Electron-transfer reorganization energies of isolated organic molecules

Article abstract of DOI:10.1021/jp014148w

He I photoelectron spectra of phenanthrene (1), 1,10-phenanthroline (2), phenazine (3), dibenzo[a,c]anthracene (4), dibenzo[a,c]phenazine (5), and dipyrido[3,2-a;2′3′-c]phenazine (6) have been obtained. Assignment of the π ionization states was aided by electronic structure calculations: the first ionization state of 1, ²B₁(π₁), is observed at 7.888 ± 0.002 eV, ²B₂(π₁) of 2 is at 8.342 ± 0.002 eV, and ²B_1g(π₁) of 3 is at 8.314 ± 0.002 eV. Spectra of 4-6 are reported for the first time: ²A₂(π₁) of 4 is at 7.376 ± 0.002 eV, and both 5 (7.983 ± 0.002 eV) and 6 (8.289 ± 0.002 eV) exhibit quasi-degenerate first and second ionization states. Quantum-mechanical reorganization energies, λ^QM, were extracted from analyses of vibrational structure: values are 149 ± 5 (1), 167 ± 5 (2), 68 ± 2 (3), and 92 ± 4 (4) meV. Low-frequency modes were treated semiclassically: values of λ^SC are estimated to be 21 ± 1 (1), 13 ± 1 (2), 22 ± 1 (3), 66 ± 1 (4), 27 ± 9 (5), and 16 ± 1 (6) meV. Reorganization energies (λ = λ^QM + λ^SC) of isolated molecules are 170 ± 5 (1), 180 ± 5 (2), 90 ± 2 (3), and 158 ± 4 (4) meV. Density functional calculations (B3LYP/6-311G++(d,p)) give λ values that are on average 63 meV lower than experimentally derived energies.

Full text of DOI:10.1021/jp014148w

J. Phys. Chem. A 2002, 106, 7593-7598
7593
Electron-Transfer Reorganization Energies of Isolated Organic Molecules†
‡
,‡
,‡
§
Xenia Amashukeli, Jay R. Winkler,* Harry B. Gray,* Nadine E. Gruhn, and
Dennis L. Lichtenberger*,§
DiVision of Chemistry and Chemical Engineering and the Beckman Institute, California Institute of Technology,
Pasadena, California 91125, and Department of Chemistry, UniVersity of Arizona, Tucson, Arizona 85721
ReceiVed: NoVember 13, 2001; In Final Form: February 20, 2002
He I photoelectron spectra of phenanthrene (1), 1,10-phenanthroline (2), phenazine (3), dibenzo[a,c]anthracene
(
4), dibenzo[a,c]phenazine (5), and dipyrido[3,2-a;2′3′-c]phenazine (6) have been obtained. Assignment of
2
the π ionization states was aided by electronic structure calculations: the first ionization state of 1, B
is observed at 7.888 ( 0.002 eV, B
eV. Spectra of 4-6 are reported for the first time: A
1
(π
1
),
2
2
2
(π
1
) of 2 is at 8.342 ( 0.002 eV, and B1g(π
1
) of 3 is at 8.314 ( 0.002
(π ) of 4 is at 7.376 ( 0.002 eV, and both 5 (7.983
0.002 eV) and 6 (8.289 ( 0.002 eV) exhibit quasi-degenerate first and second ionization states. Quantum-
2
2
1
(
QM
mechanical reorganization energies, λ , were extracted from analyses of vibrational structure: values are
49 ( 5 (1), 167 ( 5 (2), 68 ( 2 (3), and 92 ( 4 (4) meV. Low-frequency modes were treated
1
SC
semiclassically: values of λ are estimated to be 21 ( 1 (1), 13 ( 1 (2), 22 ( 1 (3), 66 ( 1 (4), 27 ( 9 (5),
and 16 ( 1 (6) meV. Reorganization energies (λ ) λ + λ ) of isolated molecules are 170 ( 5 (1), 180
QM
SC
(
5 (2), 90 ( 2 (3), and 158 ( 4 (4) meV. Density functional calculations (B3LYP/6-311G++(d,p)) give
λ values that are on average 63 meV lower than experimentally derived energies.
