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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,

 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

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

[1] A.V.Titov, N.S.Mosyagin, Int.J.Quant.Chem., v.71, 359 (1999);
    ibid, Rus. J. Phys. Chem., Suppl.2, v.74, S376 (2000);
    A.V.Titov, dissertation (2002), http://qchem.pnpi.spb.ru/Tolya.html;
    A.V.Titov, N.S.Mosyagin, T.A.Isaev, A.N.Petrov, Yadernaya Fizika,
    v.66 N6 (2003).
[2] N.S.Mosyagin, A.V.Titov, E.Eliav, and U.Kaldor,
    J.\ Chem.\ Phys., v.115, 2007 (2001).
[3] A.V.Titov, N.S.Mosyagin, A.B.Alekseyev, and R.J.Buenker,
    Int. J. Quant. Chem., v.81, 409 (2001).
[4] U.Kaldor and E.Eliav, Adv. Quant. Chem., v.31, 313 (1999).