MEEM模型下分子偶极矩的计算
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摘要
偶极矩是表示分子中电荷分布情况的物理量,可以由分子的对称性推测分子有无偶极矩,也可由分子有无偶极矩及偶极矩的大小了解分子结构的信息。偶极矩沟通了分子的微观结构与宏观性能特征,所以进行化合物偶极矩的计算和研究,具有十分重要的理论意义和工程价值。而传统的从头计算所需要的计算量太大,这主要是由于利用从头算计算偶极矩要求用很大的基组,才能得到相对准确的结果,这样就要消耗大量的机时。因而有必要发展一种准确的、计算上易于实现的方法来探讨体系的结构和性质间的内在关系。我们以密度泛函理论和电负性均衡原理为基础,应用修正的电负性均衡方法(MEEM),利用最小二乘法,拟合确定了一些分子中各种类型原子的参数。运用这些参数,计算了一些分子的偶极矩,其结果可以和从头算相关,并可以说明一些化学规律。
The calculation of dipole moment by MEEM
The dipole moment is a physical quantity, which can indicate the charge distribution of the molecule. The value of dipole moment can be conferred from the situation of the molecular symmetry, and vice versa. Since the dipole moment links up the microcosmic structure and the macroscopic performance characteristic, it is very important to calculate the dipole moment of molecules. While conventional ab initio methods is too time-consuming to afford, because the accurate prediction of dipole moments appears to be possible only with the utilization of significantly large basis sets, so we should develop an accurate and economic method to probe the relationship between structures and properties. We have proposed modified electronegativity equalization method (MEEM) based on density functional theory and electronegativity equalization principle. Using a separated program, through regression and least-squares optimization, the parameters of atoms in molecules are determined. By these parameters, the dipole moments of some molecules are calculated. The results show well agreement with those obtained by ab initio methods, and it can also account for some chemical rules.
The calculation of dipole moment by MEEM
The dipole moment is a physical quantity, which can indicate the charge distribution of the molecule. The value of dipole moment can be conferred from the situation of the molecular symmetry, and vice versa. Since the dipole moment links up the microcosmic structure and the macroscopic performance characteristic, it is very important to calculate the dipole moment of molecules. While conventional ab initio methods is too time-consuming to afford, because the accurate prediction of dipole moments appears to be possible only with the utilization of significantly large basis sets, so we should develop an accurate and economic method to probe the relationship between structures and properties. We have proposed modified electronegativity equalization method (MEEM) based on density functional theory and electronegativity equalization principle. Using a separated program, through regression and least-squares optimization, the parameters of atoms in molecules are determined. By these parameters, the dipole moments of some molecules are calculated. The results show well agreement with those obtained by ab initio methods, and it can also account for some chemical rules.
引文
Hohenberg P, Kohn W, Inhomogeneous electron gas, Phys. Rev. B, 1964, 136,864.
Kohn W, Sham L, Self-consistent equations including exchange and correlation effects, Phys. Rev. A , 1965, 140,1133.
Levy M, Perdew J, In Density-Functional Methods in Physics, edited by Dreizler R H and J da Providencia, Plenum, New York, 1985.
Parr R G, Yang W, Density-Functional Theory of Atoms and Molecules, Oxford University, New York, 1989.
Parr R G, Donnelly R A, Levy R A, Palke W E, Electronegativity: the density functional viewpoint, J. Chem. Phys, 1978, 68,3801.
Fukui K, Yonezawa T, Nagata C and Shingu H, A molecular orbital theory of reactivity in aromatic hydrocarbons, J. Chem. Phys, 1952, 20,722.
Parr R G, Yang W, Density functional approach to the frontier electron theory of chemical reactivity, J. Am. Chem. Soc, 1984, 106,4049.
Lee C, Yang W, and Parr R G, Local softness and chemical reactivity in the molecules CO, SCN-and H3CO3, J. Mol. Struct (Theochem), 1988, 163,305.
Sen K D, Jorgensen C K, Electronegativity in Structure and Bonding, New York, Heidelberg: Springer-Verlag, 1987, 66:1-25, 125-143.
