The usual approach in quantum chemistry for approximating the wave function is to build molecular wave functions from antisymmetrised products of atomic centred one-electron functions. This method is also applied to the Dirac-Coulomb-(Breit) equation. Some details of this Dirac-Fock-CI approach are discussed in this chapter. A more extended discussion of the methods that are used can be found in the thesis of Visscher.

(8)

Here Z_{K} is the charge of nucleus K and M_{K} is its mass. In this formula ksi is related to the homogeneously charged sphere model by the formula S = R / 2, with R the radius of the sphere and S the standard deviation of the radial Gaussian distribution. The formula R = 2.27D-5 * M_{K}^{1/3} is used to relate the radii and mass of the nuclei.

(9)

The basis is subdivided in a large(L) and small(S) component set, that will be used to describe the upper and lower two components of the 4-spinors respectively.

This basis set can be contracted using the general contraction scheme that was introduced by Raffenetti [2].

(10)

With these real scalar functions a set of 4-component functions is constructed:

(11)

This basis set is used to expand the atomic or molecular spinors and defines the matrix representation of the one-electron Dirac or pseudo one-electron Dirac-Fock Hamiltonian. One can use the (point group) symmetry by a unitary transformation of the 4-component functions (forming a symmetry adapted basis).

(12)

(13)

Basis sets that fulfil this relation are hence called kinetically balanced. For primitive basis sets, this concept of kinetic balance is widely accepted as method for generating small component basisfunctions.

(14)

This has lead to the development of the atomic balance procedure [4]. In this procedure one first performs calculations on the atom(s) using kinetically balanced, uncontracted, basis sets. The new large and small component basis functions are then formed by contracting the primitive basis with the spinor coefficients of these calculations. One can construct a highly contracted basis in much the same way as in non-relativistic calculations. An important difference is caused by spin-orbit splitting. The difference in radial character of the l-1/2 and l+1/2 spinors in principle doubles the number of contracted Gaussian functions relative to a non-relativistic contraction scheme.

- O.Visser, P.J.C.Aerts, D.Hegarty and W.C.Nieuwpoort, Chem.Phys.Letters
**134**, 34 (1987). - R.C.Raffenetti, J.Chem.Phys.
**58**, 4452 (1973). - A.D.McLean and Y.S.Lee, in: "Current Aspects Of Quantum Chemistry 1981", ed.R.Carbó,(Elsevier: Amsterdam 1982).
- L.Visscher, O.Visser, P.J.C.Aerts and W.C.Nieuwpoort, Int.J.Quant.Chem.: Quant.Chem.Symp.
**25**, 131 (1991). - H.A.Kramers, Proc.Acad.Amsterdam
**33**, 959 (1930).

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