分子能量和热力学函数的精确计算
|
摘要
量子化学作为研究分子微观结构、性质和分子间相互作用的最基础学科,其基础理论和计算方法在过去的20年中取得了显著进展,在解释和预测中小尺寸分子的基态电子结构,生成热,反应活化能,核磁共振谱以及功能材料的设计和优化,生物体系的结构模拟,药物分子设计、药物筛选等方面取得了令人瞩目的成功。量子化学计算的一大优势在于它可以先于实验来预测物质的性质或实验上至今无法测得的一些物理量及无法观测到的反应过程。
尽管量子化学计算在解释和预测中小分子的实验结果上显示了巨大优势,但由于从头算方法固有的各种近似导致其在计算结果上必然存在一定的误差,尤其是对复杂的大分子,计算误差甚大。理论计算误差大部分由电子相关效应和基组引起的。由于计算资源有限,电子相关效应的处理是目前量子化学计算的最大瓶颈。近年来发展的多种精确处理电子相关效应的理论和方法,如组态相互作用理论(CI)、耦合簇理论(CC)和多体微扰理论(MP)以及Gaussian-1、Gaussian-2、Gaussian-3方法、Complete Basis Set(CBS)等方法,对小分子的计算达到了非常高的精度,但是对中等或大分子体系的计算却很难实现,原因在于对计算时间及计算资源要求的急剧增加。密度泛函理论(DFT)代表了处理电子相关效应的另一种途径,目前最好的DFT方法在精度上已能和MP2方法相媲美,其计算量与HF方法相近。但是随着计算体系的增大,误差也随着增大。因此在计算精度和计算花费之间找到一个比较平衡的计算方法成为当务之急。
本文中,我们采用线性回归校正和神经网络校正与从头算相结合的方法对低水平理论计算分子能量和生成热产生的系统误差进行校正,考察了两种校正方法的校正效果,并对理论计算方法、基组及物理参数等方面做了系统研究。在简单的物理参数下,这种组合型计算方法能够大幅度减小理论计算因忽略电子相关效应和使用小基组所带来的系统误差,为准确、快捷的预测分子性质提供了一种新的研究手段。
鉴于相关能由电子之间的相互作用引起,本文选择不同价键环境下的电子对为参数,包括成键电子、孤对电子、内层电子、组成分子的基态原子未成对电子,采用线性回归方法对HF/6-31G(d),HF/6-311+G(d,p),B3LYP/6-31G(d),B3LYP/6-311+G(d,p)计算的180个闭壳层有机分子的生成热进行校正。经过线性回归校正,生成热的均方根偏差得到显著降低。HF/6-31G(d)和HF/6-311+G(d,p)计算的生成热均方根偏差分别由
Quantum chemistry, as a fundamental subject studying properties and interactions of molecules as well as their micro-mechanism, has been developed remarkably on its primary theories and methods in the past decades. It shows a great success in interpreting and predicting the properties of middle, small-sized molecules, such as electronic structure, heats of formation, active energy of reaction, NMR spectrum, and even functional materials optimization and design, bio-system modeling, drug design, drug screening, and so on. One of the Holy Grails of quantum mechanical calculation is to predict properties of matter prior to experiments, to examine the physical properties or processes that are inaccessible by experiments.Despite their success, the results of first-principles quantum mechanical calculation contain inherent numerical errors caused by various intrinsic approximations, in particular for complex systems. The origin of the calculation errors mainly comes from the electron correlation and basis set. Because of computational cost, electron correlation has always been a major stumbling block for first-principles calculations. Many methods and theories for relatively accurate evaluation of electron correlation have been proposed in recent years, such as configuration interaction (CI), coupled-cluster theory (CC), Moller-Plesset perturbation theory (MP), Gaussion-1, Gaussian-2, Gaussian-3, and complete basis set methods. These procedures are most computational resource consuming and are still inapplicable to complex systems. Density-functional theory (DFT) offers promising alternatives for tackling the electron correlation. Now, the best DFT methods have the similar precision with the MP2 methods, while the computational cost is just comparable to HF method. However, the errors of DFT calculations are accumulated with the sized of the molecule. Thus, a balance has to be found between accuracy and efficiency.In this thesis, approaches combined first-principles calculation and linear regression or neural network are proposed to correct the systematic errors of the calculated energy and heats of formation of molecules at low theory level. At the same time, we have compared the corrected results from the linear regression correction approach and the neural network correction approach, and systematically investigated the computational methods, basis set
and the physical descriptors. With general descriptors, these combined methods can greatly eliminate the systemic errors of theoretical calculation due to ignoring the electron correlation and using small basis set, and will be a novel tool for predicting the properties of the molecules.Because of the interaction of the electrons is the main origin of the electron correlation energy, we select the numbers of bonding electrons, lone-pair electrons and inner layer electrons in molecules, and the number of unpaired electrons in the composing atoms in their ground states as physical descriptors, employing the linear regression correction method (LRC) to correct the systematic errors of the calculated heats of formation of 180 middle, small-sized organic molecules. The theoretical calculation errors from the experiments are eliminated greatly, especially for HF method, the root mean square (RMS) deviations are decreased by more than 60 times. For the HF/6-31G(d) and HF/6-311 +G(d,p) methods, the RMS deviations of heats of formation of 180 molecules are reduced from 392.0 and 395.0 kcal/mol to 6.2 and 6.1 kcal/mol, respectively, and for the B3LYP/6-31G(d) and B3LYP/6-311+G(d,p) methods, the RMS deviations of heats of formation are decreased from 10.8 and 20.9 