Martin L. Sage

Morse oscillator transition probabilities for molecular bond modes

Abstract All analytical procedure is presented which allows exact computation of many matrix elements for the bound states of the Morse oscillator. Model calculations are given for the local modes model of the CH stretch in aromatic hydrocarbons.

CALCULATION OF VIBRATIONAL FUNDAMENTAL AND OVERTONE BAND INTENSITIES OF H2O

Vibrational intensities are calculated for the fundamental and overtone transitions of H2O up to approximately 18 000 cm−1. The intensities are determined from a dipole moment function expanded in the three internal bond coordinates. The expansion coefficients are computed ab initio at the second‐order Mo/ller–Plesset level of theory with a 6‐311G** basis set. Vibrational wave functions are calculated either from a three‐dimensional harmonically coupled anharmonic oscillator (HCAO) model which uses Morse oscillators to represent both the stretches and the bend of H2O, or from a variational calculation employing the best available potential energy surface and an exact kinetic energy operator. To obtain the most meaningful vibrational intensities we define dipole moment components using the Eckart embedding. Both the HCAO and the variational intensities agree quite well with the experimental results, which span eight orders of magnitude. From the calculations we predict that it may be possible to detect as ...

Intensities of high-energy molecular C–H vibrational overtones

Abstract We present an analysis of the intensities of the C–H vibrational 0-υ (υ = 2–6) of naphthalene in terms of the local bond mode model.

Energetics, wave functions, and spectroscopy of coupled anharmonic oscillators

The structure of the energy levels, wave functions, and spectroscopy of two identical coupled Morse oscillators is explored as a function of anharmonicity and of the strength of kinetic and potential coupling constants. Changes in anharmonicity are found to make relatively small changes in properties of the coupled oscillators. Natural local modes are used to discuss the nature of exact wave functions.

Application of the magnus expansion for high-order multiphoton excitation

Abstract In this paper we present the results of a study of the multiphoton dynamics of a truncated Morse oscillator, calculating the dependence of the dissociation probability from the uppermost level and of the mean vibrational excitation energy on the intensity and the frequency of the electromagnetic field. These calculations were performed for several forms of the dipole moment operator, involving linear and exponential dipole functions. These calculations establish the validity range of the rotating wave approximation (RWA), which allows the use of the effective hamiltonian formalism to treat the dynamics. The calculations demonstrate the applicability of the Magnus expansion to the multiphoton excitation of a sparse level system for which the RWA is not applicable. This work also establishes two effects of the form of the dipole moment operator on multiphoton excitation of the oscillator. These involve the possibility of the occurrence of bottlenecks in the radiative coupling matrix elements, which reduce the efficiency of multiphoton excitation and the presence of radiative coupling between nonadjacent energy levels, which greatly enhance the efficiency of excitation. Both of these effects can lead to the breakdown of the RWA, even for moderately small multilevel systems.

The vibrations and rotations of the pseudogaussian oscillator

Abstract In this paper we discuss the energy levels and wavefunctions of a rotating diatomic molecule using a three-parameter model potential called the pseudogaussian potential which is reasonably behaved for both small and large internuclear separations. The solutions to this model problem provide a reasonable description of the rotating diatomic molecule and also will be useful in discussing large amplitude vibrations in triatomic and larger molecules. A comparison is made with the Morse oscillator.

Resonance structure and background absorption in high-overtone molecular spectra

Abstract We advance a theory for intramolecular dynamics of large molecules containing X-H bonds. A random coupling model for the absorption spectra of high overtones of X-H bonds is developed.

Comparison of the Morse and Deng-Fan potentials for X-H bonds in small molecules

We use the Morse and the Deng-Fan potentials to treat the X-H stretching motion in small molecules. The Deng-Fan potential is qualitatively similar to the Morse potential but has the correct asymptotic behaviour as the internuclear distance approaches 0. We use the Deng-Fan potential to calculate transition frequencies and intensities of overtones of X-H stretching vibrations. Parameters for the Morse oscillator can readily be found from a Birge-Sponer fit of experimental transition frequencies. We describe a procedure to find the parameters for the Deng-Fan oscillator. We compare the potentials, wavefunctions, and matrix elements of the Morse and the Deng-Fan oscillator models. In the examples considered the Deng-Fan potential does not predict observed energy levels and intensities significantly better than the Morse potential despite its correct asymptotic behaviour.

High overtone C–H and O–H transitions in gaseous methanol: Theory

High vibrational overtones observed in the laser photoacoustic spectrum of gaseous methanol are interpreted in terms of coupled anharmonic C–H bond modes and an anharmonic O–H bond mode coupled to harmonic C–O and <HOC modes. An ab initio SCF calculation is used to estimate the harmonic part of the potential and the dipole moment operator.

Validity of the rotating wave approximation for high-order molecular multiphoton processes

Abstract We examine the sufficient conditions for the applicability of the rotating wave approximation (RWA) for high-order multiphoton excitation (HOME) of a sparse many-level molecular level structure, and demonstrate the breakdown of the RWA for HOME of the entire bound spectrum of a Morse oscillator. We propose that the Magnus expansion for the time-evolution operator provides a useful, practical and powerful method to surpass the RWA.