Multipole expansions for numerical orbital products

The product of two numerically defined atomic angular momentum orbitals at different centers is considered. The product can be expanded about a third center on the line segment joining the two centers. A numerical procedure for evaluating the expansion functions is developed. The application of the expansion to the evaluation of four‐center electron–electron repulsion integrals is discussed. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

A rigorous and optimized strategy for the evaluation of the Boys function kernel in molecular electronic structure theory

This work is focused on the efficient evaluation of the Boys function located at the heart of Coulomb and exchange type electron integrals. Different evaluation strategies for individual orders and arguments of the Boys function are used to achieve a minimal number of floating‐point operations. Based on previous work of other groups, two similar algorithms are derived that are compared based on both accuracy and efficiency: The first algorithm combines the work of Gill et al. (Int. J. Quantum Chem. 1991, 40, 745) and Kazuhiro Ishida (Int. J. Quantum Chem. 1996, 59, 209 and following work), amplifying the benefits of the two strategies. © 2015 Wiley Periodicals, Inc.     

Role of electron–electron coalescence density in density functional theory

An expression for the evaluation of electron–electron coalescence density as a functional of the density for any electron system is proposed. The formula, clarifies previously advanced upper bounds for this quantity and provides a method to independently estimate the system‐averaged on‐top exchange–correlation hole. The relationship with the on‐top pair density shows that producing the true electron–electron coalescense should be considered as a leading physical requirement for trial wave functions in any energy minimization scheme. © 2002 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Variational treatment on the energy of the He‐sequence ground state with weakest bound electron potential model theory

The concept of spin–orbital of the weakest bound electron is described used to construct the antisymmetric wave function of atomic or ionic systems within weakest bound electron potential model theory (WBEPM theory). The total energies of He‐sequence (Z = 2–9) in the ground states is calculated with a variational method. The effect of fixed orbital approximation is discussed quantitatively. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Recursion formula for electron repulsion integrals over Hermite polynomials

A method for computing electron repulsion integrals over contracted Gaussian functions is described in which intermediate integrals over Hermite polynomials are generated by a “pre‐Hermite” recursion (PHR) step before the conversion to regular integrals. This greatly reduces the floating‐point operation counts inside the contraction loops, where only simple “scaling”‐type operations are required, making the method efficient for contracted Gaussians, particularly of high angular momentum. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Calculating electron binding energies for quadratic fermion Hamiltonian by virtue of the IEO method

In this work, we discuss how to use the invariant eigen‐operator (IEO) method to derive the electron binding energies for the quadratic fermion Hamiltonian. We find that the task of solving the energy gap of fermion Hamiltonian can be ascribed to simply solving a standard eigenvalue problem of a numerical matrix, which is determined by the parameters of the given Hamiltonian. The IEO method provides us with a new approach for solving quadratic Hamiltonians in a more convenient and concise way. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Rayleigh–Ritz variation method and connected‐moments polynomial approach

We show that the connected‐moments polynomial approach proposed recently is equivalent to the well known Rayleigh–Ritz variation method in the Krylov space. We compare the latter with one of the original connected‐moments methods by means of a numerical test on an anharmonic oscillator. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Morse potential eigen‐energies through the asymptotic iteration method

The eigen‐energies of the rotating Morse potential based on the original Pekeris approximation are obtained by means of the asymptotic iteration method. This approach is applied to several diatomic molecules, and it is shown that the numerical results for the eigen‐energies are all in excellent agreement with the ones obtained before. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Calculation of transition matrix elements by nonsingular orbital transformations

A general strategy is described for the evaluation of transition matrix elements between pairs of full class CI wave functions built up from mutually nonorthogonal molecular orbitals. A new method is proposed for the counter‐transformation of the linear expansion coefficients of a full CI wave function under a nonsingular transformation of the molecular‐orbital basis. The method, which consists in a straightforward application of the Cauchy–Binet formula to the definition of a Slater determinant, is shown to be simple and suitable for efficient implementation on current high‐performance computers. The new method appears mainly beneficial to the calculation of miscellaneous transition matrix elements among individually optimized CASSCF states and to the re‐evaluation of the CASCI expansion coefficients in Slater‐determinant bases formed from arbitrarily rotated (e.g., localized or, conversely, delocalized) active molecular orbitals. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Thinking inside the box: Novel linear scaling algorithm for Coulomb potential evaluation

Beginning with the Poisson equation, and expanding the electronic potential in terms of sine functions, the natural orbitals for describing the particle‐in‐a‐box problem, we find that simple analytic forms can be found for the evaluation of the Coulomb energy for both the interacting and non‐interacting system of N‐electrons in a box. This method is reminiscent of fast‐Fourier transform and scales linearly. To improve the usefulness of this result, we generalize the idea by considering a molecular system, embedded in a box, within which we determine the electrostatic potential, in the same manner as that described for our model systems. Within this general formalism, we consider both periodic and aperiodic recipes with specific application to systems described using Gaussian orbitals; although in principle the method is seen to be completely general. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Minimum cross‐entropy estimation of internally folded densities from Compton profiles

