Coriolis energy

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 last term, usually very small, is known as Coriolis energy, TcorioHs = a ka)- It couples the internal motions vibrations"") within the molecule with its rotation. 

Because at higher latitudes the coriolis force deflects wind to a greater extent than in the tropics, winds become much more zonal (flow parallel to lines of latitude). Also in contrast to the persistent circulation of the tropics, the mid-latitude circulations are quite transient. There are large temperature contrasts, and temperature may vary abruptly over relatively short distances (frontal zones). In these regions of large temperature contrast, potential energy is frequently released and converted into kinetic energy as wind. Near the surface there are many closed pressure sys-... 

Coriolis operator spect An operator which gives a large contribution to the energy of an axially symmetric molecule arising from the interaction between vibration and rotation when two vibrations have equal or nearly equal frequencies. kor-e o-los, ap-3,rad-3r ... 

Coriolis resonance interactions spect Perturbationof two vibrations of a polyatomic molecule, having nearly equal frequencies, on each other, due to the energy contribution of the Coriolis operator. kor e o las rez-on-ons, in-tor,ak-shonz ) corresponding states phys chem The condition when two or more substances are at the same reduced pressures, the same reduced temperatures, and the same reduced volumes., kar-3 spand ir) stats )... 

The next step is to take care of the avoided crossings, whose presence was pointed out in DCO by R. Schinke. We believe that this can be achieved with the help of a very small number of extra parameters, of Coriolis type, also included in the second figure. Thus a well-defined and limited set of parameters is probably able to reproduce all rovibra-tional energy levels and spectral features. This should make possible refined predictions of dynamical nature. 

Two vibronic states which happen to occur at nearly the same energy will perturb one another if certain conditions are fulfilled. The interacting states may be derived from different electronic states, but in polyatomic spectra are often merely different vibrational states of the same electronic states. The perturbations, which are either homogeneous (AK = 0) (e.g. Fermi resonance) or heterogeneous (AK = 1) (Coriolis resonance) (Mulliken, 1937) are then analogous to the perturbations observed in infrared and Raman spectra. Such perturbations are commonplace in electronic bands where the completely unperturbed band is the exception rather than the rule. 

The nuclear function %a(R) is usually expanded in terms of a wave function describing the vibrational motion of the nuclei, and a rotational wave function [36, 37]. Analysis of the vibrational part of the wave function usually assumes that the vibrational motion is harmonic, such that a normal mode analysis can be applied [36, 38]. The breakdown of this approximation leads to vibrational coupling, commonly termed intramolecular vibrational energy redistribution, IVR. The rotational basis is usually taken as the rigid rotor basis [36, 38 -0]. This separation between vibrational and rotational motions neglects centrifugal and Coriolis coupling of rotation and vibration [36, 38—401. Next, we will write the wave packet prepared by the pump laser in terms of the zeroth-order BO basis as... 

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. 

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