Jeremy I. Musher

HYDROGEN-ATOM POLARIZABILITY AS A HARTREE--FOCK PERTURBATION EXPANSION: A GEOMETRIC APPROXIMATION TO ATOMIC POLARIZABILITIES.

The hydrogen‐atom dipole polarizability α is obtained by a double perturbation expansion based on a Hartree–Fock H0. The expansion α = α0 + λα1 + λ2α2 + ···, where λ is the continuous parameter for the Hartree–Fock perturbing potential, is found to be extremely close to a geometric series with αi+1 / αi = 0.433 ± 0.002. Computation of α as α0[1 − (α1 / α0)]−1 gives 4.499a03 in excellent agreement with the exact value 92a03. The origin of this geometric character is examined and its applicability to some many‐electron polarizabilities is demonstrated empirically.

On the Hartree-Fock problem☆

Abstract The Hartree-Fock problem is investigated by examining the symmetry properties of the SCF spin-orbitals. These can be classified as closed-shell, open-shell or general spin-orbitals according to the commutation rules satisfied by their one-electron SCF hamiltonians. The effect of symmetry-breaking in spin, angular momentum and space-group symmetry is considered schematically and the physical implications of such symmetry-breaking are discussed.

Molecular Orbital Theory of Electric Polarizabilities and Magnetic Susceptibilities of Hydrocarbons

Hartree–Fock perturbation theory and the molecular orbital method are used to develop a consistent theory of the polarizabilities and susceptibilities of hydrocarbons. When each unperturbed MO is expanded in terms of a set of basis orbitals it is found that in the presence of an electric or magnetic field the corresponding perturbed orbitals have two parts, a molecular or “nonlocal” one and a “local” part which takes into account the effect of the field on the basis orbitals themselves. When certain integrals are neglected the polarizability and susceptibility can also be divided into local and nonlocal parts which is a result generally assumed without proof. For saturated hydrocarbons, the contribution due to the nonlocal terms in the polarizability is zero so that there are only local terms in the final expression, while for unsaturated molecules there are both local and nonlocal contributions. In the case of the magnetic susceptibility the molecular (nonlocal) parts of the paramagnetic term are importa...

A new description of interatomic and intermolecular interactions

Abstract A preliminary account is given of a perturbation for calculating interatomic and intermolecular interaction energies in which the wave function is expanded in terms of product functions. The results obtained are compared with those found using other expansions.

A Molecular Orbital Description for Sulfur Compounds of Valences 2, 4, and 6.

The qualitative picture of the bonding involved in sulfur compounds with valences 2, 4 and 6 is discussed. Molecular orbital CNDO/2 calculations are used to describe the covalent and hypervalent bonds in the three simplest hydrides and fluorides half of which are hypothetical. The results with and without d-orbitals on the sulfur atom are compared and bonding can be understood without d-orbitals. Possible structures of a sulfurane dimer and sulfurane oxides which are likely intermediates or stable compounds in this chemistry are considered briefly.

Modified Hamiltonians for Localized Orbitals and for the Removal of Degeneracies

A single determinant approximate wavefunction ψ0 can be improved by choosing a Hamiltonian of which it is an eigenfunction and applying perturbation theory. If ψ0 is built up of orbitals which are eigenfunctions of a one‐electron operator h, an appropriate choice of H0 is Σh(i). This paper discusses two modifications to H0. One consists of adding to H0 an energy‐shift operator, and this has several applications the most interesting being the removal of any degeneracies in H0. The second consists of writing the new H0′ as Σh′(i) where h′ is different to h. The h′ can be chosen to have localized orbitals as its eigenfunctions, and this leads to a simple method of performing perturbation theory with localized orbitals. Some numerical examples are given.

Orbital Approximation to Spatial Eigenfunctions of the Many‐Electron Hamiltonian

A new procedure is developed for calculating the best wavefunction for an N‐electron atom in terms of N one‐electron orbitals which are eigenfunctions of l2, lz and sz. This is a special case of a method for calculating the best wavefunction in terms of N orbitals unrestricted in angular momentum but restricted in spin component and is thus a partial generalization of Lowdins EHF method. We calculate approximate spatial eigenfunctions of H using the function Φ[α,λ] = Dλλ[α] ∑ i = 1k δiPiφ, where φ is a product of N spatial orbitals and where the Pi are the k permutations out of which k linearly independent projections onto the Young tableau [α,λ] can be obtained. The method gives an improvement to each of Goddards GI solutions in such a way that they all give the same energy when fully minimized, while only involving k−1 additional parameters. For Li atom there is only one additional parameter and calculations are performed using Goddards GI and GF orbitals, obtaining small improvements in the energy. ...

Geometric double‐perturbation expansion of the coupled Hartree‐Fock second‐order energy

The second‐order energy of the coupled perturbed Hartree‐Fock (CHF) theory is expanded explicitly into the sum with respect to the electron‐correlation corrections. In a matrix form, the expansion is exactly geometric. The correlation effect included in the CHF theory has two origins: one represents the so‐called first‐order correlation energies intrinsic to the unperturbed ground and excited states, and the other represents the correlation effect induced by the external perturbation. The matrix geometric expansion reduces under some approximation to an ordinary scalar geometric series. This gives a basis for the geometric approximation of the CHF energy proposed empirically by Schulman and Musher. Exactly the same arguments also apply to the second‐order energy of the singly excited CI method, simply by neglecting the perturbation‐induced correlation effect.

Modes of rearrangement in substituted octahedral complexes

Abstract : The modes of rearrangement and the observable processes for octahedral dihydro-complexes containing no, one and two chelating rings are presented. The last of these can be used to indicate the actual rearrangement for such complexes when appropriate conditions regarding the effect of chelation are satisfied. The modes and observable processes for a square pyramidal molecule, an octahedral molecule containing a single lone-pair, are also presented. Some observations on related systems are developed. (Author)

Theory of bonding in ylides, acetylacetonates and π-cyclopentadienyl compounds

Abstract The theory of bonding in ylides and their oxides, acetylacetonates and π-cyclopentadienyl complexes has been discussed from the viewpoint of hypervalent bonding. The existing ylides and acetylacetonates are discussed and new ones are proposed. The π-cyclopentadienyl complexes are only speculative.