Bader R.F.W., Atoms in Molecules: A quantum Theory (Clarendon, Oxford, 1994).
Hohenberg P., Kohn W., Inhomogeneous Electron Gas, Phys. Rev. B, 1964, 136,864.
Kohn W., Sham L., Self-consistent Equations Including Exchange and Correlation Effects, Phys. Rev. A, 1965, 140,1133.
Levy M., Perdew J., In Density-Functional Methods in Physics, edited by Dreizler R H and J da Providencia. Plenum, New York, 1985.
Parr R.G., Yang W., Density-Functional Theory of Atoms and Molecules, Oxford University, New York, 1989.
Iczkowski R.P., Margrave J.L., Electronegativity, J.Am.Chem.Soc.1961, 83,3547-3551.
Parr, R.G., Pearson, R.G., Absolute Hardness: Companion Parameter to Absolute Electronegativity , J.Am.Chem.Soc.1983, 3105,7512-7516.
Pearson,R.G. Inorg.Chem, Relations between bond softness and bond valence, 1988,27,734.
Pauling L, The Nature of Chemical Bond, 3rd Ed.,Cornell University Press, Ithaca, NY, 1960.
Pauling L, Die Natur der Chemischen Binding, Verlag Chemie, Weinheim, 1973.
Huheey J. E., Inorganic Chemistry, Harper & Row, New York, 1978.
Allred A.L., Rochow E.G., J. Inorg. Nucl. Chem., 1958, 5,264.
Sanderson R.T., Chemical Bonds and Bond Energy (Academic Press, New York, 1976.)
Darrin M. York, Weitao Yang, A chemical potential equalization method for molecular simulations, J. Chem. Phys., 1996, 104(1), 159.
Sanderson R.T., Polar Covalence (Academic Press, New York, 1983.)
Politzer P., Weinstein H., Some relations between electronic distribution and electronegativity, J. Chem. Phys., 1979, 71,4218.
Mortier W.J., Ghosh S.K., Shankar S. Electronegativity equalization method for the calculation of atomic charges in molecules. J.Am.Chem.Soc. 1986,108,4315
Mortier W.J., Genechten K.V., Gasteriger J., Elementary properties of an energy functional of the first-order reduced density matrix. J.Am.Chem.Soc.1985, 1027, 829
Baekelandt B.G., Mortier W.J., Lievens J.L., Schoonheydt R., Probing the reactivity of different sites within a molecule or solid by direct
computation of molecular sensitivities via an extension of the electronegativity equalization method, J.Am.Chem.Soc. 1991, 113, 6730;
Baekelandt B.G., Mortier,W.J., Schoonheydt R.A. Structure and Bonding, 1993, 80, 187.
Baekelandt B.G., Janssens G.O.A., Toufar H., Mortier W.J., Schoonheydt R.A., Mapping between Electron Population and Vibrational Normal Modes within the Charge Sensitivity Analysis, J. Phys. Chem., 1995,99,9784-9794.
Nalewajski R.F., Electrostatic Effects in Interactions between Hard (soft) Acids and Bases, J. Am. Chem. Soc., 1984, 106, 944.
Nalewajski R.F., A Study of Electronegativity Equalization, J. Phys. Chem., 1985, 89, 2831.
Nalewajski.R.F., Normal (decoupled) Representation of Electronegativity Equalization Equations in a Molecule, Int.J.Quant.Chem., 1991, 40, 265.
Korchowiec J., Nalewajski R.F., ibid , 1992, 44, 1027.
Darrin M. Y, Yang W, A chemical potential equalization method for molecular simulations, J.Chem.Phys., 1996, 104(1),159-172.
Toufar H., Baeklandt B.G., Janssens G.O.A., Mortier W.J., Schoonheydt R.A., Investigation of supramolecular systems by a combination of the electronegativity equalization method and a Monte Carlo simulation technique, J. Phys. Chem., 1995, 99, 13876.
Darrin M.Y., Yang W., A Chemical Potential Equalization Method for Molecular Simulations, J.Chem.Phys., 1996, 104(1), 159-172.
