Variational Calculations Of Rotation Vibration Spectra For Small Molecules Of Astrophysical Interest

This work had its beginnings in the early 1980s at the University ofWollongong, with significant contributions from Dr. Margret Hamilton, Professors Peter G. Burton and Greg Doherty. The emphasis was to develop computer code to solve the nuclear Schrodinger problem. For bent triatomic molecules the project was fmally realized at the University of Newcastle a decade or so later, with the contribution from Ms. Feng Wan g. Aspects of this work are now taught in the quantum mechanics and electron spectroscopy courses at The University of Newcastle. Even now "complete" ab initio solutions of the time-independent SchrOdinger equation is not commonplace for molecules containing four atoms or more. In fact, when using the Eckart-Watson nuclear Hamiltonian a further restriction needs to be imposed; that is, the molecule is restricted to undergoing small amplitudes of vibration. This Hamiltonian is useful for molecules containing massive nuclei and moreover, has been extremely useful in interpreting the rovibrational spectra of small molecules. Nevertheless, a number of nuclear Hamiltonians that do not embed an equilibrium geometry have become well established and are extremely successful in interpreting rovibrational spectra of floppy molecules. Furthermore, solution algorithms vary greatly from research group to research group and it is still unclear which aspects will survive the next decade. For example, even for a triatomic molecule a general form of a potential function has not yet been uncovered that will generally interpolate with accuracy and precision ab initio discrete surfaces.

The book reviews the results of vibration-rotational spectroscopy of molecules obtained recently by combining modern computational methods of quantum chemistry with the new techniques of high-resolution rotational and vibration-rotational spectroscopy. It shows for example that the tunneling vibration-rotational spectroscopy of the van der Waals complexes provides a new look at intermolecular forces while the high precision and sensitivity of the submillimeter-wave and Fourier transform microwave spectroscopy make it possible to study complex rotational spectra of molecules in excited vibrational states. New results of high level ab initio quantum chemical computations of vibrational and rotational energy levels and dipole moment functions of unusual molecules will be discussed together with the recent discovery of clustering of energy levels in asymmetric tops. Group theoretical analysis of floppy molecules, especially the tunneling effects in nonrigid molecules, will also be discussed.

Molecular Symmetry and Spectroscopy deals with the use of group theory in quantum mechanics in relation to problems in molecular spectroscopy. It discusses the use of the molecular symmetry group, whose elements consist of permutations of identical nuclei with or without inversion. After reviewing the permutation groups, inversion operation, point groups, and representation of groups, the book describes the use of representations for labeling molecular energy. The text explains an approximate time independent Schrödinger equation for a molecule, as well as the effect of a nuclear permutation or the inversion of E* on such equation. The book also examines the expression for the complete molecular Hamiltonian and the several groups of operations commuting with the Hamiltonian. The energy levels of the Hamiltonian can then be symmetrically labeled by the investigator using the irreducible representations of these groups. The text explains the two techniques to change coordinates in a Schrödinger equation, namely, (1) by using a diatomic molecule in the rovibronic Schrödinger equation, and (2) by a rigid nonlinear polyatomic molecule. The book also explains that using true symmetry, basis symmetry, near symmetry, and near quantum numbers, the investigator can label molecular energy levels. The text can benefit students of molecular spectroscopy, academicians, and investigators of molecular chemistry or quantum mechanics.

The definitive text on the rotational spectroscopy of diatomic molecules.

Radiative Processes in Astrophysics: This clear, straightforward, and fundamental introduction is designed to present-from a physicist's point of view-radiation processes and their applications to astrophysical phenomena and space science. It covers such topics as radiative transfer theory, relativistic covariance and kinematics, bremsstrahlung radiation, synchrotron radiation, Compton scattering, some plasma effects, and radiative transitions in atoms. Discussion begins with first principles, physically motivating and deriving all results rather than merely presenting finished formulae. However, a reasonably good physics background (introductory quantum mechanics, intermediate electromagnetic theory, special relativity, and some statistical mechanics) is required. Much of this prerequisite material is provided by brief reviews, making the book a self-contained reference for workers in the field as well as the ideal text for senior or first-year graduate students of astronomy, astrophysics, and related physics courses. Radiative Processes in Astrophysics also contains about 75 problems, with solutions, illustrating applications of the material and methods for calculating results. This important and integral section emphasizes physical intuition by presenting important results that are used throughout the main text; it is here that most of the practical astrophysical applications become apparent.