Related papers: Recurrence relations for four-electron integrals o…

Recursive algorithms for computing the Frobenius norm of a real array are proposed, based on hypot, a hypotenuse function. Comparing their relative accuracy bounds with those of the BLAS routine DNRM2 it is shown that the proposed…

We use a post-Gaussian variational approach to non-perturbatively study a general class of interacting bosonic quantum field theories with generalized dipole symmetries and fractonic behaviour. We find that while a Gaussian approach allows…

We present a method for a recursive graphical construction of Feynman diagrams with their correct multiplicities in quantum electrodynamics. The method is first applied to find all diagrams contributing to the vacuum energy from which all…

An analytical-numeric calculation method of extremely complicated integrals is presented. These integrals appear often in magnet soliton theory. The appropriate analytical continuation and a corresponding integration contour allow to reduce…

In this work we present a coupled-cluster theory for the propagation of multireference electronic systems initiating at general quantum mechanical states. Our formalism is based on the infinitesimal analysis of modified cluster operators,…

We develop our method to prove quantum superintegrability of an integrable 2D system, based on recurrence relations obeyed by the eigenfunctions of the system with respect to separable coordinates. We show that the method provides rigorous…

An improved algorithm to evaluate the nonrelativistic three-electron Hylleraas-Configuration Interaction (Hy-CI) kinetic energy integrals over Slater orbitals and the Hamiltonian in Hylleraas coordinates is shown. The resulting analytical…

This paper introduces and analyses the new grid-based tensor approach for approximate solution of the eigenvalue problem for linearized Hartree-Fock equation applied to the 3D lattice-structured and periodic systems. The set of localized…

We construct a new scheme of approximation of any multivalued algebraic function $f(z)$ by a sequence $\{r_{n}(z)\}_{n\in \mathbb{N}}$ of rational functions. The latter sequence is generated by a recurrence relation which is completely…

In this paper we give efficient algorithms for computing second-, third-, and fourth-order linear recurrences. We also present an algorithm scheme for computing terms with the indices $N,\ldots,N+n-1$ of an $n$th-order linear recurrence.…

This short note addresses Hodge integrals over the hyperelliptic locus. Recently Afandi computed, via localisation techniques, such one-descendant integrals and showed that they are Stirling numbers. We give another proof of the same…

This paper presents the equality of finite index sums of Bessel func- tions containing arbitrary numbers of terms. These reduce to the familiar three term recursion formulas in simple cases.

We present a novel theory and implementation for computing coupled electronic and quantal nuclear subsystems on a single potential energy surface, moving beyond the standard Born-Oppenheimer (BO) separation of nuclei and electrons. We…

The cubic spline interpolation method, the Runge--Kutta method, and the Newton-Raphson method are extended to dual versions (developed in the context of dual numbers). This extension allows the calculation of the derivatives of complicated…

In a recent paper, Cohl and Costas-Santos derived a number of interesting multi-derivative and multi-integral relations for associated Legendre and Ferrers functions in which the orders of those functions are changed in integral steps.…

In a previous paper a new approach has been introduced for computing, recursively and numerically, one-loop tensor integrals. Here we describe a few modifications of the original method that allow a more efficient numerical implementation…

The impact of residual electron correlation beyond the equation-of-motion coupled-cluster singles and doubles approximation (EOM-CCSD) on positions and widths of electronic resonances is investigated. To establish a method that accomplishes…

This article proposes new perspectives for developing derivative based numerical algorithms, supported by the introduction of a generalized derivative operators. It demonstrates that these operators have the potential to enhance and extend…

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…

A new explicitly correlated functional form for expanding the wave function of an N-particle system with arbitrary angular momentum and parity is presented. We develop the projection-based approach, numerically exploited in our previous…