**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).