Gas-phase conformations and exciton couplings in 5,6,11,12-tetrahydrodibenzo[a,e]cyclooctene

Article abstract of DOI:10.1007/s11224-010-9612-z

The conformations and exciton couplings in 5,6,11,12-tetrahydrodibenzo[a,e]cyclooctene (THDC) have been studied using resonance-enhanced two-photon ionization spectroscopy in a supersonic jet expansion. It has been estimated from the spectral analysis tha

Full text of DOI:10.1007/s11224-010-9612-z

Struct Chem (2010) 21:787–793
DOI 10.1007/s11224-010-9612-z
ORIGINAL RESEARCH
Gas-phase conformations and exciton couplings
in 5,6,11,12-tetrahydrodibenzo[a,e]cyclooctene
Abdulhamid Hamza
Received: 30 November 2009 / Accepted: 12 April 2010 / Published online: 23 April 2010
Ó Springer Science+Business Media, LLC 2010
Abstract The conformations and exciton couplings in
5,6,11,12-tetrahydrodibenzo[a,e]cyclooctene (THDC) have
been studied using resonance-enhanced two-photon ioni-
zation spectroscopy in a supersonic jet expansion. It has
been estimated from the spectral analysis that 90% of
THDC exists in the twist-boat (TB) conformation; the chair
(C) conformer constitutes the remaining 10%. Most of the
vibronic activity in the spectrum of THDC is associated
with the symmetric flapping of the aromatic rings of the TB
conformer. The observed S1/S2 exciton splitting of the TB
conformer is 100 cm-1. The S1/S2 transition of the C
conformer is found to be forbidden. The exciton splittings
of the C and TB conformers were estimated by the spectral
analysis of two deuterated isotopomers of THDC. The
estimated exciton splittings of the C and TB conformers are
14.7 and 101.9 cm-1, respectively. The supramolecular
model of bichromophores with identical chromophores at
the CIS/6-31?G(d)//HF/6-31?G(d) level of theory pre-
dicted electronic coupling energies that are very close to
the experimental exciton coupling energies.
Introduction
Theconformationsof5,6,11,12-tetrahydrodibenzo[a,e]cyclo-
octene (THDC), also known as [2.2]-orthocyclophane, have
been extensively investigated by X-ray and NMR techniques
[1–3]. Previous theoretical studies of THDC were limited to
molecular mechanics and density functional theory (DFT)
calculations [3, 4]. The calculations predicted three stable
ground state conformers. The structures of the three stable
conformers are displayed in Fig. 1. The twist-boat (TB) and
chair (C) conformers have been observed in solution using
NMR techniques [2, 3]. X-ray studies show that only the C
conformer is present in the crystal [1]. The gas-phase con-
formational analysisof THDC which can be readily compared
with the results of theoretical computations of the isolated
THDC conformations has not yet been reported in the
literature.
The photophysical properties of THDC have been studied
by Longworth and Bovey [5]. THDC absorbs and fluoresces
in the same spectral region as 1,2-diphenylethane and other
alkylbenzenes. However, the fluorescence of THDC is
unstructured, and has a small quantum yield. The authors
therefore, concluded that the interaction of the two aromatic
rings of THDC in the excited state is weak, and the molecule
undergoes geometrical changes upon electronic excitation
[5]. Hence, THDC can be treated as a covalently bonded
dimer of o-xylene. The scope of the exciton theory is to relate
the excited states of dimers to those of the constituting
monomers. The excitation energy of dimers (bichromo-
phoric molecules) that incorporate two identical chro-
mophores is shared by the chromophores via exciton
coupling. The strength of the exciton coupling is determined
by the electronic coupling energy, V [6–9]. The observed
exciton splitting, 2Vvv, of the vibronic bands is com-
posed of the purely electronic and vibrational components.
