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物理化学学报  2017, Vol. 33 Issue (6): 1130-1139    DOI: 10.3866/PKU.WHXB201703221
论文     
完全活性空间组态相互作用能量的拟合和外推
曹静思,陈飞武*()
Fitting and Extrapolation of Configuration Interaction Energies in Complete Active Space
Jing-Si CAO,Fei-Wu CHEN*()
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摘要:

完全活性空间组态相互作用计算与完全活性空间中的活性电子数和活性轨道数有关,但完全活性空间组态相互作用的能量不是活性电子数和活性轨道数的单调递减函数,因此活性轨道数和活性电子数不能用来外推完全活性空间组态相互作用的能量。为此,我们定义了一个新的变量:活性空间中的最大未占满轨道数。我们对一系列单重态、双重态和三重态分子进行了完全活性空间组态相互作用的计算,并利用活性空间中的活性电子数和最大未占满轨道数这两个变量,对这些基态能量进行了拟合和外推,拟合的均方根误差都在10-6数量级。外推能量的精度优于MP4,对小分子体系,其精度高于CCSD。外推的完全的组态相互作用(FCI)能量值和实际计算的FCI值也很接近。另外,我们还利用外推能量来优化双原子分子的平衡键长,并计算谐振频率,其精度优于CASSCF。

关键词: 活性空间活性电子活性轨道能量外推键长谐振频率    
Abstract:

Configuration interaction calculation in complete active space is related to the numbers of active electrons and orbitals. However, configuration interaction energy is not a monotonically decreasing function of these two variables. Thus, the numbers of active electrons and orbitals are not proper variables to extrapolate the configuration interaction energy. In order to address this problem, we defined a new variable:maximum number of unoccupied orbitals in the complete active space. We performed a series of configuration interaction calculations on singlet, doublet, and triplet molecules, and simulated their ground state energies with the number of active electrons and the number of maximum unoccupied orbitals. The mean square root errors of these simulations were on the order of 10-6. The accuracy of the extrapolated energies was better than that of MP4 and than that of CCSD for small molecules. The extrapolated full configuration interaction energies were very close to the energy values of full configuration interactions. Furthermore, the extrapolated energies were exploited to optimize the bond distances of several diatomic molecules and to compute harmonic vibrational frequencies. Their accuracies were better than that of the complete active space self-consistent field.

Key words: Complete active space    Active electron    Active orbital    Energy extrapolation    Bond length    Harmonic vibrational frequency
收稿日期: 2016-12-02 出版日期: 2017-03-22
中图分类号:  O641  
基金资助: 国家自然科学基金资助项目(21173020);国家自然科学基金资助项目(21473008)
通讯作者: 陈飞武     E-mail: chenfeiwu@ustb.edu.cn
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引用本文:

曹静思,陈飞武. 完全活性空间组态相互作用能量的拟合和外推[J]. 物理化学学报, 2017, 33(6): 1130-1139.

Jing-Si CAO,Fei-Wu CHEN. Fitting and Extrapolation of Configuration Interaction Energies in Complete Active Space. Acta Phys. -Chim. Sin., 2017, 33(6): 1130-1139.

链接本文:

http://www.whxb.pku.edu.cn/CN/10.3866/PKU.WHXB201703221        http://www.whxb.pku.edu.cn/CN/Y2017/V33/I6/1130

