Related papers: Compact Formulae for Three-Center Nuclear Attracti…
A mid-point technique is suggested to overcome the difficulties in other techniques. The modified effective interaction quark potential which uses to calculate different properties of the NJL model such as the constituent quark mass, the…
By judicious use of extrapolations to the 1-particle basis set limit and $n$-particle calibration techniques, total atomization energies of molecules with up to four heavy atoms can be obtained with calibration accuracy (1 kJ/mol or better,…
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…
Energy integrated neutrino cross sections are integrals of nuclear responses weighted with kinematic prefactors. We decompose the prefactors into a limited set of functions of energy transfer and show the relevant integrals are the moments…
We derive some new inf-sup and sup-inf formulae for the so-called effective multiplication factor arising in the study of reactor analysis. We treat in a same formalism the transport equation and the energy-dependent diffusion equation.
Many modern semiempirical molecular orbital models are built on the neglect of diatomic differential overlap (NDDO) approximation. An in-depth understanding of this approximation is therefore indispensable to rationalize the success of…
This paper studies the numerical computation of integrals, representing estimates or predictions, over the output $f(x)$ of a computational model with respect to a distribution $p(\mathrm{d}x)$ over uncertain inputs $x$ to the model. For…
The energy and analytic gradient are developed for FMO combined with the Hartree-Fock method augmented with three empirical corrections (HF-3c). The auxiliary basis set approach to FMO is extended to perform pair interaction energy…
The distinguishable cluster approximation applied to coupled cluster doubles equations greatly improves absolute and relative energies. We apply the same approximation to the triples equations and demonstrate that it can also improve…
The double exponential formula was introduced for calculating definite integrals with singular point oscillation functions and Fourier integral. The double exponential transformation is not only useful for numerical computations but it is…
A special purpose solver, based on the Magnus expansion, well suited for the integration of the linear three neutrino oscillations equations in matter is proposed. The computations are speeded up to two orders of magnitude with respect to a…
In order to study 4-body atomic collisions such as excitation-ionization, transfer with target excitation, and double electron capture, the calculation of a nine-dimensional numerical integral is often required. This calculation can become…
The numerical computation of the exponentiation of a real matrix has been intensively studied. The main objective of a good numerical method is to deal with round-off errors and computational cost. The situation is more complicated when…
The diffusion Monte Carlo technique is used to calculate and analyze the excitation spectrum of a single 3He atom bound to a cluster with N 4He atoms, with the aim of establishing the most adequate filling ordering of single-fermion orbits…
A formalism for the numerical integration of one- and two-loop integrals is presented. It is based on subtraction terms which remove the soft, collinear and some of the ultraviolet divergences from the integrand. The numerical integral is…
The p-center problem consists in selecting p centers among M to cover N clients, such that the maximal distance between a client and its closest selected center is minimized. For this problem we propose two new and compact integer…
Numerical evaluations of Feynman integrals often proceed via a deformation of the integration contour into the complex plane. While valid contours are easy to construct, the numerical precision for a multi-loop integral can depend…
The evaluation of a matrix exponential function is a classic problem of computational linear algebra. Many different methods have been employed for its numerical evaluation [Moler C and van Loan C 1978 SIAM Review 20 4], none of which…
The machine learning explosion has created a prominent trend in modern computer hardware towards low precision floating-point operations. In response, there have been growing efforts to use low and mixed precision in general scientific…
We present a highly efficient molecular dynamics scheme for calculating the concentration depth profile of dopants in ion irradiated materials. The scheme incorporates several methods for reducing the computational overhead, plus a rare…