Localized orbital/local origin correlation

A DFT-based third order perturbation theory approach includes the FC term by FPT. Based on the perturbed nonrelativistic Kohn-Sham orbitals spin polarized by the FC operator, a sum over states treatment (SOS-DFPT) calculates the spin orbit corrections (35-37). This approach, in contrast to that of Nakatsuji et al., includes both electron correlation and local origins in the calculations of spin orbit effects on chemical shifts. In contrast to these approaches that employed the finite perturbation method the SO corrections to NMR properties can be calculated analytically from... 

Combariza et al.122 calculated the 33S shielding tensor by the ab initio LORG (localized orbital local origin) method in the following oxothiomolybdates MoSO, Mot+O, MoS2 and M0S4-. An excellent correlation between calculated and experimental chemical shifts has been found with all the basis sets used ... 

The original formulation of DFT by Kohn and Sham appeared to imply that an exact orbital theory could be expressed in terms of a local exchange-correlation potential[4] ( note added in proof , p. A1138). This conclusion would follow... 

We turn now to the operations required of any catalytic systems to effect the smooth, ground-state interconversion of two olefins and a cyclobutane ring. The construction of a cyclobutane ring requires the electronic population of the SA and SS orbitals and the electronic vacancy of the AS and A A orbitals. Two of the prerequisites—population of the SS orbital and vacancy of the AA orbital—are assured since these orbitals are correlated with the appropriate orbitals in the olefin combinations. The primary function of the catalyst, clearly, is the removal of an electron pair from the olefin AS tt combination and the insertion of an electron pair into the olefin SA it combination. A hypothetical catalyst can conceivably carry out these operations with a pair of orbitals of SA and AS symmetry and an electron pair. This operation is represented in Fig. 6 for simplicity the electron pairs have been localized (indicated by shading) in the originating and terminating bonds. 

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