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Overview of the steps in a QMC calculations |
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Written by Dominik Domin
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Sunday, 20 March 2005 |
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.
- Further improvements upon the results of DMC can possibly be made by running FMC or some other Release-Node variant Green's Function Monte Carlo.
A Quantum Monte Carlo calculation consists of the following steps.
Generation of the Trial Wave Function
Actually, generation of the trial wave function is a multi-step process. For molecules it consists of:
- Generate the anti-symmetric portion (determinantal part) of the wave function with some ab initio program such as GAMESS or ADF.
- Run a VMC to equilibrate the walkers according to the distribution of the previously generated wavefunction.
- Optimize the correlation function.
- Run a VMC to equilibrate the walkers according to the new trial
wave function which consists of one or more determinants
multiplied by one of more correlation functions.
- Re-optimize the correlation function and rerun a VMC. Repeat until satisfactory convergence.
Variational Monte Carlo Run
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.
 Diffusion Monte Carlo Run
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.
Fermion Monte Carlo or Green's Function Monte Carlo Run
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 FMC 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.
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Last Updated ( Wednesday, 23 March 2005 )
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