It might be of interest to members of this group to know that there
exist a set of symbolic procedures to generate term coefficients for
vibration-rotational energies of diatomic molecules in state singlet-SIGMA
in terms of radial coefficients in functions for potential energy,
adiabatic, nonadiabatic rotational and nonadiabatic vibrational effects,
i.e. including all terms of order m_e/M in a full effective hamiltonian,
according to a derivation by R. M. Herman in Advances in Chemical Physics,
103 (1998) 187-215; these term coefficients yield energies of which
differences correspond to transitions in infrared or Raman spectra. The
importance of the rotational g factor, in relation to nonadiabatic rotational
effects, is discussed by J. Oddershede, S.P.A. Sauer and myself in Advances
in Chemical Physics 111 (2000) 486-541. With appropriate software these
procedures can readily yield results equivalent to perturbation theory of
order 20 or more.
For intensities, procedures are also available for both vibrational
matrix elements and Herman-Wallis factors, which can be applied for
transitions of electric dipolar moment or other mechanism for spectra in
absorption or emission, or for electric dipolar polarisabilities for Raman
spectra. For matrix elements of vibrational coordinate, these elements can
be calculated for coordinate to arbitrary positive power, and for Herman-
Wallis factors the procedures generate expressions usable up to at least
DELTA v = 10. Applications of all these procedures are discussed in a
monograph The Vibrational and Rotational Spectrometry of Diatomic Molecules,
published by Academic Press, London, 1998.
Although these procedures are present in a form worksheet directly
acceptable for operation with Maple (release V 5), they can be readily
translated for use with other symbolic processors, such as Reduce.
These procedures are freely available at internet sites
www.cecm.sfu.ca/~ogilvie
or
www.maplesoft.com/apps/science/chemistry.html
The latter is part of the Share library made available by Waterloo Maple
Software Inc.
In case of any problems obtaining or operating these procedures, I
should be pleased to be of assistance.
J. F. Ogilvie
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