# qml.qchem.nuclear_attraction¶

nuclear_attraction(la, lb, ra, rb, alpha, beta, r)[source]

Compute nuclear attraction integral between primitive Gaussian functions.

The nuclear attraction integral between two Gaussian functions denoted by $$a$$ and $$b$$ can be computed as [Helgaker (1995) p820]

$V_{ab} = \frac{2\pi}{p} \sum_{tuv} E_t^{ij} E_u^{kl} E_v^{mn} R_{tuv},$

where $$E$$ and $$R$$ represent the Hermite Gaussian expansion coefficients and the Hermite Coulomb integral, respectively. The sum goes over $$i + j + 1$$, $$k + l + 1$$ and $$m + n + 1$$ for $$t$$, $$u$$ and $$v$$, respectively, and $$p$$ is computed from the exponents of the two Gaussian functions as $$p = \alpha + \beta$$.

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 the first Gaussian function

• rb (array[float]) – position vector of the the second Gaussian function

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

• beta (array[float]) – exponent of the second Gaussian function

• r (array[float]) – position vector of nucleus

Returns

nuclear attraction integral between two Gaussian functions

Return type

array[float]

Using PennyLane

Development

API