IBN AL- HAITHAM J. FOR PURE & APPL. SCI. VOL.24 (2) 2011 Vibrational Zero-Point Energies of Iodo Compounds N. Saeed Department of Chemistry, College of Education Ibn AL-Haitham, University of Baghdad Received in :11 April 2011 Accepted in :30 May 2011 Abstract In this study, the contribution of the bond C–I has been derived and incorporated in empirical formula to calculate zero-point energies (ZPE) of Iodo compounds. The calculated ZPE for 38 molecules containing this bond correlate well with experimental values. The comparison of these results with semiempirical (AM1) ZPE appears very satisfactory . Keywords: Zero-point energy; Empirical ZPE; Iodo compounds. Introduction The zero point energies (ZPE) of polyatomic molecules can be experimentally determined 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 modes of vibrations . Normal vibrations are usually determined by IR and Raman spectroscopy. This method has some difficulties, especially, for large molecules because of the existence of overtones and combination frequencies in their molecular spectra. Ab initio calculations are also used in determining the frequencies of normal modes of compounds. This method have several difficulties. Firstly, It overestimates the frequencies by about 10% [1]. Secondly, ab initio calculations require sophisticated computers and need long computing times especially for large molecules. As a consequence of the above difficulties, empirical methods had been developed to calculate the ZPE’s of organic compounds . Flanigen et al, [2] derived a simple empirical 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 hydrogen atoms, respectively. Later, Schulman and Disch [3] have developed another empirical formula for the calculation to the ZPE,s of hydrocarbons, equation (3) : IBN AL- HAITHAM J. FOR PURE & APPL. SCI. VOL.24 (2) 2011 ZPE (n,m) = 3.88n + 7.12m – 6.19 (kcal/mol) (3) Where n and m are the number of carbon and hydrogen atoms, respectively, 3.88 is the increment of carbon atom, 7.12 is the increment of hydrogen atom and 6.19 is a constant. Ibrahim, Fatafiata and AbdulHussain [4-6] used Schuman and Disch formula to calculate the ZPE,s of other organic compounds by deriving increment for N, O, Cl, F, S, Br and I atoms. Rahal et al, [7-8] established an empirical relationship making it possible to calculate the ZPE of organic compounds. This relationship was determined by relating ZPE to the nature and type 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 the number of bonds of type i and BC, the contribution of the bond i to the ZPE. This equation makes it possible to calculate the ZPE of compounds 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 applied to more than 80 chemical systems belonging to different categories of compounds (alkanes, alkenes, alkynes, cycloalkanes, cycloalkenes, ketones, aldehydes, acids, esters, alcohols, ethers, amines, amides, nitriles, thio compounds, chloro compounds, fluoro compounds, aromatics, etc. ). The correlation between the experimental and empirical ZPE values is virtually linear for the non-aromatic compounds while for aromatic compounds, the empirical values have to be adjusted using the equation (5): ZPE = 1.08 ZPE (empirical) - 1.07 (kcal/mol) (5) This correction is due to the fact that in the aromatic nucleus the CC bonds are identical by resonance, while the model supposes the presence of three C-C bonds and three C=C bonds. In this study, we determine the contribution of the C-I bond in order to calculate the ZPE of iodo compounds. The results obtained have been compared to the experimental values on the one hand, and to the values obtained using semi-empirical (AM 1) calculations on the other hand. Computational details The semiempirical calculations were carried out using the (AM1) method [9] implemented in the Gaussian 09 program [10] and Pentium IV PC at Baghdad University . Zero-point vibrational energy was calculated after optimising the geometry on the basis of normal vibration 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 experimental ZPE values are recorded in Table (1). The experimental ZPE values are calculated from the reported vibrational spectra for chosen