Generalized Relativistic Effective Core Potential Method: Theory and calculations

摘要

In calculations of heavy-atom molecules with the shape-consistentRelativistic Effective Core Potential (RECP), only valence and some outer-coreshells are treated explicitly, the shapes of spinors are smoothed in the atomiccore regions and the small components of four-component spinors are excludedfrom calculations. Therefore, the computational efforts can be dramaticallyreduced. However, in the framework of the standard nodeless radially local RECPversions, any attempt to extend the space of explicitly treated electrons morethan some limit does not improve the accuracy of the calculations. The errorscaused by these (nodeless) RECPs can range up to 2000 $cm^{-1}$ and more forthe dissociation and transition energies even for lowest-lying excitations thatcan be unsatisfactory for many applications. Moreover, the direct calculationof such properties as electronic densities near heavy nuclei, hyperfinestructure, and matrix elements of other operators singular on heavy nuclei isimpossible as a result of the smoothing of the orbitals in the core regions. In the present paper, ways to overcome these disadvantages of the RECP methodare discussed. The developments of the RECP method suggested by the authors arestudied in many precise calculations of atoms and of the TlH, HgH molecules.The technique of nonvariational restoration of electronic structure in cores ofheavy atoms in molecules is applied to calculation of the P,T-oddspin-rotational Hamiltonian parameters including the weak interaction termswhich break the symmetry over the space inversion (P) and time-reversalinvariance (T) in the PbF, HgF, BaF, and YbF molecules.