Ab Initio Variational Calculations of Molecular Vibrational-Rotational Spectra (Paperback)

Debra J. Searles

ISBN 10: 3540574654 / ISBN 13: 9783540574651

Editore: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Berlin, 1993

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Paperback. This monograph deals with ab initio variational calculations of vibrational-rotational spectra of bent triatomic molecules. It gives a comprehensive derivation of the Eckart-Watson Hamiltonian in terms of an "f" co-ordinate system. The derived Hamiltonian is in the most general form and so is shown to collapse to C2v and D3h rectilinear Hamiltonians. Concommitant with the derived Hamiltonians, a complete solution algorithm of the nuclear Schrodinger equation is detailed. The eigenfunctions of numerical finite-element solutions of three one-dimensional Schrodinger equations are spliced together to form configurational trial basis functions for the variational solution of the three-dimensional vibrational problem. These solutions, together with the symmetric top eigenfunctions, span the full vibrational-rotational Hamiltonian. Examples of variational solutions of the full vibrational-rotational Hamiltonians are given throughout the text. This Hamiltonian is useful for molecules containing massive nuclei and moreover, has been extremely useful in interpreting the rovibrational spectra of small molecules. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.

Codice articolo 9783540574651

Dati bibliografici

• Titolo: Ab Initio Variational Calculations of Molecular Vibrational-Rotational Spectra (Paperback)
• Editore: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Berlin
• Data di pubblicazione: 1993
• Lingua: Inglese
• ISBN 10: 3540574654
• ISBN 13: 9783540574651
• Rilegatura: Paperback
• Condizione: new

Descrizione articolo

Riassunto

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.

Contenuti

I. Historical Review.- II. Nuclear Motion.- III. Discrete Potential Energy Surfaces.- IV. Potential Energy Functions.- V. Finite-Element Solution of One-Dimensional Schrödinger Equations.- VI. Nuclear Schrödinger Formulation for Bent Triatomic Systems.- VII. Solution Algorithm and Integral Evaluation.- VIII. Dipole Moment Surfaces and Radiative Properties.- IX. Applications to Bent Triatomic Molecules.