J. Nig. Soc. Phys. Sci. 3 (2022) 429–445 Journal of the Nigerian Society of Physical Sciences Quantum Chemical Studies on C4H4N2 Isomeric Molecular Species E. E. Etima,∗, M. E. Khanb, O. E. Godwina, G. O. Ogofothab aDepartment of Chemical Science, Federal University Wukari, Nigeria bDepartment of Chemistry, Federal University Lokoja, Kogi State, Nigeria Abstract Quantum chemical calculations have been carried out on C4H4N2 isomeric molecular species using the G4 method and compared with experimen- tal values where available, probing parameters like thermochemistry, structural parameters (e.g. bond length, bond angles), rotational constants, vibrational spectroscopy and dipole moments. Pyrimidine was found to be the most stable of all the isomers with ∆ f H0 =37.1 kcal/mol. A critical analysis showed high correlation and consistency between the computed and experimental values of all the parameters under study and therefore providing the needed rationale to validate the values provided for the isomers which do not have available experimental data. DOI:10.46481/jnsps.2021.282 Keywords: Isomers, Pyrimidine, Experimental, Computational Article History : Received: 30 June 2021 Received in revised form: 16 August 2021 Accepted for publication: 07 September 2021 Published: 29 November 2021 c©2021 Journal of the Nigerian Society of Physical Sciences. All rights reserved. Communicated by: B. J. Falaye 1. Introduction Quantum Chemistry is an area of computational chemistry which could reproduce experimental chemical phenomena math- ematically, this branch of study avails one the opportunity to understand the electronic structures and model the nature of in- teractions molecules undergo not just for stable molecules as usually provided by experimental procedures but also for the short-lived intermediates or unstable analogues [1- 4]. It has been applied in different fields in chemistry where researchers have been able to make accurate predictions of future reactions [5, 6], physicochemical properties, docking, rate constants, pro- tein calculations, calculations of potential energy surfaces, elec- tronic structures of molecules and their isomers, molecules in the interstellar medium (ISM) [7]. ∗Corresponding author tel. no: Email address: emmaetim@gmail.com (E. E. Etim ) C4H4N2 has many isomeric species of wide spread relevance. Pyrazines (C4H4N2) also known as 1,4-Diazines are hetero- cyclic aromatic organic compounds commonly distributed in nature such as in bacteria, fungi, insects and plants e.g. pota- toes, coffee, nuts. They are responsible for the nutty and roasty smell which is reminiscent of cocoa and coffee. These com- pounds are used to improve aroma/flavor in food and cosmetic industries [8 – 11]. Nucleotides (such as cytosine, thymine), vi- tamin such as thiamine (i.e. vitamin B1), HIV drug Zidovudine and synthetic compounds like barbitutrates all contain the iso- mer pyrimidine [12]. The isomer pyridazine finds applications as herbicides (such as pyridafol, pyridate, credazine), as drugs such as