Correlation potential in density functional theory at the GWA level: Spherical atoms

Abstract

As part of a project to obtain better optical response functions for nano materials and other systems with strong excitonic effects we here calculate the exchange-correlation (XC) potential of density-functional theory (DFT) at a level of approximation which corresponds to the dynamicallyscreened-exchange or GW approximation. In this process we have designed a new numerical method based on cubic splines which appears to be superior to other techniques previously applied to the "inverse engineering problem" of DFT, i.e., the problem of finding an XC potential from a known particle density. The potentials we obtain do not suffer from unphysical ripple and have, to within a reasonable accuracy, the correct asymptotic tails outside localized systems. The XC potential is an important ingredient in finding the particle-conserving excitation energies in atoms and molecules and our potentials perform better in this regard as compared to the LDA potential, potentials from GGA:s, and a DFT potential based on MP2 theory.

Linear density response function within the time-dependent exact-exchange approximation

“…This basis set has shown to be ideally suited for solving the LSS equation, 4 an equation known to be numerically unstable when using other methods and basis functions. 31,32,33,34,35 We have here found that cubic splines also provide an efficient method for solving the equation for f x .…”

“…If the density is that given by EXX we have selfconsistency and the resulting f x is that presented here. If we instead start with a better density, much closer to the exact one, the corresponding eigenvalue differences will be much closer to real particle-hole excitation energies 4 and we will obtain an f x which will still obey the f -sum rule while giving rise to an optical spectrum with a continuum starting in almost the correct place -because the highest occupied exact DF eigenvalue equals the the negative of the ionization potential. 30 This topic is further discussed together with numerical results in Sec.…”

“…The present paper is one in a series of papers 1,2,3,4 reporting on work with the overall aim of finding computationally efficient but still accurate ways of calculating excited-state properties of systems in which excitonic effects play an important role. Traditionally, such effects have been studied by solving approximate versions of the Bethe-Salpeter equation in which the particlehole interaction is taken to be a statically screened Coulomb potential.…”

Efficient Temperature-Dependent Green’s Function Methods for Realistic Systems: Using Cubic Spline Interpolation to Approximate Matsubara Green’s Functions

“…In chemical physics, cubic spline interpolation has been applied as a basis to solve a complex differential and integral Schrödinger [13][14][15], Dirac [16], and Sham-Schlüter equations [17], Thomas-Fermi model [18], in calculations of vibrational and rotational spectra [19] and many other cases [20][21][22][23][24][25][26][27][28][29][30][31][32]. Since the derivatives of third and higher order polynomials are discontinuous, cubic spline interpolation is limited to applications that are not sensitive to the smoothness of derivatives higher than second order.…”

Justifying quasiparticle self-consistent schemes via gradient optimization in Baym–Kadanoff theory

“…The first is to constrain the types of G 0 or U xc being considered based on physical knowledge or intuition. For example, it is known that forcing U xc to be a local potential is sufficient to create a minimum for the Klein functional [32,36,37]. However, a local potential can not directly and consistently describe a number of simple non-local effects, e.g., Fock exchange which automatically removes problematic electron self-interaction effects.…”