  Destructive quantum interference (DQI) in single molecule electronics is a
purely quantum mechanical effect and entirely defined by inherent properties of
the molecule in the junction such as its structure and symmetry. This
definition of DQI by molecular properties alone suggests its relation to other
more general concepts in chemistry as well as the possibility of deriving
simple models for its understanding and molecular device design. Recently, two
such models have gained wide spread attention, where one was a graphical scheme
based on visually inspecting the connectivity of carbon sites in conjugated pi
systems in an atomic orbital (AO) basis and the other one put the emphasis on
the amplitudes and signs of the frontier molecular orbitals (MOs). There have
been discussions on the range of applicability for these schemes, but
ultimately conclusions from topological molecular Hamiltonians should not
depend on whether they are drawn from an AO or a MO representation, as long as
all the orbitals are taken into account. In this article we clarify the
relation between both models in terms of the zeroth order Green's function and
compare their predictions for a variety of systems. From this comparison we
conclude that for a correct description of DQI from a MO perspective it is
necessary to include the contributions from all MOs rather than just those from
the frontier orbitals. The cases where DQI effects can be successfully
predicted within a frontier orbital approximation we show to be limited to
alternant even-membered hydrocarbons, as a a direct consequence of the
Coulson-Rushbrooke pairing theorem in quantum chemistry.
