUN american_scientific_journal-7553 51 34 . . PUNCT american_scientific_journal-7553 52 1 initialize initialize NOUN american_scientific_journal-7553 52 2 replicas replica NOUN american_scientific_journal-7553 52 3 estimate estimate VERB american_scientific_journal-7553 52 4 the the DET american_scientific_journal-7553 52 5 diffusion diffusion NOUN american_scientific_journal-7553 52 6 and and CCONJ american_scientific_journal-7553 52 7 branching branch VERB american_scientific_journal-7553 52 8 terms term NOUN american_scientific_journal-7553 52 9 in in ADP american_scientific_journal-7553 52 10 the the DET american_scientific_journal-7553 52 11 form form NOUN american_scientific_journal-7553 52 12 of of ADP american_scientific_journal-7553 52 13 an an DET american_scientific_journal-7553 52 14 n n CCONJ american_scientific_journal-7553 52 15 dimensional dimensional ADJ american_scientific_journal-7553 52 16 matrix matrix NOUN american_scientific_journal-7553 52 17 and and CCONJ american_scientific_journal-7553 52 18 impose impose VERB american_scientific_journal-7553 52 19 the the DET american_scientific_journal-7553 52 20 limitation limitation NOUN american_scientific_journal-7553 52 21 on on ADP american_scientific_journal-7553 52 22 the the DET american_scientific_journal-7553 52 23 birth birth NOUN american_scientific_journal-7553 52 24 of of ADP american_scientific_journal-7553 52 25 a a DET american_scientific_journal-7553 52 26 new new ADJ american_scientific_journal-7553 52 27 particle particle NOUN american_scientific_journal-7553 52 28 to to PART american_scientific_journal-7553 52 29 control control VERB american_scientific_journal-7553 52 30 the the DET american_scientific_journal-7553 52 31 birth birth NOUN american_scientific_journal-7553 52 32 walk walk VERB american_scientific_journal-7553 52 33 this this PRON american_scientific_journal-7553 52 34 performs perform VERB american_scientific_journal-7553 52 35 the the DET american_scientific_journal-7553 52 36 task task NOUN american_scientific_journal-7553 52 37 of of ADP american_scientific_journal-7553 52 38 diffusion diffusion NOUN american_scientific_journal-7553 52 39 process process NOUN american_scientific_journal-7553 52 40 which which PRON american_scientific_journal-7553 52 41 generates generate VERB american_scientific_journal-7553 52 42 a a DET american_scientific_journal-7553 52 43 new new ADJ american_scientific_journal-7553 52 44 successive successive ADJ american_scientific_journal-7553 52 45 position position NOUN american_scientific_journal-7553 52 46 of of ADP american_scientific_journal-7553 52 47 x x PUNCT american_scientific_journal-7553 52 48 for for ADP american_scientific_journal-7553 52 49 different different ADJ american_scientific_journal-7553 52 50 values value NOUN american_scientific_journal-7553 52 51 of of ADP american_scientific_journal-7553 52 52 n n X american_scientific_journal-7553 52 53 by by ADP american_scientific_journal-7553 52 54 generating generate VERB american_scientific_journal-7553 52 55 the the DET american_scientific_journal-7553 52 56 series series NOUN american_scientific_journal-7553 52 57 of of ADP american_scientific_journal-7553 52 58 random random ADJ american_scientific_journal-7553 52 59 numbers number NOUN american_scientific_journal-7553 52 60 ƿn ƿn ADP american_scientific_journal-7553 52 61 , , PUNCT american_scientific_journal-7553 52 62 n=1,2,3 n=1,2,3 NUM american_scientific_journal-7553 52 63 , , PUNCT american_scientific_journal-7553 52 64 … … PUNCT american_scientific_journal-7553 52 65 . . PUNCT american_scientific_journal-7553 53 1 x0x1 x0x1 X american_scientific_journal-7553 54 1 = = X american_scientific_journal-7553 54 2 x0+σƿ1x2 x0+σƿ1x2 X american_scientific_journal-7553 54 3 = = SYM american_scientific_journal-7553 54 4 x1+σƿ2 x1+σƿ2 NOUN american_scientific_journal-7553 54 5 where where SCONJ american_scientific_journal-7553 54 6 σ σ PROPN american_scientific_journal-7553 54 7 is be AUX american_scientific_journal-7553 54 8 the the DET american_scientific_journal-7553 54 9 standard standard ADJ american_scientific_journal-7553 54 10 deviation deviation NOUN american_scientific_journal-7553 54 11 from from ADP american_scientific_journal-7553 54 12 the the DET american_scientific_journal-7553 54 13 mean mean ADJ american_scientific_journal-7553 54 14 position position NOUN american_scientific_journal-7553 54 15 . . PUNCT american_scientific_journal-7553 55 1 branch branch NOUN american_scientific_journal-7553 55 2 this this PRON american_scientific_journal-7553 55 3 performs perform VERB american_scientific_journal-7553 55 4 the the DET american_scientific_journal-7553 55 5 task task NOUN american_scientific_journal-7553 55 6 of of ADP american_scientific_journal-7553 55 7 the the DET american_scientific_journal-7553 55 8 birth birth NOUN american_scientific_journal-7553 55 9 - - PUNCT american_scientific_journal-7553 55 10 death death NOUN american_scientific_journal-7553 55 11 process process NOUN american_scientific_journal-7553 55 12 which which PRON american_scientific_journal-7553 55 13 depends depend VERB american_scientific_journal-7553 55 14 on on ADP american_scientific_journal-7553 55 15 the the DET american_scientific_journal-7553 55 16 diffusion diffusion NOUN american_scientific_journal-7553 55 17 process process NOUN american_scientific_journal-7553 55 18 and and CCONJ american_scientific_journal-7553 55 19 replication replication NOUN american_scientific_journal-7553 55 20 number number NOUN american_scientific_journal-7553 55 21 mn mn PROPN american_scientific_journal-7553 55 22 count count NOUN american_scientific_journal-7553 55 23 this this PRON american_scientific_journal-7553 55 24 performs perform VERB american_scientific_journal-7553 55 25 the the DET american_scientific_journal-7553 55 26 task task NOUN american_scientific_journal-7553 55 27 of of ADP american_scientific_journal-7553 55 28 obtaining obtain VERB american_scientific_journal-7553 55 29 the the DET american_scientific_journal-7553 55 30 ground ground NOUN american_scientific_journal-7553 55 31 state state NOUN american_scientific_journal-7553 55 32 wave wave NOUN american_scientific_journal-7553 55 33 function function NOUN american_scientific_journal-7553 55 34 . . PUNCT american_scientific_journal-7553 56 1 this this PRON american_scientific_journal-7553 56 2 will will AUX american_scientific_journal-7553 56 3 start start VERB american_scientific_journal-7553 56 4 when when SCONJ american_scientific_journal-7553 56 5 we we PRON american_scientific_journal-7553 56 6 get get VERB american_scientific_journal-7553 56 7 a a DET american_scientific_journal-7553 56 8 stationary stationary ADJ american_scientific_journal-7553 56 9 state state NOUN american_scientific_journal-7553 56 10 wave wave NOUN american_scientific_journal-7553 56 11 function function NOUN american_scientific_journal-7553 56 12 . . PUNCT american_scientific_journal-7553 57 1 this this PRON american_scientific_journal-7553 57 2 will will AUX american_scientific_journal-7553 57 3 start start VERB american_scientific_journal-7553 57 4 when when SCONJ american_scientific_journal-7553 57 5 we we PRON american_scientific_journal-7553 57 6 get get VERB american_scientific_journal-7553 57 7 a a DET american_scientific_journal-7553 57 8 stationary stationary ADJ american_scientific_journal-7553 57 9 state state NOUN american_scientific_journal-7553 57 10 and and CCONJ american_scientific_journal-7553 57 11 convergence convergence NOUN