The Chemical Shielding Tensors Fundamentals

The induced field is determined by the total electronic current density j(r) by means of the Biot-Savart law as follows  

In a crystaUine solid, in which the Bom-von Kannan periodic boundary conditions are apphcable, the cnrrent density j(r) will be periodic, and can be conveniently calcnlated in reciprocal space using the Fourier transform of Equation 12.2 [5]  

In the framework of qnantnm mechanics, the all-electron Hamiltonian H is, in atomic units. 

According to Bloch s theorem [6], the solutions to Schrodinger s equation mnst take the form  

The explicit periodicity of the Bloch wave function poses a major challenge for the calculation of aforementioned chemical shielding tensor in the solid state. Under these circumstances, the calculation of NMR parameters requires the inclusion of a macroscopic magnetic field described by a nonperiodic vector potential, yielding a new Hamiltonian  

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