Related papers: Many-electron integrals over gaussian basis functi…
An algorithm for the systematic analytical approximation of multi-scale Feynman integrals is presented. The algorithm produces algebraic expressions as functions of the kinematical parameters and mass scales appearing in the Feynman…
Coulomb interactions that occur in electronic structure calculations are correlated by allowing basis function components of the interacting densities to polarize, thereby reducing the magnitude of the interaction. Exchange integrals of…
Computation of the spherical harmonic rotation coefficients or elements of Wigner's d-matrix is important in a number of quantum mechanics and mathematical physics applications. Particularly, this is important for the Fast Multipole Methods…
We implement and benchmark the frozen core approximation, a technique commonly adopted in electronic structure theory to reduce the computational cost by means of mathematically fixing the chemically inactive core electron states. The…
We present a fast, adaptive multiresolution algorithm for applying integral operators with a wide class of radially symmetric kernels in dimensions one, two and three. This algorithm is made efficient by the use of separated representations…
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…
An efficient all-electron G$^0$W$^0$ method and a quasiparticle selfconsistent GW (QSGW) method for molecules are proposed in the molecular orbital space with the full random phase approximation. The convergence with basis set is examined.…
We present a detailed description of the recent idea for a direct decomposition of Feynman integrals onto a basis of master integrals by projections, as well as a direct derivation of the differential equations satisfied by the master…
We investigate the contributions from the $3\sigma_{g}$ and $1\pi_{u}$ and molecular orbitals in high-order harmonic generation in $N_{2}$, with particular emphasis on quantum-interference effects. We consider both the physical processes in…
In electronic structure theory, variational methods offer a valuable paradigm for approximating electronic ground states. However, for historical reasons, this principle is mostly restricted to model chemistries in pre-defined fixed basis…
Analytical Hartree-Fock gradients with respect to the cell parameter have been implemented in the electronic structure code CRYSTAL, for the case of three-dimensional periodicity. The code is based on Gaussian type orbitals, and the…
One of the major computational bottlenecks in one-body reduced density matrix (1RDM) functional theory is the evaluation of approximate 1RDM functionals and their derivatives. The reason is that more advanced approximate functionals are…
A numerical integration method for guiding-center orbits of charged particles in toroidal fusion devices with three-dimensional field geometry is described. Here, high order interpolation of electromagnetic fields in space is replaced by a…
New algebraic approach to analytical calculations of D-dimensional integrals for multi-loop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of multi-loop Feynman integrals, such as integration by parts…
The need for accurate calculations on atoms and diatomic molecules is motivated by the opportunities and challenges of such studies. The most commonly-used approach for all-electron electronic structure calculations in general - the linear…
The new combined formulas have been established for the complex and real rotation-angular functions arising in the evaluation of two-center overlap integrals over arbitrary atomic orbitals in molecular coordinate system. These formulas can…
A recently developed density functional method, within Hohenberg-Kohn-Sham framework, is used for faithful description of atoms, molecules in Cartesian coordinate grid, by using an LCAO-MO ansatz. Classical Coulomb potential is obtained by…
Highly oscillatory integrals of composite type arise in electronic engineering and their calculations is a challenging problem. In this paper, we propose two Gaussian quadrature rules for computing such integrals. The first one is…
Choosing a basis set is the first step of a quantum chemistry calculation and it sets its maximum accuracy. This choice of orbitals is limited by strong technical constraints as one must be able to compute a large number of six dimensional…
We justify and evaluate backflow-threebody wavefunctions for a two component system of electrons and protons. Based on the generalized Feynman-Kacs formula, many-body perturbation theory, and band structure calculations, we analyze the use…