Knowledge Bank

The determination of force fields has been plagued by the lack of sufficient experimental data to calculate accurately all possible independent force constants. An ill-conditioned system of equations resulting from highly correlated constants is a typical difficulty which has been overcome satisfactorily only in the few cases where additional data such as Coriolis coefficients, centrifugal stretching constants, etc. are known. These additional data are not available for many interesting molecules, however, and a method of obtaining force constants from vibrational frequencies alone is proposed. The method makes use of the off-diagonal (zero) elements in the eigenvalue matrix and involves no restraining assumptions on the value of any constant. Successful calculations have been using the frequencies of a single isotopic species, and on multiple isotopic species where frequency data are available. Test problems have ranged from simple molecules such as $NO2$ and $SO2$ to more complicated molecules, included $CH4,FNO2,HNO3$, etc.