Relativistic Basis Set

SBKJC VDZ Available for Li(4.v4/>) through Hg(7.v7/ 5d), this is a relativistic basis set created by Stevens and coworkers to replace all but the outermost electrons. The double-zeta valence contraction is designed to have an accuracy comparable to that of the 3—21G all-electron basis set. Hay-Wadt MB Available for K(5.v5/>) through Au(5.v6/ 5r/), this basis set contains the valence region with the outermost electrons and the previous shell of electrons. Elements beyond Kr are relativistic core potentials. This basis set uses a minimal valence contraction scheme. These sets are also given names starting with LA for Los Alamos, where they were developed. 

Malli and Pyper (14), reproduced with permission. Basis set same as the relativistic basis set, except that non-relativistic calculations were performed using the appropriate increased value of c (velocity of light). 

F. A. Parpia, A. K. Mohanty, Relativistic basis-set calculations for atoms with Fermi nuclei, Phys. Rev. A 46 (1992) 3735-3745. 

In developing relativistic basis sets, it is only natural to focus on the large component which clearly accounts for most of the electron density. In particular for ligh.ter elements, one would expect this to be very close to the non-relativistic wavefunction. But the relation above tells us that the small component basis is dependent on the large component basis, in particular using the expansion in eq. 10 we must have that... 

We now turn to a few specific examples of 4-coraponent basis sets and their applications. It should be realized that the derivation and testing of relativistic basis sets has not been a very systematic exercise. This is due to the fact that the calculations themselves are demanding, and in particular for the heavy elements, where the relativistic efiects are likely to be most noticable. Thus many basis sets have been developed and applied only for specific applications on one, or a limited number of molecules. Here we will review mostly those developments that have a direct bearing on the present state of molecular 4-component calculations. 

Early work was partly carried out using non-relativistic basis sets either unmodified, or augmented. However, the need to explore specially adapted basis sets quickly became apparent. At first sets of exponents were optimized by fitting the to numerical atomic DHF functions, as in the work... 

Spectroscopic constants for TlAt, Tl(117) (113)At and (113)(117) from Dirac-Hartree-Fock calculations using both relativistic and non-relativistic basis sets. Re - bond distance, k - force constant, v - vibrational frequency. 

Above we have presented some of the considerations and practical difficulties that must be taken into account in the derivation of 4-component basis sets for relativistic calculations. The ultimate validation of any basis set will have to take place through applications. Despite the availability of programs for 4-component calculations for more than 10 years, the field is still quite unexplored, compared to the wealth of information and experience that exists with regard to non-relativistic basis sets. Such experience will eventually accumulate also for relativistic work, but the size and cost of most calculations where relativity is of interest, indicates that this will be a slower process than what it has been for non-relativistic basis sets. 

As an example of such a study we pick a small molecule PbF. Suppose we want to compute the potentials for the lower electronic states of this molecule, with the relativistic CASSCF/CASPT2 approach, how do we proceed Well, it should not be difficult. Relativistic basis sets (ANO-RCC) are available for Pb and F [30] and we choose a reasonably extended set Pb 25s22pl6dl2f4g/9s8p6d4f3g and F 14s9p4d3f2g/ 5s4p3d2flg. It is of quadruple zeta accuracy. 

Fig. 3 Stationary points on the Br + H2O potential energy surface. Optimized geometrical parameters for the structures of the reactants, entrance complex, transition state, exit complex, and products from the CCSD(T) method with the relativistic basis sets cc-pVTZ-PP cc-...

Pantazis DA, Neese F. All-Electron Scalar Relativistic Basis Sets for the Lanthanides. J Chem Theory Comput. 2009 5(9) 2229-2238. 

D. A. Pantazis and F. Neese, All-electron scalar relativistic basis sets for the lanthanides,... 

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