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The authors in their previous papers obtained compact, arbitrarily accurate expressions for two-center one- and two-electron relativistic molecular integrals expressed over Slater-type orbitals. In this present study, the accuracy limits of…
Multiresolution analysis of electronic structure affords the opportunity to capture the full physics of atomic cores in a systematically improvable manner. Applying new techniques, we demonstrate for the first time that multiresolution…
The electron repulsion integrals over the Slater-type orbitals with non-integer principal quantum numbers are considered. These integrals are useful in both non-relativistic and relativistic calculations of many-electron systems. They…
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…
Theoretical approaches of electronic transport in correlated molecules usually consider an extended molecule, which includes, in addition to the molecule itself, parts of electrodes. In the case where electron correlations remain confined…
An eikonal expansion is used to provide systematic corrections to the eikonal approximation through order $1/k^2$, where $k$ is the wave number. Electron wave functions are obtained for the Dirac equation with a Coulomb potential. They are…
The double exponential formula was introduced for calculating definite integrals with singular point oscillation functions and Fourier-integrals. The double exponential transformation is not only useful for numerical computations but it is…
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…
Implementation of Effective Core Potentials (ECPs) into the molecular scattering suite UKRmol+ is presented together with a set of calculations for a range of targets relevant for plasma modeling. Continuum description in scattering and…
Empirically correlated density matrices of N-electron systems are investigated. Exact closed-form expressions are derived for the one- and two-electron reduced density matrices from a general pairwise correlated wave function. Approximate…
We present an efficient algorithm for one- and two-component relativistic exact-decoupling calculations. Spin-orbit coupling is thus taken into account for the evaluation of relativistically transformed (one-electron) Hamiltonian. As the…
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…
We consider electronic exchange and correlation effects in density-functional calculations of two-dimensional systems. Starting from wave function calculations of total energies and electron densities of inhomogeneous model systems, we…
I study the Feynman integrals needed to compute two-loop self-energy functions for general masses and external momenta. A convenient basis for these functions consists of the four integrals obtained at the end of Tarasov's recurrence…
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…
Three-centre nuclear attraction integrals, which arise in density functional and \textit{ab initio} calculations, are one of the most time-consuming computations involved in molecular electronic structure calculations. Even for relatively…
This revisit gives a survey on the analytical methods for the inverse exponential Radon transform which has been investigated in the past three decades from both mathematical interests and medical applications such as nuclear medicine…
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 work we propose a novel composite method for accurate calculation of the energies of many-electron atoms. The dominant contribution to the energy (pair energies) are calculated by using explicitly correlated factorisable coupled…
Exposing a molecule to intense light pulses may bring this molecule to a nonstationary quantum state, thus launching correlated dynamics of electronic and nuclear subsystems. Although much had been achieved in the understanding of…