Valerio Magnasco

New translation method for STOs and its application to calculation of two‐center two‐electron integrals

The new translation method for Slater-type orbitals (STOs) previously tested in the case of the overlap integral is extended to the calculation of two-center two-electron molecular integrals. The method is based on the exact translation of the regular solid harmonic part of the orbital followed by the series expansion of the residual spherical part in powers of the radial variable. Fair uniform convergence and stability under wide changes in molecular parameters are obtained for all studied two-center hybrid, Coulomb, and exchange repulsion integrals. Ten-digit accuracy in the final numerical results is achieved through multiple precision arithmetic calculation of common angular coefficients and Gaussian numerical integration of some of the analytical formulas resulting for the radial integrals. c 2000 John Wiley & Sons, Inc. Int J Quantum Chem 79: 91-100, 2000

London dispersion coefficients from static multipole polarizabilities

Second order variational calculations of static dipole, quadrupole and octupole polarizabilities have been performed at the ab initio level for the ground states of H, He, Li, Be, Na, Mg using Hartree-Fock ω0 and the whole atomic hamiltonian as ℋ0. In the frozen core approximation only valence electrons are excited to a few optimized pseudostates of appropriate symmetry. For alkaline earth atoms a limited but properly shaped electron correlation is introduced through simple configuration interaction in the ground and in the excited state. The resulting multipole polarizabilities with their associated excitation energies allow for the one-centre calculation of C6, C 8, C 10 dispersion coefficients for all possible pairs of atoms through use of the generalized London formula. The numerical results compare favourably with those from accurate calculations.

Improved bond-orbital calculations of rotation barriers and geometrical isomerism

Rotational barriers in 19 molecules possessing a single internal rotation angle around a B-N, C-C, C-N, C-O, N-N, N-O, O-O central bond and geometrical isomerism in 3 molecules possessing a N=N double bond have been studied ab initio by the improved bond-orbital method. The first approximation, where the chemical groups occurring in these molecules are described in terms of non-orthogonal SCF bond-orbitals constructed from energy-optimized bond hybrids and polarities, is improved in second order of perturbation theory by admitting single excitations from bonding to antibonding orbitals and accounting for induction including exchange (polarization and delocalization). The molecules studied possess 16 to 34 electrons and a variety of functional groups differing in their chemical structure (CH3, NH2, OH, NO, CHO, CH=CH2, NH= and some of their F-derivatives). The overall results obtained using a STO-3G basis, rigid rotation and experimental geometries, are close to experiment and to the corresponding MO-SCF c...

One-centre calculation of dispersion coefficients between ground state H atoms from pseudostate decomposition of static multipole polarizabilities

N-term pseudostate decomposition of the exact H atom static polarizabilities allows for one-centre calculation of two-body and three-body dispersion coefficients between ground state H atoms to an accuracy remarkably higher than the previously reported two-centre results. Starting from a simple power basis in the radial variable, the first-order wavefunction of the atom in the external field is expanded into a finite number N of linear pseudostates which diagonalize the matrix of the excitation energies. The expansion is rapidly convergent, and if for N = 5 the numerical results are exact to 6 significant figures, the 20-term approximation gives coefficients which are accurate to the 15th decimal place. The method can be viewed as a generalization of the Slater-Hasse-Kirkwood approximation in the context of a hypergeneralized London formula.

A minimal basis bond-orbital investigation of the linear water dimer

The perturbative configuration interaction approach based on non-orthogonal bond-orbitals previously used for dealing with rotational barriers is applied to the study of the hydrogen bonding in the linear water dimer. First and second-order interaction energies are obtained in terms of static and transition charge distributions fully accounting for intermolecular overlap. Neglecting electron correlation, the second-order calculations include all single excitations from bonding to antibonding orbitals accounting for induction including exchange and giving results close to the corresponding supermolecular SCF-MOs in the same basis. Ab initio calculations using different gaussian minimal bases show that Clementis GTO basis MEDIUM is the most suitable for describing molecular interactions. Detailed component analysis of the energy up to second order is possible and reveals the main features of the intermolecular hydrogen bonding occurring between the water molecules.

ON THE EVALUATION OF TWO-CENTRE MOLECULAR INTEGRALS OVER AN STO BASIS

Abstract Formulae and computer programs for evaluating two-centre molecular integrals over an STO basis in spheroidal coordinates are presented. A unified formula is obtained for the two-electron integrals. New formulae are suggested for the auxiliary functions that remarkably improve the accuracy and speed of calculation for high values of the quantum numbers n and l.

Self-consistent theory of induction and dispersion forces in the Hartree-Fock approximation

A variational derivation is given of non-expanded induction and dispersion energies between many-electron atoms or molecules whose unperturbed ground states are described by Hartree-Fock wavefunctions. Second-order expansion of the perturbed energy gives induction and dispersion as separate Hylleraas functionals which can be minimized with respect to the form of the perturbed spin-orbitals appearing in the first-order trial function. The resulting set of coupled integro-differential equations which determine the best excited spin-orbitals occurring under the interaction can be solved by iteration until self-consistency after expansion of the perturbed orbitals in an appropriate basis.

Long-range second-order interactions and the shape of the He-HF and Ne-HF complexes

Direct ab initio calculation of long-range induction and dispersion interactions expended up to R−8 and evaluated at the SCF intermolecular separation for the complexes of He and Ne with HF shows that the angular shapes of such van der Waals atom-dipolar molecule dimers are determined by the absolute minima of the induction interaction.

Modulated perturbation theory for molecular interactions. III. Variational calculations of the second‐order energy for the ground state of H2+

Hylleraas variational calculations of the second‐order energy for the ground state of H2+ have been performed in the modified form of Murrell–Shaw–Musher–Amos (MS–MA) perturbation theory including exchange described in Paper I. Simple first‐order trial functions consisting in a single optimized Slater function for each multipole are found to be effective in representing nonexpanded multipole components of the interaction energy. The modulated form of the theory includes a large part of the spherical component of the polarization function already in first order, leaving dipole polarization as the dominant second‐order contribution.

On the evaluation of the cofactors occurring in the matrix elements between multiply-excited determinantal wavefunctions of non-orthogonal orbitals

Lowdins formulae for the matrix elements of one- and two-electron operators between determinantal wavefunctions of non-orthogonal spin-orbitals have been modified for the case in which the actual N-electron determinants contain n-excitations from a reference determinant. Use of algebraic techniques gives a compact general formula expressing the cofactors of the inverse of the actual overlap matrix in terms of the cofactors of a smaller matrix of order n. Besides saving computational time, this formula survives even when the inverse of the overlap matrix does not exist owing to singularity problems, and it simplifies and generalizes previous work by Hayes and Stone, being particularly useful in CI or in perturbative studies including electron exchange.