L Veseth

Modifications of the doublet energy formulae of a diatomic molecule necessitated by the rotational stretching

The anomalies found in the spin splitting of a number of 2 Sigma states of diatomic molecules are explained by taking the rotational stretching (centrifugal distortion) of the molecule into account by using an adequate quantum-mechanical treatment. This calculation also yields both the true rotational dependence of the parameters p and q describing the Lambda doubling of the 2 Pi states, and the centrifugal distortion correction terms to the rotational energy. For the 2 Pi states the dependence of the spin-orbit coupling constant A on the internuclear distance gives rise to an additional correction term to the energy of the form AJJ(J+1). An expression for the parameter AJ in terms of spectroscopic quantities where values are usually known is derived, and tested for several examples.

Many‐body calculations of hyperfine constants in diatomic molecules. II. First‐row hydrides

Magnetic hyperfine parameters (Frosch and Foley parameters) have been computed for first‐row diatomic hydrides by use of many‐body perturbation theory. The computations are complete to third order in the many‐body expansion, which means that core polarization corrections are included through second and thrid order, and correlation effects by their leading third‐order corrections. Computed results are presented for the ground states, and in addition for the three excited states A 2Δ, A Π, and A 2Σ in CH, NH, and OH, respectively. The vibrational dependencies of the hyperfine parameters were also predicted, and even a hyperfine centrifugal distortion constant observed for CH was computed, in good agreement with experiment. Good agreements between computed and experimental parameters were generally obtained, in particular for the ground states, where the errors in the computed values are at most a few percent.

Term Values and Molecular Parameters for CH and CH

By using a model-independent statistical method, term values were determined for the rotational and vibrational levels of the X2Π, A2Δ, B2Σ-, and C2Σ+ electronic states of CH, and the X1Σ+ and A1Π states of CH+. Molecular parameters were obtained from a least squares fit to these term values. A method based on exact numerical diagonalization of the respective perturbation matrices yielded parameters for the X2Π and B2Σ- states of CH and the A1Π and X1Σ+ states of CH+, while the A2Δ and C2Σ+ states of CH had to be treated according to a polynomial model. In the case of CH several arguments indicate that the Λ-doubling of the X2Π ground state arises from interaction with the B2Σ- state. A discussion of the influence of the predissociation observed for the B2Σ- state on the X2Π Λ-doubling is also included. For CH+ good agreement was found between observed and pure precession values of the X1Σ+ - A1Π interaction matrix element.

Many‐body calculations of hyperfine constants in diatomic molecules. I. The ground state of 16OH

Magnetic hyperfine parameters (Frosch and Foley parameters) have been computed for the 2Π ground state of 16OH by use of many‐body perturbation theory. The computations are complete to third order in the many‐body expansion, and they were repeated for a series of internuclear distances around re to reproduce the vibrational dependencies of the parameters. Parameters were computed for the three lowest vibrational levels, and were found to be within 1%–2% of the very accurate experimental values. The rather strong vibrational dependencies of the parameters were reproduced with accuracies of 80%–90%. Finally, centrifugal distortion corrections to the magnetic hyperfine parameters were also computed, and for the one parameter (dD) observed, the error was about 5%. The vibrational wave functions needed were obtained from a published accurate CI potential curve. Thus, no empirical results are incorporated in the present ab initio calculations.

Molecular excitation energies computed with Kohn–Sham orbitals and exact exchange potentials

Exact local exchange potentials are computed for the diatomic molecules N2, O2, and CO, based on expansions in terms of molecular orbitals. Kohn–Sham orbitals and orbital energies are obtained for the exact exchange potentials, with correlation effects neglected. The ionization potential is in all cases found to be accurately predicted by the orbital energy of the highest occupied orbital. Limited configuration interaction calculations are performed based on the Kohn–Sham orbitals, and are found to yield accurate excitation energies for a series of singly excited states, in particular for N2 and CO. Clearly inferior results are obtained from similar calculations by use of Hartree–Fock orbitals. Thus Kohn–Sham orbitals obtained with exact exchange potentials tend to have an interesting potential as basis for sophisticated many-body methods.Exact local exchange potentials are computed for the diatomic molecules N2, O2, and CO, based on expansions in terms of molecular orbitals. Kohn–Sham orbitals and orbital energies are obtained for the exact exchange potentials, with correlation effects neglected. The ionization potential is in all cases found to be accurately predicted by the orbital energy of the highest occupied orbital. Limited configuration interaction calculations are performed based on the Kohn–Sham orbitals, and are found to yield accurate excitation energies for a series of singly excited states, in particular for N2 and CO. Clearly inferior results are obtained from similar calculations by use of Hartree–Fock orbitals. Thus Kohn–Sham orbitals obtained with exact exchange potentials tend to have an interesting potential as basis for sophisticated many-body methods.

