A unified derivation of Hamiltonian and optical transition matrix elements for open shell diatomic and polyatomic...

In this work, we systematically derive the matrix elements of the nuclear rotation operators for open shell diatomic and polyatomic molecules in a parity adapted Hund's case (a) basis. Our expressions are valid for an arbitrary number of electrons and arbitrary electronic configurations. The common ad hoc sign changes of angular momentum operators are shown to be equivalent to a change in phase of basis functions. We show how to relate this basis to that required for scattering calculations. We also give the expressions for Einstein A coefficients for electric dipole, electric quadrupole, and magnetic dipole transitions.