Auxiliary spinors

In the four-current version of RDFT the auxiliary spinors are chosen to reproduce the complete j... 

The relativistic Kohn-Sham scheme starts, in complete analogy to the non-relativistic case, with a representation of the four-current and of the non-interacting kinetic energy in terms of auxiliary spinor orbitals [8]. If one calculates the four-current of a system of fermions in an external potential (as indicated above), one obtains... 

Minimization of the ground-state energy with respect to the auxiliary spinor orbitals leads to the general Kohn-Sham equations ... 

The purpose of spin-polarized DFT is again to describe the system (molecule, cluster,...) with an auxiliary noninteracting system of one-particle spinors xJ/j,. ..,v]/N. The ground state density matrix of this noninteracting system... 

The basic variational principle (3.4) is applied directly in relativistic (extended) Thomas-Fermi models [12, 21,46] in which an approximate density functional representation for the complete [/] is utilised. The mainstay of applications is, however, the KS-scheme. In order to set up this scheme one first introduces auxiliary single-particle four spinors i (x), in terms of which the exact interac-... 

The next task is to derive an alternative form, more useful in practice, of the fundamental variational equations of Section 4.2.1. The basic idea is to represent the elementary density variables of RDFT in terms of auxiliary single-particle four spinors... 

We now discuss how at the DKee level of theory the transformed Hartree potential can be conveniently evaluated also for a density constructed from four-component Dirac spinors see Eqs. (6) and (26). The fitting-function (FF) technique, e.g. with an auxiliary Gaussian basis / [20,32],... 

There is an even more compact way of defining the Kramers single-replacement operators, Xfq, which also has the advantage of displaying the permutational symmetry. To do this, we introduce two auxiliary operators. One is the bar-reversal operator, Kp, which is the time-reversal operator for a spinor with index p. The effect of this operator is... 

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