Spinor radius

An important advantage of ECP basis sets is their ability to incorporate approximately the physical effects of relativistic core contraction and associated changes in screening on valence orbitals, by suitable adjustments of the radius of the effective core potential. Thus, the ECP valence atomic orbitals can approximately mimic those of a fully relativistic (spinor) atomic calculation, rather than the non-relativistic all-electron orbitals they are nominally serving to replace. The partial inclusion of relativistic effects is an important physical correction for heavier atoms, particularly of the second transition series and beyond. Thus, an ECP-like treatment of heavy atoms is necessary in the non-relativistic framework of standard electronic-structure packages, even if the reduction in number of... 

Variational one-center restoration. In the variational technique of one-center restoration (VOCR) [79, 80], the proper behavior of the four-component molecular spinors in the core regions of heavy atoms can be restored as an expansion in spherical harmonics inside the sphere with a restoration radius, Rvoa, that should not be smaller than the matching radius, Rc, used at the RECP generation. The outer parts of spinors are treated as frozen after the RECP calculation of a considered molecule. This method enables one to combine the advantages of two well-developed approaches, molecular RECP calculation in a gaussian basis set and atomic-type one-center calculation in numerical basis functions, in the most optimal way. This technique is considered theoretically in [80] and some results concerning the efficiency of the one-center reexpansion of orbitals on another atom can be found in [75]. 

The difference between the models is not large, as shown by the data in table 7.3 for hydrogen-like mercury. The effect of the finite radius is approximately 2 h, but the difference between the models is only 0.01 E. For the valence spinors of many-electron atoms, the difference between the models is well below the limits of chemical... 

The shape-consistent pseudospinor is defined to be equal to the Hartree-Fock spinor outside a certain radius rc, and inside this radius it falls smoothly to zero. 

Alternatively, the shape-consistent pseudospinor can be written in terms of the Hartree-Fock spinor and a function that is confined inside the chosen radius rc,... 

The negative sign for the coefficient of rlr, implies a reduction in the amplitude of the pseudospinor in the valence region. So, if / only contains core and valence spinors, we are in the same situation as for the Philips-Kleinman pseudospinor, with a reduction in the valence density outside the chosen radius and the resultant problems with the pseudopotential. This means that fv must contain virtual spinors as well as occupied spinors, and the sum of virtual spinors must compensate for the reduction in the valenee spinor outside the radius of the core spinors (which is not necessarily the same as rc). 

The radial maximum of the 7s falls at about the same distance as the 95% density radius of the 6p+, and only a little outside that of the 6p and the 6s. As for the 5d in the lanthanides, the radial maximum of the 6d spinors in the actinides is inside the 95% density radius of the outer core spinors, but these spinors extend out almost as far as the 7s spinors at the 95% density radius. Bonding that involves any of the valence spinors is likely to involve a fair... 

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