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.
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.
