On the use of the finite difference method in a calculation of vibration-rotation energies
The use of the finite difference method to obtain a Taylor series expansion of a potential energy function for a subsequent calculation of the rovibration energies of molecules is considered. A method is proposed that allows the stability of a finite-difference scheme to be increased against the computational inaccuracy upon numerical expansion of a multidimensional potential energy function into a high-order Taylor series. The method is based on the successive elimination of calculated expansion coefficients of a higher order in calculating the lower-order coefficients by the finite difference method. The approach is illustrated for the example of the CO and H2S molecules.
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