TRANSITION-PROBABILITY CALCULATIONS FOR ATOMS USING NONORTHOGONAL ORBITALS

Individual orbital optimization of wave functions for the initial and final states produces the most accurate wave functions for given expan sions, but complicates the calculation of transition-matrix elements s ince the two sets of orbitals will be nonorthogonal. The orbital sets can be transformed to become biorthonormal, in which case the evaluati on of any matrix element can proceed as in the orthonormal case. The t ransformation of the wave-function expansion to the new basis imposes certain requirements on the wave function, depending on the type of tr ansformation. An efficient and general method was found a few years ag o for expansions in determinants, spin-coupled configurations, or conf iguration state functions for molecules belonging to the D-2h point gr oup or its subgroups. The method requires only that the expansions are closed under deexcitation and thus applies to restricted active space wave functions. This type of expansion is efficient for correlation s tudies and includes many types of expansions as special cases. The abo ve technique has been generalized to the atomic, symmetry adapted case requiring the treatment of degenerate shells nl(N), with arbitrary oc cupation numbers 0 less than or equal to N less than or equal to 4l+2. A computer implementation of the algorithm in the multiconfiguration Hartree-Fock atomic-structure package for atoms allows the calculation of transition moments for individually optimized states. An applicati on is presented for the BI 1s(2)2s(2)2P(2)P(o)-->1s(2)2s2p(22)D electr ic dipole transition probability, which is highly sensitive to core-po larization effects.