Related papers: Molecular Algebraic Geometry: Electronic Structure…
This article is an introduction to a new approach to first principles electronic structure calculation. The starting point is the Hartree-Fock-Roothaan equation, in which molecular integrals are approximated by polynomials by way of Taylor…
This study proposes an approach toward the first principles electronic structure calculation with the aid of symbolic-numeric solving. The symbolic computation enables us to express the Hartree-Fock-Roothaan equation and the molecular…
We explore the existence and behaviour of holomorphic restricted Hartree-Fock (h-RHF) solutions for two-electron problems. Through algebraic geometry, the exact number of solutions with $n$ basis functions is rigorously identified as…
A new electronic structure model is developed in which the ground state energy of a molecular system is given by a Hartree-Fock-like expression with parametrized one- and two-electron integrals over an extended (minimal + polarization) set…
We present a fully grid-based approach for solving Hartree-Fock and all-electron Kohn-Sham equations based on low-rank approximation of three-dimensional electron orbitals. Due to the low-rank structure the total complexity of the algorithm…
This work completes the construction of purely algebraic version of the theory of non-linear quantum chemistry methods. It is shown that at the heart of these methods there lie certain algebras close in their definition to the well-known…
This chapter concerns with the recent development of a new DFT methodology for accurate, reliable prediction of many-electron systems. Background, need for such a scheme, major difficulties encountered, as well as their potential remedies…
The need for accurate calculations on atoms and diatomic molecules is motivated by the opportunities and challenges of such studies. The most commonly-used approach for all-electron electronic structure calculations in general - the linear…
We present a fully numerical framework for the optimization of molecule-specific quantum chemical basis functions within the quantics tensor train format using a finite-difference scheme. The optimization is driven by solving the…
We derive and implement symmetry-projected Hartree-Fock-Bogoliubov (HFB) equations and apply them to the molecular electronic structure problem. All symmetries (particle number, spin, spatial, and complex conjugation) are deliberately…
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…
Analytical Hartree-Fock gradients with respect to the cell parameter have been implemented in the electronic structure code CRYSTAL, for the case of three-dimensional periodicity. The code is based on Gaussian type orbitals, and the…
Exploratory variational pseudopotential density functional calculations are performed for the electronic properties of many-electron systems in the 3D cartesian coordinate grid (CCG). The atom-centered localized gaussian basis set,…
We present fully numerical electronic structure calculations on diatomic molecules exposed to an external magnetic field at the unrestricted Hartree-Fock limit, using a modified version of a recently developed finite element program,…
The Hartree-Fock equation which is the Euler-Lagrange equation corresponding to the Hartree-Fock energy functional is used in many-electron problems. Since the Hartree-Fock equation is a system of nonlinear eigenvalue problems, the study of…
The energy levels of the first few low-lying states of helium and lithium atoms in intense magnetic fields up to $\approx 10^8-10^9$~T are calculated in this study. A pseudospectral method is employed for the computational procedure. The…
The symmetry-projected Hartree--Fock ansatz for the electronic structure problem can efficiently account for static correlation in molecules, yet it is often unable to describe dynamic correlation in a balanced manner. Here, we consider a…
We present here a review of the fundamental topics of Hartree-Fock theory in Quantum Chemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for…
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…
We present a density matrix approach for computing global solutions of Hartree-Fock theory, based on semidefinite programming (SDP), that gives upper and lower bounds on the Hartree-Fock energy of quantum systems. Equality of the upper- and…