vibeqc.bond_analysis.iao_wiberg_bond_orders

vibeqc.bond_analysis.iao_wiberg_bond_orders(density_alpha, density_beta, atom_indices, n_atoms)[source]

Spin-resolved Wiberg indices in labeled orthonormal IAO bases.

B[a,b] = 2 sum_sigma sum_mu_in_a,nu_in_b |D_sigma[mu,nu]|^2. Alpha and beta may use different IAO bases, with the same atom labels. For a determinant, Wick contraction gives number covariance Cov(N_a,N_b) = -sum_sigma ||D_sigma[a,b]||_F^2 for a != b; this index is minus twice that covariance. In a restricted determinant it is the Wiberg square of the total IAO density. General correlated number covariances require the 2-RDM and are not implemented here.

Wiberg, Tetrahedron 24, 1083 (1968), doi:10.1016/0040-4020(68)88057-3; determinant interpretation discussed by de Giambiagi et al., Theor. Chim. Acta 68, 337 (1985), doi:10.1007/BF00529054. No original-AO Loewdin transform is performed.

Parameters:
Return type:

ndarray