Vibration. Coriolis Coupling. Force Constants

Molecular Vibration. Coriolis Coupling. Force Constants Fundamental Vibrations V in cm ... 

In addition to isotope frequency shifts, mean amplitudes of vibration, Coriolis coupling constants, centrifugal distortion constants, and so forth may be used to refine the force constants of small molecules (see Ref 81). 

Fundamental Vibrations. Coriolis Coupling Constants. Force Constants... 

The six fundamental vibrational frequencies for SeF and TeFe are given in Table XII (21,37,38,103). Force constants for SeFs, calculated with the frequencies from vapor-phase Raman spectra (21) and using isotope shifts and Coriolis coupling constants as additional data (103), are listed in Table XIII in comparison to TeFg (1,24,104,125,139). 

There have been a large number of determinations of molecular force constants, mean amplitudes of vibration, bond asymmetry parameters, Coriolis coupling constants (and inertia defects) and centrifugal distortion constants [146,152,259,271,304,581,840,1221,1222,1278,1312, 1416,1448,1449,1549,1550,1575-1578,1587,1618,1671,1682,1806,1807,1858,1931,1961,1984,2021,2045, 2108,2109-2111,2167a], as well as a determination of the atomic potential energy distribution... 

Force constants, Coriolis coupling constants, and mean amplitudes of vibration of InCl have also been calculated from previously reported vibrational data. The stretching force constants of the isoelectronic sequence are in the following order InCl < SnClg" < SbCl. ... 

The Coriolis coupling constants in Table 11 were derived from the effect of the zero point vibration on the rotational constants through vibration-rotation interaction [20] and from an harmonic force field [21] (symmetry of vibration A, E z C3 axis). 

Rotation-vibration constants and centrifugal distortion constants have been calculated from various sets of force constants [6,10 to 18]. The constant Dk, which apparently has not been measured so far, is predicted to be 10.30 kHz [15] and 10.098 kHz [16] from accurate force fields capable of reproducing observed frequencies of NF3, centrifugal distortion constants (Dj and Djk from [2] Dj from [3] appears to be in error, cf. footnote of Table 2, p. 190), Coriolis coupling constants [15, 16], and isotopic frequency shifts [15]. 

Root-mean-square amplitudes u(N-F) = 0.0487 A [25, 26] and u(F- F) = 0.0589 A [25], both at 298 K, have been calculated from force fields capable of reproducing rather accurately observed vibrational frequencies, Coriolis coupling constants, and centrifugal distortion constants. For calculations with approximate force fields, see [17, 22 to 24, 27 to 30]. 

Consider a degenerate ( ) vibrational mode in benzene the dipole or polarizability derivative then lies in the plane of the hexagon and the normal modes correspond to in-plane translational motion of the nuclei. Rotation around the molecular symmetry axis will produce a Coriolis force which is in the plane of the molecule (but perpendicular to the direction of translational motion). As a consequence, the dipole or the polarizability derivative (which would otherwise be fixed in the molecular frame) will rotate rapidly in the plane. Specifically, it will have a rotational velocity equal to where Q is the Coriolis coupling constant... 

A brief outline of the different sets of coordinates employed in the vibrational analysis of the various molecular parameters, and the corresponding transformations are presented in order to give explicit relationships between these different parameters, such as the force constants, the compliants, the Coriolis coupling constants, the mean square amplitudes of vibration. .. 

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