物理化学学报 >> 2017, Vol. 33 >> Issue (6): 1130-1139.doi: 10.3866/PKU.WHXB201703221

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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*()   

  • 收稿日期:2016-12-02 发布日期:2017-05-19
  • 通讯作者: 陈飞武 E-mail:chenfeiwu@ustb.edu.cn
  • 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)

Fitting and Extrapolation of Configuration Interaction Energies in Complete Active Space

Jing-Si CAO,Fei-Wu CHEN*()   

  • Received:2016-12-02 Published:2017-05-19
  • Contact: Fei-Wu CHEN E-mail:chenfeiwu@ustb.edu.cn
  • Supported by:
    National Natural Science Foundation of China(21173020);National Natural Science Foundation of China(21473008)

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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