american_scientific_journal-7553 57 12 in in ADP american_scientific_journal-7553 57 13 which which PRON american_scientific_journal-7553 57 14 energy energy NOUN american_scientific_journal-7553 57 15 values value NOUN american_scientific_journal-7553 57 16 almost almost ADV american_scientific_journal-7553 57 17 remain remain VERB american_scientific_journal-7553 57 18 the the DET american_scientific_journal-7553 57 19 same same ADJ american_scientific_journal-7553 57 20 every every DET american_scientific_journal-7553 57 21 time time NOUN american_scientific_journal-7553 57 22 stops stop VERB american_scientific_journal-7553 57 23 . . PUNCT american_scientific_journal-7553 58 1 american american ADJ american_scientific_journal-7553 58 2 academic academic ADJ american_scientific_journal-7553 58 3 scientific scientific ADJ american_scientific_journal-7553 58 4 research research NOUN american_scientific_journal-7553 58 5 journal journal NOUN american_scientific_journal-7553 58 6 for for ADP american_scientific_journal-7553 58 7 engineering engineering NOUN american_scientific_journal-7553 58 8 , , PUNCT american_scientific_journal-7553 58 9 technology technology NOUN american_scientific_journal-7553 58 10 , , PUNCT american_scientific_journal-7553 58 11 and and CCONJ american_scientific_journal-7553 58 12 sciences science NOUN american_scientific_journal-7553 58 13 ( ( PUNCT american_scientific_journal-7553 58 14 asrjets asrjet NOUN american_scientific_journal-7553 58 15 ) ) PUNCT american_scientific_journal-7553 58 16 ( ( PUNCT american_scientific_journal-7553 58 17 2022 2022 NUM american_scientific_journal-7553 58 18 ) ) PUNCT american_scientific_journal-7553 58 19 volume volume NOUN american_scientific_journal-7553 58 20 87 87 NUM american_scientific_journal-7553 58 21 , , PUNCT american_scientific_journal-7553 58 22 no no DET american_scientific_journal-7553 58 23 1 1 NUM american_scientific_journal-7553 58 24 , , PUNCT american_scientific_journal-7553 58 25 pp pp ADV american_scientific_journal-7553 58 26 32 32 NUM american_scientific_journal-7553 58 27 - - SYM american_scientific_journal-7553 58 28 38 38 NUM american_scientific_journal-7553 58 29 36 36 NUM american_scientific_journal-7553 58 30 test test NOUN american_scientific_journal-7553 58 31 to to PART american_scientific_journal-7553 58 32 check check VERB american_scientific_journal-7553 58 33 the the DET american_scientific_journal-7553 58 34 stationary stationary ADJ american_scientific_journal-7553 58 35 state state NOUN american_scientific_journal-7553 58 36 and and CCONJ american_scientific_journal-7553 58 37 convergence convergence NOUN american_scientific_journal-7553 58 38 , , PUNCT american_scientific_journal-7553 58 39 if if SCONJ american_scientific_journal-7553 58 40 not not PART american_scientific_journal-7553 58 41 then then ADV american_scientific_journal-7553 58 42 back back ADV american_scientific_journal-7553 58 43 to to PART american_scientific_journal-7553 58 44 step step VERB american_scientific_journal-7553 58 45 3 3 NUM american_scientific_journal-7553 58 46 and and CCONJ american_scientific_journal-7553 58 47 repeat repeat VERB american_scientific_journal-7553 58 48 the the DET american_scientific_journal-7553 58 49 steps step NOUN american_scientific_journal-7553 58 50 . . PUNCT american_scientific_journal-7553 59 1 output output NOUN american_scientific_journal-7553 59 2 result result NOUN american_scientific_journal-7553 59 3 of of ADP american_scientific_journal-7553 59 4 the the DET american_scientific_journal-7553 59 5 simulation simulation NOUN american_scientific_journal-7553 59 6 which which PRON american_scientific_journal-7553 59 7 is be AUX american_scientific_journal-7553 59 8 the the DET american_scientific_journal-7553 59 9 average average ADJ american_scientific_journal-7553 59 10 energy energy NOUN american_scientific_journal-7553 59 11 of of ADP american_scientific_journal-7553 59 12 reference reference NOUN american_scientific_journal-7553 59 13 energy energy NOUN american_scientific_journal-7553 59 14 of of ADP american_scientific_journal-7553 59 15 successive successive ADJ american_scientific_journal-7553 59 16 iterations.[12 iterations.[12 PROPN american_scientific_journal-7553 59 17 ] ] PUNCT american_scientific_journal-7553 59 18 figure figure NOUN american_scientific_journal-7553 59 19 1 1 NUM american_scientific_journal-7553 59 20 : : PUNCT american_scientific_journal-7553 59 21 flow flow NOUN american_scientific_journal-7553 59 22 diagram diagram NOUN american_scientific_journal-7553 59 23 of of ADP american_scientific_journal-7553 59 24 dmc dmc PROPN american_scientific_journal-7553 59 25 algorithm algorithm PROPN american_scientific_journal-7553 59 26 3 3 NUM american_scientific_journal-7553 59 27 . . NOUN american_scientific_journal-7553 59 28 results result NOUN american_scientific_journal-7553 59 29 and and CCONJ american_scientific_journal-7553 59 30 discussion discussion NOUN american_scientific_journal-7553 59 31 results result NOUN american_scientific_journal-7553 59 32 of of ADP american_scientific_journal-7553 59 33 hydro hydro NOUN american_scientific_journal-7553 59 34 helium helium NOUN american_scientific_journal-7553 59 35 cation cation NOUN american_scientific_journal-7553 59 36 two two NUM american_scientific_journal-7553 59 37 ( ( PUNCT american_scientific_journal-7553 59 38 he++h he++h PROPN american_scientific_journal-7553 59 39 ) ) PUNCT american_scientific_journal-7553 59 40 obtained obtain VERB american_scientific_journal-7553 59 41 from from ADP american_scientific_journal-7553 59 42 dmc dmc PROPN american_scientific_journal-7553 59 43 simulations simulation NOUN american_scientific_journal-7553 59 44 using use VERB american_scientific_journal-7553 59 45 python python NOUN american_scientific_journal-7553 59 46 programming programming NOUN american_scientific_journal-7553 59 47 language language NOUN american_scientific_journal-7553 59 48 and and CCONJ american_scientific_journal-7553 59 49 corresponding correspond VERB american_scientific_journal-7553 59 50 energies energy NOUN american_scientific_journal-7553 59 51 are be AUX american_scientific_journal-7553 59 52 given give VERB american_scientific_journal-7553 59 53 in in ADP american_scientific_journal-7553 59 54 the the DET american_scientific_journal-7553 59 55 tabulated tabulate VERB american_scientific_journal-7553 59 56 form form NOUN american_scientific_journal-7553 59 57 . . PUNCT american_scientific_journal-7553 60 1 table table NOUN american_scientific_journal-7553 60 2 1 1 NUM american_scientific_journal-7553 60 3 : : PUNCT american_scientific_journal-7553 60 4 an an DET american_scientific_journal-7553 60 5 example example NOUN american_scientific_journal-7553 60 6 of of ADP american_scientific_journal-7553 60 7 a a DET american_scientific_journal-7553 60 8 table table NOUN american_scientific_journal-7553 60 9 . . PUNCT american_scientific_journal-7553 61 1 bond bond NOUN american_scientific_journal-7553 61 2 laength(a laength(a PROPN american_scientific_journal-7553 61 3 ) ) PUNCT american_scientific_journal-7553 61 4 energy(hartree energy(hartree PROPN american_scientific_journal-7553 61 5 ) ) PUNCT american_scientific_journal-7553 61 6 0.05 0.05 NUM american_scientific_journal-7553 61 7 -4.86187 -4.86187 NOUN american_scientific_journal-7553 61 8 0.1 0.1 NUM american_scientific_journal-7553 61 9 -4.44004 -4.44004 NOUN american_scientific_journal-7553 61 10 0.2 0.2 NUM american_scientific_journal-7553 61 11 -4.04331 -4.04331 NOUN american_scientific_journal-7553 61 12 0.3 0.3 NUM american_scientific_journal-7553 61 13 -3.7165 -3.7165 NUM american_scientific_journal-7553 61 14 0.4 0.4 NUM american_scientific_journal-7553 61 15 -3.45833 -3.45833 NOUN american_scientific_journal-7553 61 16 0.5 0.5 NUM american_scientific_journal-7553 61 17 -3.24678 -3.24678 X american_scientific_journal-7553 61 18 0.6 0.6 NUM american_scientific_journal-7553 61 19 -3.0819 -3.0819 NOUN american_scientific_journal-7553 61 20 0.7 0.7 NUM american_scientific_journal-7553 61 21 -2.93652 -2.93652 NOUN american_scientific_journal-7553 61 22 0.8 0.8 NUM american_scientific_journal-7553 61 23 -2.82746 -2.82746 ADJ american_scientific_journal-7553 61 24 0.9 0.9 NUM american_scientific_journal-7553 61 25 -2.72232 -2.72232 NOUN american_scientific_journal-7553 61 26 1 1 NUM american_scientific_journal-7553 61 27 -2.63332 -2.63332 NOUN american_scientific_journal-7553 61 28 1.1 1.1 NUM american_scientific_journal-7553 61 29 -2.54052 -2.54052 NOUN american_scientific_journal-7553 61 30 1.2 1.2 NUM american_scientific_journal-7553 61 31 -2.46285 -2.46285 NOUN american_scientific_journal-7553 61 32 1.3 1.3 NUM american_scientific_journal-7553 61 33 -2.37703 -2.37703 NOUN american_scientific_journal-7553 61 34 1.4 1.4 NUM american_scientific_journal-7553 61 35 -2.34162 -2.34162 NOUN american_scientific_journal-7553 61 36 american american PROPN american_scientific_journal-7553 61 37 academic academic PROPN american_scientific_journal-7553 61 38 scientific scientific ADJ american_scientific_journal-7553 61 39 research research NOUN american_scientific_journal-7553 61 40 journal journal NOUN american_scientific_journal-7553 61 41 for for ADP american_scientific_journal-7553 61 42 engineering engineering NOUN american_scientific_journal-7553 61 43 , , PUNCT american_scientific_journal-7553 61 44 technology technology NOUN american_scientific_journal-7553 61 45 , , PUNCT american_scientific_journal-7553 61 46 and and CCONJ american_scientific_journal-7553 61 47 sciences science NOUN american_scientific_journal-7553 61 48 ( ( PUNCT american_scientific_journal-7553 61 49 asrjets asrjet NOUN american_scientific_journal-7553 61 50 ) ) PUNCT american_scientific_journal-7553 61 51 ( ( PUNCT american_scientific_journal-7553 61 52 2022 2022 NUM american_scientific_journal-7553 61 53 ) ) PUNCT american_scientific_journal-7553 61 54 volume volume NOUN american_scientific_journal-7553 61 55 87 87 NUM american_scientific_journal-7553 61 56 , , PUNCT american_scientific_journal-7553 61 57 no no DET american_scientific_journal-7553 61 58 1 1 NUM american_scientific_journal-7553 61 59 , , PUNCT american_scientific_journal-7553 61 60 pp pp ADV american_scientific_journal-7553 61 61 32 32 NUM american_scientific_journal-7553 61 62 - - SYM american_scientific_journal-7553 61 63 38 38 NUM american_scientific_journal-7553 61 64 37 37 NUM american_scientific_journal-7553 61 65 figure figure NOUN american_scientific_journal-7553 61 66 2 2 NUM american_scientific_journal-7553 61 67 : : PUNCT american_scientific_journal-7553 61 68 represents represent VERB american_scientific_journal-7553 61 69 the the DET american_scientific_journal-7553 61 70 potential potential ADJ american_scientific_journal-7553 61 71 energy energy NOUN american_scientific_journal-7553 61 72 curve curve NOUN american_scientific_journal-7553 61 73 ( ( PUNCT american_scientific_journal-7553 61 74 pec pec NOUN american_scientific_journal-7553 61 75 ) ) PUNCT american_scientific_journal-7553 61 76 of of ADP american_scientific_journal-7553 61 77 the the DET american_scientific_journal-7553 61 78 ground ground NOUN american_scientific_journal-7553 61 79 state state NOUN american_scientific_journal-7553 61 80 of of ADP american_scientific_journal-7553 61 81 he++h he++h NOUN american_scientific_journal-7553 61 82 using use VERB american_scientific_journal-7553 61 83 dmc dmc PROPN american_scientific_journal-7553 61 84 simulation simulation NOUN american_scientific_journal-7553 61 85 . . PUNCT american_scientific_journal-7553 62 1 as as ADP american_scientific_journal-7553 62 2 an an DET american_scientific_journal-7553 62 3 increasing increase VERB american_scientific_journal-7553 62 4 the the DET american_scientific_journal-7553 62 5 bond bond NOUN american_scientific_journal-7553 62 6 length length NOUN american_scientific_journal-7553 62 7 , , PUNCT american_scientific_journal-7553 62 8 potential potential ADJ american_scientific_journal-7553 62 9 energy energy NOUN american_scientific_journal-7553 62 10 is be AUX american_scientific_journal-7553 62 11 increased increase VERB american_scientific_journal-7553 62 12 until until SCONJ american_scientific_journal-7553 62 13 the the DET american_scientific_journal-7553 62 14 equilibrium equilibrium NOUN american_scientific_journal-7553 62 15 bond bond NOUN american_scientific_journal-7553 62 16 length length NOUN american_scientific_journal-7553 62 17 is be AUX american_scientific_journal-7553 62 18 reached reach VERB american_scientific_journal-7553 62 19 where where SCONJ american_scientific_journal-7553 62 20 the the DET american_scientific_journal-7553 62 21 interatomic interatomic ADJ american_scientific_journal-7553 62 22 forces force NOUN american_scientific_journal-7553 62 23 are be AUX american_scientific_journal-7553 62 24 zero zero NUM american_scientific_journal-7553 62 25 . . PUNCT american_scientific_journal-7553 63 1 equilibrium equilibrium NOUN american_scientific_journal-7553 63 2 bond bond NOUN american_scientific_journal-7553 63 3 length length NOUN american_scientific_journal-7553 63 4 for for ADP american_scientific_journal-7553 63 5 he++h he++h PROPN american_scientific_journal-7553 63 6 is be AUX american_scientific_journal-7553 63 7 0.4 0.4 NUM american_scientific_journal-7553 63 8 angston angston NOUN american_scientific_journal-7553 63 9 and and CCONJ american_scientific_journal-7553 63 10 corresponding corresponding ADJ american_scientific_journal-7553 63 11 energy energy NOUN american_scientific_journal-7553 63 12 is be AUX american_scientific_journal-7553 63 13 -3.45833 -3.45833 NOUN american_scientific_journal-7553 63 14 hartree hartree PROPN american_scientific_journal-7553 63 15 -94.11845 -94.11845 PUNCT american_scientific_journal-7553 63 16 ev ev PROPN american_scientific_journal-7553 63 17 . . PROPN american_scientific_journal-7553 64 1 at at ADP american_scientific_journal-7553 64 2 this this DET american_scientific_journal-7553 64 3 equilibrium equilibrium NOUN american_scientific_journal-7553 64 4 bond bond NOUN american_scientific_journal-7553 64 5 length length NOUN american_scientific_journal-7553 64 6 , , PUNCT american_scientific_journal-7553 64 7 the the DET american_scientific_journal-7553 64 8 attractive attractive ADJ american_scientific_journal-7553 64 9 force force NOUN american_scientific_journal-7553 64 10 between between ADP american_scientific_journal-7553 64 11 the the DET american_scientific_journal-7553 64 12 proton proton NOUN american_scientific_journal-7553 64 13 of of ADP american_scientific_journal-7553 64 14 helium helium NOUN american_scientific_journal-7553 64 15 and and CCONJ american_scientific_journal-7553 64 16 the the DET american_scientific_journal-7553 64 17 electron electron NOUN american_scientific_journal-7553 64 18 of of ADP american_scientific_journal-7553 64 19 the the DET american_scientific_journal-7553 64 20 hydrogen hydrogen NOUN american_scientific_journal-7553 64 21 atom atom NOUN american_scientific_journal-7553 