Odoh Samuel O, Manni Giovanni Li, Carlson Rebecca K, Truhlar Donald G, Gagliardi Laura
Department of Chemistry , Chemical Theory Center , Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , MN 55455-0431 , USA . Email:
Max-Planck Institut für Festkörperforshung , Heisenbergstraße 1 , 70569 Stuttgart , Germany.
Chem Sci. 2016 Mar 1;7(3):2399-2413. doi: 10.1039/c5sc03321g. Epub 2015 Dec 16.
Multi-configuration pair-density functional theory (MC-PDFT) has proved to be a powerful way to combine the capabilities of multi-configuration self-consistent-field theory to represent the an electronic wave function with a highly efficient way to include dynamic correlation energy by density functional theory. All applications reported previously involved complete active space self-consistent-field (CASSCF) theory for the reference wave function. For treating large systems efficiently, it is necessary to ask whether good accuracy is retained when using less complete configuration interaction spaces. To answer this question, we present here calculations employing MC-PDFT with the separated pair (SP) approximation, which is a special case (defined in this article) of generalized active space self-consistent-field (GASSCF) theory in which no more than two orbitals are included in any GAS subspace and in which inter-subspace excitations are excluded. This special case of MC-PDFT will be called SP-PDFT. In SP-PDFT, the electronic kinetic energy and the classical Coulomb energy, the electronic density and its gradient, and the on-top pair density and its gradient are obtained from an SP approximation wave function; the electronic energy is then calculated from the first two of these quantities and an on-top density functional of the last four. The accuracy of the SP-PDFT method for predicting the structural properties and bond dissociation energies of twelve diatomic molecules and two triatomic molecules is compared to the SP approximation itself and to CASSCF, MC-PDFT based on CASSCF, CASSCF followed by second order perturbation theory (CASPT2), and Kohn-Sham density functional theory with the PBE exchange-correlation potential. We show that SP-PDFT reproduces the accuracy of MC-PDFT based on the corresponding CASSCF wave function for predicting C-H bond dissociation energies, the reaction barriers of pericyclic reactions and the properties of open-shell singlet systems, all at only a small fraction of the computational cost.
多组态对密度泛函理论（MC-PDFT）已被证明是一种强大的方法，它将多组态自洽场理论表示电子波函数的能力与通过密度泛函理论高效包含动态相关能的方法相结合。此前报道的所有应用都涉及将完全活性空间自洽场（CASSCF）理论用于参考波函数。为了有效地处理大体系，有必要探讨在使用不太完整的组态相互作用空间时是否仍能保持良好的精度。为了回答这个问题，我们在此展示使用具有分离对（SP）近似的MC-PDFT进行的计算，这是广义活性空间自洽场（GASSCF）理论的一种特殊情况（在本文中定义），其中任何GAS子空间中包含的轨道不超过两个，并且子空间间的激发被排除。MC-PDFT的这种特殊情况将被称为SP-PDFT。在SP-PDFT中，电子动能和经典库仑能、电子密度及其梯度、顶对密度及其梯度是从一个SP近似波函数获得的；然后根据这些量中的前两个以及后四个的顶密度泛函来计算电子能量。将SP-PDFT方法预测十二个双原子分子和两个三原子分子的结构性质和键解离能的精度与SP近似本身以及CASSCF、基于CASSCF的MC-PDFT、CASSCF之后的二阶微扰理论（CASPT2）以及具有PBE交换相关势的Kohn-Sham密度泛函理论进行了比较。我们表明，SP-PDFT在预测C-H键解离能、周环反应的反应势垒和开壳单重态体系的性质时，再现了基于相应CASSCF波函数的MC-PDFT的精度，而计算成本仅为其一小部分。
