Properties and Core Approximations

We turn finally to the calculation of molecular electric and magnetic properties in the pseudopotential and model potential approximations. For first-order properties and variational wave functions, we can write the property using the Hellmann-Feynman theorem as 

For electric fields, this also means using the reduced nuclear charge Z for the nuclear contribution, due to the cancellation of the contribution from the core electrons with the rest of the nuclear contribution. For model potentials that are derived without further approximation, the calculation of properties follows straightforwardly from the frozen-core approximation. 

However, if the valence spinors are modified to create pseudospinors—and this applies to both model potentials and pseudopotentials— the expectation of the valence wave function over the property operator is no longer the same as in the all-electron or the frozen-core case. For external fields, where the bulk of the contribution comes from the valence region of space, the deviation of the pseudospinor property integrals from their unmodified counterparts will be small. However, for nuclear fields, the approximation to the core part of the spinors will have serious consequences for the property. Pseudospinors used with pseudopotentials are designed to have vanishing amplitude at the nucleus, and therefore the property integrals will be much smaller than they should be. This means that properties such as NMR shielding constants calculated for the pseudopotential center will inevitably be erroneous. 

The alternative is to derive pseudoproperty operators, which account for the fact that the core has been approximated, or to calculate the property integrals with the original spinors. The former has not to our knowledge been attempted the latter has been done by Kozlov et al. (1987), for example, in the calculation of parity nonconservation effects. 

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