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Torch autodiff for DFT-D4

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Torch autodiff for DFT-D4#

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Implementation of the DFT-D4 dispersion model in PyTorch. This module allows to process a single structure or a batch of structures for the calculation of atom-resolved dispersion energies.

References#

  • E. Caldeweyher, C. Bannwarth and S. Grimme, J. Chem. Phys., 2017, 147, 034112. DOI: 10.1063/1.4993215

  • E. Caldeweyher, S. Ehlert, A. Hansen, H. Neugebauer, S. Spicher, C. Bannwarth and S. Grimme, J. Chem. Phys., 2019, 150, 154122. DOI: 10.1063/1.5090222

  • E. Caldeweyher, J.-M. Mewes, S. Ehlert and S. Grimme, Phys. Chem. Chem. Phys., 2020, 22, 8499-8512. DOI: 10.1039/D0CP00502A

Examples#

The following example shows how to calculate the DFT-D4 dispersion energy for a single structure.

import torch
import tad_dftd4 as d4
import tad_mctc as mctc

numbers = mctc.convert.symbol_to_number(symbols="C C C C N C S H H H H H".split())

# coordinates in Bohr
positions = torch.tensor(
    [
        [-2.56745685564671, -0.02509985979910, 0.00000000000000],
        [-1.39177582455797, +2.27696188880014, 0.00000000000000],
        [+1.27784995624894, +2.45107479759386, 0.00000000000000],
        [+2.62801937615793, +0.25927727028120, 0.00000000000000],
        [+1.41097033661123, -1.99890996077412, 0.00000000000000],
        [-1.17186102298849, -2.34220576284180, 0.00000000000000],
        [-2.39505990368378, -5.22635838332362, 0.00000000000000],
        [+2.41961980455457, -3.62158019253045, 0.00000000000000],
        [-2.51744374846065, +3.98181713686746, 0.00000000000000],
        [+2.24269048384775, +4.24389473203647, 0.00000000000000],
        [+4.66488984573956, +0.17907568006409, 0.00000000000000],
        [-4.60044244782237, -0.17794734637413, 0.00000000000000],
    ]
)

# total charge of the system
charge = torch.tensor(0.0)

# TPSSh-D4-ATM parameters
param = {
    "s6": positions.new_tensor(1.0),
    "s8": positions.new_tensor(1.85897750),
    "s9": positions.new_tensor(1.0),
    "a1": positions.new_tensor(0.44286966),
    "a2": positions.new_tensor(4.60230534),
}

energy = d4.dftd4(numbers, positions, charge, param)
torch.set_printoptions(precision=10)
print(energy)
# tensor([-0.0020841344, -0.0018971195, -0.0018107513, -0.0018305695,
#         -0.0021737693, -0.0019484236, -0.0022788253, -0.0004080658,
#         -0.0004261866, -0.0004199839, -0.0004280768, -0.0005108935])

The next example shows the calculation of dispersion energies for a batch of structures.

import torch
import tad_dftd4 as d4
import tad_mctc as mctc

# S22 system 4: formamide dimer
numbers = mctc.batch.pack((
    mctc.convert.symbol_to_number("C C N N H H H H H H O O".split()),
    mctc.convert.symbol_to_number("C O N H H H".split()),
))

# coordinates in Bohr
positions = mctc.batch.pack((
    torch.tensor([
        [-3.81469488143921, +0.09993441402912, 0.00000000000000],
        [+3.81469488143921, -0.09993441402912, 0.00000000000000],
        [-2.66030049324036, -2.15898251533508, 0.00000000000000],
        [+2.66030049324036, +2.15898251533508, 0.00000000000000],
        [-0.73178529739380, -2.28237795829773, 0.00000000000000],
        [-5.89039325714111, -0.02589114569128, 0.00000000000000],
        [-3.71254944801331, -3.73605775833130, 0.00000000000000],
        [+3.71254944801331, +3.73605775833130, 0.00000000000000],
        [+0.73178529739380, +2.28237795829773, 0.00000000000000],
        [+5.89039325714111, +0.02589114569128, 0.00000000000000],
        [-2.74426102638245, +2.16115570068359, 0.00000000000000],
        [+2.74426102638245, -2.16115570068359, 0.00000000000000],
    ]),
    torch.tensor([
        [-0.55569743203406, +1.09030425468557, 0.00000000000000],
        [+0.51473634678469, +3.15152550263611, 0.00000000000000],
        [+0.59869690244446, -1.16861263789477, 0.00000000000000],
        [-0.45355203669134, -2.74568780438064, 0.00000000000000],
        [+2.52721209544999, -1.29200800956867, 0.00000000000000],
        [-2.63139587595376, +0.96447869452240, 0.00000000000000],
    ]),
))

# total charge of both system
charge = torch.tensor([0.0, 0.0])

# TPSSh-D4-ATM parameters
param = {
    "s6": positions.new_tensor(1.0),
    "s8": positions.new_tensor(1.85897750),
    "s9": positions.new_tensor(1.0),
    "a1": positions.new_tensor(0.44286966),
    "a2": positions.new_tensor(4.60230534),
}

# calculate dispersion energy in Hartree
energy = torch.sum(d4.dftd4(numbers, positions, charge, param), -1)
torch.set_printoptions(precision=10)
print(energy)
# tensor([-0.0088341432, -0.0027013607])
print(energy[0] - 2*energy[1])
# tensor(-0.0034314217)
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