Introduction
SCHEME 1
Electron-transfer reactions are key steps in a vast array of
1
chemical and biological processes. According to semiclassical
theory, the rates of these reactions in solution are governed by
three fundamental parameters: the reorganization energy, λ
(
where λ ) λi + λo, the inner- and outer-sphere contributions);
the electronic coupling matrix element, HAB, and the standard
free energy change, ∆G°. Both theoretical and experimental
2
investigations suggest that the solvent contribution (λo) to the
reorganization energy is much larger in most cases than the
inner-sphere contribution (λi). It also has been shown that the
3
ratio λo/λi decreases with decreasing solvent polarity. The
limiting case is a reaction in the absence of bulk solvent, as
occurs in the gas phase.4
In this paper, we report reorganization energies that were
extracted from analyses of the photoelectron spectra of six
isolated organic molecules: phenanthrene (1), 1,10-phenan-
throline (2), phenazine (3), dibenzo[a,c]anthracene (4), dibenzo-
hemispherical analyzer (McPherson). The ionization source,
detection, and control electronics have been described in detail
[a,c]phenazine (5), and dipyrido[3,2-a;2′3′-c]phenazine (6)
6,7
elsewhere. The ionization energy scale was calibrated using
(Scheme 1). These particular molecules were selected because
2
the E1/2 ionization of methyl iodide (9.538 eV), with the Ar
they are often employed as redox active components in donor-
2
P3/2 ionization (15.759 eV) used as an internal energy scale
bridge-acceptor systems.5
lock during data collection. During data collection, the instru-
ment resolution, measured as full-width-at-half-maximum of the
Experimental Section
2
Ar P3/2 ionization, was 0.019-0.025 eV for 1-4 and 6 and
0
.033 eV for 5. Since the He I discharge source is not
Materials. 1-4 were obtained from Aldrich. 5 was prepared
by refluxing 9,10-phenanthrenequinone (3 mmol) and 1,2-
diaminobenzene (3 mmol) in dry methanol. A sample of 6 was
kindly provided by Sarah Delaney (Caltech).
Photoelectron Spectroscopy. He I photoelectron spectra were
recorded using an instrument with a 36-cm diameter, 8-cm gap
8
2
monochromatic, the spectra collected with He IR (1s r 1s2p,
2
2
2
1.218 eV) source were corrected for He Iâ line (1s r 1s3p,
3.085 eV, and 3% of the intensity of the He IR line). Data
-
4
collection temperatures (∼10 Torr, monitored using a “K”
type thermocouple passed through a vacuum feed and attached
directly to the ionization cell): phenanthrene, 47-58 °C; 1,-
10-phenanthroline, 102-108 °C; phenazine, 63-83 °C; dibenzo-
†
Part of the special issue “G. Wilse Robinson Festschrift”.
California Institute of Technology.
University of Arizona.
‡
§
[a,c]anthracene, 141-152 °C; dibenzo[a,c]phenazine, 156-172
°C; dipyrido[3,2-a;2′3′-c]phenazine, 183-201 °C.
1
0.1021/jp014148w CCC: $22.00 © 2002 American Chemical Society
Published on Web 04/10/2002

7
594 J. Phys. Chem. A, Vol. 106, No. 33, 2002
Amashukeli et al.
