NMR Parameters Defined as Second-Order Energy Perturbations

NMR Parameters Defined as Second-Order Energy Perturbations 

In first-principles quantum theories of molecules, a system is characterized by its potential (nuclear coordinates and charges), its number of electrons and its 

Taking the derivatives of E with respect to p,A and p,B or Bext involves first taking the derivatives of the operators that constitute the Hamiltonian H or the Kohn-Sham density functional and that are dependent on p,A and/or p,B 

The notation in Eqs. (6a) and (6b) corresponds to the usual notation of perturbation theory [18] in which it is understood that the derivatives of the Hamiltonian as well as all variational and nonvariational parameters (i.e., including the dependence of the wavefunction on the perturbations) are taken. Some authors prefer to write Eqs. (6a) and (6b) as total derivatives of E in order to indicate that all dependencies of E on the perturbation parameters must be considered [19,20], Ultimately one needs to consider an explicit energy expression in which no hidden dependencies on any of the perturbations are left. This also includes a possible dependence of the basis set on the perturbation. 

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