Numerov-Cooley numerical integration

The RKR potential may be tested against the input G(v) and B(v) values by exact solution of the nuclear Schrodinger equation [see Wicke and Harris, 1976, review and compare various procedures, e.g., Numerov-Cooley numerical integration (Cooley, 1961), finite difference boundary value matrix diagonaliza-tion (Shore, 1973), and the discrete variable representation (DVR) (Harris, et al., 1965)]. G(v) + y00 typically deviates from EVjj=o by < 1 cm-1 except near dissociation. Bv may be computed from Xv,J=o(R) by... 

We have used the Numerov-Cooley method of numerical integration to solve the Schrodinger equation... 

The difference equation or numerical integration method for vibrational wavefunctions usually referred to as the Numerov-Cooley method [111] has been extended by Dykstra and Malik [116] to an open-ended method for the analytical differentiation of the vibrational Schrodinger equation of a diatomic. This is particularly important for high-order derivatives (i.e., hyperpolarizabilities) where numerical difficulties may limit the use of finite-field treatments. As in Numerov-Cooley, this is a procedure that invokes the Born-Oppenheimer approximation. The accuracy of the results are limited only by the quality of the electronic wavefunction s description of the stretching potential and of the electrical property functions and by the adequacy of the Born-Oppenheimer approximation. 

For diatomic molecules, if the potential curve is known, numerical vibrational wavefunctions can be determined by the standard Numerov-Cooley technique [49] and for which computer programmes are available [50], The vibrational averaging for any state is then simply the numerical integration of , where v> is the vibrational wavefunction for the state of interest (usually the ground state). This, obviously, requires knowledge of the property P for a number of intemuclear separations (R). Alternatively, simple perturbation... 

Ingamells, Papadopoulos and Sadlej have introduced a new semi-numerical method based on Numerov-Cooley integration to calculate the vibrational... 

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