State density matrix analysis

Analysis of state and difference density matrices is performed via theodore analyze_sden. In the case of an analysis of natural orbital (NO) files, also the shortcut theodore analyze_nos may be invoked.

For NO files, it may be necessary to adjust the occupations manually (or use the -o option). Bond-order and unpaired electrons analysis currently only works for spin-restricted orbitals. Population and attachement-detachment analysis also works for unrestricted orbitals.

Population analysis

TheoDORE features Mulliken population analysis capabilities, which can be applied to normal densities, densities of effectively unpaired electrons or attachment/detachment densities (see below).

Unpaired electrons

Two measures for a number of effectively unpaired electrons can be computed:

\[n_u=\sum_i \min \left(n_i,2-n_i\right)\]

and

\[n_{u,nl} = \sum_i n_i^2 (2-n_i^2)\]

where \(n_i\) marks the occupation number of natural orbital i.

Attachment/detachment analysis and natural difference orbitals

The difference density between an excited and a reference state can be diagonalized to provide the natural difference orbitals (NDOs). Summing over all NDOs of positive (negative) sign, the attachment (detachment) densities can be constructed. This has to be performed by an external program.

Bond order and valence analysis

Bond order and valences are computed according to the formulas given by I. Mayer, see Int. J. Quant. Chem. 1986 XXIX, 477 for more information.