Relativistic effects on molecular properties

Relativistic effects on molecular properties of the heaviest elements... 

We then turn to the question of how to eliminate the spin-orbit interaction in four-component relativistic calculations. This allows the assessment of spin-orbit effects on molecular properties within the framework of a single theory. In a previous publication [13], we have shown how the spin-orbit interaction can be eliminated in four-component relativistic calculations of spectroscopic properties by deleting the quaternion imaginary parts of matrix representations of the quaternion modified Dirac equation. We show in this chapter how the application of the same procedure to second-order electric properties takes out spin-forbidden transitions in the spectrum of the mercury atom. Second-order magnetic properties require more care since the straightforward application of the above procedure will extinguish all spin interactions. After careful analysis on how to proceed we... 

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. 

System of Elements, (b) P. Pyykko, Chem. Rev., 88, 563 (1988). Relativiestic Effects in Structural Chemistry, (c) K. S. Pitzer, Acc. Chem. Res., 12,271 (1979). Relativistic Effects on Chemical Properties, (d) W. Kutzelnigg, Physica Scripta, 36, 416 (1987). The Relativistic Many Body Problem in Molecular Theory. 

Hydrides. DHF, DFC, PP, RECP and 2c- and 4c-DFT calculations were performed forMH (M = 113-118) [139, 198, 228-230, 243-250] and II3H3 [251] and their lighter homologs in the chemical groups. An aim of these studies was the investigation of the influence of relativistic effects on molecular spectroscopic properties. Most representative results are shown in Table 18 and Fig. 44. 

EFGs and other electric-field-related properties are dealt with in a somewhat different manner. The EFG and multipole moments are calculated as expectation values with the relevant operators and the electron charge density. To avoid PC errors, if the operators are the four-component versions this charge density has to be the four-component (Dirac) density. The latter differs from the two-component density [24,25] already in order which is the same leading order as the relativistic effects on the properties. In the so-called ZORA-4 (Z4) framework, the relevant operators are kept in their four-component form, and an approximate four-component electron charge density is reconstructed from the two-component ZORA density. As was shown by van Lenthe and Baerends [26], the Z4 method eliminates most of the PC errors in order c , with relatively small residual errors. In a Kohn-Sham (KS) DFT framework with two-component molecular orbitals y>, with occupations the ZORA two-component density is... 

The influence of relativistic effects on the electronic structure and properties of the 6d transactinides was analyzed in detail on the example of MCE (M = V, Nb, Ta and Db) [117]. Opposite trends in the relativistic and non-relativistic energies of the valence orbitals from the 5d to the 6d elements were shown to result in opposite trends in molecular orbital (MO) energies, see Figure 12. Thus, the highest occupied MO (HOMO) of the 3p(Cl)... 

The self-consistent treatment of the SO interaction is an important aspect of the relativistic simulation of atomic and molecular systems. It is known that the electron-electron contributions are mq>ortant for a quantitative description of these relativistic effects [19,80-86]. The SO terms derived from the electron-electron interaction can be even more important than the corresponding SR terms [87], e.g. when spectroscopic properties are of interest. SR corrections have larger effects on other properties, e.g. binding energies. 

In Science, every concept, question, conclusion, experimental result, method, theory or relationship is always open to reexamination. Molecules do exist Nevertheless, there are serious questions about precise definition. Some of these questions lie at the foundations of modem physics, and some involve states of aggregation or extreme conditions such as intense radiation fields or the region of the continuum. There are some molecular properties that are definable only within limits, for example, the geometrical stmcture of non-rigid molecules, properties consistent with the uncertainty principle, or those limited by the negleet of quantum-field, relativistic or other effects. And there are properties which depend specifically on a state of aggregation, such as superconductivity, ferroelectric (and anti), ferromagnetic (and anti), superfluidity, excitons. polarons, etc. Thus, any molecular definition may need to be extended in a more complex situation. 

Schwerdtfeger, P. (1991) Relativistic and Electron Correlation Contributions in Atomic and Molecular Properties. Benchmark Calculations on Au and Au2. Chemical Physics Letters, 183, 457 163. Neogrady, P., Kello, V., Urban, M. and Sadlej, A.J. (1997) Ionization Potentials and Electron Affinities of Cu, Ag, and Au Electron Correlation and Relativistic Effects. International Journal of Quantum Chemistry, 63, 557-565. 

---