Thorvaldsen Andreas J, Ruud Kenneth, Kristensen Kasper, Jørgensen Poul, Coriani Sonia
Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Tromsø, Norway.
J Chem Phys. 2008 Dec 7;129(21):214108. doi: 10.1063/1.2996351.
A general method is presented for the calculation of molecular properties to arbitrary order at the Kohn-Sham density functional level of theory. The quasienergy and Lagrangian formalisms are combined to derive response functions and their residues by straightforward differentiation of the quasienergy derivative Lagrangian using the elements of the density matrix in the atomic orbital representation as variational parameters. Response functions and response equations are expressed in the atomic orbital basis, allowing recent advances in the field of linear-scaling methodology to be used. Time-dependent and static perturbations are treated on an equal footing, and atomic basis sets that depend on the applied frequency-dependent perturbations may be used, e.g., frequency-dependent London atomic orbitals. The 2n+1 rule may be applied if computationally favorable, but alternative formulations using higher-order perturbed density matrices are also derived. These may be advantageous in order to minimize the number of response equations that needs to be solved, for instance, when one of the perturbations has many components, as is the case for the first-order geometrical derivative of the hyperpolarizability.
提出了一种在Kohn-Sham密度泛函理论水平上计算任意阶分子性质的通用方法。将准能量和拉格朗日形式主义相结合，通过使用原子轨道表示中的密度矩阵元素作为变分参数，对准能量导数拉格朗日进行直接微分，从而导出响应函数及其留数。响应函数和响应方程以原子轨道基表示，这使得线性标度方法领域的最新进展得以应用。含时和静态微扰在同等基础上处理，并且可以使用依赖于所施加的频率相关微扰的原子基组，例如频率相关的伦敦原子轨道。如果计算上有利，可以应用2n + 1规则，但也推导了使用高阶微扰密度矩阵的替代公式。这些公式可能有利于最小化需要求解的响应方程的数量，例如，当其中一个微扰有许多分量时，超极化率的一阶几何导数就是这种情况。
