Gauge-invariant atomic orbital

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... 

Unrestricted coupled perturbed Kohn-Sham calculations in gauge invariant atomic orbitals. [151]. Unrestricted coupled perturbed Kohn-Sham calculations. 

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 >,... 

The GIAO method has roots in the old idea of London who introduced field-dependent gauge-invariant atomic orbitals. These are constructed from real atomic orbitals multiplied by a field-dependent phase factor... 

For the NMR chemical shieldings of four polymers, the chemical shielding tensors were calculated in the coupled perturbed Hartree-Fock (CPHF) method with the gauge-invariant atomic orbital (GIAO) [10], The calculated chemical shift for is defined by... 

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