Maurice E. Schwartz

Direct calculation of binding energies of inner-shell electrons in molecules

Abstract The calculation of binding energies of molecular inner-shell electrons as the difference between the SCF energies of ground state and inner-shell hole state is discussed. A flexible Gaussian orbital basis set gives good results for the 1s binding energies in Ne and CH 4 , where unambiguous data from other sources exist for comparison. Calculated predicted 1s binding energies for the heavy atoms in first row hydrides are (in eV): BH 3 , 197.5; CH 4 , 291.0; NH 3 , 405.7; H 2 O, 539.4; HF, 693.3.

Correlation of 1s binding energy with the average quantum mechanical potential at A nucleus

Abstract Changes in binding energies of 1s core electrons for C, N, O, and F atoms in different molecular environments have been studied by examination of negatives of inner-shell orbital energies (−ϵ Is ) from ab initio “double-ξ” quality LCAO SCF MO wavefunctions. As contrasted with many previous correlations of binding energies with point charge models, changes of orbital energies have been related to the potential at the nucleus on which the 1s orbital sits, properly calculated as a quantum mechanical expectation value. The contribution of the 1s to the potential is insensitive to environment, and consideration focuses on the “external potential” Φ ext due to the remainder of the system outside of the 1s. Shifts in −ϵ 1s are in all cases nearly the same as shifts in Φ ext (using atomic units), the average of eleven cases giving Δ(−ϵ 1s )/Δ(Φ ext ) = 1.11. An analysis of the equations, based on localized valence MOs and supported by numerical examples, shows this to be a generally expected result, with some possible exceptions being outlined.

Valence Electron Studies with Gaussian‐Based Model Potentials and Gaussian Basis Functions. I. General Discussion and Applications to the Lowest s and p States of Li and Na

A new model potential for one‐valence‐electron atoms is introduced. It consists [Eq. (6)] of a core Coulomb potential modified by the addition of a Gaussian screened Coulomb potential. This potential has the desired features outlined for a model potential, and it has particularly convenient and simple mathematical properties when used with Gaussian basis functions. Since the smooth valence orbitals are sought, Gaussian functions are a good basis set because their deficiencies in nuclear regions do not enter the problem. The potential is calibrated to experimental energies for the 2s and 2p states of Li and 3s and 3p states of Na, using extended basis sets. The model Hamiltonians so defined are used with a variety of more modest basis sets to determine pseudowavefunctions. Based on comparisons with ab initio orbitals, energy analyses, radial density calculations, and overlap and expectation value calculations, the conclusion is that good valence pseudowavefunctions can be obtained by this approach with rel...

Theoretical Study of the Barriers to Internal Rotation in Formic Acid

Nitrous acid, HONO, has been studied for three geometries by the ab initio LCAO SCF MO method with a basis of accurate gaussian atomic orbitals. The trans geometry is correctly predicted to be most stable, lying about 2 kcal/mole lower than the cis form, and 9 kcal/mole lower than the 90° form (experimental estimates being 0.4 and 11.6 kcal/mole, respectively). Population analysis, dipole moment components, and properties related to nuclear-nuclear and nuclear-electron potentials all show a partial breaking of the hydroxyl oxygen-nitrogen bond at 90° compared to cis and trans, as well as the effects of electronic rearrangement for nuclear screening in the high nuclear repulsion cis form. The cis to 90° barrier is dominated by the attractive components of the total energy, while the trans to 90° one is dominated by repulsive components, in agreement with our analysis and an earlier prediction by Allen.

Study of the structure of molecular complexes. IX. The Hartree–Fock energy surface for the H2O–Li–F complex

A large number of geometrical configurations (250) are computed with a large Gaussian basis set in the Hartree–Fock approximation for the H2O–Li–F complex. The many‐dimensional potential energy surface has been sampled by keeping the molecule of water at a fixed position and by allowing the lithium and the fluorine to assume many positions in space. Because of the symmetry (C2v) of the water molecule, the 250 computations correspond to a sampling of about 600 configurations. The sampling includes a few highly repulsive configurations (up to about 300 kcal/mole in repulsion); the remaining points are either in the strongly attractive regions or in the weakly attractive regions of the surface. The stabilization energy of the complex reveals the existence of at least three possible structures: the Li–F–H2O structure (with C2v symmetry), with a stabilization energy (relative to H2O, F−, and Li+) of about −186 kcal/mole; a second Li–F–H2O structure with the fluorine forming a hydrogen bond (with one of the H–O...

