C. W. Kern

Zero-point vibrational corrections to one-electron properties of the water molecule in the near-Hartree-Fock limit

The zero‐point vibrational motion of the water molecule in its ground electronic state is analyzed with a near‐Hartree—Fock potential energy surface constructed from a (9s5p2d/4s1p) /[4s3p2d/2s1p] basis set of contracted Gaussian orbitals. The harmonic and cubic force constants relative to the computed minimum are obtained, and a normal coordinate analysis is carried out for several isotopic variants. A set of one‐electron properties including molecular moments, field gradients, forces, and densities is computed at each point on the potential surface, and then averaged over the zero‐point motion with a vibrational wavefunction which contains anharmonicity terms through the cubic constants. The vibrational corrections are typically about 1% of the equilibrium values, but are as large as 20% in cases such as the 17O quadrupole coupling constant along the C2 axis. The theoretical isotope shifts for the quadrupole moments of H2O and D2O are in good agreement with experiment. Predictions are made for isotope s...

Nuclear Corrections to Electronic Expectation Values: Zero‐Point Vibrational Effects in the Water Molecule

A variation–perturbation approach is used to determine nuclear corrections to electronic properties of polyatomic molecules. To illustrate the technique, general expressions for the first‐order zero‐point vibrational corrections are derived and applied to various one‐electron properties of the water molecule. These include the electric dipole and molecular quadrupole moments, the diamagnetic susceptibility, the diamagnetic shielding constants, the quadrupole coupling constants, and the Hellmann–Feynman forces. The numerical results, which depend upon the combined use of the LCAO MO CI wavefunctions of Reeves and Boys and of the experimental data of Papousek and Pliva, show that electronic expectation values need to be vibrationally corrected for quantitative comparisons of theory with experiment. For the water molecule, these corrections are typically about 1%, but can be as large as 10%, of the equilibrium values. The net sign of each correction is determined by the symmetric stretching mode in H2O and ...

Properties of the benzene molecule near the Hartree‐Fock limit

The ground electronic state of the benzene molecule is studied with a (9s5p1d/4s1p)/[4s2p1d/2s1p] contracted Gaussian basis set in the traditional Hartree‐Fock approximation. It is estimated that the Hartree‐Fock limit is approached within 0.07 ± 0.02u2009a.u. Technical problems associated with large‐scale calculations of this type are discussed. One‐electron properties are determined, including second moments, average diamagnetic shielding constants, Hellmann‐Feynman forces, electric‐field gradients, and charge densities. Comparisons are made with the available experimental data and with other calculations.

Theoretical Model for the Differential Quenching Rates of CO Fluorescence by Ortho‐ and Parahydrogen

The experimental measurements of Millikan and co‐workers, which show that para‐H2 quenches vibrationally excited CO faster than normal‐H2 (14para, 34ortho) at temperatures below 500°K, are analyzed in the Born–Bethe approximation. Beginning with the observation that the rotational transition ju2009=u20092u2009→u2009ju2009=u20096 in H2 has almost the same energy as the vibrational transition υu2009=u20091u2009→u2009υu2009=u20090 in CO and invoking the assumption that long‐range forces are solely responsible for the difference in quenching rates between the two spin species of H2, we find that the temperature dependence of the measured rate differences can be reproduced almost quantitatively by truncating the Born–Bethe series at second order and by using an interaction potential derived from a multipole expansion of nonoverlapping charge distributions. The implications of this result, and the assumptions on which it is based, are discussed in considerable detail.

Erratum: Fine‐Structure Studies of Diatomic Molecules: Two‐Electron Spin‐Spin and Spin‐Orbit Integrals

The two‐electron integrals that contribute to the spin–spin and spin–orbit interactions in diatomic molecules are evaluated for wavefunctions constructed from Slater orbitals. For arbitrary combinations of quantum numbers, expressions are derived in tensor–operator form for all the one‐ and two‐center Coulomb, hybrid, and exchange terms that occur. An attempt is made in the analysis to maximize compatibility with some of the previous treatments of interelectronic repulsion integrals.

On a Perturbed Hartree‐Fock Study of the Magnetic Susceptibility and the 13C and 17O NMR Shielding Constants in Formaldehyde with Slater Basis Sets

The theoretical study of Flygare et al. on one‐electron properties of the formaldehyde molecule is extended to include the paramagnetic susceptibility and the 13C and 17O NMR shielding constants and to investigate their sensitivity to Slater basis‐set quality. The Gaussian transform method is used to evaluate the necessary integrals. Using the fully coupled perturbed Hartree‐Fock formalism, we find that improvements in the wavefunction produce significant changes in most components of the second‐order properties. The best shielding calculations, obtained with a double‐zeta Slater set, are within the rather large experimental uncertainties, whereas the agreement between the theoretical and experimental susceptibility results is less satisfactory. The complete paramagnetic tensors are analyzed in terms of MO and AO contributions. Comparisons are made with other ab initio calculations and with simplified forms of the theory.

Analysis of the D and 17O Quadrupole Coupling Constants in Ice Ih

Hydrogen bond formation in enriched heavy ice is observed experimentally to alter the D and 17O quadrupole coupling constants relative to the vapor. In this study the dependence of these coupling constant shifts on electronic structure is examined theoretically with two types of all‐electron, single‐determinant wavefunctions constructed from Slater‐orbital basis sets for the water monomer, dimer, trimer, and pentamer. SCF computations are first performed with the various multimers constrained to a geometry based on the observed structure of ice (Ih). The sensitivity of these results to geometry and to the electron distribution is then examined with bond‐orbital wavefunctions. It is concluded that the solid—vapor coupling‐constant shifts can be accounted for with a representation of the crystal which includes exchange forces between bonds, direct charge transfer due to hydrogen bond formation, and elongation of the normal O–D bond. The relative importance of these contributions is discussed for both nuclei.

Orbit–Orbit Integrals for Diatomic Molecules

The one‐ and two‐center Coulomb, hybrid, and exchange integrals that contribute to the orbit–orbit interaction in diatomic molecules are evaluated for arbitrary combinations of Slater orbitals. The basic formulation and the results are compatible with some previous treatments of interelectronic‐repulsion and fine‐structure integrals.

Spin-orbit configuration-interaction study of valence and Rydberg states of LiBe

Ab initio spin–orbit full configuration‐interaction calculations in the context of relativistic effective core potentials are reported for the weakly bound metal dimer LiBe, a three‐valence‐electron system. The effects of basis set on the energies of valence and Rydberg states of the cluster are discussed, as are the effects of configuration space selection on the energy of the latter states. Results at the dissociative limit are compared to the experimental atomic spectra. Potential‐energy curves and spectroscopic constants are presented for the ground state and fourteen excited states, which includes the Li and Be 2p valence states, the Li 3s, 3p, 3d, and 4s Rydberg states, as well as three low‐lying states of the molecular cation.

Relativistic Effects in Diatomic Molecules: Evaluation of One‐Electron Integrals

One‐ and two‐center matrix elements over the kinetic‐energy‐shift, the spin–orbit, the Dirac, and the Fermi‐contact operators are evaluated for arbitrary combinations of Slater orbitals. The analysis is compatible with previous treatments of the two‐electron Breit–Pauli operators.