TABLE 2: Selected Vibrational Frequencies (cm-1)
TABLE 1: Ionization Energies (eV)
IE(calcd,
IE(obsd)
(ref 18)
molecule mode ν(calcd) neutral ν(calcd) cation ν(obsd) neutral
bands
(π
IE(obsd)a IE(calcd, raw)b compressed)c
a
1
23a
22a
21a
11a
10a
1
1
1
1
1
242
405
549
1356
1426
1441
237
244
401
547
1365
1417
1430
233
247
a
b
1
408 /398
a
1
1
)
7.888
8.289
9.277
9.872
7.751
8.059
9.556
7.888
8.123
9.276
9.940
7.87
(8.30)d
9.28
548
a
b
b
2
(π
2
)
1352 /1340
1431
a,b
2
(π
(π
3
)
)
a
4
10.429
9.90
9a
21a
0a
1
1443 /1446
c
2
1
1
1
1
249
408
550
2
8.227
8.643
c
2
408
554
399
547
2
(π
1
8.342
8.523
(9.433)
8.342
8.662
8.35
c
(8.82)d
19a
10a
2
(π
c
d
d
1349
1387
1450
1282
1406
1481
579
1328
1389
1416
1268
1395
1486
573
1343
1404
1444
1280
1403
1479
9.39
c
9
a
1
c
3
8.150
8.703
9.765
8a1
6ag
5ag
4ag
d
B
B
A
1g (π
2g (π
1
)
8.314
8.928
9.519
8.314
8.739
9.556
8.33
(9.06)d
9.56
3
4
d
2
)
d
u
(π
3
)
σ
N
(9.158)
9.2
32a1
3
3
1
1
1
1a
0a
7a
6a
5a
1
1
1
1
1
632
701
1337
1372
1405
624
704
1356
1384
1404
4
7.250
7.808
8.325
9.539
9.862
10.502
A
2
(π
2
1
)
)
7.376
7.880
8.254
9.114
9.367
9.899
7.376
7.805
8.203
9.137
9.385
9.877
B
1
(π
1360e
A
A
2
(π
(π
3
)
)
2
4
B
B
1
(π
(π
5
)
)
a
Polarized IR/Raman spectra of single-crystal phenanthrene (ref 19).
1
6
b
Gas-phase IR spectra of phenanthrene (ref 20). c Polarized IR/Raman
d
5
8.007
8.052
8.651
9.719
10.143
10.691
spectra of single-crystal 1,10-phenanthroline (ref 21). Polarized Raman
spectra of single-crystal phenazine (ref 22). e IR spectra of thin solid
films of dibenzo[a,c]anthracene (ref 23).
A
2
(π
1
)
)
7.983
7.983
8.018
8.478
9.300
9.626
10.048
B
1
(π
(π
(π
2
A
A
2
3
)
)
8.589
9.318
9.676
2
4
B
B
1
(π
(π
5
)
)
1
6
10.016
6
8.332
8.335
9.289
10.567
10.888
A
2
(π
1
)
)
8.289
8.289
8.291
9.025
10.008
10.255
B
1
(π
(π
(π
2
A
A
2
3
)
)
9.106
9.997
10.265
2
4
B
1
(π
5
)
a
Vertical ionizations; this work. The error in the ionization energy
measurements was determined by fitting 12 individual scans of the
photoelectron spectra of 1 with a series of Gaussian functions. Since
all the measurements were carried out under similar conditions and
the instrument resolution was nearly the same in all cases, the same
error, (0.002, was applied to the rest of the ionization energy values.
b
Calculated using RHF/6-311G++(2d,2p). c Calculated values are
shifted to match the first ionization energy and compressed by a factor
of 1.3 (ref 16). Tentative experimental assignment.
d
Computational Details. Electronic structure calculations
were carried out using Jaguar 4.19 and GAUSSIAN 98
programs. The geometries of all the molecules were optimized
using the Becke three-parameter Lee-Yang-Parr functional
10
(
B3LYP) and 6-31G(d,p) basis sets. B3LYP consists of the
Figure 1. He I photoelectron spectra: (a) phenanthrene (1); (b) 1,-
10-phenanthroline (2); (c) phenazine (3). Experimental data (‚‚‚) are
fit with Gaussian functions (-) on a baseline (‚‚‚) giving total fit (-).
11
hybrid exchange functional proposed by Becke and the Lee-
Yang-Parr12 correlation functional. Reorganization energies
were calculated using B3LYP/6-311G++(2d,2p) level of theory.
