Please wait a minute...
物理化学学报  2017, Vol. 33 Issue (6): 1130-1139    DOI: 10.3866/PKU.WHXB201703221
研究论文     
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
北京科技大学化学与生物工程学院化学与化学工程系, 功能分子与晶态材料科学与应用北京市重点实验室, 北京 100083
Fitting and Extrapolation of Configuration Interaction Energies in Complete Active Space
CAO Jing-Si, CHEN Fei-Wu
Department of Chemistry and Chemical Engineering, School of Chemistry and Biological Engineering, University of Science and Technology Beijing;Beijing Key Laboratory for Science and Application of Functional Molecular and Crystalline Materials, Beijing 100083, P. R. China
 全文: PDF(2856 KB)   输出: BibTeX | EndNote (RIS) |
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(21173020,21473008)资助项目

通讯作者: 陈飞武     E-mail: chenfeiwu@ustb.edu.cn
服务  
把本文推荐给朋友
加入引用管理器
E-mail Alert
RSS
作者相关文章  
曹静思
陈飞武

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.

CAO Jing-Si, CHEN Fei-Wu. 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/Jwk_wk/wlhx/CN/10.3866/PKU.WHXB201703221        http://www.whxb.pku.edu.cn/Jwk_wk/wlhx/CN/Y2017/V33/I6/1130

(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. [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.; CornellUniversity Press: Ithaca, New York, 1960.
(4) Fu, R.; Lu, T.; Chen, F. W. Acta Phys. -Chim. Sin. 2014, 30 (4), 628. [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. [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. [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. [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. [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.[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.[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.[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. [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), 2787.]doi: 10.6023/A1106172
(29) Li, S.; Chen, S. J.; Zhu, D. S.; Wei, J. J. Acta Phys. -Chim. Sin. 2013, 29 (4), 737. [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. Å.; 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 andApplications of Computational Chemistry: the First Forty Years;Amsterdam: Elsevier, 2005; p 1167.
(36) Huber, K. P. Molecular Spectra and Molecular Structure: IV.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

[1] 范志辉, 陈飞武. 二阶多参考态微扰理论计算电子亲和势[J]. 物理化学学报, 2015, 31(11): 2064-2076.
[2] 张愚, 马宁, 王伟周. 氢键复合物中键长变化与振动频率移动相关性重访[J]. 物理化学学报, 2012, 28(03): 499-503.
[3] 周桃, 徐灿, 张小芳, 程川, 陈亮, 许莹. 环和纳米管径向呼吸振动模式的一个简单理论模型[J]. 物理化学学报, 2008, 24(09): 1579-1583.
[4] 胡盛志. 导出铅(II)—卤素键价参数的一条新途径[J]. 物理化学学报, 2007, 23(05): 786-789.
[5] 吕瑾;许小红;武海顺. Con(n=2~10)团簇的结构和磁性[J]. 物理化学学报, 2004, 20(09): 1118-1122.
[6] 王珺;郭迎春;杨晓华;吴升海;刘煜炎;陈扬骎. CASSCF方法对H2O激发态势能面的研究[J]. 物理化学学报, 2004, 20(08): 877-881.
[7] 叶元杰. 蛋白质的电子结构与活性关系——理论与计算方法[J]. 物理化学学报, 1991, 7(03): 257-259.