64 22 is be AUX american_scientific_journal-7553 64 23 balanced balance VERB american_scientific_journal-7553 64 24 by by ADP american_scientific_journal-7553 64 25 repulsive repulsive ADJ american_scientific_journal-7553 64 26 force force NOUN american_scientific_journal-7553 64 27 between between ADP american_scientific_journal-7553 64 28 the the DET american_scientific_journal-7553 64 29 proton proton NOUN american_scientific_journal-7553 64 30 of of ADP american_scientific_journal-7553 64 31 the the DET american_scientific_journal-7553 64 32 helium helium NOUN american_scientific_journal-7553 64 33 atom atom NOUN american_scientific_journal-7553 64 34 and and CCONJ american_scientific_journal-7553 64 35 the the DET american_scientific_journal-7553 64 36 proton proton NOUN american_scientific_journal-7553 64 37 of of ADP american_scientific_journal-7553 64 38 the the DET american_scientific_journal-7553 64 39 hydrogen hydrogen NOUN american_scientific_journal-7553 64 40 atom atom NOUN american_scientific_journal-7553 64 41 . . PUNCT american_scientific_journal-7553 65 1 after after ADP american_scientific_journal-7553 65 2 the the DET american_scientific_journal-7553 65 3 equilibrium equilibrium NOUN american_scientific_journal-7553 65 4 bond bond NOUN american_scientific_journal-7553 65 5 length length NOUN american_scientific_journal-7553 65 6 , , PUNCT american_scientific_journal-7553 65 7 attractive attractive ADJ american_scientific_journal-7553 65 8 force force NOUN american_scientific_journal-7553 65 9 becomes become VERB american_scientific_journal-7553 65 10 dominant dominant ADJ american_scientific_journal-7553 65 11 from from ADP american_scientific_journal-7553 65 12 repulsive repulsive ADJ american_scientific_journal-7553 65 13 force force NOUN american_scientific_journal-7553 65 14 and and CCONJ american_scientific_journal-7553 65 15 these these DET american_scientific_journal-7553 65 16 two two NUM american_scientific_journal-7553 65 17 atoms atom NOUN american_scientific_journal-7553 65 18 feel feel VERB american_scientific_journal-7553 65 19 the the DET american_scientific_journal-7553 65 20 force force NOUN american_scientific_journal-7553 65 21 of of ADP american_scientific_journal-7553 65 22 attraction attraction NOUN american_scientific_journal-7553 65 23 . . PUNCT american_scientific_journal-7553 66 1 as as SCONJ american_scientific_journal-7553 66 2 we we PRON american_scientific_journal-7553 66 3 increase increase VERB american_scientific_journal-7553 66 4 the the DET american_scientific_journal-7553 66 5 bond bond NOUN american_scientific_journal-7553 66 6 length length NOUN american_scientific_journal-7553 66 7 more more ADV american_scientific_journal-7553 66 8 and and CCONJ american_scientific_journal-7553 66 9 more more ADJ american_scientific_journal-7553 66 10 slope slope NOUN american_scientific_journal-7553 66 11 of of ADP american_scientific_journal-7553 66 12 the the DET american_scientific_journal-7553 66 13 graph graph NOUN american_scientific_journal-7553 66 14 approaches approach NOUN american_scientific_journal-7553 66 15 to to ADP american_scientific_journal-7553 66 16 zero zero NUM american_scientific_journal-7553 66 17 which which PRON american_scientific_journal-7553 66 18 means mean VERB american_scientific_journal-7553 66 19 at at ADP american_scientific_journal-7553 66 20 a a DET american_scientific_journal-7553 66 21 larger large ADJ american_scientific_journal-7553 66 22 distance distance NOUN american_scientific_journal-7553 66 23 , , PUNCT american_scientific_journal-7553 66 24 the the DET american_scientific_journal-7553 66 25 atom atom NOUN american_scientific_journal-7553 66 26 feels feel VERB american_scientific_journal-7553 66 27 the the DET american_scientific_journal-7553 66 28 weak weak ADJ american_scientific_journal-7553 66 29 force force NOUN american_scientific_journal-7553 66 30 of of ADP american_scientific_journal-7553 66 31 attraction attraction NOUN american_scientific_journal-7553 66 32 . . PUNCT american_scientific_journal-7553 67 1 dissociation dissociation NOUN american_scientific_journal-7553 67 2 bond bond NOUN american_scientific_journal-7553 67 3 length length NOUN american_scientific_journal-7553 67 4 for for ADP american_scientific_journal-7553 67 5 he++h he++h PROPN american_scientific_journal-7553 67 6 is be AUX american_scientific_journal-7553 67 7 1.4 1.4 NUM american_scientific_journal-7553 67 8 angstron angstron NOUN american_scientific_journal-7553 67 9 . . PUNCT american_scientific_journal-7553 68 1 after after ADP american_scientific_journal-7553 68 2 this this DET american_scientific_journal-7553 68 3 dissociation dissociation NOUN american_scientific_journal-7553 68 4 , , PUNCT american_scientific_journal-7553 68 5 both both DET american_scientific_journal-7553 68 6 atoms atom NOUN american_scientific_journal-7553 68 7 are be AUX american_scientific_journal-7553 68 8 free free ADJ american_scientific_journal-7553 68 9 and and CCONJ american_scientific_journal-7553 68 10 have have VERB american_scientific_journal-7553 68 11 no no DET american_scientific_journal-7553 68 12 force force NOUN american_scientific_journal-7553 68 13 of of ADP american_scientific_journal-7553 68 14 attraction attraction NOUN american_scientific_journal-7553 68 15 . . PUNCT american_scientific_journal-7553 69 1 4 4 X american_scientific_journal-7553 69 2 . . X american_scientific_journal-7553 69 3 conclusion conclusion NOUN american_scientific_journal-7553 69 4 we we PRON american_scientific_journal-7553 69 5 have have AUX american_scientific_journal-7553 69 6 calculated calculate VERB american_scientific_journal-7553 69 7 the the DET american_scientific_journal-7553 69 8 ground ground NOUN american_scientific_journal-7553 69 9 state state NOUN american_scientific_journal-7553 69 10 energy energy NOUN american_scientific_journal-7553 69 11 of of ADP american_scientific_journal-7553 69 12 ground ground NOUN american_scientific_journal-7553 69 13 state state NOUN american_scientific_journal-7553 69 14 of of ADP american_scientific_journal-7553 69 15 hydro hydro PROPN american_scientific_journal-7553 69 16 helium helium NOUN american_scientific_journal-7553 69 17 cation cation NOUN american_scientific_journal-7553 69 18 ( ( PUNCT american_scientific_journal-7553 69 19 2++ 2++ NUM american_scientific_journal-7553 69 20 ) ) PUNCT american_scientific_journal-7553 69 21 he he PRON american_scientific_journal-7553 70 1 + + PROPN american_scientific_journal-7553 70 2 + + X american_scientific_journal-7553 70 3 h h NOUN american_scientific_journal-7553 70 4 using use VERB american_scientific_journal-7553 70 5 approximation approximation NOUN american_scientific_journal-7553 70 6 method method NOUN american_scientific_journal-7553 70 7 i.e i.e ADP american_scientific_journal-7553 70 8 diffusion diffusion NOUN american_scientific_journal-7553 70 9 quantum quantum PROPN american_scientific_journal-7553 70 10 monte monte PROPN american_scientific_journal-7553 70 11 carlo carlo PROPN american_scientific_journal-7553 70 12 ( ( PUNCT american_scientific_journal-7553 70 13 dmc dmc PROPN american_scientific_journal-7553 70 14 ) ) PUNCT american_scientific_journal-7553 70 15 , , PUNCT american_scientific_journal-7553 70 16 which which PRON american_scientific_journal-7553 70 17 is be AUX american_scientific_journal-7553 70 18 one one NUM american_scientific_journal-7553 70 19 type type NOUN american_scientific_journal-7553 70 20 of of ADP american_scientific_journal-7553 