Harmonic potential, truncated, matrix

E Matrix elements of the truncated harmonic potential F Matrix elements in Gaussian primitive basis functions... 

If, however, the ab-initio calculation of a specific molecule jdelds the complete potential energy hypersurface (as discussed above) the FG-matrix method (7) can be used. This was done by, e.g. AUavena (52), Hartmann and Gliemann (55) and Menna, Mocda and Randaccio (44). Huff and Ellison (144) present an easier and simpler method which is very favourable for computational purposes it also depends on truncating the potential after the harmonic term the 3 N mass-weighted (mi) Cartesian displacement co-ordinates Axi are called qi, and are given by... 

As mentioned in the introduction, most of the QM calculations of vibrational frequencies are performed within the double-harmonic approximation, that is, the truncation of the expansion of the potential energy as a function of the nuclear coordinates to the quadratic term (mechanical harmonic approximation) and the consideration of the hnear term only in the expansion of the dipole moment as a function of the nuclear coordinates (electric harmonic approximation). In such a framework, the QM calculation of vibrational frequencies can be reduced to the evaluation of the components of the Hessian matrix followed by diagonalization of the corresponding mass-weighted matrix [1]. Let us start by writing out the energy of a... 

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