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Directional centrifugal constants and effective vibrational frequencies

Chemical Physics
Publication Date
DOI: 10.1016/s0301-0104(02)00506-2


Abstract The directional centrifugal distortion constant D v( u ) of a molecule in the direction of a unit vector u is defined as D v( u )=− 1 4 ∑ αβγδτ v αβγδu αu βu γu δ, where τ v αβγδ is the effective Wilson–Howard centrifugal tensor in the vibrational state v. Observable directional centrifugal constants are limited in two ways: (i) they are averaged over the eight octants, (± u a , ± u b , ± u c ) with uncorrelated ± signs, so that it is sufficient to consider the average D v( u ) with u in the positive octant, and (ii) the D v( u ) can only be measured for directions u satisfying a certain equation. The observable directions u consist of the isolated direction b along the b-axis, and the directions corresponding to a continuous curve on the unit sphere from a along the a-axis to c along the c-axis. Intermediate directions on this curve include the diagonal d =(1,1,1)/ 3 and the equipartition direction e =(A v −1/2 , B v −1/2, C v −1/2)/( A v −1+ B v −1+ C v −1) 1/2, where A v , B v and C v are the principal rotational constants. One choice of the five determinable centrifugal constants of an asymmetric top consists of D v A , D v B , D v C , D v D and D v E , which are the values of D v( u ) for u= a, b, c, d and e, respectively. From D v( u ) an effective vibrational frequency ω v( u ) is defined for each u. This is a measure of the stiffness of the molecule opposing centrifugal expansion about the axis u. The equilibrium values ω e ( u ) lie between the lowest and highest harmonic frequencies of the molecule. Zero-point values ω 0( u ) calculated from experimental data for a variety of molecules show interesting patterns of behaviour that should assist in the prediction of approximate centrifugal constants.

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