Wilfried Meyer

A variational method for the calculation of vibrational energy levels of triatomic molecules using a Hamiltonian in hyperspherical coordinates

A full variational procedure is presented which is particularly suited to the calculation of vibrational (J=0) energy levels of triatomic potentials with large amplitude motions and also allows for high permutational symmetries. Starting from simple basis functions reflecting the structure of the kinetic energy operator, an optimized basis set is derived by a step‐wise contraction scheme. The method is applied to H+3 and Na+3 (D3h) and to model potentials for H2O+ (C2v) and HLiH− (D∞h). The results for H+3 are shown to be superior to all previous calculations, in particular for those energy levels that lie above 20u2009000 cm−1. A new ab initio potential is presented for Na+3, for which converged energy levels are calculated up to 3500 cm−1. For H2O+ and HLiH−, the calculated energy levels agree with those obtained from a variational procedure in internal valence coordinates.

The ground state potential of the beryllium dimer

Abstract An ab initio X1Σg+Be2 ground state potential is determined from all-electron SCF/valence-shell MR-CI calculations which account for core-valence correlation by an effective core polarization potential. The position of the minimum is found at Re=4.627 bohr in full agreement with experiment and the dissociation energy is obtained to De=4.068 mEh (893 cm−1, significantly larger than the experimental estimate of D e =790 ± 30 cm −1 . ΔG 1 2 is calculated from an analytical form of the potential to be 218.4 cm−1, in slight variance with the observed value of 223.8 cm−1. Discrepancies below 10 cm−1 remain with the observed (less accurate) higher vibrational spacings. The deep inner minimum is shown to be related to chemical binding from interaction with a promoted configuration of spin-paired 3P atoms.

Long-range interactions in H-He:ab initio potential, hyperfine pressure shift and collision-induced absorption in the infrared

SummaryThe collisional complex H-He, with both atoms in their electronic ground-states, is treated as a molecule in self-consistent field (SCF) and multi-reference configuration interaction (MR-CI) calculations to determine interaction energy, dipole moment and spin density as function of internuclear separation. A basis set tailored for long-range interactions was used and the basis set super-position errors were controlled. The resulting functions are analyzed and presented in analytical form, in terms of exchange and damped dispersion contributions. For all three properties there is full agreement with the accurately known long-range coefficients, but the dipole moment function shows rather large overlap effects even at large distances which obscure higher-order dispersion coefficients. The well depth of 22.56 µEh is significantly deeper than most recentab initio calculations and model potentials have suggested, but our number corroborates existing semi-empirical values. Likewise, the calculated spin density variations are more pronounced than recent work has suggested. The resulting hyperfine pressure shift of H atoms in a helium buffer gas is in very good agreement with experiment, except for temperatures of the order of 1 K. Infrared absorption continua associated with the induced dipole moment are evaluated for their astrophysical interest.

On the bonding in doubly charged diatomics

SummaryThe potential energy of interacting atomic ions A++B+ often shows a shallow local minimum separated by a broad potential barrier from the dissociation products at much lower energy. Early interpretations of dication potential shapes were based on the similarity of the electronic structure between isoelectronic neutral and ionic species and led to a picture of a chemical bond superimposed on a repulsive Coulomb potential. More recently, barriers in dication potentials have commonly been interpreted as avoided curve crossings involving covalent and ionic structures. In this paper, we demonstrate that the former model is the appropriate one except in cases with very small asymptotic ionic/covalent energy splittings. By deriving dication wavefunctions from their neutral isoelectronic counterparts, we obtain upper bound dication potential curves which show all the characteristic features. By further modeling induction effects, we arrive at an almost quantitative fit of accurateab initio dication potentials. The “chemical bond plus electrostatic repulsion’ interpretation of dication interactions also explains why the accurate calculation of potential curves appears to be much more demanding for dications than for isoelectronic neutrals.

Long‐range interaction coefficients for the metastable states of He

Following the lines presented in a recent paper [J. Chem. Phys. (unpublished)] reduced spectra representing the dynamic polarizabilities are reported with special emphasis on accurate values for the metastable states of the He atom. Together with the reduced spectra taken from Ref. 1, long range interaction coefficients are computed for all combinations between the three lowest He states and the atoms H, Li, Na, K, and H−.

Collision-induced emission and sonoluminescence

It is well known that infrared inactive gases such as hydrogen and nitrogen are capable of absorbing infrared radiation efficiently if the gas densities are sufficiently high. The absorption is due to dipole moments induced by exchange, overlap, and dispersion forces, and/or multipolar induction, in pairs (triples, etc.) of interacting molecules. These collision-induced dipoles also emit radiation in the infrared and, at sufficiently high temperatures, in the visible and near ultraviolet as well. We estimate the shape and intensity of the binary emission spectra of nitrogen and nitrogen-argon mixtures, along with the opacities of such sources. At densities of several times 1021 molecules per cubic centimeter and temperatures in the ten thousand kelvin range, the computed spectra match the spectral profiles and emission intensities of sonolumiscence in air, nitrogen, and nitrogen-argon mixtures, etc., at wavelengths from 200 to 700 nm. The work suggests that the radiation source is optically thin. Detailed...

Ab initio Interaction-Induced Dipoles and Related Absorption Spectra

The interaction-induced dipole moments of pairs like H-He, He-Ar, H2-He, H2-Ar, and H2-H2 have been calculated by treating the complex of the two molecules as a supermolecule in the self-consistent-field and size-consistent, coupled-electron pair approximations as well as by the multi-reference-configuration-interaction method. Whenever H2 is involved, rotovibrational matrix elements of the induced dipole components are calculated and used as input for the line shape calculations of rototranslational, fundamental and first overtone induced absorption bands of H2. For comparison with spectroscopic measurements, we also compute interaction-induced absorption line shapes, taking into account the dependences of the interaction potential on vibrational excitation. Measured and calculated spectra are found to be in close agreement, even in the far wings.

High resolution studies of the dissociative attachment of low energy electrons to state‐selected sodium dimers

We present data on the vibrational level dependence of negative ion formation by dissociative attachment (DA) to Na2(v), together with preliminary theoretical results for vibrational enhancement derived from the relevant potential energy curves. We show that, for sodium molecules and our electron energy distribution, the DA rate increases with v″ by more than three orders of magnitude. Above a critical value, here identified as v″c=12, the DA rate is rather insensitive to v″. Preliminary results obtained with a newly developed photoelectron source show that the rate for DA to levels v″≥12 decreases rapidly with the electron energy Eel in the range 0≤Eel<10 meV.