minaprine, cadralazine, cefozopran[13]. It has been cumbersome studying certain molecules whose iso- mers or themselves are unstable molecules such as the present case. This challenge may be overcome to a certain level by the application of computational approach which has been shown 429 Etim et al. / J. Nig. Soc. Phys. Sci. 3 (2022) 429–445 430 Table 1: Standard enthalpy of formation of C4H4N2 isomeric species Molecules ∆ f H0 (kcal/mol) 1,2-diisocyanoethane 92.4 1,3-butadiene-1,4-diimine 88.0 4-amino-2-butynenitrile 83.0 Iminopyrrole 62.3 2-methylene-2H-imidazole 60.1 Pyridazine 59.0 1,1-dicyanoethane 54.7 Pyrazine 41.0 Pyrimidine 37.1 to be a relative good substitute for experimental approach. Thus, the present study aims at using computational methods to in- vestigate the isomers of the C4H4N2 group by predicting the standard enthalpy of formation, bond length and angles, dipole moment, vibrational frequencies, rotational constants etc., and comparing their results with the available experimental values where available. 2. Computational Methods GAUSSIAN 09 suite of program was employed in perform- ing all the quantum chemical calculations reported in this study. The effectiveness of the G4 composite method has been re- ported in many literatures [14-16] in addition to experience from our previous studies [17- 23]; as such the molecule un- der study was optimized using the G4 level of theory. 3. Result and Discussion The possible isomers of the C4H4N2 isomeric group in- clude; 1,2-diisocyanoethane, 1,3-butadiene-1,4-diimine, 4-amino- 2-butynenitrile, iminopyrrole, 2-methylene-2H-imidazole, pyri- dazine, 1,1-dicyanoethane, pyrazine, pyrimidine. The results of the quantum chemical calculations carried out on the C4H4N2 isomeric species using the G4 level of theory are presented and discussed below under the different subheadings: 3.1. Thermochemistry The focal point of thermochemistry is energy changes such as enthalpy of formation and many other energy related parame- ters. Fig 1 shows the optimized geometries of the C4H4N2 iso- meric molecular species while the standard enthalpies of forma- tion (∆fHO) computed for these isomeric species are presented in Table 1. Pyrimidine has the least enthalpy of formation of 37.1 Kcal/mol which corresponds to the most stable of all the isomers, 1,2-diisocyanoethane is shown to be the least stable of all the isomers of the C4H4N2 isomeric group having the value of 92.4 Kcal/mol as the heat of formation. The experimentally reported standard heat of formation of pyrimidine ranges from 46.1±0.5 to 47.75± 0.4 [24-26], the disparity between the com- puted and experimental values point towards the possibility of an error in the experimentally reported value as Weisenburger and co-workers [27]. According to them, experimental mea- surement of heat of formation is always inaccurate and imprac- tical. From previous studies, the G4 method has proven to be effective in predicting the enthalpy of formation that is in good accuracy with experimental results [14-23]. Standard enthalpy of formation is an important parameter that can be applied for safe and scaling up of chemical processes involving thermal sta- bility. It helps researchers in predicting the spontaneity of a re- action, know whether a reaction can be favourable or not and the reactants and products quantities [27]. 