The internally folded density or reciprocal form factor B( r ) of many‐electron systems is tightly estimated from the knowledge of a small discrete set of values of the Compton profile J( q ). In doing so, the minimum cross‐entropy technique is employed. A numerical analysis of the approximations is carried out for the Helium atom. © 2002 John Wiley & Sons, Inc. Int J Quantum Chem, 2002     

A Dirac–Fock self-consistent field method for closed-shell molecules including Breit interaction

We present a method for including the Breit interaction in relativistic self-consistent field calculations for closed-shell molecular systems using atomic basis spinors of kinetically balanced Gaussian-type functions. The method extends the formalism described in a previous paper [A. Mohanty and E. Clementi, Int. J. Quantum Chem. 39 , 487–517 (1991)] that dealt with the two-electron effect due to Coulomb interaction only. It is shown that both frequency-dependent and frequency-independent Breit interactions can be treated on equal footing, and the corresponding matrix elements are evaluated following the well-known Fourier transform technique applied to electron repulsion integral evaluation in nonrelativistic molecular calculations.     

Quantum fidelity for analyzing atoms and fragments in molecule: Application to similarity,chirality, and aromaticity

Quantum information theory is applied to formulate a new technique for dealing with molecular similarity problems. In this technique, the so‐called quantum fidelity appears to be a counterpart of the conventional similarity measure due to Carbo (Carbo, R.; Leyda, L.; Arnau, M. Int J Quantum Chem 1980, 17, 1185). We define many‐body spin‐free density matrices for atoms and fragments in molecule, and compute corresponding fidelity measures for molecular subsystems. It allows us to treat the problem from the beginning within a many‐electron setting. The approach is employed for analyzing similarity between free atoms and atoms in molecule. A new chirality index, as based on the fidelity between molecule and its mirror image, is suggested to be an approximately additive nonnegative quantity. We also examine a local aromaticity by computing the fidelity measures for benzenoid fragments in polyaromatic hydrocarbons. A detailed study of the proposed indices is reported at the ab initio or semiempirical levels. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Scaling relations,virial theorem,and energy densities for long‐range and short‐range density functionals

Decomposition of the Coulomb electron–electron interaction into a long‐range and a short‐range part is described within the framework of density functional theory, deriving some scaling relations and the corresponding virial theorem. We study the behavior of the local density approximation in the high‐density limit for the long‐range and the short‐range functionals by carrying out a detailed analysis of the correlation energy of a uniform electron gas interacting via a long‐range‐only electron–electron repulsion. Possible definitions of exchange and correlation energy densities are discussed and clarified with some examples. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

On the calculation of arbitrary multielectron molecular integrals over Slater‐type orbitals using recurrence relations for overlap integrals. III. Auxiliary functions \documentclass{article}\pagestyle{empty}\begin{document}$Q_{nn'}^{q}$\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$G_{-nn'}^{q}$\end{document}

The auxiliary functions $Q_{nn'}^{q}(p,pt)$ and $G_{-nn'}^{q}(p_{a},p,pt)$ which are used in our previous paper [Guseinov, I. I.; Mamedov, B. A. Int J Quantum Chem 2001, 81, 117] for the computation of multicenter electron‐repulsion integrals over Slater‐type orbitals (STOs) are discussed in detail, and the method is given for their numerical computation. The present method is suitable for all values of the parameters p_a, p, and pt. Three‐ and four‐center electron‐repulsion integrals are calculated for extremely large quantum numbers using relations for auxiliary functions obtained in this paper. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Comment on “On the original proof by reductio ad absurdum of the Hohenberg–Kohn theorem for many‐electron Coulomb systems”

We argue with Kryachko's criticism [Int J Quantum Chem 2005, 103, 818] of the original proof of the second Hohenberg‐Kohn theorem. The Kato cusp condition can be used to refute a “to‐be‐refuted” statement as an alternative to the original proof by Hohenberg and Kohn applicable for Coulombic systems. Since alternative ways to prove falseness of the “to‐be‐refuted” statement in a reduction ad absurdum proof do not exclude each other, Kryachko's criticism is not justified. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

The rotation‐vibration spectrum of diatomic molecules with the tietz‐hua rotating oscillator

The Tietz‐Hua (TH) potential is one of the very best analytical model potentials for the vibrational energy of diatomic molecules. By using the Nikiforov‐Uvarov method, we have obtained the exact analytical s‐wave solutions of the radial Schrödinger equation for the TH potential. The energy eigenvalues and the corresponding eigenfunctions are calculated in closed forms. Some numerical results for diatomic molecules are also presented. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Basis sets generation: Relation between Adamowicz's and the maximum overlap method

It is shown that the method of Adamowicz for basis sets reduction [Int. J. Quantum Chem. 19 , 545 (1981)] is, in practice, a particular case of the method of maximum overlap. The relationships between these two methods are discussed analytically and by means of a simple numerical example.     

Exact S‐wave solution of the trigonometric pöschl‐teller potential

The trigonometric Pöschl‐Teller (PT) potential describes the diatomic molecular vibration. By using the Nikiforov‐Uvarov method, we have obtained the exact analytical s‐wave solutions of the radial Schrödinger equation (SE) for the trigonometric PT potential. The energy eigenvalues and corresponding eigenfunctions are calculated in closed forms. Some numerical results are presented too. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012