Loading [MathJax]/jax/output/HTML-CSS/jax.js

qml.qchem.gaussian_kinetic

gaussian_kinetic(la, lb, ra, rb, alpha, beta)[source]

Compute the kinetic integral for two primitive Gaussian functions.

The kinetic integral between two Gaussian functions denoted by a and b is computed as [Helgaker (1995) p805]:

Tab=12(D2ijD0klD0mn+D0ijD2klD0mn+D0ijD0klD2mn),

where D0ij=S0ij is an overlap integral and D2ij is computed from overlap integrals S and the Gaussian exponent β as

D2ij=j(j1)S0i,j22β(2j+1)S0i,j+4β2S0i,j+2.
Parameters
  • la (tuple[int]) – angular momentum for the first Gaussian function

  • lb (tuple[int]) – angular momentum for the second Gaussian function

  • ra (array[float]) – position vector of the first Gaussian function

  • rb (array[float]) – position vector of the second Gaussian function

  • alpha (array[float]) – exponent of the first Gaussian function

  • beta (array[float]) – exponent of the second Gaussian function

Returns

kinetic integral between two Gaussian functions

Return type

array[float]

Example

>>> la, lb = (0, 0, 0), (0, 0, 0)
>>> ra = np.array([0., 0., 0.])
>>> rb = rb = np.array([0., 0., 0.])
>>> alpha = np.array([np.pi/2])
>>> beta = np.array([np.pi/2])
>>> t = gaussian_kinetic(la, lb, ra, rb, alpha, beta)
>>> t
array([2.35619449])