图1  CH4分子的E与活性空间中最大未占满轨道数Mmax的关系图
图2  CH4分子E与活性电子数Nele的关系图
MoleculeNele = 2Nele = 4Nele = 6Nele = 8Nele = 10R2-M aSe-M b
CH4?40.195727?40.222980?40.258960?40.299640?40.3008370.99730.6583 × 10?6
H2O?75.995708?76.025908?76.076865?76.118908?76.1194500.99081.8218 × 10?6
HF?99.994106?100.022484?100.076012?100.113805?100.1146770.99450.9384 × 10?6
HCl?460.040777?460.050411?460.075289?460.094432?460.0947110.99550.0410 × 10?6
C2H4?78.036773?78.051796?78.086919?78.127227?78.1370240.99470.4622 × 10?6
N2H4?111.097151?111.113767?111.137168?111.185411?111.2053070.98300.5837 × 10?6
O3?224.203067?224.225559?224.264612?224.310388?224.3664410.97590.3973 × 10?6
Cl2?918.865005?918.871332?918.879059?918.888453?918.9320420.99270.0135 × 10?6
表1  单重态分子的外推能量(hartree)及拟合参数
MoleculeB3LYPMP2MP4CCSDExtra.*FCI
CH4?39.973539?39.802466?39.816872?39.855656?40.300837?40.300835
H2O?75.868653?75.821248?75.925882?75.817822?76.119450?76.120838
HF?100.267014?100.058036?99.988922?100.071557?100.114677?100.114307
C2H4?77.791740?77.491723?77.497659?77.603125?78.138748**
N2H4?111.151725?111.057303?110.957610?111.067759?111.249844**
HCl?460.647716?460.076776?459.987620?460.112090?460.096813**
Cl2?920.217791?919.130112?918.968190?919.162674?918.957751**
O3?224.952575?224.568669?224.229338?224.662578?224.391424**
表2  利用6种方法计算单重态分子的单点能(hartree)
图3  MgH分子E与活性空间中最大未占满轨道数Mmax的关系图
图4  O2分子E与活性空间中最大未占满轨道数Mmax的关系图
MoleculeNele = 3Nele = 5Nele = 7Nele = 9Nele = 11R2-M aSe-M b
doublet
CH?38.278501?38.316570?38.317560_d_d0.99542.5961 × 10?6
NH2?55.551240?55.592851?55.633837?55.635109_d0.98112.9242 × 10?6
MgH?200.155490?200.155730?200.156500?200.157750?200.1582500.98940.1459 × 10?6
CN_c?92.267993?92.327288?92.366993?92.3680980.97921.3202 × 10?6
NO_c?129.259794?129.319029?129.362475?129.4071960.98550.9284 × 10?6
MoleculeNele = 2Nele = 4Nele = 6Nele = 8Nele = 10R2-M aSe-M b
triplet
CH2?38.910163?38.937379?38.980092?38.981150_d0.99421.0792 × 10?6
NH?54.942410?54.972083?55.011873?55.012792_d0.99671.1471 × 10?6
OH+?74.946500?74.976967?75.015879?75.016735_d0.99870.4998 × 10?6
PH?341.097250?341.112110?341.132901?341.133321?341.1339790.99420.0476 × 10?6
SiH2_c?289.846197?289.873244?289.873604?289.8745410.98460.3962 × 10?6
NF?153.730305?153.761556?153.791543?153.833042?153.8939670.99390.3777 × 10?6
O2_c?149.563901?149.625447?149.688563?149.7315430.98690.6808 × 10?6
表3  多重态分子的外推能量(hartree)及拟合参数
MoleculeUB3LYPUMP2UMP4UCCSDExtra.*FCI
doublet
CH?38.374599?38.245978?38.220027?38.278615?38.317560?38.317560
NH2?55.606183?55.438307?55.420849?55.502775?55.635109?55.634553
MgH?200.582497?200.127416?200.121352?200.140603?200.158250?200.158250
CN?92.454861?92.200641?92.132753?92.245942?92.374824**
NO?129.658134?129.156903?129.078059?129.217100?129.407196**
triplet
CH2?38.897733?38.738979?38.714131?38.792961?38.981150?38.981093
NH?55.108368?54.966748?54.921893?54.990677?55.012793?55.013001
OH+?75.154984?74.972583?74.916438?75.003497?75.016735?75.016885
