Calculation of molecular geometries and force constants from CNDO wavefunctions by the force method

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Abstract
The semi-empirical quantum chemical calculation of molecular geometries and force constants by the usual energy hypersurface method rapidly becomes impractical as the size of the molecule increases. Here we show that the application of the force method to semi-empirical wavefunctions makes an economic and simple calculation of molecular geometries and force constants possible. Problems which are virtually insoluble by the classical method, such as full geometry optimization in large molecules, can be solved this way. The calculation of forces as exact negative derivatives of the total SCF energy is given for CNDO wavefunctions. Two geometry optimization schemes are discussed ; it is concluded that a steepest descent method is the most practical in semi-empirical calculations. As an example the fully optimized equilibrium geometry of pyrrole has been determined. Except for the CH and NH bond lengths, the calculated geometry agrees almost perfectly with the experimental one. The calculation of force constants from the forces is discussed. The force constants of CH4 and H2O have been determined, including the interaction ones. The signs and magnitudes of the stretch-bend interaction constants agree with experiment.