pyscfad.gto.mole_lite.gto_norm#

pyscfad.gto.mole_lite.gto_norm(l, expnt)[source]#

Normalized factor for GTO radial part \(g=r^l e^{-\alpha r^2}\)

\[\frac{1}{\sqrt{\int g^2 r^2 dr}} = \sqrt{\frac{2^{2l+3} (l+1)! (2a)^{l+1.5}}{(2l+2)!\sqrt{\pi}}}\]

Ref: H. B. Schlegel and M. J. Frisch, Int. J. Quant. Chem., 54(1995), 83-87.

Parameters:

  • l (int) – angular momentum

  • expnt (ArrayLike) – exponent \(\alpha\)

Returns:

normalization factor

Return type:

Array

Examples:

>>> print(gto_norm(0, 1))
2.5264751109842591