kcal/mol to 3.4 and 3.0 kcal/mol, respectively. Most importantly, the deviations of large molecules are of the same magnitude as those of small molecules after linear regression correction for both HF and DFT methods, which proves that our linear regression correction method does not discriminate against the large molecules and can potentially be applied to much larger systems. The coefficients of partial correlation Vj are calculated to assess the validation of physical descriptors. It is found that the bonding electrons, inner layer electrons and unpaired electrons in the composing atoms are very important for correcting the systematic errors of heats of formation. At the same time, we test the relative contribution of an individual physical descriptor by leaving out one descriptor and examining the increase of the RMS deviations. The results are consistent with the analysis of the coefficients of partial correlation. Our linear regression correction approach has accounted for the most errors caused by ignoring electron correlation energy and using small basis set, and the physical descriptors are not limited to the specific properties of the molecules, and thus this combined method is feasible for accurate prediction of the properties of the molecules.
Since the physical descriptors taken from the electron pairs with different chemical environment might result in non-continuous potential energy surface and the training set are only closed-shell organic molecules, we improve on the linear regression correction method from the following two terms, (1) The electron populations of different types of natural bond orbital (NBO) are used as the physical descriptors including 2-center bonds (BD), 1-center core pair (CR), 1-center valence lone pair (LP), 1-center Rydberg (RY*), 2-center anti-bond (BD*), and valence non-Lewis lone pair (LP*), and the number of the unpaired electrons of the composing atom in its ground state is also included as a descriptor. (2) The training set is enlarged to contain 350 heats of formation of small and medium-sized organic, inorganic molecules and radicals. The heats of formation calculated by the HF/6-31 G(d), HF/6-31 \G(2d,d,p), B3LYP/6-3\G(d), B3LYP/6-31 \+G(d,p), B3LYP/6-31 \G(2d,d,p) and B3LYP/6-31 \+G(3df,2p) methods are corrected by the linear regression correction method. The RMS deviations of 350 heats of formation are reduced from 327.1, 330.6, 11.2, 19.6, 15.3, 6.7 kcal/mol to 10.2, 9.6, 4.5, 5.6, 4.0, 3.2 kcal/mol upon the linear regression correction. We also calculate the partial correlation coefficients for assessing the relative importance of the physical descriptors. It is found that the bonding electrons, inner layer electrons and unpaired electrons, but also the low-occupied electrons, have significant effect on the correction of the systematic errors. We have compared the correction results by using different descriptors: NBO descriptors and electron pair descriptor, and found that the correction results with NBO descriptors are better. Reaction barrier heights can also be corrected by using the current LRC approach. Employed the correction coefficients obtained from the B3LYP/6-31 \G(2d,d,p)- linear regression correction method, the 12 barrier heights of 6 reactions are corrected. The mean absolute deviation of the 12 barrier heights is reduced from 5.3 kcal/mol to 2.9 kcal/mol after the linear regression correction, and almost to the same accuracy as that for the heats of formation.On the other hand, The neural network (NN) method employing the NBO descriptors is used to correct the heats of formation calculated by the HF/6-3 lG(d), HF/6-311 G(2d,d,p), B3LYP/6-31G(
尽管量子化学计算在解释和预测中小分子的实验结果上显示了巨大优势,但由于从头算方法固有的各种近似导致其在计算结果上必然存在一定的误差,尤其是对复杂的大分子,计算误差甚大。理论计算误差大部分由电子相关效应和基组引起的。由于计算资源有限,电子相关效应的处理是目前量子化学计算的最大瓶颈。近年来发展的多种精确处理电子相关效应的理论和方法,如组态相互作用理论(CI)、耦合簇理论(CC)和多体微扰理论(MP)以及Gaussian-1、Gaussian-2、Gaussian-3方法、Complete Basis Set(CBS)等方法,对小分子的计算达到了非常高的精度,但是对中等或大分子体系的计算却很难实现,原因在于对计算时间及计算资源要求的急剧增加。密度泛函理论(DFT)代表了处理电子相关效应的另一种途径,目前最好的DFT方法在精度上已能和MP2方法相媲美,其计算量与HF方法相近。但是随着计算体系的增大,误差也随着增大。因此在计算精度和计算花费之间找到一个比较平衡的计算方法成为当务之急。
本文中,我们采用线性回归校正和神经网络校正与从头算相结合的方法对低水平理论计算分子能量和生成热产生的系统误差进行校正,考察了两种校正方法的校正效果,并对理论计算方法、基组及物理参数等方面做了系统研究。在简单的物理参数下,这种组合型计算方法能够大幅度减小理论计算因忽略电子相关效应和使用小基组所带来的系统误差,为准确、快捷的预测分子性质提供了一种新的研究手段。
鉴于相关能由电子之间的相互作用引起,本文选择不同价键环境下的电子对为参数,包括成键电子、孤对电子、内层电子、组成分子的基态原子未成对电子,采用线性回归方法对HF/6-31G(d),HF/6-311+G(d,p),B3LYP/6-31G(d),B3LYP/6-311+G(d,p)计算的180个闭壳层有机分子的生成热进行校正。经过线性回归校正,生成热的均方根偏差得到显著降低。HF/6-31G(d)和HF/6-311+G(d,p)计算的生成热均方根偏差分别由
