The ab initio calculation of molecular electric, magnetic and geometric properties
The ab initio calculation of molecular electric, magnetic and geometric properties
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DOI：
10.1039/c0cp01647k
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发表时间：
2011-01-01
影响因子：
3.3
通讯作者：
Thorvaldsen, Andreas J.
中科院分区：
文献类型：
--
作者：
Bast, Radovan;Ekstrom, Ulf;Thorvaldsen, Andreas J.
我们介绍了用于计算分子响应特性的从头算方法开发的一些最新进展，涉及电、磁和几何扰动。特别关注基函数明确依赖于时间和所施加的扰动的性质，例如当使用伦敦原子轨道时涉及核位移或外部磁场的扰动。我们总结了一个基于准能量的通用框架，用于使用原子轨道基础上的密度矩阵元素作为基本变量来计算任意阶分子性质。我们证明，可以从一组线性方程组确定任意阶的必要扰动密度矩阵，这些线性方程组与确定线性响应方程（或瞬态自洽场方程）时遇到的线性方程组具有相同的形式结构。计算涉及扰动相关基组的属性所需的附加组件是用于几何或磁场微分积分的灵活的一电子和二电子积分技术；在Kohn-Sham密度泛函理论（KS-DFT）中，我们还需要计算交换相关泛函的导数。我们描述了最近基于自动微分评估这些贡献的提案。在这个框架内，现在可以计算任意自洽场参考态的任何分子性质，包括二分量和四分量相对论自洽场波函数。给出了可以用该公式进行的计算的示例。
We give an account of some recent advances in the development of ab initio methods for the calculation of molecular response properties, involving electric, magnetic, and geometric perturbations. Particular attention is given to properties in which the basis functions depend explicitly both on time and on the applied perturbations such as perturbations involving nuclear displacements or external magnetic fields when London atomic orbitals are used. We summarize a general framework based on the quasienergy for the calculation of arbitrary-order molecular properties using the elements of the density matrix in the atomic-orbital basis as the basic variables. We demonstrate that the necessary perturbed density matrices of arbitrary order can be determined from a set of linear equations that have the same formal structure as the set of linear equations encountered when determining the linear response equations (or time-dependent self-consistent-field equations). Additional components needed to calculate properties involving perturbation-dependent basis sets are flexible one-and two-electron integral techniques for geometric or magnetic-field differentiated integrals; in Kohn-Sham density-functional theory (KS-DFT), we also need to calculate derivatives of the exchange-correlation functional. We describe a recent proposal for evaluating these contributions based on automatic differentiation. Within this framework, it is now possible to calculate any molecular property for an arbitrary self-consistent-field reference state, including two-and four-component relativistic self-consistent-field wave functions. Examples of calculations that can be performed with this formulation are presented.