Jerzy Cioslowski, Boris B., Stefanov Electron Flow and Electronegativity Equation in the Process of Bond Formation, J. Chem. Phys., 1999, 99, 5151.
Jerzy Cioslowski, Martin Martinov, The atomic softness matrix, J. Chem. Phys., 1994, 101, 366.
Jerzy Cioslowski, Martin Martinov, Electronegativity Equalization in Polyyne Carbon Chains, J. Chem. Phys., 1996, 100, 6156.
Jerzy Cioslowski, Martin Martinov, Spin-resolved Analysis of Electronegativity Equalization and Electron Flow in Molecules, J.Chem.Phys.,1995, 102, 7499.
Tapan K., Ghanty and Swapan K., Ghosh, Electornegativity and Covalent Binding in Homonuclear Diatomic Molecules, J. Phys. Chem., 1991, 95, 6512.
Swapan K. Ghosh, Electronegativity, Hardness, and a Semiempirical Density Functional Theory of Chemical Binding, Int. J. Quantum Chem., 1994, 49, 239.
Bultinck P., Langenaeker W., Lahorte P., et al., The Electronegativity Equalization Method I: Parametrization and Validation for Atomic Charge calculations, J. Phys. Chem., 2002, 106, 7887-7894.
Bultinck P., Langenaeker W., Lahorte P, et al., The Electronegativity Equalization Method II: Applicability of Different Atomic Charge Schemes, J. Phys. Chem., 2002, 106, 7895-7901.
郭燕文, 甲苯硝基化合物的偶极矩及介电特性, 火炸药学报,1999, 22, 3.
余红霞, 朱传方, 分子的偶极矩对化合物香味的影响研究, 岳阳师范学院学报(自然科学版), 2001, 14, 2, 24-26.
R. Antoine. I. Compagono, D. Rayane, M Broyer, Ph. Dugourd, G. Breaux, F. C, Hagemeister, D. Pippen, R. R. Hudgins, M.F. Jarrold,Electric dipole moments and conformations of isolated peptides,Eur. Phys. J. D,2002,20,583-587.
HU Zeng-Jian, JIANG Hua-Liang, CHEN Jian-Zhong,CHEN Kai-Xian, JI Ru-Yun, Analysis of electronic structures of physostigmine analogs, 中国药理学报, 1998, 4.
C.H.Worner, On the Teaching of the electric dipole, The Physics Teacher,
2001, 39,462-463.
蔡显鄂, 项一非, 刘衍光, 物理化学实验, 高等教育出版社, 第二版, 211.
周公度, 段连运, 结构化学基础, 北京大学出版社, 第二版, 197.
A.H. Nethercot Jr., Molecular dipole moments and electronegaticity, chemical physica letters, 1978, 59, 346.
B.P. Dailey and C.H. Townes, Electron density distribution in 2-nitro-5-methylimidazole, J. Chem. Phys, 1955, 23, 118.
Andreya, Toropov, Ozodm, Nabiev, QSPR modeling of hydrocarbon dipole moments by means of correlation weighting of local graph invariants, Journal of Theoretical and computational chemistry, 2003, 2:139.
Yang Z.Z., Shen E Z., Direct Calculation of Group Electronegativity and the Atomic Charges in a Group, Science in China (Series B), 1996, 39, 20-28.
Yang Z.Z., Shen E.Z., Wang L.H., A Scheme for Calculation Atomic Charge-Distribution in Large Molecules Based on Density-Functional Theory and Electronegativity Equalization, J. Mol. Structure (Theochem), 1994, 118, 167-173.
沈尔忠,杨忠志, 密度泛函理论下的分子电负性—I. 由电负性均衡原理直接计算分子中的原子电荷, 中国科学(B辑),1995,25(2),126-131.
杨忠志,沈尔忠, 密度泛函理论下的分子电负性——II.基团电负性及基团中原子电荷分布的直接计算, 中国科学(B辑),1995,25(12),1233-1239.
