Robert J. Le Roy

Anisotropic intermolecular potentials from an analysis of spectra of H2‐ and D2‐inert gas complexes

A method is developed for analyzing the discrete infrared absorption spectra of the van der Waals complexes formed between H2 or D2 and Xe, Kr, Ar, or Ne. Its application involves automatic nonlinear least squares fits of trial spectra calculated from realistic three‐dimensional intermolecular potential models, to the experimental data. The secular determinant method used for calculating the energy levels of the anisotropic trial potentials proves to be highly reliable and relatively inexpensive. As a result, the present techniques should be readily applicable to cases where the anisotropic part of the potential is much stronger than it is here. The potential form used here is a Lennard‐Jones (m, 6) function with independent long‐ and short‐range anisotropy coefficients, and independent parameters characterizing the effect of the stretching of the hydrogen bond on the attractive and repulsive parts of the potential. The final fits concurrently used all uniquely assigned and nonoverlapping lines of both is...

Improved potential energy surfaces for the interaction of H2 with Ar, Kr, and Xe

A combined analysis of discrete infrared and microwave spectra, elastic and inelastic differential cross section measurements, and virial coefficient data has been used to determine improved potential energy surfaces for the H2–Ar, –Kr, and –Xe systems. Key improvements over previous surfaces for these species are an improved delineation of the diatom bond length dependence of the potential anisotropy, and the first experimental determination of a distinct P4(cos θ) anisotropy for an atom–diatom system. The effective anisotropy strength seen by bound state properties (such as transition frequencies) is found to increase from H2–Ar to H2–Kr to H2–Xe, although that seen by properties sensitive to the short‐range potential (such as rotational predissociation and rotational inelasticity) decreases along this series. This reflects the lack of conformality of the various potentials; however, both these and analogous trends predicted for properties such as vibrational frequency shifts and vibrational inelasticit...

Nonadiabatic eigenvalues and adiabatic matrix elements for all isotopes of diatomic hydrogen

Abstract For all bound and quasibound levels of the ground electronic state of all six isotopes of diatomic hydrogen, wavefunctions obtained from the most recent ab initio potentials are used to calculate expectation values of the nuclear kinetic energy, of various powers of R , and of the average polarizability and polarizability anisotropy, together with the off-diagonal matrix elements of the polarizability required for predicting the intensities of Raman transitions for Δ J = 0, ±2 and Δ v = 0, −1, and −2. A scaling procedure for treating the nonadiabatic eigenvalue corrections is developed, which allows an extrapolation beyond results reported for H 2 , HD, and D 2 to yield nonadiabatic level shift predictions for the three tritium isotopes. Features of this procedure which take account of implicit centrifugal distortion effects lead to significant improvements in the agreement between theory and experiment.

An accurate analytic potential function for ground-state N2 from a direct-potential-fit analysis of spectroscopic data

Two types of combined-isotopologue analysis have been performed on an extensive spectroscopic data set for ground-state N2 involving levels up to v=19, which is bound by half the well depth. Both a conventional Dunham-type analysis and a direct-potential-fit (DPF) analysis represent the data within (on average) the estimated experimental uncertainties. However, the Dunham-type parameters do not yield realistic predictions outside the range of the data used in the analysis, while the potential function obtained from the DPF treatment yields quantum mechanical accuracy over the data region and realistic predictions of the energies and properties of unobserved higher vibrational levels. Our DPF analysis also introduces a compact new analytic potential function form which incorporates the two leading inverse-power terms in the long-range potential.

Shape Resonances and Rotationally Predissociating Levels: The Atomic Collision Time‐Delay Functions and Quasibound Level Properties of H2(X 1Σg+)

The energy dependence of the collisional time‐delay function has been computed for H(1S) atoms interacting via the ab initio H2(X 1Σg+) potential. Peaks in this function determine the scattering resonance energies Er and widths Γ, and the lifetimes for each of the corresponding quasibound vibrational–rotational levels. Small differences are found between these Er and Γ, and the values obtained by a “maximum internal amplitude” approach (intended to characterize the spectroscopically observable predissociating levels). Approximate procedures for rapid, accurate numerical evaluation of Er are appraised; a new outer‐boundary‐condition criterion for resonances leads to the best agreement with the exact results. Also, a primitive WKB procedure yields Γs of usable accuracy. For ground‐state H2, HD, and D2 the onset of line broadening due to centrifugal barrier penetration is found to occur at energies some hundreds of cm−1 below the locus of barrier maxima. The predissociation method of estimating long‐range i...