PH?341.828742?341.320647?341.246246?341.350612?341.135901?341.135910
NF?154.306964?153.979267?153.865934?154.006754?153.931458**
SiH2?290.359061?289.875054?289.829758?289.899624?289.874660**
O2?150.048948?149.940643?149.821090?149.722662?149.779525**
表4  利用6种方法计算多重态分子的单点能(hartree)
MoleculeHFNaHCHMgHNHOH+
singletdoublettriplet
re(HF/6-31G)0.92081.91741.10661.75091.00011.0070
re(MP2/6-31G)0.94701.92941.13661.77051.05221.0454
re(CASSCF/6-31G)0.94901.95651.14031.80251.02341.0413
re(Extra.)a0.94951.95411.12851.80061.03601.0346
re(Exp)b0.91681.88741.11991.72971.03621.0289
we(HF/6-31G)4149.431186.192957.201549.733441.703242.45
we(MP2/6-31G)3788.681143.412790.251460.383220.162976.43
we(CASSCF/6-31G)3746.701068.142638.141333.523034.043011.83
we(Extra.)a3750.871074.362808.411356.973019.553108.53
we(Exp)b4138.301172.202858.501495.203282.273113.37
表5  4种方法计算的平衡键长(re, 10-10 m)和谐振频率(we, cm-1)的比较
1 Jensen, F. Introduction to Computational Chemistry, 2nd ed.; WestSussex: John Wiley & Sons, 2007; p 487.
2 Cao J. S. ; Wei M. J. ; Chen F. W. Acta Phys. -Chim. Sin. 2016, 32 (7), 1639.
doi: 10.3866/PKU.WHXB201604062
曹静思; 韦美菊; 陈飞武. 物理化学学报, 2016, 32 (7), 1639.
doi: 10.3866/PKU.WHXB201604062
3 Pauling L. The Nature of the Chemical Bond 3rd ed Ithaca, New York: CornellUniversity Press, 1960.
4 Fu R. ; Lu T. ; Chen F. W. Acta Phys. -Chim. Sin. 2014, 30 (4), 628.
doi: 10.3866/PKU.WHXB201401211
付蓉; 卢天; 陈飞武. 物理化学学报, 2014, 30 (4), 628.
doi: 10.3866/PKU.WHXB201401211
5 Zhou X. Y. ; Rong C. Y. ; Lu T. ; Liu S. B. Acta Phys. -Chim. Sin. 2014, 30 (11), 2055.
doi: 10.3866/PKU.WHXB201409193
周夏禹; 荣春英; 卢天; 刘述斌. 物理化学学报, 2014, 30 (11), 2055.
doi: 10.3866/PKU.WHXB201409193
6 Cao J. S. ; Ren Q. ; Chen F. W. ; Lu T. Sci. China Chem. 2015, 58 (12), 1845.
doi: 10.1007/s11426-015-5494-7
7 Liu S. B. Acta Phys. -Chim. Sin. 2016, 32 (1), 98.
doi: 10.3866/PKU.WHXB201510302
刘述斌. 物理化学学报, 2016, 32 (1), 98.
doi: 10.3866/PKU.WHXB201510302
8 Luo Q. Q. ; Cao C. T. ; Cao C. Z. Acta Phys. -Chim. Sin. 2016, 32 (7), 1691.
doi: 10.3866/PKU.WHXB201604061
罗青青; 曹朝暾; 曹晨忠. 物理化学学报, 2016, 32 (7), 1691.
doi: 10.3866/PKU.WHXB201604061
9 Lu T. ; Chen F. W. J. Mol. Model. 2013, 19 (12), 5387.
doi: 10.1007/s00894-013-2034-2
10 Esrafili M. D. ; Mohammadian-Sabet F. Int. J. Quantum Chem. 2016, 116 (7), 529.
doi: 10.1002/qua.25076
11 Zhao Q. ; Qi B. Y. ; Wang B. J. ; Chen F. W. Acta Chim. Sin. 2015, 74 (3), 285.
doi: 10.6023/A15100641
赵清; 齐博宇; 王宝金; 陈飞武. 化学学报, 2015, 74 (3), 285.
doi: 10.6023/A15100641
12 Horn M. ; Schappele L. H. ; Lang-Wittkowski G. ; Mayr H. ; Ofial A. R. Chem. -Eur. J. 2013, 19 (1), 249.
doi: 10.1002/chem.201202839
13 Cao J. S. ; Chen F. W. Chin. J. Org. Chem. 2016, 36 (10), 2463.
doi: 10.6023/cjoc201602026
曹静思; 陈飞武. 有机化学, 2016, 36 (10), 2463.
doi: 10.6023/cjoc201602026
14 Bartlett R. J. ; Purvis G. D. Int. J. Quantum Chem. 1978, 14 (5), 561.
doi: 10.1002/qua.560140504
15 Chen F. W. J. Chem. Theory Comput. 2009, 5 (4), 931.
doi: 10.1021/ct800546g
16 Fan Z. H. ; Chen F. W. Acta Phys. -Chim. Sin. 2015, 31 (11), 2064.
