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Algebraic Theory of Molecules$
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F. Iachello and R. D. Levine

Print publication date: 1995

Print ISBN-13: 9780195080919

Published to Oxford Scholarship Online: November 2020

DOI: 10.1093/oso/9780195080919.001.0001

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Prologue to the Future

Prologue to the Future

(p.190) Chapter 8 Prologue to the Future
Algebraic Theory of Molecules

F. Iachello

R. D. Levine

Oxford University Press

At this point, we hope to have demonstrated that the algebraic approach provides a viable method for the quantitative description of molecular vibrotational spectra. Chapters 4 (triatomic molecules, both linear and bent) and 5 (linear tetratomic molecules) and Appendix C provide extensive documentation for the quantitative applications, while Chapter 6 shows that larger molecules can also be treated. Throughout, but most particularly in Chapter 7, we have sought to forge a link with the more familiar geometrical approach. It is precisely our requirement that even in zeroth order the Hamiltonian with which we start describes an anharmonic motion, which makes this link not trivial. The advantage of our approach in providing, even in zeroth order, high overtone spectra that are typically more accurate than 10 cm−1, should not be overlooked. Yet much remains to be done. In this chapter we look to the future: Where and why do we think that the algebraic approach will prove particularly advantageous? Of course, what we really hope for is to be surprised by unexpected new developments and applications. Here, however, is where we are certain that some of the future progress will be made, with special reference to the spectroscopy of higher-energy states of molecules. One area of spectroscopy where the Hamiltonian in matrix form is the route of choice is that of large polyatomics, particularly so when in an electronically excited state (see Note 3 of the Introduction). Such states are isoenergetic with very high vibrational overtones of the ground electronic states so that a fully geometrical approach is impractical. Even at lower energies, the exceedingly high density of vibrational states strongly favors an alternative approach, and the use of model Hamiltonian matrices is not uncommon. Such model matrices are introduced in order to account for the regularities that often survive in the observed spectrum. One such striking feature is often referred to as a “clump” (Hamilton, Kinsey, and Field, 1986). Consider a pure vibrational progression of states, as can be observed in stimulated emission spectroscopy.

Keywords:   clump, electron-molecule scattering, sequential coupling, spectral clump, sudden approximation

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