Keywords
5,6,11,12-Tetrahydrodibenzo[a,e]cyclooctene ꢀ
Conformation ꢀ Exciton coupling ꢀ Spectroscopy ꢀ
Ab initio calculations
A. Hamza (&)
Petroleum Chemistry and Engineering Program, School of Arts
and Sciences, American University of Nigeria, PMB 2250, Yola,
Nigeria
e-mail: abdulhamid.hamza@aun.edu.ng; abbamid@yahoo.com
123

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Struct Chem (2010) 21:787–793
0 °C. 20 mL of cold water was then slowly added to destroy
the remaining lithium granules. The organic layer was
extracted with diethylether. The product was purified by
column chromatography on silica gel (petroleum ether) to
give pure THDC-d0. A statistical mixture of THDC-d0,
THDC-d4, and THDC-d8 was synthesized by coupling of
a,a0-dibromooxylene-d4 (4 mmol) and a,a0-dibromoxylene-
d0 (4 mmol) following the same procedure as for THDC-d0.
a,a-Dibromooxylene-d4 was synthesized in two steps. A
mixture of phthalic acid-d4 (5.8 mmol) and LiAlH4
(6.5 mmol) in 20 mL of THF was refluxed for 15 h to yield
a,a0-benzenedimethanol-d4. Reaction of a,a0-benzenedi-
methanol-d4 (5 mmol) with 1.5 equivalent of PBr3 in 20 mL
of dichloromethane at 20 °C for 2 h yielded a,a0-dibro-
mooxylene-d4. The identity of the synthesized compounds
was confirmed by GC/MS analysis.
Fig. 1 Optimized ground state structures of the a chair (C), b twist-
boat (TB), c twist (T), and d boat (B) conformations of THDC. The
boat conformation corresponds to a transition state between two
equivalent TB conformers
The supersonic jet spectrometer used in this work has
been described in details elsewhere [11]. Briefly, the
spectrometer is composed of two differentially pumped
expansion and ionization chambers. The sample of THDC
isotopomers is heated to 140 °C, and seeded in a carrier gas
(helium or neon) at a backing pressure of 2–3 atm. The free
jet in the expansion chamber is skimmed, and the resulting
molecular beam in the ionization chamber is perpendicu-
larly crossed by a frequency doubled, Nd:YAG pumped
dye laser beam. Molecular ions are formed by sequential
absorption of resonant and ionizing laser photons. The
molecular ions are then detected and mass analyzed using a
time of flight mass spectrometer. Resonance-enhanced
two-photon ionization (R2PI) spectra are measured using a
boxcar integrator interfaced with a personal computer.
Ground state geometry optimizations were carried out at
the Hartree–Fock (HF), the density functional theory (DFT)
with the B3LYP functional, and the second-order Møller–
Plesset perturbation (MP2) levels of theory. Harmonic fre-
quency calculations were done at the HF and DFT levels
using the HF and DFT optimized geometries, respectively.
Configuration interaction singles (CIS) method was used for
computing vertical excitation energies using the HF opti-
mized S0 geometries. The computations were performed
using the 6-31?G(d) basis set. All calculations were per-
formed using Gaussian 03 suite of programs [12].
The vibrational component is determined by the Franck–
Condon factor, FCvv, of the vibronic transition [9]. The
electronic component, V, is composed of terms describing
the through-space (Coulombic and exchange) and through-
bond mediated interactions of the chromophores [6–9]. The
electronic component, V, can be estimated from the experi-
mental data by dividing Vvv with FCvv [9].
In this work, THDC and its two selectively deuterated
isotopomers have been synthesized. The structures of the
synthesized isotopomers are shown in Fig. 2. The gas-
phase electronic spectra of the THDC isotopomers have
been recorded in a supersonic jet. Analysis of the experi-
mental data in combination with ab initio electronic
structure calculations provides information about the con-
formational preferences of THDC in the gas phase and the
S1/S2 exciton coupling energies of THDC conformers.
Experimental and computational methods
A modified procedure of Boudjouk et al. [10] was used for
the synthesis of THDC-d0 in about 80% yield. The pro-
cedure involves sonication of a,a0-dibromooxylene
(7.6 mmol) and lithium granules (30 mmol) in 15 mL of
THF under argon atmosphere. After 3 h of sonication at
room temperature, the reaction mixture was cooled to ca.
