Geometry Optimization
We present here a complete example on how to use QMCTorch to optimize the geometry of a H2 molecule. As previously the first task is to import all the modules needed
[1]:
from torch import optim
from torch.optim import Adam
from qmctorch.wavefunction import SlaterJastrow
from qmctorch.solver import Solver
from qmctorch.sampler import Metropolis
from qmctorch.scf import Molecule
from qmctorch.utils.plot_data import plot_energy
from qmctorch.utils import set_torch_double_precision
set_torch_double_precision()
INFO:QMCTorch| ____ __ ______________ _
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INFO:QMCTorch|\___\_\/_/ /_/\___/ /_/ \___/_/ \__/_//_/
We then define the molecule. We create a H2 molecule with a short atomic distance that we will then try to relax
[2]:
mol = Molecule(atom = 'H 0. 0. -0.5; H 0. 0. 0.5', unit='bohr',
calculator='pyscf', basis='sto-3g', redo_scf=True)
INFO:QMCTorch|
INFO:QMCTorch| SCF Calculation
INFO:QMCTorch| Running scf calculation
converged SCF energy = -1.06599946214331
INFO:QMCTorch| Molecule name : H2
INFO:QMCTorch| Number of electrons : 2
INFO:QMCTorch| SCF calculator : pyscf
INFO:QMCTorch| Basis set : sto-3g
INFO:QMCTorch| SCF : HF
INFO:QMCTorch| Number of AOs : 2
INFO:QMCTorch| Number of MOs : 2
INFO:QMCTorch| SCF Energy : -1.066 Hartree
As for the wave function optimization example we need to define a wave function, a sampler an optimizer and a solver.
[3]:
# wave function with only the ground state determinant
wf = SlaterJastrow(mol, configs='single_double(2,2)').gto2sto()
# sampler
sampler = Metropolis(nwalkers=1000, nstep=200, step_size=0.5,
nelec=wf.nelec, ndim=wf.ndim,
ntherm=-1, ndecor=100,
init=mol.domain('normal'),
move={'type': 'all-elec', 'proba': 'normal'})
# optimizer
opt = Adam(wf.parameters(), lr=0.005)
# scheduler
scheduler = optim.lr_scheduler.StepLR(opt, step_size=20, gamma=0.75)
INFO:QMCTorch|
INFO:QMCTorch| Wave Function
INFO:QMCTorch| Jastrow factor : True
INFO:QMCTorch| Jastrow kernel : ee -> PadeJastrowKernel
INFO:QMCTorch| Highest MO included : 2
INFO:QMCTorch| Configurations : single_double(2,2)
INFO:QMCTorch| Number of confs : 4
INFO:QMCTorch| Kinetic energy : jacobi
INFO:QMCTorch| Number var param : 21
INFO:QMCTorch| Cuda support : False
INFO:QMCTorch| Fit GTOs to STOs :
INFO:QMCTorch|
INFO:QMCTorch| Wave Function
INFO:QMCTorch| Jastrow factor : True
INFO:QMCTorch| Jastrow kernel : ee -> PadeJastrowKernel
INFO:QMCTorch| Highest MO included : 2
INFO:QMCTorch| Configurations : single_double(2,2)
INFO:QMCTorch| Number of confs : 4
INFO:QMCTorch| Kinetic energy : jacobi
INFO:QMCTorch| Number var param : 17
INFO:QMCTorch| Cuda support : False
INFO:QMCTorch|
INFO:QMCTorch| Monte-Carlo Sampler
INFO:QMCTorch| Number of walkers : 1000
INFO:QMCTorch| Number of steps : 200
INFO:QMCTorch| Step size : 0.5
INFO:QMCTorch| Thermalization steps: -1
INFO:QMCTorch| Decorelation steps : 100
INFO:QMCTorch| Walkers init pos : normal
INFO:QMCTorch| Move type : all-elec
INFO:QMCTorch| Move proba : normal
[4]:
solver = Solver(wf=wf,
sampler=sampler,
optimizer=opt,
scheduler=None)
solver.configure(loss='energy', grad='auto', track=['local_energy','geometry'], freeze = ['ao'])
INFO:QMCTorch|
INFO:QMCTorch| QMC Solver
INFO:QMCTorch| WaveFunction : SlaterJastrow
INFO:QMCTorch| Sampler : Metropolis
INFO:QMCTorch| Optimizer : Adam
Note that we must set grad='auto' to perform a geometry optimization. To optimize the geometry of the molecule we must use the set_params_requires_grad method of the solver. We here set all the wave function parameters and all the atomic positions as variational parameters, leading to a simultaneous optimization of the wave function and of the atomic coordinates. We can then run the optimization here using 50 epochs
[5]:
solver.set_params_requires_grad(wf_params=False, geo_params=True)
obs = solver.run(50)
INFO:QMCTorch|
INFO:QMCTorch| Optimization
INFO:QMCTorch| Task :
INFO:QMCTorch| Number Parameters : 6
INFO:QMCTorch| Number of epoch : 50
INFO:QMCTorch| Batch size : 1000
INFO:QMCTorch| Loss function : energy
INFO:QMCTorch| Clip Loss : False
INFO:QMCTorch| Gradients : auto
INFO:QMCTorch| Resampling mode : update
INFO:QMCTorch| Resampling every : 1
INFO:QMCTorch| Resampling steps : 25
INFO:QMCTorch| Output file : H2_pyscf_sto-3g_QMCTorch.hdf5
INFO:QMCTorch| Checkpoint every : None
INFO:QMCTorch|
INFO:QMCTorch|
INFO:QMCTorch| epoch 0 | 1000 sampling points
INFO:QMCTorch| energy : -1.051299 +/- 0.011930
INFO:QMCTorch| variance : 0.377259
INFO:QMCTorch| epoch done in 0.08 sec.
