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qml.qchem.VibrationalPES

class VibrationalPES(freqs=None, grid=None, gauss_weights=None, uloc=None, pes_data=None, dipole_data=None, localized=True, dipole_level=1)[source]

Bases: object

Data class to store information needed to construct a vibrational Hamiltonian for a molecule.

Parameters:

  • freqs (array[float]) – normal-mode frequencies in atomic units

  • grid (array[float]) – grid points to compute potential energy surface data. Should be the sample points of the Gauss-Hermite quadrature.

  • gauss_weights (array[float]) – weights associate with each point in grid. Should be the weights of the Gauss-Hermite quadrature.

  • uloc (TensorLike[float]) – normal mode localization matrix with shape (m, m) where m = len(freqs)

  • pes_data (list[TensorLike[float]]) – list of one-mode, two-mode and three-mode potential energy surface data, with shapes (m, l), (m, m, l, l) (m, m, m, l, l, l), respectively, where m = len(freqs) and l > 0

  • dipole_data (list[TensorLike[float]]) – list of one-mode, two-mode and three-mode dipole moment data, with shapes (m, l, 3), (m, m, l, l, 3) (m, m, m, l, l, l, 3), respectively, where m = len(freqs) and l > 0

  • localized (bool) – Whether the potential energy surface data correspond to localized normal modes. Default is True.

  • dipole_level (int) – The level up to which dipole moment data are to be calculated. Input values can be 1, 2, or 3 for up to one-mode dipole, two-mode dipole and three-mode dipole, respectively. Default value is 1.

Example

This example shows how to construct the VibrationalPES object for a linear diatomic molecule, e.g., \(H_2\), with only one vibrational normal mode. The one-mode potential energy surface data is obtained by sampling 9 points along the normal mode, with grid points and weights that correspond to a Gauss-Hermite quadrature.

>>> freqs = np.array([0.01885397])
>>> grid, weights = np.polynomial.hermite.hermgauss(9)
>>> pes_onemode = [[0.05235573, 0.03093067, 0.01501878, 0.00420778, 0.0,
...                 0.00584504, 0.02881817, 0.08483433, 0.22025702]]
>>> vib_pes = qml.qchem.VibrationalPES(freqs=freqs, grid=grid,
...           gauss_weights=weights, pes_data=[pes_onemode])
>>> vib_pes.freqs
array([0.01885397])

The following example shows how to construct the VibrationalPES object for a nonlinear triatomic molecule, e.g., \(H_3^+\), with three vibrational normal modes. We assume that the potential energy surface and dipole data are obtained by sampling 5 points along the normal mode, with grid points and weights that correspond to a Gauss-Hermite quadrature.

>>> freqs = np.array([0.00978463, 0.00978489, 0.01663723])
>>> grid, weights = np.polynomial.hermite.hermgauss(5)
>>>
>>> uloc = np.array([[-0.99098585,  0.13396657,  0.],
...                  [-0.13396657, -0.99098585,  0.],
...                  [ 0.        ,  0.        ,  1.]])
>>>
>>> pes_onemode = np.random.rand(3, 5)
>>> pes_twomode = np.random.rand(3, 3, 5, 5)
>>> pes_threemode = np.random.rand(3, 3, 3, 5, 5, 5)
>>>
>>> dipole_onemode = np.random.rand(3, 5, 3)
>>> dipole_twomode = np.random.rand(3, 3, 5, 5, 3)
>>> dipole_threemode = np.random.rand(3, 3, 3, 5, 5, 5, 3)
>>>
>>> localized = True
>>> dipole_level = 3
>>>
>>> vib_obj = qml.qchem.VibrationalPES(freqs=freqs, grid=grid, gauss_weights=weights,
...           uloc=uloc, pes_data=[pes_onemode, pes_twomode, pes_threemode],
...           dipole_data=[dipole_onemode, dipole_twomode, dipole_threemode],
...           localized=True, dipole_level=3)
>>> print(vib_obj.dipole_threemode.shape)
(3, 3, 3, 5, 5, 5, 3)
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