BIRADICALS STABILIZED BY INTRAMOLECULAR CHARGE
TRANSFER
S. Zilberg
Institute of Chemistry and the Lise-Meitner-Minerva Center
for Computational Quantum Chemistry,
The Hebrew University of Jerusalem, Givat Ram, 91904,
Jerusalem, Israel
Abstract
The formally biradicals are theoretically predicted to be stable
persistent molecules, as supported by high level quantum chemical
calculations. The singlet–triplet energy gaps and the S0-S1 excitation
energies
of
2,5-di-heterosubstituted-pentalenes
and
1,5-diheterosubstituted-cyclooctatetraenes are similar to those of aromatic
molecules rather than to standard biradicals. Open form of hetero
derivatives of bicyclo[2.1.0]pentane (which is a cyclopentane-1,3-diyl
derivative) are the stable bond-stretch isomers. These formal biradicals
have a pronounced zwitterion character with a singlet ground state. The
marked stabilization of the ground state singlet for these non-Kekule
molecules is accompanies by a significant increasing of the HOMO
level, leading to a unusual low ionization potential (IP). In the case of diaza-pentalene, the energy of the first electronic excited state is only
slightly lower than the ionization potential, making it a candidate for
molecular auto-ionization.
Introduction
Substantial efforts have been made to design and prepare
persistent non-classical molecules such as diradicals [1] and triplet [2] or
singlet carbenes [3], yet ‘bottleable’ non-Kekule molecules remain a
challenge (Scheme 1):
Scheme 1. Experimentally observed stable carbenes [2].
180
Non-Kekule molecules are molecules with a completely
conjugated -system, for which no classical Kekule structures can be
written [4].
Different kinds of stable biradicals [1, 5, 6] are known. The first
stable carbon-based Schlenk’s diradical (a) was prepared in 1915 [7].
(a)
(b)
cc
(c)
Scheme 2. Experimentally observed stable singlet diradicals [5].
The most stable localized singlet diradical known to date, (b), has
a lifetime of microseconds at room temperature [5]. Lambert quite
recently reviewed the designing and synthesizing of relatively stable
polycyclic aromatic hydrocarbons (type c), that show pronounced singlet
open-shell character [8].
A pair of nonbonding molecular orbitals (NBMO’s) that are
occupied by two electrons is the MO portrayal of the diradical‘s
electronic origin in non-Kekule hydrocarbons [9]. Tetramethyleneethane
(TME) is one of the prototype non-Kekule molecules. Other types of
fully -conjugated diradicals are antiaromatic species such as
cyclobutadiene (CBD), cyclooctatetraene (COT) or pentalene (PNT).
Borden and Davidson predicted the violation of Hund’s rule for
diradicals that have disjoint NBMOs [5, 10]. Thus, the ground state of
TME is a singlet with a modest singlet-triplet gap ΔEST = ES-ET = -2
kcal/mol, as verified experimentally by negative ion photoelectron
spectroscopy [11]. Incorporating the TME fragment in a five-membered
ring, as in the case of 3,4-dimethylenecyclopentane-1,3-diyl, Ia, changes
the ground state to a triplet [12]. The singlet-triplet gap ΔEST for
hydrocarbon disjoint diradicals is usually small, consistent with the high
181
reactivity of these molecules. Qualitative MO arguments suggest that the
lowest singlet state can be stabilized by replacing a carbon atom by a
heteroatom [13]. Thus, the hetero-derivatives of Ia (Fig. 1) show
substantial stabilization of singlet vs. triplet, as has been shown
computationally [14, 15] and experimentally [16].
3
1
6
7
2 X
X
2
X 5
4
1 X
X 5
8
3
I
4
8
II
N
NH
IV
6
III
NH
NH
7
NH
V
N
VI
Fig. 1. The structures of molecules discussed in the text. (X: a=CH2, b=NH,
c=O, d=S).
Semiempirical quantum chemical calculations [17] were used to
assess the properties of diradicals (I) and (II). The large value of singlettriplet gap (ΔEST) computed for pentalene (II) derivatives led them to
discuss criteria for determining whether these systems should be
described as biradicals or zwitterions. It was noted that the ratio (C1/C2)2
of the squares of the coefficients of the two leading configurations in the
electronic wave function of the ground state singlet is a useful criterion
for this purpose. The system has a pronounced zwitterion character if
one configuration is dominant (i.e C1>>C2). Thus the ratio was found to
be 8.05, 3.28 and 2.46 for IIb, IIc and IId, respectively, showing that IIb
is best described as a zwitterion.
Cava and coworkers isolated the tetraphenyl substituted derivative
of IId, tetraphenylthieno(3,4-c)thiophene (hereafter designated as IIe),
leading to the elucidation of its electronic spectrum [18], x-ray structure
[19] and photoelectron spectrum [20]. Derivatives of IIb and IIc, as well
as of III have not yet been reported to the best of our knowledge. In this
work we report high level CASSCF and DFT calculations on these
182
molecules, predicting that all hetero-substituted derivatives (X= NH, O
or S) are stable (though possibly reactive) compounds with a singlet
ground state. The aza-pentalene derivative IIb is calculated to have an
exceptionally low ionization potential, due to a high lying HOMO
orbital. Fig. 2 shows the structures of some cyclopentane-1,3-diyl
diradicals that were examined as possible stable singlet diradicals.