3.2. Vibrational Spectroscopy Table 2 depicts the vibrational frequencies of pyrimidine (the most stable isomer of the C4H4N2 isomeric group) with the cor- responding spectrum in Figure 2. The vibrational frequencies and the corresponding spectra for other isomers of the C4H4N2 isomeric group are presented in the appendix (Tables A1-A3 and Figure A respectively). Table 1 contains the calculated and experimental values of the vibrational frequencies of pyrimi- dine. The error between the values ranges between 0.3-4 cm−1. The computed values are in excellent agreement with the re- ported experimental values. Thus, for the other isomers with no experimentally measured vibrational frequencies, the val- ues computed at the G4 level (presented in the appendix) are believed to be accurate. The G4 composite method has also been reported to give accurate predictions for vibrational spec- troscopic parameters for other molecular species with experi- mentally known values [14-23]. Among other applications, the vibrational spectroscopy parameters are useful in the chemical examination of the interstellar medium especially for the astro- nomical observation of interstellar molecular species with no dipole moment [17,20]. 3.3. Rotational Constants Rotational spectroscopy remains the most important spectro- scopic technique employed in the astronomical observation of molecular species from different regions of the interstellar medium. The experimentally measured rotational constants (from the NIST Webbook) for pyrimidine and the values obtained at the G4 level are presented in Table 3 below. As shown in the Table, there is a good agreement between the experimental and the computed values of the rotational constant of pyrimidine. The Table also contains the rotational constants calculated for other isomers of the C4H4N2 isomeric group at the G4 level of theory with no experimentally measured values. Analysis of the dif- ference showed errors of 0.0261635, 0.0330026 and 0.0156889 GHz for the A, B and C rotational constants of pyrimidine re- spectively. This level of accuracy suggests a good level of ac- curacy for the rotational constants obtained for other isomers at the G4 level with no experimentally measured values. 3.4. Structural Parameters The bond lengths and bond angles of Pyrimidine are pre- sented in Table 4 while Fig. 3 depicts the optimized geom- etry. As shown in the Table, there is an excellent agreement 430 Etim et al. / J. Nig. Soc. Phys. Sci. 3 (2022) 429–445 431 1,2-diisocyanoethane 1,3-butadiene-1,4-diimine 4-amino-2-butynenitrile Iminopyrrole 2-methylene-2H-imidazole Pyridazine 1,1-dicyanoethane Pyrazine Pyrimidine Figure 1: Optimized geometry of C4H4N2 isomeric groups Figure 2: Calculated IR frequencies of pyrimidine between the experimentally