Quantum chemistry, as a fundamental subject studying properties and interactions of molecules as well as their micro-mechanism, has been developed remarkably on its primary theories and methods in the past decades. It shows a great success in interpreting and predicting the properties of middle, small-sized molecules, such as electronic structure, heats of formation, active energy of reaction, NMR spectrum, and even functional materials optimization and design, bio-system modeling, drug design, drug screening, and so on. One of the Holy Grails of quantum mechanical calculation is to predict properties of matter prior to experiments, to examine the physical properties or processes that are inaccessible by experiments.Despite their success, the results of first-principles quantum mechanical calculation contain inherent numerical errors caused by various intrinsic approximations, in particular for complex systems. The origin of the calculation errors mainly comes from the electron correlation and basis set. Because of computational cost, electron correlation has always been a major stumbling block for first-principles calculations. Many methods and theories for relatively accurate evaluation of electron correlation have been proposed in recent years, such as configuration interaction (CI), coupled-cluster theory (CC), Moller-Plesset perturbation theory (MP), Gaussion-1, Gaussian-2, Gaussian-3, and complete basis set methods. These procedures are most computational resource consuming and are still inapplicable to complex systems. Density-functional theory (DFT) offers promising alternatives for tackling the electron correlation. Now, the best DFT methods have the similar precision with the MP2 methods, while the computational cost is just comparable to HF method. However, the errors of DFT calculations are accumulated with the sized of the molecule. Thus, a balance has to be found between accuracy and efficiency.In this thesis, approaches combined first-principles calculation and linear regression or neural network are proposed to correct the systematic errors of the calculated energy and heats of formation of molecules at low theory level. At the same time, we have compared the corrected results from the linear regression correction approach and the neural network correction approach, and systematically investigated the computational methods, basis set
and the physical descriptors. With general descriptors, these combined methods can greatly eliminate the systemic errors of theoretical calculation due to ignoring the electron correlation and using small basis set, and will be a novel tool for predicting the properties of the molecules.Because of the interaction of the electrons is the main origin of the electron correlation energy, we select the numbers of bonding electrons, lone-pair electrons and inner layer electrons in molecules, and the number of unpaired electrons in the composing atoms in their ground states as physical descriptors, employing the linear regression correction method (LRC) to correct the systematic errors of the calculated heats of formation of 180 middle, small-sized organic molecules. The theoretical calculation errors from the experiments are eliminated greatly, especially for HF method, the root mean square (RMS) deviations are decreased by more than 60 times. For the HF/6-31G(d) and HF/6-311 +G(d,p) methods, the RMS deviations of heats of formation of 180 molecules are reduced from 392.0 and 395.0 kcal/mol to 6.2 and 6.1 kcal/mol, respectively, and for the B3LYP/6-31G(d) and B3LYP/6-311+G(d,p) methods, the RMS deviations of heats of formation are decreased from 10.8 and 20.9 kcal/mol to 3.4 and 3.0 kcal/mol, respectively. Most importantly, the deviations of large molecules are of the same magnitude as those of small molecules after linear regression correction for both HF and DFT methods, which proves that our linear regression correction method does not discriminate against the large molecules and can potentially be applied to much larger systems. The coefficients of partial correlation Vj are calculated to assess the validation of physical descriptors. It is found that the bonding electrons, inner layer electrons and unpaired electrons in the composing atoms are very important for correcting the systematic errors of heats of formation. At the same time, we test the relative contribution of an individual physical descriptor by leaving out one descriptor and examining the increase of the RMS deviations. The results are consistent with the analysis of the coefficients of partial correlation. Our linear regression correction approach has accounted for the most errors caused by ignoring electron correlation energy and using small basis set, and the physical descriptors are not limited to the specific properties of the molecules, and thus this combined method is feasible for accurate prediction of the properties of the molecules.
