Two-step method for precise calculation of core properties in molecules
 
 A.V.Titov, N.S.Mosyagin, A.N.Petrov, and T.A.Isaev
 
  Petersburg Nuclear Physics Institute RAS
  Gatchina, St.-Petersburg  188300, RUSSIA

 Precise calculations of ``core'' properties which are described by the
 operators heavily concentrated in atomic cores, like to hyperfine structure
 (HFS) and P,T-parity nonconservation (PNC) effects, usually require
 accounting for relativistic effects.  Unfortunately, even completely
 relativistic calculations of diatomics containing elements from fourth period
 are very consuming already on the stages of calculation and transformation of
 two-electron integrals with a basis of four-component spinors. The
 complexity of such calculations becomes very high for compounds of d- and,
 especially, f-elements.

 In turn, the relativistic effective core potential (RECP) calculations of
 ``valence'' (spectroscopic, chemical etc.) properties of molecules are very
 popular now because the RECP method allows one to treat satisfactory the
 correlation and relativistic effects in the valence region of a molecule with
 minimal efforts. However, the accuracy of the conventional RECPs is
 limited [1]. Besides, the valence molecular spinors are usually smoothed in
 atomic cores and, as a result, direct calculation of electronic densities
 near heavy nuclei is impossible.

 The former circumstance stimulated further development of the RECP approaches
 and, in particular, the generalized RECP (GRECP) concept was proposed [1]
 employing the idea of different treatment of inner core, outer core and
 valence shells. The latter had led to the methods of nonvariational [2] and
 variational [3] one-center restoration of correct shapes of four-component
 spinors in atomic cores after a two-component (G)RECP calculation of a
 molecule.  In the report, the restoration and correlation methods are
 discussed and their efficiency is illustrated in calculations of HFS and PNC
 effects in heavy-atom molecules [2].

 The present work was supported by U.S. CRDF grant No. RP2-2339-GA-02 and RFBR
 grant No. 03-03-32335. N.M. is supported by the grants of the Leningrad
 district governor and Russian science support foundation. A.P. is
 grateful to the Ministry of Education RF (Grant PD02-1.3-236) and to
 St.Petersburg Committee on Science and HE (Grant PD03-1.3-60). T.I. thanks
 INTAS for Grant YSF 2001/2-164.

[1] A.V.Titov, N.S.Mosyagin, Int.J.Quant.Ch. 71, 359 (1999); A.V.Titov,
    DSc Thesis (PNPI, 2002); see also http://qchem.pnpi.spb.ru.
[2] A.V.Titov, PhD Thesis (Leningrad University, 1985);
    A.V.Titov, N.S.Mosyagin, V.F.Ezhov, Phys.Rev.Lett. 77, 5346 (1996);
    M.G.Kozlov, A.V.Titov, N.S.Mosyagin, Phys.Rev.A 56, R3326 (1997);
    N.S.Mosyagin, M.G.Kozlov, A.V.Titov, J.Phys.B 31, L763 (1998);
    A.N.Petrov et al., Phys.Rev.Lett. 88, 073001 (2002);
    T.A.Isaev et al., Phys.Rev.A (Rapid Comm.), in press.
[3] A.V.Titov, Int.J.Quant.Chem. 57, 453 (1996).