Richard M. Stevens

Perturbed Hartree—Fock Calculations. I. Magnetic Susceptibility and Shielding in the LiH Molecule

The limited basis set Hartree—Fock problem is solved in the presence of a perturbation term in the Hamiltonian to obtain the first‐order perturbed wavefunction. The formulation is applied to the calculation of electric polarizability, magnetic susceptibility, and magnetic shielding. The effect of the limited basis set on the gauge invariance of the magnetic quantities is discussed. The magnetic susceptibility and shielding, the rotational magnetic moment, and the spin rotational constants are calculated for lithium hydride using two different wavefunctions. The agreement with experiment is reasonably good for the spin rotational constants and rotational magnetic moment. It is felt that further refinement of the calculation would not change the results by more than a few percent.

Geometry Optimization in the Computation of Barriers to Internal Rotation

A minimum basis set of STOs has been used to compute wavefunctions for eclipsed and staggered C2H6 and for several forms of H2O2. For each form all the exponents and free geometric parameters have been varied to obtain the minimum energy. It has been found that the geometry variation has little effect on the computed barrier in C2H6, and the results agree well with experiment. For H2O2, it has been found that the minimum geometry changes substantially between the cis and trans forms, and the results agree poorly with experiment. However, the geometry variation does produce better agreement for the barrier than similar calculations with fixed geometry.

Perturbed Hartree—Fock Calculations. III. Polarizability and Magnetic Properties of the HF Molecule

Optimal basis sets within the perturbed Hartree—Fock theory have been found for the first‐order wavefunction for the hydrogen fluoride molecule for the operators x, z, Mx (F), and Mx (H). These sets have yielded calculated values of the polarizability components, magnetic susceptibility, magnetic shielding at H and F, rotational magnetic moment and spin rotational constants of both H and F. Excellent agreement with experimental molecular‐beam values is found for the rotational magnetic moment and the spin rotation constants. Good results were obtained for the magnetic properties only if the origin is chosen at the F atom. Maps are presented for the first‐order change of the electron density in the presence of an electric field, but, owing to the asymmetry of the charge distribution, reliable maps of the first‐order induced current density in the presence of a magnetic field could not be obtained.

Perturbed Hartree—Fock Calculations. II. Further Results for Diatomic Lithium Hydride

The previous calculations for the susceptibility and shielding of lithium hydride are extended and refined. It is shown that the basis sets for the first‐order wavefunction are invariant under small variations of the other parameters and that the basis sets used in the final calculations are essentially complete. Results from calculations at three internuclear distances have yielded vibrational corrections. The computed rotational magnetic moment is —0.667 nuclear magnetons, and the computed spin rotational constants of lithium and hydrogen are +9.45 and —9.38 kc/sec, respectively, in substantial agreement with experiment. The method is also applied to the perpendicular component of the electric polarizability, which has a calculated value of 4.063 A3.

Symmetric H3: A Semiempirical and Ab Initio Study of a Simple Jahn–Teller System

Semiempirical and multiconfiguration ab initio results for the potential energy of H3 are used to obtain a detailed description of the potential‐energy surface in the region of interest for the Jahn–Teller problem. Topographical properties of truncated perturbation expansions of the potential‐energy function about the D3h minimum are compared with those of the complete semiempirical contour map; six symmetric dissociation “troughs” are found in the complete semiempirical surface, in contrast to three stable basins in the second‐order surface and three dissociative troughs in the third‐order surface. The relationships among the various parts of the complete three‐dimensional H3 potential‐energy hypersurface are discussed and illustrated by means of a single compact diagram. A convenient matrix‐projection method for identifying normal‐mode coordinate and electronic wavefunction partners associated with degenerate representations is discussed in an appendix.

Accurate SCF Calculation for Ammonia and Its Inversion Motion

A series of SCF calculations for the ammonia molecule in various gemoetries have been performed, using large basis sets of STOs. It is found that the height of the inversion barrier can be accurately predicted in the Hartree–Fock approximation, but that the basis set must be close to complete. Our largest calculations are in excellent agreement with previously reported calculations using Gaussian basis orbitals. A potential curve has been computed for the inversion motion using a near‐Hartree–Fock basis set. The computed spectrum is in qualitative agreement with experiment; quantitative accuracy is not obtained, probably because the computed NH bond distance is too short.

Magnetic Properties and Dipole Moment of CO

An extensive coupled Hartree–Fock calculation of the second‐order magnetic properties of CO has been made. The susceptibility, shielding, rotational magnetic moment, and spin rotation constants were determined and are in reasonable agreement with the available experimental data. The calculations were carried out for four different internuclear distances; it was found that the error caused by not reoptimizing the basis set for the first‐order wavefunction at the changed distances was small. The results for the susceptibility were used to determine the effect of vibrational averaging on the dipole moment obtained from the isotope shift in the rotational magnetic moment. The effect was found to be negligible and the previously determined sign was confirmed.

Magnetic Properties of AlH and N2 from Coupled Hartree–Fock Theory

The magnetic susceptibility and nuclear magnetic shielding in AlH and N2 have been calculated using coupled Hartree–Fock theory. The perpendicular component of the AlH susceptibility tensor is predicted to be positive, i.e., paramagnetic. Thus, AlH becomes a second example, in addition to BH, of a gas‐phase molecule which has a component which should exhibit the phenomenon of temperature‐independent paramagnetism. Results for N2 yield a total susceptibility within 5% of the experimental value. Although the nitrogen nucleus is correctly predicted to be antishielded, the quantitative agreement of the shielding with experiment is not as good as has previously been obtained from coupled Hartree–Fock calculations on other diatomics.

Reaction paths on the H4 potential energy surface

Portions of the electronic potential energy surface corresponding to various nuclear geometries of the H4 molecular system have been studied. The variational calculations employed double‐zeta basis sets (1s and 1s′ Slater‐type orbitals on each center) to form configuration interaction wavefunctions. At selected points on the surface, the effects of exponent optimization and increased basis set size (1s, 1s′, and 2p orbitals per center) were assessed. A low energy reaction path allowing a bimolecular mechanism for exchange, requiring less energy than a single H2 dissociation, was not found. However, a path leading from trapezoidal to linear structures (and vice versa) was found to offer the possibility of exchange with less than 6 kcal/mole of energy above this dissociation limit.

Localized Bonds in SCF Wavefunctions for Polyatomic Molecules. I. Diborane

Molecular SCF orbitals of B2H6 have been computed from optimized minimum basis sets which employ isotropic or anisotropic atomic 2p orbitals. These SCF wavefunctions have been transformed to localized MOs which maximize the self‐energy, D = Σi(φiφi | φiφi). This objective procedure strongly supports the three‐center bond for each BHB bridge. The resulting hybrids are sp2.5, with ∠Ht–B–Ht=125° and ∠Hb–B–Hb=93° for terminal and bridge Hs, respectively.