qsym2::target::noci::backend::denmat

Function calc_unweighted_codensity_matrix

Source 
pub fn calc_unweighted_codensity_matrix<T>(
    lowdin_paired_coefficients: &LowdinPairedCoefficients<T>,
    i: usize,
) -> Result<Array2<T>, Error>
where
    T: ComplexFloat + 'static,
Expand description

Calculates the unweighted codensity matrix between two Löwdin-paired spin-orbitals $i$ in determinants $^{w}\Psi$ and $^{x}\Psi$.

The unweighted codensity matrix between the above two spin-orbitals is given by

    ^{wx}\mathbf{P}_i
      = \ ^{w}\mathbf{C}_i \otimes
        (^{x}\mathbf{G}_i^{\star})^{\lozenge}
      = \ ^{w}\mathbf{C}_i
        \ ^{x}\mathbf{C}_i^{\dagger\lozenge},

where $\mathbf{C}_i$ is the coefficient column vector for spin-orbital $\chi_i$ such that

    \chi_i(\mathbf{x}) = \sum_{\mu} \psi_{\mu}(\mathbf{x}) C_{\mu i}.

§Arguments

  • lowdin_paired_coefficients - Structure containing the Löwdin-paired coefficient matrices.
  • i - Index of the corresponding Löwdin-paired spin-orbitals for which the unweighted codensity matrix is to be computed.

§Returns

The unweighted codensity matrix $^{wx}\mathbf{P}_i$.