qml.qchem.vscf_integrals

vscf_integrals(h_integrals, d_integrals=None, modals=None, cutoff=None, cutoff_ratio=1e-06)

Generates vibrational self-consistent field rotated integrals.

This function converts the Christiansen vibrational Hamiltonian integrals obtained in the harmonic oscillator basis to integrals in the vibrational self-consistent field (VSCF) basis. The implementation is based on the method described in J. Chem. Theory Comput. 2010, 6, 235–248.

Parameters

• h_integrals (list[TensorLike[float]]) – List of Hamiltonian integrals for up to 3 coupled vibrational modes. Look at the Usage Details for more information.

• d_integrals (list[TensorLike[float]]) – List of dipole integrals for up to 3 coupled vibrational modes. Look at the Usage Details for more information.

• modals (list[int]) – list containing the maximum number of modals to consider for each vibrational mode. Default value is the maximum number of modals.

• cutoff (float) – threshold value for including matrix elements into operator

• cutoff_ratio (float) – ratio for discarding elements with respect to biggest element in the integrals. Default value is 1e-6.

Returns

a tuple containing:

• list[TensorLike[float]]: List of Hamiltonian integrals in VSCF basis for up to 3 coupled vibrational modes.

• list[TensorLike[float]]: List of dipole integrals in VSCF basis for up to 3 coupled vibrational modes.

None is returned if d_integrals is None.

Return type

tuple

Example

>>> h1 = np.array([[[0.00968289, 0.00233724, 0.0007408,  0.00199125],
...                 [0.00233724, 0.02958449, 0.00675431, 0.0021936],
...                 [0.0007408,  0.00675431, 0.0506012,  0.01280986],
...                 [0.00199125, 0.0021936,  0.01280986, 0.07282307]]])
>>> qml.qchem.vscf_integrals(h_integrals=[h1], modals=[4,4,4])
([array([[[ 9.36124041e-03, -4.20128342e-19,  3.25260652e-19,
        1.08420217e-18],
        [-9.21571847e-19,  2.77803512e-02, -3.46944695e-18,
        5.63785130e-18],
        [-3.25260652e-19, -8.67361738e-19,  4.63297357e-02,
        -1.04083409e-17],
        [ 1.30104261e-18,  5.20417043e-18, -1.38777878e-17,
        7.92203227e-02]]])],
None)

Usage Details

The h_integral tensor must have one of these dimensions:

• 1-mode coupled integrals: (n, m)

• 2-mode coupled integrals: (n, n, m, m, m, m)

• 3-mode coupled integrals: (n, n, n, m, m, m, m, m, m)

where n is the number of vibrational modes in the molecule and m represents the number of modals.

The d_integral tensor must have one of these dimensions:

• 1-mode coupled integrals: (3, n, m)

• 2-mode coupled integrals: (3, n, n, m, m, m, m)

• 3-mode coupled integrals: (3, n, n, n, m, m, m, m, m, m)

where n is the number of vibrational modes in the molecule, m represents the number of modals and the first axis represents the x, y, z component of the dipole. Default is None.

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