Mark M. Law

The intermolecular potential energy surface for CO2–Ar: Fitting to high‐resolution spectroscopy of Van der Waals complexes and second virial coefficients

Two potential energy surfaces for CO2–Ar are obtained by least‐squares fitting to the high‐resolution spectra of Van der Waals complexes and the second virial coefficients of Ar+CO2 gas mixtures. The potentials incorporate a repulsive wall based on monomer ab initio calculations and the assumption that the repulsion potential is proportional to the overlap of the monomer charge densities. The dispersion energy is represented in a two‐site model, with dispersion centers located along the C–O bonds of CO2. The resulting potentials give a good representation of all the experimental data with only three or four adjustable parameters. They are quite different from previous empirical CO2–Ar potentials, which all have either a poor representation of the attractive well or a poor representation of the repulsive wall.

A study of vibrational anharmonicity, fermi resonance interactions, and local mode behavior in CH3Cl

Abstract The infrared spectrum of CH 3 Cl has been studied up to 16 500 cm −1 and vibrational assignments made for up to six quanta of excitation in CH stretching. Analysis of a total of 66 vibrational levels has been made in terms of a joint local mode and normal mode model, local with respect to CH stretching vibrations and normal with respect to other vibrations. Fermi resonance interactions with CH 3 deformation overtones must be included in the analysis. Reproduction of the observed vibration levels with a rms error of 2.61 cm −1 is achieved in terms of a 37-parameter model, with the four anharmonicity constants and two Darling-Dennison constants associated with CH 3 group stretchings constrained to be interrelated through local mode relations. The parameters obtained are in excellent accord with those available for the other methyl halides, and with established structural differences between the molecules.

Microwave spectroscopy and interaction potential of the long‐range He...Ar+ ion

We have measured and interpreted a microwave spectrum of the HeAr+ ion in which all of the observed energy levels lie within 8 cm−1 of the lowest dissociation limit, He(1S)+Ar+(2P3/2). We use an ion beam technique in which the HeAr+ ions are formed by electron impact, accelerated to kilovolt potentials, and mass‐analyzed. After passage through an appropriate section of waveguide, the ions enter an electric field lens in which state‐selective fragmentation occurs; the Ar+ ions produced in the lens are separated from all other ions by means of an electrostatic analyser and detected with an electron multiplier. Microwave transitions induced in the waveguide section result in population transfer which produces detected changes in the electric field‐induced Ar+ fragment current. Many transitions have also been observed by a microwave–microwave double resonance technique. We have observed 68 lines spanning the frequency range 6–170 GHz; no immediately recognizable pattern is apparent. We have measured the Zeema...

I-NoLLS: a program for interactive nonlinear least-squares fitting of the parameters of physical models

Abstract The I-NoLLS program is a package for carrying out interactive nonlinear least-squares fits to determine the parameters of physical or mathematical models from experimental or other data, under circumstances where automated least-squares procedures are excessively computationally expensive and the user needs interactive control to apply physical insight to the fitting process. The program was developed to facilitate the fitting of molecular potential energy surfaces (PES) to spectroscopic and scattering data, but is also applicable to a variety of other optimization problems. A range of different algorithms adapted to highly nonlinear least-squares problems may be selected. The interactive nature of the code permits rapid and flexible control over the progress of the fit. I-NoLLS is written in a modular way that allows the easy incorporation of new modules for calculating observable quantities from model parameters. The structure of the program allows straightforward parallelisation of the time-consuming property calculations. In pilot applications, I-NoLLS has been interfaced with programs for calculating bound states of Van der Waals complexes, cross sections for molecular scattering processes, and second virial coefficients of gas mixtures. Parallelisation of the property calculations has been achieved using PVM running on a cluster of workstations.

Calculating energy levels of isomerizing tetra-atomic molecules. II. The vibrational states of acetylene and vinylidene

A general, full-dimensional computational method for the accurate calculation of rotationally and vibrationally excited states of tetra-atomic molecules is further developed. The resulting computer program may be run in serial and parallel modes and is particularly appropriate for molecules executing wide-amplitude motions and isomerizations. An application to the isomerizing acetylene/vinylidene system is presented. Large-scale calculations using a coordinate system based on orthogonal satellite vectors have been performed in six dimensions and vibrational term values and wave functions for acetylene and vinylidene states up to approximately 23 000 cm(-1) above the potential minimum have been determined. This has permitted the characterization of acetylene and vinylidene states at and above the isomerization barrier. These calculations employ more extensive vibrational basis sets and hence consider a much higher density of states than in any variational calculations reported hitherto for this system. Comparison of the calculated density of states with that determined empirically suggests that our calculations are the most realistic achieved for this system to date. Indeed more states have been converged than in any previous study of this system. Calculations on lower lying excited states of acetylene based on HC-CH diatom-diatom coordinates give nearly identical results to those based on orthogonal satellite vectors. Comparisons are also made with calculations based on HH-CC diatom-diatom coordinates.