Since the physical descriptors taken from the electron pairs with different chemical environment might result in non-continuous potential energy surface and the training set are only closed-shell organic molecules, we improve on the linear regression correction method from the following two terms, (1) The electron populations of different types of natural bond orbital (NBO) are used as the physical descriptors including 2-center bonds (BD), 1-center core pair (CR), 1-center valence lone pair (LP), 1-center Rydberg (RY*), 2-center anti-bond (BD*), and valence non-Lewis lone pair (LP*), and the number of the unpaired electrons of the composing atom in its ground state is also included as a descriptor. (2) The training set is enlarged to contain 350 heats of formation of small and medium-sized organic, inorganic molecules and radicals. The heats of formation calculated by the HF/6-31 G(d), HF/6-31 \G(2d,d,p), B3LYP/6-3\G(d), B3LYP/6-31 \+G(d,p), B3LYP/6-31 \G(2d,d,p) and B3LYP/6-31 \+G(3df,2p) methods are corrected by the linear regression correction method. The RMS deviations of 350 heats of formation are reduced from 327.1, 330.6, 11.2, 19.6, 15.3, 6.7 kcal/mol to 10.2, 9.6, 4.5, 5.6, 4.0, 3.2 kcal/mol upon the linear regression correction. We also calculate the partial correlation coefficients for assessing the relative importance of the physical descriptors. It is found that the bonding electrons, inner layer electrons and unpaired electrons, but also the low-occupied electrons, have significant effect on the correction of the systematic errors. We have compared the correction results by using different descriptors: NBO descriptors and electron pair descriptor, and found that the correction results with NBO descriptors are better. Reaction barrier heights can also be corrected by using the current LRC approach. Employed the correction coefficients obtained from the B3LYP/6-31 \G(2d,d,p)- linear regression correction method, the 12 barrier heights of 6 reactions are corrected. The mean absolute deviation of the 12 barrier heights is reduced from 5.3 kcal/mol to 2.9 kcal/mol after the linear regression correction, and almost to the same accuracy as that for the heats of formation.On the other hand, The neural network (NN) method employing the NBO descriptors is used to correct the heats of formation calculated by the HF/6-3 lG(d), HF/6-311 G(2d,d,p), B3LYP/6-31G(
引文
1 A. C. Hurley, Electron correlation in Small Molecules, New York: Academic Press, 1976.
2 H. F. Schaefer, Modern Theoretical Chemistry: Methods of Electronic Structure Theory, New York: Plenum, 1977.
3 I. Shavitt, In Modern Theoretical Chemistry, Ed. by H. F. Schaefer, New York, Plenum Press: 1977, 3:189
4 A. O. Mitrushenkov, Chem. Phys. Lett. 1994, 217(5-6): 559-565.
5 Z. He, E. Kraka, D. Cremer, Int. J. Quantum Chem. 1996, 57(2): 157-172.
6 H. F. Schaefer, J. R. Thomas, Y. Yamaguchi, B. J. Deleeuw, G. Vacek, In Modern Electronic Structure Theory, Ed. by D. R. Yarkony, Singapore, World Scientific, 1995, 345.