70 21 quantum quantum ADJ american_scientific_journal-7553 70 22 monte monte PROPN american_scientific_journal-7553 70 23 carlo carlo PROPN american_scientific_journal-7553 70 24 ( ( PUNCT american_scientific_journal-7553 70 25 qmc qmc PROPN american_scientific_journal-7553 70 26 ) ) PUNCT american_scientific_journal-7553 70 27 method method NOUN american_scientific_journal-7553 70 28 . . PUNCT american_scientific_journal-7553 71 1 we we PRON american_scientific_journal-7553 71 2 have have AUX american_scientific_journal-7553 71 3 developed develop VERB american_scientific_journal-7553 71 4 the the DET american_scientific_journal-7553 71 5 code code NOUN american_scientific_journal-7553 71 6 of of ADP american_scientific_journal-7553 71 7 simulation simulation NOUN american_scientific_journal-7553 71 8 of of ADP american_scientific_journal-7553 71 9 qmc qmc VERB american_scientific_journal-7553 71 10 in in ADP american_scientific_journal-7553 71 11 python python NOUN american_scientific_journal-7553 71 12 programming programming NOUN american_scientific_journal-7553 71 13 language language NOUN american_scientific_journal-7553 71 14 . . PUNCT american_scientific_journal-7553 72 1 we we PRON american_scientific_journal-7553 72 2 have have AUX american_scientific_journal-7553 72 3 prepared prepare VERB american_scientific_journal-7553 72 4 the the DET american_scientific_journal-7553 72 5 trial trial NOUN american_scientific_journal-7553 72 6 wave wave NOUN american_scientific_journal-7553 72 7 function function NOUN american_scientific_journal-7553 72 8 of of ADP american_scientific_journal-7553 72 9 slater slater NOUN american_scientific_journal-7553 72 10 - - PUNCT american_scientific_journal-7553 72 11 jastrow jastrow NOUN american_scientific_journal-7553 72 12 type type NOUN american_scientific_journal-7553 72 13 with with ADP american_scientific_journal-7553 72 14 introduction introduction NOUN american_scientific_journal-7553 72 15 of of ADP american_scientific_journal-7553 72 16 important important ADJ american_scientific_journal-7553 72 17 sampling sampling NOUN american_scientific_journal-7553 72 18 technique technique NOUN american_scientific_journal-7553 72 19 to to PART american_scientific_journal-7553 72 20 improve improve VERB american_scientific_journal-7553 72 21 the the DET american_scientific_journal-7553 72 22 accuracy accuracy NOUN american_scientific_journal-7553 72 23 of of ADP american_scientific_journal-7553 72 24 our our PRON american_scientific_journal-7553 72 25 result result NOUN american_scientific_journal-7553 72 26 for for ADP american_scientific_journal-7553 72 27 dmc dmc PROPN american_scientific_journal-7553 72 28 . . PUNCT american_scientific_journal-7553 73 1 the the DET american_scientific_journal-7553 73 2 ground ground NOUN american_scientific_journal-7553 73 3 state state NOUN american_scientific_journal-7553 73 4 energy energy NOUN american_scientific_journal-7553 73 5 of of ADP american_scientific_journal-7553 73 6 he he PRON american_scientific_journal-7553 73 7 + + PROPN american_scientific_journal-7553 73 8 + + NUM american_scientific_journal-7553 73 9 h h NOUN american_scientific_journal-7553 73 10 is be AUX american_scientific_journal-7553 73 11 -3.45833 -3.45833 NOUN american_scientific_journal-7553 73 12 hartree hartree NOUN american_scientific_journal-7553 73 13 or or CCONJ american_scientific_journal-7553 73 14 94.11845 94.11845 NUM american_scientific_journal-7553 73 15 ev ev NOUN american_scientific_journal-7553 73 16 for for ADP american_scientific_journal-7553 73 17 dmc dmc PROPN american_scientific_journal-7553 73 18 method method NOUN american_scientific_journal-7553 73 19 at at ADP american_scientific_journal-7553 73 20 equilibrium equilibrium NOUN american_scientific_journal-7553 73 21 wavelength wavelength NOUN american_scientific_journal-7553 73 22 of of ADP american_scientific_journal-7553 73 23 0.4 0.4 NUM american_scientific_journal-7553 73 24 angston angston NOUN american_scientific_journal-7553 73 25 . . PUNCT american_scientific_journal-7553 74 1 references reference NOUN american_scientific_journal-7553 74 2 [ [ X american_scientific_journal-7553 74 3 1 1 X american_scientific_journal-7553 74 4 ] ] PUNCT american_scientific_journal-7553 74 5 w.m.c w.m.c ADJ american_scientific_journal-7553 74 6 folkes folke NOUN american_scientific_journal-7553 74 7 , , PUNCT american_scientific_journal-7553 74 8 l.mitas l.mita NOUN american_scientific_journal-7553 74 9 , , PUNCT american_scientific_journal-7553 74 10 r.j.needs r.j.need NOUN american_scientific_journal-7553 74 11 and and CCONJ american_scientific_journal-7553 74 12 g.rajagopal g.rajagopal NOUN american_scientific_journal-7553 74 13 , , PUNCT american_scientific_journal-7553 74 14 “ " PUNCT american_scientific_journal-7553 74 15 quantum quantum PROPN american_scientific_journal-7553 74 16 monte monte PROPN american_scientific_journal-7553 74 17 carlo carlo PROPN american_scientific_journal-7553 74 18 simulations simulation NOUN american_scientific_journal-7553 74 19 of of ADP american_scientific_journal-7553 74 20 solids solid NOUN american_scientific_journal-7553 74 21 , , PUNCT american_scientific_journal-7553 74 22 ” " PUNCT american_scientific_journal-7553 74 23 rev rev X american_scientific_journal-7553 74 24 . . PROPN american_scientific_journal-7553 74 25 mod mod PROPN american_scientific_journal-7553 74 26 . . PUNCT american_scientific_journal-7553 75 1 phys phy NOUN american_scientific_journal-7553 75 2 . . PUNCT american_scientific_journal-7553 75 3 , , PUNCT american_scientific_journal-7553 75 4 vol vol NOUN american_scientific_journal-7553 75 5 . . PROPN american_scientific_journal-7553 76 1 73 73 NUM american_scientific_journal-7553 76 2 , , PUNCT american_scientific_journal-7553 76 3 no no INTJ american_scientific_journal-7553 76 4 . . NOUN american_scientific_journal-7553 76 5 1 1 NUM american_scientific_journal-7553 76 6 , , PUNCT american_scientific_journal-7553 76 7 pp-83 pp-83 PRON american_scientific_journal-7553 76 8 , , PUNCT american_scientific_journal-7553 76 9 2001 2001 NUM american_scientific_journal-7553 76 10 . . PUNCT american_scientific_journal-7553 77 1 [ [ X american_scientific_journal-7553 77 2 2 2 NUM american_scientific_journal-7553 77 3 ] ] PUNCT american_scientific_journal-7553 77 4 h.toffoli h.toffoli NOUN american_scientific_journal-7553 77 5 , , PUNCT american_scientific_journal-7553 77 6 “ " PUNCT american_scientific_journal-7553 77 7 lecture lecture VERB american_scientific_journal-7553 77 8 04 04 NUM american_scientific_journal-7553 77 9 : : PUNCT american_scientific_journal-7553 77 10 the the DET american_scientific_journal-7553 77 11 hartree hartree ADV american_scientific_journal-7553 77 12 - - PUNCT american_scientific_journal-7553 77 13 fock fock ADJ american_scientific_journal-7553 77 14 method method NOUN american_scientific_journal-7553 77 15 , , PUNCT american_scientific_journal-7553 77 16 ” " PUNCT american_scientific_journal-7553 77 17 princ princ PROPN american_scientific_journal-7553 77 18 . . PUNCT american_scientific_journal-7553 78 1 density density PROPN american_scientific_journal-7553 78 2 funct funct PROPN american_scientific_journal-7553 78 3 . . PUNCT american_scientific_journal-7553 79 1 theory theory NOUN american_scientific_journal-7553 79 2 , , PUNCT american_scientific_journal-7553 79 3 vol.1 vol.1 PROPN american_scientific_journal-7553 79 4 , , PUNCT american_scientific_journal-7553 79 5 no.7 no.7 PROPN american_scientific_journal-7553 