How does one calculate chemical shift in a gauge independent manner? The literature on ab initio calculations of chemical shift in NMR experiments usually provide Lamb's and Ramsey's formulae as the solution. Yet the expressions explicitly depend on vector potential gauge choise. Some authors claim that the theory is intrinsically gauge invariant, giving no proper proof yet. Can the solution be expressed in an explicitly gauge invariant form? Some literature on this.

NOTE: I know about London orbitals theory, yet it's still not fully understood by me, how it can deliver a type of expression I want. Some suggestion on where this is clarified are very welcome.
The references below describe the answer.

Prog Nucl Magn Reson Spectrosc. Author manuscript; available in PMC 2012 May 1.
Published in final edited form as:
Prog Nucl Magn Reson Spectrosc. 2011 May; 58(3-4): 176–201.
Published online 2010 Dec 15. doi: 10.1016/j.pnmrs.2010.10.003
PMCID: PMC3058154
NIHMSID: NIHMS248338
Chemical shift tensors: Theory and application to molecular structural problems
Julio C. Facelli

Nucleic Acids Res. 2014 Dec 16; 42(22): e173.
Published online 2014 Nov 17. doi: 10.1093/nar/gku1006
PMCID: PMC4267612
Accurate ab initio prediction of NMR chemical shifts of nucleic acids and nucleic acids/protein complexes
Andrea Victora,1 Heiko M. Möller,2 and Thomas E. Exner1,3,*

A comparison of models for calculating nuclear magnetic resonance
shielding tensors
James R. Cheeseman, Gary W. Trucks, Todd A. Keith, and Michael J. Frisch

J. Chem. Phys. 104 (14), 8 April 1996