Through-Bond Interactions in the Diradical Intermediates Formed in the Rearrangements of Bicyclo[n.m.0]alkatetraenes Page: 14,620
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ARTICLES Lovitt et a!.
Table 1. UB3LYP and (6/6)CASPT2/6-31 G(d) Values of the
Singlet-Triplet Energy Differences (AEST) in Diradicals 2c, 15, and
12b and of the Ionization Energies (IEs)a of the Two
Singly-Occupied MOs in the Triplet States (kcal/mol). The (S2)
Values in the "Singlet" UHF Calculations and the Natural Orbital
Occupancy Numbers (NOONs) of the HOMO and LUMO in the
(6/6)CASSCF Singlet Wave Functions Are Also GivenAEST
(UB3)b (c2)c
21.4 0.0
3.7 0.85
1.6 0.96AEST
(PT2)d
25.5
5.9
2.4IEs
NOONse (UB3)'
1.62, 0.38 130.3, 173.4
1.31, 0.69 139.0, 156.8
1.20, 0.80 140.5, 154.2IEs
(PT2)9
124.9, 173.7
135.3, 155.5
137.2, 153.2- a2 (a*)
S LUIMO
b1
,Ob, (a)a The negative of the IE of an electron in an MO can be taken as the
energy of that MO. b UB3LYP values of AEST. c Values of (S2) in the
"singlet" UB3LYP wave functions. d (6/6)CASPT2 values of AEST.
eNatural orbital occupation numbers in the (6/6)CASSCF wave
functions for the singlets. fUB3LYP ionization energies of the two
singly occupied MOs in the triplet. g CASPT2 ionization energies of the
two singly occupied MOs in the triplet.
whereas a presumably much less strained six-membered ring
is created in the formation of 12b from 11b.
Also worthy of note is that 15 can undergo ring-opening to
bicyclo[4.4.1]undeca-2,4,7,9-tetraene (17), as well as to 14 and
16. However, the bond between C-9 and C-10 in 15 overlaps
poorly with the two sets of allylic 7t orbitals. Therefore, the
UB3LYP barrier to the ring-opening reaction of 15 to 17 is
computed to be 5.1 kcal/mol higher than that for ring-opening
of 15 to 14 or 16. Consequently, our calculations predict that
an experimental study would find the degenerate rearrangement
of 14 to 16 to be much faster than the formation of 17.1 411
17
The results of our CASPT2 and UB3LYP calculations on
the singlet-triplet energy differences in diradicals 2c, 12b, and
15 are summarized in Table 1. For each diradical, CASPT2 and
UB3LYP give similar values of AEST, although the CASPT2
calculations uniformly give slightly higher values than UB3LYP.
The values of AEST decrease with increasing ring size. AEST in
2c is more than five times larger than AEST in 15 and more
than a factor of 10 larger than AEST in 12b. Clearly, the four-
membered ring in 2c allows much stronger through-bond
interactions between the localized allylic radicals than either
the five-membered ring in 15 or the six-membered ring in 12b.
The (S2) values for the "singlet" UB3LYP wave functions in
Table 1 tell the same story as the AEsT values. The singlet state
of hydrocarbon 2c has S2 0= ; so by this criterion, 2c actually
has a closed-shell B3LYP wave function. In contrast, singlet
12b and singlet 15 both have (S2) values close to 1.00; so they
are both predicted to have a great deal more diradical character
than 2c.
The slightly smaller value of (S2) = 0.85 in singlet 15,
compared with (S2) = 0.96 in singlet 12b, provides confirmatory
evidence that the five-membered ring in the former diradical
provides stronger through-bond interactions between the local-
ized allylic radicals than the six-membered ring in the latter.
The ratios of the NOON values, 4.3 in 2c, 1.9 in 15, and 1.5 in
12b, also indicate that the through-bond interactions between
14620 J. AM. CHEM. SOC. VOL. 132, NO. 41, 2010allylic NBMOs
2c
ring orbitals
Figure 5. Orbital interaction diagram showing schematically how the bl
and a2 combinations of the allylic nonbonding MOs interact with the bl
bonding and a2 antibonding MOs of the bridged cyclobutane ring of 2c to
create the HOMO and LUMO of the singlet state. The positions of the
nodal carbons in the allylic nonbonding MOs are indicated by a dot.
the pairs of allylic radicals in these three molecules decrease as
the size of the ring through which two radicals interact increases.
All of these indicators are consistent with the energy
difference between the highest occupied (HO)MO and the lowest
unoccupied (LU)MO in the singlet state being largest in 2c and
smallest in 12b. As shown in Table 1 the IEs of these two,
singly occupied MOs in the triplet state confirm this conclusion.
The UB3LYP (CASPT2) differences between the IEs of these
two orbitals decrease from 43.1 (48.8) kcal/mol in 2c, to 17.8
(20.2) kcal/mol in 15, to 13.7 (16.0) kcal/mol in 12b.
The IE values in Table 1 show that there are two contributors
to the much larger energy difference between the HOMO and
LUMO in 2c than in 15 and in 12b. First, the four-membered
ring in 2c interacts with the two bridging allylic radicals in such
a way that the LUMO of singlet 2c (i.e., the singly occupied
MO in the triplet with the lower IE) is about 10 kcal/mol higher
in energy than the LUMOs of 15 and 12b. However, the second
and larger contributor to the much bigger HOMO-LUMO
energy difference in 2c is the fact that the HOMO of singlet 2c
(i.e., the singly occupied MO in the triplet with the higher IE)
is ca. 20 kcal/mol lower in energy than the HOMOs of 15 and
12b. In order to explain these differences between the frontier
orbitals of 2c and those of 15 and 12b, we begin by briefly
recapitulating the previously published discussion of the interac-
tions between the nonbonding orbitals of the two allylic radicals
and the four-membered ring in 2c.3
As shown in Figure 5, the bl combination of allylic non-
bonding orbitals in 2c interacts with only a filled, o, bonding
orbital of the four-membered ring, whereas the a2 combination
of allylic nonbonding orbitals interacts with only an unfilled,
a*, antibonding orbital. The former interaction destabilizes the
bl (in-phase) combination of allylic nonbonding orbitals; but
the latter actually provides some stabilization for the a2 (out-
of-phase) combination.
The resulting a2 and b1 MOs, which are, respectively, the
HOMO and LUMO of singlet 2c, are shown in Figure 6. The
energy difference between the b1 combination of allylic non-
bonding orbitals and the filled b1 bonding orbital of the ring is
considerably smaller than the energy difference between the a2diradical
2c
15
12bARTICLES
Lovitt et al
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Lovitt, Charity Flener; Dong, Hao; Hrovat, David A.; Gleiter, Rolf & Borden, Weston T. Through-Bond Interactions in the Diradical Intermediates Formed in the Rearrangements of Bicyclo[n.m.0]alkatetraenes, article, September 24, 2010; [Washington, D.C.]. (https://digital.library.unt.edu/ark:/67531/metadc71806/m1/4/: accessed April 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT College of Arts and Sciences.