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To perform a VMC calculation using an excited state Slater
determinant, it is necessary to optimise the Jastrow and functions
to minimise the energy/variance of the energy of the wavefunction
containing this new determinant. In an attempt to speed up the turn
around for performing QMC calculations on excited states, it was
decided to experiment with omitting the extra optimisation required to
convert the ground state Jastrow and functions to excited state
Jastrow and functions. Instead of performing this extra
optimisation for each excitation we proceed straight to the DMC
calculations. This is possible as long as the trial/guiding
wavefunction is of sufficient quality. In the case of DMC
calculations this implies two basic requirements;

- The trial/guiding wavefunction for the excited state must be
orthogonal to the ground state wavefunction and all lower energy exact
eigenstates or the DMC algorithm will simply propagate out the lowest
energy solution.
- The trial/guiding wavefunction must have an acceptably low
variance of the local energy to ensure that the fluctuations in the
population of walkers are manageable (see
chapters and for details).

In all the excitation calculations described here, the excited
orbitals in the excited state Slater determinants have different values to the ground state orbital they replace, i.e. they are indirect
excitations. This ensures that, on the grounds of translational
symmetry, all the excited state wavefunctions are orthogonal to the
ground state wavefunction, hence satisfying condition (i). Condition
(ii) is not so clear cut. In section , where one is
adding and removing electrons from the system, the relaxation in the
Jastrow and functions between systems with *N*-1, *N* and *N*+1
electrons was significant. This made it necessary to re-optimise the
trial/guiding wavefunction for each system. When one promotes an
orbital within the Slater determinant as in these calculations, the
resulting change in the charge density and hence the change in the
Jastrow and functions is not as severe and so it was decided to
attempt the DMC calculations for promoted states using the same one-
and two-body functions as those in the trial/guiding wavefunction used
for the ground state DMC calculation. This will not affect the DMC
estimate of the total energy, but it will increase its variance by an
amount dependent on the quality of the trial/guiding wavefunction.

** Next:** Electron-Electron Interaction for Promoted
**Up:** Trial Wavefunctions for Promoted
** Previous:** Spin Contamination
*Andrew Williamson *

Tue Nov 19 17:11:34 GMT 1996