Error Potential and Double Perturbation Theory

As is illustrated by the example of nuclear spin-spin couphng constants, it is possible to estimate the consequences of correlation effects on the values of physical properties computed from IPM wave functions by mixing the perturbations due to electron correlation and external fields 

Perturbation theory can be formulated in terms of a complete set of functions Wo. Wt, which may be eigenfunctions of Ho (although this is not necessary and may in fact yield a poor convergence). If an external perturbation is apphed, for example an electric or magnetic field, a second perturbation operator must be added to Ho and the Hamiltonian becomes 

The perturbation expansion of the total energy can be written in the form 

Even in the calculation of first-order properties, i.e. properties depending on terms linear in Ai, the inaccuracy of the wave function If o wiU have repercussions through the matrix element of A2- This point becomes clear by rewriting the Ai A2 term in the form 

The so-called correlation effects on the calculation of molecular properties refer to the effect of the terms in 2 only. Therefore, the energy has to be expanded as follows  

---