Imposing Orthogonality QMC Techniques

Quantum Monte Carlo (QMC) methods are computations that use a statistical integration to calculate integrals which could not be evaluated analytically. These calculations can be extremely accurate, but often at the expense of enormous CPU times. There are a number of methods for obtaining excited-state energies from QMC calculations. These methods will only be mentioned here and are explained more fully in the text by Hammond, Lester, and Reynolds. 

Computations done in imaginary time can yield an excited-state energy by a transformation of the energy decay curve. If an accurate description of the ground state is already available, an excited-state description can be obtained by forcing the wave function to be orthogonal to the ground-state wave function. 

Dilfusion and Green s function QMC calculations are often done using a fixed-node approximation. Within this scheme, the nodal surfaces used define the state that is obtained as well as ensuring an antisymmetric wave function. 

Matrix QMC procedures, similar to configuration interaction treatments, have been devised in an attempt to calculate many states concurrently. These methods are not yet well developed, as evidenced by oscillatory behavior in the excited-state energies. 

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