79 6 , , PUNCT american_scientific_journal-7553 79 7 pp1 pp1 PROPN american_scientific_journal-7553 79 8 - - PUNCT american_scientific_journal-7553 79 9 9,2012 9,2012 PROPN american_scientific_journal-7553 79 10 [ [ X american_scientific_journal-7553 79 11 3 3 NUM american_scientific_journal-7553 79 12 ] ] X american_scientific_journal-7553 79 13 j.b.anderson j.b.anderson NOUN american_scientific_journal-7553 79 14 , , PUNCT american_scientific_journal-7553 79 15 “ " PUNCT american_scientific_journal-7553 79 16 quantum quantum PROPN american_scientific_journal-7553 79 17 monte monte NOUN american_scientific_journal-7553 79 18 carlo carlo PROPN american_scientific_journal-7553 79 19 : : PUNCT american_scientific_journal-7553 79 20 atoms atom NOUN american_scientific_journal-7553 79 21 , , PUNCT american_scientific_journal-7553 79 22 molecules molecule NOUN american_scientific_journal-7553 79 23 , , PUNCT american_scientific_journal-7553 79 24 clustrs clustrs PROPN american_scientific_journal-7553 79 25 , , PUNCT american_scientific_journal-7553 79 26 liquids liquid NOUN american_scientific_journal-7553 79 27 , , PUNCT american_scientific_journal-7553 79 28 and and CCONJ american_scientific_journal-7553 79 29 solids solid NOUN american_scientific_journal-7553 79 30 , , PUNCT american_scientific_journal-7553 79 31 ” " PUNCT american_scientific_journal-7553 79 32 vol.13 vol.13 NOUN american_scientific_journal-7553 79 33 . . PUNCT american_scientific_journal-7553 80 1 [ [ X american_scientific_journal-7553 80 2 4 4 X american_scientific_journal-7553 80 3 ] ] X american_scientific_journal-7553 80 4 a a DET american_scientific_journal-7553 80 5 .zen .zen PROPN american_scientific_journal-7553 80 6 , , PUNCT american_scientific_journal-7553 80 7 j. j. PROPN american_scientific_journal-7553 80 8 g. g. PROPN american_scientific_journal-7553 80 9 brandenburg brandenburg PROPN american_scientific_journal-7553 80 10 , , PUNCT american_scientific_journal-7553 80 11 j.klimes j.klime NOUN american_scientific_journal-7553 80 12 , , PUNCT american_scientific_journal-7553 80 13 a.tkatchenko a.tkatchenko PROPN american_scientific_journal-7553 80 14 , , PUNCT american_scientific_journal-7553 80 15 d. d. PROPN american_scientific_journal-7553 80 16 alfe alfe PROPN american_scientific_journal-7553 80 17 , , PUNCT american_scientific_journal-7553 80 18 and and CCONJ american_scientific_journal-7553 80 19 a. a. NOUN american_scientific_journal-7553 80 20 michaeldes michaelde NOUN american_scientific_journal-7553 80 21 , , PUNCT american_scientific_journal-7553 80 22 “ " PUNCT american_scientific_journal-7553 80 23 fast fast ADJ american_scientific_journal-7553 80 24 and and CCONJ american_scientific_journal-7553 80 25 accurate accurate ADJ american_scientific_journal-7553 80 26 american american ADJ american_scientific_journal-7553 80 27 academic academic ADJ american_scientific_journal-7553 80 28 scientific scientific ADJ american_scientific_journal-7553 80 29 research research NOUN american_scientific_journal-7553 80 30 journal journal NOUN american_scientific_journal-7553 80 31 for for ADP american_scientific_journal-7553 80 32 engineering engineering NOUN american_scientific_journal-7553 80 33 , , PUNCT american_scientific_journal-7553 80 34 technology technology NOUN american_scientific_journal-7553 80 35 , , PUNCT american_scientific_journal-7553 80 36 and and CCONJ american_scientific_journal-7553 80 37 sciences science NOUN american_scientific_journal-7553 80 38 ( ( PUNCT american_scientific_journal-7553 80 39 asrjets asrjet NOUN american_scientific_journal-7553 80 40 ) ) PUNCT american_scientific_journal-7553 80 41 ( ( PUNCT american_scientific_journal-7553 80 42 2022 2022 NUM american_scientific_journal-7553 80 43 ) ) PUNCT american_scientific_journal-7553 80 44 volume volume NOUN american_scientific_journal-7553 80 45 87 87 NUM american_scientific_journal-7553 80 46 , , PUNCT american_scientific_journal-7553 80 47 no no DET american_scientific_journal-7553 80 48 1 1 NUM american_scientific_journal-7553 80 49 , , PUNCT american_scientific_journal-7553 80 50 pp pp ADV american_scientific_journal-7553 80 51 32 32 NUM american_scientific_journal-7553 80 52 - - SYM american_scientific_journal-7553 80 53 38 38 NUM american_scientific_journal-7553 80 54 38 38 NUM american_scientific_journal-7553 80 55 quantum quantum NOUN american_scientific_journal-7553 80 56 monte monte NOUN american_scientific_journal-7553 80 57 carlo carlo NOUN american_scientific_journal-7553 80 58 for for ADP american_scientific_journal-7553 80 59 molecular molecular ADJ american_scientific_journal-7553 80 60 crystals crystal NOUN american_scientific_journal-7553 80 61 , , PUNCT american_scientific_journal-7553 80 62 ” " PUNCT american_scientific_journal-7553 80 63 proc proc NOUN american_scientific_journal-7553 80 64 . . PUNCT american_scientific_journal-7553 81 1 natl natl PROPN american_scientific_journal-7553 81 2 . . PUNCT american_scientific_journal-7553 82 1 acad acad PROPN american_scientific_journal-7553 82 2 . . PUNCT american_scientific_journal-7553 83 1 sci sci PROPN american_scientific_journal-7553 83 2 . . PROPN american_scientific_journal-7553 83 3 , , PUNCT american_scientific_journal-7553 83 4 vol vol NOUN american_scientific_journal-7553 83 5 . . PROPN american_scientific_journal-7553 83 6 0 0 NUM american_scientific_journal-7553 83 7 , , PUNCT american_scientific_journal-7553 83 8 p. p. NOUN american_scientific_journal-7553 83 9 201715434 201715434 NUM american_scientific_journal-7553 83 10 , , PUNCT american_scientific_journal-7553 83 11 2018 2018 NUM american_scientific_journal-7553 83 12 . . PUNCT american_scientific_journal-7553 84 1 [ [ X american_scientific_journal-7553 84 2 5 5 NUM american_scientific_journal-7553 84 3 ] ] PUNCT american_scientific_journal-7553 84 4 o. o. PROPN american_scientific_journal-7553 84 5 witham witham PROPN american_scientific_journal-7553 84 6 , , PUNCT american_scientific_journal-7553 84 7 r. r. PROPN american_scientific_journal-7553 84 8 j. j. PROPN american_scientific_journal-7553 84 9 hunt hunt PROPN american_scientific_journal-7553 84 10 , , PUNCT american_scientific_journal-7553 84 11 and and CCONJ american_scientific_journal-7553 84 12 n. n. PROPN american_scientific_journal-7553 84 13 d. d. PROPN american_scientific_journal-7553 84 14 drummond drummond PROPN american_scientific_journal-7553 84 15 , , PUNCT american_scientific_journal-7553 84 16 " " PUNCT american_scientific_journal-7553 84 17 stability stability NOUN american_scientific_journal-7553 84 18 of of ADP american_scientific_journal-7553 84 19 trions trion NOUN american_scientific_journal-7553 84 20 in in ADP american_scientific_journal-7553 84 21 coupled couple VERB american_scientific_journal-7553 84 22 quantum quantum ADJ american_scientific_journal-7553 84 23 wells well NOUN american_scientific_journal-7553 84 24 modeled model VERB american_scientific_journal-7553 84 25 by by ADP american_scientific_journal-7553 84 26 two two NUM american_scientific_journal-7553 84 27 - - PUNCT american_scientific_journal-7553 84 28 dimensional dimensional ADJ american_scientific_journal-7553 84 29 bilayers bilayer NOUN american_scientific_journal-7553 84 30 , , PUNCT american_scientific_journal-7553 84 31 " " PUNCT american_scientific_journal-7553 84 32 phys phy NOUN american_scientific_journal-7553 84 33 . . PUNCT american_scientific_journal-7553 85 1 rev rev PROPN american_scientific_journal-7553 85 2 . . PROPN american_scientific_journal-7553 86 1 