The A Matrix in Molecular Vibration-Rotation Theory

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DOIResolve DOI: http://doi.org/10.1006/jmsp.2000.8268
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TypeArticle
Journal titleJournal of Molecular Spectroscopy
Volume205
Issue2
Pages227231; # of pages: 5
SubjectCartesian coordinates; internal coordinates; A matrix; force constants; ab initio force fields
AbstractCrawford's A matrix in the theory of molecular vibrations is, in a sense, the inverse of Wilson's B matrix, but is not unique because B is rectangular. We consider the general form of A and then use the Eckart conditions to obtain the solution A = M-1BTG-1, which has been widely used. Although the internal-coordinate harmonic force constants F = ATFXA, where FX are the Cartesian force constants, are superficially isotope-dependent, we show that this dependence vanishes. More generally, solutions of the form A = WBT(BWBT)-1, where W is an arbitrary nonsingular square matrix, are shown to give an f matrix that is independent of W.
Publication date
AffiliationNational Research Council Canada; NRC Steacie Institute for Molecular Sciences
Peer reviewedNo
NPARC number12338888
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Record identifierec8f2b7e-eb08-4fc3-88fc-3d6bc809e7e4
Record created2009-09-11
Record modified2016-05-09
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