Frank O. Ellison

Modified Atoms‐in‐Molecules Model for Predicting Diatomic Ground‐ and Excited‐State Potential‐Energy Curves. I. LiH, BeH, and BH

A model is proposed for the approximate calculation, starting with theoretical atoms‐in‐molecules‐like composite functions (or linear combinations of valence bond structures) of potential‐energy curves for ground and excited diatomic systems. The assumptions which define the model may be summarized as follows: (1) diatomic electronic eigenstates are represented by a linear combination of composite functions which, in their orbital approximation, are constructed from a common basis set of atomic orbitals; (2) all valence (or peel) orbitals associated with a given nucleus contain a common orbital exponent, which is a nonlinear variational parameter in the molecular calculation; (3) the total molecular energy is separated into its intra‐atomic and interatomic parts; (4) the intra‐atomic energy of a given atom (or ion) is separated into its core (inner‐shell) and peel (valence‐shell) contributions; (5) the peel energy of a given atom (or ion) in the molecule is estimated from the experimental peel energy of t...

Calculation of Atomic Valence State Energies

Given a molecular valence‐bond wave function (constructed according to the approximation of perfect pairing), the general theory is presented for calculating either (1) the energy following complete nonadiabatic dissociation of the atoms (hence, the promotional energy) or (2) the intra‐atomic energy of the molecule for equilibrium positions of the nuclei. It is found that existent methods and tables are generally sufficient for treating only molecules having less than two unpaired electrons and, if hybridization is admitted, only molecules having less than two bonds. Tables are here given which serve the needs with respect to all possible structures involving s‐ and p‐valence electrons. Promotional energies for the CH and CH2 molecules are derived for illustration.

On the Theoretical Calculation of Vibrational Frequencies and Intensities of Polyatomic Molecules; H3+, H2D+, HD2+, and D3+

A straightforward method is described for calculating the fundamental vibrational frequencies and intensities for a polyatomic molecule starting with a theoretically obtained potential energy surface and associated electronic state wavefunction. Given the latter two quantities, this method is much easier to carry out than the common reverse problem of predicting force constants from observed frequencies and molecular dipole moment derivatives from absolute intensities. The proposed method can be programmed easily and generally to handle any polyatomic system for which a theoretical energy surface and electronic‐state wave‐function are available. An application to H3+ and its isotopic counterparts is described.

Role of Exchange Energy in Intermediate‐Range Interactions

Computations have been made of the Coulomb and exchange parts of the interaction energies of a proton with a hydrogen atom and of two hydrogen atoms. It is found that the exchange energy becomes a more important and Coulomb energy becomes a less important fraction of the first‐order interactions (i.e., interaction of ground‐state atoms with no configuration interaction) as the internuclear distance is increased. It is also shown that the first‐order contribution is necessary to bring the perturbation calculations of Coulson on H2+ and of Lowdin and Hirschfelder on H2 into good agreement with experiment for intermediate separations.

Calculation of Atomic Valence State Energies of B—, C, and N+ in BHn—, CHn, and NHn+, n = 1 to 4

A general procedure described previously for calculating atomic valence state energies is simplified and extended to calculation of the intra‐atomic portion of resonance energies of two or more valence bond structures. The revised method is illustrated by its detailed application to the 1A1 state of CH2 (in which, however, the nuclei are displaced to a linear configuration). The atomic valence state and intra‐atomic resonance energies of B—, C, and N+ in various electronic states of BHn—, CHn, and NHn+, respectively, are then given as a function of hybridization.

Semiempirical Valence Bond Calculations of Electronic Energies of CH, CH2, CH3, and CH4

A new energy formula based upon valence bond theory is derived for the ground and some low‐lying excited states of CHn molecules. The formula essentially partitions the molecular energy into the following parts: promotional energy, Coulomb energy, bond exchange energy, exchange energy from nonbonded interactions (homogeneous and heterogeneous separately), and resonance energy (involving covalent structures only). Dependencies of all parts on hybridization are taken into account. Experimental energies of atomization of the 2Π and 2Δ states of CH, and of CH4, are used to calibrate the method, and a C–H distance of 1.12 A is used throughout. The unobserved 4Σ— state of CH is predicted to be 10.4 kcal (0–0 difference) above the ground state. A linear 3B1 ground state of CH2 is obtained; 0–0 transitions to strongly bent (100°) 1A1 and linear 1B1 states are predicted at 12.4 and 25.0 kcal, respectively. The energy of CH3 is minimum when planar. C–H bond dissociation energies (in kcal) are predicted as follows: ...

Intensities of Vibrational and Rotational Spectra of Charged Diatomic Molecules

It is shown that there exists a contribution to the transition moment (and hence to the spectral intensity) associated with pure rotational and with vibration‐rotational transitions which is proportional to the net charge residing on the molecule and to the difference in masses of the nuclei. Hence, molecule‐ions such as HD+ and (Cl35Cl37)+ should absorb and emit dipole radiation with significant intensity in the vibrational and rotational spectral regions.

Calculation of the Dissociation Energy of NH by a Semiempirical Interpolative Method

Simple valence bond wave functions (using hybridized orbitals) are constructed for the CH, NH, and OH molecules. The intraatomic energy is evaluated by Moffitts atoms‐in‐molecules method. The interatomic energy is approximated by: (1) replacing heavy‐atom 1s electrons by point charges at their nuclei; (2) restricting exchange energy contribution to permutation of bonding electrons; (3) using Mulliken approximation to reduce exchange and hybrid integrals to Coulomb and overlap types; (4) evaluating one‐center integrals by the Pariser approximation and by a new method which utilizes the virial theorem; and (5) expressing two‐center integrals by simplified expressions which give correct semiempirical values at R=0 limit and which contain two arbitrary parameters. The latter are adjusted so as to yield correct dissociation energies of CH and OH. The dissociation energy of NH is then found to be 3.61 ev, which lies within the uncertainty of the best experimental result 3.7±0.5 ev. Calculated degrees of hybrid...

Nuclear Magnetic Shielding Constants for Two‐, Three‐, and Four‐Electron Atoms and Ions

Values of nuclear magnetic shielding constants for two-, three-, and four-electron atoms and ions are compared and discussed. It was concluded that the error sigma /sub NR/-- sigma /sub HF/ = delta sigma approximates 0 for two- and three-electron systems, but delta sigma > 0 or sigma /sub NR/ > sigma /sub HF/ for four-electron systems. (P.C.H.)

Approximating Two‐Electron Atomic Energies Using Scaled Eigenfunctions : Semiempirical Coulomb‐Repulsion Integrals

If all electron coordinates in an exact atomic eigenfunction are multiplied by a scaling factor, the kinetic, potential and total energies are modified. Exact equations are derived for these changes. The one‐electron energy for a two‐electron atom is approximated using scaled one‐electron eigenfunctions leading to a semiempirical estimate of the (1s1s:1s1s) Coulomb‐repulsion integral. Finally, two‐electron atomic energies are approximated using scaled eigenfunctions for the corresponding one‐electron atom and a two‐electron atom of different nuclear charge.