IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL. 24 (2) 2011 Vibrational Zero-Point Energies of Iodo Compounds N. Saeed Departme nt of Chemistry, College of Education Ibn AL-Haitham, Unive rsity of Baghdad Received in :11 April 2011 Accepte d in :30 May 2011 Abstract In this st udy , the contribution of the bond C–I has been d erived and incorp orated in emp irical formula to calcu late zero-point energies (ZPE) of Iodo comp ounds. The calculated ZPE for 38 molecules containing this bond correlate well with exp erimental values. The comp arison of t hese results with semiemp irical (AM 1) ZPE app ears very satisfactory . Keywords: Zero-point energy ; Empirical ZPE; Iodo comp ounds. Introduction The zero p oint energies (Z PE) of p olyatomic molecu les c an be exp erimentally determin ed via equation (1): ZPE = 1/2 hvi (1) Where h Planck's constant,Vi is the frequency of fundamental vibration i, and k the normal mod es of vibrations . Normal vibrations are usually determined by IR and Raman sp ectroscopy . This method has some difficulties, esp ecially , for large molecules because of the exist ence of overtones and combination frequencies in their mo lecular sp ectra. Ab initio calcu lations are also used in determining the frequencies of normal modes of comp ounds. This method have several difficulties. First ly, It overest imates the frequencies by about 10% [1]. Secondly, ab initio calcu lations require sop histicated comp uters and need long comp uting times esp ecially for lar ge mo lecules. As a consequence of the above difficulties, emp irical methods had been developed to calcu late the ZPE’s of organic comp ounds . Flanigen et al, [2] deriv ed a simple emp irical formula for the calculation of the ZPE of a hydrocarbon, equation (2): ZPE = 2n + 7m (kcal/mol) (2) Where n, m are the number of carbon and hy drogen atoms, resp ectively. Later, Schulman and Disch [3] have develop ed another emp irical formula for the calculation to the ZPE,s of hy drocarbons, equation (3) : IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL. 24 (2) 2011 ZPE (n,m) = 3.88n + 7.12m – 6.19 (kcal/mo l) (3) Where n and m are the number of carbon and hydrogen atoms, resp ectively, 3.88 is the increment of carbon atom, 7.12 is the increment of hy drogen atom and 6.19 is a const ant. Ibrahim, Fatafiata and AbdulHussain [4-6] used Schuman and Disch formula to calcu late the ZPE,s of other organic comp ounds by deriving increment for N, O, Cl, F, S, Br and I atoms. Rahal et al, [7-8] established an emp irical relationship making it p ossible to calculate the ZPE of organic comp ounds. This relationship was determined by relating ZPE to the nature and typ e of bonds forming the molecule. The empirical formula found is written as follows : ZPE (kcal/mol) (4) with p the number of bonds in the molecule, N t he number of bonds of t yp e i and BC, the contribution of the bond i to the ZPE. This equation makes it p ossible to calculate the ZPE of comp ounds containing the bonds C-H, N-H, O-H, S-H, C-O, C-C, C-N, C-S, N-N, C-F, C-Cl, C-Br, C=C, C=N, C=O, C=S, C≡C, and C≡N. It has been app lied to more than 80 chemical sy stems belonging to different categor ies of comp ounds (alkanes, alkenes, alkynes, cycloalkanes, cycloalk enes, ketones, aldehydes, acids, esters, alcohols, ethers, amines, amides, nitriles, thio comp ounds, chloro comp ounds, fluoro comp ounds, aromatics, etc. ). The correlation between the