qmctorch.wavefunction.slater_jastrow module

class qmctorch.wavefunction.slater_jastrow.SlaterJastrow(mol, configs='ground_state', kinetic='jacobi', jastrow_kernel=<class 'qmctorch.wavefunction.jastrows.elec_elec.kernels.pade_jastrow_kernel.PadeJastrowKernel'>, jastrow_kernel_kwargs={}, cuda=False, include_all_mo=True)[source]

Bases: qmctorch.wavefunction.slater_jastrow_base.SlaterJastrowBase

Slater Jastrow wave function with electron-electron Jastrow factor

\[\Psi(R_{at}, r) = J(r)\sum_n c_n D^\uparrow_n(r^\uparrow)D^\downarrow_n(r^\downarrow)\]

with

\[J(r) = \exp\left( K_{ee}(r) \right)\]

with K, a kernel function depending only on the electron-eletron distances

Parameters:
  • mol (Molecule) – a QMCTorch molecule object
  • configs (str, optional) – defines the CI configurations to be used. Defaults to ‘ground_state’. - ground_state : only the ground state determinant in the wave function - single(n,m) : only single excitation with n electrons and m orbitals - single_double(n,m) : single and double excitation with n electrons and m orbitals - cas(n, m) : all possible configuration using n eletrons and m orbitals
  • kinetic (str, optional) – method to compute the kinetic energy. Defaults to ‘jacobi’. - jacobi : use the Jacobi formula to compute the kinetic energy - auto : use automatic differentiation to compute the kinetic energy
  • jastrow_kernel (JastrowKernelBase, optional) – Class that computes the jastrow kernels
  • jastrow_kernel_kwargs (dict, optional) – keyword arguments for the jastrow kernel contructor
  • cuda (bool, optional) – turns GPU ON/OFF Defaults to Fals e.
  • include_all_mo (bool, optional) – include either all molecular orbitals or only the ones that are popualted in the configs. Defaults to False
Examples::
>>> from qmctorch.scf import Molecule
>>> from qmctorch.wavefunction import SlaterJastrow
>>> mol = Molecule('h2o.xyz', calculator='adf', basis = 'dzp')
>>> wf = SlaterJastrow(mol, configs='cas(2,2)')
forward(x, ao=None)[source]

computes the value of the wave function for the sampling points

\[\Psi(R) = J(R) \sum_{n} c_n D^{u}_n(r^u) \times D^{d}_n(r^d)\]
Parameters:
  • x (torch.tensor) – sampling points (Nbatch, 3*Nelec)
  • ao (torch.tensor, optional) – values of the atomic orbitals (Nbatch, Nelec, Nao)
Returns:

values of the wave functions at each sampling point (Nbatch, 1)
Return type:

torch.tensor
Examples::
>>> mol = Molecule('h2.xyz', calculator='adf', basis = 'dzp')
>>> wf = SlaterJastrow(mol, configs='cas(2,2)')
>>> pos = torch.rand(500,6)
>>> vals = wf(pos)
ao2mo(ao)[source]

Get the values of the MO from the values of AO.

pos2mo(x, derivative=0)[source]

Get the values of MOs

Parameters:{torch.tensor} -- positions of the electrons [nbatch, nelec*ndim] (x) –
Keyword Arguments:
 {int} -- order of the derivative (default (derivative) – {0})
Returns:torch.tensor – MO matrix [nbatch, nelec, nmo]
kinetic_energy_jacobi(x, **kwargs)[source]

Compute the value of the kinetic enery using the Jacobi Formula. C. Filippi, Simple Formalism for Efficient Derivatives .

\[\frac{\Delta \Psi(R)}{\Psi(R)} = \Psi(R)^{-1} \sum_n c_n (\frac{\Delta D_n^u}{D_n^u} + \frac{\Delta D_n^d}{D_n^d}) D_n^u D_n^d\]

We compute the laplacian of the determinants through the Jacobi formula

\[\frac{\Delta \det(A)}{\det(A)} = Tr(A^{-1} \Delta A)\]

Here \(A = J(R) \phi\) and therefore :

\[\Delta A = (\Delta J) D + 2 \nabla J \nabla D + (\Delta D) J\]
Parameters:x (torch.tensor) – sampling points (Nbatch, 3*Nelec)
Returns:values of the kinetic energy at each sampling points
Return type:torch.tensor
gradients_jacobi(x, sum_grad=False, pdf=False)[source]

Compute the gradients of the wave function (or density) using the Jacobi Formula C. Filippi, Simple Formalism for Efficient Derivatives.

\[\frac{K(R)}{\Psi(R)} = Tr(A^{-1} B_{grad})\]

The gradients of the wave function

\[\Psi(R) = J(R) \sum_n c_n D^{u}_n D^{d}_n = J(R) \Sigma\]

are computed following

\[\nabla \Psi(R) = \left( \nabla J(R) \right) \Sigma + J(R) \left(\nabla \Sigma \right)\]

with

\[\nabla \Sigma = \sum_n c_n (\frac{\nabla D^u_n}{D^u_n} + \frac{\nabla D^d_n}{D^d_n}) D^u_n D^d_n\]

that we compute with the Jacobi formula as:

\[\nabla \Sigma = \sum_n c_n (Tr( (D^u_n)^{-1} \nabla D^u_n) + Tr( (D^d_n)^{-1} \nabla D^d_n)) D^u_n D^d_n\]
Parameters:
  • x (torch.tensor) – sampling points (Nbatch, 3*Nelec)
  • pdf (bool, optional) – if true compute the grads of the density
Returns:

values of the gradients wrt the walker pos at each sampling points
Return type:

torch.tensor
get_kinetic_operator(x, ao, dao, d2ao, mo)[source]

Compute the Bkin matrix

Parameters:
  • x (torch.tensor) – sampling points (Nbatch, 3*Nelec)
  • mo (torch.tensor, optional) – precomputed values of the MOs
Returns:

matrix of the kinetic operator
Return type:

torch.tensor