A rapidly convergent expansion technique for local quantum mechanical operators

A general technique is described for efficiently expanding quantum mechanical operators. The basis is a particular set of wave functions and the expansion coefficients are physically meaningful matrix elements of the operator. Two applications to molecular properties, the transition dipole operator and the anharmonic force field, are discussed. We demonstrate that the entire force field can be expressed exactly in terms of anharmonic perturbations of the ground state, and that a great deal of information can be easily obtained from the spectroscopic frequencies. Similarly, the dipole moment matrix elements in any vibrational band are shown to be given in terms of a sum of only the R(1) matrix elements for various vibrational levels. Numerical results are presented for HCl rotational line strengths. These applications are only two examples of the potential experimental and theoretical uses of this method.