Redundancy coefficients for vibrations involving atoms with four bonds

Simple expressions for the first-order redundancy coefficients in vibrational problems involving atoms with four bonds are given. The general case of no local symmetry is treated as well as the specialization to O_h, C_3v, and C_s symmetry. The elements of the U matrix resulting from the orthogonalization of the local symmetry coordinates with respect to the redundancy condition are given for two suitable sets of symmetry coordinates. The theoretical results are illustrated with the numerical values for ethylsilane.