7 J. A. Pople, M. Head-Gordon, K. Raghavachari, J. Chem. Phys. 1987, 87(10): 5968-5975.
8 J. Cizek, J. Chem. Phys. 1966, 45(11): 4256-4266.
9 J. Crizek, Adv. Chem. Phys., 1969, 14: 35.
10 G. D. Purvis, R. J. Bartlett, J. Chem. Phys. 1982, 76(4): 1910-1918.
11 K. Raghavachari, G. W. Trucjs, J. A. Pople, M. Head-Gordon, Chem. Phys. Lett., 1989, 157: 479-483.
12 C. Mφller, M. S. Plesset, Phys. Rev., 1934, 46: 618.
13 R. Krishnan, J. A. Pople, Int. J. Quantum Chem. 1978, 14: 91.
14 R. Krishnan, M. J. Frisch, J. A. Pople, J. Chem. Phys. 1980, 72(7): 4244-4245.
15 R. J. Bartlett, I. Shavitt, Chem. Phys. Lett. 1977, 50: 190.
16 R. J. Bartlett, G. D. Purvis, J. Chem. Phys. 1978(5), 68:2114-2124.
17 R. J. Barlett, H. Sekino, G. D. Purvis, Chem. Phys. Lett. 1983, 98: 66.
18 K. Raghavachari, J. A. Pople, E. S. Replogle, M. Head-Gordon, J. Phys. Chem. 1990, 94(14): 5579-5586.
19 J. A. Pople, M. Head-Gorden, D. J. Fox, K. Raghavachari, L. A. Curtiss, J. Chem. Phys. 1989, 90(10): 5622-5629.
20 L. A. Curtiss, K. Raghavachari, G. W. Trucks, and J. A. Pople, J. Chem. Phys. 1991, 94(11): 7221-7230.
21 L. A. Curtiss, J. E. Carpenter, K. Raghavachari, and J. A. Pople, J. Chem. Phys. 1992, 96(12): 9030-9034.
22 L. A. Curtiss, K. Raghavachari, and J. A. pople, J. Chem. Phys. 1995, 103(10): 4192-4200.
23 L. A. Curtiss, K. Raghavachari, P. C. Redfern, V. Rassolov, J. A. Pople, J. Chem. Phys. 1998, 109(18): 7764-7776.
24 A. G. Baboul, L. A. Curtiss, P. C. Redfern, K. Raghavachari, J. Chem. Phys. 1999, 110(16): 7650-7657.
25 L. A. Curtiss, K. Raghavachari, P. C. Redfern, J. A. Pople, J. Chem. Phys. 2000, 112(17): 7374-7383.
26 G. A. Petersson, T. G. Tensfeldt, J. A. Montgomery, Jr. J. Chem. Phys. 1991, 94(9): 6091-6101
27 J. A. Montgomery Jr., J. W. Ochterski, G. A. Petersson, J. Chem. Phys. 1994, 101(7): 5900-5909.
28 Ochterski, J. W.; Petersson, G. A.; J. A. Montgomery Jr., J. Chem. Phys. 1996, 104(7): 2598-2619.
29 T. H. Dunning, Jr. J. Chem. Phys. 1989, 90(2): 1007-1023.
30 R. O. Jones, O. Gunnarsson, Rev. Mod. Phys. 1989, 61(3): 689-746.
31 L. H. Thomas, Proc. Camb. Phil. Soc. 1927, 23: 542.
32 E. Fermi, Rend. Accad. Lincei 1927, 6: 602.
33 P. C. Redfern, P. Zapol, L. A. Curtiss, and K. Raghavachari, J. Phys. Chem. A 2000, 104(24): 5850-5854.
34 C. Hollister, O. Sinanoglu, J. Am. Chem. Soc. 1966, 88(1): 13-21.
35 D. Cremer, J. Comput. Chem. 1982, 3(2): 165-177.
36 L. C. Synder, H. Basch, J. Am. Chem. Soc. 1969, 91(9): 2189-2198.
37 S. Kristyan, Chem. Phys. 1997, 224: 33-51.
38 S. Kristydn, A. Ruzsinszky, G. I. Csonka, J. Phys. Chem. A, 2001, 105(10): 1926-1933.
39 S. Kristydn, A. Ruzsinszky, G. I. Csonka, Theor. Chem. Acc. 2001, 106: 319-328.
40 S. Kristydn, A. Ruzsinszky, G. I. Csonka, Theor. Chem. Acc. 2001, 106: 404-411.
41 S. Kristydn, G. I. Csonka, Chem. Phys. Lett. 1999, 307(5-6): 469-478.
42 S. Kristydn, Chem. Phys. Lett. 1995, 247(1-2): 101-111.
43 S. Kristydn, G. I. Csonka, J. Comput. Chem. 2001, 22(2): 241-254
44 G. Rauhut, J. W. Boughton, P. Pulay, J. Chem. Phys. 1995,103(13): 5662-5673.
45 S. W. Benson, F. R. Cruickshank, D. M. Golden, G. R. Haugen, H. E. O'Neal, A. S. Rodgers, R. Shaw, R. Walsh, Chem. Rev. 1969, 69(3): 279-324.
