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Adding a new Function to Chi

Having failed to resolve the difference in the VMC and DMC energies by adding a new functional form to the Jastrow factor, it was decided to return attention to and to see if a new short range function, again centered on the ion cores, could produce any further reduction in the VMC energy.

The requirements for the function are very similar to those of . It must be the most general polynomial function, subject to the constraint that it has zero derivative as and has zero value and derivative at r=L. The function is of course much simpler in that it is a function of one variable, r, the electron-ion separation.

where L again is the range of the function, is a rescaled r and the are the Chebyshev coefficients.

Another set of optimisations of were performed in which 6 stars of were optimised and a further 6 parameters in were optimised (5 for to and B). Again the 10,000 configurations used were those calculated from a VMC calculation based on the best so far. The same values of L=3.0, 3.5, 4.0, 5.0 were used. The best results obtained are illustrated in Figure gif.

  
Figure: Reduction in energy using g(r) in ¸

As can be seen in Figure gif, the introduction of g(r) reduces the VMC energy by a further 0.05eV per atom compared to the best result when optimising expressed as a Fourier expansion. Again g(r) has little effect on the variance, it was reduced from 2.56 to 2.54.


Andrew Williamson
Mon May 22 14:48:37 BST 1995