沈尔忠,杨忠志, 密度泛函理论下的分子电负性—III.分子总能量的直接计算, 化学学报,1996,54,152-159.
Yang Z.Z., Shen E.Z., Niu S.Y., Molecular Electronegativity in Density Functional Theory.5. Relationship between the Global and Harmonic Mean Electronegativities for a Molecule, Chemical Research in Chinese University, 1996, 12(2), 159-163.
Handbook of chemistry and physics, CRC press, 1983-1984, 64th Edition.
Dea-Sik Hong,Soo Gyeong Cho, Ab Initio Study of Chlorosilanes: Dipole Moment and Charge Distributions,J.Chem.Inf.Comput.Sci,1999,39,537-542
F.deproft,C.van alsenor,A.peters,W.langenaeker,P.geerlings,Atomic charges, Dipole Moments, and Fukui Functions Using the Hirshfeld Partitioning of the Electron Density, Journal of Computational chemistry,23, 12, 1198-1209
Alexandr V.,Yatsenko,Ksenia A,Paseshnichenko,On the performance of semiempirical MO theory for dipole moments of dye molecules,J. Mol Model, 2001, 7, 384-391.
Jiabo li,Christopher J. Cramer,Donald G. Truhlar,MIDI! Basis set for silicon,bromine,and iodine,Theoretical chemistry Accounts,1998,99, 192-196.
刘次全,量子生物学及其应用,高等教育出版社,1990,第一版,99.
曾昭琼,有机化学,高等教育出版社,1993,第三版,12.
p.w. 阿特金斯,量子物质结构概念手册,科学出版社,91.
Williams, D. E.; Yan, J. M. Adv. At. Mol. Phys. 1987, 23, 87.
Colonna, F.; Evleth, E ; Angyan, J. G. Critical analysis of electric field modeling: Formamide, J. Comput. Chem. 1992, 13, 1234.
Chipot, C.; Maigret, B.; Rivail, J.-L.; Scheraga, H. A. Modeling amino acid side chains.1.Determination of net atomic charges from ab initio self-consistent field molecular electrostatic properties, J. Phys. Chem. 1992, 96, 10276
Chipot, C.; Angyan, J. G.; Ferenczy, G. G.; Scheraga, H. A. Transferable net atomic charges from distributed multipole analysis for the description of electrostatic properties. A case study of saturated hydrocarbons, J. Phys.
Chem. 1993, 97, 6628.
Christophe Chipot, Janos G. Angyan, and Bernard Maigret, Harold A. Scheraga, Modelling Amino Acid Side Chains. 2. Determination of Point Charges from Electrostatic Properties: Toward Transferable Point Charge Models,J. Phys. Chem,1993, 97, 9788-9796.
Yang Z Z, Wang C S, Atom-bond electronegativity method, I. Calculation of the charge distribution in large molecules. J Phys Chem A, 1997, 101:6315.
Wang C S, Li S M, Yang Z Z, Calculation of molecular energies by atom-bond electronegativity equalization method, J Mol Struct. (Theochem), 1998, 430, 191.
Yang Z Z, Wang C S, Tang A Q, Molecular electronegativity in the density functional theory-atom-bond electonegativity equalization model, Science in China (Series B), 1998, 41, 331.
Wang C S, Yang Z Z, Atom-bond electronegativity method, II. Lone-pair electron model, J Chem Phys, 1999, 110(13), 6189.
Yao Cong, Zhong-Zhi Yang, General atom-bond electronegativity equalization method and its application in prediction of charge distributions in polypeptide, Chem Phys Lett, 2000, 316, 324-329.
杨忠志,丛尧,王长生, 原子—键电负性均衡方法中的((模型及其应用, 高等学校化学化学学报,1999, 20 (11), 1781.
Kohn W, Sham L, Self-consistent equations including exchange and correlation effects, Phys. Rev. A , 1965, 140,1133.
Levy M, Perdew J, In Density-Functional Methods in Physics, edited by Dreizler R H and J da Providencia, Plenum, New York, 1985.
Parr R G, Yang W, Density-Functional Theory of Atoms and Molecules, Oxford University, New York, 1989.
