Overview of running QMC calculations

Overview of running QMC calculations

In this section a brief overview of the procedure necessary to complete a successful QMC calculation will be given. The steps in a QMC are as follows: * Generate and optimize the trial wave function.
* Equilibrate the walkers in one or more VMC calculations.
* Run a VMC to obtain the VMC results (if one desires a VMC calculation)
* If one desires higher level of accuracy than can usually be provided by VMC one may run a DMC calculation.

A Quantum Monte Carlo calculation consists of the following steps.


Table of contents
1 Generation of Trial Wave Function
2 Running Variational Monte Carlo
3 Running Diffusion Monte Carlo
4 Further improvements upon the Fixed-Node Approximation

Generation of Trial Wave Function
Actually, generation of the trial wave function is a multi-step process. For molecules it consists of:
1. Generate the anti-symmetric portion (determinantal part) of the wave function with some ab initio program such as GAMESS or ADF. 2. Run a VMC to equilibrate the walkers according to the distribution of the previously generated wavefunction. 3. Optimize the correlation function. 4. Run a VMC to equilibrate the walkers according to the new trial wave function. This wave function consists of one or more determinants multiplied by one or more correlation functions. 5. Re-optimize the correlation function and rerun a VMC. Repeat until satisfactory convergence.

Running Variational Monte Carlo
Once an appropriate trial wavefunction is generated, a VMC can be run. If one is interested in ground state properties one must not forget to remove the decay curve before the data from the VMC is used.

Running Diffusion Monte Carlo
DMC is significantly more computationally expensive than VMC and hence it is desirable for initial walkers to be as close to the DMC distribution as is feasible. A common practice, to reduce the number of DMC steps until the walkers become equilibrated, is to use walkers from an equilibrated VMC run as the starting point for DMC.

Further improvements upon the Fixed-Node Approximation

One could possibly attempt to improve upon the results of a DMC calculation by attempting to remove the Fixed-Node Approximation (and its associated error) by running some Release-Node method such as Fermion Monte Carlo or some Green's Function Monte Carlo on the walkers from an equilibrated DMC run. Many of these methods are still in the active development phase or not yet implemented into Zori. One must also note that these methods tend to be significantly more expensive than DMC. No documentation available nor will there be any further discussion of GFMC or FMC.