Results and discussion
Ab initio calculations
The calculated S0 relative energies and molecular sym-
metries of the three stable conformers of THDC are
presented in Table 1. The MP2 calculations predicted
more stable TB conformer. Whereas, the C conformer is
predicted to be the most stable at the HF and DFT levels of
Fig. 2 Investigated isotopomers of THDC
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Struct Chem (2010) 21:787–793
789
Table 1 Relative energies (in kJ/mol) and symmetries of the three
stable conformers of THDC at various levels of theory with
6-31G?(d) basis set
Conformer
Symmetry
HF
DFT
MP2
MP2//HF
TB
C
C2
0
0
0
0
C2h
D2
-3.52
12.73
-3.76
10.89
11.76
27.91
5.84
22.33
T
theory. The difference between the MP2 and HF/DFT
results can be attributed to the fact that the MP2 method
better accounts for the non-bonded intramolecular disper-
sive interactions between the p electron clouds of the
aromatic rings [13]. These interactions are particularly
important in the TB conformer, where the aromatic rings
are closer and partially overlapping. However, the MP2
method often overestimates conjugation [14], which might
lead to overestimation of the relative stability of the TB
conformer in which dispersive interactions between the p
electron clouds are possible. Smith et al. [15] reported that
better relative energies of the various configurations of the
benzene dimer (where dispersive interactions play an
important role in determining the relative stability of the
various configurations of the dimer) are obtained by per-
forming single point MP2 energy calculations on HF
optimized geometries. The results of this work also reveal
that the single point MP2 relative energies on HF opti-
mized geometries of THDC conformers are in excellent
agreement with the experimental relative conformational
energies (vide infra).
Fig. 3 R2PI spectra of a THDC-d8, b THDC-d4, and c THDC-d0.
Two localized electronic origins of each conformer appear in the
spectrum of THDC-d4
frequencies of vibrational transitions than on the relative 000
transition energies of conformers [16]. Therefore, vibra-
tionless electronic origins of conformers can be readily
distinguished from vibronic peaks based on the observed
isotope effects. Herein, the isotope effect on the relative
frequencies of the observed peaks in the R2PI spectrum of
THDC has been studied in order to determine the number
of THDC conformers that are present in the gas phase and
assign their vibronic transitions.
The T conformer is predicted to be the highest in energy
by the HF, DFT, and MP2 methods. Therefore, the T
conformer may not be observed in the supersonic jet
experiments owing to negligible Boltzmann factors at the
experimental temperature of 140 °C. The B conformation
corresponds to a transition state between two equivalent
TB conformers, as the single imaginary frequency (-109
and -123 cm-1 at the DFT and HF levels, respectively)
that is associated with torsions about the central Csp3 ꢁ Csp3
a bond implies.
The spectrum of the symmetrically deuterated THDC-
d8, shown in Fig. 3a is qualitatively similar to that of
THDC-d0 (Fig. 3c), as both THDC-d0 and THDC-d8 have
the same symmetry. The first electronic origin of THDC-d8
is however blue-shifted by 130.1 cm-1 relative to the first
electronic origin of THDC-d0 because of the changes in
zero point vibrational energies in the ground and excited
states upon deuteration. Listed in Table 2 are: the fre-
quencies of the observed peaks in the spectra of THDC-d0
and THDC-d8, the isotope effects in THDC-d8, and the
proposed assignments of the observed peaks. The isotope
effects, IE, were calculated as the percentage decrease of
the frequencies (relative to the first observed peak at
36956.3 cm-1) of the observed peaks in the spectrum of
THDC-d8 with respect to the frequencies of the corre-
sponding peaks in the spectrum of THDC-d0. As seen in
Table 3, the peak at 37147.9 cm-1 has a negligible isotope
effect of 0.4%, suggesting that the peak at 37147.9 cm-1 is
an electronic origin of another THDC conformer [16]. All
other peaks have isotope effects of at least -3%. These
observations indicate that only two THDC conformers with
electronic origins at 36956.3 and 37147.9 cm-1 are present
R2PI spectra
The R2PI spectra of THDC-d0, THDC-d4, and THDC-d8
are presented in Fig. 3. The first band in the spectrum of
THDC-d0 appears at 36956.3 cm-1; scanning to the red of
this peak did not reveal additional spectral features.
