qmctorch.wavefunction.orbitals.spherical_harmonics module¶

class qmctorch.wavefunction.orbitals.spherical_harmonics.Harmonics(type, **kwargs)[source]¶

Bases: object

Compute spherical or cartesian harmonics and their derivatives

Keyword Arguments:
Parameters:	type (str) – harmonics type (cart or sph)
	bas_l (torch.tensor) – second quantum numbers (sph) bas_m (torch.tensor) – third quantum numbers (sph) bas_kx (torch.tensor) – x exponent (cart) bas_ky (torch.tensor) – xy exponent (cart) bas_kz (torch.tensor) – z exponent (cart) cuda (bool) – use cuda (defaults False)

Examples::

>>> mol = Molecule('h2.xyz')
>>> harm = Harmonics(cart)
>>> pos = torch.rand(100,6)
>>> hvals = harm(pos)
>>> dhvals = harm(pos,derivative=1)

qmctorch.wavefunction.orbitals.spherical_harmonics.CartesianHarmonics(xyz, k, mask0, mask2, derivative=[0], sum_grad=True, sum_hess=True)[source]¶

Computes Real Cartesian Harmonics

\[\begin{split}Y = x^{k_x} \\times y^{k_y} \\times z^{k_z}\end{split}\]

Parameters:	xyz (torch.tensor) – distance between sampling points and orbital centers n size : (Nbatch, Nelec, Nbas, Ndim) k (torch.tensor) – (kx,ky,kz) exponents mask0 (torch.tensor) – precomputed mask of k=0 mask2 (torch.tensor) – precomputed mask of k=2 derivative (int, optional) – degree of the derivative. Defaults to 0. sum_grad (bool, optional) – returns the sum of the derivative if True. Defaults to True. sum_hess (bool, optional) – returns the sum of the 2nd derivative if True. Defaults to True.
Returns:	values of the harmonics at the sampling points
Return type:	torch.tensor

qmctorch.wavefunction.orbitals.spherical_harmonics.SphericalHarmonics(xyz, l, m, derivative=0, sum_grad=True, sum_hess=True)[source]¶

Compute the Real Spherical Harmonics of the AO.

Parameters:

xyz (torch.tensor) – distance between sampling points and orbital centers n size : (Nbatch, Nelec, Nbas, Ndim)
l (torch.tensor) – l quantum number
m (torch.tensor) – m quantum number

Returns:

value of each harmonics at each points (or derivative) n: size : (Nbatch,Nelec,Nrbf) for sum_grad=True n size : (Nbatch,Nelec,Nrbf, Ndim) for sum_grad=False

Return type:

Y (torch.tensor)

qmctorch.wavefunction.orbitals.spherical_harmonics.get_spherical_harmonics(xyz, lval, m, derivative)[source]¶

Compute the Real Spherical Harmonics of the AO.

Parameters:

xyz (torch.tensor) – distance between sampling points and orbital centers n size : (Nbatch, Nelec, Nbas, Ndim)
l (torch.tensor) – l quantum number
m (torch.tensor) – m quantum number

Returns:

value of each harmonics at each points (or derivative) n: size : (Nbatch,Nelec,Nrbf)

Return type:

Y (torch.tensor)

qmctorch.wavefunction.orbitals.spherical_harmonics.get_grad_spherical_harmonics(xyz, lval, m)[source]¶

Compute the gradient of the Real Spherical Harmonics of the AO.

Parameters:

xyz (torch.tensor) – distance between sampling points and orbital centers n size : (Nbatch, Nelec, Nbas, Ndim)
l (torch.tensor) – l quantum number
m (torch.tensor) – m quantum number

Returns:

value of each harmonics at each points (or derivative) n: size : (Nbatch,Nelec,Nrbf,3)

Return type:

Y (torch.tensor)