Related papers: Spherical-harmonic-analysis-based optimization of …
A common way to evaluate electronic integrals for polyatomic molecules is to use Becke's partitioning scheme [J. Chem. Phys.88, 2547 (1988)] in conjunction with overlapping grids centered at each atomic site. The Becke scheme was designed…
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…
A general procedure for the optimization of atomic density-fitting basis functions is designed with the balance between accuracy and numerical stability in mind. Given one-electron wavefunctions and energies, weights are assigned to the…
Real-space refinement of atomic models in macromolecular crystallography or in cryo electron microscopy fits a model to a map obtained experimentally. This requires generating model maps of a limited resolution which moreover may vary from…
The auxiliary functions provide efficient computation of integrals arising at the self-consistent field (SCF) level for molecules using Slater-type bases. This applies both in relativistic and non-relativistic electronic structure theory.…
Evaluating multi-center molecular integrals with Cartesian Gaussian-type basis sets has been a long-standing bottleneck in electronic structure theory calculation for solids and molecules. We have developed a vector-coupling and…
The performance of basis sets made of numerical atomic orbitals is explored in density-functional calculations of solids and molecules. With the aim of optimizing basis quality while maintaining strict localization of the orbitals, as…
We propose a unique scheme to construct fully optimized atomic basis sets for density-functional calculations. The shapes of the radial functions are optimized by minimizing the {\it spillage} of the wave functions between the atomic…
Recent microscopy imaging techniques allow to precisely analyze cell morphology in 3D image data. To process the vast amount of image data generated by current digitized imaging techniques, automated approaches are demanded more than ever.…
A new approach for describing the effective electronic states of "atoms in compounds" to study the properties of molecules and condensed matter which are circumscribed by the operators heavily concentrated in atomic cores is proposed. Among…
Single-center two-electron integration is an important core technology in ab initio calculation of atomic and molecular structures. Therefore, this paper reviews and optimizes the method of Zhao et al., and draws a conclusion: Because this…
This paper studies numerical integration over the unit sphere $ \mathbb{S}^2 \subset \mathbb{R}^{3} $ by using spherical $t$-design, which is an equal positive weights quadrature rule with polynomial precision $t$. We investigate two kinds…
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…
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…
The alignment of the frontier orbital energies of an adsorbed molecule with the substrate Fermi level at metal-organic interfaces is a fundamental observable of significant practical importance in nanoscience and beyond. Typical density…
Spherical Bessel functions appear commonly in many areas of physics wherein there is both translation and rotation invariance, and often integrals over products of several arise. Thus, analytic evaluation of such integrals with different…
We derive analytical solutions for the system of two ultracold spin-polarized fermions interacting in p wave and confined in an axially symmetric harmonic trap. To this end we utilize p-wave pseudopotential with an energy-dependent…
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…
3D image processing constitutes nowadays a challenging topic in many scientific fields such as medicine, computational physics and informatics. Therefore, development of suitable tools that guaranty a best treatment is a necessity.…
Spin-weighted spheroidal harmonics are useful in a variety of physical situations, including light scattering, nuclear modeling, signal processing, electromagnetic wave propagation, black hole perturbation theory in four and higher…