Hernández-Segura Luis I, Olvera-Rubalcava Flor A, Flores-Moreno Roberto, Calaminici Patrizia, Köster Andreas M
Chemistry Department, CINVESTAV, Av. Instituto Politecnico Nacional 2508, Col. San Pedro Zacatenco, Del. Gustavo A. Madero, Mexico City, C.P. 07360, Mexico.
Departamento de Química, Universidad de Guadalajara, Blvd. Gral. Marcelino García Barragán 1421, Guadalajara, Jal., C.P. 44430, Mexico.
J Mol Model. 2024 Aug 8;30(9):302. doi: 10.1007/s00894-024-06091-z.
Analytic exchange-correlation kernel formulations are of the outermost importance for density functional theory (DFT) perturbation calculations. In this paper, the working equation for the exchange-correlation kernel of the generalized gradient approximation (GGA) for perturbation dependent auxiliary functions is derived and discussed in the framework of auxiliary density functional theory (ADFT). The presented new formulation is extended to the unrestricted approach, too. A comprehensive discussion of the implementation of the GGA ADFT kernel, using either the native exchange-correlation functional implementations in deMon2k or the ones from the LibXC library, is given. Calculations with analytic exchange-correlation kernels are compared to their finite difference counterparts. The obtained results are in quantitative agreement. Nevertheless, analytic GGA ADFT kernel implementations show substantial improvement in the computational performance. Similar results are reported for analytic second derivatives of effective core potential (ECP) and model core potential (MCP) matrix elements when compared to their finite difference counterparts in molecular frequency analyses.
All calculations are performed in the framework of ADFT as implemented in deMon2k. In the ADFT analytic frequency calculations, auxiliary density perturbation theory was used. The underlying two-center exchange-correlation kernel matrix elements are calculated by numerical integration either with analytic or finite difference kernel expressions. Validation calculations are performed with the VWN and PBE functionals employing DFT-optimized DZVP basis sets in conjunction with automatically generated GEN-A2 auxiliary density function sets. In the (PtCu) cluster benchmark calculations, the RPBE functional was used. For Pt atoms, the quasi-relativistic LANL2DZ effective core potential with the corresponding valence basis set was employed, whereas for Cu atoms, the all-electron DFT-optimized TZVP basis was applied. The auxiliary density was expanded by the automatically generated GEN-A2* auxiliary function set. We run all benchmark calculations in parallel on 24 cores.
解析交换关联核公式对于密度泛函理论（DFT）微扰计算至关重要。本文在辅助密度泛函理论（ADFT）框架下，推导并讨论了用于依赖微扰的辅助函数的广义梯度近似（GGA）交换关联核的工作方程。所提出的新公式也扩展到了非限制方法。本文还全面讨论了使用deMon2k中的原生交换关联泛函实现或LibXC库中的实现来实现GGA ADFT核的方法。将解析交换关联核的计算结果与其有限差分对应结果进行了比较。所得结果在定量上是一致的。然而，解析GGA ADFT核实现的计算性能有显著提升。在分子频率分析中，将有效核势（ECP）和模型核势（MCP）矩阵元的解析二阶导数与其有限差分对应结果进行比较时，也报告了类似的结果。
所有计算均在deMon2k中实现的ADFT框架下进行。在ADFT解析频率计算中，使用了辅助密度微扰理论。通过数值积分，利用解析或有限差分核表达式计算基础的两中心交换关联核矩阵元。使用VWN和PBE泛函，结合自动生成的GEN - A2辅助密度函数集，采用DFT优化的DZVP基组进行验证计算。在（PtCu）团簇基准计算中，使用了RPBE泛函。对于Pt原子，采用了具有相应价基组的准相对论LANL2DZ有效核势，而对于Cu原子，则应用了全电子DFT优化的TZVP基组。辅助密度由自动生成的GEN - A2*辅助函数集展开。我们在24个核心上并行运行所有基准计算。
