Self-Consistent Auxiliary Density Perturbation Theory

Abstract

The working equations for the extension of auxiliary density perturbation theory (ADPT) to hybrid functionals, employing the variational fitting of the Fock potential, are derived. The response equations in the resulting self-consistent ADPT (SC-ADPT) are solved iteratively with an adapted Eirola–Nevanlinna algorithm. As a result, a memory and CPU time efficient implementation of perturbation theory free of four-center electron repulsion integrals (ERIs) is obtained. Our validation calculations of SC-ADPT static and dynamic polarizabilities show quantitative agreement with corresponding coupled perturbed Hartree–Fock and Kohn–Sham results employing four-center ERIs. The comparison of SC-ADPT hybrid functional polarizabilities with coupled cluster reference calculations yield semiquantitative agreement. The presented systematic study of the dynamic polarizabilities of oligothiophenes shows that hybrid functionals can overcome the pathological misplacement of excitation poles by the local density and generalized gradient approximations. Good agreement with experimental dynamic polarizabilities for all studied oligothiophenes is achieved with range-separated hybrid functionals in the framework of SC-ADPT.

Optimization of density fitting auxiliary Slater‐type basis functions for time‐dependent density functional theory

“…As a final test, we have considered that in a recent work from Della Sala group, 15 it has been found that for silver clusters, it is possible to obtain very accurate photoabsorption spectra by using a minimal auxiliary basis set to fit the transition density. So we have directly optimized the exponent of a single 1 s STO function for a collection consisting of only the Ag 20 T d neutral cluster, obtaining a best exponent value equal to 0.40.…”

“…13 It is worth noting that auxiliary Gaussian-Hertmite functions (named GEN-An GEN-An*) 14 have proven more general as fitting functions, in fact the same set can be used to fit: in SCF both the Coulomb potential and the Fock nonlocal exchange when hybrid functionals are employed, in TDDFT, the perturbed density. 15 At variance, STO functions seem to have quite different requirements depending on the object to be fitted, this should likely ascribed to the cusp at the origin which is retained when the STO products are performed, while for Gaussian the cusp absence, although being unphysical, makes the fitting much easier.…”

DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science

“…Here, the long-range behaviour of the functional used is critical. 279 The polarizabilities of small metal clusters can be significantly influenced by temperature effects. 280 Furthermore, the experimental references for static polarizabilities of such clusters are not always reliable.…”

Semiempirical Approach to the Fukui Function Analysis of Uric Acid under Different pH Conditions

“…Auxiliary function sets of the type GEN-A2* − were automatically generated. Analytic Fukui functions and second-order electron binding energies , were computed using auxiliary density perturbation theory. − Colored isosurfaces of Fukui functions were prepared using Sinapsis software…”