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Dispersion energy

Dispersion energy#

This module provides the dispersion energy evaluation for the pairwise interactions.

Example

>>> import torch
>>> import tad_dftd3 as d3
>>> numbers = torch.tensor([  # define fragments by setting atomic numbers to zero
...     [8, 1, 1, 8, 1, 6, 1, 1, 1],
...     [0, 0, 0, 8, 1, 6, 1, 1, 1],
...     [8, 1, 1, 0, 0, 0, 0, 0, 0],
... ])
>>> positions = torch.tensor([  # define coordinates once
...     [-4.224363834, +0.270465696, +0.527578960],
...     [-5.011768887, +1.780116228, +1.143194385],
...     [-2.468758653, +0.479766200, +0.982905589],
...     [+1.146167671, +0.452771215, +1.257722311],
...     [+1.841554378, -0.628298322, +2.538065200],
...     [+2.024899840, -0.438480095, -1.127412563],
...     [+1.210773578, +0.791908575, -2.550591723],
...     [+4.077073644, -0.342495506, -1.267841745],
...     [+1.404422261, -2.365753991, -1.503620411],
... ]).repeat(numbers.shape[0], 1, 1)
>>> ref = d3.reference.Reference()
>>> param = dict( # r²SCAN-D3(BJ)
...     a1=torch.tensor(0.49484001),
...     s8=torch.tensor(0.78981345),
...     a2=torch.tensor(5.73083694),
... )
>>> cn = d3.ncoord.coordination_number(numbers, positions)
>>> weights = d3.model.weight_references(numbers, cn, ref)
>>> c6 = d3.model.atomic_c6(numbers, weights, ref)
>>> energy = d3.disp.dispersion(numbers, positions, param, c6)
>>> torch.set_printoptions(precision=7)
>>> print(torch.sum(energy[0] - energy[1] - energy[2]))  # energy in Hartree
tensor(-0.0003964, dtype=torch.float64)
tad_dftd3.disp.dftd3(numbers, positions, param, *, ref=None, rcov=None, rvdw=None, r4r2=None, cutoff=None, counting_function=<function exp_count>, weighting_function=<function gaussian_weight>, damping_function=<function rational_damping>)[source]#

Evaluate DFT-D3 dispersion energy for a batch of geometries.

Parameters:

  • numbers (torch.Tensor) – Atomic numbers of the atoms in the system.

  • positions (torch.Tensor) – Cartesian coordinates of the atoms in the system.

  • param (dict[str, Tensor]) – DFT-D3 damping parameters.

  • ref (reference.Reference, optional) – Reference C6 coefficients.

  • rcov (torch.Tensor, optional) – Covalent radii of the atoms in the system.

  • rvdw (torch.Tensor, optional) – Van der Waals radii of the atoms in the system.

  • r4r2 (torch.Tensor, optional) – r⁴ over r² expectation values of the atoms in the system.

  • damping_function (Callable, optional) – Damping function evaluate distance dependent contributions.

  • weighting_function (Callable, optional) – Function to calculate weight of individual reference systems.

  • counting_function (Callable, optional) – Calculates counting value in range 0 to 1 for each atom pair.

Returns:

Atom-resolved DFT-D3 dispersion energy for each geometry.

Return type:

Tensor

tad_dftd3.disp.dispersion(numbers, positions, param, c6, rvdw=None, r4r2=None, damping_function=<function rational_damping>, cutoff=None, **kwargs)[source]#

Calculate dispersion energy between pairs of atoms.

Parameters:

  • numbers (Tensor) – Atomic numbers of the atoms in the system.

  • positions (Tensor) – Cartesian coordinates of the atoms in the system.

  • param (dict[str, Tensor]) – DFT-D3 damping parameters.

  • c6 (Tensor) – Atomic C6 dispersion coefficients.

  • rvdw (Tensor) – Van der Waals radii of the atoms in the system.

  • r4r2 (Tensor) – r⁴ over r² expectation values of the atoms in the system.

  • damping_function (Callable) – Damping function evaluate distance dependent contributions. Additional arguments are passed through to the function.

Returns:

Atom-resolved DFT-D3 dispersion energy for each geometry.

Return type:

Tensor

tad_dftd3.disp.dispersion2(numbers, positions, param, c6, r4r2, damping_function, cutoff, **kwargs)[source]#

Calculate dispersion energy between pairs of atoms.

Parameters:

  • numbers (Tensor) – Atomic numbers of the atoms in the system.

  • positions (Tensor) – Cartesian coordinates of the atoms in the system.

  • param (dict[str, Tensor]) – DFT-D3 damping parameters.

  • c6 (Tensor) – Atomic C6 dispersion coefficients.

  • r4r2 (Tensor) – r⁴ over r² expectation values of the atoms in the system.

  • damping_function (Callable) – Damping function evaluate distance dependent contributions. Additional arguments are passed through to the function.

tad_dftd3.disp.dispersion3(numbers, positions, param, c6, rvdw, cutoff, rs9=tensor(1.3333))[source]#

Three-body dispersion term. Currently this is only a wrapper for the Axilrod-Teller-Muto dispersion term.

Parameters:

  • numbers (Tensor) – Atomic numbers of the atoms in the system.

  • positions (Tensor) – Cartesian coordinates of the atoms in the system.

  • param (dict[str, Tensor]) – Dictionary of dispersion parameters. Default values are used for missing keys.

  • c6 (Tensor) – Atomic C6 dispersion coefficients.

  • rvdw (Tensor) – Van der Waals radii of the atoms in the system.

  • cutoff (Tensor) – Real-space cutoff.

  • rs9 (Tensor, optional) – Scaling for van-der-Waals radii in damping function. Defaults to 4.0/3.0.

Returns:

Atom-resolved three-body dispersion energy.

Return type:

Tensor

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