Fig. 2. Open form cyclopentane-1,3-diyl diradicals VIIa-VIIg and closed form
heterosubstituted bicyclo[2.1.0]pentane VIIIa-VIIIg (a. X=CH2;
b. X=CF2; c. X=C(SiH3)2; d. X=O; e. X=S; f. X=NH; g. X=N(CH3)).
Buchwalter and Closs showed in 1975 [21] that triplet diradicals
of cyclopentane-1,3-diyl (VIIa) can be prepared and observed by ESR.
The triplet-singlet gap (EST) was calculated to be a few kcal/mol, the
triplet being more stable. The singlet diradical was taken as the
transition state between the two closed forms of the bicyclic compound.
Borden et al. [22] proposed that the singlet diradical can be stabilized by
substituting the two geminal hydrogen atoms with fluorine ones (VIIb).
The idea was that the fluorine atoms will act as electron acceptors and
help to delocalize the electronic charge in the singlet state. Indeed, the
singlet of 1b was calculated to lie well below the triplet at all geometries
but it turned out to be a transition state between the two classical closed
structures [22]. Other modes of substitution were proposed theoretically
and tested experimentally; Adam et al. [23] presented evidence for the
existence of a reactive intermediate Ic, though it could not be observed
directly. In an effort to stabilize carbon-based diradicals the Z=SiH3
group was proposed [24] as a potent stabilizer of singlet diradicals with
respect to the triplet one; the calculation showed that the singlet is
indeed lower than the triplet, but only by about 2 kcal/mol. The singlet
open form of VIId was calculated to be 20.8 kcal/mol higher, with a
barrier of 9.5 kcal/mol from the open form side.
183
We propose an computational design approach that leads to
substantially better stabilization of a singlet state of the open form in
comparison to the corresponding triplet and more importantly, to the
singlet of the closed isomer in which the two atoms – C1 and C3 - are
covalently bonded. In other words, the system is shown to have two
stable, iso-energetic bond-stretch singlet isomers, separated by a
substantial barrier.
Results
All computations were carried out using the GAMESS program
suite [25], using the cc-pVDZ basis set. GAUSSIAN program suite [26]
was used for DFT calculations on the B3LYP/cc-pVDZ level. A
complete vibrational analysis was performed at the optimised geometry.
Calculations on the parent molecules IIa and IIIa were done only in
order to compare with the substituted derivative. Since their singlet
states were found to be planar (D2h symmetry), calculations were
performed on the X=CH2 molecules at this symmetry also.
CASSCF [27] calculations (CAS(8/7)/cc-pVDZ with a full 
active space) show that the ground state of Ib, Ic and Id is a singlet for
all substituents; however only for the aza-derivative (Ib) ΔEST reaches
the sizeable value of -10.1 kcal/mol.
A more substantial stabilization of singlet ground state and a
corresponding increase of the singlet–triplet gap for non-Kekule
molecules can be expected for molecules isoelectronic with the dianions
of antiaromatic hydrocarbons. Hückel’s (4n+2) rule predicts an aromatic
character for dianions of 4n-annulens, but notwithstanding, isolated
COT-2 and CBD-2 are known to be unstable with respect to electron loss
[28]. Substitution of two carbon atoms by two more electronegative
hetero-atoms X adds two electrons to the -system, while keeping the
system electrically neutral. The extent of the interaction of these extra
electrons with the rest of the -electron system depends on the
electronegativity of X and on the overlap of the non-bonding electrons
of X with the -electronic structure of the TME fragment in IIb-d or of
the two allyl fragments in IIIb-d (Fig. 1).
Tables 1 and Tables 2 report the absolute energies and the
structure of several 2,5-heterosubstituted pentalenes and 1,5heterosubstituted cyclooctatetraenes. The parent systems IIa and IIIa are
184
typical disjoint diradicals, because the CH2 bridges do not take part in the
-delocalization (Table 1, 2).
Table 1. Absolute energies (Hartree), bond distances Rij (Å) and the Mulliken
charge of X, qx (electronic charge units) for 2,5-di-X-pentalenes IIa-d
(CASSCF(10/8)/cc-pVDZ). Δqx(ST) is the excess of charge transferred in the
singlet over the triplet. It is a measure of the zwitterion character of the singlet
X
State
Energy
CH2
11Ag ( D2h )
-307.55414
1.518 1.391 1.449 +0.05
3
R12
R17
R78
qx
CH2
1 B2u ( D2h )
-307.54887
1.516 1.387 1.463 +0.04
NH
11Ag ( D2h )
-339.62983
1.363 1.405 1.443 +0.25
NH
13Au ( C2h )
-339.56190
1.417 1.394 1.456 +0.09
O
11Ag ( D2h )
-379.24513
1.341 1.394 1.445 +0.12
O
13B2u ( D2h )
-379.20886
1.374 1.388 1.454 +0.01
S
11Ag ( D2h )
-1024.61791 1.714 1.403 1.452 +0.43
S
3
1 B2u (D2h)
-1024.58510 1.768 1.394 1.461 +0.29
Δqx(ST)
+0.01
+0.16
+0.11
+0.14
Table 2. Absolute energies (Hartree), bond distances Rij (angstroms) and the
charge of X qx (electronic charge units) for 1,5-di-X-cyclooctatetraenes IIIa-d
(CASSCF(10/8)/cc-pVDZ). qx(ST) is the excess of charge transferred in the
singlet over the triplet. It is a measure of the zwitterion character of the singlet
X
CH2
CH2
NH
NH
O
O
S
S
State
11Ag ( D2h )
13B1u( D2h )
11Ag ( D2h )
13Au ( C2h )
11Ag ( D2h )
13B1u( D2h )
11Ag ( D2h )
13Au ( C2h )
Energy
-308.72286
-308.71720
-340.75304
-340.70574
-380.39435
-380.34580
-1025.73221
-1025.59031
R12
1.495
1.502
1.355
1.395
1.319
1.354
1.699
1.763
R23
1.392
1.393
1.389
1.390
1.385
1.386
1.388
1.391
qx
+0.06
+0.05
+0.25
+0.10
+0.14
+0.02
+0.43
+0.28
Δqx (ST)
+0.01
+0.15
+0.12
+0.15
As seen from Tables 1 and Tables 2, the geometry of the
hydrocarbon part does not change much upon substitution. Also, the
185
structures of the singlet and triplet states are very similar, in spite of the
different spin state and electric charge distribution. This is a first
indication that the two extra electrons find themselves in a non-bonding
orbital.
