Spin-Free Effects on Molecular Structure

The lowest-order effect of relativity on energetics of atoms and molecules—and hence usually the largest—is the spin-free relativistic effect (also called scalar relativity), which is dominated by the one-electron relativistic effect. For light atoms, this effect is relatively easily evaluated with the mass-velocity and Darwin operators of the Pauli Hamiltonian, or by direct perturbation theory. For heavier atoms, the Douglas-Kroll-Hess method or the NESC le method provide descriptions of the spin-independent relativistic effect that are satisfactory for all but the highest accuracy. 

These two methods include terms beyond first order in perturbation theory that are important for heavy elements. Spin-free relativistic effects are also well described by relativistic effective core potentials and ab initio model potentials. In this section, we discuss the energetic and structural changes that result from these effects. 

From the form of the mass-velocity and Darwin operators, it is clear that the largest contributions to the direct scalar relativistic effect come from s electrons. Consequently, sa bonds should be strengthened by relativity. The coinage metals have valence configurations and we would expect compounds of these elements to exhibit such effects in their bonding properties. Table 22.3 shows the bond lengths, harmonic 

Molecule Method ySCF e J.MP2 e jySCF DMP2 CF JUP2 

NR - nonrelativistic, PT-MVD - pCTturbative treatment of mass-velocity and Darwin operators (only SCF), DKH - Douglas-Kroll-Hess, RECP — relativistic effective core potential, DC - four-component Dirac-Coulomb, Exp - experiment. 

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