Relativistic effects bond-length contraction

One-center expansion was first applied to whole molecules by Desclaux Pyykko in relativistic and nonrelativistic Hartree-Fock calculations for the series CH4 to PbH4 [81] and then in the Dirac-Fock calculations of CuH, AgH and AuH [82] and other molecules [83]. A large bond length contraction due to the relativistic effects was estimated. However, the accuracy of such calculations is limited in practice because the orbitals of the hydrogen atom are reexpanded on a heavy nucleus in the entire coordinate space. It is notable that the RFCP and one-center expansion approaches were considered earlier as alternatives to each other [84, 85]. 

Pyykkb et al. [4] pointed out the Z -dependence of the relativistic hond-length contraction, but did not give its reason. Presumably, the Z -dependence of the bond length contraction can also he explained by the same reason. For homonuclear diatomic molecules containing heavy elements such as Ph, relativistic effects should be taken into account for both atoms when considering the atomic-numher dependence of the bond overlap population. 

A comparison of different methods was undertaken for the hydride of element 111 (Seth et al. 1996). The conclusion of this study was that Dirac-Fock calculations, all-electron DKH calculations and relativistic pseudopotential calculations give very similar results, showing that relativistic effects are also well described in the more approximate methods. A large relativistic bond length contraction of about 50 pm was found, which makes the bond length of (111)H even slightly shorter than that of AuH, which is 152.4 pm, with a relativistic effect of the order of 20 pm (see Kaldor and Hess 1994). 

Figure 5. Relativistic effects on bond lengths and binding energies of group 4 tctrahydrides XH. The bond length contraction (in A) and bond destabilization (in eV) were obtained as the difference between relativistic Dirac-Hartree-Fock calculations based on the Dirac-Coulomb-Gaunt Hamiltonian and corresponding nonrelativistic Hartree-Fock calculations [28,29].

PyykkO and Desclaux have calculated properties of several transition metal hydrides including (106)H6 by applying the Dirac-Fock one-center expansion method. The calculations show that relativistic effects become more important with increasing nuclear charge of the transition element. For example, the relativistic bond length contraction scales approximately as Z (Z is the nuclear charge). Schadel et al. carried out aqueous chemistry on element 106 (isotopes 265 and 266) which showed that the most stable oxidation state is -f6, and like Us homologs Mo and W, element 106 forms neutral... 

In many simple cases, in particular when the bonding is accomplished by the outer s and p electrons or suitable hybrids, we experience a relativistic bond length contraction. For the same column of the Periodic Table it is also proportional to Z (which is generally true also for other relativistic effects in the valence shell down a column of the Periodic Table), and can be over 10% for Au compounds. 

Snijders, J.G. and Pyykko, P. (1980) Is the relativistic contraction of bond lengths an orbital contraction effect Chemical Physics Letters, 75, 5-8. 

Further aspects governing computational effort and accuracy are related to the explicit treatment of relativistic effects, which are pronounced for atoms with high atomic numbers, as their core electrons reach velocities that make the influence of special relativity significant. Contraction of bond lengths and a shifting of orbital energies are observed compared to the non-relativistic treatment. An efficient way to include a major fraction of these... 

Martin " was the first to estimate the effects of relativity on the spectroscopic constants of Cu2. The scalar relativistic (mass-velocity and Darwin) terms were evaluated perturbatively using Hartree-Fock or GVB (Two configuration SCF (ffg -mTu)) wavefunctions. At these levels the relativistic corrections for r, cu and D, were found to be — 0.05 A, 15 cm and -h0.06eV for SCF, and —0.05 A, + 14 cm and -l-0.07eV for GVB. The shrinking of the bond length is less than half of the estimate based on the contraction of the 4s atomic orbital. 

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