Walter B. England

Accurate ab initio scf energy curves for the lowest electronic states of co2/co−2

Abstract Accurate ab imtio SCF calculations show that CO − 2 is metastable, with an electron affinity that is significantly larger in magnitude than previously calculated. C 2v group vibrational frequencies and a barrier height for autodetachment are determined for CO − 2 . Agreement with experiment is good.

Ab initio study of CaO. The importance of atomic correlation and a bondlength question

Abstract Extensively correlated ab initio potential energy and dipole moment curves are calculated for the X 1 Σ + , a 3 Π, A 1 Σ + , and 3 Σ + states of CaO over the range 3.0 au ⩽ R ⩽ 6.0 au. The calculations are the first which correctly predict that X 1 Σ + is the ground state of CaO. Vertical spectra, adiabatic spectra, spectroscopic constants, curve crossings, and dipole moments are determined. The 3 Σ + results are apparently the first accurate values available. The dipole moment function is a linear function of bondlength for the Π states and 3 Σ + . Two extrema occur in the dipole moment function of X 1 Σ + . Combined with experimental results, this suggests that μ(X 1 Σ + ) exhibits a maximum near R e in the heavy alkaline earth monoxides. The μ(A 1 Σ + ) increases sharply near R e . The X 1 Σ + calculations require special attention near R e : Localized ionic entities are involved which have different MO configurations and different correlation requirements. A second-order theory which correctly describes atomic correlation is necessary. The ab initio bondlengths are systematically larger than the experimental bondlengths by amounts that are greater than the expected accuracy limits of the calculations. This overestimation is also observed in KF, KCl and KOH, but ab initio bondlengths of the lighter metal alkali halides and alkaline earth monoxides agree closely with experiment. It appears that the core electrons must be responsible, possibly because of explicit core correlation requirements and/or relativistic corrections.

A field‐theoretic model Hamiltonian for the proper dissociation of multiple bonds

Lipkin’s modified eigenvalue problem is derived for a BCS function which violates general conservation laws. The results allow for the proper description of multiple bond formation and dissociation, and provide a zeroth‐order problem for ordinary many‐body perturbation theory. The method is illustrated for the proper dissociation of N2.

A simple CI model for the valence CI bands in CO+2 and isovalent ions. Ionization potentials of CO2 in the 20–30 eV range

The qualitatively correct Mulliken–Walsh Aufbau rules are used to derive a simple CI model for the energy differences between the valence CI bands and the valence MO bands in CO+2 and isovalent ions. The essence of the model is that the valence CI bands form multiplet terms, and at least one member of the multiplet has the same symmetry as, and interacts weakly with, at least one MO ion level. In this case, a common set of orbitals may be derived and modest CI calculations simultaneously provide accurate term splittings and at least one accurate energy separation between one term and one known lower energy MO ion state. CI calculations which include roughly 2000 or fewer spin and space adapted configurations are used to determine all valence CI band ionization potentials of CO2 in the 20–30 eV range. Agreement with observed peaks is typically very good.

Quantum field theoretical methods in chemically bonded systems

A new perturbative method is applied to single bonds. The starting model is the second-quantized self-consistent Heitler-London model. The unperturbed function is a four-determinant Bardeen-Cooper-Schrieffer function. Perturbative corrections are computed with renormalized Feynman diagrams. Convergence is satisfactory by third order. Calculated (experimental) dissociation energies in eV are 4.61 (4.75) for H2, 2.37 (2.52) for LiH, 6.22 (6.13) for FH, and 1.88 (1.66) for F2. Calculated (experimental) equilibrium bond distances in A are 0.739 (0.741) for H2, 1.598 (1.596) for LiH, 0.903 (0.917) for FH, and 1.395 (1.412) for F2. Calculated (experimental) vibrational frequencies in cm−1 are 4578 (4401) for H2, 1396 (1406) for LiH, 4447 (4138) for FH, and 927 (916) for F2. Other spectroscopic constants agree with experiment to within 11% except for anharmonicities which differ from experiment by up to 20%.

Nondegenerate many‐body theory and the treatment of conservation principles

Projection operators are used to formulate Lipkin’s modified Hamiltonian. By projecting from independent quasiparticle states, a convenient general nondegenerate many‐body perturbation theory is generated. A unique feature is that the final results satisfy conservation principles. Practical consequences include ordinary diagrammatic expansions and equations‐of‐motion for treatments of alternant molecular orbital wave functions.

POSITIVE ORBITAL ENERGIES AND THE INSTABILITIES OF ORBITAL-OPTIMIZED WAVE-FUNCTIONS

A simple relation between positive orbital energies and the instability of many‐particle wave functions is established for many‐particle systems. Positive orbital energies in Hartree–Fock wave functions imply many‐particle wave function instability. Positive orbital energies in multiconfiguration self‐consistent‐field wave functions do not necessarily imply total wave function instability. The determining factor is the occupation number of the orbital having the positive energy. Based on this, an approximate stability condition is stated for general multideterminantal wave functions.

VALENCE STATES OF C2 FEYNMAN'S WAY

Feynman’s way is used to calculate total-energy curves for the X 1Σg+, a 3Πu, b 3Σg−, A 1Πu, c 3Σu+, 1 1Δg, 2 1Σg+, d 3Πg, C 1Πg, e 3Πg, D 1Σu+, and C′ 1Πg valence states of C2. Lewis structures are derived for each state. Average (maximum) deviations of calculated spectroscopic constants from experiment are 1.9 (4.3) pm for Re, 18 (32) kJ/mol for De, 12 (36) kJ/mol for Te, 62 (162) cm−1 for ωe, and 16 (31) kJ/mol for asymptotic excitation energies.