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.
