Extended floating spherical gaussian basis sets for molecules. Generation procedure and result for H2O

A procedure is proposed to generate extended floating spherical gaussian orbital (FSGO) basis sets for molecular SCF calculations by projecting large basis set SCF results onto FSGOs. This replaces the need for repeated evaluation of energy integrals and SCF iterations for extensive non-linear optimizations of FSGOs.     

Integral evaluation in the case of a helium atom positioned off‐center in a spherical box

A variational approach to the problem of multielectron atoms placed off‐center in a spherical box leads to the difficult evaluation of electron repulsion integrals in an environment where spherical symmetry is no longer present. A technique for the evaluation of the electron repulsion integrals generated by this situation is developed and tested for the case of a helium atom placed off‐center in a spherical box. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 459–467, 1999     

Analytical second derivatives of molecular electronic energy integrals obtained by spherical gaussian orbital

In this research, the complete general formulas for the analytical second derivative of the molecular integrals for spherical gaussian orbitals of electronic energy are presented. Formulas were given for the second derivative for orbital exponent, orbital and nuclear cartesian coordinates and coefficients of contracted gaussians. In order to save computational time, the formulas for the second derivative are written in terms of the original integrals. Although the formulas were presented in general for any type of application, the Floating Spherical Gaussian Orbital (FSGO) method is applied to some molecules such as LiH, H₂O and CH₂ (singlet) to check the formulas. The results were compared with the results of the finite difference method. Besides the accuracy of the analytical derivative, the saving in computational time is significant.     

Derivation of a total charge and dipole moment-preserving population analysis for FSGO wavefunctions

A population analysis scheme is derived especially for floating spherical gaussian orbital (FSGO) wavefunctions. The overlap populations are redistributed into the basis FSGO's in such a way that the total charge and dipole moment of the system are preserved. The small set of point charges generated by this population analysis should provide a rapid and convenient way to calculate (i) coulombic potential surfaces outside the molecule and (ii) coulombic intermolecular interaction energies.     

Grid‐based density functional calculations of many‐electron systems

Exploratory variational pseudopotential density functional calculations are performed for the electronic properties of many‐electron systems in the 3D cartesian coordinate grid (CCG). The atom‐centered localized gaussian basis set, electronic density, and the two‐body potentials are set up in the 3D cubic box. The classical Hartree potential is calculated accurately and efficiently through a Fourier convolution technique. As a first step, simple local density functionals of homogeneous electron gas are used for the exchange‐correlation potential, while Hay‐Wadt‐type effective core potentials are employed to eliminate the core electrons. No auxiliary basis set is invoked. Preliminary illustrative calculations on total energies, individual energy components, eigenvalues, potential energy curves, ionization energies, and atomization energies of a set of 12 molecules show excellent agreement with the corresponding reference values of atom‐centered grid as well as the grid‐free calculation. Results for three atoms are also given. Combination of CCG and the convolution procedure used for classical Coulomb potential can provide reasonably accurate and reliable results for many‐electron systems. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Electron momentum distributions and compton profiles of some alkali halides with FSGO model

The electron momentum distributions (EMD's) and Compton profiles (CP's) of LiF, LiCl, NaF and NaCI have been calculated using the floating spherical gaussian orbital (FSGO) model wavefunctions. The calculated FSGO Compton profiles are in good agreement with the available experimental data considering the simplicity of the model used. The calculated EMD and CP values in these systems are nearly equal to the sum of the contributions of respective cations and anions.     

Extended floating spherical Gaussian basis sets for molecules. Alternative correlating orbitals for molecular energy calculations

A procedure previously described for representing large basis SCF results in terms of a smaller floating spherical Gaussian orbital (FSGO) basis set is generalized to apply to the virtual orbitals from the SCF calculation. This provides a method for systematically reducing the dimensions of the virtual space or replacing the virtual orbitals with a simpler, compact basis set. The method is illustrated by application to Lill.     

B‐spline one‐center method for molecular Hartree–Fock calculations

We introduce one‐center method in spherical coordinates to carry out Hartree–Fock calculations. Both the radial wave function and the angular wave function are expanded by B‐splines to deal with electron‐nucleus cusps, which results in the improved convergence for several typical closed‐shell diatomic molecules with moderate basis numbers. B‐splines could represent both the bound state and continuum state wave functions properly, and the present approach has been applied to investigate the ionization dynamics for H₂ in the intense laser field adopting single‐active‐electron model. © 2013 Wiley Periodicals, Inc.     

