Spin-Orbit Coupling and Relativistic Effective Potentials—Applications

Spin-Orbit Coupling and Relativistic Effective Potentials—Applications 

More recently Ziegler, Snijders, and co-workers have suggest that the bond-length contraction is independent of the orbital contraction but rather it is a direct result of the Dirac Hamiltonian (63,64)- They observed that the contraction could be computed from the nonrelativistic molecular wave 

This analysis has been tested for Xe2+ and Au2 within the effective core potential approximation (65). Four sets of calculations have been carried out nonrelativistic, first-order relativistic, fully relativistic, and first-order nonrelativistic (relativistic wave function with nonrelativistic Hamiltonian). The computed Rc values were 3.01, 2.67, 2.58, and 3.14 A, respectively, for Au2 and 3.24, 3.18, 3.19, and 3.24 A for Xe2+. For these cases then, the analysis of Schwarz et al. is clearly inappropriate. It may be the case that the nonrelativistic electronic contraction stabilized in first-order calculations is independent of the usual relativistic AO contraction. However since the contraction is only stable in the presence of the relativistic Hamiltonian, it is still a relativistic orbital contraction, but now at a molecular level. 

The origin of relativistic bond-length contraction is still somewhat of an open question. First, the precise mechanism by which it occurs has not been determined unequivocally. In addition, the computed magnitudes often vary by as much a factor of two or more from calculation to calculation. 

To date, the best ab initio all-electron molecular calculations involving heavy elements are those of Lee and McLean, who published LCAO-MO SCF relativistic calculations on AgH and AuH (75). They reported relativistic bond-length contractions of 0.08 and 0.25 A, respectively, and increases in 

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IV. Spin-Orbit Coupling and Relativistic Effective Potentials—Applications... 

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