measured values and the computa- tionally predicted values. For example, both the experimental (1.087Å) and the computational (1.087Å) values for rCH bond length. For the other bond lengths reported for pyrimidine, the difference between the experimental and the computational val- ues range 0.36-0.46 Å while for the predicted bond angles, the difference between the experimental and the computational val- ues range from 0.19-1.10 degrees. These findings suggest that 431 Etim et al. / J. Nig. Soc. Phys. Sci. 3 (2022) 429–445 432 Table 2: Vibrational frequencies of pyrimidine Calculated Frequency (cm−1) ExperimentalFrequency (cm−1) Error(cm−1) 353 347 1.69 411 398 2.9 632 621 1.58 693 679 1.45 744 719 3.36 835 804 3.59 988 960 2.74 1009 969 3.96 1011 980 2.97 1030 1033 -0.29 1083 1065 1.01 1095 1155 2.7 1165 1158 0.85 1227 1224 5.6 1260 1356 2.78 1395 1224 2.79 1439 1356 1.95 1496 1411 2.07 1610 1465 2.55 1612 1569 2.48 3154 1572 3.36 3157 3047 3.39 3165 3053 3.51 3207 3082 3.89 Table 3: Rotational Constant of C4H4N2 isomers Molecules Rotation constants (GHz) A B C Pyrimidine Calculated 6.3010414 6.0983826 3.0990279 Experimental 6.2748779 6.06538 3.083339 Error 0.0261635 0.0330026 0.0156889 1,2- diisocyanoethane Calculated 7.4362588 2.5722569 2.0604923 1,3- butadiene- 1,4-diimine Calculated 23.1647044 1.3418215 1.2867453 4-amino-2- butynenitrile Calculated 23.0996150 1.3419073 1.2868109 Iminopyrrole Calculated 8.5048965 4.1234186 2.7770331 2-methylene- 2H-imidazole Calculated 8.7736412 4.2378633 2.8575861 Pyridazine Calculated 6.4337599 5.9503379 3.0913068 Pyrazine Calculated 6.4337599 5.9503379 3.0913068 the bond lengths and bond angles predicted with the G4 method for the other isomers of the C4H4N2 isomeric group presented in the appendix (Tables A4-A6) with no experimental values will have a good level of accuracy and can be used when re- quired. 3.5. Dipole Moments Dipole moment is useful in determining the polar nature of the chemical bond. It is also useful in astrophysics and related ar- eas such as astrochemistry and astrobiology as the dipole of a molecule plays an important role in the astronomical obser- vation of such molecule [2]. The dipole moments obtained at the G4 level for all the isomeric molecular species in this study 432 Etim et al. / J. Nig. Soc. Phys. Sci. 3 (2022) 429–445 433 Table 4: Bond Distances/ Angles of Pyrimidine and its Isomers Description Calculated Value (Å) Exp. Value (Å) Error Connectivity Atom 1 Atom 2 Atom 3 rCH 1.087 1.087 0 4 4 - rCH 1.079 1.083 0.36 3 3 - rCH 1.082 1.087 0.46 2 2 - rCC 1.393 1.389 0.29 3 2 - rCN 1.328 1.334 0.45 1 1 - aCCC 117.8 116.5 1.10 4 3 2 aHCC 120.90 121.13 0.19 2 2 3 aCCN 121.20 122.37 0.97 3 4 2 Table 5: Dipole Moment of C4H4N2 isomers Molecule Calculated Dipole moment (Debye) Experimental Dipole moment (Debye) 1,2-diisocyanoethane 5.1506 - 1,3-butadiene-1,4- diimine 3.6290 - 4-amino-2-butynenitrile 3.7238 - Iminopyrrole 3.2055 - 2-methylene-2H- imidazole 1.0758 - Pyridazine 4.5926 - 1,1-dicyanoethane 4.5904 - Pyrazine 0.0000 - Pyrimidine 2.4133 2.33 