Knowledge Bank

“The detailed analysis of the vibrational spectra of the biphenyl molecule is currently being undertaken. A general potential function for the molecule conforming to $D2$ symmetry has been set up. The potential function contains an arbitrary torsional angle as a parameter and so the model will reduce to $D2h$ or $D2d$ symmetries as special cases. Because of the symmetry group, a Cartesian coordinate system has been used and an orthonormal set of symmetry coordinates has been generated using the $D2$ character table. Contrary to custom, these symmetry coordinates have not been orthogonalized to the translational and rotational modes. This increases the order of the secular equation by six but greatly simplifies the compilation of the potential function. The potential function has also been set up so that the frequencies of any deutero-substituted biphenyls of $D2$ symmetry can be computed. In addition, any changes in C-C or C-X (X being hydrogen, deuterium or halide) bond lengths in different substituted biphenyls can be incorporated. The first approximation includes a torsional vibration mode and assumes an infinite barrier to free rotation. A second approximation will include a torsional angle dependence and two equilibrium positions. If necessary, a third approximation will introduce cross-terms into the potential function. The complication of solving the larger secular equation obtained by not orthogonalizing to the translational and rotational modes is trivial since the entire problem of diagonalization of the secular equation is being programmed for solution on an IBM 704 using the Fortran coding method. As yet, no numerical results have been obtained.”