Weber Valéry, Daul Claude, Challacombe Matt
Department of Chemistry, University of Fribourg, 1700 Fribourg, Switzerland.
J Chem Phys. 2006 Jun 7;124(21):214105. doi: 10.1063/1.2207625.
Recently, linear scaling construction of the periodic exact Hartree-Fock exchange matrix within the Gamma-point approximation has been introduced [J. Chem. Phys. 122, 124105 (2005)]. In this article, a formalism for evaluation of analytical Hartree-Fock exchange energy gradients with respect to atomic positions and cell parameters at the Gamma-point approximation is presented. While the evaluation of exchange gradients with respect to atomic positions is similar to those in the gas phase limit, the gradients with respect to cell parameters involve the accumulation of atomic gradients multiplied by appropriate factors and a modified electron repulsion integral (ERI). This latter integral arises from use of the minimum image convention in the definition of the Gamma-point Hartree-Fock approximation. We demonstrate how this new ERI can be computed with the help of a modified vertical recurrence relation in the frame of the Obara-Saika and Head-Gordon-Pople algorithm. As an illustration, the analytical gradients have been used in conjunction with the QUICCA algorithm [K. Nemeth and M. Challacombe, J. Chem. Phys. 121, 2877 (2004)] to optimize periodic systems at the Hartree-Fock level of theory.
最近，已引入了在Γ点近似下对周期性精确哈特里 - 福克交换矩阵的线性缩放构造[《化学物理杂志》122, 124105 (2005)]。在本文中，提出了一种在Γ点近似下评估关于原子位置和晶胞参数的解析哈特里 - 福克交换能量梯度的形式体系。虽然关于原子位置的交换梯度评估与气相极限下的类似，但关于晶胞参数的梯度涉及原子梯度乘以适当因子的累积以及一个修正的电子排斥积分（ERI）。后一个积分源于在Γ点哈特里 - 福克近似定义中使用的最小镜像约定。我们展示了如何在小原 - 酒井算法和黑德 - 戈登 - 波普尔算法的框架内借助修正的垂直递推关系来计算这个新的ERI。作为一个示例，解析梯度已与QUICCA算法[K. 内梅特和M. 查拉科姆贝，《化学物理杂志》121, 2877 (2004)]结合使用，以在哈特里 - 福克理论水平上优化周期性体系。