Therefore, the band at 36956.3 cm-1 can be assigned to the
electronic origin of one of the THDC conformers. Gener-
ally, a peak in any vibrationally resolved electronic spec-
trum may be assign to vibrationless electronic origins (000)
of conformers or vibrational modes. It is well known that
isotopic substitution has much higher effect on the
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Struct Chem (2010) 21:787–793
Table 2 Assignment of the observed peaks in the R2PI spectra of THDC-d0 and THDC-d8
THDC-d0
THDC-d8
Assignment
Transition energy
(cm-1
Vibrational energy td
Transition energy
(cm-1
Vibrational energy td
Isotope effect
(%)
0
8
)
(cm-1
)
)
(cm-1
)
36956.3
0.0
37086.4
0.0
S1 / S0 origin of the TB
conformer
36984.8
37012.7
37039.7
37056.3
28.5
56.4
37113.3
37139.4
37164.9
37183.2
26.9
53.0
78.5
96.8
-5.6
-6.0
-5.9
-3.1
v1
2v1
3v1
83.4
100.0
S2 / S0 origin of the TB
conformer
37065.7
37070.7
37100.1
37132.6
37147.9
109.4
114.4
143.8
176.3
191.6
37189.3
37197.3
37225.4
37257.4
37278.7
102.9
110.9
139.0
171.0
192.3
-5.9
-3.1
-3.3
-3.0
0.4
4v1
v2 or v3
v2 (or v3)? v1
v5
S1 / S0 origin of the C
conformer
conformers. The first electronic origin at 36956.3 cm-1 is
thus assigned to the electronic origin of the TB conformer
(in which the two aromatic chromophores point toward one
another), and the second electronic origin at 37147.9 cm-1
is assigned to the origin of the C conformer.
Table 3 Assignment of the observed bands in the R2PI spectrum of
THDC-d4
Transition
energy (cm-1
Vibrational energy Assignment
td (cm-1
)
)
4
36993.2
0.0
S1 / S0 origin (dꢂ ꢁ d4),
0
The relative population of conformers can be estimated
by integrating the areas under the vibronic peaks of each
conformer in the electronic origin region of supersonic jet
electronic spectrum [18, 19]. The relative abundance of the
TB and C conformers was estimated by integrating the area
under the origin peak of the C conformer, and the areas
under the whole vibronic envelope of the TB conformer in
the origin region of the R2PI spectrum [19]. The estimated
TB:C population ratio is 9.1:1. Hence, 90% of THDC
exists in the TB conformation in the gas phase; the C
conformer constitutes the remaining 10%. The Boltzmann
distribution law was then used to estimate their relative
energy, DE ¼ EC ꢁ ETB. The statistical weight of 2 for the
TB conformer, and the pre-expansion temperature of
413 K (140 °C) were used in the calculations [19]. The
estimated value of DE is 5.20 kJ/mol. The estimated value
of DE is very close to the MP2/6-31?G(d)//HF/6-31?G(d)
calculated relative energy of 5.84 kJ/mol (Table 1).
The latter is about half of the MP2/6-31?G(d)//MP2/
6-31?G(d) calculated relative energy of 11.76 kJ/mol. The
failure of the MP2/6-31?G(d)//MP2/6-31?G(d) calcula-
tions to reproduce the experimental relative energy can be
attributed to the overestimation of conjugation by the MP2
method [14]. It was concluded from NMR experiments in
CD2Cl2 solution that THDC exists as a mixture of the TB
(88%) and C (12%) conformers [3]. Therefore, the TB
conformer predominates in the gas and liquid phases. The
higher stability of the TB conformer can be attributed to
TB conformer
37021.6
37049.2
37076.1
37102.4
37151.4
28.4
56.0
v1
2v1
3v1
4v1
82.9
109.2
158.2
S2 / S0 origin (d4ꢂ ꢁ d0),
TB conformer
S1 / S0 origin (dꢂ ꢁ d4), C
37154.6
161.4
0
conformer
37167.2
37169.3
37181.3
37187.0
37196.3
37205.0
37217.6
37224.6
37286.7
174.0
176.1
188.1
193.8
203.1
211.8
224.4
231.4
293.5
S2 / S0 origin (d4ꢂ ꢁ d0),
C conformer
in the gas phase. The two electronic origins can be assigned
by comparison with the previously analyzed electronic
spectra of allylbenzene [13] and alkylbenzenes [17]. The
electronic origins of the compact gauche conformers of
alkylbenzenes and allylbenzene (in which the substituent
group points toward the aromatic chromophores) are
red-shifted relative to the electronic origins of the anti
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Struct Chem (2010) 21:787–793
791
non-bonded intramolecular dispersive interactions between
the p electron clouds of the aromatic rings [13].