Infrared spectrum and potential energy surface of He–CO

For 3He–CO and 4He–CO van der Waals bimers, fully resolved infrared spectra in the 4.7 μm region near the fundamental band origin of the CO monomer have been measured for the first time. Only a small fraction of the observed lines could be assigned using conventional empirical spectroscopic techniques, and little additional insight was gained from synthetic spectra generated from a published ab initio potential for this system. However, a complete set of unique assignments was made on the basis of comparisons with synthetic spectra generated from a variety of trial potential energy surfaces, and least‐squares fits to the observed transition frequencies were used to determine a new anisotropic potential energy surface for this system. This new surface is much deeper and has a much stronger well depth anisotropy than the best previous one, and its predictions of very low temperature microwave line broadening cross sections raise serious questions regarding the methodology for calculating that property.

Energies and widths of quasibound levels (orbiting resonances) for spherical potentials

Various methods for calculating the energies and widths of quasibound levels (orbiting or shape resonances) for spherical potentials are critically compared. A derivation for the previously‐proposed Airy function boundary condition method is presented, and a Weber function boundary condition method for locating resonances which lie above the potential barrier maximum is derived, tested, and found wanting. It is shown that the Weyl m‐function method of Hehenberger et al. [J. Chem. Phys. 65, 4559 (1976)] yields results in essentially exact agreement with the time‐delay maximum method of Le Roy and Bernstein [J. Chem. Phys. 54, 5114 (1971)]. An improved semiclassical method of calculating these resonance widths, suggested by M.S.Child, is presented and shown to be reliable even for levels lying right at a potential barrier maximum.

Diatom potential curves and transition moment functions from continuum absorption coefficients: Br2

A program for calculating diatomic molecule absorption coefficients using ’’exact’’ numerically computed radial wavefunctions was developed and used to examine critically a number of approximations which are frequently used in absorption coefficient calculations. These tests showed that both use of the delta function approximation, and fixing the rotational quantum number in the radial overlap integrals at J=0, introduce errors of ?4%–6% of the absorption coefficient maximum emax. Similarly, errors of ?1%–2% of emax are introduced by either fixing the initial state J at the average value for the given temperature, or by using Gislason’s Airy‐function approximation for the unbound state wavefunction. A simple procedure for shrinking the sum over initial state J’s without significant loss of accuracy was therefore devised. These techniques were then applied to the analysis of the visible absorption continuum of Br2, and a nonlinear least‐squares fitting procedure used to determine optimized final state pote...

Monte Carlo simulations of structural properties and infrared spectra of SF6–(Ar)n clusters

A method for predicting the perturbed infrared spectrum of a solvated chromophore such as SF6 in a mixed van der Waals cluster is developed and applied to a realistic model for SF6–(AR)n clusters with n=1–100. The dominant contribution to the band shift arises from the interaction of an induced dipole on the perturber with the oscillating instantaneous dipole of the vibrationally distorted SF6. Spectra generated by Monte Carlo averaging these frequency shifts over a canonical distribution of cluster configurations and over a plausible assumed cluster size distribution are in near‐quantitative agreement with experiment. For the smaller clusters (n≲18), features of the simulations point to the presence of two distinct classes of cluster structure, one in which the chromophore is wrapped in a unimolecular layer of atoms, and a second in which the solvent atoms have multilayered structures. However, the question of whether the infrared spectra can provide evidence for the presence of the kind of phase coexist...

Near-dissociation expansions in the spectroscopic determination of diatom dissociation energies: method, and application to BeAr+

A simple method for determining improved diatomic molecule dissociation energies by imposing the theoretically-known limiting behaviour at dissociation on experimental vibrational data which do not include levels lying in the limiting neardissociation region is described and demonstrated. Its application to BeAr+(X2∑+) yields XXXe = 4500 (±50) cm−1 and vD = 40.8(±0.5).