Hamiltonian Coriolis coupling

Thus the inclusion of the geometric phase in this case adds two terms to the Hamiltonian. The first is an additional potential term and the second has the effect that 2R is added to Py in the Coriolis coupling term [see Eq. (35)]. 

In his early study of nonadiabatic transitions of a diatomic molecule due to the Coriolis coupling, H. Nakamura proposed a new electronic Hamiltonian [290], in which a part of the rotational interactions is explicitly taken into account as... 

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. 

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 ... 

With the above approach we can combine the use of curvilinear normal coordinates with the Eckart frame. When we do so, the harmonic oscillator, rigid rotor, and, to lowest order, the Coriolis and centrifugal coupling contributions to H have exactly the same form as those found for the more commonly used Watson Hamiltonian (58). 

---