The spectrum of THDC-d4 presented in Fig. 3b was
recorded for the purpose of obtaining the experimental
exciton splitting of the C conformer, and confirming the
tentative assignment of the S2 / S0 transition of the TB
conformer. Listed in Table 3 are the frequencies of the
observed spectral features of THDC-d4, and their proposed
assignments. A four-membered progression with a funda-
mental frequency of 28.4 cm-1 also appears in the spec-
trum of THDC-d4. As shown in Fig. 3b, four localized
electronic origins have been identified in the spectrum of
THDC-d4. The four origins are associated with the local-
ized excitations of the deuterated (d4ꢂ ꢁ d0) and undeuter-
ated (d0ꢂ ꢁ d4) aromatic rings of the C and TB conformers.
The S2 / S0 transitions are localized on the deuterated
aromatic rings (d4ꢂ ꢁ d0); while the S1 / S0 transitions are
localized on the undeuterated aromatic rings. The zeroth-
order excited states are no longer degenerate in THDC-d4.
Thus, there exists a possibility of resonance and/or near
resonance interactions between the vibronic states that are
more or less localized on the undeuterated ring of THDC-
d4 with those localized on the deuterated ring, and vice
versa. This, together with the lower symmetry of THDC-d4
may lead to a complex vibronic pattern in the spectrum of
THDC-d4.
Listed in Tables 2 and 3 are the proposed assignments of
the observed peaks in the R2PI spectra of THDC isotop-
omers. Assignments of vibrational modes was performed
by comparison with the HF/6-31?G(d) and B3LYP/
6-31?G(d) calculated vibrational modes. THDC has 90
normal modes; listed in Table 4 are the HF/6-31?G(d) and
B3LYP/6-31?G(d) calculated frequencies and approxi-
mate descriptions of the five lowest frequency vibrational
modes of the TB conformer in the ground state. A pro-
gression with a fundamental frequency of 28.5 cm-1 is
built off of the electronic origin of the TB conformer. The
first two calculated lowest frequency modes differ signifi-
cantly in frequency (47 vs. 95 cm-1 at the HF/6-31?G(d)
level, 42 vs. 88 cm-1 at the B3LYP/6-31?G(d) level).
Therefore, the plausible assignment for the observed
28.5 cm-1 fundamental is to the lowest frequency mode,
labeled v1 in Table 4. This mode involves symmetric
flapping of the two aromatic rings. The appearance of a
progression in a flapping mode with the first and second
members of the progression being more intense than the
electronic origin indicates geometrical changes in the
excited state of the TB conformer. The geometrical chan-
ges are along the flapping mode of the two aromatic rings
(i.e., the values of the four Csp2 ꢁCsp3 ꢁCsp3 angles would
change upon excitation to the S1 state). The change in the
values of the four Csp2 ꢁCsp3 ꢁCsp3 angles is the most likely
reason for the observation of unstructured fluorescence of
THDC in solution [5]. This provides additional evidence
for the predomination of the TB conformer in both liquid
and gas phases. More theoretical work is needed to deter-
mine the exact changes in the values of the four
Csp2 ꢁCsp3 ꢁCsp3 angles.
Exciton couplings
The method outlined by Baum and McClure [9] was used to
estimate the exciton splittings, 2V00, in the electronic
spectrum of THDC using the observed 000 transition ener-
gies of THDC-d0 and THDC-d8 (Table 2), and the localized
000 transition energies of THDC-d4 (Table 3). The estimated
values of 2V00 in the TB and C conformers are 101.9 and
14.7 cm-1
, respectively. These experimentally based
The peak at 114.4 cm-1 can be assigned to mode v2 or
v3 based on the similar values of the observed and calcu-
lated frequencies. This mode appears in combination
with mode v1 at 143.8 cm-1. Similarly, the very weak peak
at 176.3 cm-1 can be assigned to mode v5. The peak at
100.0 cm-1 is not associated with an overtone or combi-
nation peak; hence, it is tentatively assigned to the S2 / S0
origin of the TB conformer.
results confirm the assignment of the band at 100.0 cm-1 in
the spectrum of THDC-d0 to the S2 / S0 origin of the TB
conformer, and that the S2 / S0 origin of the C conformer
is forbidden in the symmetric THDC-d0 and THDC-d8.
