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In this work, we present a general formulation for the evaluation of many-electron integrals which arise when traditional one particle expansions are augmented with explicitly correlated Gaussian geminal functions. The integrand is expressed as a product of charge distributions, one for each electron, multiplied by one or more Gaussian geminal factors. Our formulation begins by focusing on the quadratic form that arises in the general n-electron integral. Using the Rys polynomial method for the evaluation of potential energy integrals, we derive a general formula for the evaluation of any n-electron integral. This general expression contains four parameters ω, θ, v, and h, which can be evaluated by an examination of the general quadratic form. Our analysis contains general expressions for any n-electron integral over s-type functions as well as the recursion needed to build up arbitrary angular momentum. The general recursion relation requires at most n + 1 terms for any n-electron integral. To illustrate the general method, we develop explicit expressions for the evaluation of two, three, and four particle electron repulsion integrals as well as two and three particle overlap and nuclear attraction integrals. We conclude our exposition with a discussion of a preliminary computational implementation as well as general computational requirements. Implementation on parallel computers is briefly discussed. [ABSTRACT FROM AUTHOR]

Perturbed localized molecular orbitals (LMOs), correct to first order in an applied static perturbation and consistent with a chosen localization functional, are calculated using analytic derivative techniques. The formalism is outlined for a general static perturbation and variational localization functionals. Iterative and (formally) single-step approaches are compared. The implementation employs an iterative sequence of 2×2 orbital rotations. The procedure is verified by calculations of molecular electric-field perturbations. Boys LMO contributions to the electronic static polarizability and the electric-field perturbation of the expectation value are calculated and analyzed for ethene, ethyne, and fluoroethene (H2C==CHF). For ethene, a comparison is made with results from a Pipek–Mezey localization. The calculations show that a chemically intuitive decomposition of the calculated properties is possible with the help of the LMO contributions and that the polarizability contributions in similar molecules are approximately transferable. [ABSTRACT FROM AUTHOR]

We propose a method, using low order, Rayleigh Schrödinger perturbation theory (RSPT), for systematically increasing the accuracy of traditional, orbital-based, ab initio electronic structure computations. The method is designed to be equally applicable to closed- or open-shell systems. The interelectron interaction is partitioned into long- and short-range components using an expression containing an arbitrary smoothing parameter, γ. The smooth, nonsingular, long-range component of the interelectron interaction is retained in the reference Hamiltonian, and the exponentially-short-range component is included in the perturbation. Modified Fock operators are introduced to prevent spurious core shrinkage. Orbital-based methods are employed for the reference problem. Explicitly correlated Gaussian geminal basis functions are used for variational solution of the RSPT equations. The computational burden shifts from solution of the reference problem to that of the RSPT equations as the extent of smoothing is increased, i.e., as γ is decreased. It is shown that smoothing the interelectron interaction out to a distance of about one Bohr for the helium atom is a reasonable compromise yielding satisfactory rates of convergence of both CI and RSPT expansions. The accuracy of the computed energy increases by two decimal digits for each additional perturbation order in the wave function. Expanding the wave function through third order for γ = 2 bohr[SUP-1] yields the helium atom energy in error by only 4 nanohartrees. [ABSTRACT FROM AUTHOR]

Optimized geometries and relative energies for three states of the C4 molecule have been obtained from single-reference configuration interaction (SRCI) calculations. The 1Σ+g state, which is formed without activation from the dimerization of ground state C2 molecules, is calculated to lie approximately 25 kcal above the 3Σ-g state. At the SRCI level, a rhombic form is calculated to lie 1.2 kcal below the triplet form; consideration of the Davidson correction reduces this difference to 0.4 kcal, inclusion of a second set of diffuse d functions increased the difference only by about 0.2 kcal. Consideration of these effects, the difference in zero-point energy and previous results for methylene leads to a final estimated separation of 4.9 kcal, favoring the rhombus. Electron density distribution analysis for the rhomb is consistent with the existence of a bond between inverted sp2 carbon atoms. To aid the detection of this unusual molecule, preliminary estimates of the lowest optical transitions were obtained from SRCI calculations and vibrational frequencies were obtained from SCF calculations. Comparison of the calculated results with experimentally obtained spectra suggest the possibility that both the linear triplet and the rhombus may have already been observed. [ABSTRACT FROM AUTHOR]