Table 3 reports the data obtained for the singlet-triplet gap (ΔEST),
the excitation energy of the first electronic excited singlet state (E(S 1)E(S0)) and the first ionization potential (IP). It is seen that the singlettriplet energy gap for the hydrocarbons IIa and IIIa are small: 0.14 and
0.15 eV respectively, very similar to the gap in the prototype TME [7].
Table 3. Singlet-triplet gap, Excitation energy (E(S1)-E(S0)) and the Ionization
potential for 2,5-di-X-pentalene and 1,5-di-X-cyclooctatetraenes derivatives
(CASSCF(10/8)/cc-pVDZ) (in eV)
X
CH2
NH
O
S
ΔEST
0.14
1.66
0.99
0.89
PEN derivatives
E(S1)-E(S0)
4.30
4.89
5.43
4.47
IP
6.31
4.85
7.16
6.35
ΔEST
0.15
2.16
1.32
1.29
COT derivatives
E(S1)-E(S0)
5.25
4.54
5.39
4.65
IP
6.21
5.08
6.02
6.30
In contrast, the oxygen and sulphur derivatives IIc, IIIc and IId,
IIId and especially the aza substituted derivatives IIb and IIIb are
calculated to have a much larger ΔEST. The large ΔEST computed for the
aza-derivatives are in fact typical for aromatic compounds thus
confirming the substantial stabilization of the ground singlet state for
these non-Kekule molecules. Further evidence for the large stability of
these species comes from comparison of the relative stabilization of IIb
with its valence isomers IV, V and VI (Figure 1). IV and V have a
regular bonding pattern and may be considered as normal Kekule
structures, expected therefore to be quite stable. The relative stability of
IIb may thus be estimated by comparison with these isomers: a
calculation shows that IV (the most stable isomer) is only 10.7 kcal/mol
lower in energy than IIb while V – the other ‘normal’ isomer - is more
stable by only 6.3 kcal/mol (CASSCF-MP2 results for IIb, IV, V and VI;
all structures are optimised on CAS(10/8)/cc-pVDZ level with a full 
active space). Moreover, the energy of VI – the other non-Kekule isomer
- is higher than that of IIb by 20.8 kcal/mol. Thus, the thermodynamic
186
stability of IIb is of the same order as the normal aromatic heterocyclic
molecules IV and V, in spite of the loss of one -bond in IIb.
The ionization potentials (IPs) of II-type molecules are calculated
to be fairly small, especially for IIb. For this compound, IP is of the
same order as the energy of the first excited state (CASSCF and also
DFT). Even though CAS is known to overestimate the energy of
electronic excited states, the very low ionization potential indicates a
facile auto-ionization for this molecule. The data are summarized in
Table 3.
All stable bicyclic compounds VIII considered in this work have
Cs symmetry, the symmetry plane being perpendicular to the carbon
frame. In contrast, all triplet states were found to have a minimum at C 2
symmetry, due to the release of strain in the small rings. The ground
states of open singlet species VII were also found to have a minimum at
C2 symmetry, except for X=CH2 and X=CF2 which was a transition state
(C2v) between two closed forms (Cs). Table 4 lists the calculated
structures and energies of the singlet and triplet forms of all open
species, as well as those of the bicyclic compounds. The data show that
the X-C1(3) distance is shorter in the open isomer than in the triplet,
which is in turn shorter than in the closed bicyclic isomer. The C1 -C3
distances in both the open isomer and the triplet are about 2.3Å.
In all calculated species except for the parent cyclopentane-1,3diyl (VII) the singlet form is more stable than the triplet. ΔE ST increases
in the sequence X= CH2<CF2<O≈S<NH≈NCH3. The relative stabilities
of the open singlet forms vs. the closed ones are drastically changed
upon substitution: whereas bicyclo[2.1.0]pentane (VIIIa) is >20kcal/mol
more stable than open isomer, the aza-analogs shows preference for the
open isomer (-3.2 kcal/mol for X=NH (VIIe) and -6.5 kcal/mol for
X=NMe, (VIIf)). The energy difference between the closed form (S0)
and the open triplet 1,3-diradical (T1) is much less sensitive to the nature
of X: it is 21.9 kcal/mol for the parent hydrocarbon vs. 31.5 kcal/mol for
the aza-derivatives. These results hold also upon application of the MP2
correction. Evidently, the open singlet form is more strongly affected by
the heteroatom-substituent than the open triplet or closed form singlet.
