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(2lx−1)!!(2ly−1)!!(2lz−1)!!2lx+ly+lz∑i,jaiaj(αi+αj)lx+ly+lz+3/2]−1/2where 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