Parr R G, Donnelly R A, Levy R A, Palke W E, Electronegativity: the density functional viewpoint, J. Chem. Phys, 1978, 68,3801.
Fukui K, Yonezawa T, Nagata C and Shingu H, A molecular orbital theory of reactivity in aromatic hydrocarbons, J. Chem. Phys, 1952, 20,722.
Parr R G, Yang W, Density functional approach to the frontier electron theory of chemical reactivity, J. Am. Chem. Soc, 1984, 106,4049.
Lee C, Yang W, and Parr R G, Local softness and chemical reactivity in the molecules CO, SCN-and H3CO3, J. Mol. Struct (Theochem), 1988, 163,305.
Sen K D, Jorgensen C K, Electronegativity in Structure and Bonding, New York, Heidelberg: Springer-Verlag, 1987, 66:1-25, 125-143.
Bader R.F.W., Atoms in Molecules: A quantum Theory (Clarendon, Oxford, 1994).
Hohenberg P., Kohn W., Inhomogeneous Electron Gas, Phys. Rev. B, 1964, 136,864.
Kohn W., Sham L., Self-consistent Equations Including Exchange and Correlation Effects, Phys. Rev. A, 1965, 140,1133.
Levy M., Perdew J., In Density-Functional Methods in Physics, edited by Dreizler R H and J da Providencia. Plenum, New York, 1985.
Parr R.G., Yang W., Density-Functional Theory of Atoms and Molecules, Oxford University, New York, 1989.
Iczkowski R.P., Margrave J.L., Electronegativity, J.Am.Chem.Soc.1961, 83,3547-3551.
Parr, R.G., Pearson, R.G., Absolute Hardness: Companion Parameter to Absolute Electronegativity , J.Am.Chem.Soc.1983, 3105,7512-7516.
Pearson,R.G. Inorg.Chem, Relations between bond softness and bond valence, 1988,27,734.
Pauling L, The Nature of Chemical Bond, 3rd Ed.,Cornell University Press, Ithaca, NY, 1960.
Pauling L, Die Natur der Chemischen Binding, Verlag Chemie, Weinheim, 1973.
Huheey J. E., Inorganic Chemistry, Harper & Row, New York, 1978.
Allred A.L., Rochow E.G., J. Inorg. Nucl. Chem., 1958, 5,264.
Sanderson R.T., Chemical Bonds and Bond Energy (Academic Press, New York, 1976.)
Darrin M. York, Weitao Yang, A chemical potential equalization method for molecular simulations, J. Chem. Phys., 1996, 104(1), 159.
Sanderson R.T., Polar Covalence (Academic Press, New York, 1983.)
Politzer P., Weinstein H., Some relations between electronic distribution and electronegativity, J. Chem. Phys., 1979, 71,4218.
Mortier W.J., Ghosh S.K., Shankar S. Electronegativity equalization method for the calculation of atomic charges in molecules. J.Am.Chem.Soc. 1986,108,4315
Mortier W.J., Genechten K.V., Gasteriger J., Elementary properties of an energy functional of the first-order reduced density matrix. J.Am.Chem.Soc.1985, 1027, 829
Baekelandt B.G., Mortier W.J., Lievens J.L., Schoonheydt R., Probing the reactivity of different sites within a molecule or solid by direct
computation of molecular sensitivities via an extension of the electronegativity equalization method, J.Am.Chem.Soc. 1991, 113, 6730;
Baekelandt B.G., Mortier,W.J., Schoonheydt R.A. Structure and Bonding, 1993, 80, 187.
Baekelandt B.G., Janssens G.O.A., Toufar H., Mortier W.J., Schoonheydt R.A., Mapping between Electron Population and Vibrational Normal Modes within the Charge Sensitivity Analysis, J. Phys. Chem., 1995,99,9784-9794.
Nalewajski R.F., Electrostatic Effects in Interactions between Hard (soft) Acids and Bases, J. Am. Chem. Soc., 1984, 106, 944.
