Relativistic Extended Hiickel method

Fig. 25. Valence band of PUO2 and PU2O3 by XPS (from Ref. 117). REX Relativistic Extended Hiickel method)...

Relativistic calculations of a number of polyatomic molecules have been carried out by both semi-empirical and ab initio methods. Many of the earlier calculations have been reviewed by Pyykko" as well as by Christiansen, Ermler and Pitzer. The semi-empirical methods include the relativistic extended Hiickel method, relativistic Xa method, etc. Most of the ab initio calculations on polyatomics initially omit the spin-orbit interaction. This is introduced at a later stage as a perturbation or by a semi-empirical scheme. 

There are several other semi-empirical methods such as the relativistic extended Hiickel method formulated by Pyykko and co-workers. The Dirac-Slater multiple Xa method (Case 1982) has also been employed to include relativistic effects approximately. Zerner and co-workers use the INDO/CI method to study lathanide compounds. We will discuss these in section 3.2. 

While the relativistically parameterised extended Hiickel approach to the calculation of molecular parity violating effects has the merit of simplicity, it suffers in particular from the non-self-consistent character of the extended Hiickel method. This problem is avoided in the four-component Dirac Hartree-Fock approaches to the computation of parity violating potentials in chiral molecules introduced by Quiney, Skaane and Grant [155] as well as Laerdahl and Schwerdtfeger [156]. These will be described in the following section. 

The first numerical calculations within a four-component framework were done at the semi-empirical relativistic extended-Hiickel (REX) level [26]. This provided the first qualitative insights into SO contributions to the proton shieldings in the hydrogen halides and related cases (cf section 3). Attempts to obtain more quantitative results include the finite-perturbation Dirac-Fock implementation of Ishikawa, Nakatsuji and coworkers [21], and the more recent Dirac-Fock implementation of Visscher et al. [27]. The calculations of ref [21] used basis sets too small to provide useful numerical results (later calculations employed in roved basis sets [28]). Both methods were applied mainly to... 

Since the early relativistic extended Hiickel (REX) method of Pyykko, much progress has been made towards developing methods for performing relativistic calculations of coupling constants. Several approaches were presented during the review period. 

More approximate four-component schemes of solution of the relativistic electronic structure problem have been used to obtain insight in chemical properties connected with relativistic effects. This comprises semiempirical methods such as the Relativistic Extended Hiickel (REX) method as well as the Dirac-Fock-Slater (DFS) method, the relativistic analogue of the Hartree-Fock-Slater (HFS) approach. 

The most widely used semiempirical quantum chemistry technique for theoretical chemisorption studies is the Extended Hiickel Theory (EHT). The method was first proposed by Hoffmann/95/ in its nonrelativistic form, and by Lohr and Pyykko/96/ and also Messmer/97/ in its relativistic form, based on the molecular orbital theory for calculating molecular electronic and geometric properties. For a cluster the molecular orbitals are expanded as linear combinations of atomic orbitals... 

A more ambitious Extended Hiickel Treatment has been developed by Pyykko and Lohr [76] allowing the inclusion of relativistic effects with refined orbital exponents. In its most recent form the method, known as REX, does not rely on empirical parameters but rather derives its parameterisation from ab initio atomic calculations, and allows for charge-consistency [51], The importance of charge-consistency in EHT calculations was pointed out long ago... 

The semiempirical relativistically parametrized extended Hiickel scheme developed by Pyykkd and Lohr was one of the first methods at hand to investigate the electronic structure of polyatomic lanthanide and actinide molecules, albeit only in a rather approximate way. Since this is an effective one-particle model, it is possible to discuss quantities... 

Quantum chemistry for lanthanides and actinides is an active area of current research. The applicable methods range from relativistically parametrized semiempirical extended Hiickel-type approaches to fully relativistic allelectron Dirac-Hartree-Fock calculations with a subsequent correlation treatment. It is emphasized that electron correlation effects and relativistic effects including spin-orbit coupling have to be treated simultaneously in order to avoid errors arising from the nonadditivity of these effects. Considerable progress is expected, especially on the ab initio side of quantum chemical applications, for small lanthanide and actinide systems during the next few years. 

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