Related papers: Derivative discontinuity with localized Hartree-Fo…
We introduce the concept of self-energy dispersion as an error bound on local theories and apply it to the two-dimensional Hubbard model on the square lattice at half-filling. Since the self-energy has no single-particle analog and is not…
Self-interactions (SIs) are a major problem in density functional approximations and the source of serious divergence from experimental results. Here, we propose to optimize density functional total energies in terms of the effective local…
In order to investigate the nature of the phase transition, we study the finite temperature effective potential for the $\lambda \Phi^4$ theory in the Hartree-Fock approximation, which sums up all the daisy and superdaisy diagrams.
Properties of the wave function equivalent potentials introduced by HAL QCD collaboration are studied in a non-relativistic coupled-channel model. The derivative expansion is generalized, and then applied to the energy-independent and…
This work outlines a time-domain numerical integration technique for linear hyperbolic partial differential equations sourced by distributions (Dirac $\delta$-functions and their derivatives). Such problems arise when studying binary black…
Empirical fitting of parameters in approximate density functionals is common. Such fits conflate errors in the self-consistent density with errors in the energy functional, but density-corrected DFT (DC-DFT) separates these two. We…
Density functional approximations to the exchange-correlation energy of Kohn-Sham theory, such as the local density approximation and generalized gradient approximations, lack the well-known integer discontinuity, a feature that is critical…
Four-component Dirac Hartree--Fock is an accurate mean-field method for treating molecular systems where relativistic effects are important. However, the computational cost and complexity of the two-electron interaction makes this method…
Recent results in the literature have provided connections between the so-called turnpike property, near optimality of closed-loop solutions, and strict dissipativity. Motivated by applications in economics, optimal control problems with…
It is found that, in closed-$l$-shell atoms, the exact local exchange potential $v_{\text{x}}(\bf r)$ of the density functional theory (DFT) is very well represented, within the region of every atomic shell, by each of the suitably shifted…
This paper addresses the approximation of fractional harmonic maps. Besides a unit-length constraint, one has to tackle the difficulty of nonlocality. We establish weak compactness results for critical points of the fractional Dirichlet…
The Hartree-Fock (HF) approximation has been an important tool for quantum-chemical calculations since its earliest appearance in the late 1920s, and remains the starting point of most single-reference methods in use today. Intuition…
We want to obtain derivatives in discontinuous program code, where default Algorithmic Differentiation may not perform well. Specifically, we consider discontinuities induced by control flow statements, where meaningful derivatives should…
By exploiting freedoms in the definitions of 'correlation', 'exchange' and 'Hartree' physics in ensemble systems we better generalise the notion of 'exact exchange' (EXX) to systems with fractional occupations functions of the frontier…
For neutral and positively charged atoms and molecules, we prove the existence of infinitely many Hartree-Fock critical points below the first energy threshold (that is, the lowest energy of the same system with one electron removed). This…
Ground state energies and decay widths of particle unstable nuclei are calculated within the Hartree-Fock approximation by performing a complex scaling of the many-body Hamiltonian. Through this transformation, the wave functions of the…
We present a density functional scheme for calculating the pair density (PD) by means of the correlated wave function. This scheme is free from both of problems related to PD functional theory, i.e., (a) the need to constrain the…
The Hartree-Fock-Bogolyubov (HFB) problem for the cutoff local energy-density functional is solved numerically by using the Gor'kov formalism with an exact treatment of the particle continuum. The contributions from the resonant and "gas"…
Ab initio calculations are fundamentally bottlenecked for large systems by the steep computational scaling of solving self-consistent field (SCF) equations. While machine learning offers potential accelerations, existing methods often…
The extension of the density functional theory (DFT) to include pairing correlations without formal violation of the particle-number conservation condition is described. This version of the theory can be considered as a foundation of the…