Nalewajski R.F., A Study of Electronegativity Equalization, J. Phys. Chem., 1985, 89, 2831.
Nalewajski.R.F., Normal (decoupled) Representation of Electronegativity Equalization Equations in a Molecule, Int.J.Quant.Chem., 1991, 40, 265.
Korchowiec J., Nalewajski R.F., ibid , 1992, 44, 1027.
Darrin M. Y, Yang W, A chemical potential equalization method for molecular simulations, J.Chem.Phys., 1996, 104(1),159-172.
Toufar H., Baeklandt B.G., Janssens G.O.A., Mortier W.J., Schoonheydt R.A., Investigation of supramolecular systems by a combination of the electronegativity equalization method and a Monte Carlo simulation technique, J. Phys. Chem., 1995, 99, 13876.
Darrin M.Y., Yang W., A Chemical Potential Equalization Method for Molecular Simulations, J.Chem.Phys., 1996, 104(1), 159-172.
Jerzy Cioslowski, Boris B., Stefanov Electron Flow and Electronegativity Equation in the Process of Bond Formation, J. Chem. Phys., 1999, 99, 5151.
Jerzy Cioslowski, Martin Martinov, The atomic softness matrix, J. Chem. Phys., 1994, 101, 366.
Jerzy Cioslowski, Martin Martinov, Electronegativity Equalization in Polyyne Carbon Chains, J. Chem. Phys., 1996, 100, 6156.
Jerzy Cioslowski, Martin Martinov, Spin-resolved Analysis of Electronegativity Equalization and Electron Flow in Molecules, J.Chem.Phys.,1995, 102, 7499.
Tapan K., Ghanty and Swapan K., Ghosh, Electornegativity and Covalent Binding in Homonuclear Diatomic Molecules, J. Phys. Chem., 1991, 95, 6512.
Swapan K. Ghosh, Electronegativity, Hardness, and a Semiempirical Density Functional Theory of Chemical Binding, Int. J. Quantum Chem., 1994, 49, 239.
Bultinck P., Langenaeker W., Lahorte P., et al., The Electronegativity Equalization Method I: Parametrization and Validation for Atomic Charge calculations, J. Phys. Chem., 2002, 106, 7887-7894.
Bultinck P., Langenaeker W., Lahorte P, et al., The Electronegativity Equalization Method II: Applicability of Different Atomic Charge Schemes, J. Phys. Chem., 2002, 106, 7895-7901.
郭燕文, 甲苯硝基化合物的偶极矩及介电特性, 火炸药学报,1999, 22, 3.
余红霞, 朱传方, 分子的偶极矩对化合物香味的影响研究, 岳阳师范学院学报(自然科学版), 2001, 14, 2, 24-26.
R. Antoine. I. Compagono, D. Rayane, M Broyer, Ph. Dugourd, G. Breaux, F. C, Hagemeister, D. Pippen, R. R. Hudgins, M.F. Jarrold,Electric dipole moments and conformations of isolated peptides,Eur. Phys. J. D,2002,20,583-587.
HU Zeng-Jian, JIANG Hua-Liang, CHEN Jian-Zhong,CHEN Kai-Xian, JI Ru-Yun, Analysis of electronic structures of physostigmine analogs, 中国药理学报, 1998, 4.
C.H.Worner, On the Teaching of the electric dipole, The Physics Teacher,
2001, 39,462-463.
蔡显鄂, 项一非, 刘衍光, 物理化学实验, 高等教育出版社, 第二版, 211.
周公度, 段连运, 结构化学基础, 北京大学出版社, 第二版, 197.
A.H. Nethercot Jr., Molecular dipole moments and electronegaticity, chemical physica letters, 1978, 59, 346.
B.P. Dailey and C.H. Townes, Electron density distribution in 2-nitro-5-methylimidazole, J. Chem. Phys, 1955, 23, 118.
Andreya, Toropov, Ozodm, Nabiev, QSPR modeling of hydrocarbon dipole moments by means of correlation weighting of local graph invariants, Journal of Theoretical and computational chemistry, 2003, 2:139.
