3.7.1. horton.meanfield.bond_order – Generic implementation of bond orders for mean-field wavefunctions

In the context bond orders and self-electron delocatization indices (SEDI’s) are always one an the same thing. For two AIM overlap perators, $S_A$ and $S_B$, the bond order is defined as:

$$\text{BO}_{AB} = 2 \mathrm{Tr}\left[ (D^{\alpha} S^A)(D^{\alpha} S^B) + (D^{\beta} S^A)(D^{\beta} S^B) \right]$$

where $D^{\alpha}$ and $D^{\beta}$ are the density matrices of the $\alpha$ and $\beta$ electrons, respectively. A related quantity is the valence of an atom. It is defined as:

$$V_A = 2 N_A - \mathrm{Tr}\left[ (D S^A)(D S^A) \right]$$

where $D$ is the sum of the $\alpha$ and $\beta$ electron density matrices, and $N_A$ is the population of atom $A$. The free valence is defined as:

$$F_A = V_A - \sum_{B \neq A} \text{BO}_{AB}$$

horton.meanfield.bond_order.compute_bond_orders_cs(dm_alpha, operators)

Compute bond orders, valences and free valences (closed-shell case)

Arguments:

dm_alpha

The density matrix of the alpha electrons

operators

A list of one-body operators.

Returns:

bond_orders

A symmetric N by N matrix with bond orders.

valences

A vector with atomic valences

free_valences

A vector with atomic free valences

horton.meanfield.bond_order.compute_bond_orders_os(dm_alpha, dm_beta, operators)

Compute bond orders, valences and free valences (open-shell case)

Arguments:

dm_alpha

The density matrix of the alpha electrons

operators

A list of one-body operators.

Returns:

bond_orders

A symmetric N by N matrix with bond orders.

valences

A vector with atomic valences

free_valences

A vector with atomic free valences