QMC wave function optimizations

In this section, we will optimize a Jastrow factor for each state, and we will the re-optimize the CI coefficients in the presence of the Jastrow. The setup of the CHAMP files is similar to what we have done in the Setup

Here, we have 12 electrons, 6 up and 6 down.

Optimization of the ground state

Create a new directory, and copy the COH2_GS.trexio TREXIO file inside it. Convert the TREXIO file into CHAMP files:

python3 /path/champ/tools/trex-tools/trex2champ.py \
                        --trex          "COH2_GS.trexio" \
                        --motype        "Canonical" \
                        --backend       "HDF5" \
                        --basis_prefix  "BFD-aug-cc-pVDZ" \
                        --lcao \
                        --geom \
                        --basis \
                        --ecp \
                        --sym \
                        --det

\(COH_2\) has three different atom types, so the Jastrow factor file will be slightly different from the file for water with one extra line for $a$ parameters. You can start by creating a file called jastrow.start:

jastrow_parameter   1
  5  5  0           norda,nordb,nordc
   0.60000000   0.00000000     scalek,a21
   0.00000000   0.00000000  0. 0. 0. 0. (a(iparmj),iparmj=1,nparma) ! e-n C
   0.00000000   0.00000000  0. 0. 0. 0. (a(iparmj),iparmj=1,nparma) ! e-n O
   0.00000000   0.00000000  0. 0. 0. 0. (a(iparmj),iparmj=1,nparma) ! e-n H
   0.50000000   1.00000000  0. 0. 0. 0. (b(iparmj),iparmj=1,nparmb)
 (c(iparmj),iparmj=1,nparmc) ! e-e-n C
 (c(iparmj),iparmj=1,nparmc) ! e-e-n O
 (c(iparmj),iparmj=1,nparmc) ! e-e-n H
end

Start by optimizing the Jastrow factor and perform a "quick" optimization. The following champ input file (vmc_quick.inp) contains the parameters for such a "quick" optimization.

%module optwf
    ioptwf        1
    ioptci        0
    ioptjas       1
    ioptorb       0
    method        'sr_n'

    ncore         0
    nextorb       600
    nblk_max      5000

    nopt_iter     10
    sr_tau        0.05
    sr_eps        0.01
    sr_adiag      0.01
%endmodule


%module blocking_vmc
    vmc_nstep     20
    vmc_nblk      20
    vmc_nblkeq    1
    vmc_nconf_new 0
%endmodule

Move the jastrow_optimal.1.iter10 file to jastrow_optimal.rough_GS and load this optimized Jastrow factor. You can now optimize also the CI coefficients together with the Jastrow factor by setting:

ioptci        1

Use some more Monte Carlo steps to perform a more strict optimization.

%module blocking_vmc
    vmc_nstep     20
    vmc_nblk      500
    vmc_nblkeq    1
    vmc_nconf_new 0
%endmodule

In your directory, you will now have jastrow_optimal.1.iterX and det_optimal.1.iterX files.

Set up a DMC calculation where you use the optimal Jastrow and CI coefficients. Adjust the etrial to be a bit below the VMC energy. Recall that you will have to generate the mc_configs file.

Tip

You could have also optimized the orbitals but we did not do it here to keep the calculations short. If you are setting optorb=1, load also the symmetry file.

load symmetry champ_v2_COH2_GS_symmetry.sym

Optimization of the excited state

Create a new directory, and copy the COH2_ES.trexio TREXIO file inside it. Apply the same procedure as for the ground state.

Repeat what you have done for the ground state. Start to perform a quick optimization of the Jastrow factor but do not start from zero's: start from the Jastrow factor you have for the ground state, namely, jastrow_optimal.rough_GS.

Do all step until when you obtain the DMC energy.

Compute the VMC and DMC excitation energies. Recall that if your energies are \(E_{\rm GS}+\delta E_{\rm GS} \text{ and } E_{\rm ES}+\delta E_{\rm ES},\)

where \(\delta E\) is the statistical error, the error on

\(\Delta E= E_{\rm ES}-E_{\rm GS}\) is given by