Diffusion Monte Carlo¶

After optimizing the Jastrow factor, we can perform a Diffusion Monte Carlo (DMC) simulation. DMC provides a more accurate energy by projecting out the ground state component of the trial wavefunction.

1. Generate Walkers¶

First, perform a short VMC run using the optimized Jastrow factor to generate a population of walkers distributed according to \(|\Psi_T|^2\).

Create an input file vmc_generate_walkers.inp:

%module general
    title           'Generate Walkers'
    mode            'vmc_one_mpi1'
%endmodule

load trexio         h2o_hf.trexio
load jastrow        jastrow_optimal.1.iter20  # Use your best Jastrow

%module electrons
    nup           4
    nelec         8
%endmodule

%module blocking_vmc
    vmc_nstep     20
    vmc_nblk      200
    vmc_nblkeq    1
    vmc_nconf_new 100   # Generate 100 walkers per core
%endmodule

Run this. It will produce mc_configs_newX files. Concatenate them into a single mc_configs file:

cat mc_configs_new* >> mc_configs
rm mc_configs_new*

2. Run DMC¶

Create the DMC input file dmc_h2o.inp. Note the change in mode and the inclusion of the dmc and blocking_dmc modules.

%module general
    title           'DMC Run'
    mode            'dmc_one_mpi1'  # Switch to DMC mode
%endmodule

load trexio         h2o_hf.trexio
load jastrow        jastrow_optimal.1.iter20
# Walker file 'mc_configs' is read automatically if present

%module electrons
    nup           4
    nelec         8
%endmodule

%module blocking_dmc
    dmc_nstep     60       # Steps per block
    dmc_nblk      40       # Number of blocks
    dmc_nblkeq    1        # Equilibration blocks
    dmc_nconf     100      # Target population per core
%endmodule

%module dmc
    tau           0.05     # Time step (try 0.05, 0.02, 0.01)
    etrial        -17.240  # Estimate from VMC
    icasula       -1       # Algorithm choice (standard)
%endmodule

Run the DMC calculation:

/bin/dmc.mov1 -i dmc_h2o.inp -o dmc_ß2o.out -e error

3. Analyze Results¶

Check the output file for the average DMC energy:

grep 'total E' dmc_h2o.out

Or look for the summary at the end of the blocks.

Time Step Bias

DMC has a time-step error. Run calculations with different tau values (e.g., 0.05, 0.02, 0.01) and extrapolate to \(\tau \to 0\) for high precision results.

Orbital Optimization (Optional)¶

You can also optimize the orbital coefficients (ioptorb 1) along with the Jastrow factor to further improve the node surface and variational energy.