Scalar relativity

Diffuse augmented basis sets were also developed for both the NR and DK cases by simple even tempered extensions. Valence electrons correlated CCSD(T) dipole polarizabilities calculated with the inclusion of DK scalar relativity are 35.08 and 35.07 a.u. for aug-cc-pVQZ-DK and aug-cc-pV5Z-DK, respectively. These values are about 0.3 a.u. larger than the PP values and therefore somewhat further away from experiment. 

In the absence of conductivity a, external charge pext, and externally applied currents ext, with spatially unvarying scalar relative e and /< in each region, the Maxwell equations... 

The details of implementation of scalar relativity in GTOFF were presented in [41] and reviewed in [75], so we summarize the essential assumptions and methodological features here. First, all practical DFT implementations of relativistic corrections of which we are aware assume the validity (either explicitly or implicitly) of an underlying Dirac-Kohn-Sham four-component equation. We do also. The Hamiltonian is therefore a relativistic free particle Hamiltonian augmented by the usual non-relativistic potentials... 

Scalar relativistic effects (e.g. mass-velocity and Darwin-type effects) can be incorporated into a calculation in two ways. One of these is simply to employ effective core potentials (ECPs), since the core potentials are obtained from calculations that include scalar relativistic terms [50]. This may not be adequate for the heavier elements. Scalar relativity can be variationally treated by the Douglas-Kroll (DK) [51] method, in which the full four-component relativistic ansatz is reduced to a single component equation. In gamess, the DK method is available through third order and may be used with any available type of wavefunction. 

We first consider relativistic effects at the SCF step. The first two entries of Table 1 show the influence of the scalar relativity compared to U ),... 

Computational quantum chemistry has made enormous advances in the last 20 years, arguably nowhere more so than in the f block. Calculations have, in this period, advanced sufficiently such that they can now be used as reliable, predictive methods for deepening our understanding of the fundamentals of bonding in these systems. The effects of scalar relativity are now routinely incorporated, and methods for the inclusion of spin-orbit coupling have also progressed significantly [32]. 

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. 

Therefore, we have first studied the influence of the protein on the spin-populations in the Cu-S bond. In this study, the effects of scalar relativity were also probed on the basis of the popular ZORA approach [153], which is implemented into the ORCA package as described by van Willlen [154], Rather pronounced effects of the protein environment were found in these calculations. Although the spin-population is not a physical observable, our reference value was taken to be 41% spin-population on copper, which was advocated after the extensive studies of Solomon and coworkers [144,146-152], If this value is accepted. 

The preaveraging approximation given in Eq. 107 is again used. The memory matrix then becomes a scalar relative to space rotations, and does not depend on the momentary configuration of the tagged chain ... 

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