Arthur A. Frost

Floating Spherical Gaussian Orbital Model of Molecular Structure. I. Computational Procedure. LiH as an Example

The Kimball—Neumark spherical Gaussian orbital model is extended to apply to the singlet ground states of the general molecule with localized orbitals. Formulas are presented for energy, electron density, dipole moment, and the forces on nuclei and the computational procedure is described. The model is applied to LiH and the results are discussed in detail.

Floating Spherical Gaussian Orbital Model of Molecular Structure. II. One‐ and Two‐Electron‐Pair Systems

The floating spherical Gaussian orbital (FSGO) model is applied to the He and Be atom isoelectronic sequences and to the molecules and ions: H2, He2+ +, HeH+, H3+, H4+ +, HeH−, LiH, and BeH+. Bond lengths are predicted generally to within 5% of accurate values. The He–He repulsive interaction is also calculated.

The Approximate Solution of Schrödinger Equations by a Least Squares Method

A method of approximation to the solution of a Schrodinger equation has been developed in which variation functions are used but no integrations are involved. The procedure involves the evaluation of the energy for a set of representative points in configuration space. The parameters in the variation function are then chosen by applying the condition that the mean square deviation of the energy from the average should be a minimum.

A Semi‐Empirical Equation for the Vapor Pressure of Liquids as a Function of Temperature

The slight reverse curvature in the plot of logP versus 1/T (P, vapor pressure; T, absolute temperature) may be explained on the basis of the nonideal behavior of the vapor together with the change in heat of vaporization with temperature. If it is assumed that ΔH is linear with T and that the van der Waals a/V2 term is a first approximation to the deviation from the ideal, the following equation may be obtained by integration of the Clapeyron equation: logP=A+BT+C logT+DPT2. The last term is the nonideal gas correction with constant D=a/2.303R2. With constants A, B, and C determined empirically, the equation reproduces experimental vapor pressures from the triple point to the critical point with an average deviation of 0.3 percent.

Delta‐Function Model. I. Electronic Energies of Hydrogen‐Like Atoms and Diatomic Molecules

The electron in a one‐electron atom or diatomic molecule is considered to move in one dimension on a line through the nuclei. The potential energy is taken as zero except at the nuclei where it goes to minus infinity as negative delta functions. The exact solution is easily obtained with the wave function accurately expressible as a linear combination of atomic orbitals. In contrast to the free electron model this method handles heteronuclear molecules, does not arbitrarily limit the coordinate, and can predict ionization energies.

Semiempirical Potential Energy Functions. I. The H2 and H2+ Diatomic Molecules

After setting up certain theoretical criteria for a semiempirical potential energy function, two such functions for H2+ and H2 are constructed, the simplest of which has the form V=e‐aR(e2R−b), where V is the potential energy with its zero corresponding to infinite separation. R is the internuclear distance, e the electronic charge, and a and b parameters. This function is used to correlate the experimental quantities: dissociation energy, equilibrium internuclear distance, force constant, third and fourth derivatives of V with respect to R, united atom energy, and critical distance.A more complicated function is also presented which with one molecular parameter fixed by the dissociation energy is capable of then predicting internuclear distance and force constant.

Approximate Series Solutions of Nonseparable Schrödinger Equations. II. General Three‐Particle System with Coulomb Interaction

The series solution method developed by Pekeris for the Schrodinger wave equation of two‐electron atoms has been generalized to handle any three particles with Coulomb interaction. Calculations have been carried out with wavefunctions through the sixth degree which result in a linear combination of 84 terms for the unsymmetrical case. Systems for which numerical results are given are: the hydride ion with nuclear motion, the trielectron (e+e—e—) or positronium ion, the positron—hydrogen atom interaction (e+e—p+), and the mu‐mesonic isotopic hydrogen molecule‐ion (p+μ—d+).

A floating spherical Gaussian orbital model of molecular structure

The FSGO model has been used to make ab initio calculations of the geometrical structures of borazane and diborane. Where experimental data are available there is good agreement between calculated and observed values.ZusammenfassungFür ab initio-Rechnungen zur geometrischen Struktur des Borazans und Diborans wurde das FSGO-Modell benutzt. Soweit experimentelle Werte vorhanden sind, stimmen die berechneten und beobachteten Werte gut überein.RésuméLa méthode FSGO a été utilisée pour effectuer des calculs ab-initio sur les structures géométriques du borazane et du diborane. Un bon accord est obtenu entre les valeurs calculées et les valeurs expérimentales existantes.

Floating Spherical Gaussian Orbital Model of Molecular Structure. IX. Diatomic Molecules of First‐Row and Second‐Row Atoms

The FSGO model is applied to a large group of diatomic molecules of first‐row and second‐row atoms, namely, Li2, Be2, B2, C2, N2, O2, F2, CO, PN, P2, CS, SiO, LiF, LiCl, NaF, NaCl, LiNa, and Na2. Groups of diatomic molecules of similar assumed bond structure—CO and N2; N2, PN, and P2; CO, CS, and SiO; LiF, LiCl, NaF, and NaCl; Li2, LiNa, and Na2—are compared within each group. All the bond lengths of the previous systems are predicted quantitatively with an average deviation of 7%.

Floating Spherical Gaussian Orbital Model of Molecular Structure. VI. Double‐Gaussian Modification

The floating spherical gaussian orbital model is modified to improve molecular energies and geometry by using a linear combination of two concentric spherical Gaussian orbitals (a double Gaussian) as the localized orbital. The double‐Gaussian model was applied to hydrogen, the first‐row atom hydrides, and a series of hydrocarbons. Bond lengths are predicted within 5.8% and bond angles within 6.6% for all the cases investigated. Molecular energies are generally 96% of Hartree–Fock values, and bond angles are improved.