Evaluation of integrals over STOs on different centers and the complementary convergence characteristics of ellipsoidal‐coordinate and zeta‐function expansions

One‐electron integrals over three centers and two‐electron integrals over two centers, involving Slater‐type orbitals (STOs), can be evaluated using either an infinite expansion for 1/r₁₂ within an ellipsoidal‐coordinate system or by employing a one‐center expansion in spherical‐harmonic and zeta‐function products. It is shown that the convergence characteristics of both methods are complimentary and that they must both be used if STOs are to be used as basis functions in ab initio calculations. To date, reports dealing with STO integration strategies have dealt exclusively with one method or the other. While the ellipsoidal method is faster, it does not always converge to a satisfactory degree of precision. The zeta‐function method, however, offers reliability at the expense of speed. Both procedures are described and the results of some sample calculation presented. Possible applications for the procedures are also discussed. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 1–13, 1999     

Quantum molecular mechanics—a noniterative procedure for the fast Ab Initio calculation of closed shell systems

In this article, we advance the foundations of a strategy to develop a molecular mechanics method based not on classical mechanics and force fields but entirely on quantum mechanics and localized electron‐pair orbitals, which we call quantum molecular mechanics (QMM). Accordingly, we introduce a new manner of calculating Hartree–Fock ab initio wavefunctions of closed shell systems based on variationally preoptimized nonorthogonal electron pair orbitals constructed by linear combinations of basis functions centered on the atoms. QMM is noniterative and requires only one extremely fast inversion of a single sparse matrix to arrive to the one‐particle density matrix, to the electron density, and consequently, to the ab initio electrostatic potential around the molecular system, or cluster of molecules. Although QMM neglects the smaller polarization effects due to intermolecular interactions, it fully takes into consideration polarization effects due to the much stronger intramolecular geometry distortions. For the case of methane, we show that QMM was able to reproduce satisfactorily the energetics and polarization effects of all distortions of the molecule along the nine normal modes of vibration, well beyond the harmonic region. We present the first practical applications of the QMM method by examining, in detail, the cases of clusters of helium atoms, hydrogen molecules, methane molecules, as well as one molecule of HeH⁺ surrounded by several methane molecules. We finally advance and discuss the potentialities of an exact formula to compute the QMM total energy, in which only two center integrals are involved, provided that the fully optimized electron‐pair orbitals are known. © 2012 Wiley Periodicals, Inc.     

On the electronic structure of Li2 (X 1\documentclass{article}\pagestyle{empty}\begin{document}$\Sigma^{+}_{\mathrm{g}}$\end{document}) and its changes with internuclear distance

A compact, yet accurate, and strictly virial‐compliant ab initio electronic wavefunction for ground‐state Li₂ is exploited for a study of the molecule's electronic structure and electron density. Symmetry‐breaking problems that emerge at the single‐configuration level are solved in a multiconfigurational spin‐coupled approach that enables simultaneous optimization of angularly correlated “resonating” configurations. Particular emphasis is placed on the accurate determination of the electron density's bifurcation points and of the quadrupole moment as a function of internuclear distance R. Tentative connections are drawn between the R dependence of the electron density's topological structure and quadrupole moment and that of the electronic wavefunction. Computation of the latter constitutes the first application to systems other than isolated atoms of the optimized basis set generalized multiconfiguration spin‐coupled method, which entails use of nonorthogonal orbitals and Slater‐type basis functions with variationally optimized exponential parameters. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 378–397, 2000     

On the calculation of arbitrary multielectron molecular integrals over Slater‐type orbitals using recurrence relations for overlap integrals I. Single‐center expansion method

The multicenter charge‐density expansion coefficients [I. I. Guseinov, J Mol Struct (Theochem) 417 , 117 (1997)] appearing in the molecular integrals with an arbitrary multielectron operator were calculated for extremely large quantum numbers of Slater‐type orbitals (STOs). As an example, using computer programs written for these coefficients, with the help of single‐center expansion method, some of two‐electron two‐center Coulomb and four‐center exchange electron repulsion integrals of Hartree–Fock–Roothaan (HFR) equations for molecules were also calculated. Accuracy of the results is quite high for the quantum numbers, screening constants, and location of STOs. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 146–152, 2000     

Localization function study of excitation processes in a set of small isoelectronic molecules

Electron localization function (ELF) theory is used to characterize changes that occur upon excitation from ground singlet to first excited triplet states in a series of isoelectronic 16‐electron molecules including H₂CCH₂, HNCH₂, H₂CO, HNNH, HNO, and O₂ (ground triplet to excited singlet). ELF allows one to visualize lone pair or nonbonding electrons, and in these cases the π→π* or n→π excitation processes involved lead to an effective 90° rotation of the electronic structure about one heavy atom center and consequent distortion towards pyramidal symmetry about both heavy atom centers. The heavy atom bond lengths change very little in those cases where effectively two‐center three‐electron bonds can be formed (HNNH, HNO, and O₂) while a significant lengthening occurs in those cases where hydrogen atoms prevent such interactions (H₂CCH₂, HNCH₂, and H₂CO). It is shown that both ELF basin populations and atoms‐in‐molecules (AIM) delocalization indices reflect expected bond orders for conventional single and double bonds provided one compares the ratio of the molecular quantities rather than their absolute magnitudes. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1702–1711, 2001     

