GIAO-SCF method

Calculations were performed with the ab initio Hartree-Fock method (4) and in some cases with methods incorporating electron correlation such as MP2 (5) or BLYP (6), Geometry optimizations were initally done with relativistic effective core potential polarized valence double-zeta bases (7) and then refined with standard 6-3IG bases (8). NMR shieldings were evaluated using the GIAO-SCF method (9) and 6-3IG bases. We used the quantum chemical software GAMESS (10) and GAUSSIAN (11). 

It shows l3C absorptions (-135 °C) at <5I3C 234.18 (C+), 21.21 (C2), 38.15 (C3, C4), 51.67 (C5), 43.9 (C6, C7). Compared to dicyclopropylcarbinyl cation, the l3C signal for the cationic center is shielded by 20 ppm, indicating cyclopropyl group participation in the stabilization of the cation. The chemical shifts were compared with the values obtained from GIAO-SCF and GIAO-MP2 methods. 

Biihl, M., Thiel, W., Fleischer, U., and Kutzelnigg, W., Ab initio computation of Se NMR chemical shifts with the IGLO-SCF, the GIAO-SCF, and the GIAO-MP2 methods, J. Phys. Chem. 99, 4000-4007 (1995). 

Another major point in which the theoretical methods differ is the quantum chemical approach to solve the operator equation of the Hamilton operator itself. The most important schemes are Hartree-Fock self consistent field (HF-SCF), density functional theory (DFT) and multi-body second order perturbation theory (MP2). Different combinations have been established, so for instance GIAO-SCF, GlAO-DI I, (,IA()-MI>2, or DF I-IGLO. Most precise measurements on small systems were done with coupled cluster methods, as for instance GIAO-CCSDT-n. ... 

The [BHJ- ion has been used as a model to probe electron densities and the work indicates that the Hartree-Fock method can be used to investigate the corresponding proton densities in coordinate space and in momentum space [10]. The NMR chemical shift and shift derivative based on bond extension have been calculated for the [BHJ- ion to be 154.1 ppm and -27 ppm/A, respectively, using the GIAO SCF approach [11]. 

For strained or unsaturated cations such as the cyclobutenyl cation (6), or the cyclohexadienyl cation (7) (i.e., protonated benzene), no good agreement between IGLO (or GIAO)-SCF and experimental chemical shifts could initially be obtained. In these cases, electron correlation effects need to be included in the chemical shift calculations, in addition to the geometry optimizations which have to be performed at correlated levels as well. This necessity could be demonstrated with the advent of electron-correlated methods such as GIAO-MP2. 

In practice, calculations of xHF are based on the uncoupled Hartree-Fock, the finite field, and the self-consistent perturbation methods. Some workers use gauge-invariant atomic orbitals (GIAOs). A full review of the gauge invariance of SCF wavefunctions has been given by Epstein. 6... 

---