Related papers: Unique Solutions to Hartree-Fock Equations for Clo…
The density of an atom in a state of well-defined angular momentum has a specific finite spherical harmonic content, without and with interactions. Approximate single-particle schemes, such as the Hartree, Hartree-Fock, and Local Density…
We study a generalized defocusing Hartree equation with nonlocal exchange potential and repulsive Hartree--Fock interaction. Using an inverse optimal problem (IOP) approach, we prove the existence and uniqueness of ground state solutions.…
Many-electron systems at substantial finite temperatures and densities present a major challenge to density functional theory. Very little is known about the free-energy behavior over the temperature range of interest, for example, in the…
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…
We prove the existence of solutions of the reduced Hartree-Fock equations at finite temperature for a periodic crystal with a small defect, and show total screening of the defect charge by the electrons. We also show the convergence of the…
We present a group theoretical study of the symmetry-broken unrestricted Hartree-Fock orbitals and electron densities in the case of a two-dimensional N-electron single quantum dot (with and without an external magnetic field). The breaking…
Electromagnetic and weak transitions tell us a great deal about the structure of atomic nuclei. Yet modeling transitions can be difficult: it is often easier to compute the ground state, if only as an approximation, than excited states. One…
For the Hirshfeld-I atom-in-molecule model, associated single-atom energies and interaction energies at the Hartree-Fock level are determined efficiently in one-electron Hilbert space. In contrast to most other approaches, the energy terms…
We study the ground state properties of an atom with nuclear charge $Z$ and $N$ bosonic ``electrons'' in the presence of a homogeneous magnetic field $B$. We investigate the mean field limit $N\to\infty$ with $N/Z$ fixed, and identify three…
We calculate the ground state phase diagram of the homogeneous electron gas in three dimensions within the Hartree-Fock approximation and show that broken symmetry states are energetically favored at any density against the homogeneous…
Ground state properties of the superheavy elements (SHE) with Z from 108 to 128 and N from 150 to 192 are investigated using both the Skyrme-Hartree-Fock method with a density-independent contact pairing interaction and the…
The usual Hartree-Fock approximation to the Hubbard model is based on eigenstates of the electron number operator. But this formulation is not unique. A different (and inequivalent) version, formulated in terms of Nambu two-component…
We study the states of one and two atoms in a rotating ring lattice in a Hubbard type tight-binding model. The model is developed carefully from basic principles in order to properly identify the physical observables. The one-particle…
We derive the photoionisation cross section in dipole approximation for many-electron atoms and ions for neutron star magnetic field strengths in the range of 10^7 to 10^9 T. Both bound and continuum states are treated in adiabatic…
A practical electronic structure method in which a two-body functional is the fundamental variable is constructed. The basic formalism of our method is equivalent to Hartree-Fock density matrix functional theory [M. Levy in {\it Density…
Simplified Hartree-Fock computations are carried out on the atoms He through Ne, using orthonormalized basis functions for the 1s, 2s and 2p orbitals dependent on three parameters. Using Mathematica with the new Apple M1 chip, computations…
We consider a trapped atomic ensemble of interacting bosons in the presence of a single trapped ion in a quasi one dimensional geometry. Our study is carried out by means of the newly developed multilayer-multiconfiguration time-dependent…
In this contribution, I will discuss two topics related to the clustering of atomic nuclei. The first is dual character of the ground state. Recently, it was pointed out that the ground states of atomic nuclei have dual character of shell…
This paper reports an implementation of Hartree-Fock linear response with complex orbitals for computing electronic spectra of molecules in a strong external magnetic fields. The implementation is completely general, allowing for…
We calculate ground state energies in the Brueckner-Hartree-Fock theory for $N$ electrons (with $N\le 20$) confined to a circular quantum dot and in presence of a static magnetic field. Comparison with the predictions of Hartree-Fock,…