**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.**

[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).