Relativistic molecular orbitals, types

Most of the molecular relativistic calculations were performed for compounds studied experimentally various halides, oxyhalides and oxides of elements 104 through 108 and of their homologs in the chemical groups. The aim of those works was to predict stability, molecular geometry, type of bonding (ionic/covalence effects) and the influence of relativistic effects on those properties. On their basis, predictions of experimental behavior were made (see Section 3). A number of hydrides and fluorides of elements 111 and 112, as well as of simple compounds of the 7p elements up to Z=118 were also considered with the aim to study scalar relativistic and spin-orbit effects for various properties. 

To go beyond the Hartree-Fock limit and obtain the full solution to the Schrodinger equation (in the non-relativistic and Bom-Oppenheimer limit), one would have to combine various solutions of the product type. In any calculation one obtains more molecular orbitals than needed to accommodate all the electrons in the system. In a system with 2n electrons, the n molecular orbitals with the lowest molecular orbital energies are used in the Hartree-Fock solution for the ground state (this assumes a closed shell system, where two electrons are paired up in each molecular orbital). The rest of the molecular orbitals obtained will be excited molecular orbitals. Of course, other possible wavefunctions of the product type can be formed by using excited molecular orbitals in the product. The set of all such possible products can be used as a basis set to solve the full Schrodinger equation. The solution now looks like ... 

For the non-relativistic case various functions have been tried, and discussions of their respective merits may be found in the literature [3]. The simplest has been to use hydrogenic functions, or suitably modified La-guerre polynomials. This may be useful for purposes of analysis in simple atomic systems, but has had little impact on the molecular field. The reason for this is the complicated form of the integrals. A somewhat more efficient choice is the Slater type orbital (STO) of the form... 

The fully relativistic (four-component) LCAO calculations of molecular systems use contracted Gaussian-type spinors as the basis two scalar wavefunctions within a two-component basis spinor are multiplied by a common expansion coefficient, for dimensions n of both the large and small components the total number of variational parameters (the scalar expansion coefficients) is equal to 2n [496]. In the relativistic correlated calculations the atomic basis sets should be optimized in the atomic correlated calculations. As Almlof and Taylor showed [538], atomic basis sets optimized to describe correlations in atoms also describe correlation effects in molecules very well. The two main types of basis sets are used in correlation calculations of molecules basis of atomic natural orbitals (ANO) suggested by Ahnlof and Taylor [538] correlation-consistent (CC) basis set suggested by Dunning [462]. 

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