Ionization energies were estimated from restricted Hartree-
Fock (RHF) calculations with a 6-311G++(2d,2p) basis set
the peak height, p is the peak position, H is the average
1
4
full-width at half-maximum, and R is 4 ln(2)). Sums of the
Gaussian functions gave fits to the experimental data. Ionization
energies of 1-6 are set out in Table 1. The bands were assigned
to the ionization of π- or σN-electrons, where σN is the nitrogen
(Table 1). Vibrational frequencies were calculated using B3LYP/
6
0
-31G(d,p) and scaled by 0.987 (for low-frequency modes) and
.973 (for high-frequency modes) (Table 2).13
1
5
lone pair state. Koopmans’ theorem aided the assignment of
π-states. To compensate for the relaxation and electronic
correlation effects that are neglected by Koopmans’ theorem,
the calculated energies were shifted to match the first experi-
mental ionization energies and then compressed by the factor
Results
Photoelectron spectra. He I spectra of 1-6 are shown in
Figures 1 and 2. The data were fit with a series of Gaussian
functions (eq 1, in which A is
16
of 1.3. σN-states were assigned on the basis of comparisons
between diaza molecules and their carbon analogues. The σN-
(
hν - p) 2
state in the phenazine spectrum was identified by comparison
T ) A exp(-R)[
(1)
]
H
17
to the previously reported anthracene photoelectron spectrum.

ET Reorganization Energies of Organic Molecules
J. Phys. Chem. A, Vol. 106, No. 33, 2002 7595
Figure 3. Low binding energy region in He I photoelectron spectrum
of 1. Experimental data (‚‚‚) are fit with Gaussian functions corre-
sponding to vibrational progressions (s) used in λ calculation, and π
2
ionization (- - -) on a baseline (‚‚‚). Other Gaussian functions (-)
describe spectral features of π
Figure 2. He I photoelectron spectra: (a) dibenzo[a,c]anthracene (4);
1
.
(
b) dibenzo[a,c]phenazine (5); (c) dipyrido[3,2-a; 2′3′-c]phenazine (6).
Experimental data (‚‚‚) are fit with Gaussian functions (-) on a baseline
‚‚‚) giving total fit (s).
(
Since σN bands are broad, featureless, and low intensity, their
assignment is tentative. The σN-states in 5 and 6 were not
assigned due to spectral congestion. The first two ionizations
of 5 are nearly degenerate; the bands are poorly resolved (the
first band is at 7.983 ( 0.002 eV). Calculations suggest that
the first and second ionizations of 6 are separated by 3 meV.
These two bands, which were not experimentally resolved, are
assigned an average value of 8.238 ( 0.002 eV.
Quantum-Mechanical Analysis (λQM). Quantum-mechanical
analysis of fine structure in the spectra yielded distortion
QM
parameters (S), which are related to λ according to eq 2 (h is
QM
λ
)
Skhνk
(2)
∑
k
Planck’s constant and νk is the vibrational frequency of mode
1
8
k). The first ionization bands in the spectra of 1-6 exhibit
vibrational progressions (Figures 3-8). The bands in each
spectrum were fit with a series of Gaussian functions; widths
Figure 4. Low binding energy region in He I photoelectron spectrum
of 2. Experimental data (‚‚‚) are fit with Gaussian functions corre-
sponding to vibrational progressions (s) used in λ calculation, and π
2
and π
3
ionizations (- - -) on a baseline (‚‚‚). Other Gaussian functions
(H) of the vibrational components in each progression were kept
(
-) describe spectral features of π .
1
fixed for molecules 1-4. In all cases, hot bands were included
as part of the fitting procedure.
Poisson distribution (eq 3, where In is the intensity of the nth
The first ionization band of 1 exhibits a high-frequency
-1
progression (1455 ( 34 cm ) corresponding to the 10a1 mode,
n
In ) e-S
S
n!
