Related papers: Transferable relativistic Dirac-Slater pseudopoten…
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…
A new method for solving the time-dependent two-center Dirac equation is developed. The time-dependent Dirac wave function is represented as a sum of atomic-like Dirac-Sturm orbitals, localized at the ions. The atomic orbitals are obtained…
In this study, we show that the energy eigenvalues and the eigenfunctions of the Schrodinger equation for the power-law and the logarithmic potential can be easily obtained by using variation technique for special type wave functions. The…
Relativistic atomic structure calculations are carried out in alkaline-earth-metal ions using a semiempirical-core-potential approach. The systems are partitioned into frozen-core electrons and an active valence electron. The core orbitals…
In this paper, we propose an efficient implementation of combining Dynamical Mean field theory (DMFT) with electronic structure calculation based on the local density approximation (LDA). The pseudo-potential-plane-wave method is used in…
We obtain accurate eigenvalues of the one-dimensional Schr\"odinger equation with a Hamiltonian of the form $H_{g}=H+g\delta (x)$, where $\delta (x)$ is the Dirac delta function. We show that the well known Rayleigh-Ritz variational method…
The magnetic, noncollinear parametrization of Dudarev's DFT+$U$ method is generalized to fully-relativistic ultrasoft pseudopotentials. We present the definition of the DFT+$U$ total energy functional, and the calculation of forces and…
We introduce an extended Kepler-Coulomb quantum model in spherical coordinates. The Schr\"{o}dinger equation of this Hamiltonian is solved in these coordinates and it is shown that the wave functions of the system can be expressed in terms…
We solve the problem of electron scattering at a soft temporal potential step. Given the relativistic nature of the problem, we use the Dirac equation, with its spinor wavefunction. We find solutions in terms of hypergeometric functions,…
Spectrum of the Dirac Equation is obtained algebraically for arbitrary combination of Lorentz-scalar and Lorentz-vector Coulomb potentials using the Witten's Superalgebra approach. The result coincides with that, known from the explicit…
We show that one of exact solutions of the second-order Dirac-Coulomb equation were pseudo. In the corresponding original literature, it was considered that the mass of the electron with a Coulomb potential was position-dependent, but the…
We show how to describe the coupling of electrons to non-uniform magnetic fields in the framework of the widely used norm-conserving pseudopotential appro ximation for electronic structure calculations. Our derivation applies to magnetic…
We consider the radial Schr\" odinger equation with the pseudo-Gaussian potential. By making an ansatz to the solution of the eigenvalue equation for the associate Hamiltonian, we arrive at the general exact eigenfunction. The values of…
In this paper we investigate a solution of the Dirac equation for a spin-$\frac{1}2$ particle in a scalar potential well with full spherical symmetry. The energy eigenvalues for the quark particle in $s_{1/2}$ states (with $\kappa=-1$) and…
We have optimized the exponents of Gaussian s and p basis functions for the elements H, B-F, and Al-Cl using the pseudopotentials of Goedecker, Teter, and Hutter [Phys. Rev. B 54, 1703 (1996)] by minimizing the total energy of dimers. We…
We calculate for the first time the static properties of the deuteron, within the framework of supersymmetric quantum mechanics, analytically. A new effective potential and its partner are derived from a superpotential so that all…
We make use of a recently developed method to, not only obtain the exactly known eigenstates and eigenvalues of a number of quasi-exactly solvable Hamiltonians, but also construct a convergent approximation scheme for locating those levels,…
We present an optimization algorithm to construct pseudopotentials and use it to generate a set of Optimized Norm-Conserving Vanderbilt (ONCV) pseudopotentials for elements up to Z=83 (Bi) (excluding Lanthanides). We introduce a quality…
Variational (Rayleigh-Ritz) methods are applied to local quantum field theory. For scalar theories the wave functional is parametrized in the form of a superposition of Gaussians and the expectation value of the Hamiltonian is expressed in…
The Dirac equation for an electron in an external electromagnetic field can be regarded as a singular set of linear equations for the vector potential. Radford's method of algebraically solving for the vector potential is reviewed, with…