The nitrogen derivatives exhibit exceptional stabilization of their open
form isomers.
187
Table 4. Bond lengths and energies in singlet (S0) and triplet (T1) states of some
cyclopentane-1,3-diyl species (CASSCF(10/8)/cc-pVDZ); the relative energies
of the different structures of a given species are with respect to the closed form.
CASMP2 data are also given for of the energy difference (ΔΔE) between the
open (VII) and closed (VIII) forms.
Structure a
R12(23)
R13
ΔΔE kcal/mol ( a.u.)
Closed (S0)
1.496
1.557 0.0 ( -193.99196 )
CH2
Open -TS (S0)
1.537
2.395
22.7 {31.6}c
Open (T1)
1.533
2.386
21.9
Closed (S0)
1.494
1.560 0.0 ( -391.72874 )
CF2
Open –TS (S0)
1.474
2.314
12.3 {16.0}c
Open (T1)
1.492
2.371
17.8
Closed (S0)
1.455
1.455 0.0 ( -229.85729 )
Open (S0)
1.365
2.256
18.1 {26.0} c
O
b
TSOC ( S0)
1.396 (1.446) 2.108
47.7
Open (T1)
1.412
2.259
33.8
Closed (S0)
1.864
1.534 0.0 ( -552.50698 )
Open (S0)
1.717
2.443
12.8 {15.1}c
S
b
TSOC ( S0)
1.801 (1.803) 2.452
42.5
Open (T1)
1.801
2.436
27.7
Closed (S0)
1.510
1.511 0.0 ( -210.00437 )
Open (S0)
1.371
2.234
-3.2 {-3.7} c
NH
b
TSOC ( S0)
1.420 (1.457) 2.132
38.5
Open (T1)
1.426
2.235
31.4
Closed (S0)
1.509
1.473 0.0 ( -249.03280 )
NCH3
Open (S0)
1.372
2.309
-6.5 {-8.7} c
Open (T1)
1.423
2.283
31.5
a
The open form is a transition state for X= CH2 and X= CF2, a minimum for all
others.
b
TS is the transition state for the bond stretch reaction (Fig. 2). In it R12≠R23.
c
CASMP2
X
Table 4 also reports some properties of the transition state for the
cyclization reaction between the closed and open singlet isomers (a
single imaginary frequency was found in all cases). It is evident that the
barrier for the reaction from both sides is substantial (~40 kcal/mol in
the case of X=NH) – the open form is consequently predicted to be both
thermodynamically and kinetically stable. The singlet transition state
188
between the open and closed (bicyclic) forms for all 2-heterosubstitutedcyclopentanes was found to transform as C1, as expected since the point
groups C2 and Cs have no common symmetry element (Fig. 3 shows the
structures calculated for the case of IIe).
Fig. 3. The calculated structures of the two isomers of the aza analog of 2cyclopentane-1,3-diyl diradical (VIIe) in two projections: left - open
form (C2), right - closed (Cs) form and middle - non-symmetric (C1)
transition states between them.
Further differences between the closed and open forms of the
hetero-substituted cyclopentan-1,3-diyls are revealed in Table 5 which
reports some electronic properties.
Table 5 shows that S0-S1 excitation energies for all open isomers
are more or less equal (~5eV, CASSCF level, 3.5-4 eV, CASMP2 level)
and similar to the case of ordinary unsaturated molecules. The ΔEST gap
strongly depends on the type of heteroatom: for the parent hydrocarbons
(X= CH2) the singlet and triplet states are nearly degenerate; X=CF2
leads to the considerable stabilization of singlet state [7] – T1 is a 0.25
eV above the S0.
189
Table 5. The singlet (S0) - triplet (T1) gap, S0-S1 excitation energy, Ionization
Potential, energy of HOMO cyclopentane-1,3-diyls (CAS(10/8)/cc-pVDZ) (in
eV); the relative energies of the different structures are with respect to the
energy of S0 (open form). In each column the left value is calculated using
CASSCF(10/8)/cc-pVDZ, the right CASMP2(10/8)/cc-pVDZ.
ΔΔE (S0-S1;
IP (D1)
IP (D1,2) c
11A-11B)b
Closed form
HOMOd
CAS CASMP2 CAS CASMP2 CASSCF CASMP2 CASSCF CASMP2
6.98 (12A) 7.50 (12A) 8.28
9.15
CH2 -0.04 -0.05 5.28 3.41
7.34 (12B) 7.71 (12B) (12A’) (12A’)
7.77 (12B) 8.57 (12B) 9.08
9.99
CF2 0.24
0.44 6.49 4.16
7.76
9.61 (12A) 10.16(12A) (12A”) (12A”)
2
2
6.02 (1 A) 7.20 (1 A) 9.03
9.54
O 0.68
0.76 5.19 3.75
6.25
8.88 (12B) 9.36 (12B) (12A’) (12A’)
6.03 (12A) 6.97 (12A) 7.76
8.41
S 0.65
0.73 4.34 3.29
6.64
8.33 (12B) 8.90 (12B) (12A)
(12A)
2
2
5.16 (1 A) 6.34 (1 A) 7.91
8.69
NH 1.50
1.37 5.31 3.99
5.87
8.45 (12B) 9.10 (12B) (12A’) (12A’)
5.02
6.09
7.66
7.66
NCH3 1.65
1.30 5.10 3.70
5.79
8.17
8.81
(12A’) (12A’)
X
ΔE ST a
a) ΔE ST=ΔE (S0-T1)
b) Vertical excitation energy.
c) IP1,2=E(S0) - E(D1,2) is a difference between energy of neutral molecule and
corresponding cation (vertical IP).
d) Energy of the HOMO of the open form, by Koopmans theorem, an estimate
of the first IP.