6‐31G* basis set for third‐row atoms

Medium basis sets based upon contractions of Gaussian primitives are developed for the third‐row elements Ga through Kr. The basis functions generalize the 6‐31G and 6‐31G* sets commonly used for atoms up to Ar. A reexamination of the 6‐31G* basis set for K and Ca developed earlier leads to the inclusion of 3d orbitals into the valence space for these atoms. Now the 6‐31G basis for the whole third‐row K through Kr has six primitive Gaussians for 1s, 2s, 2p, 3s, and 3p orbitals, and a split‐valence pair of three and one primitives for valence orbitals, which are 4s, 4p, and 3d. The nature of the polarization functions for third‐row atoms is reexamined as well. The polarization functions for K, Ca, and Ga through Kr are single set of Cartesian d‐type primitives. The polarization functions for transition metals are defined to be a single 7f set of uncontracted primitives. Comparison with experimental data shows good agreement with bond lengths and angles for representative vapor‐phase metal complexes. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 976–984, 2001     

Confinement effects on the electronic structure of M‐shell atoms: A study with explicitly correlated wave functions

The ground and some excited states of Na and Mg atoms confined at the center of a spherical box with impenetrable walls are studied. Variational wave functions including dynamic correlations and configuration mixing have been obtained. Level crossings induced by confinement have been analyzed in terms of the energy of the occupied orbitals of the M shell and the weight of the different configurations. Confinement effects on the correlation energy have been studied. The parameterized optimized effective potential and the variational Monte Carlo methods have been employed. A cut off‐factor has been included to account for the hard wall confinement.     

Explicitly correlated configuration interaction studies using spherical Gaussians. II. Exploratory studies on LiH

Ab initio self-consistent-field and configuration interaction studies have been carried out on the ground state of the LiH molecule at its equilibrium distance. Floating spherical Gaussian basis orbitals (FSGO ) were employed, along with spherical Gaussian correlation factors, using the procedure described in the preceding paper. A near-Hartree–Fock function was found using only 13 FSGO . Exploratory configuration interaction studies recovered approximately 73% of the inner shell correlation energy and approximately 56% of the total correlation energy with five configurations plus the Hartree–Fock configuration. These studies indicate that, by using spherical Gaussian correlation factors, direct introduction of interelectronic coordinates into trial wave functions can be accomplished for molecular systems. It was also shown that correlating configurations need not utilize the full Hartree–Fock basis, but may use substantially smaller bases and still recover correlation energy effectively. Finally, the results indicate that, in spite of their improper cusp behavior, FSGOS and spherical Gaussian correlation factors can be used for construction of high accuracy wave functions.     

Tuning the Electronic Properties of the Dative N−B Bond with Associated O−B Interaction: Electron Localizability Indicator from X‐Ray Wavefunction Refinement

Despite the immense growth in interest in difluoroborate dyes, the nature of the interactions of the boron atom within the N‐BF₂‐O kernel is not yet fully understood. Herein, a set of real‐space bonding indicators is used to quantify the electronic characteristics of the dative N?B bond in difluoroborate derivatives. The atoms‐in‐molecules (AIM) partitioning scheme is complemented by the electron localizability indicator (ELI‐D) approach, and both were applied to experimental and theoretical electron‐density distributions (X‐ray constrained wavefunction fitting vs. DFT calculations). Additionally, Fermi orbital analysis was introduced for small DFT models to support and extend the findings for structures that contain BF₂.     

Use of promolecular ASA density functions as a general algorithm to obtain starting MO in SCF calculations

Atomic shell approximation (ASA) constitutes a way to fit first‐order density functions to a linear combination of spherical functions. The ASA fitting method makes use of positive definite expansion coefficients to ensure appropriate probability distribution features. The ASA electron density is sufficiently accurate for the practical implementation of quantum similarity measures, as was proved in previous published work. Here, a new application of the ASA density formalism is analyzed, and employed to obtain an initial guess of the density matrix for SCF procedures. The number of cycles needed to assess the convergence criterion in electronic energy calculations appears comparable to or less than those obtained by other means. Several molecular structures of different classes, including organic systems and metal complexes, were chosen as representative test cases. In addition, an ASA basis set for atoms Sc‐Kr fitted to an ab initio 6‐311G basis set is also presented. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

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