Unambiguous optimization of effective potentials in finite basis sets

Jacob, Christoph R.

doi:doi:10.1063/1.3670414

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Localization scheme for relativistic spinors

A new method to determine localized complex-valued one-electron functions in the occupied space is presented. The approach allows the calculation of localized orbitals regardless of their structure and of the entries in the spinor coefficient matrix, i.e., one-, two-, and four-component Kramers-restricted or unrestricted one-electron functions with real or complex expansion coefficients. The method is applicable to localization schemes that maximize (or minimize) a functional of the occupied spi...

Exact on-lattice stochastic reaction-diffusion simulations using partial-propensity methods

Stochastic reaction-diffusion systems frequently exhibit behavior that is not predicted by deterministic simulation models. Stochastic simulation methods, however, are computationally expensive. We present a more efficient stochastic reaction-diffusion simulation algorithm that samples realizations from the exact solution of the reaction-diffusion master equation. The present algorithm, called partial-propensity stochastic reaction-diffusion (PSRD) method, uses an on-lattice discretization of th...

The optimization of effective potentials is of interest in density-functional theory (DFT) in two closely related contexts. First, the evaluation of the functional derivative of orbital-dependent exchange-correlation functionals requires the application of optimized effective potential methods. Second, the optimization of the effective local potential that yields a given electron density is important both for the development of improved approximate functionals and for the practical application of embedding schemes based on DFT. However, in all cases this optimization turns into an ill-posed problem if a finite basis set is introduced for the Kohn–Sham orbitals. So far, this problem has not been solved satisfactorily. Here, a new approach to overcome the ill-posed nature of such finite-basis set methods is presented for the optimization of the effective local potential that yields a given electron density. This new scheme can be applied with orbital basis sets of reasonable size and makes it possible to vary the basis sets for the orbitals and for the potential independently, while providing an unambiguous potential that systematically approaches the numerical reference.

Article Outline

INTRODUCTION
THEORETICAL BACKGROUND
COMPUTATIONAL DETAILS
ILL-POSED NATURE OF THE OPTIMIZATION OF EFFECTIVE POTENTIALS
SINGLING OUT ONE OPTIMIZED POTENTIAL
SINGLING OUT THE OPTIMAL OPTIMIZED POTENTIAL
OPTIMAL OPTIMIZED POTENTIALS FOR ATOMS
OPTIMAL OPTIMIZED POTENTIALS FOR MOLECULES
CONCLUSIONS

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KEYWORDS and PACS

Keywords

density functional theory, electron density, optimisation, orbital calculations

PACS

31.15.eg

Exchange-correlation functionals (in current density functional theory)

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http://dx.doi.org/10.1063/1.3670414

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0021-9606 (print)

1089-7690 (online)

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$abstract.society.value is a Member of CrossRef

American Institute of Physics

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