A modest gap is found for X= O or S (~0.6eV). For the azaderivatives the gap is considerably larger (~1.3eV) a typical value for
hetero-substituted conjugated molecules. The trends found for the first
ionization potentials (IP) are also informative: the IP of the parent
cyclopenta-1,3-diyl and the fluoro-substituted analog are typical to
organic radicals ~8 eV (MP2 level). In contrast the IPs of the azacompounds are unusually low compared to stable organic molecules only about 6 eV. The IPs of the closed isomers are 2-3 eV higher than
those of the open ones. For the parent molecule (VIIa) the difference
between the first two ionization potentials are quite modest, indicating a
strong biradical character. In the nitrogen substituted ones (VIIe and
VIIf) the difference is much larger – about 2.5-3 eV. This result suggests
that the first electron is held much less strongly than the second one. The
190
estimation of the IPs using Koopmans theorem shows reasonable
agreement with the more sophisticated CASSCF method in which the
energies of the cation and the neutral molecule were compared.
Table 6 reports data relating to the electronic structure of the
molecules; the second column shows that the principal two
configurations account for over 95% of the electronic density
population, justifying the use of a two-configuration approximation for
further discussion. Column 3 reports the amount of charge transferred
from X to rest of the molecule in units of electronic charge and column 4
the charge transferred to each of the two neighboring carbon atoms (in
fact, the CH group).
Table 6. The contribution of the two leading configurations and the changes in
charge distribution in electron charge units (Δq, S0 vs. T1) (CASSCF(10/8)/ccpVDZ)
CH2
CF2
O
S
NH
NMe
Coefficients of the two
Leading Configurations:
(CA:CB)
0.70:0.69
0.53:0.83
0.90:0.39
0.91:0.35
0.93:0.31
0.94:0.30
ΔqX
ΔqHC1(3)
-0.001
-0.054
+0.147
+0.208
+0.207
+0.260
+0.000
+0.020
-0.068
-0.097
-0.092
-0.117
Almost no charge is transferred for X=CH2, in both the singlet and
triplet states and ΔEST is negligibly small (~1 kcal/mol). X=CF2 is an
electron acceptor, whereas O, S and the nitrogen-based substituents are
all donors. A measure for the "diradical-zwitterion"(BR-ZW) vs. the
"ylide" (YL) character of the open form may be correlated with the
charge transfer. Complete one-electron charge transfer would result in a
unit of positive charge on X and 0.5 units each on C1 and C3. However,
the charge transfer, even in the case of the aza-derivatives, is limited to
only about 0.2e. The fact that even in the case of the most potent donor
(NMe) only about a quarter of an electronic charge unit is transferred
means that the contribution of the diradicaloid VB structures (BR and
ZW) is more significant than that of the polar one (YL).
191
Discussion
Pentalene (II) and Cyclooctatetraene (III) [29]. Comparison with
experiment
A large singlet – triplet splitting for a formal biradical, as
displayed in Table 3 for the hetero-substituted molecules, was found in
the recently prepared di-tert-butyl derivative of 2,5-diamino-1,4benzoquinonediimine, which exists in a persistent zwitterionic form in
the singlet ground state [30, 31].
Apart from tetraphenylthieno(3,4-c)thiophene (IIe) [14, 15, 16]
there is no experimental evidence for molecules IIb-d or their derivatives
(though Closs et al. reported [32] experimental evidence for II with
X=N) nor for IIIb-d, but crystal structures of potassium and ammonium
salts of dianion of 1,3,4,6-tetranitro-2,5-diazapentalene have been
published [33, 34]. 7,8-diazapentalene, VI, is the least stable
diazapentalene isomer, nevertheless its derivatives were obtained and the
crystal structures of nitro-substituted-7,8-diazapentalenes were reported
[35, 36].
The calculated structure of IId (Table 1) agrees well with the
structure of IIe; The calculated ionization potential (6.35 eV, Table 3) is
also in good agreement with experiment (6.19 eV [16]). The lowest
lying excited singlet of IId is calculated to be about 4.47 eV by CASSCF
and 2.82 eV by TDDFT. We propose that the lower experimental value
(2.24 eV for IIe) reflects a bathochromic shift due to the interaction
between the four phenyl groups and the central bicycle moiety.
Electronic structure of II and III and the rationale for the high
stability and low IP of S0.
The difference between the calculated charge distributions in the
singlet and triplet states Δqx(ST) (Table 3) shows that about 0.12÷0.15
electronic charge is transferred from the donor-heteroatom X to the
TME fragment in IIb-d or to the two allyl units and IIIb-d. Significantly,
IIa and IIIa (X=CH2) do not show any differences in the electronic
distribution between the singlet and triplet states, as expected. The same
donor groups in 2-heterosubstituted-3,4-dimethylenecyclopentane-1,3diyls, Ib-d, show considerably less tendency for intramolecular charge
transfer of this type in the singlet state: Δq= qx(singlet) - qx(triplet) is
+0.08 for aza-derivative, Ib; +0.03 for oxa-derivative, Ic, and +0.06 for
thia-derivative. Obviously, the degree of donor-acceptor charge transfer
192
and the relative stabilization of the singlet state in IIb-d and IIIb-d are
correlated.