exp erimental and emp irical ZPE valu es is virtually linear for the non-aromatic compounds while for aromatic co mpounds, t he empirical values hav e to be adjust ed using the equ ation (5): ZPE = 1.08 ZPE (emp irical) - 1.07 (kcal/mol) (5) This correction is due to t he fact t hat in the aromatic nucleus t he CC bonds are identical by resonance, while the model sup p oses the p resence of three C-C bonds and three C=C bonds. In this st udy , we determine the contribution of the C-I bond in order to c alculate the ZPE of iodo comp ounds. The results obtained have been comp ared to the exp erimental values on the one hand, and to the values obtained usin g semi- emp irical (AM 1) calculations on the other hand. Computational details The semiemp irical calculations were carried out using the (AM 1) method [9] imp lemented in the Gaussian 09 p rogram [10] and Pentium IV PC at Baghdad University . Zero-point vibrational energy was calculated after op timising the geometry on the basis of normal vibr ation frequencies. Results and Discussion The derivation of bond contribution for any type bond requires molecules have reliable ZPE values. The set molecules used in the derivation of C-I bond contribution with their exp erimental ZPE values are recorded in Table (1). The exp erimental ZPE values are calcu lated from the reported vibrational sp ectra for chosen or ganic iodo comp ounds belong to different or ganic classes of comp ounds such as acy clic, cyclic, saturated and unsaturated. Ot her functional group s such as OH are also p resent in the chosen molecu les. T he chosen = N B C -2 .0 9 (e mpirical) p i i i IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL. 24 (2) 2011 comp ounds can be also divid ed into mono-, di- and tetra- iodo comp ounds. T hus , t he chosen molecu les include various classes of iodo compounds. By using the least squares method and Eq. (4) can derive C-I bond contribution to calcu late ZPE value. The contribution of C-I bond as well as the contributions already established [7-8] for the other bonds are given in Table (2). The deriv ed C-I bond contribution value is 1.6344 kcal/mo l. To test the reliability of the generalized emp irical formula, it is applied to 38 iodo comp ounds of various classes (iodoalkanes, iodoalkenes, iodoalky nes, iodoaromatics, etc.). The results in Table (1) show that the calculated v alues correlate well with the exp erimental values. The correlation between the exp erimental and emp irical values list in Fig (1), st andard deviation, SD, is 0.681, slop e is close to unity 1.013 , correlation coefficient is 099979 and average error is 0.47. This means the develop ed C-I bond contribution could rep roduce the exp erimental ZPE values for an iodo organic comp ounds. The Table (1) shows that there is little difference between the exp erimental values of ZPE and those calculated empirically, less than 1.3 k cal/mol in all cases excep t tert-Butyl iodide was 2.29 kcal/mol. The st andard deviation, SD, average error, slop e and correlation coefficient will b e imp roved to 0.579, 0.42, 1.011 and 0.99984 r esp ectively if the tert- Butyliodide valu e is ne glected Fig (2). The same Iodo comp ounds are calculated by using the semi emp irical (AM 1) method. The results are corrected by a factor of 0.96 Table (1). The st andard division, SD, slop e, average error, and correlation coefficient are 0.824, 1.011, 0.646 and 0.99963 resp ectively