Gauge-invariant atomic orbital theory

An additional source of chemical shielding anisotropies is that of ab initio theoretical calculations.20 25 There has been considerable progress in this area of molecular quantum mechanics, particularly with the use of gauge-invariant atomic orbitals within the framework of self-consistent-field (SCF) perturbation theory.26 In many cases the theoretical quantities have been extremely accurate and have served not only as a corroboration of experimental quantities but also as a reliable source of new data for molecules of second-row atoms (i.e., Li through F). 

A basic defect of this type of theory is that it does not give a correct description of an isolated atom in a magnetic field. To remedy this, we follow London49 and write each molecular orbital as a linear combination of gauge-invariant atomic orbitals (GIAO) x >,... 

P. D. Ellis, Y. C. Chou, and P. A. Dobosh, /. Magn. Reson., 1980, 39, 529. Semiempirical theory of boron chemical shifts utilising gauge-invariant atomic orbitals. 

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