No abstract

The exact wavefunction of an N-electron atom or molecule contains, after the Hartree-Fock (HF) part, correlation terms involving successively one, two, … N electrons at a time. Particularly in closed shells, one-electron terms f̂i result mainly from pair correlations. The f̂i were previously neglected in the many-electron theory. Reasons for the smallness of f̂i are summarized. Different types of correlation effects are classified, and methods for estimating each type of f̂i are given. f̂i in closed form, i.e., including infinitely many single excitations is less than 2.8% of the Hartree-Fock orbital in He with an energy contribution 0.0001 a.u. (63 cal/mole). In the H2 molecule f̂i is negligible for (R/Re) <2. At larger R, as (1σg)2 becomes degenerate with (1σu)2 the f̂i effect increases to ∼0.4 eV at dissociation. However, in such cases and in actual nonclosed shells, these nondynamical f̂i are removed if HF orbitals are obtained after the removal of degeneracies. Dynamical correlation effects give negligible f̂i and so generalized SCF methods are not necessary. Qualitative quantum chemistry can be based on just HF orbitals or approximations to them, though energies include localized pair correlations.

Viscosities and densities of a series of quaternary salts have been measured in acetonitrile and several other solvents; some electro-neutral solutes were also investigated. Up to about 0.2 mole/L, viscosities satisfy the equation 77/170 = 1 + Ac1/2 + Be and the densities are given by p/pa = 1 + (Me/1000) -v.,) where vs is the specific volume of the solute in solution and the other symbols have their usual meanings. Assuming the Einstein viscosity mechanism (spheres in a continuum), B = Mvs/400. It was found that B and V = 10~3Mva are additive in contributions from the constituent ions. For large ions (e.g., B14N +, PIuB-), the radii calculated from B and V agree, confirming the theory and model. But, for small ions, the 5-values are larger than the values computed from V, and the more so, the smaller the ion. Neutral molecules, on the other hand, give smaller 5's than expected from the F's. Electrostriction in the first case and slipping in the second are proposed as explanations. This suggestion is confirmed by the behavior of dipolar solutes.

Ab initio configuration interaction (CI) calculations were performed on the ground and excited state of Hf@C28 and its positive and negative ions. Relativistic core potentials, spin-orbit operators, and symmetry-adapted functions were included in the calculations to take into account the relativistic effects of the heavy atom and to reduce the time and effort of the computation. Double-zeta basis sets were used. Single and double excitations were included in the CI calculations. A number of excitation energies were obtained for Hf@C28 and its ions. The ground states of Hf@C28+, Hf@C28, and Hf@C28-in T d symmetry were found to be 2 A~, 'AI, and 2E. For Hf@C28, values found were the following: ionization potential, 8.08 eV; electron affinity, 0.66 eV; and first excitation energy (to 3E state), 5.26 eV. The binding energy for Hf and c 2 8 to form Hf@C28 was obtained as 0.71 eV. These results were compared with those from our previous SCF calculations and with experimental data or other theoretical values where available.

It is shown that if one uses the uncoupled Hartree—Fock method as a zero-order approximation for calculating atomic and molecular second-order properties (either static or dynamic), then the first-order corrections to this approximation are determined solely by quantities already available from the zero-order calculations. No new equations need be solved.