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(j−1)S0i,j−2−2β(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])