Numerically stable optimized effective potential method with balanced Gaussian basis sets

Abstract

A solution to the long-standing problem of developing numerically stable optimized effective potential (OEP) methods based on Gaussian basis sets is presented by introducing an approach consisting of an exact exchange OEP method with an accompanying construction and balancing scheme for the involved auxiliary and orbital Gaussian basis sets that is numerically stable and that properly represents an exact exchange Kohn-Sham method. The method is a purely analytical method that does not require any numerical grid, scales like Hartree-Fock or B3LYP procedures, is straightforward to implement, and is easily generalized to take into account orbital-dependent density functionals other than the exact exchange considered in this work. Thus, the presented OEP approach opens the way to the development and application of novel orbital-dependent exchange-correlation functionals. It is shown that adequately taking into account the continuum part of the Kohn-Sham orbital spectrum is crucial for numerically stable Gaussian basis set OEP methods. Moreover, it is mandatory to employ orbital basis sets that are converged with respect to the used auxiliary basis representing the exchange potential. OEP calculations in the past often did not meet the latter requirement and therefore may have led to erroneously low total energies.

Precise response functions in all-electron methods: Application to the optimized-effective-potential approach

“…(37). It is difficult to compare the efficiency of the calculations, since the least accurate calculation with the IBC is still more accurate than the most accurate one without.…”

“…A similar behavior was observed for Gaussian basis sets. 37 In this paper, we present a numerical correction for the response functions, with which the balance condition is achieved with a considerably smaller LAPW basis leading to much faster and numerically more stable calculations. Furthermore, much fewer empty bands are needed for the construction of the response functions.…”

Exchange-only optimized-effective-potential calculations using Slater-type basis functions: Atoms and diatomic molecules

“…An expansion of the exchange part of the local potential is assumed in terms of an appropriate set of functions [20,22,24,25,29,30],…”

“…* jjfernandez@fisfun.uned.es Application of the xOEP formalism to polyatomic molecules requires its formulation in terms of basis sets suitable for molecular calculations. Currently, there exist several formulations of the xOEP method in terms of basis sets of local Gaussian-type-orbital (GTO) functions [19][20][21][22][23]. The most popular implementation of the xOEP formalism employs two different basis sets, one for the expansion of the KS orbitals and another one for representing the local multiplicative potential [22,24,25].…”

“…Currently, there exist several formulations of the xOEP method in terms of basis sets of local Gaussian-type-orbital (GTO) functions [19][20][21][22][23]. The most popular implementation of the xOEP formalism employs two different basis sets, one for the expansion of the KS orbitals and another one for representing the local multiplicative potential [22,24,25]. Within this approach, special care must be taken when selecting the auxiliary basis set for the potential, thus leading to the concept of a balanced basis set firmly connected to the orbital basis set [25].…”