Related papers: Molecular calculations with B functions
Analytical expressions are derived for classical trajectories in repulsive Coulomb plus multi-step attractive potentials. Thereafter the closed form expressions are obtained for classical deflection functions. The expressions are expected…
We establish a link between quantum mechanical molecular simulations and the transfer matrix of a molecule. The transfer matrix (T-matrix) of an object provides a complete description of its electromagnetic response. Once the T-matrices of…
Molecular dynamics (MD) simulations are used in biochemistry, physics, and other fields to study the motions, thermodynamic properties, and the interactions between molecules. Computational limitations and the complexity of these problems,…
A general approach to evaluation of two-centre two-electron exponential integrals with arbitrary parameters is presented. The results for the Born-Oppenheimer potential for various excited states of molecular hydrogen with Ko{\l}…
The paper proposes an approximate expression for calculating very complex one-dimensional integrals depending on the parameter $a$. These integrals often occur in computational problems theory of magnetic solitons. The resulting analytical…
This paper formalizes the use of integral and differential cumulants for measurements of multi-particle event-by-event transverse momentum fluctuations, rapidity fluctuations, as well as net charge fluctuations. This enables the…
In this paper a double integral containing two Gaussian hypergeometric functions is discussed. The integral is not found in the literature and a direct computation is not (yet) possible. Therefore, a complete different integral is computed…
The derivatives of a Boolean function are defined up to any order. The Taylor and MacLaurin expansions of a Boolean function are thus obtained. The last corresponds to the ring sum expansion (RSE) of a Boolean function, and is a more…
Numerical projection methods are elaborated for the calculation of eigenstates of the non-relativistic many-particle Coulomb Hamiltonian with selected rotational and parity quantum numbers employing shifted explicitly correlated Gaussian…
We point out that a typical two-electron distribution function in atoms and molecules often called the intracule depends sensitively on the electron-electron repulsion which leads to the so-called Coulomb correlation. The difference between…
$B$ functions are a class of relatively complicated exponentially decaying basis functions. Since the molecular multicenter integrals of the much simpler Slater-type functions are notoriously difficult, it is not at all obvious why $B$…
All-atom dynamics simulations are an indispensable quantitative tool in physics, chemistry, and materials science, but large systems and long simulation times remain challenging due to the trade-off between computational efficiency and…
The molecular electric dipole, quadrupole and octupole moments of a selected set of 21 spin-compensated molecules are determined employing the extended version of the Piris natural orbital functional 6 (PNOF6), using the triple-$\zeta$…
We investigated an integral representation of a complex function which was obtained from the molecular beam magnetic resonance, and named it as `$g$- function' because it was connected with Gamma function as a special case. We introduced a…
Molecular biology and biochemistry interpret microscopic processes in the living world in terms of molecular structures and their interactions, which are quantum mechanical by their very nature. Whereas the theoretical foundations of these…
The well-known spatial integration schemes in molecular electronic structure theory, immune to cusps and point singularities of some kind at atomic positions, use a set of weighting functions to split the integrand into a sum of…
Explicitly correlated quantum chemical calculations require calculations of five types of molecular integrals beyond the standard electron repulsion integrals. We present a novel scheme, which utilises general ideas of the…
We introduce machine learning models of quantum mechanical observables of atoms in molecules. Instant out-of-sample predictions for proton and carbon nuclear chemical shifts, atomic core level excitations, and forces on atoms reach…
Quantum chemical studies of reactivity involve calculations on a large number of molecular structures and comparison of their energies. Already the set-up of these calculations limits the scope of the results that one will obtain, because…
In the article we outline the set of Matlab functions that enable the computation of elliptic Integrals and Jacobian elliptic functions for real arguments. Correctness, robustness, efficiency and accuracy of the functions are discussed in…