Yang Z.Z., Shen E Z., Direct Calculation of Group Electronegativity and the Atomic Charges in a Group, Science in China (Series B), 1996, 39, 20-28.
Yang Z.Z., Shen E.Z., Wang L.H., A Scheme for Calculation Atomic Charge-Distribution in Large Molecules Based on Density-Functional Theory and Electronegativity Equalization, J. Mol. Structure (Theochem), 1994, 118, 167-173.
沈尔忠,杨忠志, 密度泛函理论下的分子电负性—I. 由电负性均衡原理直接计算分子中的原子电荷, 中国科学(B辑),1995,25(2),126-131.
杨忠志,沈尔忠, 密度泛函理论下的分子电负性——II.基团电负性及基团中原子电荷分布的直接计算, 中国科学(B辑),1995,25(12),1233-1239.
沈尔忠,杨忠志, 密度泛函理论下的分子电负性—III.分子总能量的直接计算, 化学学报,1996,54,152-159.
Yang Z.Z., Shen E.Z., Niu S.Y., Molecular Electronegativity in Density Functional Theory.5. Relationship between the Global and Harmonic Mean Electronegativities for a Molecule, Chemical Research in Chinese University, 1996, 12(2), 159-163.
Handbook of chemistry and physics, CRC press, 1983-1984, 64th Edition.
Dea-Sik Hong,Soo Gyeong Cho, Ab Initio Study of Chlorosilanes: Dipole Moment and Charge Distributions,J.Chem.Inf.Comput.Sci,1999,39,537-542
F.deproft,C.van alsenor,A.peters,W.langenaeker,P.geerlings,Atomic charges, Dipole Moments, and Fukui Functions Using the Hirshfeld Partitioning of the Electron Density, Journal of Computational chemistry,23, 12, 1198-1209
Alexandr V.,Yatsenko,Ksenia A,Paseshnichenko,On the performance of semiempirical MO theory for dipole moments of dye molecules,J. Mol Model, 2001, 7, 384-391.
Jiabo li,Christopher J. Cramer,Donald G. Truhlar,MIDI! Basis set for silicon,bromine,and iodine,Theoretical chemistry Accounts,1998,99, 192-196.
刘次全,量子生物学及其应用,高等教育出版社,1990,第一版,99.
曾昭琼,有机化学,高等教育出版社,1993,第三版,12.
p.w. 阿特金斯,量子物质结构概念手册,科学出版社,91.
Williams, D. E.; Yan, J. M. Adv. At. Mol. Phys. 1987, 23, 87.
Colonna, F.; Evleth, E ; Angyan, J. G. Critical analysis of electric field modeling: Formamide, J. Comput. Chem. 1992, 13, 1234.
Chipot, C.; Maigret, B.; Rivail, J.-L.; Scheraga, H. A. Modeling amino acid side chains.1.Determination of net atomic charges from ab initio self-consistent field molecular electrostatic properties, J. Phys. Chem. 1992, 96, 10276
Chipot, C.; Angyan, J. G.; Ferenczy, G. G.; Scheraga, H. A. Transferable net atomic charges from distributed multipole analysis for the description of electrostatic properties. A case study of saturated hydrocarbons, J. Phys.
Chem. 1993, 97, 6628.
Christophe Chipot, Janos G. Angyan, and Bernard Maigret, Harold A. Scheraga, Modelling Amino Acid Side Chains. 2. Determination of Point Charges from Electrostatic Properties: Toward Transferable Point Charge Models,J. Phys. Chem,1993, 97, 9788-9796.
Yang Z Z, Wang C S, Atom-bond electronegativity method, I. Calculation of the charge distribution in large molecules. J Phys Chem A, 1997, 101:6315.
Wang C S, Li S M, Yang Z Z, Calculation of molecular energies by atom-bond electronegativity equalization method, J Mol Struct. (Theochem), 1998, 430, 191.
Yang Z Z, Wang C S, Tang A Q, Molecular electronegativity in the density functional theory-atom-bond electonegativity equalization model, Science in China (Series B), 1998, 41, 331.
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