A fully numerical method for the time-dependent Kohn-Sham (TDKS) response theory is presented in a multiresolution analysis (MRA) approach. The formalism previously reported by Yanai was limited to excited states calculation. Here we present an extension to the formalism to compute linear and nonlinear response properties. The extension by Furche in 2001 leads to compact expressions for the frequency-dependent response functions. We obtain a general form of the TDKS linear response equations in the first quantization formalism from a reformulation with effective use of the density matrix operator. It can be readily rewritten as an integral equation with the bound-state Helmholtz (BSH) kernel for Green’s function. The MRA implementation of the resultant equation permit excited state and frequency-dependent response calculations without virtual orbitals. The integral equation is efficiently and adaptively solved using the MRA approach with multiwavelet bases. Our massively-parallel, high-performance implementation of TDKS is used to calculate the static and dynamic dipole hyperpolarizability of various molecules.

Multiresolution quantum chemistry in multiwavelet bases: Linear and nonlinear time-dependent density functional theory response properties

ACS Fall 2021

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