Bonding, relativistic effects Darwin correction

Fully relativistic calculations even for atoms are quite complicated. The relativistic ECP parameters are, therefore, usually derived from atomic calculations that include only the most important relativistic terms of the Dirac-Fock Hamiltonian, namely, the mass-velocity correction, the spin-orbit coupling, and the so-called Darwin term.6 This is why the reference atomic calculations and the derived ECP parameters are sometimes termed quasi-relativistic. The basic assumption of relativistic ECPs is that the relativistic effects can be incorporated into the atom via the derived ECP parameters as a constant, which does not change during formation of the molecule. Experience shows that this assumption is justified for calculating geometries and bond energies of molecules. 

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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