b b X american_scientific_journal-7553 86 2 , , PUNCT american_scientific_journal-7553 86 3 vol vol NOUN american_scientific_journal-7553 86 4 . . PROPN american_scientific_journal-7553 87 1 97 97 NUM american_scientific_journal-7553 87 2 , , PUNCT american_scientific_journal-7553 87 3 no no INTJ american_scientific_journal-7553 87 4 . . NOUN american_scientific_journal-7553 87 5 7 7 NUM american_scientific_journal-7553 87 6 , , PUNCT american_scientific_journal-7553 87 7 pp pp ADJ american_scientific_journal-7553 87 8 . . PUNCT american_scientific_journal-7553 88 1 1 1 NUM american_scientific_journal-7553 88 2 - - SYM american_scientific_journal-7553 88 3 6 6 NUM american_scientific_journal-7553 88 4 , , PUNCT american_scientific_journal-7553 88 5 2018 2018 NUM american_scientific_journal-7553 88 6 . . PUNCT american_scientific_journal-7553 89 1 [ [ X american_scientific_journal-7553 89 2 6 6 NUM american_scientific_journal-7553 89 3 ] ] PUNCT american_scientific_journal-7553 89 4 s. s. PROPN american_scientific_journal-7553 89 5 b. b. PROPN american_scientific_journal-7553 89 6 doma doma PROPN american_scientific_journal-7553 89 7 and and CCONJ american_scientific_journal-7553 89 8 a. a. NOUN american_scientific_journal-7553 89 9 a. a. PROPN american_scientific_journal-7553 89 10 amer amer PROPN american_scientific_journal-7553 89 11 , , PUNCT american_scientific_journal-7553 89 12 " " PUNCT american_scientific_journal-7553 89 13 ground ground NOUN american_scientific_journal-7553 89 14 - - PUNCT american_scientific_journal-7553 89 15 state state NOUN american_scientific_journal-7553 89 16 calculations calculation NOUN american_scientific_journal-7553 89 17 of of ADP american_scientific_journal-7553 89 18 confined confine VERB american_scientific_journal-7553 89 19 hydrogen hydrogen NOUN american_scientific_journal-7553 89 20 molecule molecule NOUN american_scientific_journal-7553 89 21 h h NOUN american_scientific_journal-7553 89 22 2 2 NUM american_scientific_journal-7553 89 23 using use VERB american_scientific_journal-7553 89 24 variational variational ADJ american_scientific_journal-7553 89 25 monte monte PROPN american_scientific_journal-7553 89 26 carlo carlo PROPN american_scientific_journal-7553 89 27 method method PROPN american_scientific_journal-7553 89 28 ground ground NOUN american_scientific_journal-7553 89 29 - - PUNCT american_scientific_journal-7553 89 30 state state NOUN american_scientific_journal-7553 89 31 calculations calculation NOUN american_scientific_journal-7553 89 32 of of ADP american_scientific_journal-7553 89 33 confined confine VERB american_scientific_journal-7553 89 34 hydrogen hydrogen NOUN american_scientific_journal-7553 89 35 molecule molecule NOUN american_scientific_journal-7553 89 36 h h NOUN american_scientific_journal-7553 89 37 2 2 NUM american_scientific_journal-7553 89 38 using use VERB american_scientific_journal-7553 89 39 variational variational ADJ american_scientific_journal-7553 89 40 , , PUNCT american_scientific_journal-7553 89 41 " " PUNCT american_scientific_journal-7553 89 42 vol vol NOUN american_scientific_journal-7553 89 43 . . PROPN american_scientific_journal-7553 89 44 8976 8976 NUM american_scientific_journal-7553 89 45 , , PUNCT american_scientific_journal-7553 89 46 2018 2018 NUM american_scientific_journal-7553 89 47 . . PUNCT american_scientific_journal-7553 90 1 [ [ X american_scientific_journal-7553 90 2 7 7 X american_scientific_journal-7553 90 3 ] ] X american_scientific_journal-7553 90 4 n. n. PROPN american_scientific_journal-7553 90 5 y. y. PROPN american_scientific_journal-7553 90 6 astrakhantsev astrakhantsev PROPN american_scientific_journal-7553 90 7 , , PUNCT american_scientific_journal-7553 90 8 v. v. PROPN american_scientific_journal-7553 90 9 v. v. ADP american_scientific_journal-7553 90 10 braguta braguta PROPN american_scientific_journal-7553 90 11 , , PUNCT american_scientific_journal-7553 90 12 m. m. PROPN american_scientific_journal-7553 90 13 i. i. PROPN american_scientific_journal-7553 90 14 katsnelson katsnelson PROPN american_scientific_journal-7553 90 15 , , PUNCT american_scientific_journal-7553 90 16 a. a. NOUN american_scientific_journal-7553 90 17 a. a. NOUN american_scientific_journal-7553 90 18 nikolaev nikolaev ADV american_scientific_journal-7553 90 19 , , PUNCT american_scientific_journal-7553 90 20 and and CCONJ american_scientific_journal-7553 90 21 m. m. NOUN american_scientific_journal-7553 90 22 v. v. CCONJ american_scientific_journal-7553 90 23 ulybyshev ulybyshev ADJ american_scientific_journal-7553 90 24 , , PUNCT american_scientific_journal-7553 90 25 " " PUNCT american_scientific_journal-7553 90 26 quantum quantum PROPN american_scientific_journal-7553 90 27 monte monte PROPN american_scientific_journal-7553 90 28 carlo carlo PROPN american_scientific_journal-7553 90 29 study study NOUN american_scientific_journal-7553 90 30 of of ADP american_scientific_journal-7553 90 31 electrostatic electrostatic ADJ american_scientific_journal-7553 90 32 potential potential NOUN american_scientific_journal-7553 90 33 in in ADP american_scientific_journal-7553 90 34 graphene graphene NOUN american_scientific_journal-7553 90 35 , , PUNCT american_scientific_journal-7553 90 36 " " PUNCT american_scientific_journal-7553 90 37 phys phy NOUN american_scientific_journal-7553 90 38 . . PUNCT american_scientific_journal-7553 91 1 rev rev PROPN american_scientific_journal-7553 91 2 . . PROPN american_scientific_journal-7553 92 1 b b X american_scientific_journal-7553 92 2 , , PUNCT american_scientific_journal-7553 92 3 vol vol NOUN american_scientific_journal-7553 92 4 . . PROPN american_scientific_journal-7553 93 1 97 97 NUM american_scientific_journal-7553 93 2 , , PUNCT american_scientific_journal-7553 93 3 no no INTJ american_scientific_journal-7553 93 4 . . NOUN american_scientific_journal-7553 93 5 3 3 NUM american_scientific_journal-7553 93 6 , , PUNCT american_scientific_journal-7553 93 7 pp pp ADJ american_scientific_journal-7553 93 8 . . PUNCT american_scientific_journal-7553 94 1 1 1 NUM american_scientific_journal-7553 94 2 - - SYM american_scientific_journal-7553 94 3 6 6 NUM american_scientific_journal-7553 94 4 , , PUNCT american_scientific_journal-7553 94 5 2018 2018 NUM american_scientific_journal-7553 94 6 . . PUNCT american_scientific_journal-7553 95 1 [ [ X american_scientific_journal-7553 95 2 8 8 X american_scientific_journal-7553 95 3 ] ] PUNCT american_scientific_journal-7553 95 4 j. j. PROPN american_scientific_journal-7553 95 5 trail trail PROPN american_scientific_journal-7553 95 6 , , PUNCT american_scientific_journal-7553 95 7 b. b. PROPN american_scientific_journal-7553 95 8 monserrat monserrat PROPN american_scientific_journal-7553 95 9 , , PUNCT american_scientific_journal-7553 95 10 and and CCONJ american_scientific_journal-7553 95 11 l. l. PROPN american_scientific_journal-7553 95 12 pablo pablo PROPN american_scientific_journal-7553 95 13 , , PUNCT american_scientific_journal-7553 95 14 " " PUNCT american_scientific_journal-7553 95 15 quantum quantum PROPN american_scientific_journal-7553 95 16 monte monte PROPN american_scientific_journal-7553 95 17 carlo carlo PROPN american_scientific_journal-7553 95 18 study study NOUN american_scientific_journal-7553 95 19 of of ADP american_scientific_journal-7553 95 20 the the DET american_scientific_journal-7553 95 21 energetics energetic NOUN american_scientific_journal-7553 95 22 of of ADP american_scientific_journal-7553 95 23 the the DET