Up to 80 parameters in the Jastrow factor were optimized for every structure using the method of variance minimization described in chapter 5. In excess of 75% of the DMC correlation energy was obtained in all cases. No attempt to obtain ``benchmark'' accuracy VMC results was made: the aim was to obtain wavefunctions of sufficient accuracy for use in DMC calculations.
For the fixed-node DMC calculations, a timestep of 0.003 a.u. and an ensemble of 640 walkers were used. The DMC calculations averaged moves in length.
A special consideration was made for the ring. The ring is ``cumulenic'' whereas the other rings in the study are ``polyacetylenic''8.2and have two unique bond lengths. MCHF and CI calculations show that the , cumulenic rings have significant multi-determinantal character, unlike the rings.  Due to the likely improvement in the trial wavefunction, a CISD calculation was performed and the configurations with largest weight used to form a multi-determinant trial wavefunction. 43 determinants, including the HF reference determinant were selected. Although only a small reduction in the variance of the trial wavefunction resulted (by a.u. to a.u.), a small reduction in DMC energy was found due to the improved nodal structure of the wavefunction. Results comparing single and multi-determinant wavefunctions for this isomer are presented in the next section.