organic iodo compounds belong to different organic classes of compounds such as acyclic, cyclic, saturated and unsaturated. Other functional groups such as OH are also present in the chosen molecules. The chosen = N B C -2 .0 9 (e m p ir ica l ) p i i i IBN AL- HAITHAM J. FOR PURE & APPL. SCI. VOL.24 (2) 2011 compounds can be also divided into mono-, di- and tetra- iodo compounds. Thus , the chosen molecules include various classes of iodo compounds. By using the least squares method and Eq. (4) can derive C-I bond contribution to calculate 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 derived C-I bond contribution value is 1.6344 kcal/mol. To test the reliability of the generalized empirical formula, it is applied to 38 iodo compounds of various classes (iodoalkanes, iodoalkenes, iodoalkynes, iodoaromatics, etc.). The results in Table (1) show that the calculated values correlate well with the experimental values. The correlation between the experimental and empirical values list in Fig (1), standard deviation, SD, is 0.681, slope is close to unity 1.013 , correlation coefficient is 099979 and average error is 0.47. This means the developed C-I bond contribution could reproduce the experimental ZPE values for an iodo organic compounds. The Table (1) shows that there is little difference between the experimental values of ZPE and those calculated empirically, less than 1.3 kcal/mol in all cases except tert-Butyl iodide was 2.29 kcal/mol. The standard deviation, SD, average error, slope and correlation coefficient will be improved to 0.579, 0.42, 1.011 and 0.99984 respectively if the tert- Butyliodide value is neglected Fig (2). The same Iodo compounds are calculated by using the semi empirical (AM 1) method. The results are corrected by a factor of 0.96 Table (1). The standard division, SD, slope, average error, and correlation coefficient are 0.824, 1.011, 0.646 and 0.99963 respectively Fig (3). The comparison between the semi empirical (AM 1) values and empirical estimation values shows that the empirical estimation values are closer to experimental values. Conclusion In this study the zero point energy ZPE values of iodo organic compounds are calculated using the contribution of the C-I bond determined. The results obtained are compared with the experimental results available and with the results obtained using the semi-empirical method (AM1). The empirical method provides a simple and quick method of calculating ZPE values of iodo compounds. References 1.Martin, M. L. (1998) “Ab initio Thermochemistry Beyond Chemical Accuracy for First-and Second-Row Compounds” Physics,Cornell ,Ithaca New York ,980813. 2.Flanigan, M. C.; Kormornicki, A. and Mclver, J. W. Jr, (1977), “Electronic structure calculation”, in Seg G. A. ed. (Plenum press, New Yourk). 3.Schulman, J. M . and Disch, R. L., (1985), “A simple formula for the zero-point energies of hydrocarbons”, Chem. Phys. Lett. 113, 291-293. 4.Ibrahim, M. R. and Fataftah, Z. A., (1986), “Estimation of zero-point energies of compounds containing N, O, Cl and F atoms”, Chem. Phys. 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 carboxylic acids, esters and iodo compounds”, Theses, Yarmouk University . 7.Rahal, M.; Hilali, M.; El Mouhtadi, A. and El Hajab, A., (2001), “Calculation of vibrational zero-point energy”, J. Mol. Struct (Themochem)., 572, 73-80. 8.Rahal M. and El Hajab, A., (2004), “Vibrational zero-point energies of bromo compounds”, J. Mol. Struct (Themochem)., 668, 197-200. IBN AL- HAITHAM J. FOR PURE & APPL. SCI. VOL.24 (2) 2011 9.Dewar, M. J. S.; Zoebisch, E.G.; Healy, E.F. and Stewart, J., (1985), “Development and use of quantum mechanical molecular models. 76. AM 1: a new general purpose quantum mechanical molecular model”, J.P J. Am. Chem. Soc. 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.; Mennucci,B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M. X. Li.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A. Jr.,; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, Raghavachari, J.; K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; A. Austin, J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, O.; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; and Fox, D. J.; Gaussian, Inc., Wallingford CT, 2009. 