46 M. J. S. Dewar, E. G. Zoebisch, E. F. Healy, J. J. P. Stewar, J. Am. Chem. Soc. 1985, 107(13): 3902-3909
47 J. J. P. Stewart, J. Comput. Chem. 1989, 10(2): 221-264.
48 N. L. Allinger, J. Am. Chem. Soc. 1977, 99(25): 8127-8134.
49 N. L. Allinger, y. H. Yuh, J. H. Lii, J. Am. Chem. Soc. 1989, 111(23): 8551-8566.
50 J. H. Lii, N. L. Allinger, J. Am. Chem. Soc. 1989, 111(23): 8566-8575.
51 N. L. Allinger, k. Chen, J. H. Lii, J. Comput. Chem. 1996, 17(5-6): 642-668.
52 L. A. Curtiss, K. Raghavachari, P. C. Redfern, J. A. Pople, J. Chem. Phys. 1997,106(3): 1063-1079.
53 A. Nicolaides, A. Rauk, M. N. Glukhovtsev, L. Radom, J. Phys. Chem. 1996,100(44): 17460-17464.
54 N. L. Allinger, L. R. Schmitz, I. Motoc, C. Bender, and J. K. Labanowski, J. Am. Chem. Soc. 1992, 114(8): 2880-2883.
35 L. R. Schmitz, I. Motoc, C. Bender, J. K. Labanowski, and N. L. Allinger, J. Phys. Org. Chem. 1992, 5(5): 225-229.
56 N. L. Allinger, L. R. Schmitz, I. Motoc, C. Bender, and J. K. Labanowski, J. Comput. Chem. 1992, 13(7): 838-841.
57 N. L. Allinger, K. Sakakibara, and J. K. Labanowski, J. Phys. Chem. 1995, 99(23): 9603-9610.
58 J. Labanowski, L. Schmitz, K. H. Chen, N. L. Allinger, J. Comput. Chem. 1998,19(12): 1421-1430.
59 L. R. Schmitz, K. H. Chen, J. Labanowski, N. L. Allinger, J. Phys. Org. Chem. 2001, 14: 90-96.
60 L. A. Curtiss, D. L. Kock, J. A. Pople, J. Chem. Phys. 1991, 95(6): 4040-4043.
61 J. A. Pople, L. A. Curtiss, J. Chem. Phys. 1991, 95(6): 4385-4388.
62 R. H. Nobes, L. Radom, Chem. Phys. Lett. 1992, 189(6): 554-559.
63 M. W. Wong, L. Radom, J. Am. Chem. Soc. 1993, 115(4): 1507-1514.
64 A. Nicolaides, L. Radom, J. Phys. Chem. 1994, 98(12): 3092-3093.
65 M. N. Glukhovtsev, A. Pross, L. Radom, J. Phys. Chem. 1996,100(9): 3498-3503
66 D. A. Armstrong, A. Rauk, D. Yu, J. Am. Chem. Soc. 1993, 115(2): 666-673.
67 D. Yu, A. Rauk, D. A. Armstrong, Can. J. Chem. 1994, 72(3): 471-483.
68 D. Yu, A. Rauk, D. A. Armstrong, J. Chem. Soc, Perkin Trans. 1994, 2(10): 2207-2215.
69 A. Nicolardes, A. Rauk, M. N. Glukhovtsev, L. Radom, J. Phys. Chem. 1996, 100(44): 17460-17464.
70 J. Zupan and J. Gasteiger, Neural Network for Chemists, VHC, Weinheim, 1993.
71 B.G. Sumpter, C. Getino, and D.W. Noid, Annu. Rev. Phys. Chem. 1994, 45: 439-481.
72 J.A. Darsey, D.W. Noid, and B.R. Upadhyaya, Chem. Phys. Lett. 1991,177(2): 189-194.
2 H. F. Schaefer, Modern Theoretical Chemistry: Methods of Electronic Structure Theory, New York: Plenum, 1977.
3 I. Shavitt, In Modern Theoretical Chemistry, Ed. by H. F. Schaefer, New York, Plenum Press: 1977, 3:189
4 A. O. Mitrushenkov, Chem. Phys. Lett. 1994, 217(5-6): 559-565.
5 Z. He, E. Kraka, D. Cremer, Int. J. Quantum Chem. 1996, 57(2): 157-172.
6 H. F. Schaefer, J. R. Thomas, Y. Yamaguchi, B. J. Deleeuw, G. Vacek, In Modern Electronic Structure Theory, Ed. by D. R. Yarkony, Singapore, World Scientific, 1995, 345.
