Energy and MO analysis

MOs expanded in SFOs

This gives a useful characterization of the character of the self-consistent molecular orbitals. Additional information is supplied by the SFO population analysis, see below.
The definition of the SFOs in terms of the Fragment MOs has been given in a earlier part of output (section build). The SFO occupation numbers that applied in the fragments are printed. This allows a determination of the orbital interactions represented in a MO.
Be aware that the bonding/antibonding nature of a SFO combination in a mo is determined by the relative signs of the coefficients and by the overlap of the SFOs. This overlap may be negative! Note also that SFOs are generally not normalized functions. The SFO overlap matrix is printed later, in the SFO-populations part below.

Bond Energy analysis

The bond energy and its decomposition in conceptually useful terms: Pauli (exchange) repulsion, total steric repulsion, orbital interactions (partitioned into the contributions from the distinct irreducible representations), and corrections for some approximations (fitting and Transition State analysis procedure).
For a discussion of bonding energy decompositions and applications see e.g. [110, 112, 130-136]

SFO population analysis

For each irrep:

- Overlap matrix of the SFOs. Diagonal elements are not equal to 1.0 if the SFO is a linear combination of two or more Fragment Orbitals. The Fragment Orbitals themselves are normalized so the diagonal elements of the SFO overlap matrix give information about the overlap of the Fragment Orbitals that were combined to build the SFO.
- Populations on a per-fragment basis for a selected set of MOs (see EPrint, subkey OrbPop). This part is by default not printed, see EPRINT subkey SFO.
- SFO contributions per MO: populations for each of the selected MOs. In these data the MO occupation numbers are not included, so that also useful information about the virtual MOs is obtained. The printout is in matrix form, with the MOs as columns. In each printed matrix a row (corresponding to a particular SFO) is omitted if all populations of that SFO are very small in all of the MOs that are represented in that matrix. See eprint, subkey orbpop.
Note that this method to define SFO populations (for orbitals) is very similar to the classical Mulliken type analysis, in particular regarding the aspect that gross populations are obtained as the diagonal (net) populations plus half of the related off-diagonal (overlap) populations. Occasionally this may result in negative (!) values for the population of certain SFOs, or in percentages higher than 100%. If you have such results and wonder if they can be right, work out one of the offending cases by hand, using the printed SFO overlap matrix and the printed expansion of the MOs in SFOs to compute 'by hand' the population matrix of the pertaining MO. To avoid doing large calculations it is usually sufficient to take only the few largest MO expansion coefficients; this should at least qualitatively give the correct outcomes.
- Total SFO gross populations in a symmetry representation: from a summation over all MOs (not only those analyzed in the previous section of output) in the symmetry representation under consideration. In the gross populations the MO occupation numbers have been included.
- (Per spin): A full list of all MOs (combining all symmetry representations), ordered by energy, with their most significant SFO populations. Since there might be several significant SFO populations for a particular MO, and an SFO may actually be a linear combination of several (symmetry-related) Fragment Orbitals, this table could get quite extensive. In order to confine each SFO population specification to one line of output, the SFOs are indicated by the characteristics of the first term (Fragment Orbital) of its expansion in Fragment Orbitals. So, if you see the SFO given as the '2 P:x on the first Carbon fragment', it may actually refer to the symmetry combination of, for instance, 2P:x and 2P:y orbitals on the first, second and third Carbon fragments. A full definition of all SFOs in terms of the constituting Fragment Orbitals is given in an early part of the output.