Figure 3: Optimized geometry of pyrimidine are presented in Table 5. The experimental dipole moment of 2.33D [29] reported for pyrimidine is in good agreement with the value (2.41D) calculated at the G4 level. There are no exper- imentally reported dipole moments values for the other isomers of the pyrimidine isomeric group. However, the good agree- ment between the experinmentally measured and the compu- tationally calculated values for pyrimidine suggest a good ac- curacy for the dipole moments predicted for those molecular species with no experimental values. 4. Conclusion The Gaussian G4 compound model has been applied in com- puting some quantum chemical properties for the C4H4N2 isomeric molecular species. Spectroscopic parameters (rotational and vibrational), bond distances, bond angles and dipole moments have been calculated for all the isomeric molecular species con- sidered in this study. The results show a good agreement be- tween the values obtained with the G4 method and the available experimentally measured values. This good agreement suggests a good accuracy for those the computationally predicted values with no experimental values. Thus, the predicted values at the G4 level of theory could serve as useful data where there are no experimental values. Acknowledgments The authors will like to appreciate the handling editor and the anonymous reviewers for their advice to make this work a success. Appendix Figure A: IR spectra of C4H4N2 isomeric species. 433 Etim et al. / J. Nig. Soc. Phys. Sci. 3 (2022) 429–445 434 Table A1: IR Frequencies and Intensities of C4H4N2 isomers Pyrazine 1,1-dicyanoethane Pyridazine Frequency (cm−1) IR Intensi- ties Frequency (cm−1) IR Intensi- ties Frequency (cm−1) IR Intensities 350.2454 0 142.6498 10.3325 377.4241 8.4376 436.8441 20.8309 212.9721 0.0061 378.1465 0 609.3268 0 217.325 10.417 629.7531 0.1251 718.6392 0 232.5641 0.1562 678.7734 3.7111 784.4478 0 390.8231 0.6653 773.826 26.977 813.6882 16.8768 501.3777 0.5045 784.7741 0 954.5671 0 577.079 2.0394 955.9237 0 995.7849 0 591.9736 0.0401 988.5043 0.0273 1004.4743 0 789.326 0.9436 1015.5701 6.7412 1032.2801 41.3863 924.1966 0.5222 1025.6928 0 1043.5004 0 1024.5549 3.0293 1057.3562 1.8513 1091.2542 11.3623 1077.6373 1.9773 1085.4055 1.9376 1168.3175 3.0353 1137.7852 11.4915 1094.3822 10.9875 1234.2883 3.3451 1293.1894 0.2956 1172.7042 0 1257.5615 0 1325.8192 10.5516 1198.4094 0.0296 1377.4992 0 1412.7563 0.8374 1315.9121 2.7813 1443.5577 32.5811 1489.6743 7.1366 1438.4468 17.1702 1516.3516 1.6121 1495.8979 2.9216 1480.3479 1.0699 1581.3618 0 2369.8219 1.4472 1604.0217 4.1776 1617.6288 0 2375.5886 1.0261 1608.3885 6.5778 3154.1328 0 3040.9897 0.0176 3171.291 11.3104 3154.5805 6.8491 3064.7956 7.0787 3175.4201 0.6737 3170.0288 69.5698 3150.5629 6.2676 3191.228 18.3941 3176.6122 0 3154.8613 4.5128 3205.5438 8.2119 434 Etim et al. / J. Nig. Soc. Phys. Sci. 3 (2022) 429–445 435 Table A2: IR Frequencies and Intensities of C4H4N2 isomers 2-methylene-2H- imidazole Iminopyrrole 4-amino-2-butynenitrile Frequency (cm−1) IR Intensi- ties