Spin dependent UGA

Keywords Unitary group approach (UGA) Graphical unitary group approach (GUGA) Correlation problem Spin-dependent UGA... 

We have shown that one-electron spin-dependent terms, Eq. (36), in the electronic Hamiltonian, Eq. (33), may be efficiently handled in much the same way as the standard spin-independent two-electron (i.e., Coulomb) terms. Indeed, as clearly implied by Eqs. (70), (73), and (76), the MEs of spin-dependent one-body operators in the U(2 ) D U(n)(8> SU(2) basis may be evaluated as MEs of spin-independent two-body operators in a standard U( -1-1) electronic G-T basis (see also [37, 39]). Since the MEs of generator products within the spin-independent UGA approach are well known, the above presented development should facilitate the implementation of the spin-dependent UGA formalism. This opens a possible avenue enabling us to handle spin-dependent MBPT terms via a simple modification of the existing UGA and GUGA codes, similarly as done by Yabushita et al. [37]. We emphasize that all the required segment values may be found in [36], and a few additional ones that are specific to a spin-dependent case are given in Tables 1 and 2. 

An Implementation of Spin-Orbit Direct Cl Method Based on the Spin-Dependent UGA [20]... 

The eigenstates of Hq are pure spin states with a good total spin quantum number S that are often generated via Cl approaches based on UG A or GUGA. It is thus convenient to extend efficient spin-independent UGA codes to those that can also account for spin-dependent operators. 

The coefficients being independent of the spin component Ms are completely determined by the spin-independent UGA so that the key to the evaluation of relativistic effects is the evaluation of MEs of spin-dependent operators in the basis (37). 

The segmentation of MEs of spin-dependent one-body operators is very similar to that for spin-independent two-body operators. This is a very useful fact in view of an actual implementation of this formalism, since it enables an evaluation of MEs of spin-dependent one-body operators by exploiting presently available UGA or GUGA codes. We now compare both formalisms in greater detail. 

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