The Microscopic Mechanisms Involved in Superexchange

In earlier work, we previously established a formalism that allows to express the exchange energy J vs. fundamental molecular integrals without crystal field, for a fragment A–X–B, where A and B are 3d1 ions and X is a closed-shell diamagnetic ligand. In this article, we recall this formalism and give a physical interpretation: we may rigorously predict the ferromagnetic (J < 0) or antiferromagnetic (J > 0) character of the isotropic (Heisenberg) spin-spin exchange coupling. We generalize our results to ndm ions (3 £ n £ 5, 1 £ m £ 10). By introducing a crystal field we show that, starting from an isotropic (Heisenberg) exchange coupling when there is no crystal field, the appearance of a crystal field induces an anisotropy of exchange coupling, thus leading to a z-z (Ising-like) coupling or a x-y one. Finally, we discuss the effects of a weak crystal field magnitude (3d ions) compared to a stronger (4d ions) and even stronger one (5d ions). In the last step, we are then able to write the corresponding Hamiltonian exchange as a spin-spin one.

Molint 1.0: An Application Programming Interface Framework for the Computation of Molecular Integrals and Their First Derivatives for the Density-Fitted Methods

The efficient computation of molecular integrals and their derivatives is a crucial step in molecular property evaluation in modern quantum chemistry. As an integral tensor decomposition technique, the density-fitting (DF) approach becomes a popular tool to reduce the memory and disk requirements for the electron repulsion integrals. In this study, an application programming interface (API) framework, denoted Molint (MFW), for the computation of molecular integrals and their first derivatives, over contracted Gaussian functions, for the density-fitted methods is reported. The MFW is free software and it includes overlap, dipole, kinetic, potential, metric, and 3-index integrals, and their first derivatives. Furthermore, the MFW provides a smooth approach to build the Fock matrix and evaluate analytic gradients for the density-fitted methods. The MFW is a C++/Fortran hybrid code, which can take advantage of shared-memory parallel programming techniques. Our results demonstrate that the MFW is an efficient and user-friendly API for the computation of molecular integrals and their first derivatives.

Molint 1.0: An Application Programming Interface Framework for the Computation of Molecular Integrals and Their First Derivatives for the Density-Fitted Methods

The efficient computation of molecular integrals and their derivatives is a crucial step in molecular property evaluation in modern quantum chemistry. As an integral tensor decomposition technique, the density-fitting (DF) approach becomes a popular tool to reduce the memory and disk requirements for the electron repulsion integrals. In this study, an application programming interface (API) framework, denoted Molint (MFW), for the computation of molecular integrals and their first derivatives, over contracted Gaussian functions, for the density-fitted methods is reported. The MFW is free software and it includes overlap, dipole, kinetic, potential, metric, and 3-index integrals, and their first derivatives. Furthermore, the MFW provides a smooth approach to build the Fock matrix and evaluate analytic gradients for the density-fitted methods. The MFW is a C++/Fortran hybrid code, which can take advantage of shared-memory parallel programming techniques. Our results demonstrate that the MFW is an efficient and user-friendly API for the computation of molecular integrals and their first derivatives.

On the use of the Obara–Saika recurrence relations for the calculation of structure factors in quantum crystallography

Modern methods of quantum crystallography are techniques firmly rooted in quantum chemistry and, as in many quantum chemical strategies, electron densities are expressed as two-centre expansions that involve basis functions centred on atomic nuclei. Therefore, the computation of the necessary structure factors requires the evaluation of Fourier transform integrals of basis function products. Since these functions are usually Cartesian Gaussians, in this communication it is shown that the Fourier integrals can be efficiently calculated by exploiting an extension of the Obara–Saika recurrence formulas, which are successfully used by quantum chemists in the computation of molecular integrals. Implementation and future perspectives of the technique are also discussed.

Computing Four-Center Two-Electron Coulomb Integrals Using Exponential Transformations and Trapezoidal Rule

The numerical evaluations of the four-center two-electron Coulomb integrals are among the most time-consuming computations involved in molecular electronic structure calculations. In the present paper we extend the double exponential (DE) transform method, previously developed for the numerical evaluation of threecenter one-electron molecular integrals [J. Lovrod, H. Safouhi, Molecular Physics (2019) DOI:10.1030/0026867.2019.1619854], to four-center two-electron integrals. The fast convergence properties analyzed in the numerical section illustrate the advantages of the new approach.