The Validity of Different Approximations in the Determination of Molecular Force Fields
Open Access
- 1 July 1968
- journal article
- Published by Walter de Gruyter GmbH in Zeitschrift für Naturforschung A
- Vol. 23 (7) , 1029-1033
- https://doi.org/10.1515/zna-1968-0712
Abstract
Various approximate solutions to the second order secular equation ((G·F)L = LΛ) in molecular spectroscopy are considered. New relations between them are developed and their validities tested empirically. It is found that the methods are decreasingly valid in the following order: a. „Verfahren der nächsten Lösung“ which considers the point on the surface of all real allowed solutions of F nearest to that corresponding to completely uncoupled oscillators. b. A distribution of the potential energy in v1 of V22= — V12 or V11 = 100%. c. F22 a minimum, equivalent to L12=0, V12= —2 V22 in v1 and in v2 V22=100%. This is the easiest solution to calculate (L matrix approximation method). d. The “Modified Valence Force Field” where F12=0. e. L matrix of maximum trace, equivalent to L = G1/2, having L12=L21 . f. F11 a maximum, equivalent to L21=0; V12= —2 V11 in v2 and in v1,V11=100%, being the second root of a quartic equation in F22 of which solution (b) is the first.Keywords
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