Relativistic effective core potentials providing ``chemical accuracy'' in calculation of heavy-atom compounds

Anatoly V. Titov and Nikolai S. Mosyagin

St.-Petersburg Nuclear Physics Institute, Gatchina, Leningrad district 188300, Russia

 The effective Hamiltonians which allow one to attain ``chemical accuracy'' (about 1 kcal/mol or 350 1/cm for excitation and dissociation energies) in calculations of low-lying electronic states of molecules containing heavy atoms are discussed.
 The main attention is paid to the analysis of the two-component relativistic effective core potential (RECP) versions including the radially-local "shape-consistent'' RECPs and "energy-adjusted/consistent'' pseudopotentials (PPs) as well as the separable PPs.  It is shown that the "shape-consistent'' RECP concept can be derived on the basis of two propositions: (1) the property of proportionality of the original valence spinors and pseudospinors in the heavy-atom cores and (2) the requirement of  absence of the ``unphysical'' RECP terms in the valence region.  The conventional radially-local RECP/PP and separable PP operators are compared to the generalized RECP (GRECP) one [1], in which separable and other terms are added to the radially-local operator. (The GRECP concept exploits the idea of separation of the physical space into three regions with respect to a heavy atom: inner core, outer core and valence, which are treated differently by the GRECP operator.)  It is shown that the difference between the RECP components, $U_{nlj}(r)$, for the valence and outer core spinors with the same $lj$ cannot be eliminated in the "shape-consistent'' RECPs by any special smoothing procedure at the pseudospinor generation stage without lost of accuracy.  The ``energy-adjusted/consistent'' PPs have uncontrollable radii of the unphysical contributions to $U_{nlj}(r)$ in addition. Thus, typical errors of the radially-local RECPs range up to 1000 1/cm and more for  dissociation and transition energies even for lowest-lying states.
The importance of addition of the GRECP components depending on the occupation numbers of the outermost core shells (which, in particular, account for relaxation of the inner core shells) and some two-electron terms to the GRECP operator is discussed in connection with optimal RECPs for transition metals, lanthanides and actinides.  It is shown that Breit effects and correlations with the core shells, which are not treated explicitly, can be efficiently accounted for with the help of GRECPs.

 The RECPs of different groups were compared in precise calculations of valence properties of atoms and heavy-atom molecules, including spectroscopic constants in HgH [2] and TlH [3].  The most accurate results were obtained when using the relativistic coupled cluster method [4] and the correlation basis sets [2] employed in correlation calculations of both valence and core properties.

 We are grateful to CRDF for the Grant No. RP2-2339-GA-02 and RFBR for the Grant No. 03--03--32335.

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