Related papers: An efficient basis set representation for calculat…
Coulomb integrals, i.e., matrix elements of bare or screened Coulomb interaction between one-electron orbitals, are fundamental objects in many approaches developed to tackle the challenging problem of calculating the electronic structure…
We give a detailed account of an $\it{ab}$ $\it{initio}$ spectral approach for the calculation of energy spectra of two active electron atoms in a system of hyperspherical coordinates. In this system of coordinates, the Hamiltonian has the…
The two-center two-electron Coulomb and hybrid integrals arising in relativistic and nonrelativistic ab-initio calculations of molecules are evaluated over the non-integer Slater-type orbitals via ellipsoidal coordinates. These integrals…
A novel Gaussian-Sinc mixed basis set for the calculation of the one-electron electronic structure within a uniform magnetic field in three dimensions is presented. The one-electron system is used to demonstrate the utility of this new…
We proposed a distributed approximating functional method for efficiently describing the electronic dynamics in atoms and molecules in the presence of the Coulomb singularities, using the kernel of a grid representation derived by using the…
We present a fast algorithm to calculate Coulomb/exchange integrals of prolate spheroidal electronic orbitals, which are the exact solutions of the single-electron, two-center Schr\"odinger equation for diatomic molecules. Our approach…
Electronic structure methods for accurate calculation of molecular properties have a high cost that grows steeply with the problem size, therefore, it is helpful to have the underlying atomic basis functions that are less in number but of…
In this paper, which constitutes the first part of the series, we consider calculation of two-centre Coulomb and hybrid integrals over Slater-type orbitals (STOs). General formulae for these integrals are derived with no restrictions on the…
We propose a general method for constructing system-dependent basis functions for correlated quantum chemical calculations. Our construction combines features from several traditional approaches: plane waves, localized basis functions, and…
Evaluating multi-center molecular integrals with Cartesian Gaussian-type basis sets has been a long-standing bottleneck in electronic structure theory calculation for solids and molecules. We have developed a vector-coupling and…
In the framework of the study of helium-like atomic systems possessing the collinear configuration, we propose a simple method for computing compact but very accurate wave functions describing the relevant $S$ state. It is worth noting that…
The paper compares the methods used to calculate matrix elements of the operator of radail electron coordinates in an arbitrary order in the Foldy-Wouthuysen representation and with the use of the Dirac equation for 1s-states of the…
We demonstrate how to determine numerically nearly exact orthonormal orbitals that are optimal for evaluation of the energy of arbitrary (correlated) states of atoms and molecules by minimization of the energy Lagrangian. Orbitals are…
Electronic structure calculation of atoms and molecules, in the past few decades has largely been dominated by density functional methods. This is primarily due to the fact that this can account for electron correlation effects in a…
Molecule-optimized basis sets, based on approximate natural orbitals, are developed for accelerating the convergence of quantum calculations with strongly correlated (multi-referenced) electrons. We use a low-cost approximate solution of…
Exact calculation of electronic properties of molecules is a fundamental step for intelligent and rational compounds and materials design. The intrinsically graph-like and non-vectorial nature of molecular data generates a unique and…
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 Slater orbitals are the natural basis functions in quantum molecular calculations. Three-center repulsion Coulomb-exchange integrals over Slater orbitals are evaluated analytically with arbitrary orbital exponents, first for linear…
An explicitly orbital-dependent correlation energy functional is proposed, which is to be used in combination with the orbital-dependent exchange energy functional in energy-band calculations. It bears a close resemblance to the…
The most advanced techniques using fault-tolerant quantum computers to estimate the ground-state energy of a chemical Hamiltonian involve compression of the Coulomb operator through tensor factorizations, enabling efficient block-encodings…