Eckart-Watson Hamiltonians

Along these lines an efficient protocol, called DEWE has been developed [155] which is based on the DVR of the Eckart-Watson Hamiltonians involving an exact inclusion of potentials expressed in an arbitrary set of coordinates. The DEWE procedure has been tested both for nonlinear (H2O, H3, and CH4) and linear (CO2, HCN, and HNC) molecules. 

Matyus, E., Czako, G., Sutcliffe, B.T. Csaszar, A.G. Vibrational energy levels with arbitrary potentials using the Eckart-Watson Hamiltonians and the discrete variable representation, J. Chem. Phys. 2007, in press. 

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). 

Here, Aftot is the total mass of the nuclei. Note that when eliminating the motion of the center-of-mass we arbitrarily eliminated the first nuclear coordinate (we could eliminate any single coordinate y). Equation (1-13) can further be transformed to the body-fixed frame. When applying the so-called Eckart conditions35 one would get the standard Watson s Hamiltonian describing the nuclear motions in molecules36. 

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