Frequency (cm−1) IR Intensi- ties Frequency (cm−1) IR Intensi- ties 231.2641 16.2028 222.6459 1.5177 102.9298 3.212 367.2831 5.0478 437.8852 15.624 136.5392 6.7159 545.8568 0 513.7051 0.5416 249.5854 0.2682 729.7105 0.9392 673.5182 13.329 273.9337 21.0114 757.4695 6.9218 709.63 1.5332 384.9431 30.924 778.714 0.0001 821.884 0.5162 500.8402 11.2464 893.0866 0.2762 839.2175 34.5306 575.9942 2.9544 912.9179 8.5062 878.6648 11.3524 582.7078 1.7895 915.8468 10.8072 926.5924 10.2062 699.5133 11.1841 954.3095 42.6853 967.2053 5.8961 889.2243 0.0003 961.4052 0.0001 969.8546 11.5774 895.8998 201.8104 979.8251 16.2158 993.4477 44.2831 1098.3395 26.2627 991.4666 31.7917 1058.7038 51.7342 1148.1344 4.2125 1202.2146 17.8701 1093.3592 5.4566 1183.4347 0.2291 1303.1681 6.2567 1280.4929 34.9662 1356.3555 33.0669 1346.2606 21.0282 1341.6019 75.8567 1383.0345 0.0121 1412.9732 17.8688 1353.3948 11.9765 1459.7535 5.1009 1496.1998 11.0291 1548.0035 19.6616 1669.8384 18.9874 1613.199 2.8089 1646.7243 11.3723 2258.8654 0.001 1714.8692 3.0856 1740.6104 20.5283 2396.7797 101.4735 3180.8768 0.0002 3175.7293 18.3444 3036.9215 13.0137 3196.1465 6.9809 3234.5262 3.2481 3070.8682 4.6604 3211.1464 15.5153 3266.179 1.1482 3496.6081 1.6966 3283.7487 0.0178 3434.2972 4.1245 3574.5662 3.4152 435 Etim et al. / J. Nig. Soc. Phys. Sci. 3 (2022) 429–445 436 Table A3: IR Frequencies and Intensities of C4H4N2 isomers 1,3-butadiene- 1,4-diimine 1,2-diisocyanoethane Frequency (cm−1) IR Intensities Frequency (cm−1) IR Intensities 83.6289 4.2328 78.7298 4.2564 127.629 1.9142 168.9156 0.5605 247.6388 0 192.4169 3.7141 413.9178 39.0839 262.623 0.1196 422.8897 0.0001 299.0842 0.3214 553.3442 90.5491 389.5249 0.2258 572.2602 0.0004 551.2205 13.3477 602.0439 17.4793 827.5204 7.2786 678.4837 0 859.6152 9.5185 879.0897 0.0004 1035.2344 3.9097 905.6999 99.6452 1041.9629 7.1071 1033.4248 0.0001 1091.3162 0.7493 1042.7608 612.5875 1268.8807 1.8639 1064.7913 0.0002 1304.1572 0.188 1144.81 40.0234 1384.277 13.328 1186.8856 0 1392.4053 22.9043 1291.0522 42.9681 1485.0234 17.2458 1485.9837 0 1486.765 0.1757 2123.9009 896.411 2224.3091 150.9267 2130.4724 0.1389 2226.309 166.4745 3174.8502 0.0003 3052.5648 3.5487 436 Etim et al. / J. Nig. Soc. Phys. Sci. 3 (2022) 429–445 437 Table A4: Bond radius and angles of C4H4N2 isomers Pyrazine 1,1-dicyanoethane Pyridazine Description Cal. Value Description Cal. Value Description Cal. Value R(1-2) 1.393 R(1-2) 1.154 R(1-2) 1.333 R(1-6) 1.334 R(1-3) 1.470 R(1-6) 1.332 R(1-7) 1.087 R(3-4) 1.470 R(2-3) 1.395 R(2-3) 1.334 R(3-6) 1.549 R(2-8) 1.086 R(2-8) 1.087 R(3-10) 1.098 R(3-4) 1.381 R(3-4) 1.334 R(4-5) 1.154 R(3-7) 1.084 R(4-5) 1.393 R(6-7) 1.092 R(4-5) 1.395 R(4-9) 1.087 R(6-8) 1.091 R(4-9) 1.084 R(5-6) 1.334 R(6-9) 1.092 R(5-6) 1.333 R(5-10) 1.087 A(2-1-3) 178.0 R(5-10) 1.086 A(2-1-6) 122.1 A(1-3-4) 110.7 A(2-1-6) 119.4 A(2-1-7) 120.8 A(1-3-6) 111.3 A(1-2-3) 123.8 A(1-2-3) 122.1 A(1-3-10) 107.3 A(1-2-8) 114.9 A(1-2-8) 120.8 A(4-3-6) 111.3 A(1-6-5) 119.4 A(6-1-7) 117.1 A(4-3-10) 107.3 A(3-2-8) 121.2 A(1-6-5) 115.9 A(3-4-5) 178.0 