Note on a Form of the Secular Equation for Molecular Vibrations

By starting with the Hamiltonian form of the equations of motion, the problem of the small vibrations of a polyatomic molecule can be solved with the aid of a secular equation twice the usual size. This equation, however, is readily adapted to solution by electrical circuits and has the important advantage of having as elements the force constants and inverse kinetic energy coefficients (``G'' matrix elements) directly. The force constant matrix elements occupy one off-diagonal corner of the secular equation, the G matrix elements are in the other off-diagonal corner, the circular frequencies (2πν) appear on the principal diagonal, and all other elements are zero.