A simple electrostatic model accounts for the physical origin of
the extra-stabilization of singlet state for IIb-d and IIIb-d. Transferring δ
units of charge from the donor X to the acceptor TME fragment in I
leads to a Coulomb stabilization Ecoul=-δ2/R, where R is a distance
between the centers of the positively charged X and the negatively
charged accepting group. The same amount of charge transferred from X
to TME for II results in a much larger Coulomb stabilization, Ecoul =
= -4δ2/R – four times larger (Fig. 4 shows the charge distribution in
these molecules).
Fig. 4. The intra-molecular charge separation in I vs. II.
The electrostatic argument cannot account for the low IP of these
molecules. An MO-based model can be proposed to explain both the
extra stabilization and the low IP. In ref. 20 an MO diagram for IIe was
used to account for the observed photoelectron spectrum. Fig. 5 shows a
schematic diagram in which the MOs of the IIb molecule is constructed
by the interaction between the MOs of the TME fragment and the two
donor groups.
As seen from the diagram the only high lying orbitals that can
interact are the b2g-type orbitals. The two b2g and au orbitals of the TME
biradical fragment are practically degenerate, as are the b2g and b1u
orbitals of the two NH groups. In the TME biradical two electrons
occupy the two NBOs; the interaction between the two b2g fragment
orbitals lifts the degeneracy of both TME and NH-NH orbitals. It turns
out that the interaction is very strong – the in-phase combination of the
two b2g orbitals is stabilized with respect to the au orbital by about 9 eV!
(HF/cc-pVDZ calculation). The other b2g orbital (formed by out-ofphase combination) is strongly destabilized and becomes the LUMO.
193
LUMO (b2g)
(au)
HOMO (au)
(b2g)
(b1u)
(b2g)
(b1u)
( b2g )
Fig. 5. A π-orbital diagram showing the origin of the low ionization potential of
2,5-diheterosubstituted pentalenes IIb-d as well as its high stability as a
singlet zwitterion. The left hand π-orbitals are of the carbon skeleton and
the right hand ones of the donor X group. The middle ones are the
resulting molecular orbitals of II.
This strong interaction is the MO manifestation of the
stabilization of the singlet state. It is proportional to the orbital overlap
and inversely proportional to the energy gap between the NBO and NHNH donor orbitals. The oxo-substitution provides effective overlap, but
large energy difference between TME NBO’s level and p-AO of O atom
reduce the effectiveness of the interaction. The relatively weak
stabilization by S-substitution is due to small overlap between the porbitals of the small carbon atoms with a big S atom. The interaction is
especially strong for the aza substituent since only in this case both
conditions for strong stabilization are fulfilled.
The other TME NBO (au) does not interact with the donor and
becomes the HOMO; it is populated by the two electrons which
originally occupied the two different, though iso-energetic, au and b2g
orbitals. Being now in a single non-bonding orbital, the repulsion
interaction between them is stronger, reducing the ionization potential.
Moreover, the TME-fragment has also significant additional population
on the stabilized b2g MO, as the electrons that occupied the X-X orbital
are now partially transferred to the common orbital. These effects lead to
194
the concentration of an electron density on the atoms, but not on the
bonds - between atoms. The strong electron-electron repulsion pushes up
this HOMO and it results in a very low IP.
The electronic structure shown in Fig. 5 is compatible with the
data of Table 1 – the similar geometry of all molecules is due to the fact
that the two extra electrons find themselves in a non-bonding orbital and
thus their effect on bond-lengths is minimal.
The dominant ground state electronic configuration of IIb may be
written as 1Ag = (b1u)2(au)2(b2g)0(b1u)0. Removal of one electron yields the
cation radical with configuration 2Au = (b1u)2(au)1. The first excited
electronic state has the configuration 1B2u = (b1u)2(au)1(b2g)1(b1u)0. The
transition 1Au →1B2u is allowed, with oscillator strength (TDDFT/B3LYP-cc-pVDZ) of 0.14. As shown in Fig. 6, the system can be
readily ionized using UV light.
Autoionization
1B
1g
1B
2u
M++ e-
2A
u
h
1A
g
M
Fig. 6. A schematic energy level diagram of IIb showing the S 0-S1 optical
transition with a vibronic progression that can lead to autoionization.
The high level CASSCF calculations show that the aza-substituted
compound has a much more pronounced zwitterion character than the
oxo- or thio-substituted ones.
The squared ratio of the coefficients of the two principal singlet
configurations of the singlet ground state (C1/C2)2 can serve to estimate
the nature of these formal biradicals – for a covalent biradical it is near
unity, and for a zwitterion it is much larger.
195
Table 6 lists the numerical values for this squared ratio. It is seen
that for x=CH2 the singlet ground states of both pentalene (IIa) and
cyclooctatetraene (IIIa) are largely biradicals, while for x = NH, they are
zwitterions. The oxo and thio compounds are of intermediate nature, but
also mostly zwitterions. Comparing with the semi-empirical results, it is
seen that the (C1/C2)2 ratio is much larger, by approximately a factor of
three. Another quantitative difference is the fact that the (C1/C2)2 ratio is
larger by a factor of two for IIb, IIc and IId as compared to the
semiempirical result.