11.Zhou, X. and Allinger, N. L., (1994), “Molecular mechanics calculations (MM 3) on alkyl iodides”, J. Phys. Org. Chem., 7, 420-430. 12.Sverdlov, L.M.; Kovner, M.A and Krainov, E.P. (1974) “Vibrational spectra of polyatomic molecules” , John Wiley & Sons, New York and Toronto. 13.Shimanouchi, T., (1974), “Tables of Molecular Vibrational Frequencies. Part 8”, J. Phys. Chem. Ref. Data., 3, 269-308. 14.Shimanouchi, T., (1973), “Tables of Molecular Vibrational Frequencies: Part 6” “, J. Phys. Chem. Ref. Data., 2, 121-162. 15.Tsuchiya, S., (1974), “Molecular structures of acety l fluoride and acety l iodide”, J. Mol. Struct., 22, 77-95. 16.Tanabe, K., (1974), “Vibrational frequencies, infrared absorption intensities and energy difference of rotational isomers of 1,2-diiodoethane”, Spectrochim. Acta., 30A, 1901- 1914. 17.Shimanouchi, T., (1980), “Tables of Molecular Vibrational Frequencies Part 10”, J. Phys. Chem. Ref. Data., 9, 1149-1254. 18.Rogstad, A. and Cyvin, S. J., (1974), “Vibrational frequencies, force constants, mean amplitudes, shrinkage effects and thermodynamic functions for monohaloacetylenes”, J. Mol. Struct., 20, 373-379. 19.Flourie, E. J. and Jones, W. D., (1969), “The vibrational spectra and assignments of tetraiodoethylene”, Spectrochim. Acta., 25A, 653-659. 20.Whitmer, J. C., (1974), “Normal coordinates and potential energy distributions of methyl acety lene and some halogen substituted analogues”, J. Mol. 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 Spectra and Structure”, vol.7, Elseveir Scientific Publish ing Company, Amsterdam. 23.Klaboe, P. and Jenesn, E. K., (1967), “Raman spectra and revised vibrational assignments of some halogeno cyanoacetylenes”,Spectrochim. Acta., 23A, 1981-1990. 24.Durig, R.; Thompson, J. W.; Thyagsean, U. W. and Witt, J. D., (1975), “Vibrational spectra of ethyl iodedes”, J. Mol. Struct., 24, 41-58. 25.Rogstad, A.; Benestad, L. and Cyvin, S. J., (1974), “Vibrational frequencies, force constants, coriolis constants, mean amplitudes and shrinkage effects for CH3CC-CCX (X = H, Cl, Br or I)”, J. Mol. Struct., 23, 265-272. 26.Faerman and Bonadeo, H., (1980), “Vibrational spectra, packing calculations and crystal structure of 1,2-diiodobenzene”, Chem. Phys. Let. 69, 91-96. IBN AL- HAITHAM J. FOR PURE & APPL. SCI. VOL.24 (2) 2011 27.Woldbeak, T. and Klaebe, P., (1980), “The conformation and vibrational spectra of trans- 1,4-dihalocyclohexanes : 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 spectra and conformation of six trans-1,4-dihalocyclohexanes(Cl, Br, I)” J. Mol. Struct., 60, 121-126. IBN AL- HAITHAM J. FOR PURE & APPL. SCI. VOL.24 (2) 2011 Table ( 1): Comparison of calculated (empirical, AM 1) zero-point energy with experimental values. Formula Molecular ZPE (Kcal/mol) DIF (Kcal/mol) a Ref Exp. Emp. AM1b 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 Trichloroiodomethane 5.36 6.16 5.76 -0.80 -0.40 [11] CF3I Triiodoflurooiodomethane 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 Tetraiodoethene 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 Iodopropadiene 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 Iodocyclopropane 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 Iododiacetylene 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-Iodopentane 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-chloroiodocyclohexane 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-iodobromocyclohexane 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 54.72c 55.57 -0.04 -0.89 [28] a ZPE (experimental) – ZPE(calculated) . b Values adjust by 0.96 . c Adjust value by Eq. (5) IBN AL- HAITHAM J. FOR PURE & APPL. SCI. VOL.24 (2) 2011 Table (2) Contribution of each bond toZPE (in Kcal/mol) Bond 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. SCI. VOL.24 (2) 2011 ZPE(exp.) = 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 xp .) ( k ca l/ m ol ) ZPE(emp.) (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. SCI. 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 Semiempirical (AM وكذلك مقارنة هذه النتائج مع قیم طاقات نقطة الصفر المحسوبة بـ . تبدو مقنعة جدا (1