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The hydrogen molecules $H_2$ and $(H_2)_2$ are analyzed with electronic correlations taken into account between the $1s$ electrons exactly. The optimal single-particle Slater orbitals are evaluated in the correlated state of $H_2$ by…
The Dirac equation for H$_2^+$ is solved numerically by expansion in a basis set of two-center exponential functions, using different kinetic balance schemes. Very high precision (27-32 digits) is achieved, either with the dual kinetic…
Correlation functions measured as a function of $\Delta \eta, \Delta \phi$ have emerged as a powerful tool to study the dynamics of particle production in nuclear collisions at high energy. They are however subject, like any other…
An analytical-numeric calculation method of extremely complicated integrals is presented. These integrals appear often in magnet soliton theory. The appropriate analytical continuation and a corresponding integration contour allow to reduce…
An alternative multipole expansion of the correlation term is derived. Modified spherical Bessel type functions which simplify as a summation of multiple orders of basic trigonometric functions are generated from this new method. We use…
We point out that a typical two-electron distribution function in atoms and molecules often called the intracule depends sensitively on the electron-electron repulsion which leads to the so-called Coulomb correlation. The difference between…
We investigate the possibility of using a transcorrelated Hamiltonian to describe electron correlation. Amethod to obtain transcorrelatedwavefunctionswas developed based on the mathematical framework of the bi-variational principle. This…
The paper proposes an approximate expression for calculating very complex one-dimensional integrals depending on the parameter $a$. These integrals often occur in computational problems theory of magnetic solitons. The resulting analytical…
Structural properties of a finite number ($N = 2 - 20$) of point charges (classical electrons) confined laterally in a two-dimensional two-minima potential are calculated as a function of the distance ($d$) between the minima. The particles…
We present a reciprocal space technique for the calculation of the Coulomb integral in two dimensions in systems with reduced periodicity, i.e., finite systems, or systems that are periodic only in one dimension. The technique consists in…
This chapter gives an introduction to qualitative and quantitative topological analyses of molecular electronic transitions. Among the possibilities for qualitatively describing how the electronic structure of a molecule is reorganized upon…
We consider density functionals for exchange and correlation energies in two-dimensional systems. The functionals are constructed by making use of exact constraints for the angular averages of the corresponding exchange and correlation…
The unitary coupled cluster (UCC) approximation is one of the more promising wave-function ans\"atze for electronic structure calculations on quantum computers via the variational quantum eigensolver algorithm. However, for large systems…
Multiple Mellin-Barnes integrals are often used for perturbative calculations in particle physics. In this context, the evaluation of such objects may be performed through residues calculations which lead to their expression as multiple…
Core-polarization interactions are investigated in low-energy electron elastic scattering from the atoms In,Sn,Eu,Au and At through the calculation of their electron affinities. The complex angular momentum method wherein is embedded the…
We develop a fundamental theory of the long-range electrostatic interactions in two-dimensional crystals by performing a rigorous study of the nonanalyticities of the Coulomb kernel. We find that the dielectric functions are best…
Entropic entanglement measures of a two-dimensional system of two Coulombically interacting particles confined in an anisotropic harmonic potential are discussed in dependence on the anisotropy and the interaction strength. The harmonic…
By the use of the variational method with exponential trial functions the upper and lower bounds of energy are calculated for a number of non-relativistic three-body Coulomb and nuclear systems. The formulas for calculation of upper and…
We have obtained an analytic expression for the ring diagrams contribution to the correlation energy of a two dimensional electron liquid as a function of the uniform fractional spin polarization. Our results can be used to improve on the…
We present two related techniques to measure the two-point correlation function and the power spectrum with edge correction in any spatial dimensions. The underlying algorithm uses fast Fourier transforms for calculating the two-point…