Related papers: Many-electron integrals over gaussian basis functi…
A precise understanding of mechanisms governing the dynamics of electrons in atoms and molecules subjected to intense laser fields has a key importance for the description of attosecond processes such as the high-harmonic generation and…
Gaussian processes are popular and flexible models for spatial, temporal, and functional data, but they are computationally infeasible for large datasets. We discuss Gaussian-process approximations that use basis functions at multiple…
We introduce a novel, systematic method for the complete symbolic reduction of multi-loop Feynman integrals, leveraging the power of generating functions. The differential equations governing these generating functions naturally yield…
The key task of physical simulation is to solve partial differential equations (PDEs) on discretized domains, which is known to be costly. In particular, high-fidelity solutions are much more expensive than low-fidelity ones. To reduce the…
We present a method which computes many-electron energies and eigenfunctions by a full configuration interaction which uses a basis of atomistic tight-binding wave functions. This approach captures electron correlation as well as atomistic…
We describe the analytic calculation of the master integrals required to compute the two-mass three-loop corrections to the $\rho$ parameter. In particular, we present the calculation of the master integrals for which the corresponding…
The finite basis set method is commonly used to calculate atomic spectra, including QED contributions such as bound-electron self-energy. Still, it remains problematic and underexplored for vacuum-polarization calculations. We fill this gap…
We present a formalism for the calculation of multi-particle one-loop amplitudes, valid for an arbitrary number N of external legs, and for massive as well as massless particles. A new method for the tensor reduction is suggested which…
The parallel orbital-updating approach is an orbital/eigenfunction iteration based approach for solving eigenvalue problems when many eigenpairs are required. It has been proven to be efficient, for instance, in electronic structure…
The method of evaluation outlined in a previous work has been utilized here to evaluate certain other three- electron and four- electron atomic integrals involving s Slater-type orbitals and exponential correlation with unlinked $r_{ij}$'s.…
We describe a new method of calculation of generic multi-loop master integrals based on the numerical solution of systems of difference equations in one variable. We show algorithms for the construction of the systems using…
Organic electronics is a rapidly developing technology. Typically, the molecules involved in organic electronics are made up of hundreds of atoms, prohibiting a theoretical description by wavefunction-based ab-initio methods.…
From the literature it is known that orthogonal polynomials as the Jacobi polynomials can be expressed by hypergeometric series. In this paper, the authors derive several contiguous relations for terminating multivariate hypergeometric…
Methods for calculating lower bounds to the exact energy using the variance of the upper bound energy are discussed and explored. All the matrix elements of the Hamiltonian squared are collected and considered, and those for which no known…
In this study, we employ Euler's method and Richardson's extrapolation to solve a triple integral, which is then transformed into a third-order initial value problem. Our objective is to resolve the computational challenges associated with…
In this work we include electron-electron interaction beyond Hartree-Fock level in our non-equilibrium Green's function approach by a crude form of GW through the Single Plasmon Pole Approximation. This is achieved by treating all…
Stochastic orbital techniques offer reduced computational scaling and memory requirements to describe ground and excited states at the cost of introducing controlled statistical errors. Such techniques often rely on two basic operations,…
Density Functional Theory has long struggled to obtain the exact exchange-correlational (XC) functional. Numerous approximations have been designed with the hope of achieving chemical accuracy. However, designing a functional involves…
In this paper we discuss the reliability of two computational methods (numerical integration on Cartesian grids, and population analysis) used for evaluating scalar quantities related to the nature of electronic transitions. These…
Traditional theory of many-electron atoms and ions is based on the coefficients of fractional parentage and matrix elements of tensorial operators, composed of unit tensors. Then the calculation of spin-angular coefficients of radial…