The electronic coupling energy, V, was then estimated
by dividing V00 with the Franck–Condon factor, FC0–0, for
the 000 transition of o-xylene (the presumed monomer of
THDC) [9]. A FC0–0 of 0.25 was estimated by dividing the
Table 4 Summary of the HF/6-31?G(d) and B3LYP/6-31?G(d) calculated lowest frequency vibrational modes of the TB conformer
Mode
Freq. (cm-1
)
Approximate description
HF
B3LYP
v1
v2
v3
v4
v5
47
95
42
88
Symmetric flapping of aromatic rings
Symmetric torsion about Csp3 ꢁCsp2 bonds
Asymmetric torsion about Csp3 ꢁCsp3 bonds ? asymmetric flapping of aromatic rings
Asymmetric torsion about Csp3 ꢁCsp2 bonds
–CH2–CH2– bridge deformation
139
149
178
127
139
163
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Struct Chem (2010) 21:787–793
Table 5 CIS/6-31?G(d)//HF/6-31?G(d) calculated vertical S1 / S0 and S2 / S0 excitation energies (E1 and E2, cm-1) with their oscillator
strengths (f1 and f2), and the symmetries of the excited states of the TB and C conformers
Conformer
S1 / S0
S2 / S0
E2 - E1
E1
f1
Symmetry
E2
f2
Symmetry
TB
C
48440
48713
0.0051
0.0042
B
48807
48772
0.0016
0.0000
A
367
59
Bu
Ag
area under the 000 band to that under the whole Lb band of
the room temperature absorption spectrum of o-xylene.
Hence, the experimental values of V are 200.0 and
29.4 cm-1 for the TB and C conformers, respectively.
The supramolecular model of dimers that is composed
of two identical chromophores takes into account all kinds
of through-space and through-bond exciton interactions
[6–8]. According to the supramolecular model, the elec-
tronic coupling energy, V, is equal to the half of the energy
gap between the calculated S1 / S0 and S2 / S0 vertical
excitation energies. The intensities of the S1 / S0 and
S2 / S0 transitions are proportional to their oscillator
strengths. As seen in Table 5, the S1 and S2 states of the C
conformer have Bu and Ag symmetries, respectively; hence,
the S2 / S0 transition of the C conformer is predicted to
be one-photon forbidden. The calculated energy gap
between the two states is 59 cm-1. On the other hand, the
S1 and S2 states of the TB conformer have B and A sym-
metries, respectively. Both S1 / S0 and S2 / S0 transi-
tions of the TB conformer are predicted to be allowed, the
former being ca. three times more intense than the latter.
The calculated energy gap between the S2 and S1 states of
the TB conformer is 367 cm-1. Therefore, at the CIS/6-
31?G(d)//HF/6-31?G(d) level of theory, the electronic
coupling energies, V, of the C and TB conformers are 29.5
and 183.5 cm-1, respectively. These values are very close
to the experimentally estimated coupling energies of 29.4
and 200 cm-1 for the C and TB conformers, respectively.
However, it should be noted that the results of the supra-
molecular model are very sensitive to the level of theory
employed [6, 8]; hence, the good agreement with the
experimentally estimated results obtained in this work is
accidental.
length of the central Csp3 ꢁCsp3 of 1,2-diphenylethane is
calculated to be equal to 0.3 eV for both gauche and anti
conformers of 1,2-diphenylethane [20].
Conclusions
In the gas phase, THDC predominantly exists (about 90%)
in the twist-boat (TB) conformation; the chair (C) con-
former constitutes the remaining 10%. Most of the vibronic
peaks in the spectrum of THDC are associated with the
symmetric flapping of the aromatic rings of the TB con-
former. The S2 / S0 transition of the C conformer is
forbidden. The observed exciton splitting of the TB con-
former is 100 cm-1. The estimated exciton splittings in the
spectra of the C and TB conformers are 14.7 and
101.9 cm-1, respectively. The supramolecular model of
bichromophores with identical chromophores at the CIS/
6-31?G(d) level of theory predicted electronic coupling
energies that are very close to the experimental coupling
energies.
Acknowledgment The author is grateful to Dr. John R. Cable,
Bowling Green State University, Ohio, for his generous support of
this work.
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The large difference in the exciton coupling energies of
the two conformers is attributed to through-space interac-
tions. Effective orbital overlap of the two aromatic rings of
the compact TB conformer enhances through-space inter-
actions of the two aromatic chromophores. Through-bond
interactions generally depend on the number of r bonds
between the chromophores, and the energy gap between the
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be similar in the two THDC conformers. For instance, the
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