Kumar Ashutosh, Crawford T Daniel
Department of Chemistry, Virginia Tech , Blacksburg, Virginia 24061, United States.
J Phys Chem A. 2017 Jan 26;121(3):708-716. doi: 10.1021/acs.jpca.6b11410. Epub 2017 Jan 11.
The frozen-virtual natural-orbital (NO) approach, whereby the unoccupied-orbital space is constructed using a correlated density such as that from many-body perturbation theory, has proven to yield compact wave functions for determining ground-state correlation energies and associated properties, with corresponding occupation numbers providing a guide to the truncation of the virtual space. In this work this approach is tested for the first time for the calculation of higher-order response properties, particularly frequency-dependent dipole polarizabilities using coupled-cluster theory. We find that such properties are much more sensitive to the truncation of virtual space in the NO basis than in the original canonical molecular orbital (CMO) basis, with truncation errors increasing linearly with respect to the number of frozen virtual NOs. The reasons behind this poor performance include the more diffuse nature of NOs with low occupation numbers as well as the reduction in sparsity of the perturbed singles amplitudes in the NO basis and the neglect of orbital response. We tested a number of approaches to improve the performance of the NO space, including the use of a field-perturbed density to define the virtual orbitals and various external-space corrections. The truncation of the CMO space, on the other hand, yields errors in coupled-cluster dipole polarizabilities of less than 2% even after removing as much as 50% of the full virtual space. We find that this positive performance of the CMO space results from a cancellation of errors due to the truncation of the unperturbed and perturbed amplitudes, as well as sparsity of the singles amplitudes. We introduce a simple criterion called a dipole amplitude to use as a threshold for truncating the CMO basis for such property calculations.
冻结虚拟自然轨道（NO）方法，即使用诸如多体微扰理论中的关联密度来构建未占据轨道空间，已被证明能产生紧凑的波函数，用于确定基态关联能及相关性质，相应的占据数为虚拟空间的截断提供了指导。在这项工作中，首次对该方法进行测试，以计算高阶响应性质，特别是使用耦合簇理论计算频率相关的偶极极化率。我们发现，与原始的正则分子轨道（CMO）基相比，这些性质对NO基中虚拟空间的截断更为敏感，截断误差随冻结虚拟NO的数量线性增加。这种不佳表现背后的原因包括低占据数的NO具有更弥散的性质，以及NO基中受扰单激发振幅稀疏性的降低和轨道响应的忽略。我们测试了多种方法来改善NO空间的性能，包括使用场微扰密度来定义虚拟轨道以及各种外部空间校正。另一方面，即使去除多达50%的完整虚拟空间，CMO空间的截断在耦合簇偶极极化率中产生的误差仍小于2%。我们发现，CMO空间的这种良好性能源于未受扰和受扰振幅截断导致的误差抵消以及单激发振幅的稀疏性。我们引入了一个称为偶极振幅的简单标准，用作截断CMO基进行此类性质计算的阈值。