This paper considers three functions of several variables, W(r,x), λ(r), and E(r), related by E(r)=W[r,λ(r)] and the condition that W(r,x) be stationary with respect to variations of x when x=λ. Formulas are presented which relate coefficients in the Taylor series expansions of these three functions. We call λ the response function. Partial derivatives of the response function are obtained by solution of a recursive system of linear equations. Solution through order n yields derivatives of E through order 2n+1. This analysis extends Pulay’s demonstration of the applicability of Wigner’s 2n+1 rule to partial derivatives in coupled perturbation theory. A four-term second derivative formula is shown to be numerically more stable than the usual two-term formula. We refute previous claims in the literature that energy derivatives are stationary properties of the wave function. [ABSTRACT FROM AUTHOR]

Efficient methods are developed for the computation of spin-orbit coupling constants in polyatomic molecules using complete active space multiconfiguration self-consistent field wave functions. All electron–nuclear and electron–electron spin-orbit interactions in the Breit–Pauli Hamiltonian are retained without storing or transforming spin-orbit integrals. This technique is applied to the calculation of spin-orbit coupling constants between singlet and triplet electronic states. Allowing nonorthogonality of the singlet and triplet molecular orbitals in the active space improves the quality of the wave functions and presents no serious computational difficulties. To test the method, spin-orbit coupling constants are computed for the diatomic molecules NH, OH+, PH, and O2 and compared with similar calculations reported in the literature. Calculations are also carried out for the organic biradical trimethylene (ĊH2CH2ĊH2). The coupling constant is found to vary from 0 to 2.5 cm-1 depending upon geometry. It is very sensitive to rotation of the terminal methylenes but relatively insensitive to the CCC angle. These results contribute to our understanding of the role of the triplet state in biradical reactions. [ABSTRACT FROM AUTHOR]

Comments on the analysis of energy derivatives. Observation on Sellers' Lagrangian multipliers; Discussion on how the correction to the gradient or to the force constant is computed.

Comments on the article entitled 'Translation-rotation invariance for N-particle systems: Internal coordinates and search for stationary points in reduced spaces' that was published in one the issues in 1985 of the periodical 'Journal of Chemistry and Physics.'

We have carried out inelastic neutron scattering studies of the methane/C[sub 60] system in order to understand the hindered rotational and vibrational dynamics of methane trapped in C[sub 60] interstices and to determine the structure around the interstitial site. At temperatures of 20 K and below, we observe inelastic peaks from rotational transitions of the CH[sub 4]. These transitions allow unambiguous assignment of the hindered rotational energy levels and a determination of the interaction potential. The appearance of two peaks for one of the J=0→3 transitions implies the existence of two distinct kinds of interstitial sites and the measured transition energies suggest rotational barriers of about 26 and 16 meV for these sites. Time-dependent changes in peak heights indicate slow (t[sub 1/2]approx. 2.6 h) triplet→quintet nuclear spin conversion that necessarily accompanies the J=1→0 rotational relaxation. We also have observed an inelastic peak at 10.9 meV in a region where there is a gap in the calculated, and otherwise dense, rotational spectrum. We believe that this must correspond to a local vibrational mode of CH[sub 4] rattling in its cage at ∼2.6 THz. Other peaks involving higher-energy vibrational excitations in CD[sub 4]/C[sub 60] correspond in energy to assigned peaks in the inelastic neutron scattering spectra of C[sub 60], albeit sometimes with different intensities. Taken together, these findings suggest the rotation of CH[sub 4] is hindered by the C[sub 60] cage and that the vibrations of CH[sub 4] and C[sub 60] are loosely coupled. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]