Fig (3). The comp arison between the semi emp irical (AM 1) values and emp irical estimation values shows t hat the empirical est imation valu es are closer to exp erimental values. Conclusion In this st udy the zero p oint energy ZPE values of iodo organic comp ounds are calcu lated using the contribution of the C-I bond determined. The results obtained are comp ared with the exp erimental results available and with the results obtained using the semi-emp irical method (AM 1). The emp irical method p rovides a simple and quick method of calcu lating ZPE values of iodo compounds. Re ferences 1.M artin, M . L. (1998) “Ab initio Thermochemistry Bey ond Chemical Accuracy for First -and Second-Row Comp ounds” Phy sics,Cornell ,Ithaca New York ,980813. 2.Flanigan, M . C.; Kormornick i, A. and M clver, J. W. Jr, (1977), “Electronic st ructure calcu lation”, in Seg G. A. ed. (Plenu m press, New Yourk). 3.Schulman, J. M . and Disch, R. L., (1985), “A simp le formula for the zero-p oint energies of hy drocarbons”, Chem. Phy s. Lett. 113, 291-293. 4.Ibrahim, M . R. and Fataftah, Z. A., (1986), “Estimation of zero-p oint energies of comp ounds containing N, O, Cl and F atoms”, Chem. Phy s. Let. 125, 149-154. 5.Ibrahim, M . R. and Fataftah, Z. A., (1987), “Estimation of zero-point energies of bromo and thio compounds”, Chem. Phys. Let. 136, 583-587. 6.Abdulhussain, Nasser Saeed. (1999), “Thermochemical data of carboxy lic acids, esters and iodo compounds”, Theses, Yarmouk University . 7.Rahal, M .; Hilali, M .; El M ouhtadi, A. and El Ha jab, A., (2001), “ Calculation of vibrational zero-point energy ”, J. M ol. Struct (Themochem)., 572, 73-80. 8.Rahal M . and El Hajab, A., (2004), “ Vibrational zero-point energies of bro mo co mpounds”, J. M ol. Struct (T hemochem)., 668, 197-200. IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL. 24 (2) 2011 9.Dewar, M . J. S.; Zoebisch, E.G.; Healy , E.F. and Stewart, J., (1985), “Develop ment and use of quantum mechanical molecular models. 76. AM 1: a new gener al p urp ose quantum mechan ical molecular model”, J.P J. Am. Chem. So c. 107 3902–3909. 10.Gaussian 09, Revision A.02, Frisch, M . J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M . A.; Cheeseman, J. R.; Scalmani, G.; Barone, V. ; M ennucci,B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M . X. Li.; Hratchian, H. P.; Izmay lov, A. F.; Bloino, J.; Zheng, G.; Sonnenber g, J. L. ; Hada, M .; Ehara, M .; Toy ota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M .; Nakajima, T.; Honda, Y. ; Kitao, O.; Nakai, H.; Vreven, T.; M ontgomery , J. A. Jr.,; Peralta, J. E.; Ogliaro, F.; Bearp ark, M .; Hey d, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobay ashi, R.; Normand, Raghavachari, J.; K.; Rendell, A.; Burant, J. C.; Iyengar, S. S. ; Tomasi, J.; Cossi, M .; Rega, N.; M illam, J. M .; Klene, M .; Knox, J. E. ; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomp erts, R.; Stratmann, R. E.; Yazy ev, O.; A. Austin, J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; M artin, R. L.; M orokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salv ador, P.; Dannenberg, J. J.; Dapp rich, S.; Daniels, A. D.; Farkas, O.; Foresman, J. B. ; Ortiz, J. V.; Cioslowski, J.; and Fox, D. J.; Gaussian, Inc., Wallin gford CT, 2009. 11.Zhou, X. and Allinger, N. L., (1994), “M olecular mechanics calculations (MM 3) on alky l iodides”, J. Phy s. Org. Chem., 7, 420-430. 