Related papers: OEP calculations using Slater-type basis functions…
Optical scatterometry is a method to measure the size and shape of periodic micro- or nanostructures on surfaces. For this purpose the geometry parameters of the structures are obtained by reproducing experimental measurement results…
The method of evaluation outlined in a previous work has been utilized here to evaluate certain other three- electron and four- electron atomic integrals involving s Slater-type orbitals and exponential correlation with unlinked $r_{ij}$'s.…
An efficient method for calculating the electronic structure of systems that need a very fine sampling of the Brillouin zone is presented. The method is based on the variational optimization of a "single" (i.e. common to all points in the…
We report state-of-the-art ab initio calculations of the potential energy curve for the $a^3\Sigma_u^+$ state of the lithium dimer conducted to achieve spectroscopic accuracy ($<$1cm$^{-1}$) without any prior adjustment to fit the…
The method of effective interaction, traditionally used in the framework of an harmonic oscillator basis, is applied to the hyperspherical formalism of few-body nuclei (A=3-6). The separation of the hyperradial part leads to a state…
Partial differential equations can be used to model many problems in several fields of application including, e.g., fluid mechanics, heat and mass transfer, and electromagnetism. Accurate discretization methods (e.g., finite element or…
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 developed and implemented a self-consistent density functional method using standard norm-conserving pseudopotentials and a flexible, numerical LCAO basis set, which includes multiple-zeta and polarization orbitals. Exchange and…
Density functional theory has been an essential analysis tool for both theoretical and experimental chemists since accurate hybrid functionals were developed. Here we propose a local hybrid method derived from the optimized effective…
In this study, we propose high-order implicit and semi-implicit schemes for solving ordinary differential equations (ODEs) based on Taylor series expansion. These methods are designed to handle stiff and non-stiff components within a…
This paper addresses a multi-scale finite element method for second order linear elliptic equations with arbitrarily rough coefficient. We propose a local oversampling method to construct basis functions that have optimal local…
The operator method is used to construct the solutions of the problem of the polaron in the strong coupling limit and of the helium atom on the basis of the Hartree-Fock equation. $E_0=-0.1085128052\alpha^2$ is obtained for the polaron…
With the aim of describing bound and continuum states for diatomic molecules, we develop and implement a spectral method that makes use of Generalized Sturmian Functions (GSF) in prolate spheroidal coordinates. In order to master all…
We present a numerical method for computing optimal transition pathways and transition rates in systems of stochastic differential equations (SDEs). In particular, we compute the most probable transition path of stochastic equations by…
While ab initio many-body techniques have been able to successfully describe the properties of light and intermediate mass nuclei based on chiral effective field theory interactions, neutron-rich nuclei still remain out of reach for these…
Density functional theory (DFT) has emerged as one of the most versatile and lucrative approaches in electronic structure calculations of many-electron systems in past four decades. Here we give an account of the development of a…
We present enhancements to the computational efficiency of exact exchange calculations using the density matrix and local support functions. We introduce a numerical method which avoids the explicit calculation the four-center two-electron…
Dirac-Coulomb type differential equation and its solution relativistic exponential-type spinor orbitals are introduced. They provide a revised form for operator invariants, namely Dirac invariants, simplifying the treatment of the angular…
We present a new method to renormalize stochastic differential equations subjected to multiplicative noise. The method is based on the widely used concept of effective potential in high energy physics, and has already been successfully…
The Gaussian Process (GP) based Chance-Constrained Optimal Power Flow (CC-OPF) is an open-source Python code developed for solving economic dispatch (ED) problem in modern power grids. In recent years, integrating a significant amount of…