Table 6. The squared ratio of the coefficients of the two leading configurations
of the singlet CI wave function as obtained by the CASSCF calculation.
Molecule
(C1/C2)2
(C1/C2)2
(ref. 12a)
IIa
1.1
IIb
23.9
IIc
9.6
IId
10.3
8.05
3.28
2.46
IIIa
2.2
IIIb
23.9
IIIc
11.3
IIId
13.2
Cyclopentane-1,3-diyl diradicals [37]
The open forms of the 1,3-diyls cannot be described by a single
Lewis structure. A non-Lewis molecule with two equivalent radical
centers is a diradical according to chemical intuition and simple VB
description (BR, Fig. 7). However, other VB structures may contribute:
the zwitterion (ZW) and the ylide-type structure (YL), see Fig. 7.
Fig. 7. VB structures of 2-heterosubstituted-cyclopenta-1,3-diyl: covalent
diradical –BR; zwitterion –ZW and ylide – YL.
A diradical is defined in the MO approach as a structure with two
unpaired electrons populating two degenerate or nearly degenerate MOs
[38, 39, 40]. If the molecules under study were predominantly
represented by structure BR (Fig. 7), they could be classifies as
196
diradicals. However, it turns out that except for the carbon derivatives
(VIIa and VIIb) they exhibit considerable zwitterion character, as
expected for structure ZW and ylide-type charge transfer for YL (Fig. 7).
This is evident from the large singlet-triplet splitting and the large
difference between the first and second IPs. An insight into their nature
may be gained by considering a simple two-configuration model. The
wave function of the parent 1,3-diyl is usually described in the FMO
model by an anti-combination of two configurations distinguished by
highest occupied orbitals – non-bonding MOs: A=(φ1-φ3) and
B=(φ1+φ3), where φ1 and φ3 are the two atomic orbitals, localized on the
C1 and C3 atoms. These two orbitals are degenerate and the
corresponding configurations contribute equivalently to the ground state
wave function. According to a basic biradical model, the anticombination of degenerate configurations (CA=CB) defines a purely
covalent diradical without any ionic contributions:
(CA  CB  1)  BB  A A 
 (1  3 )(1  3 )  (1  3 )(1  3 )  (13 )  (13 )
In contrast, when the two configurations are not equivalent a non-zero
ionic term appears:
 (C A  CB )  CB BB  C A AA  CB (1  3 )(1  3 )  C A (1  3 )(1  3 ) 
(C A  CB ){13  13 }  (CB  C A ){11  33}
Thus, the ratio (CB - CA)/(CB + CA) can serve as an index for the
relative contributions of an zwitterion form and a diradical one to the
electronic wave function at the two-configuration approximation. The
computational evidence of the diradical character, based on the ratio of
the coefficients of leading configurations in a CI expansion, was
discussed by Davidson [41, 42]. Within the two-configuration
approximation the square of the ratio will be used as an estimate for the
contribution of ZW.
Dewar [43] pointed out the importance of weak interaction
between the radical centers for the pure diradical character. In the case
of the hetero-substituted 1,3-diyls the direct C1-C3 interaction is weak,
but the three-centered C1-X-C3 one is quite strong. The interaction of
197
the apical group with the 1,3-diradical moiety leads to the splitting of the
degenerate non-bonding pair. Fig. 8 shows two different ways leading to
orbital splitting of the two degenerate orbitals (C2 symmetry is used): an
acceptor stabilizes the B type orbital, which becomes the HOMO
whereas the LUMO is of A symmetry; in contrast, a π-donor inverts this
order: the A-type orbital becomes the HOMO, and the B-symmetry one
is the LUMO .
X
2B
X
A
A
X
A
B
X
B
Donor
X=NH
X=CH2
1B
Ψ= CB{…(B)2} -CA{…(A)2}
CB ˜ CA
Ψ= CA{…(1B)2 (A)2} –CB{…(1B)2(2B)2}
CA > CB
Acceptor
X=CF2
Ψ= CB{…(B)2} -CA{…(A)2}
CB > C A
Fig. 8. Orbital interaction diagram between 1,3-diyl unit and donor (left) or
acceptor (right) apical group. C2 symmetry is assumed; the HOMO and
LUMO orbitals are highlighted by a black solid and a grey dotted circle,
respectively.
In both of these cases the increased HOMO-LUMO splitting
means the increased contribution of one configuration over the other and
a larger singlet-triplet splitting, reducing the diradical character. Fig. 8
shows the order of the combined orbitals and, consequently, defines the
dominant configuration. Although this is clearly an oversimplified
picture in the case of the weak coupling, because the second
configuration (of the occupied LUMO, marked by grey color) must also
be taken into account, the basic characteristics are explained by the
dominant configuration. The relative contribution of these two
configurations: (HOMO)2 vs. (LUMO)2 determines the ratio between the
198
covalent diradical contribution (BR) and the zwitterion one (ZW). This
reasoning can be compared to Head-Gordon’s suggestion to use the
LUMO-occupation numbers as an indication of the extent diradical
character [40].
Table 7 summarizes the contribution of the three main VB
structures for the different diyls.
Table 7. The relative weight (%) of the three main VB structures (Figure 7), the
LUMO occupation numbers for and the percentage of charge transferred in
electron charge units (Lowdin charges) calculated for the open form of 2-Xcyclopentane-1,3-diyl compounds (CASSCF(10/8)/cc-pVDZ).
