qml.qchem.mol_density_matrix¶

mol_density_matrix(n_electron, c)[source]¶

Compute the molecular density matrix.

The density matrix $P$ is computed from the molecular orbital coefficients $C$ as

$$P_{\mu \nu} = \sum_{i=1}^{N} C_{\mu i} C_{\nu i},$$

where $N = N_{electrons} / 2$ is the number of occupied orbitals. Note that the total density matrix is the sum of the $\alpha$ and $\beta$ density matrices, $P = P^{\alpha} + P^{\beta}$.

Parameters

• n_electron (integer) – number of electrons

• c (array[array[float]]) – molecular orbital coefficients

Returns

density matrix

Return type

array[array[float]]

Example

>>> c = np.array([[-0.54828771,  1.21848441], [-0.54828771, -1.21848441]])
>>> n_electron = 2
>>> mol_density_matrix(n_electron, c)
array([[0.30061941, 0.30061941], [0.30061941, 0.30061941]])