In the Born–Oppenheimer approximation the wavefunction of a molecule is factorized into a nuclear and an electronic part and the electronic energy as a function of the nuclear geometry forms a potential energy surface (PES) for the motion of the nuclei. This PES can be evaluated using any of the various electronic structure methods available.

Molecular properties such as NMR parameters can also be calculated at a given nuclear geometry using a wide range of methods.¹  Since NMR properties do not depend on nuclear momentum, one can similarly calculate the NMR property in the Born–Oppenheimer approximation for any nuclear geometry and think of this as constituting a property surface P(q). However, in the Born–Oppenheimer approximation the correct value of a property is not simply the value P_eq calculated with an electronic structure method at the geometry corresponding to the minimum of the potential energy surface, the so-called equilibrium geometry. Rather, one has to calculate the expectation value of the property as a function of the nuclear coordinates, i.e. the property surface P(q), with the nuclear wavefunction Ψ of the appropriate vibrational state