LORG methods

This is a variant of the sum-over-states perturbation theory which applies the random phase approximation (RPA) to deal effectively with the paramagnetic contribution. A localised orbital scheme is utilised to ascribe the local gauge origins [12,13]. Complex (gauge-dependent) orbitals are not introduced. 

In SOS-PT a magnetic parameter can be expressed as the sum of two contributions the diamagnetic term involving only the ground-state wave function, and the paramagnetic term containing the resolvant operator 

We have already found out that within the RPA the resolvant operator can be expressed as 

For a closed shell system and spin-free one-electron operators this reduces to the form where integrals over MOs occur 

The LORG method assumes that each occupied molecular orbital is localised (e.g. using the Boys criterion), and an origin vector rNo = r0 — rN relative to the magnetic nucleus is associated with each localised orbital ( t 0) so that it holds true that 

---

There are several alternative computational methods for obtaining NMR data such as the GIAO method (Wolinski et al., 1990), the LORG method (Bouman and Hansen, 1989), and IGAIM (Keith and Bader, 1992). 

Another approach involves the so-called localized orbital/local origin (LORG) scheme in conjunction with the random phase approximation (RPA). It was formulated but not implemented. In the LORG method, each localized (occupied) molecular orbital carries its own gauge origin. 

A Comparison of the IGLO and LORG Methods for the Calculation of Nuclear... 

In order to rationally connect the NMR spectral information to the solution conformation of the oUgomers, the chemical shifts of the main-chain methylene and terminal methine or ethyl protons were computationally estimated by density functional theory (DFT) [78] calculation for some optimized conformers of 1 of n=2 and 2 of n=2 and 4. The conformer structures optimized by the semiempirical PM5 method [51] are shown in Fig. 17 with their heats of formation (PM5) and theoretical chemical shifts obtained by the LORG method [79] using B88 [80]... 

---