1. Oxygen Atom (UHF Trial Wavefunction)#

This example demonstrates an AFQMC calculation of an isolated oxygen atom using an unrestricted Hartree-Fock (UHF) trial wavefunction. The Oxygen atom has a ground state with $S=2$ (quartet state)

1.1. Running the Example#

The workflow includes the following steps:

Generate the trial wavefunction and orbital basis: Execute scf/scf.py to run PySCF calculations generating both ROHF and UHF checkpoint files.
Create AFQMC input files: Execute ham/ham.py to generate the Hamiltonian in Cholesky-decomposed form and format the trial wavefunction. Note that we used the ROHF orbitals as a basis, since they are spin-independent. The UHF wavefunction will be used as the trial wavefunction for AFQMC. The write_wfn_mol () function directly handles the change of basis as demonstrated in this example. This produces afqmc.h5 containing the Hamiltonian and trial wavefunction.
Run SAFIRE: Run SAFIRE using the provided json input file (see below):
```
$ mpirun -n 16 safire afqmc.json
```
The AFQMC calculation will perform sampling and output energy estimates and other observables.

analyze the results: Use the scalar_stats command-line tool from afqmctools to analyze the energy output:

$ scalar_stats qmc.s000.scalar.dat -s time -e 5.0 -t

This will compute the average AFQMC energy and stochastic uncertainty, using an equilibration time of 5.0 $Ha^{-1}$. The -t flag will generate a plot of the energy as a function of imaginary time if running locally. If running remotely, you can save the plot of the energy vs imaginary time to a file using the –savefig [name].png option. In either case, you should see the following output if you used the same settings as in the provided afqmc.json file and above.

====== [analyze_scalar_data Settings] ======

[+] fname            = qmc.s000.scalar.dat
[+] mark_header      = #
[+] series_column    = time
[+] nequil           = 5.0
[+] estimate_equil   = False
[+] column           = LocalEnergy
[+] reblock          = 1
[+] ndiscard         = None
[+] list             = False
[+] trace            = False
[+] append           = None
[+] dump             = False
[+] dump_fname       = trace.dat
[+] verbose          = True
[+] autocorr         = None
[+] savefig          = None
[+] dump_avail_columns = False

AFQMC Energy   -74.909596 +/-   0.000328 4.22  5.0/60.0

1.2. Files#

SCF Calculation (scf/scf.py):

#!/usr/bin/env python3

# This file is distributed under the Apache License, Version 2.0 License.
# See LICENSE file in top directory for details.
#
# Copyright (c) 2021-2025 The Simons Foundation, Inc.
#
# You may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#      http://www.apache.org/licenses/LICENSE-2.0


from pyscf import gto, scf

def main():
    """
    Computing the energy of ferro-magnetically coupled
       Vandium atoms.       
    """
    mol = gto.M(
        atom='O 0. 0. 0.',
        basis='ccpvdz',
        spin=2,
        verbose=4
    )

    mf = scf.ROHF(mol).newton()
    mf.chkfile = 'rohf.chk'
    mf.kernel()

    mf = scf.UHF(mol).newton()
    mf.chkfile = 'uhf.chk'
    mf.kernel()

if __name__ == '__main__':
    main()

Hamiltonian and Wavefunction Generation (ham/ham.py):

# This file is distributed under the Apache License, Version 2.0 License.
# See LICENSE file in top directory for details.
#
# Copyright (c) 2021-2025 The Simons Foundation, Inc.
#
# You may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#      http://www.apache.org/licenses/LICENSE-2.0

from afqmctools.utils.pyscf_utils import load_from_pyscf_chk_mol
from afqmctools.hamiltonian.mol import write_hamil_mol
from afqmctools.wavefunction.mol import write_wfn_mol


def main():

    # inputs
    orbital_basis_chk = '../scf/rohf.chk'
    wavefunction_chk = '../scf/uhf.chk'

    chol_tol = 1e-5

    # output
    fout = 'afqmc.h5'

    #####################################
    #                                   #
    #  Write Hamiltonian in ROHF basis  #
    #                                   #
    #####################################

    scf_data = load_from_pyscf_chk_mol(
        orbital_basis_chk,
        'scf'
    )

    write_hamil_mol(
        scf_data=scf_data,
        hamil_file=fout, 
        chol_cut=chol_tol, 
        real_chol=True, 
        verbose=True
    )
    
    #####################################
    #                                   #
    #      Write Trial Wavefunction     #
    #                                   #
    #####################################

    write_wfn_mol(
        scf_data=load_from_pyscf_chk_mol(
            wavefunction_chk,
            'scf'
        ),
        basis_scf_data=scf_data,
        filename=fout
    )


if __name__ == '__main__':
    main()

AFQMC Input File (afqmc.json):

{
    "afqmc" :{
        "project": {
      "id": "qmc",
      "series": 0
    },
    "execute": {    
      "walker_set": {
        "walker_type": "COLLINEAR"
      },
       "wavefunction": {
         "filename": "../ham/afqmc.h5"
       },
       "timestep": "0.01",
       "steps": "6000",
       "population_control_interval": "10",
       "measure_interval_multiplier": "1",
       "n_walkers_per_mpi_task": "100",
       "seed": "42"
    }
  }
}