INFO:QMCTorch|
INFO:QMCTorch| epoch 1 | 1000 sampling points
INFO:QMCTorch| energy : -1.039677 +/- 0.011319
INFO:QMCTorch| variance : 0.357927
INFO:QMCTorch| epoch done in 0.11 sec.
INFO:QMCTorch|
INFO:QMCTorch| epoch 2 | 1000 sampling points
INFO:QMCTorch| energy : -1.083498 +/- 0.011489
INFO:QMCTorch| variance : 0.363315
INFO:QMCTorch| epoch done in 0.13 sec.
INFO:QMCTorch|
INFO:QMCTorch| epoch 3 | 1000 sampling points
INFO:QMCTorch| energy : -1.096306 +/- 0.012919
INFO:QMCTorch| variance : 0.408541
INFO:QMCTorch| epoch done in 0.12 sec.
INFO:QMCTorch|
INFO:QMCTorch| epoch 4 | 1000 sampling points
INFO:QMCTorch| energy : -1.073275 +/- 0.011114
INFO:QMCTorch| variance : 0.351444
INFO:QMCTorch| epoch done in 0.14 sec.
INFO:QMCTorch|
INFO:QMCTorch| epoch 5 | 1000 sampling points
INFO:QMCTorch| energy : -1.091809 +/- 0.011652
INFO:QMCTorch| variance : 0.368468
INFO:QMCTorch| epoch done in 0.11 sec.
INFO:QMCTorch|
INFO:QMCTorch| epoch 6 | 1000 sampling points
INFO:QMCTorch| energy : -1.086389 +/- 0.011696
INFO:QMCTorch| variance : 0.369854
INFO:QMCTorch| epoch done in 0.51 sec.
INFO:QMCTorch|
INFO:QMCTorch| epoch 7 | 1000 sampling points
INFO:QMCTorch| energy : -1.106363 +/- 0.015236
INFO:QMCTorch| variance : 0.481804
INFO:QMCTorch| epoch done in 0.09 sec.
INFO:QMCTorch|
INFO:QMCTorch| epoch 8 | 1000 sampling points
INFO:QMCTorch| energy : -1.103029 +/- 0.011551
INFO:QMCTorch| variance : 0.365266
INFO:QMCTorch| epoch done in 0.09 sec.
INFO:QMCTorch|
INFO:QMCTorch| epoch 9 | 1000 sampling points
INFO:QMCTorch| energy : -1.104694 +/- 0.010543
INFO:QMCTorch| variance : 0.333408
INFO:QMCTorch| epoch done in 0.13 sec.
INFO:QMCTorch|
INFO:QMCTorch| epoch 10 | 1000 sampling points
INFO:QMCTorch| energy : -1.101184 +/- 0.010772
INFO:QMCTorch| variance : 0.340643
INFO:QMCTorch| epoch done in 0.83 sec.
INFO:QMCTorch|
INFO:QMCTorch| epoch 11 | 1000 sampling points
INFO:QMCTorch| energy : -1.118775 +/- 0.010548
INFO:QMCTorch| variance : 0.333553
INFO:QMCTorch| epoch done in 0.09 sec.
INFO:QMCTorch|
INFO:QMCTorch| epoch 12 | 1000 sampling points
INFO:QMCTorch| energy : -1.111163 +/- 0.010536
INFO:QMCTorch| variance : 0.333193
INFO:QMCTorch| epoch done in 0.10 sec.
INFO:QMCTorch|
INFO:QMCTorch| epoch 13 | 1000 sampling points
INFO:QMCTorch| energy : -1.093243 +/- 0.010991
INFO:QMCTorch| variance : 0.347571
INFO:QMCTorch| epoch done in 0.15 sec.
INFO:QMCTorch|
INFO:QMCTorch| epoch 14 | 1000 sampling points
INFO:QMCTorch| energy : -1.098148 +/- 0.009786
INFO:QMCTorch| variance : 0.309451
INFO:QMCTorch| epoch done in 0.10 sec.
INFO:QMCTorch|
INFO:QMCTorch| epoch 15 | 1000 sampling points
INFO:QMCTorch| energy : -1.110943 +/- 0.009883
INFO:QMCTorch| variance : 0.312525
INFO:QMCTorch| epoch done in 0.12 sec.
