Abstract
IN this communication I shall point out a matrix multiplication property possessed by arrays of vibrational overlap integrals of diatomic molecular band systems. Consider any three electronic states L, M, N between which the L↔M, L↔N and M↔N transitions are allowed. Each of the wavefunctions ψ1 associated with vibrational levels l of L, and each of the wavefunctions ψn associated with the vibrational levels n of N, may be represented by an eigenfunction expansion of the wave-functions ψm of the levels m of M as follows: 
where 
is the vibrational overlap integral, r is the internuclear separation and (a,b)2 is the Franck–Condon factor qab.
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References
Murty, M. F., and Nicholls, R. W., Nature, 213, 1010 (1967).
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An erratum to this article is available at https://doi.org/10.1038/219544d0
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NICHOLLS, R. Matrix Property of Vibrational Overlap Integrals. Nature 219, 151–152 (1968). https://doi.org/10.1038/219151b0
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DOI: https://doi.org/10.1038/219151b0
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