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qml.qchem.contracted_norm

contracted_norm(l, alpha, a)[source]

Compute the normalization constant for a contracted Gaussian function.

A contracted Gaussian function is defined as

ψ=a1G1+a2G2+a3G3,

where a denotes the contraction coefficients and G is a primitive Gaussian function. The normalization constant for this function is computed as

N(l,α,a)=[π3/2(2lx1)!!(2ly1)!!(2lz1)!!2lx+ly+lzi,jaiaj(αi+αj)lx+ly+lz+3/2]1/2

where l and α denote the angular momentum quantum number and the exponent of the Gaussian function, respectively.

Parameters
  • l (tuple[int]) – angular momentum quantum number of the primitive Gaussian functions

  • alpha (array[float]) – exponents of the primitive Gaussian functions

  • a (array[float]) – coefficients of the contracted Gaussian functions

Returns

normalization coefficient

Return type

array[float]

Example

>>> l = (0, 0, 0)
>>> alpha = np.array([3.425250914, 0.6239137298, 0.168855404])
>>> a = np.array([1.79444183, 0.50032649, 0.18773546])
>>> n = contracted_norm(l, alpha, a)
>>> print(n)
0.39969026908800853