The DMC method is based on the observation that the Schrodinger
equation in imaginary time (),
|
(5) |
is a diffusion equation plus a branching/annihilation term given by the
potential. If the parameter is tuned to the groundstate energy
the trial wavefunction is projected to the ground state of
the Hamiltonian. The anti-symmetric nature of the electronic
wavefunction poses serious problems for the numerical solution of Eq
(). A way out of to this difficulty is to introduce the
so called fixed-node approximation, in which a modification of Eq
() is used, that projects the wavefunction onto the ground
state wavefunction which has the same nodal surface of a trial
wavefunction. Practical computations show that this is a very good
approximation.