american_scientific_journal-7553 95 24 rutile rutile NOUN american_scientific_journal-7553 95 25 , , PUNCT american_scientific_journal-7553 95 26 anatase anatase NOUN american_scientific_journal-7553 95 27 , , PUNCT american_scientific_journal-7553 95 28 brookite brookite VERB american_scientific_journal-7553 95 29 , , PUNCT american_scientific_journal-7553 95 30 and and CCONJ american_scientific_journal-7553 95 31 columbite columbite NOUN american_scientific_journal-7553 95 32 tio tio NOUN american_scientific_journal-7553 95 33 2 2 NUM american_scientific_journal-7553 95 34 polymorphs polymorph NOUN american_scientific_journal-7553 95 35 , , PUNCT american_scientific_journal-7553 95 36 " " PUNCT american_scientific_journal-7553 95 37 vol vol NOUN american_scientific_journal-7553 95 38 . . PROPN american_scientific_journal-7553 95 39 121108 121108 NUM american_scientific_journal-7553 95 40 , , PUNCT american_scientific_journal-7553 95 41 2017 2017 NUM american_scientific_journal-7553 95 42 . . PUNCT american_scientific_journal-7553 96 1 [ [ X american_scientific_journal-7553 96 2 9 9 NUM american_scientific_journal-7553 96 3 ] ] PUNCT american_scientific_journal-7553 96 4 l. l. PROPN american_scientific_journal-7553 96 5 q. q. PROPN american_scientific_journal-7553 96 6 monte monte PROPN american_scientific_journal-7553 96 7 - - PUNCT american_scientific_journal-7553 96 8 carlo carlo PROPN american_scientific_journal-7553 96 9 , , PUNCT american_scientific_journal-7553 96 10 " " PUNCT american_scientific_journal-7553 96 11 a a DET american_scientific_journal-7553 96 12 benchmark benchmark ADJ american_scientific_journal-7553 96 13 study study NOUN american_scientific_journal-7553 96 14 of of ADP american_scientific_journal-7553 96 15 li li PROPN american_scientific_journal-7553 96 16 2 2 PROPN american_scientific_journal-7553 96 17 + + CCONJ american_scientific_journal-7553 96 18 , , PUNCT american_scientific_journal-7553 96 19 li li PROPN american_scientific_journal-7553 96 20 2- 2- PROPN american_scientific_journal-7553 96 21 , , PUNCT american_scientific_journal-7553 96 22 lih lih PROPN american_scientific_journal-7553 96 23 + + CCONJ american_scientific_journal-7553 96 24 and and CCONJ american_scientific_journal-7553 96 25 lih lih PROPN american_scientific_journal-7553 96 26 - - PUNCT american_scientific_journal-7553 96 27 : : PUNCT american_scientific_journal-7553 96 28 quantum quantum ADJ american_scientific_journal-7553 96 29 montecarlo montecarlo NOUN american_scientific_journal-7553 96 30 and and CCONJ american_scientific_journal-7553 96 31 coupled couple VERB american_scientific_journal-7553 96 32 - - PUNCT american_scientific_journal-7553 96 33 cluster cluster NOUN american_scientific_journal-7553 96 34 computations computation NOUN american_scientific_journal-7553 96 35 , , PUNCT american_scientific_journal-7553 96 36 " " PUNCT american_scientific_journal-7553 96 37 comput comput NOUN american_scientific_journal-7553 96 38 . . PUNCT american_scientific_journal-7553 97 1 theor theor PROPN american_scientific_journal-7553 97 2 . . PUNCT american_scientific_journal-7553 97 3 chem chem PROPN american_scientific_journal-7553 97 4 . . PUNCT american_scientific_journal-7553 97 5 , , PUNCT american_scientific_journal-7553 97 6 2017 2017 NUM american_scientific_journal-7553 97 7 . . PUNCT american_scientific_journal-7553 98 1 [ [ X american_scientific_journal-7553 98 2 10 10 NUM american_scientific_journal-7553 98 3 ] ] X american_scientific_journal-7553 98 4 i. i. PROPN american_scientific_journal-7553 98 5 terrell terrell PROPN american_scientific_journal-7553 98 6 , , PUNCT american_scientific_journal-7553 98 7 " " PUNCT american_scientific_journal-7553 98 8 diffusion diffusion NOUN american_scientific_journal-7553 98 9 quantum quantum PROPN american_scientific_journal-7553 98 10 monte monte PROPN american_scientific_journal-7553 98 11 carlo carlo PROPN american_scientific_journal-7553 98 12 : : PUNCT american_scientific_journal-7553 98 13 a a DET american_scientific_journal-7553 98 14 java java NOUN american_scientific_journal-7553 98 15 based base VERB american_scientific_journal-7553 98 16 simulation simulation NOUN american_scientific_journal-7553 98 17 and and CCONJ american_scientific_journal-7553 98 18 visualization visualization NOUN american_scientific_journal-7553 98 19 , , PUNCT american_scientific_journal-7553 98 20 " " PUNCT american_scientific_journal-7553 98 21 pp pp ADP american_scientific_journal-7553 98 22 . . PUNCT american_scientific_journal-7553 98 23 1 1 NUM american_scientific_journal-7553 98 24 - - SYM american_scientific_journal-7553 98 25 12 12 NUM american_scientific_journal-7553 98 26 , , PUNCT american_scientific_journal-7553 98 27 2004 2004 NUM american_scientific_journal-7553 98 28 . . PUNCT american_scientific_journal-7553 99 1 [ [ X american_scientific_journal-7553 99 2 11 11 NUM american_scientific_journal-7553 99 3 ] ] PUNCT american_scientific_journal-7553 99 4 j. j. PROPN american_scientific_journal-7553 99 5 k. k. PROPN american_scientific_journal-7553 99 6 nilsen nilsen PROPN american_scientific_journal-7553 99 7 , , PUNCT american_scientific_journal-7553 99 8 " " PUNCT american_scientific_journal-7553 99 9 montepython montepython PROPN american_scientific_journal-7553 99 10 : : PUNCT american_scientific_journal-7553 99 11 implementing implement VERB american_scientific_journal-7553 99 12 quantum quantum PROPN american_scientific_journal-7553 99 13 monte monte PROPN american_scientific_journal-7553 99 14 carlo carlo NOUN american_scientific_journal-7553 99 15 using use VERB american_scientific_journal-7553 99 16 python python NOUN american_scientific_journal-7553 99 17 , , PUNCT american_scientific_journal-7553 99 18 " " PUNCT american_scientific_journal-7553 99 19 comput comput NOUN american_scientific_journal-7553 99 20 . . PUNCT american_scientific_journal-7553 100 1 phys phy NOUN american_scientific_journal-7553 100 2 . . PUNCT american_scientific_journal-7553 101 1 commun commun PROPN american_scientific_journal-7553 101 2 . . PROPN american_scientific_journal-7553 101 3 , , PUNCT american_scientific_journal-7553 101 4 vol vol NOUN american_scientific_journal-7553 101 5 . . PROPN american_scientific_journal-7553 101 6 177 177 NUM american_scientific_journal-7553 101 7 , , PUNCT american_scientific_journal-7553 101 8 no no INTJ american_scientific_journal-7553 101 9 . . NOUN american_scientific_journal-7553 101 10 10 10 NUM american_scientific_journal-7553 101 11 , , PUNCT american_scientific_journal-7553 101 12 pp pp ADJ american_scientific_journal-7553 101 13 . . PUNCT american_scientific_journal-7553 102 1 799 799 NUM american_scientific_journal-7553 102 2 - - SYM american_scientific_journal-7553 102 3 814 814 NUM american_scientific_journal-7553 102 4 , , PUNCT american_scientific_journal-7553 102 5 2007 2007 NUM american_scientific_journal-7553 102 6 . . PUNCT american_scientific_journal-7553 103 1 [ [ X american_scientific_journal-7553 103 2 12 12 NUM american_scientific_journal-7553 103 3 ] ] PUNCT american_scientific_journal-7553 103 4 i. i. PROPN american_scientific_journal-7553 103 5 kosztin kosztin PROPN american_scientific_journal-7553 103 6 , , PUNCT american_scientific_journal-7553 103 7 " " PUNCT american_scientific_journal-7553 103 8 kosztin1996.pdf kosztin1996.pdf NOUN american_scientific_journal-7553 103 9 . . PUNCT american_scientific_journal-7553 103 10 " " PUNCT american_scientific_journal-7553 103 11 1996 1996 NUM american_scientific_journal-7553 103 12 . . PUNCT