Related papers: Derivative discontinuity with localized Hartree-Fo…
Rigorous mathematical foundations of density functional theory are revisited, with some use of infinitesimal (nonstandard) methods. A thorough treatment is given of basic properties of internal energy and ground-state energy functionals…
We study the properties of the hadron-hadron potentials and quark-antiquark potentials from the viewpoint of the channel coupling. We demonstrate that, for finite quark masses, the coupling to the two-hadron continuum induces the imaginary…
One of the few exact results for the description of the time-evolution of an inhomogeneous, interacting many-particle system is given by the Harmonic Potential Theorem (HPT). The relevance of this theorem is that it sets a tight constraint…
The Hartree-Fock equation is a fundamental equation in many-electron problems. It is of practical importance in quantum chemistry to find solutions to the Hartree-Fock equation. The self-consistent field (SCF) method is a standard numerical…
The Hartree-Fock approximation for bosons employs variational wave functions that are a combination of permanents. These are bosonic counterpart of the fermionic Slater determinants, but with the significant distinction that the…
Projected Hartree-Fock theory provides an accurate description of many kinds of strong correlations but does not properly describe weakly-correlated systems. On the other hand, single-reference methods such as configuration interaction or…
We study the regional controllability problem for delayed fractional control systems through the use of the standard Caputo derivative. First, we recall several fundamental results and introduce the family of fractional-order systems under…
The recent progress in the localized covariant density functional constrained by the relativistic Hartree-Fock theory is briefly presented by taking the Gamow-Teller resonance in 90Zr as an example. It is shown that the constraints…
We establish necessary and sufficient conditions for the N-representability of the universal one-electron reduced density matrix functional. Functionals satisfying these conditions are guaranteed to yield variational upper bounds on the…
We propose an efficient and accurate solver for the nonlocal potential in the Davey-Stewartson equation using nonuniform FFT (NUFFT). A discontinuity in the Fourier transform of the nonlocal potential causes accuracy locking if the…
We study the well-posedness of the reduced Hartree-Fock model for molecules and perfect crystals when taking into account a self-generated magnetic field. We exhibit a critical value $\alpha_c > 0$ such that, if the fine structure constant…
The derivative discontinuity of the exchange-correlation functional of density-functional theory is cast as the difference of two types of electron affinities. We show that standard Kohn-Sham calculations can be used to calculate both…
We propose a novel scheme to bring reduced density matrix functional theory (RDMFT) into the realm of density functional theory (DFT) that preserves the accurate density functional description at equilibrium, while incorporating accurately…
We present an accurate and efficient framework for real-space Hubbard-corrected density functional theory. In particular, we obtain expressions for the energy, atomic forces, and stress tensor suitable for real-space finite-difference…
We consider a Cauchy problem of energy-critical fractional Schr\"odinger equation with Hartree nonlinearity below the energy space. Using a method of randomization of functions on $\mathbb{R}^d$ associated with the Wiener decomposition,…
The locality hypothesis in density-functional theory (DFT) states that the functional derivative of the Hohenberg-Kohn universal functional can be expressed as a local multiplicative potential function, and this is the basis of DFT and of…
Hamiltonian Monte Carlo has emerged as a standard tool for posterior computation. In this article, we present an extension that can efficiently explore target distributions with discontinuous densities. Our extension in particular enables…
Using the self-consistent Hartree-Fock approximation for spinless electrons at zero temperature, we study the persistent current of the interacting electron gas in a one-dimensional continuous ring containing a single $\delta$ barrier. We…
We present a novel energy-based localization procedure able to localize molecular orbitals into specific spatial regions. The method is applied to several cases including both conjugated and non-conjugated systems. The obtained localized…
The Hartree-Fock based diagonalization is a computational method for the investigation of the low-energy properties of correlated electrons in disordered solids. The method is related to the quantum-chemical configuration interaction…