Coriolis coefficients

Prop. Spectra IR (957), (far) IR, Raman and assignment (I3I5, 208l), NMR (259, 582, 735, 1821), microwave (957, 1556), Coriolis coefficient and ground state centrifugal distortions (869), dipole moment (582), deuterium effect on dipole moment (1556), nonbonded electron effect on internal rotation (II6I), electrostatic model to treat hindered rotation force constant (I38,... 

The scheme we employ uses a Cartesian laboratory system of coordinates which avoids the spurious small kinetic and Coriolis energy terms that arise when center of mass coordinates are used. However, the overall translational and rotational degrees of freedom are still present. The unconstrained coupled dynamics of all participating electrons and atomic nuclei is considered explicitly. The particles move under the influence of the instantaneous forces derived from the Coulombic potentials of the system Hamiltonian and the time-dependent system wave function. The time-dependent variational principle is used to derive the dynamical equations for a given form of time-dependent system wave function. The choice of wave function ansatz and of sets of atomic basis functions are the limiting approximations of the method. Wave function parameters, such as molecular orbital coefficients, z,(f), average nuclear positions and momenta, and Pfe(0, etc., carry the time dependence and serve as the dynamical variables of the method. Therefore, the parameterization of the system wave function is important, and we have found that wave functions expressed as generalized coherent states are particularly useful. A minimal implementation of the method [16,17] employs a wave function of the form ... 

The vibration-rotation hamiltonian of a polyatomic molecule is more complicated than that of a diatomic molecule, both because of the increased number of co-ordinates, and because of the presence of Coriolis terms which are absent from the diatomic hamiltonian. These differences lead to many more terms in the formulae for a and x values obtained from the contact transformation, and they also lead to various kinds of vibrational and rotational resonance situations in which two or more vibrational levels are separated by so small an energy that interaction terms in the hamiltonian between these levels cannot easily be handled by perturbation theory. It is then necessary to obtain an effective hamiltonian over these two or more vibrational levels, and to use special techniques to relate the coefficients in this hamiltonian to the observed spectrum. 

Cyvin, S. J., J. Brunvoll, B. N. Cyvin, L. A. Kristiansen, and E. Meising-seth Influence of Atomic Masses on the Coriolis Coupling Coefficients in Some Symmetrical Molecules. I. Tetrahedral XY4-Type Molecules. J. chem. Physics 40, 96—104 (1964). 

Due to the rotational structure as well as the so-called hot hand absorptions (Sec. 2.5.3), the contour of a rovibrational band depends on the temperature. Today it is possible to determine molecular constants such as moments of inertia, Coriolis coupling constants, centrifugal distortion constants, and anharmonicity coefficients by FTIR as precisely as possible in order to calculate the intensity and shape of an absorption band. In such a simulation process the temperature may be used as a parameter. The results can be compared to the experimental spectra and the temperature may be deduced by fitting the calculated to the observed bands. This is possible with IR as well as with Raman bands. A review of curve fitting procedures and their limitations has been given by Maddams (1980). 

Fig. 14.7. A scheme the Coriolis coupling coefficient (B12) and the curvature coefficients (Bij and B2s) related to the normal modes 1 and 2 and reaction coordinate Diagonalization of the two Hessians calculated at points = and s = S2 gives two corresponding normal mode eigenvectors L (si) and L2 ( si) as well as Li ( 2) and La 2)- At points si and S2, we also calculate the versors w (si) and w (si) that are tangent to the IRC (curved linej. Hie calculated vectors inserted into the formulas give the approximations to Bij, B2j and B12-...

We have shown that we can come from collision theory to the transition state result by assuming (in accordance with classical transition state theory) that the reaction probability is unity for kinetic energies in the RP motion above the potential activation barrier (see fig. 4.1). It is now also possible to demonstrate that the transition state result can be obtained from the RP hamiltonian directly (see appendix of [16]) or ref. [18], i.e. without any reference to the reactant hamiltonian. This derivation shows that the total TST reaction rate is independent of the Coriolis coupling coefficients Bkk and Ckk These coefficients only affect the internal distribution on vibrational levels. 

Another example of Coriolis interaction is presented in Section 4.13. J. Watson recently published an excellent paper on the determination of the centrifugal distortion coefficient of asymmetric top molecules. [ 1-... 

Figure 17 Normal mode frequencies cu s) of the 3ai and 2ai symmetric mode ( 11 and 8) and the corresponding Coriolis coupling coefficient for the reaction CH3 -h H -> CH4 + H. Repro-...

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