Valence Electron Studies with Gaussian‐Based Model Potentials and Gaussian Basis Functions. II. Discussion of the One‐Valence‐Electron Molecular Theory and Applications to Li2+, Na2+, and LiH+

A one‐electron theory for one‐valence‐electron molecules is developed. It assumes nuclear‐nuclear repulsions to be between net core atomic charges, and that the potential seen by the valence electron is a superposition of atomic model potentials. The atomic model potentials are the core Coulomb potentials modified by Gaussian screened Coulomb potentials, as found in earlier atomic studies. Such model potentials are quite convenient for the use of Gaussian basis functions, which are also taken from the atomic studies, and for which potential energy matrix elements are simply calculated from physically based rules. The theory is applied to the ground states of Li2+, Na2+, and LiH+, using a variety of basis sets. Increasing the basis set flexibility lowers the energy, as in ordinary all‐electron variational calculations. Binding energies and internuclear distances from the most extended basis calculations are: Li2+: De=1.23 eV, Re = 5.8 a.u.; Na2+: De=0.97 eV, Re = 6.7 a.u.; LiH+: De = 0.090 eV, Re = 4.5 a.u...

Valence electron studies with Gaussian‐based model potentials and Gaussian basis functions. IV. Application to molecular systems containing first row atoms

The previously developed simple valence−only electronic structure theory based on atomic core model potentials is extended to many−electron systems containing first row atoms. For a given atom, two additional parameters have been incorporated into the theory to deal with the electron−electron repulsion in the valence shells. Any molecular studies using the atom are then well defined without further calibration. The molecules considered in this study are CH4, NH3, H2O, HF, C2H4, C2H2, N2H2, N2, H2O2, CO, N2O, H2CO, HCONH2, CH3F, LiCN, and LiNC. The valence basis sets in the LCAO SCF MO studies were of ’’double−zeta’’ quality. Calculated orbital energies and dipole moments for the molecules compare favorably with those from analogous all−electron calculations of Synder and Basch. Some molecular conformational calculations have also been done: the relative stability of LiNC is correctly predicted compared to LiCN; the bond angle of H2O is predicted at 105; the bond lengths of HF and N2 predicted at 1.65 and ...

Valence electron studies with Gaussian‐based model potentials and Gaussian basis functions. III Applications to two‐valence‐electron systems composed of combinations of Li, Na, H, or their unipositive ions

A previously developed simple valence‐only electronic structure theory based on atomic core model potentials and using flexible Gaussian valence basis functions is applied to the two‐valence electron systems Li2, Na2, NaLi, LiH, NaH, Li3+, Na3+, Li2Na+, LiNa2+, LiH2+, Li2H+, NaH2+, Na2H+, and H2, within the SCF MO model. Results for calculated equilibrium geometries and energy changes for certain chemical reactions are compared to the corresponding quantities from analogous all‐electron ab initio calculations. The model potential results are quite similar to those from the ab initio ones and are generally satisfactory for such a simple theory. There is a tendency toward slightly long internuclear distances (average deviation of all unique independent distances is +0.06 bohr) and slightly high energy of complex relative to separate constituents (average deviation of dissociation reaction energies is −2.1 kcal/mole) in these calculations relative to the all‐electron ones, the explanation of which will requi...

Theoretical Study of the Barriers to Internal Rotation in Hydrogen Persulfide, HSSH

Hydrogen persulfide, HSSH, has been studied by the ab initio self‐consistent‐field molecular‐orbital method for the four dihedral angles of 0°, 90°, 135°, and 180°. The basis set consisted of Gaussian orbital expansions of best‐atom Slater‐type orbitals through 3p, tested in other calculations on H2S. The molecule has a calculated energy minimum for a dihedral angle in the range 90°–100°, in fair agreement with experiment (about 90.5°). The cis barrier is high (7.4 kcal), but the smaller trans barrier (1.9 kcal) seems low for consistency with experimental studies of the torsional vibrational levels. The S–S overlap population shows a pronounced maximum near a dihedral angle of 90°, just where the total energy shows a minimum. This reflects larger S–S bonding character near equilibrium and furnishes semiquantitative support for the discussion based on hyperconjugation used by the experimentalists to explain the structure. A partitioning of the total energy into attractive and repulsive components shows tha...

Theoretical Studies of the Binding Energy and Geometry of the H5+ Molecular Ion

The geometry and binding energy of the H5+ molecular ion have been examined by two different ab initio quantum mechanical variational methods. In the first a CI wavefunction was made from the 10 covalent valence‐bond structures which could be constructed from 1s orbitals at the nuclei, each 1s orbital being represented by a five‐term Gaussian expansion and having a variable scale factor. For geometries identical or similar to the D2d geometry previously predicted from analogous calculations with cruder basis sets, we found no stability with respect to H3++H2. Other geometries were examined, especially those arising naturally from the approach of H3+ and H2; however, binding was never greater than a tiny 0.6 kcal/mole. We thus concluded that the method had failed adequately to describe H5+, as it had for H3+, and that it is probably unreliable for studying ions with small binding energies. The second method used the SCF MO model with a flexible basis set to account for distortion and polarization. This gav...