David B. Cook

Ab initio calculations with small ellipsoidal gaussian basis sets. I

The use of ellipsoidal gaussian type orbitals in ab initio calculations on molecular systems of small and intermediate size is demonstrated, in both non-linear and SCF MO schemes. The method is an extension of Frosts Floating Gaussian Orbital Method. Results for conformational properties (barriers to internal rotation in ethane and 1,3-butadiene) are better than those obtained with basis sets containing only spherical gaussians. The usefulness of very small basis sets is discussed.

A note on the magnetic susceptibility of hydrogen and its isotopomers

Abstract A wavefunction used in an earlier calculation of the nuclear shielding of the hydrogen molecule has been tested by comparing the calculated magnetic susceptibility against that of Kolos and Wolniewicz. Good agreement is obtained. The procedure of Herman and Short for averaging over the nuclear motion has also been tested by comparing the predicted susceptibilities of H 2 , Hd and D 2 with those obtained from averages of the Rydberg-Klein-Rees potential curves by Jain and Sahni. Again, good agreement is found. For the first time calculated values have been obtained for the susceptibilities of the isoropomers of hydrogen which contain tritium. It is predicted that accurate susceptibility measurements should not only be able to distinguish between all the various isotopomers but should also detect the temperature dependence of the susceptibility of any one isotopomer.

The muonium bond

Abstract Muonium is a light isotope of hydrogen, so light that in strong hydrogen bonds its zero-point energy is close to or above the energy barrier; this favours the formation of symmetrical muonium bonds. In water, muons will exist as Mu(H2O)6+ in contrast to H(H2O)4+; the stability of this species will slow the exchange of Mu and H. With alkenes and alkynes, muons will preferentially form non-classical complexes because of their lower zero-point energy in weak bonds: in liquids, a muon will attach two molecules via a symmetrical muonium bond.

“Mixed basis” calculation of hyperfine coupling constants

Abstract A recently developed method of non-empirical wave-function calculation is applied to the calculation of ESR hyperfine coupling constants. In particular the effect of d orbitals on the computed values of these constants is investigated for H 2 S − and H 2 S + .

The “invariance principle” in approximate molecular orbital theories

The widely used invariance “principle” of approximate MO theories is shown to be physically unreasonable and formally unnecessary. The use of ZDO-type schemes in an internally-defined orbital basis is proposed to replace this restrictive principle.

Molecular integrals in the approximate calculation of electronic structure

A self-consistent set of new proposals is made for the calculation of the largest molecular integrals over orthogonal hybrid orbitals used in “neglect of differential overlap” schemes.

Molecular integrals in terms of ellipsoidal gaussian-type orbitals

Abstract A method for the evaluation of molecular integrals over generalised gaussian functions is given.

Unrestricted Hartree-Fock functions for the carbon and fluorine atoms

An attempt to solve the Hartree-Fock equations for the (non-relativistic) carbon and fluorine atoms is reported. No constraints are placed on the minimisation of the parametrised energy function arising from the use of the finite expansion method within the single determinant model of atomic electronic structure except those implicit in the expansion method itself.

An optimum minimal basis of exponential atomic orbitals

An analysis of some of the energetic properties of the conventional minimal STO basis is used to suggest a new optimum set of exponential functions for use in molecular calculations.