INFO:QMCTorch|
INFO:QMCTorch| epoch 16 | 1000 sampling points
INFO:QMCTorch| energy : -1.130522 +/- 0.010770
INFO:QMCTorch| variance : 0.340589
INFO:QMCTorch| epoch done in 0.10 sec.
INFO:QMCTorch|
INFO:QMCTorch| epoch 17 | 1000 sampling points
INFO:QMCTorch| energy : -1.119832 +/- 0.010397
INFO:QMCTorch| variance : 0.328774
INFO:QMCTorch| epoch done in 0.84 sec.
INFO:QMCTorch|
INFO:QMCTorch| epoch 18 | 1000 sampling points
INFO:QMCTorch| energy : -1.114476 +/- 0.010044
INFO:QMCTorch| variance : 0.317618
INFO:QMCTorch| epoch done in 0.11 sec.
INFO:QMCTorch|
INFO:QMCTorch| epoch 19 | 1000 sampling points
INFO:QMCTorch| energy : -1.127139 +/- 0.009782
INFO:QMCTorch| variance : 0.309344
INFO:QMCTorch| epoch done in 0.09 sec.
INFO:QMCTorch|
INFO:QMCTorch| epoch 20 | 1000 sampling points
INFO:QMCTorch| energy : -1.141108 +/- 0.010158
INFO:QMCTorch| variance : 0.321225
INFO:QMCTorch| epoch done in 0.16 sec.
INFO:QMCTorch|
INFO:QMCTorch| epoch 21 | 1000 sampling points
INFO:QMCTorch| energy : -1.120979 +/- 0.009740
INFO:QMCTorch| variance : 0.307994
INFO:QMCTorch| epoch done in 0.09 sec.
INFO:QMCTorch|
INFO:QMCTorch| epoch 22 | 1000 sampling points
INFO:QMCTorch| energy : -1.130151 +/- 0.010171
INFO:QMCTorch| variance : 0.321641
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INFO:QMCTorch|
INFO:QMCTorch| epoch 23 | 1000 sampling points
INFO:QMCTorch| energy : -1.126904 +/- 0.009565
INFO:QMCTorch| variance : 0.302478
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INFO:QMCTorch| epoch 24 | 1000 sampling points
INFO:QMCTorch| energy : -1.140780 +/- 0.009760
INFO:QMCTorch| variance : 0.308645
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INFO:QMCTorch| epoch 25 | 1000 sampling points
INFO:QMCTorch| energy : -1.122666 +/- 0.009864
INFO:QMCTorch| variance : 0.311916
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INFO:QMCTorch| epoch 26 | 1000 sampling points
INFO:QMCTorch| energy : -1.124710 +/- 0.009316
INFO:QMCTorch| variance : 0.294589
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INFO:QMCTorch| epoch 27 | 1000 sampling points
INFO:QMCTorch| energy : -1.130382 +/- 0.009266
INFO:QMCTorch| variance : 0.293020
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INFO:QMCTorch| epoch 28 | 1000 sampling points
INFO:QMCTorch| energy : -1.124134 +/- 0.009203
INFO:QMCTorch| variance : 0.291026
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INFO:QMCTorch| epoch 29 | 1000 sampling points
INFO:QMCTorch| energy : -1.148873 +/- 0.008958
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INFO:QMCTorch| epoch 30 | 1000 sampling points
INFO:QMCTorch| energy : -1.151410 +/- 0.009124
INFO:QMCTorch| variance : 0.288521
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INFO:QMCTorch| epoch 31 | 1000 sampling points
INFO:QMCTorch| energy : -1.132741 +/- 0.008910
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INFO:QMCTorch| epoch 32 | 1000 sampling points
INFO:QMCTorch| energy : -1.157418 +/- 0.009251
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INFO:QMCTorch| epoch 33 | 1000 sampling points
INFO:QMCTorch| energy : -1.139773 +/- 0.009447
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INFO:QMCTorch| energy : -1.141193 +/- 0.009174
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INFO:QMCTorch| energy : -1.142530 +/- 0.011028
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INFO:QMCTorch| energy : -1.135991 +/- 0.009584
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INFO:QMCTorch| energy : -1.146994 +/- 0.009392
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INFO:QMCTorch| energy : -1.146822 +/- 0.008714
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INFO:QMCTorch| energy : -1.137690 +/- 0.008836
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INFO:QMCTorch| epoch 42 | 1000 sampling points
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INFO:QMCTorch| energy : -1.156989 +/- 0.008510
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INFO:QMCTorch| epoch 45 | 1000 sampling points
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INFO:QMCTorch| epoch 46 | 1000 sampling points
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INFO:QMCTorch| epoch 47 | 1000 sampling points
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INFO:QMCTorch| epoch 48 | 1000 sampling points
INFO:QMCTorch| energy : -1.142816 +/- 0.008155
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INFO:QMCTorch| epoch 49 | 1000 sampling points
INFO:QMCTorch| energy : -1.140517 +/- 0.008837
INFO:QMCTorch| variance : 0.279447
INFO:QMCTorch| epoch done in 0.12 sec.
[6]:
solver.save_traj('h2_traj.xyz', obs)
[7]:
plot_energy(obs.local_energy)