7 J. A. Pople, M. Head-Gordon, K. Raghavachari, J. Chem. Phys. 1987, 87(10): 5968-5975.
8 J. Cizek, J. Chem. Phys. 1966, 45(11): 4256-4266.
9 J. Crizek, Adv. Chem. Phys., 1969, 14: 35.
10 G. D. Purvis, R. J. Bartlett, J. Chem. Phys. 1982, 76(4): 1910-1918.
11 K. Raghavachari, G. W. Trucjs, J. A. Pople, M. Head-Gordon, Chem. Phys. Lett., 1989, 157: 479-483.
12 C. Mφller, M. S. Plesset, Phys. Rev., 1934, 46: 618.
13 R. Krishnan, J. A. Pople, Int. J. Quantum Chem. 1978, 14: 91.
14 R. Krishnan, M. J. Frisch, J. A. Pople, J. Chem. Phys. 1980, 72(7): 4244-4245.
15 R. J. Bartlett, I. Shavitt, Chem. Phys. Lett. 1977, 50: 190.
16 R. J. Bartlett, G. D. Purvis, J. Chem. Phys. 1978(5), 68:2114-2124.
17 R. J. Barlett, H. Sekino, G. D. Purvis, Chem. Phys. Lett. 1983, 98: 66.
18 K. Raghavachari, J. A. Pople, E. S. Replogle, M. Head-Gordon, J. Phys. Chem. 1990, 94(14): 5579-5586.
19 J. A. Pople, M. Head-Gorden, D. J. Fox, K. Raghavachari, L. A. Curtiss, J. Chem. Phys. 1989, 90(10): 5622-5629.
20 L. A. Curtiss, K. Raghavachari, G. W. Trucks, and J. A. Pople, J. Chem. Phys. 1991, 94(11): 7221-7230.
21 L. A. Curtiss, J. E. Carpenter, K. Raghavachari, and J. A. Pople, J. Chem. Phys. 1992, 96(12): 9030-9034.
22 L. A. Curtiss, K. Raghavachari, and J. A. pople, J. Chem. Phys. 1995, 103(10): 4192-4200.
23 L. A. Curtiss, K. Raghavachari, P. C. Redfern, V. Rassolov, J. A. Pople, J. Chem. Phys. 1998, 109(18): 7764-7776.
24 A. G. Baboul, L. A. Curtiss, P. C. Redfern, K. Raghavachari, J. Chem. Phys. 1999, 110(16): 7650-7657.
25 L. A. Curtiss, K. Raghavachari, P. C. Redfern, J. A. Pople, J. Chem. Phys. 2000, 112(17): 7374-7383.
26 G. A. Petersson, T. G. Tensfeldt, J. A. Montgomery, Jr. J. Chem. Phys. 1991, 94(9): 6091-6101
27 J. A. Montgomery Jr., J. W. Ochterski, G. A. Petersson, J. Chem. Phys. 1994, 101(7): 5900-5909.
28 Ochterski, J. W.; Petersson, G. A.; J. A. Montgomery Jr., J. Chem. Phys. 1996, 104(7): 2598-2619.
29 T. H. Dunning, Jr. J. Chem. Phys. 1989, 90(2): 1007-1023.
30 R. O. Jones, O. Gunnarsson, Rev. Mod. Phys. 1989, 61(3): 689-746.
31 L. H. Thomas, Proc. Camb. Phil. Soc. 1927, 23: 542.
32 E. Fermi, Rend. Accad. Lincei 1927, 6: 602.
33 P. C. Redfern, P. Zapol, L. A. Curtiss, and K. Raghavachari, J. Phys. Chem. A 2000, 104(24): 5850-5854.
34 C. Hollister, O. Sinanoglu, J. Am. Chem. Soc. 1966, 88(1): 13-21.
35 D. Cremer, J. Comput. Chem. 1982, 3(2): 165-177.
36 L. C. Synder, H. Basch, J. Am. Chem. Soc. 1969, 91(9): 2189-2198.
37 S. Kristyan, Chem. Phys. 1997, 224: 33-51.
38 S. Kristydn, A. Ruzsinszky, G. I. Csonka, J. Phys. Chem. A, 2001, 105(10): 1926-1933.
39 S. Kristydn, A. Ruzsinszky, G. I. Csonka, Theor. Chem. Acc. 2001, 106: 319-328.
40 S. Kristydn, A. Ruzsinszky, G. I. Csonka, Theor. Chem. Acc. 2001, 106: 404-411.
