Knowledge Bank

In recent years force constants of many simple molecules have been calculated from vibrational-frequency data by the method of least squares, and this technique has now been extended to larger and more complex molecules. An important new development in the least-squares technique is the construction of the normal equations by the overlay principle, which allows a problem to be broken down so that the largest secular equation handled by the computer at any time is that of a single symmetry species. Yet it is possible to fit a set of force constants simultancously to a virtually unlimited number of symmetry species, isotopes, or different molecules. We have also explored the problem of instability in the normal equations, and propose a criterion for the selections of force constants to be refined. It is obvious in at the number of frequency data must exceed the number of independent parameters in a potential function, but in practice this criterion is seldom sufficient: in fact many force constants prove to be indeterminate even when there is a large excess of frequency data, and a stable solution of the normal equations can be achieved only by constraining certain force constants at arbitrary values. There are two problems associated with this technique; first, to determine the maximum number of force constants which can be determined significantly, second, to determine the particular force constants which contribute to the indeterminacy. These developments, together with other useful points in the calculation of force constants, will be discussed.