Related papers: A tight distance-dependent estimator for screening…
We extend the tight distance-dependent estimator proposed by Hollman et al. [J. Chem. Phys. 142, 154106 (2015)] for the three-center Coulomb integrals over Gaussian atomic orbitals to handle the two-center case. We also propose minor…
We derive distance-dependent estimators for two-center and three-center electron repulsion integrals over a short-range Coulomb potential, $\textrm{erfc}(\omega r_{12})/r_{12}$. These estimators are much tighter than one based on the…
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…
Good robust estimators can be tuned to combine a high breakdown point and a specified asymptotic efficiency at a central model. This happens in regression with MM- and tau-estimators among others. However, the finite-sample efficiency of…
In this paper methods for calculations of multi-center integrals of squared Coulomb potentials and Slater-type orbitals (STO) are derived. These integrals are necessary for accurate lower bounds to energy levels of molecular systems. All…
To improve the efficiency of Gaussian integral evaluation on modern accelerated architectures FLOP-efficient Obara-Saika-based recursive evaluation schemes are optimized for the memory footprint. For the 3-center 2-particle integrals that…
We present an efficient implementation of periodic Gaussian density fitting (GDF) using the Coulomb metric. The three-center integrals are divided into two parts by range-separating the Coulomb kernel, with the short-range part evaluated in…
Various many-body perturbation theory techniques for calculating electron behavior rely on {\it W}, the screened Coulomb interaction. Computing {\it W} requires complete knowledge of the dielectric response of the electronic system, and the…
The Slater orbitals are the natural basis functions in quantum molecular calculations. Three-center repulsion Coulomb-exchange integrals over Slater orbitals are evaluated analytically with arbitrary orbital exponents, first for linear…
In this document, we briefly review the two-electron integral algorithms based on the range-separated algorithms and Fourier transform integral algorithms that are implement ed in the PySCF package. For each integral algorithm, we estimate…
The three-dimensional half-shell t-matrix for a sharply cut-off Coulomb potential is analytically derived together with its asymptotic form without reference to partial wave expansion. The numerical solutions of the three-dimensional…
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…
We introduce a scheme to include many-body screening processes explicitly into a set of self-consistent equations for electronic structure calculations using the Gutzwiller approximation. The method is illustrated by the application to a…
The evaluation of electrostatic energy for a set of point charges in a periodic lattice is a computationally expensive part of molecular dynamics simulations (and other applications) because of the long-range nature of the Coulomb…
We present a reciprocal space technique for the calculation of the Coulomb integral in two dimensions in systems with reduced periodicity, i.e., finite systems, or systems that are periodic only in one dimension. The technique consists in…
We perform an integral reduction for the 3-loop effective gauge coupling and screening mass of QCD at high temperatures, defined as matching coefficients appearing in the dimensionally reduced effective field theory (EQCD). Expressing both…
An integral scheme for the efficient evaluation of two-center integrals over contracted solid harmonic Gaussian functions is presented. Integral expressions are derived for local operators that depend on the position vector of one of the…
Third-order lensing statistics contain a wealth of cosmological information that is not captured by second-order statistics. However, the computational effort for estimating such statistics on forthcoming stage IV surveys is prohibitively…
Various properties of the general two-center two-electron integral over the explicitly correlated exponential function are analyzed for the potential use in high precision calculations for diatomic molecules. A compact one dimensional…
We introduce an accurate and efficient method for a class of nonlocal potential evaluations with free boundary condition, including the 3D/2D Coulomb, 2D Poisson and 3D dipolar potentials. Our method is based on a Gaussian-sum approximation…