Neil S. Ostlund

Ghost orbitals and the basis set extension effects

Abstract The use of identical basis sets for monomer and dimer, in intermolecular calculations, is discussed. Evidence is presented that such a technique eliminates a basis set extension effect and gives a considerably better description of the intermolecular interaction than normal supermolecule calculations.

The correlation energy in the random phase approximation: Intermolecular forces between closed‐shell systems

A new expression for the correlation energy within the random phase approximation (RPA) is presented. It has the following properties: it is (1) size consistent, (2) invariant to unitary transformations of degenerate orbitals, (3) correct to second order in perturbation theory, and (4) when applied to a supermolecule comprised of two interacting closed‐shells, it describes the dispersive part of the interaction at the coupled Hartree–Fock (HF) level, i.e., the van der Waals’ coefficient extracted from its long‐range behavior is identical to that obtained from the Casimir–Polder expression using the dynamic coupled Hartree–Fock polarizabilities of the isolated systems. This expression, which requires only particle–hole two‐electron integrals for its evaluation, is expected to yield considerably more accurate potential energy curves between closed‐shell systems than second‐order Moller–Plesset perturbation theory which, as is shown, describes dispersion forces at the less accurate uncoupled HF level. In add...

Complex and Unrestricted Hartree‐Fock Wavefunctions

The general conditions under which real, restricted Hartree‐Fock wavefunctions become unstable with respect to variation of the orbitals are derived. It is shown that complex solutions to the Hartree‐Fock equations are associated with a singlet instability in the usual real, restricted solution. A comment is made concerning the complex wavefunctions found by Harris and Pohl for hydrogen halides at short internuclear distances.

Perturbation calculation of correlation energies for polyatomic molecules I. Initial results

The calculation of correlation energies for polyatomic molecules is discussed. Four second-order perturbation expressions are considered; only the simplest, a Rayleigh-Schroedinger expansion with the Moller-Plesset partitioning of the Hamiltonian is invariant to an arbitrary mixing of degenerate orbitals and has the correct dependence on the number of particles. In the absence of degeneracies an iterative Brillouin-Wigner method is proposed. Calculations predict that correlation effects favor the non-classical form of carbonium ions.

Polyatomic scattering integrals with gaussian orbitals

Abstract The ab initio calculation of the electronic effects of non-adiabatic molecular collisions, using gaussian atomic orbitals, is considered. Simple analytical expressions for the many-center integrals, required for such calculations, are derived.

Perturbation calculation of atomic correlation energies for the first transition period

Abstract Results are presented for calculations of Hartree—Fock and correlation energies for the 3d n 4s 2 and 3d n +1 4s ground and excited states of the first transition series atoms using second-order Moller—Plesset perturbation theory starting with an unrestricted Hartree—Fock wavefunction.

Generalized oscillator strengths for the lowest Π λ Σ transitions in CO and N2

The generalized oscillator strength as a function of momentum transfer is calculated for the lowest Π ← Σ transition in CO and N2 using the Tamm-Dancoff (TDA) and random phase (RPA) approximations and a minimal basis set of atomic orbitals. Only qualitative agreement is obtained with experiment and it is suggested that the calculated excited states are too compact

Calculation of high energy elastic electron-molecule scattering cross sections with CNDO wavefunctions

Differential cross sections for the elastic scattering of electrons from H2 are calculated within the Born approximation using molecular wavefunctions of different sophistication to determine the sensitivity of the cross sections to the quality of the wavefunction. An approximation to the molecular form factors based on the use of CNDO wavefunctions, which incorporates the distortion of the charge density upon the formation of the molecule without the necessity of calculating two center integrals, is used to calculate differential cross sections for electron scattering from CO, N2, NH3, H2O, and CH4 as a function of momentum transfer. For CO and N2 the CNDO calculations are in good agreement with results obtained using ab initio minimal basis wavefunctions and evaluating all integrals. The CNDO calculation describes the recently measured cross sections for NH3 much better than the method based on the independent atom approximation.