qmctorch.wavefunction.orbitals.radial_functions module

qmctorch.wavefunction.orbitals.radial_functions.radial_slater(R, bas_n, bas_exp, xyz=None, derivative=0, sum_grad=True, sum_hess=True)

Compute the radial part of STOs (or its derivative).

Parameters:

• R (torch.tensor) – distance between each electron and each atom
• bas_n (torch.tensor) – principal quantum number
• bas_exp (torch.tensor) – exponents of the exponential

Keyword Arguments:  

• xyz (torch.tensor) – positions of the electrons (needed for derivative) (default: {None})
• derivative (int) – degree of the derivative (default: {0}) 0 : value of the function 1 : first derivative 2 : pure second derivative 3 : mixed second derivative
• sum_grad (bool) – return the sum_grad, i.e the sum of the gradients (default: {True})
• sum_hess (bool) – return the sum_hess, i.e the sum of the diag hessian (default: {False})
• mixed_hess (bool) –

  return the full hessian for each electron

  i.e. dxdy dxdz dydz … mixed derivatives

  (default: {False})

Returns:

values of each orbital radial part at each position

Return type:

torch.tensor

qmctorch.wavefunction.orbitals.radial_functions.radial_gaussian(R, bas_n, bas_exp, xyz=None, derivative=[0], sum_grad=True, sum_hess=True)

Compute the radial part of GTOs (or its derivative).

Parameters:

• R (torch.tensor) – distance between each electron and each atom
• bas_n (torch.tensor) – principal quantum number
• bas_exp (torch.tensor) – exponents of the exponential

Keyword Arguments:  

• xyz (torch.tensor) – positions of the electrons (needed for derivative)(default: {None})
• derivative (int) – degree of the derivative(default: {0})
• sum_grad (bool) – return the sum_grad, i.e the sum of the gradients (default: {True})

Returns:

values of each orbital radial part at each position

Return type:

torch.tensor

qmctorch.wavefunction.orbitals.radial_functions.radial_gaussian_pure(R, bas_n, bas_exp, xyz=None, derivative=[0], sum_grad=True, sum_hess=True)

Compute the radial part of GTOs (or its derivative).

Parameters:

• R (torch.tensor) – distance between each electron and each atom
• bas_n (torch.tensor) – principal quantum number
• bas_exp (torch.tensor) – exponents of the exponential

Keyword Arguments:  

• xyz (torch.tensor) – positions of the electrons (needed for derivative)(default: {None})
• derivative (int) – degree of the derivative(default: {0})
• sum_grad (bool) – return the sum_grad, i.e the sum of the gradients (default: {True})
• sum_hess (bool) – return the sum_hess, i.e the sum of the lapacian (default: {True})

Returns:

values of each orbital radial part at each position

Return type:

torch.tensor

qmctorch.wavefunction.orbitals.radial_functions.radial_slater_pure(R, bas_n, bas_exp, xyz=None, derivative=0, sum_grad=True, sum_hess=True)

Compute the radial part of STOs (or its derivative).

Parameters:

• R (torch.tensor) – distance between each electron and each atom
• bas_n (torch.tensor) – principal quantum number
• bas_exp (torch.tensor) – exponents of the exponential

Keyword Arguments:  

• xyz (torch.tensor) – positions of the electrons (needed for derivative)(default: {None})
• derivative (int) – degree of the derivative(default: {0})
• sum_grad (bool) – return the sum_grad, i.e the sum of the gradients (default: {True})
• sum_hess (bool) – return the sum_hess, i.e the sum of the laplacian (default: {True})

Returns:

values of each orbital radial part at each position

Return type:

torch.tensor

qmctorch.wavefunction.orbitals.radial_functions.return_required_data(derivative, _kernel, _first_derivative_kernel, _second_derivative_kernel, _mixed_second_derivative_kernel)

Returns the data contained in derivative

Parameters:

• derivative (list) – list of the derivatives required
• _kernel (callable) – kernel of the values
• _first_derivative_kernel (callable) – kernel for 1st der
• _second_derivative_kernel (callable) – kernel for 2nd der

Returns:

values of the different der requried

Return type:

list