A(2-3-4) 116.8 A(3-2-8) 117.1 A(6-3-10) 108.9 A(2-3-7) 120.9 A(2-3-4) 115.9 A(3-6-7) 109.5 A(4-3-7) 122.3 A(3-4-5) 122.1 A(3-6-8) 110.5 A(3-4-5) 116.8 A(3-4-9) 117.1 A(3-6-9) 109.5 A(3-4-9) 122.3 A(5-4-9) 120.8 A(7-6-8) 109.0 A(5-4-9) 120.9 A(4-5-6) 122.1 A(7-6-9) 109.3 A(4-5-6) 123.8 A(4-5-10) 120.8 A(8-6-9) 109.0 A(4-5-10) 121.2 A(6-5-10) 117.1 R(1-2) 1.154 A(6-5-10) 114.9 R(1-2) 1.393 R(1-3) 1.470 R(1-2) 1.333 R(1-6) 1.334 R(3-4) 1.470 R(1-6) 1.332 R(1-7) 1.087 R(3-6) 1.549 R(2-3) 1.395 R(2-3) 1.334 R(3-10) 1.098 R(2-8) 1.086 R(2-8) 1.087 R(4-5) 1.154 R(3-4) 1.381 R(3-4) 1.334 R(6-7) 1.092 R(3-7) 1.084 R(4-5) 1.393 R(6-8) 1.091 R(4-5) 1.395 R(4-9) 1.087 R(6-9) 1.092 R(4-9) 1.084 R(5-6) 1.334 A(2-1-3) 178.0 R(5-6) 1.333 R(5-10) 1.087 A(1-3-4) 110.7 R(5-10) 1.086 A(2-1-6) 122.1 A(1-3-6) 111.3 A(2-1-6) 119.4 A(2-1-7) 120.8 A(1-3-10) 107.3 A(1-2-3) 123.8 A(1-2-3) 122.1 A(4-3-6) 111.3 A(1-2-8) 114.9 A(1-2-8) 120.8 A(4-3-10) 107.3 A(1-6-5) 119.4 A(6-1-7) 117.1 A(3-4-5) 178.0 A(3-2-8) 121.2 A(1-6-5) 115.9 A(6-3-10) 108.9 A(2-3-4) 116.8 A(3-2-8) 117.1 A(3-6-7) 109.5 A(2-3-7) 120.9 A(2-3-4) 115.9 A(3-6-8) 110.5 A(4-3-7) 122.3 A(3-4-5) 122.1 A(3-6-9) 109.5 A(3-4-5) 116.8 A(3-4-9) 117.1 A(7-6-8) 109.0 A(3-4-9) 122.3 A(5-4-9) 120.8 A(7-6-9) 109.3 A(5-4-9) 120.9 A(4-5-6) 122.1 A(8-6-9) 109.0 A(4-5-6) 123.8 A(4-5-10) 120.8 R(1-2) 1.154 A(4-5-10) 121.2 A(6-5-10) 117.1 R(1-3) 1.470 A(6-5-10) 114.9 437 Etim et al. / J. Nig. Soc. Phys. Sci. 3 (2022) 429–445 438 Table A5: Bond radius and angles of C4H4N2 isomers 2-methylene- 2H-imidazole Iminopyrrole 4-amino-2-butynenitrile Description Cal. Value Description Cal. Value Description Cal. Value R(1-2) 1.413 R(1-2) 1.437 R(1-2) 1.466 R(1-3) 1.295 R(1-3) 1.289 R(1-5) 1.465 R(2-5) 1.414 R(2-8) 1.484 R(1-9) 1.097 R(2-8) 1.339 R(2-9) 1.270 R(1-10) 1.097 R(3-4) 1.473 R(3-4) 1.486 R(2-3) 1.209 R(3-7) 1.084 R(3-7) 1.087 R(3-4) 1.365 R(4-5) 1.295 R(4-6) 1.081 R(4-6) 1.162 R(4-6) 1.084 R(4-8) 1.341 R(5-7) 1.016 R(8-9) 1.082 R(5-8) 1.079 R(5-8) 1.016 R(8-10) 1.083 R(9-10) 1.025 A(2-1-5) 115.2 A(2-1-3) 103.6 A(2-1-3) 104.8 A(2-1-9) 108.9 A(1-2-5) 113.0 A(1-2-8) 109.2 A(2-1-10) 108.9 A(1-2-8) 123.6 A(1-2-9) 125.3 A(1-2-3) 177.1 A(1-3-4) 109.9 A(1-3-4) 114.1 A(5-1-9) 108.7 A(1-3-7) 122.8 A(1-3-7) 121.5 A(5-1-10) 108.7 A(5-2-8) 123.5 A(8-2-9) 125.5 A(1-5-7) 109.7 A(2-5-4) 103.5 A(2-8-4) 106.2 A(1-5-8) 109.7 A(2-8-9) 120.3 A(2-8-5) 124.1 A(9-1-10) 106.0 A(2-8-10) 120.2 A(2-9-10) 108.7 A(2-3-4) 179.7 A(4-3-7) 127.2 A(4-3-7) 124.4 A(3-4-6) 180.0 A(3-4-5) 110.0 A(3-4-6) 125.4 A(7-5-8) 106.2 A(3-4-6) 127.2 A(3-4-8) 105.9 W1(A) 102.9 A(5-4-6) 122.8 A(6-4-8) 128.7 W2(A) 136.5 A(9-8-10) 119.5 A(4-8-5) 129.8 W3(A) 249.6 W1(A) 231.3 W1(A) 222.6 W4(A) 273.9 W2(A) 367.3 W2(A) 437.9 W5(A) 384.9 W3(A) 545.9 W3(A) 513.7 W6(A) 500.8 W4(A) 729.7 W4(A) 673.5 W7(A) 576.0 W5(A) 757.5 W5(A) 709.6 W8(A) 582.7 W6(A) 778.7 W6(A) 821.9 W9(A) 699.5 W7(A) 893.1 W7(A) 839.2 W10(A) 889.2 W8(A) 912.9 W8(A) 878.7 W11(A) 895.9 W9(A) 915.8 W9(A) 926.6 W12(A) 1098.3 W10(A) 954.3 W10(A) 967.2 W13(A) 1148.1 W11(A) 961.4 W11(A) 969.9 W14(A) 