qmctorch.wavefunction.orbitals.atomic_orbitals_backflow module

class qmctorch.wavefunction.orbitals.atomic_orbitals_backflow.AtomicOrbitalsBackFlow(mol, backflow_kernel, backflow_kernel_kwargs={}, cuda=False)[source]

Bases: qmctorch.wavefunction.orbitals.atomic_orbitals.AtomicOrbitals

Computes the value of atomic orbitals

Parameters:
  • mol (Molecule) – Molecule object
  • cuda (bool, optional) – Turn GPU ON/OFF Defaults to False.
forward(pos, derivative=[0], sum_grad=True, sum_hess=True, one_elec=False)[source]

Computes the values of the atomic orbitals.

\[\phi_i(q_j) = \sum_n c_n \text{Rad}^{i}_n(q_j) \text{Y}^{i}_n(q_j)\]

where :math: text{Rad}^{i}_n(r_j) is the radial part and :math: text{Y}^{i}_n(r_j) the spherical harmonics part.

The electronic positions are calculated via a backflow transformation :

\[q_i = r_i + \sum_{j\neq i} \text{Kernel}(r_{ij}) (r_i-r_j)\]

It is also possible to compute the first and second derivatives

\[ \begin{align}\begin{aligned}\nabla \phi_i(r_j) = \frac{d}{dx_j} \phi_i(r_j) + \frac{d}{dy_j} \phi_i(r_j) + \frac{d}{dz_j} \phi_i(r_j)\\\text{grad} \phi_i(r_j) = (\frac{d}{dx_j} \phi_i(r_j), \frac{d}{dy_j} \phi_i(r_j), \frac{d}{dz_j} \phi_i(r_j))\\\Delta \phi_i(r_j) = \frac{d^2}{dx^2_j} \phi_i(r_j) + \frac{d^2}{dy^2_j} \phi_i(r_j) + \frac{d^2}{dz^2_j} \phi_i(r_j)\end{aligned}\end{align} \]
Parameters:
  • pos (torch.tensor) – Positions of the electrons Size : Nbatch, Nelec x Ndim
  • derivative (int, optional) – order of the derivative (0,1,2,). Defaults to 0.
  • sum_grad (bool, optional) – Return the sum_grad (i.e. the sum of the derivatives) or the individual terms. Defaults to True.
  • sum_hess (bool, optional) – Return the sum_hess (i.e. the sum of the derivatives) or the individual terms. Defaults to True.
  • one_elec (bool, optional) – if only one electron is in input
Returns:

Value of the AO (or their derivatives)

size : Nbatch, Nelec, Norb (sum_grad = True)

size : Nbatch, Nelec, Norb, Ndim (sum_grad = False)
Return type:

torch.tensor
Examples::
>>> mol = Molecule('h2.xyz')
>>> ao = AtomicOrbitalsBackflow(mol)
>>> pos = torch.rand(100,6)
>>> aovals = ao(pos)
>>> daovals = ao(pos,derivative=1)