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Two body Jastrow term
As it is well known, the Jastrow term plays a crucial role in treating
many body correlation effects. One of the most important correlation
contribution arises from the electronelectron interaction. Therefore it is
important to use at least a twobody Jastrow factor in the trial wave
function. Moreover this term reduces the probability for two electrons to be close, and so decreases the average value of the repulsive interaction, providing a clear energy gain.
The twobody Jastrow function reads:

(1.26) 
where
depends only on the relative distance
between
two electrons and allows to fulfill the cusp conditions
for opposite spin electrons as long as
for small electronelectron distance.
The pair correlation function
can be parametrized successfully by
few variational parameters.
We have adopted a functional form
proposed by Fahy (38), that we found particularly convenient:

(1.27) 
where the variational parameter
has been optimized for each system.
In this functional form
the cusp condition for antiparallel spin electrons is satisfied, whereas
the one for parallel spins is neglected in order to avoid the
spin contamination (for more details about spin contamination see
Ref. (39) ).
This allows to remove the singularities of the local energy due to the
collision
of two opposite spin electrons, yielding a smaller variance and a more
efficient VMC calculation.
Next: Three Body Jastrow term
Up: Functional form of the
Previous: One body term
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Claudio Attaccalite
20051107