X
BR
ZW
YL
LUMO
Occupation Numbers
ΔqX
CH2
100
0
0
0.947 (0.927) [40]
-0.001
CF2
91
4
5
0.562 (0.583) [40]
-0.054
O
673
12
15
0.304
+0.147
S
65
14
21
0.245
+0.208
NH
64
15
21
0.192
+0.207
NMe
58
16
26
0.180
+0.260
As a rough approximation, the fraction of charge transferred
(Table 6) is used as an estimate for the contribution of the polar form
YL; the balance is distributed between the dot-dot form (BR) and the
zwitterion one (ZW) using the ratio [(CB - CA)/(CB + + CA)]2:
%of ZW = (1- ΔqX)( [(CB - CA)/(CB + CA)]2)
%of BR = (1- ΔqX)( [1-(CB - CA)/(CB + CA)]2
where ΔqX is the fraction of charge transferred (Table 7).
The last column of Table 7 reports the LUMO occupation
numbers [39]; it is evident that the magnitude of charge transfer is
closely correlated with these numbers.
In the case of the parent singlet cyclopentane-1,3-diylVIIa, which
is a well-known perfect diradical [22] the electronic wave function can
be described adequately as the anti-combination of two configurations
199
with equivalent weights, which indicates according to Eq. (1) a purely
diradical character (BR contributes 100%). Almost no charge is
transferred for X=CH2, in both the singlet and triplet states and ΔEST is
negligibly small (~1 kcal/mol). In the hetero-substituted molecules the
contribution of the two configurations is not equal, leading to two
different ionization potentials as found computationally. This difference
can be readily verified experimentally by photoelectron spectroscopy. In
these molecules the contribution of the polar structure is non-negligible.
Borden considered the case of 2,2-difluoro-cyclopentane-1,3-diyl
as an acceptor hyperconjugation [22]. An analysis of the Lowdin charge
distribution shows that in this case only 0.054 electronic charges is
transferred to the CF2 group in the singlet state relative to a perfect
diradical triplet. Among the systems considered, this molecule is the
only case for which the dominant configuration is B-type (Fig. 8, right);
Here CB>CA and the contribution of the covalent configurations is
dominant, leading to a relative small ionic contribution: only 4%. All
other studied molecules show the domination of the A-type
configuration (CA≥0.9), indicating donor substitution (Fig. 8, left). The
contribution of the B-type configuration, although small, increases in the
sequence CH2<CF2<O<S<NH (Table 6), indicating the decreasing
importance of the pure diradical character. The open forms containing
X=O and S show 3-4 times larger charge transfer compared to X=CF2.
The largest transfer (compared to the triplet) occurs with X=NH(NCH3),
wherein about a quarter of an atomic unit charge is transferred. As in the
case of the hetero-substituted pentalenes and cyclooctatetraenes,
nitrogen proves to be the most efficient atom for stabilizing diradicals.
[29] A possible explanation is that although oxygen and sulfur also
transfer non-bonding electrons, the effect is smaller in oxygen since it is
more electronegative and a weaker donor. Sulfur has a comparable
electron affinity to nitrogen; however its larger size leads to a smaller
overlap with the orbitals of the neighboring carbon atoms, making it less
efficient as an electron donor .
The calculated charge transfer indicates the importance of the
ylide form YL (Fig. 7). In a previous paper [29] it was proposed that
formal diradicals may be stabilized by charge transfer. The systems
discussed there (hetero-substituted di-X-pentalenes and di-Xcyclooctatetraenes) were 4n+2 electron systems, so that the stabilization
might be assigned to increased aromaticity. The systems studied in this
200
work have four interacting electrons (one each on carbon atoms C1 and
C3, two on the heteroatom), yet they are also remarkably stabilized .
The upshot of the analysis given above is that these non-Lewis
systems are expected to exhibit "normal" properties of a species having
partial polar and partial diradical character. Yet, the unusually low IP,
especially in the case of aza-derivatives for which it is only ~6eV, is
surprising at first sight. It cannot be explained by the contribution of
either the biradical structure (BR) or the ylide one (YL). We propose
that it is due to the importance of the zwitterion structure ZW in which
two electrons occupy a single non- bonding orbital centered on carbon
atoms. The simultaneous occupation of an orbital by half electron pair
on C1 and C3 increases the electrostatic repulsion, compared to single
electron on C1 and C3 in the diradical BR structure. This accumulation
of negative charge is equivalent to imparting these species with a quasianion character. Unlike a lone pair on a nitrogen atom, a lone pair on a
carbon atom leads to excess charge and strong inter-electron repulsion.
An experimental method to probe this prediction is by photoelectron
spectroscopy – the open form is predicted to show a much smaller IP
than the closed one .
Concluding remarks
In conclusion, it was shown that formal diradicals - 2,5-diheterosubstituted-pentalenes, 1,5-di-heterosubstituted-cyclooctatetraenes
and cyclopentane-1,3-diyl are predicted to be stable persistent nonKekule molecules, due to strong stabilization by intra-molecular charge
transfer. The overall stabilization of the singlet is accompanied by a high
lying HOMO, resulting in a low ionization potential. The low ionization
potential (~5 eV) allows in principle facile auto-ionization in the near
UV.
1.
2.
3.
4.
5.
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