Many-body calculations of atomic properties. I. gj factors

Many-body perturbation theory has been applied to compute expectation values of the one- and two-electron interactions which yield the relativistic corrections (Abragam-Van Vleck terms) to the atomic gJ factors. A two-electron term due to the motion of the atomic nucleus is also considered. The present calculations are based on analytic expansions of the single-particle states, and a main purpose of the work is to investigate the capability of this method for computations of complex atomic properties. The examples considered are the ground states of the alkali atoms up to rubidium, the ground states of the first-row atoms, and chlorine. The calculations are complete to third order and some fourth-order diagrams are also included. For the first-row atoms energy lowerings ranging from 82-92% of the experimental correlation energies were obtained, showing that a considerable amount of correlation has been included. The computed gJ factors are compared with high-precision experimental values and reasonable agreements for the troublesome cases of nitrogen and the fluorine 2P1/2 state are among the present achievements. Correlation effects were in several cases found to be of importance for the computed gJ factors.

Abinitio calculation of higher order corrections to Λ doubling and spin splitting in diatomic molecules

Higher order corrections to the L doubling in 2R states and spin splitting in 2S states of diatomic molecules have been derived by use of a Van Vleck transformation to third order. The corrections are expressed in terms of the parameters pJ, qJ, and gN, normally introduced through the phenomenological replacements pv→pv+pJJ(J+1), qv→qv+qJJ(J+1), and gv→gv+gNN(N+1). The molecules investigated are OH, OD, and SH, and ab initio values for pJ, qJ, and gN are computed for the X 2R,v = 0 and A 2S+,v = 0 states. The electronic matrix elements were obtained within the Hartree–Fock approximation, and vibrational eigenfunctions were computed from Morse curves for OH and OD and from RKR potentials for SH. Comparison of ab initio values and experimentally derived parameters shows reasonable agreement.

Fine Structure of 4Π States in Diatomic Molecules

The fine structure theory of 4Π states in diatomic molecules is reconsidered from the point of view of exact numerical diagonalization of the four-by-four perturbation matrix. The interaction with other electronic states is accounted for through a second order Van Vleck transformation. Centrifugal distortion corrections are also added to the matrix elements, and a new spin-spin matrix element of the type ΔΛ = -ΔΣ = ±2 is in particular found to contribute to the Λ-doubling. The theoretical results are applied to the a4Πu state in O2+ and the B4Π state in VO.

Hund's coupling case (c) in diatomic molecules. II. Examples

For pt. I see ibid., vol. 6, 1479 (1973). A theoretical discussion of the rotational energy and fine structure of Hunds case (c) states in diatomic molecules was given in Pt. I. In this paper the theoretical results are applied to several electronic states of heavy diatomic molecules. The states chosen are the E1/2 and F1/2 states of YbH and YbD, and A2 pi , B2 Sigma and C2 Sigma states of HgH and the x3 Sigma - ground states of AsF and SO. This variety of states exemplifies several aspects of the theory, which in particular for the 3 Sigma states gives a much more the traditional Hunds case (a)-(b) model.

Many-body calculations of atomic isotope shifts

The specific mass shift contribution to the isotopic shift in ionisation energies or selected transition frequencies has been computed for a series of atoms ranging from lithium to potassium. Many-body perturbation theory within the algebraic approximation was used to compute separate expectation values of the specific mass shift Hamiltonian for upper and lower states, and the computations are complete to third order. The nuclear field shift was also considered in some cases, and computed to third order. Good agreements with experiments were obtained in most of the cases investigated. The computed residual isotopic shift (specific+field shift) between 25Na and 23Na for the 2P-2S transition is 386.5 MHz, compared with an experimental shift of 375.4(1.3) MHz. Similarly the computed residual shift in the potassium ionisation energy (41K-39K) is found to be -59.8 MHz, in complete agreement with the experimental value of -61(2) MHz.