12.Sverdlov, L.M .; Kovner, M .A and Krainov, E.P. (1974) “ Vibrational sp ectra of polyatomic molecu les” , John Wiley & Sons, New York and Toront o. 13.Shimanouchi, T., (1974), “Tables of M olecular Vibrational Frequencies. Part 8”, J. Phy s. Chem. Ref. Data., 3, 269-308. 14.Shimanouchi, T., (1973), “Tables of M olecular Vibrational Frequ encies: Part 6” “, J. Phy s. Chem. Ref. Data., 2, 121-162. 15.Tsuchiya, S., (1974), “Molecular st ructures of acety l fluoride and acety l iodide”, J. M ol. Struct., 22, 77-95. 16.Tanabe, K., (1974), “Vibrational frequencies, infrared absorp tion intensities and ener gy difference of rotational isomers of 1,2-diiodoethane”, Sp ectrochim. Acta., 30A, 1901- 1914. 17.Shimanouchi, T., (1980), “Tables of M olecular Vibrational Frequencies Part 10”, J. Phy s. Chem. Ref. Data., 9, 1149-1254. 18.Rogst ad, A. and Cy vin, S. J., (1974), “Vibrational frequen cies, force constants, mean amp litudes, shrinkage effects and thermody namic functions for monohaloacety lenes”, J. M ol. Struct., 20, 373-379. 19.Flourie, E. J. and Jones, W. D., (1969), “The vibrational sp ectra and assignments of tetraiodoethy lene”, Sp ectrochim. Acta., 25A, 653-659. 20.Whitmer, J. C., (1974), “Normal coordinates and p otential energy distributions of methy l acety lene and some halo gen subst itut ed analogues”, J. M ol. Struct., 21, 173-183. 21.Jorgensem, W. L. and Salem, L. (1973), “The Organic Chemist’s Book of Orbitals”, Acadimic Press, New York. 22.Durig, R. (1978), “Vibrational Sp ectra and Structure”, vol.7, Elseveir Scientific Publish ing Company, Amst erdam. 23.Klaboe, P. and Jenesn, E. K., (1967), “Raman sp ectra and revised vibrational assignments of some halogeno cyanoacety lenes”,Sp ectrochim. Acta., 23A, 1981-1990. 24.Durig, R.; Thompson, J. W.; Thy agsean, U. W. and Witt, J. D., (1975), “Vibrational sp ectra of ethy l iodedes”, J. M ol. Struct., 24, 41-58. 25.Rogst ad, A.; Benest ad, L. and Cy vin, S. J., (1974), “Vibrational frequen cies, force constants, coriolis constants, mean amp litudes and shrinkage effects for CH3CC-CCX (X = H, Cl, Br or I)”, J. M ol. Struct., 23, 265-272. 26.Faerman and Bonadeo, H., (1980), “Vibrational sp ectra, p acking calculations and cryst al st ructure of 1,2-diiodobenzene”, Chem. Phy s. Let. 69, 91-96. IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL. 24 (2) 2011 27.Woldbeak, T. and Klaebe, P., (1980), “The conformation and vibrational sp ectra of trans- 1,4-dihalocy clohexanes : Part III. trans-1,4-Diiodo-, trans-1,4-bromoiodo- and trans-1,4- dibromocyclohexane”, J. M ol. Struct., 63, 195-219. 28.Klaeboe, P.; Nielsen, C. J. and Woldbaek, T., (1981), “The vibrational sp ectra and conformation of si x trans-1,4-dihalocy clohexanes(Cl, Br, I)” J. M ol. Struct., 60, 121-126. IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL. 24 (2) 2011 Table ( 1): Comparison of c alculated (empirical, AM 1) zero-p oint energy with exp erimental values. Formula M olecular ZPE (Kcal/mol) DIF (Kcal/mol) a Ref Exp . Emp . AM 1 b Emp . AM1 CH3I Methyliodide 22.02 22.31 21.65 -0.29 0.37 [11] CHI3 Iodoform 10.90 10.40 10.25 0.50 0.65 [12] CCl3I T richloroiodomethane 5.36 6.16 5.76 -0.80 -0.40 [11] CF 3I T riiodoflurooiodomethane 8.69 9.47 9.17 -0.78 -0.48 [13] CH2I2 Diiodomethan 16.30 16.35 16.12 -0.05 0.18 [13] CI4 Carbontetraiodide 3.42 4.45 4.16 -1.03 -0.74 [11] ICN Cyanogeniodide 4.70 4.36 5.31 0.34 -0.61 [14] C2BrI Bromoiodoacetylene 5.75 5.94 6.48 -0.19 -0.73 [14] C2ClI