Related papers: Evaluation of Hylleraas-CI atomic integrals by int…
Hylleraas-Configuration Interaction (Hy-CI) calculations on the ground $1^1$S state of helium atom are presented using s-, p-, d-, and f-Slater orbitals of both real and complex form. Techniques of construction of adapted configurations,…
Some typical overlap/potential energy integrals which occur in the use of extended Hylleraas-configuration interaction (E-Hy-CI) functions with Slater-type orbital (STO) basis for two-electron atomic structure calculations, have been…
The total energies of twenty eight bound S-, P-, D-, F-, G-, H-, and I-states in the three-electron systems Li atom and Be+ ion, respectively, are determined with the use of the Configuration Interaction (CI) with Slater orbitals and L-S…
Some typical kinetic energy integrals which arise in the application of extended Hylleraas-configuration interaction (E-Hy-CI) function in the framework of Rayleigh-Ritz method of variation, have been evaluated analytically for two-electron…
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…
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…
The Slater-type orbital basis with non-integer principal quantum numbers is a physically and mathematically motivated choice for molecular electronic structure calculations in both non-relativistic and relativistic theory. The…
Recursion relations for Hylleraas three-electron integral are obtained in a closed form by using integration by parts identities. Numerically fast and well stable algorithm for the calculation of the integral with high powers of…
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…
Calculations of the leading quantum electrodynamics effects in few electron systems involve singular matrix elements of the inter-electronic distances of the form $1/r_i^3$ and $1/r_{ij}^3$. Integrals that result when the nonrelativistic…
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 derive direct single-stage numerical evaluation of the electronic overlap integral between arbitrary atomic orbitals (including STOs). Integration is over cartesian co-ordinates, and replaces previous sums over 'special' functions. The…
A closed form expression for the three-electron Hylleraas integral involving the inverse quadratic power of one inter-particle coordinate is obtained, and recursion relations are derived for positive powers of other coordinates. This result…
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…
This work describes the fully analytical method for calculation of the molecular integrals over Slater-type orbitals with non-integer principal quantum numbers. These integrals are expressed through relativistic molecular auxiliary…
In recent years, energy correlators have emerged as powerful observables for probing the fragmentation dynamics of high-energy collisions. We introduce the first numerical strategy for calculating energy correlators using the Hamiltonian…
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…
In this work we demonstrate that the heat bath configuration interaction (HCI) and its semistochastic extension can be used to treat relativistic effects and electron correlation on an equal footing in large active spaces to calculate the…
We present an efficient method of inclusion of the core-valence correlations into the configuration interaction (CI) calculations. These correlations take place in the core area where the potential of external electrons is approximately…
The Hylleraas coordinates $s=r_{1}+r_{2}$, $t=r_{1}-r_{2}$, $u=|{\bf r}_{1}-{\bf r}_{2}|$ are the natural coordinates for the determination of properties of the Helium atom, the positive ions of its isoelectronic sequence, and the negative…