doi: 10.3866/PKU.WHXB201508201
范志辉; 陈飞武. 物理化学学报, 2015, 31 (11), 2064.
doi: 10.3866/PKU.WHXB201508201
17 Li W. ; Ni Z. ; Li S. Mol. Phys. 2016, 114 (9), 1447.
doi: 10.1080/00268976.2016.1139755
18 Liu W. J. ; Hoffmann M. R. J. Chem. Theory Comput. 2016, 12 (3), 1169.
doi: 10.1021/acs.jctc.5b01099
19 Schwartz C. Phys. Rev. 1962, 126 (3), 1015.
doi: 10.1103/PhysRev.126.1015
20 Kutzelnigg W. ; Morgan J. D. Ⅲ J. Chem. Phys. 1992, 96 (6), 4484.
doi: 10.1063/1.462811
21 Feller D. J. Chem. Phys. 1993, 98 (9), 7059.
doi: 10.1063/1.464749
22 Feller D. ; Peterson K. A. ; Hill J. G. J. Chem. Phys. 2011, 135 (4), 044102.
doi: 10.1063/1.3613639
23 Peterson K. A. ; Woon D. E. ; Dunning T. H. Jr. J. Chem. Phys. 1994, 100 (10), 7410.
doi: 10.1063/1.466884
24 Feller D. J. Chem. Phys. 2013, 138 (7), 074103.
doi: 10.1063/1.4791560
25 Martin J. M. L. Chem. Phys. Lett. 1996, 259 (5), 669.
doi: 10.1016/0009-2614(96)00898-6
26 Seino J. ; Nakai H. J. Comput. Chem. 2016, 37 (25), 2304.
doi: 10.1002/jcc.2455
27 Tu Z. Y. ; Wang W. L. Acta Phys. -Chim. Sin. 2015, 31 (6), 1054.
doi: 10.3866/PKU.WHXB201503261
涂喆研; 王文亮. 物理化学学报, 2015, 31 (6), 1054.
doi: 10.3866/PKU.WHXB201503261
28 Lin X. F. ; Sun C. K. ; Yang S. Y. ; Yu S. W. ; Yao L. F. ; Chen Y. S. Acta Chim. Sin. 2011, 69 (23), 2787.
doi: 10.6023/A1106172
林雪飞; 孙成科; 杨思娅; 余仕问; 姚立峰; 陈益山. 化学学报, 2011, 69 (23), 2787d.
doi: 10.6023/A1106172
29 Li S. ; Chen S. J. ; Zhu D. S. ; Wei J. J. Acta Phys. -Chim. Sin. 2013, 29 (4), 737.
doi: 10.3866/PKU.WHXB201301311
李松; 陈善俊; 朱德生; 韦建军. 物理化学学报, 2013, 29 (4), 737.
doi: 10.3866/PKU.WHXB201301311
30 Daudey J. P. ; Heully J. L. ; Malrieu J. P. J. Chem. Phys. 1993, 99 (2), 1240.
doi: 10.1063/1.465368
31 Veryazov V. ; Malmqvist P. ; Roos B. O. Int. J. Quantum Chem. 2011, 111 (13), 3329.
doi: 10.1002/qua.23068
32 Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; et al. Gaussian 03, Revision A.01; Gaussian Inc.: Pittsburgh, PA, 2003.
33 Koseki S. ; Schmidt M. W. ; Gordon M. S. J. Phys. Chem. 1992, 96 (26), 10768.
doi: 10.1021/j100205a033
34 Schmidt M. W. ; Baldridge K. K. ; Boatz J. A. ; Elbert S. T. ; Gordon M. S. ; Jensen J. J. ; Koseki S. ; Matsunaga N. ; Nguyen K. A. ; Su S. ; Windus T. L. ; Dupuis M. ; Montgomery J. A. J.Comput. Chem. 1993, 14 (11), 1347.
doi: 10.1002/jcc.540141112
35 Dykstra, C.; Frenking, G.; Kim, K.; Scuseria, G. Theory and Applications of Computational Chemistry: the First Forty Years; Amsterdam: Elsevier, 2005; p 1167.
36 Huber, K. P. Molecular Spectra and Molecular Structure: .Constants of Diatomic Molecules; Springer: New York, 2013; p 8. doi: 10.1007/978-1-4757-0961-2
37 Chen F. W. ; Wei M.J. ; Liu W. J. Sci. China Chem. 2011, 54 (3), 446.
doi: 10.1007/s11426-010-4199-1
38 Chen F. W. ; Fan Z. H. J. Comput. Chem. 2014, 35 (2), 121.
doi: 10.1002/jcc.23471
39 Wang Z. ; Wang F. Phys. Chem. Chem. Phys. 2013, 15 (41), 17922.
doi: 10.1039/c3cp51749g
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