相关论文: Performance of numerical approximation on the calc…
We present a variational approach to evaluate relativistic corrections of order \alpha^2 to the Bethe logarithm for the ground electronic state of the Coulomb two center problem. That allows to estimate the radiative contribution at…
In this work, the transition matrix elements for inelastic electron--electron scattering are investigated. The angular part is given by spherical harmonics. For the weighted radial wave function overlap, analytic expressions are derived in…
We investigate the numerical approximation of integrals over $\mathbb{R}^d$ equipped with the standard Gaussian measure $\gamma$ for integrands belonging to the Gaussian-weighted Sobolev spaces $W^\alpha_p(\mathbb{R}^d, \gamma)$ of mixed…
The dynamic structure factor ${\tilde S}({\bf k},\omega)$ and the two-particle distribution function $g({\bf r},t)$ of ions in a Coulomb crystal are obtained in a closed analytic form using the harmonic lattice (HL) approximation which…
We give a detailed account of an $\it{ab}$ $\it{initio}$ spectral approach for the calculation of energy spectra of two active electron atoms in a system of hyperspherical coordinates. In this system of coordinates, the Hamiltonian has the…
Three-centre nuclear attraction integrals, which arise in density functional and \textit{ab initio} calculations, are one of the most time-consuming computations involved in molecular electronic structure calculations. Even for relatively…
The presence of outliers can significantly degrade the performance of ellipse fitting methods. We develop an ellipse fitting method that is robust to outliers based on the maximum correntropy criterion with variable center (MCC-VC), where a…
Circular targets are widely used in LiDAR-camera extrinsic calibration due to their geometric consistency and ease of detection. However, achieving accurate 3D-2D circular center correspondence remains challenging. Existing methods often…
Virtual two-loop corrections to scattering amplitudes are a key ingredient to precision physics at collider experiments. We compute the full set of planar master integrals relevant to five-point functions in massless QCD, and use these to…
The analysis of RHIC hydrogen gas jet target polarimeter measurements of transverse analyzing powers $A_\text{N}(t)$ in proton-nucleus scattering requires accurate Coulomb corrections to both spin-flip and non-flip amplitudes. These…
In this study, the one-center expansion formulas in terms of complete orthonormal sets of -exponential type orbitals (-ETOs,) are established for the Slater type orbitals (STOs) and Coulomb-Yukawa like correlated interaction potentials…
Many boundary element integral equation kernels are based on the Green's functions of the Laplace and Helmholtz equations in three dimensions. These include, for example, the Laplace, Helmholtz, elasticity, Stokes, and Maxwell's equations.…
Based on the tensor method, a q-analoque of the spin-orbit coupling is introduced in a q-deformed Schroedinger equation, previously derived for a central potential. Analytic expressions for the matrix elemnets of the representation j=l\pm…
We present a new adaptive method for electronic structure calculations based on novel fast algorithms for reduction of multivariate mixtures. In our calculations, spatial orbitals are maintained as Gaussian mixtures whose terms are selected…
In this paper, we propose an orbital iteration based parallel approach for electronic structure calculations. This approach is based on our understanding of the single-particle equations of independent particles that move in an effective…
We investigate the existence of resonances for two-centers Coulomb systems with arbitrary charges in two dimensions, defining them in terms of generalised complex eigenvalues of a non-selfadjoint deformation of the two-centers Schr\"odinger…
Accurate predictions for hydrogen molecular levels require the treatment of electrons and nuclei on an equal footing. While nonrelativistic theory has been effectively formulated this way, calculation of relativistic and quantum…
We describe a method for imposing the correct electron-nucleus (e-n) cusp in molecular orbitals expanded as a linear combination of (cuspless) Gaussian basis functions. Enforcing the e-n cusp in trial wave functions is an important asset in…
We present a new hybrid method to solve the relativistic Hartree-Fock-Roothan equations where the one- and two-electron radial integrals are evaluated numerically by defining the basis functions on a grid. This procedure reduces the…
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…