Related papers: An efficient basis set representation for calculat…
In computational molecular science, calculation of electrostatic interactions involving charged atoms - the strongest interactions in condensed phases, is a major bottleneck. We propose a quantum-classical algorithm for fast, yet, accurate…
Explicitly-correlated F12 methods are becoming the first choice for high-accuracy molecular orbital calculations, and can often achieve chemical accuracy with relatively small gaussian basis sets. In most calculations, the many three- and…
The Complex Kohn variational method for electron-polyatomic molecule scattering is formulated using an overset grid representation of the scattering wave function. The overset grid consists of a central grid and multiple dense,…
For a given many-electron molecule, it is possible to define a corresponding one-electron Schr\"odinger equation, using potentials derived from simple atomic densities, whose solution predicts fairly accurate molecular orbitals for single-…
The three-body Schr\"odinger equation of the H$_2^+$ hydrogen molecular ion with Coulomb potentials is solved in perimetric coordinates using the Lagrange-mesh method. The Lagrange-mesh method is an approximate variational calculation with…
A fully analytical approximation for the observable characteristics of many-electron atoms is developed via a complete and orthonormal hydrogen-like basis with a single-effective charge parameter for all electrons of a given atom. The basis…
An outstanding challenge in chemical computation is the many-electron problem where computational methodologies scale prohibitively with system size. The energy of any molecule can be expressed as a weighted sum of the energies of…
Electronic structure calculations are mostly carried out with Coulomb potential singularity adapted basis sets like STO or contracted GTO. With other basis or for heavy elements the pseudopotentials may appear as a practical alternative.…
The emergence of machine learning methods in quantum chemistry provides new methods to revisit an old problem: Can the predictive accuracy of electronic structure calculations be decoupled from their numerical bottlenecks? Previous attempts…
Encoding the electronic structure of molecules using 2-electron reduced density matrices (2RDMs) as opposed to many-body wave functions has been a decades-long quest as the 2RDM contains sufficient information to compute the exact molecular…
Leveraging matrix sparsity has proven a fruitful strategy for accelerating quantum chemical calculations. Here we present the hierarchical SOS-MP2 algorithm, which uses hierarchical matrix ($\mathcal{H}^{2}$) compression of the electron…
Quantum algorithms for molecular electronic structure have been developed with lower computational scaling than their classical counterparts, but emerging quantum hardware is far from being capable of the coherence,connectivity and gate…
A detailed formulation of the relativistic plane-wave Born approximation for inelastic collisions of charged particles with free atoms and positive ions is presented. The wave functions of the target atom or ion are calculated from a…
This paper aims at introducing the formal foundations of the application of reduced density-matrix theory and Green's function theory to the analysis of molecular electronic transitions. For this sake, their mechanics, applied to specific…
A recently developed density functional method, within Hohenberg-Kohn-Sham framework, is used for faithful description of atoms, molecules in Cartesian coordinate grid, by using an LCAO-MO ansatz. Classical Coulomb potential is obtained by…
An alternative methodology to evaluate two-electron-repulsion integrals based on numerical approximation is proposed. Computational chemistry has branched into two major fields with methodologies based on quantum mechanics and classical…
Methods of angular momenta are modified and used to solve some actual problems in quantum mechanics. In particular, we re-derive some known formulas for analytical and numerical calculations of matrix elements of the vector physical…
A general method is described for finding algebraic expressions for matrix elements of any one- and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional…
We study the decomposition of the Coulomb integrals of periodic systems into a tensor contraction of six matrices of which only two are distinct. We find that the Coulomb integrals can be well approximated in this form already with small…
A general procedure for the optimization of atomic density-fitting basis functions is designed with the balance between accuracy and numerical stability in mind. Given one-electron wavefunctions and energies, weights are assigned to the…