Alternatively, we may order the orbitals according to their
``activity'' (i.e. frozen, occupied, unoccupied, etc). The
Quantum Trio standard order calls for all frozen core orbitals
to come first, then all doubly-occupied orbitals, then all singly-occupied
orbitals, then unoccupied active orbitals, and finally
all frozen virtual orbitals. Within each major section, orbitals
are numbered according to irreducible representation. Within each
irrep, orbitals are numbered according to energy (if they are
molecular orbitals).
This is particularly useful in, for instance, a
CI calculation. Since all frozen core orbitals have consecutive
indices, removing the core orbitals from explicit consideration
in the correlated wavefunction simply means starting the loops over
orbitals with the first active orbital. Likewise, removing the
frozen virtual orbitals means tossing out all orbitals with an index
greater than that of the last active orbital. Loops over occupied
and virtual orbitals are also easier to deal with since the orbitals
in each of these groups are numbered consecutively.