Exchange-correlation kernel for perturbation dependent auxiliary functions in auxiliary density perturbation theory

Autores: Luis I. Hernández-Segura, Flor A. Olvera-Rubalcava, Roberto Flores-Moreno, Patrizia Calaminici & Andreas M. Köster

Revista. Journal of Molecular Modeling

https://link.springer.com/article/10.1007/s00894-024-06091-z

Resumen. 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.