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Separation of variables by means of the orbit method is implemented to integrable systems on coadjoint orbits in an $\mathfrak{sl}(4)$ loop algebra. This is a development and a kind of explanation for Sklyanin's procedure of separation of…

A construction of integrable hamiltonian systems associated with different graded realizations of untwisted loop algebras is proposed. Such systems have the form of Euler - Arnold equations on orbits of loop algebras. The proof of…

Localization of molecular orbitals finds its importance in the representation of chemical bonding (and anti-bonding) and in the local correlation treatments beyond mean-field approximation. In this paper, we generalize the intrinsic atomic…

Explicitly-correlated F12 methods are becoming the first choice for high-accuracy molecular orbital calculations, and can often achieve chemical accuracy with relatively small gaussian basis sets. In most calculations, the many three- and…

We compare the results of our two papers with the results of the paper Aratyn H., Gomes J.F., Zimerman A.H., Higher order Painlev\'e equations and their symmetries via reductions of a class of integrable models, J. Phys. A: Math. Theor., V.…

For the investigation of higher order Feynman integrals, potentially with tensor structure, it is highly desirable to have numerical methods and automated tools for dedicated, but sufficiently 'simple' numerical approaches. We elaborate two…

We present a unified treatment of the quantum mechanics of B-factory and neutrino oscillation experiments. While our approach obtains the usual phenomenological predictions for these experiments, it does so without having to invoke…

Analytic energy gradients with respect to nuclear motion are derived for non-singlet compounds in the natural orbital functional theory. We exploit the formulation for multiplets in order to obtain a simple formula valid for any…

The wavefunction for the multiparticle Schr\"odinger equation is a function of many variables and satisfies an antisymmetry condition, so it is natural to approximate it as a sum of Slater determinants. Many current methods do so, but they…

We present methods for the numerical evaluation of the master integrals that appear in the calculation of scattering amplitudes at higher order in perturbative quantum field theory. We follow the general strategy of solving first-order…

The key formula for computing the orbital magnetization of a crystalline system has been recently found [D. Ceresoli, T. Thonhauser, D. Vanderbilt, R. Resta, Phys. Rev. B {\bf 74}, 024408 (2006)]: it is given in terms of a Brillouin-zone…

In this work we propose a novel composite method for accurate calculation of the energies of many-electron atoms. The dominant contribution to the energy (pair energies) are calculated by using explicitly correlated factorisable coupled…

We have developed a McMurchie-Davidson-like recursion formula for efficient evaluation of the Coulomb attraction and interaction matrix elements between two-dimensional primitive Cartesian Gaussian type orbitals. We also present recurrence…

This paper is a self-contained presentation of certain aspects of the theory of weighted Sobolev spaces and elliptic operators on non-compact Riemannian manifolds. Specifically, we discuss (i) the standard and weighted Sobolev Embedding…

In this paper, we propose an orbital iteration based parallel approach for electronic structure calculations. This approach is based on our understanding of the single-particle equations of independent particles that move in an effective…

This article reviews recent developments in multiresolution analysis which make it a powerful tool for the systematic treatment of the multiple length-scales inherent in the electronic structure of matter. Although the article focuses on…

We first give an abstract framework to show the uniqueness of Ground State Solutions (GSS) for a large class of PDEs. To the best of our knowledge, all the existing results in the literature only addressed particular cases. Moreover, our…

The interpretation of experimental spatially resolved scanning tunneling spectroscopy (STS) maps of close-shell molecules on surfaces is usually interpreted within the framework of oneelectron molecular orbitals. Although this standard…

We present an implementation of range separated functionals utilizing the Slater-function on grids in real space in the projector augmented waves method. The screened Poisson equation is solved to evaluate the necessary screened exchange…

Various properties of the general two-center two-electron integral over the explicitly correlated exponential function are analyzed for the potential use in high precision calculations for diatomic molecules. A compact one dimensional…