The cube in Fig. below is a supercell of a nitrogen solid structure. It contains N electrons
which are described by the wave function
Psi(**r**_{1},
**r**_{2},...,**r**_{N}).
The wave function fulfills the Schrodinger equation:

The fermion node represents a boundary condition in the so-called fixed-node quantum Monte Carlo methods which solve the Schrodinger equation by exploring the power and efficiency of a combination of analytical insights and stochastic techniques. Although the fermion node is extremely complex, the stochastic methods can deal with these and other many-body effects very efficiently. We develop and use quantum Monte Carlo methods for high accuracy electronic structure calculations of various systems such as clusters, molecules and solids. The quantum Monte Carlo methods are unique because of genuine many-body framework, applicability to large systems and high accuracy (read more in our reviews).

Fig.: 3D cut through 59-dimensional fermion node of the electronic wave
function in nitrogen solid.