Related papers: OEP calculations using Slater-type basis functions…
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…
We propose a simple linear scaling expression in reciprocal space for evaluating the ion--electron potential of crystalline solids. The expression replaces the long-range ion--electron potential with an equivalent localized charge…
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…
We discuss a variational calculation for nuclear shell-model calculations and propose a new procedure for the energy-variance extrapolation (EVE) method using a sequence of the approximated wave functions obtained by the variational…
This paper advocates use of the atomic orbitals which have direct physical interpretation, i.e. Coulomb Sturmians and hydrogen-like orbitals. They are exponential type orbitals (ETOs). Their radial nodes are shown to be essential in…
We show that both confined atoms and electron-atom scattering can be described by a unified basis set method. The central idea behind this method is to place the atom inside a hard potential sphere, enforced by a standard Slater type basis…
Quantum mechanical methods based on the density functional theory (DFT) offer a realistic possibility of first-principles design of organic donor-acceptor systems and engineered band-gap materials. This promise is contingent upon the…
Due to efficient scaling with electron number N, density functional theory (DFT) is widely used for studies of large molecules and solids. Restriction of an exact mean-field theory to local potential functions has recently been questioned.…
The numerical solution of problems in nonlinear magnetostatics is typically based on a variational formulation in terms of magnetic potentials, the discretization by finite elements, and iterative solvers like the Newton method. The vector…
In many recent applications when new materials and technologies are developed it is important to describe and simulate new nonlinear and nonlocal diffusion transport processes. A general class of such models deals with nonlocal fractional…
A recently proposed method for computer simulations in the isothermal-isobaric (NPT) ensemble, based on Langevin-type equations of motion for the particle coordinates and the ``piston'' degree of freedom, is re-derived by straightforward…
A local optimization method based on Bayesian Gaussian Processes is developed and applied to atomic structures. The method is applied to a variety of systems including molecules, clusters, bulk materials, and molecules at surfaces. The…
The application of error-free transformation (EFT) is recently being developed to solve ill-conditioned problems. It can reduce the number of arithmetic operations required, compared with multiple precision arithmetic, and also be applied…
One-particle Schrodinger equations are considered, e.g., the Hartree--Fock equations, that contain a nonlocal operator, e.g., the Hartree--Fock exchange operator, where this operator depends on the one-particle density-matrix of a…
Probabilistic solvers for ordinary differential equations (ODEs) have emerged as an efficient framework for uncertainty quantification and inference on dynamical systems. In this work, we explain the mathematical assumptions and detailed…
This paper presents an intrinsic approach for addressing control problems with systems governed by linear ordinary differential equations (ODEs). We use computer algebra to constrain a Gaussian Process on solutions of ODEs. We obtain…
Orbital-free density functional theory (OF-DFT) is a promising method for large-scale quantum mechanics simulation as it provides a good balance of accuracy and computational cost. Its applicability to large-scale simulations has been aided…
A new numerical method for solving a scalar ordinary differential equation with a given initial condition is introduced. The method is using a numerical integration procedure for an equivalent integral equation and is called in this paper…
This article studies Gauss-Newton-type methods for over-determined systems to find solutions to bilevel programming problems. To proceed, we use the lower-level value function reformulation of bilevel programs and consider necessary…
Several types of numerical and combinatorial optimization algorithms have been used as useful tools to minimize functional forms. Generally, when those forms are non-linear or occur in problems without a specific optimization method,…