1,3-Propanediyl, trimethylene.Using general valence bond (GVB) calculations,
Getty and coworkers found eight stationary points with trimethylene-like structures
[ 56 ]. The GVB method is somewhat related to the complete active space method,
discussed below, in that as in a CAS calculation electrons are promoted from
occupied to virtual orbitals in a limited form of configuration interaction. The
emphasis on the promotion of electrons from orbitals that can be identified with
bonds into their antibonding counterparts makes this a valence bond method
(Section 4.3.1). Looking back at our model chemistry calculations on trimethylene,
above, let’s focus on the MP2 calculations as the most reliable: in a general sense
correlated ab initio calculations are more reliable than those at the HF level and
arguably more reliable than DFT – granting that MP2 is not really averyhigh-level
method [ 57 ]. The MP2 calculations could be construed as giving a C2v1,3-diradical
transition state and a Cs1,3-diradical relative minimum, but the proximity of the
end carbons in these species, 2.663 and 2.654 A ̊, does not quite dispel the possibility
that we are dealing with an unusual closed-shell molecule, a kind of cyclopropane
with a very long CC bond. Indeed, a reaction of cyclopropane, stereomutation, has
been the main impetus for the study of singlet 1,3-propanediyl [ 58 ]. Stereomutation
is the interconversion ofcisandtrans1,2-substituted cyclopropanes (for the parent
compound deuterium is used as a stereochemical marker), and in principle can
occur by ring opening to a diradical and rotation about a C–C bond. For a detailed
experimental investigation, see Berson et al. [ 59 ]. Among the eight species revealed
by the exhaustive GVB search of the 1,3-propanediyl potential energy surface by
Getty et al. were a C2vhilltop (two imaginary frequencies) and two Csspecies, one a
relative minimum and one a transition state [ 56 ]. These three arep-cyclopropane
structuresand resemble our MP2 species. The termp-cyclopropane appears to have
been coined by Crawford and Mishra [ 60 ] to denote a trimethylene in which the
atomic p orbitals can, hypothetically at least, form a purep-type CC single bond:
HHHH HHAp-cyclopropane with the end methylene groups coplanar, as shown here, is
(0,0)-trimethylene; specifying the twist dihedral allows designation of the other
conformers, e.g. (0,90)-trimethylene in which the putativepbond is completely
broken [ 56 ]. The model chemistries, then, each led to two trimethylene stationary
points: HF to a hilltop and a transition state, MP2 to a transition state and a relative
minimum, and B3LYP to two transition states.
1,4-Butanediyl, tetramethylene.Using complete active space (CAS) calculations
(below), Doubleday found ten stationary points with tetramethylene-like structures, in
work connected with ring-opening of cyclobutane [ 61 ]. We saw that model chemis-
tries simply lead to closure or dissociation of input tetramethylene-type structures.
538 8 Some “Special” Topics