Calculating energy levels of isomerizing tetra-atomic molecules. I. The rovibrational bound states of Ar2HF

A general, six-dimensional computational method for the accurate calculation of rotationally and vibrationally excited states of tetra-atomic molecules is developed. The resulting program is particularly appropriate for molecules executing wide-amplitude motions and isomerizations. An application to the Ar2HF van der Waals trimer is presented in which the HF intramolecular stretching coordinate is separated out adiabatically and is not treated explicitly. Vibrational term values up to about 100 cm–1 with absolute convergence to better than 0.1 cm–1 are reported. These calculations employ more extensive vibrational basis sets and hence consider a much higher density of states than hitherto. States that sample Ar–Ar–HF linear configurations and approach Ar–HF–Ar linear configurations are characterized for the first time. Results for total angular momentum J = 0 and 1 provide the first accurate calculations of rotational constants for this system. The rotational constants for the HF bending states of Ar2HF in the ground and first vibrationally excited states of the HF monomer are in good agreement with experiment, confirming the accuracy of the potential used in this work.

Microwave spectroscopy and interaction potential of the long‐range He⋯Kr+ ion: An example of Hund’s case (e)

We have observed a microwave spectrum of the HeKr+ ion in which all of the observed levels lie within a few cm−1 of either the first or second dissociation limit. We use an ion beam technique in which HeKr+ ions, formed by electron impact, are mass analyzed. Passage of the ion beam through an electric field lens results in selective fragmentation of energy levels lying close to dissociation. Kr+ ions formed in the lens are separated from all other ions by means of an electrostatic analyzer, and are detected with an electron multiplier. Microwave radiation induces transitions which result in population transfer and produce detected changes in the electric field‐induced Kr+ fragment ion current. Additional transitions have been detected by a microwave–microwave double resonance method, and we have also made extensive use of the Zeeman effects produced by small applied coaxial magnetic fields to identify the J quantum numbers of the levels involved. Coupled channel calculations of the bound states of the He⋯...

Joint local- and normal-mode studies of the overtone spectra of the methyl halides: CH3F,CH3Cl,CH3Br,CD3Br, and CH3I

The infrared spectra of CH3F, CH3Cl, CH3Br, and CH3I have been investigated in the range 2500–16u200a500u200acm−1 and that of CD3Br in the range 2000–7000u200acm−1. New experimental data are reported for CH3F and CD3Br and these data together with existing literature data for CH3Cl, CH3Br, and CH3I have been analyzed in terms of a hybrid local-mode/normal-mode model. Local-mode basis functions have been used for the C–H(D) stretching vibrations and normal-mode basis functions to describe the C–H(D) bending vibrations. This joint approach, which also takes account of Fermi resonances, enabled the determination of stretch/bend anharmonicity and Fermi-resonance parameter sets which reproduce the observed data over wide energy ranges and compare much more favorably with literature ab initio results than previous parameter sets. The analyses have lead to a new vibrational assignment in CH3Cl and two corrected band centers in CH3Br and CH3I and predictions of unassigned bands raise several challenges to experiment.

Vibrational anharmonicity in dideuteromethane: a study of its infrared spectrum up to 17 000 cm−1

Abstract Vibrational assignments for CH 2 D 2 are made from a detailed study of its gas-phase infrared spectrum below 17u2008000 cm −1 , up to six quanta of CH stretching excitation. Some 77 overtone and combination vibration levels are identified. These allow extraction of empirical values for approximately one-half of the 45 normal mode anharmonicity constants, and their comparison with recent ab initio predictions. Severe Fermi resonance perturbations at low excitation levels in both CD 2 stretching manifolds preclude the direct extraction of any of the 17 associated anharmonicity constants. However, observation of seven Fermi resonance diads below 4000 cm −1 permits the accurate definition of the corresponding cubic resonance parameters, and the determination of unperturbed CD 2 stretching fundamental wavenumbers. A simple local mode interpretation of the unperturbed stretching vibrational manifold in CH 2 D 2 is attempted. This then yields the 10 corresponding normal mode CH and CD stretching anharmonicity constants consistent with the model applied.

General internal coordinate gradient vectors and the vibrational kinetic energy operator of centrally-connected penta-atomic systems. Part I

New internal coordinate gradients, s-vectors, are derived using geometric algebra. The internal coordinates are based on a completely general description of the molecular geometry in terms of internal vectors. The internal coordinate gradients allow kinetic energy operators to be easily expressed in terms of orthogonal or non-orthogonal coordinate systems. Using this approach, a new exact vibrational kinetic energy operator for centrally-connected penta-atomic systems is derived for an internal polyspherical coordinate system based on orthogonal internal vectors. Difficulties associated with the well known coordinate redundancy in centrally-connected penta-atomic systems are discussed and overcome.