qml.qchem.primitive_norm

primitive_norm(l, alpha)

Compute the normalization constant for a primitive Gaussian function.

A Gaussian function centred at the position \(r = (x, y, z)\) is defined as

\[G = x^{l_x} y^{l_y} z^{l_z} e^{-\alpha r^2},\]

where \(l = (l_x, l_y, l_z)\) defines the angular momentum quantum number and \(\alpha\) is the Gaussian function exponent. The normalization constant for this function is computed as

\[N(l, \alpha) = (\frac{2\alpha}{\pi})^{3/4} \frac{(4 \alpha)^{(l_x + l_y + l_z)/2}} {(2l_x-1)!! (2l_y-1)!! (2l_z-1)!!)^{1/2}}.\]

Parameters

• l (tuple[int]) – angular momentum quantum number of the basis function

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

Returns

normalization coefficient

Return type

array[float]

Example

>>> l = (0, 0, 0)
>>> alpha = np.array([3.425250914])
>>> n = primitive_norm(l, alpha)
>>> print(n)
array([1.79444183])

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