Structural optimization of the hydrogen dimer

In this tutorial, you will compute atomic forces for the hydrogen dimer (H2) and optimize its geometry. All input and output files for this tutorial can be downloaded here.

12 Preparing a JAGP wavefuction of the H dimer with a shorter bond distance

This section describes the procedure for preparing a JAGP wavefunction for the H2 dimer at a shorter bond distance.

  1. Prepare a molecular structure file H2_dimer_short.xyz in which H atoms are relocated, e.g.:

2
H2_dimer 
  H      0.00000000          0.00000000         -0.27050000000000000000
  H      0.00000000          0.00000000          0.27050000000000000000

  1. Run the PySCF calculation

    cd 12_jagp_wf_shorter_distance
python3 pyscf_H2.py

  2. Convert the generated PySCF checkpoint file to a TREXIO file

    trexio convert-from -t pyscf -i H2.chk -b hdf5 H2.hdf5

  3. Convert from the TREXIO file to the TurboRVB wavefunction

    trexio-to-turborvb H2.hdf5 -jasbasis cc-pVDZ -jascutbasis

  4. Convert from JDFT wavefunction to JAGP wavefunction

    turbogenius convertwf -to agps

    then, check the conversion by typing:

    grep Overlap out_conv

13 Nodal surface optimization (WF=JsAGPs)

In this step, the Jastrow factors and the determinant part are optimized at the VMC level using vmcopt module of Turbo-Genius. The procedure is almost the same as in 08 Nodal surface optimization (WF=JsAGPs).

First, copy the converted wavefunction fort.10

cd ../13_nodal_surface_optimization/
cp ../12_jagp_wf_shorter_distance/fort.10 .
cp ../12_jagp_wf_shorter_distance/pseudo.dat .

Next, generate the input file for VMC optimization datasmin.input using:

turbogenius vmcopt -g -opt_onebody -opt_twobody -opt_jas_mat -opt_det_mat -optimizer lr -vmcoptsteps 1000 -steps 100 -nw 128

Run the VMC optimization. Note that there are several options for running the VMC optimization. See 12 Preparing a JAGP wavefuction of the H dimer with a shorter bond distance.

export TURBOVMC_RUN_COMMAND="mpirun -np 16 turborvb-mpi.x"
turbogenius vmcopt -r

Finally, run the post-processing using:

turbogenius vmcopt -post -optwarmup 80 -plot

14 VMC before structural optimization

In this step, a single-shot VMC calculation is performed before the structural optimization.

First, copy fort.10 from the previous step.

cd ../14_vmc_before_structural_optimization/
cp ../13_nodal_surface_optimization/fort.10 .
cp ../13_nodal_surface_optimization/pseudo.dat .

Next, generate the input file for VMC calculation datasvmc.input using:

turbogenius vmc -g -steps 1000 -nw 128 -force

Run the VMC calculation, for example, using:

export TURBOVMC_RUN_COMMAND="mpirun -np 16 turborvb-mpi.x"
turbogenius vmc -r

Finally, run the post-processing using:

turbogenius vmc -post -bin 10 -warmup 5

and check the force term:

$ cat forces_vmc.dat
Force component 1
Force   = -0.581448055902718       3.012635556421040E-002
1.943226397097583E-003
Der Eloc = -0.566537913456315       2.996930056497041E-002
<OH> =  0.890900221204126       4.750020105279961E-002
<O><H> = -0.898355292427328       4.681606812429169E-002
2*(<OH> - <O><H>) = -1.491014244640310E-002  3.607617628391403E-003

15 Structural optimization

In this step, the structural optimization is performed using the vmcopt module of Turbo-Genius.

First, copy fort.10 from the previous step.

cd ../15_structural_optimization
cp ../13_nodal_surface_optimization/fort.10 .
cp ../13_nodal_surface_optimization/pseudo.dat .

Next, generate the input file for VMC optimization datasmin.input using:

turbogenius vmcopt -g -opt_onebody -opt_twobody -opt_jas_mat -opt_det_mat -optimizer lr -vmcoptsteps 1000 -steps 100 -nw 128 -opt_structure -strlearn 1.0e-6

Note that the -opt_structure option is used to perform the structural optimization. The learning rate is set to 10-6.

Run the VMC optimization, for example, using:

export TURBOVMC_RUN_COMMAND="mpirun -np 16 turborvb-mpi.x"
turbogenius vmcopt -r

Finally, run the post-processing using:

turbogenius vmcopt -post -optwarmup 80 -plot

16 VMC after structural optimization

In this step, the VMC calculation is performed after the structural optimization.

First, copy fort.10 from the previous step.

cd ../16_vmc_after_structural_optimization/
cp ../15_structural_optimization/fort.10 .
cp ../15_structural_optimization/pseudo.dat .

Next, generate the input file for VMC calculation datasvmc.input using:

turbogenius vmc -g -steps 1000 -nw 128 -force

Run the VMC calculation, for example, using:

export TURBOVMC_RUN_COMMAND="mpirun -np 16 turborvb-mpi.x"
turbogenius vmc -r

Finally, run the post-processing using:

turbogenius vmc -post -bin 10 -warmup 5

and check the force term:

$ cat forces_vmc.dat
Force component 1
Force   =  8.845943906431761E-003  2.073719499651680E-002
1.397654468993750E-003
Der Eloc =  6.856205295579485E-003  2.011093288033853E-002
<OH> =  0.901136545231286       3.656293234452725E-002
<O><H> = -0.900141675925860       3.673121825334205E-002
2*(<OH> - <O><H>) =  1.989738610852276E-003  3.770140210987045E-003

This series of calculations yields the optimal structure and wavefunction for the H2 dimer. The significant change in force values before and after structural optimization confirms that the structure has approached its equilibrium position.