Leverentz Hannah R, Gao Jiali, Truhlar Donald G
Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, MN 55455-0431, USA.
Theor Chem Acc. 2011 May 1;129(1):3-13. doi: 10.1007/s00214-011-0889-9. Epub 2011 Jan 26.
The equations defining the variational explicit polarization (X-Pol) potential introduced in earlier work are modified in the present work so that multipole point charge distributions are used instead of Mulliken charges to polarize the monomers that comprise the system. In addition, when computing the electrostatic interaction between a monomer whose molecular orbitals are being optimized and a monomer whose electron density is being used to polarize the first monomer, the electron densities of both monomers are represented by atom-centered multipole point charge distributions. In the original formulation of the variational X-Pol potential, the continuous electron density of the monomer being optimized interacts with external Mulliken charges, but this corresponds to the monopole truncation in a multipole expansion scheme in the computation of the Fock matrix elements of the given monomer. The formulation of the variational X-Pol potential introduced in this work (which we are calling the "multipole variational X-Pol potential") represents the electron density of the monomer whose wave function is being variationally optimized in the same way that it represents the electron densities of external monomers when computing the Coulomb interactions between them.
在本工作中，对早期工作中引入的定义变分显式极化（X-Pol）势的方程进行了修改，以便使用多极点电荷分布而非穆利肯电荷来极化构成系统的单体。此外，在计算分子轨道正在优化的单体与用于极化第一个单体的电子密度的单体之间的静电相互作用时，两个单体的电子密度均由以原子为中心的多极点电荷分布表示。在变分X-Pol势的原始公式中，正在优化的单体的连续电子密度与外部穆利肯电荷相互作用，但这对应于在计算给定单体的福克矩阵元时多极展开方案中的单极截断。本工作中引入的变分X-Pol势的公式（我们称之为“多极变分X-Pol势”），在计算它们之间的库仑相互作用时，以与表示外部单体的电子密度相同的方式来表示波函数正在进行变分优化的单体的电子密度。