1183.4 W12(A) 979.8 W12(A) 993.4 W15(A) 1356.4 W13(A) 991.5 W13(A) 1058.7 W16(A) 1383.0 W14(A) 1202.2 W14(A) 1093.4 W17(A) 1459.8 W15(A) 1303.2 W15(A) 1280.5 W18(A) 1669.8 W16(A) 1346.3 W16(A) 1341.6 W19(A) 2258.9 W17(A) 1413.0 W17(A) 1353.4 W20(A) 2396.8 W18(A) 1496.2 W18(A) 1548.0 W21(A) 3036.9 W19(A) 1613.2 W19(A) 1646.7 W22(A) 3070.9 W20(A) 1714.9 W20(A) 1740.6 W23(A) 3496.6 W21(A) 3180.9 W21(A) 3175.7 W24(A) 3574.6 W22(A) 3196.1 W22(A) 3234.5 R(1-2) 1.466 W23(A) 3211.1 W23(A) 3266.2 R(1-5) 1.465 W24(A) 3283.7 W24(A) 3434.3 R(1-9) 1.097 438 Etim et al. / J. Nig. Soc. Phys. Sci. 3 (2022) 429–445 439 Table A6: Bond radius and angles of C4H4N2 isomers 1,3-butadiene- 1,4-diimine 1,2-diisocyanoethane Description Cal. Value Description Cal. Value R(1-2) 1.316 R(1-5) 1.173 R(1-5) 1.226 R(2-3) 1.538 R(2-3) 1.461 R(2-5) 1.416 R(2-9) 1.085 R(2-7) 1.094 R(3-4) 1.316 R(2-8) 1.095 R(3-10) 1.085 R(3-6) 1.416 R(4-6) 1.225 R(3-9) 1.095 R(5-7) 1.023 R(3-10) 1.094 R(6-8) 1.023 R(4-6) 1.173 A(2-1-5) 173.7 A(1-5-2) 179.0 A(1-2-3) 124.3 A(3-2-5) 112.1 A(1-2-9) 116.9 A(3-2-7) 109.7 A(1-5-7) 115.8 A(3-2-8) 108.4 A(3-2-9) 118.8 A(2-3-6) 112.1 A(2-3-4) 124.3 A(2-3-9) 108.4 A(2-3-10) 118.8 A(2-3-10) 109.7 A(4-3-10) 116.9 A(5-2-7) 109.2 A(3-4-6) 173.7 A(5-2-8) 109.2 A(4-6-8) 115.8 A(7-2-8) 108.1 W1(A) 83.6 A(6-3-9) 109.2 W2(A) 127.6 A(6-3-10) 109.2 W3(A) 247.6 A(3-6-4) 179.1 W4(A) 413.9 A(9-3-10) 108.1 W5(A) 422.9 W1(A) 78.7 W6(A) 553.3 W2(A) 168.9 W7(A) 572.3 W3(A) 192.4 W8(A) 602.0 W4(A) 262.6 W9(A) 678.5 W5(A) 299.1 W10(A) 879.1 W6(A) 389.5 W11(A) 905.7 W7(A) 551.2 W12(A) 1033.4 W8(A) 827.5 W13(A) 1042.8 W9(A) 859.6 W14(A) 1064.8 W10(A) 1035.2 W15(A) 1144.8 W11(A) 1042.0 W16(A) 1186.9 W12(A) 1091.3 W17(A) 1291.1 W13(A) 1268.9 W18(A) 1486.0 W14(A) 1304.2 W19(A) 2123.9 W15(A) 1384.3 W20(A) 2130.5 W16(A) 1392.4 W21(A) 3174.9 W17(A) 1485.0 W22(A) 3183.6 W18(A) 1486.8 W23(A) 3422.3 W19(A) 2224.3 W24(A) 3422.6 W20(A) 2226.3 R(1-2) 1.316 W21(A) 3052.6 R(1-5) 1.226 W22(A) 3056.6 R(2-3) 1.461 W23(A) 3096.1 R(2-9) 1.085 W24(A) 3107.6 R(3-4) 1.316 R(1-5) 1.173 439 Etim et al. / J. Nig. Soc. Phys. Sci. 3 (2022) 429–445 440 Pyrazine 440 Etim et al. / J. Nig. Soc. Phys. Sci. 3 (2022) 429–445 441 1,1-dicyanoethane Pyridazine 441 Etim et al. / J. Nig. Soc. Phys. Sci. 3 (2022) 429–445 442 2-methylene-2H-imidazole Iminopyrrole 442 Etim et al. / J. Nig. Soc. Phys. Sci. 3 (2022) 429–445 443 4-amino-2-butynenitrile 1,3-butadiene-1,4-diimine 443 Etim et al. / J. Nig. Soc. Phys. Sci. 3 (2022) 429–445 444 1,2-diisocyanoethane 444 Etim et al. / J. Nig. Soc. Phys. Sci. 3 (2022) 429–445 445 References [1] E. E. Etim, A. I. Onen, C. Andrew, U. Lawal, I.S. Udegbunam & O. A. Ushie, “Computational Studies of C5H5N Isomers”, J. Chem Soc. Nige- ria, 43 (2018) 1. [2] E. E. Etim, U. Lawal, C. Andrew & I.S. Udegbunam, ”Computational Studies on C3H4N2 Isomers”, International Journal of Advanced Re- search in Chemical Science (IJARCS), 5 (2018) 29. [3] E. E Etim, G. E. Oko, A. I. Onen, O. A. Ushie, C. Andrew, U. Lawal & G. 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