Chloroiodoacetylene 6.11 6.16 6.91 -0.05 -0.80 [14] C2H3OI Acetyliodide 28.16 28.32 28.30 -0.16 -0.14 [13] C2H4I2 1,2-Diiodoethane 33.60 33.60 33.39 0.00 0.21 [15] C2H5I Ethyliodide 39.60 39.56 39.14 0.04 0.46 [16] C2H5OI Iodoethanol 43.16 41.96 42.28 1.20 0.88 [17] C2HI Iodoacetylene 10.95 11.54 11.96 -0.59 -1.01 [18] C2I2 Diiodoacetylene 5.55 5.59 6.34 -0.04 -0.79 [14] C2I4 T etraiodoethene 6.86 7.10 7.69 -0.24 -0.83 [19] C3H3I Methyliodoacetylene 28.33 28.79 28.70 -0.46 -0.37 [20] C3H3I Iodopropadien e 28.16 27.61 28.41 0.55 -0.25 [14] C3H3I Propargyliodide 28.00 28.79 28.70 -0.79 -0.70 [21] C3H5I Iodocycloprop ane 43.51 43.71 43.81 -0.20 -0.30 [22] C3H5I 3-iodopropene 42.74 42.21 42.61 0.53 0.13 [11] C3H6I2 1,3-Diiodopropane 50.98 50.85 50.63 0.13 0.35 [17] C3H7I 1-Propyliodide 56.80 56.81 56.48 -0.01 0.32 [11] C3H7I Isopropyliodide 56.63 56.81 56.30 -0.18 0.33 [17] C3H7OI 2-iodoethylmethyllether 59.95 60.13 59.83 -0.18 0.12 [23] C3NI Iodocyanoethyne 10.97 10.85 12.29 0.12 -1.32 [14] C4H8I2 1,4-Diiodobutane 68.23 68.10 67.92 0.13 0.31 [20] C4H9I 1-Iodobutane 74.10 74.06 73.85 0.04 0.25 [24] C4H9I tert-Butyliodide 76.35 74.06 73.25 2.29 3.10 [20] C4HI Iododiacetylen e 17.33 18.03 18.82 -0.70 -1.49 [17] C4O3I2 Diiodomalaicanhydride 21.84 21.24 23.16 0.60 -1.32 [24] C5H11I 1-Iodopentan e 91.37 91.31 91.09 0.06 0.28 [20] C5H3I 1-Iodo-1,3-Pentadiyne 34.51 35.28 35.51 -0.77 -1.00 [25] C6H10ClI 1,4-chloroiodocyclohex ane 91.38 90.08 91.72 1.30 -0.34 [26] C6H10I2 1,4-diiodocyclohexane 90.62 89.51 91.18 1.11 -0.56 [21] C6H10IBr 1,4-iodobromocyclohexan e 91.05 89.86 91.29 1.19 -0.24 [27] C6H4I2 1,2-Diiodobenzene 48.10 48.29 c 49.40 -0.19 -1.30 [28] C6H5I Iodobenzene 54.68 54.72 c 55.57 -0.04 -0.89 [28] a ZPE (e xper imental) – ZPE(ca lculate d) . b Valu es adjust by 0.96 . c Adjust value by Eq. (5) IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL. 24 (2) 2011 Table (2) Contr ibution of each bond toZPE (in Kcal/mol) Bo nd Bond contribtion (BCi C-H N-H O-H S-H C-O C-C C-N C-S N-N C-F C-Cl C=C C=N C=O C=S C≡C C≡N C-Br C-I 7.5877 a 7.2013a 7.2964 a 5.6921 a 2.6985 a 2.0751 a 4.1409 a 1.4403 a 6.8372a 3.3078 a 2.2051a 2.6501 a 3.8852a 3.9343 a 2.7319a 4.4125 a 4.8169a 1.9837 b 1.6344 c a Ref [7 ]. b Ref [8]. c This study. IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL. 24 (2) 2011 ZPE(e xp.) = 1.011*ZPE(emp.) - 0.397 R = 0.99984 , SD = 0.579 , N = 37 0 10 20 30 40 50 60 70 80 90 100 0 20 40 60 80 100 Z P E (e x p .) ( k ca l/ m o l) ZPE(e mp.) (kcal/mol) Fig. (1) Comparison between experimental ZPE’s and empirical values calculated using Eq.(4) Fig. (2) Comparison between ZPE’s experimental and empirical values except tert-Butyl iodide value’s IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL. 24 (2) 2011 Fig. (3) Comparison between experimental ZPE’s and theortical (AM1) ZPE 2011) 2( 24المجلد مجلة ابن الھیثم للعلوم الصرفة والتطبیقیة طاقات نقطة الصفر لمركبات الیود ناصر سعید قسم الكیمیاء، ابن الهیثم، جامعة بغداد كلیة التربیة 2011نیسان 11: استلم البحث في 2011آیار 30 :قبل البحث في الخالصة ة وضمت C-Iمساهمة االصرة تفي هذه الدراسة ، اشتق مع مساهمات االواصر المشتقة سابقا في الصیغ وجد ان و طاقات نقطة الصفر لمركبات الیود من خالل مساهمات االواصر المشتقة ، حسبت والوضعیة لمركبات الیود ، محسوبة لـ ةقیم طاقبین عالقة ال ، هي عالقة جیدة القیم التجریبیةمع جزیئة تحتوي هذه االصرة 38نقطة الصفر ال Semiemp وكذلك مقارنة هذه النتائج مع قیم طاقات نقطة الصفر المحسوبة بـ irical (AM . تبدو مقنعة جدا (1