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## Which Part of to Optimise?

As described in chapter , the many-body wavefunction can be written in the following form;

The trial wavefunction in Eq.() is commonly referred to as the Hartree-Fock-Jastrow-Chi wavefunction. All three parts of the wavefunction, i.e. the HF Slater determinant of one-electron orbitals, the Jastrow factor, and the Chi function, would benefit from some form of optimisation of parameters, and so deciding which part to optimise is a matter of deciding which part should yield the greatest improvement in the quality of .

The Chi function has previously been constructed according to a scheme introduced by Fahy [26], using Eq.(). Of the three parts of the Hartree-Fock-Jastrow-Chi trial wavefunction, this function has the weakest theoretical justification for its form. It is constructed on an ad hoc basis by making the assumption that the LDA charge density is reasonably close to the real charge density. The function is then constructed according to

where is the density produced by a VMC calculation using a trial wavefunction, , with . The overall trial wavefunction should then reproduce a charge density close to the LDA form. Equation () certainly does produce a ţhat is able to reduce the energy of the system (compared to a with , see figure ) and produce a charge density that is a reasonable reflection of the LDA charge density (see figure ). However, there is nothing to suggest that a function constructed using Eq.() is the best possible function either in terms of total energy or charge density. Indeed, there is little hard evidence [66] of exactly how accurate the LDA charge density is. It therefore seemed sensible to start optimising by optimising .

Figure: Charge density along the Ge-Ge bond for different functions.

Next: Choice of Parameters Up: Optimising the function Previous: Optimising the function

Andrew Williamson
Tue Nov 19 17:11:34 GMT 1996