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QMC of nitrogen atom, dimer and solids

L. Mitas, R.M. Martin, Phys.Rev.Lett., **72**, 2438 (1994)

In this project
we have carried out variational and fixed-node diffusion Monte Carlo
calculations for nitrogen in atomic, molecular, and
compressed solid forms.
This is the first work which treats the electron correlation in nitrogen
solids with accuracy
comparable to the most exact results on the
atom and molecule.
Comparison with Local Density Approximation (LDA)
calculations reveals LDA total energy errors varying from
2.1 eV in the atom to 0.7 eV/at. in the solid.
We have also calculated the electronic energy gap for the compressed solid
and compared it with the
LDA (30% lower) and Hartree-Fock (100% higher) estimations

This is a snapshot of the supercell from the variational Monte Carlo
simulation of the compressed
nitrogen solid in atomic I213 structure.
The black spheres are ions while the small red and magenta spheres are
electrons. The color on the cutting plane in the lower part is the
square of wavefunction and is found by scanning this plane by
of the electrons
while keeping the rest of electrons static. The two white paths
are cuts through the fermion nodal surface.

animation (239kb)
image

The green isosurface is a cut through the
nodal surface found by scanning the supercell
volume by one of the electrons while keeping the others intact.
The red colors represent the positive part of the wavefunction while
the blue part is the complementary negative part. The complete nodal
surface is (3N-1)-dimensional where N is the number of the electrons
with the same spin (in our case N=20).

The surface in this case is the square of the wavefunctions
while the color is the potential energy experienced by one of the
eletrons as it moves in the immediate vicinity of another electron
of opposite spin. The wavefunction is explicitly correlated so
that the region of electron-electron cusp (correlation hole)
is clearly visible.