Potential energy, anharmonic terms minimum

A harmonic potential is a good approximation of the bond stretching function near the energy minimum (Fig. 2.7). Therefore, most programs use this approximation (see Eq. 2.6) however the limits of the simplification have to be kept in mind, in those cases where the anharmonicity becomes important. Apart from the possibility of including cubic terms to model anharmonicity fsee the second term in Eq. 2.14), which is done in the programs MM2 and MM3[1,2,2 241, the selective inclusion of 1,3-nonbonded interactions can also be used to add anharmonicity to the total potential energy function. 

The microwave spectrum of oxetanone-3 has been studied by Gibson and Harris 1S In the case of small-amplitude harmonic vibrations, the rotational constants should vary linearly with vibrational quantum number. For a single-minimum anharmonic potential representing a large-amplitude coordinate, deviation from this linear dependence is expected on two accounts. If we express the dependence on the large-amplitude coordinate in a power series, it may be necessary to carry the series past the quadratic term. Also, the contribution of the quartic term in the potential energy may cause deviations from linearity. 

Also, since we are considering infinitesimal vibrational amplitudes, the terms higher than quadratic can be neglected because qt qj qt qj qt-(This approximation will be inadequate when strong anharmonicities are present.) If we choose the minimum of energy, Fo °, as the arbitrary zero of our energy scale, the potential energy, within our approximation is ... 

The computed potential energy surfaces are often expanded in polynomials of nth (n > 3) degree and the minimum R, the zero-point frequency co. the anharmonicity co x (and corresponding terms in the other dimensions) and... 

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