41 S. Kristydn, G. I. Csonka, Chem. Phys. Lett. 1999, 307(5-6): 469-478.
42 S. Kristydn, Chem. Phys. Lett. 1995, 247(1-2): 101-111.
43 S. Kristydn, G. I. Csonka, J. Comput. Chem. 2001, 22(2): 241-254
44 G. Rauhut, J. W. Boughton, P. Pulay, J. Chem. Phys. 1995,103(13): 5662-5673.
45 S. W. Benson, F. R. Cruickshank, D. M. Golden, G. R. Haugen, H. E. O'Neal, A. S. Rodgers, R. Shaw, R. Walsh, Chem. Rev. 1969, 69(3): 279-324.
46 M. J. S. Dewar, E. G. Zoebisch, E. F. Healy, J. J. P. Stewar, J. Am. Chem. Soc. 1985, 107(13): 3902-3909
47 J. J. P. Stewart, J. Comput. Chem. 1989, 10(2): 221-264.
48 N. L. Allinger, J. Am. Chem. Soc. 1977, 99(25): 8127-8134.
49 N. L. Allinger, y. H. Yuh, J. H. Lii, J. Am. Chem. Soc. 1989, 111(23): 8551-8566.
50 J. H. Lii, N. L. Allinger, J. Am. Chem. Soc. 1989, 111(23): 8566-8575.
51 N. L. Allinger, k. Chen, J. H. Lii, J. Comput. Chem. 1996, 17(5-6): 642-668.
52 L. A. Curtiss, K. Raghavachari, P. C. Redfern, J. A. Pople, J. Chem. Phys. 1997,106(3): 1063-1079.
53 A. Nicolaides, A. Rauk, M. N. Glukhovtsev, L. Radom, J. Phys. Chem. 1996,100(44): 17460-17464.
54 N. L. Allinger, L. R. Schmitz, I. Motoc, C. Bender, and J. K. Labanowski, J. Am. Chem. Soc. 1992, 114(8): 2880-2883.
35 L. R. Schmitz, I. Motoc, C. Bender, J. K. Labanowski, and N. L. Allinger, J. Phys. Org. Chem. 1992, 5(5): 225-229.
56 N. L. Allinger, L. R. Schmitz, I. Motoc, C. Bender, and J. K. Labanowski, J. Comput. Chem. 1992, 13(7): 838-841.
57 N. L. Allinger, K. Sakakibara, and J. K. Labanowski, J. Phys. Chem. 1995, 99(23): 9603-9610.
58 J. Labanowski, L. Schmitz, K. H. Chen, N. L. Allinger, J. Comput. Chem. 1998,19(12): 1421-1430.
59 L. R. Schmitz, K. H. Chen, J. Labanowski, N. L. Allinger, J. Phys. Org. Chem. 2001, 14: 90-96.
60 L. A. Curtiss, D. L. Kock, J. A. Pople, J. Chem. Phys. 1991, 95(6): 4040-4043.
61 J. A. Pople, L. A. Curtiss, J. Chem. Phys. 1991, 95(6): 4385-4388.
62 R. H. Nobes, L. Radom, Chem. Phys. Lett. 1992, 189(6): 554-559.
63 M. W. Wong, L. Radom, J. Am. Chem. Soc. 1993, 115(4): 1507-1514.
64 A. Nicolaides, L. Radom, J. Phys. Chem. 1994, 98(12): 3092-3093.
65 M. N. Glukhovtsev, A. Pross, L. Radom, J. Phys. Chem. 1996,100(9): 3498-3503
66 D. A. Armstrong, A. Rauk, D. Yu, J. Am. Chem. Soc. 1993, 115(2): 666-673.
67 D. Yu, A. Rauk, D. A. Armstrong, Can. J. Chem. 1994, 72(3): 471-483.
68 D. Yu, A. Rauk, D. A. Armstrong, J. Chem. Soc, Perkin Trans. 1994, 2(10): 2207-2215.
69 A. Nicolardes, A. Rauk, M. N. Glukhovtsev, L. Radom, J. Phys. Chem. 1996, 100(44): 17460-17464.
70 J. Zupan and J. Gasteiger, Neural Network for Chemists, VHC, Weinheim, 1993.
71 B.G. Sumpter, C. Getino, and D.W. Noid, Annu. Rev. Phys. Chem. 1994, 45: 439-481.
72 J.A. Darsey, D.W. Noid, and B.R. Upadhyaya, Chem. Phys. Lett. 1991,177(2): 189-194.