Polyatomics, relativistic calculations

It is hoped that with the availability of faster supercomputers ab initio (all-electron) fully relativistic calculations for polyatomics containing heavy atoms will become feasible in the near future. 

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. 

Many relativistic calculations on atoms have been published in the last 10 years.Molecular calculations, on the other hand, are more complicated and resource-demanding, and fewer publications treating molecules have appeared in the literature. - The first Dirac-Fock calculations using kinet-ically balanced basis sets were carried out by McLean and Lee on AuH and AgH, and by Datta and Ewig studying Be2. The first calculations on polyatomic molecules were done by Aerts and Nieuwpoort for CH4, SiH4, and GeH4. 

Of first priority is the proof or disproof of the conjecture about the spin density. It is hoped in the not-to-distant future, several significant systems of multi-electron atoms in the ground and excited states, through polyatomic molecules will be calculated and used as evidence of the efficacy of this method. Eventually, a fully relativistically covariant model will be developed. Beside philosophical interest, and fundamental scientific interest, there is potential commercial interest (Eberhart 1994)24. The process... 

Recently many quantum chemists have dedicated a lot of elforts to the calculation and treatment of the electronic structures of polyatomic systems including heavy elements, which are involved in many interesting chemical and physical phenomena. They still present unique difficulties to the theoretical study. Until recently, the relativistic effect had ever been thought less important for chemical properties because the relativity appears primarily in the core electrons, which had been believed to be unlikely to affect chemically active valence regions dramatically. Recent studies, however, have revealed not only quantitatively but also quahtatively that the relativistic effect plays essential and comprehensive roles in total natures of molecular electronic structures for heavy-element systems. We are nowadays convinced that the relativistic effect is definitely important for the accurate theoretical treatment of heavy-element systems as well as the electron correlation effect. 

Polarizabilities and Hyperpolarizabilities of Small Molecules. - 5.2.1 Diatomic Molecules. - The methods usually employed for diatomic response function calculations are often identical with those used for polyatomic molecules but some features are more typical of diatomic studies the use of very large atomic basis sets, the more frequent use of complete Cl as a benchmark, the inclusion of relativistic effects and calculations that do not assume the Bom-Oppenheimer approximation. Work on diatomics is also... 

Dyall, K.G., 1994a, Polyatomic molecular Dirac-Hartiee-Fock calculations with Gaussian basis sets theory, implementation and applications, in Relativistic and Electron Correlation Effects in Molecules and Solids, NATO ASI Series, Series B Physics, Vol. 318, ed. G.L. Malli (Plenum, New York) p. 17. 

K. Balasubramanian. Relativistic configuration interaction calculations for polyatomics Applications to PbH2, SnH2, and GeH2. /. Chem. Phys., 89 (1988) 5731-5738. 

Several groups have developed four-component methods for the calculation of polyatomic molecules in the last decade. While several codes for DHF calculations exist by now, " programs for calculations on polyatomic molecules including correlation by means of ab initio techniques appeared only very recently. They feature relativistic multi-reference configuration interaction, second-order M0ller-Plesset coupled-cluster methods. ... 

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