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.