A Consequence of the Instability in First-order Properties

A Consequence of the Instability in First-order Properties.—Suppose a first-order property which is stable to small changes in the wavefunction (though is not necessarily close to the experimental value) is calculated to, say, three decimal places does an error in the fourth matter To provide a concrete example for discussion, a method described in the next section will be anticipated, namely the finite field method for calculating electric polarizability a. In this method a perturbation term Ai—— fix(F)Fa is added to the Hartree-Fock hamiltonian and an SCF wave-function calculated as usual. For small uniform fields, 

In any finite field calculation, the choice of F is important because of the conflicting requirements of a small Fto make truncation valid and a large Fto minimize the rounding errors in the differences. The optimum choice clearly depends on the relative values of K0), a, / , etc. for the molecule concerned. 

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