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This short paper summarizes the local energy calculation problem of the calculation of the Slater-Jastrow wave function. This wave function has number
of desirable properties for many-body quantum Monte-Carlo calculations
of electrons in the presence of ions.
The Slater-Jastrow wave function
is a product of Slater determinants and the Jastrow correlation factor:
 |
(1) |
Here, the
and
are defined as the
Slater matrices of the single particle up and down
orbitals, respectively. That is
![\begin{displaymath}A = \left[
\begin{array}{ccccl}
\phi_1({\mathbf r}_1) & \phi...
...\vdots & \vdots & \vdots & \vdots & \ddots
\end{array}\right]
\end{displaymath}](img4.gif) |
(2) |
Where
are molecular orbitals centered at
ck:
 |
(3) |
The Jastrow correlation factor Uij terms are defined in the following manner:
 |
(4) |
where
and
 |
|
|
(5) |
This trial wave function (1) has a number of desirable
properties:
- 1.
- The corerct cusp conditions for both like and unlike electron
spins.
- 2.
- The coorect cusp behavior as the electron-nuclear separation
becomes small.
- 3.
- The variational parameters in (1) have a simple
physical interpretation at large separations.
- (a)
can be related to the polarizability of a molecule
- (b)
the maximum value of
is equal to
where I is the first ionization potential.
Next: Local Energy
Up: Local Energy Calculation of
Previous: Local Energy Calculation of
Nichols A. Romero
1999-12-17