Knowledge Bank

A computer program, coded in Fortran IV, has been written to perform a normal coordinate calculation and improve the values of the force constants by a least-squares analysis. The secular equation is set up in the form $|F-G-1\lambda |=0$; the $G-1$ matrix is calculated directly by use of Polo ‘s $\backslash pounds$ vectors. In addition to the frequencies of vibration, the program calculates centrifugal distortion constants, Coriolis coupling constants and inertial defects of ground and excited vibrational states. All of these quantities may be included as observables in the least-squares analysis, with appropriate weighting factors; similar data from other isotopic species of the molecule may also be included. The non-linear least-squares analysis proceeds in an iterative fashion; changes in the force field at a given stage of the iteration may be damped to prevent divergence of the iteration. In this way, convergence to a reasonable force field may be achieved even when starting far from the correct values of the force constants. In order to test the method and program, the force fields of $OF2$ and $SO2$ have been redetermined. The values to which the program converges agree closely with previous values obtained in other ways. Using this method, improved force fields for carbonyl fluoride and cis-difluorodiazine have been calculated.