For the 2nd order approach, one needs to calculate σ, χ and τ from the analytical sumover-states equations using the eigenstates and energy eigenvalues of the field-free Hamiltonian. For the FC shifts, the field-free Hamiltonian is S T DS and for the PCS, it is the LFT Hamiltonian in the absence of the field. Furthermore, the Hamiltonian derivatives with respect to the nuclear magnetic moment and external field are needed. The latter is given by