(3)
-1
and a low-frequency progression (379 ( 34 cm ) arising from
the 22a1 mode (Table 3). The first ionization band of 2 exhibits
two vibrational progressions similar to those observed for 1: a
vibrational band).24 Since only the first two vibrational bands
are well-resolved, the values of S were extracted from the ratio
of I1 to I0. The results are summarized in Table 3. According
to the RHF/6-311G++(2d,2p) calculation (Table 1), the first
and second ionization energies of 5 are nearly the same; although
vibrational structure is present in the spectrum, it is difficult to
determine the mode to which it corresponds. Thus, values of S
were not obtained for this molecule. Similar problems compli-
cated the analysis of the photoelectron spectrum of 6.
-
1
high-frequency progression with a spacing of 1461 ( 34 cm
-
1
and a low-frequency progression spaced by 420 ( 34 cm .
The first ionization band of 3 exhibits a well-resolved vibrational
-
1
progression spaced by 1415 ( 34 cm corresponding to the
ag mode (Table 3). The first ionization band of 4 is similar to
those observed in the 1 and 2 spectra: a high-frequency
progression (1357 ( 34 cm ) corresponding to the 16a1 mode
and a low-frequency progression (632 ( 34 cm ) attributable
5
-
1
-
1
to the 31a1 mode (Table 3).
SC
We assume that the intensities of the individual Gaussian
Semiclassical Analysis (λ ). Distortions along low-fre-
bands in each vibrational progression (Figures 3-6) follow a
quency modes and small frequency changes between the neutral

7596 J. Phys. Chem. A, Vol. 106, No. 33, 2002
Amashukeli et al.
Figure 5. Low binding energy region in He I photoelectron spectrum
of 3. Experimental data (‚‚‚) are fit with Gaussian functions corre-
sponding to vibrational progressions (s) used in λ calculation on a
baseline (‚‚‚). Other Gaussian functions (-) describe spectral features
Figure 7. Low binding energy region in He I photoelectron spectrum
of 5. Experimental data (‚‚‚) are fit with Gaussian functions corre-
sponding to π ionizations (- - -) on a baseline (‚‚‚). Only one Gaussian
3
function (s) is used in λ calculation. Other Gaussian functions (-)
describe spectral features of π and π
of π
1
.
1
2
.
Figure 6. Low binding energy region in He I photoelectron spectrum
of 4. Experimental data (‚‚‚) are fit with Gaussian functions corre-
Figure 8. Low binding energy region in He I photoelectron spectrum
of 6. Experimental data (‚‚‚) are fit with Gaussian functions corre-
sponding to vibrational progressions (s) used in λ calculation, and π
2
sponding to π ionizations (- - -) on a baseline (‚‚‚). Only one Gaussian
3
and π
3
ionizations (- - -) on a baseline (‚‚‚). Other Gaussian functions
function (s) is used in λ calculation. Other Gaussian functions (-)
describe spectral features of π and π .
(
-) describe spectral features of π .
1
1
2
SC
and cation states (Table 2) can contribute to the breadth of
individual vibronic lines in photoelectron spectra. Such band
profiles are treated semiclassically (eq 4, IE is the ionization
line-shape function and is related to λ , according to eq 6. The
results are summarized in Table 4.
2
SC
H
2
SC
2
-(hν-IE) /4kBTλ
λ
)
(6)
G ) |D| e
(4)
1
6 ln(2) kBT
energy and D is related to the transition moment).24 The
Gaussian functions, T(ν) (eq 1), that were used to fit the
experimental spectra are convolutions of G (eq 4) and another
Gaussian function, R, defined by the resolution of the instrument
Reorganization Energies. Calculations employed B3LYP/
-31G(d,p) optimized geometries. B3LYP/6-311G++(2d,2p)
6
single-point energies were calculated for four cases: (1) neutral
optimized geometry, charge zero, and singlet multiplicity; (2)
neutral geometry, charge plus one, and doublet multiplicity; (3)
radical cation geometry, charge zero, and singlet multiplicity;
and (4) radical cation geometry, charge plus one, and doublet
multiplicity (Figure 9). The energy difference between (1) and
2
5
(eq 5).
ν
T(ν) )
∫
G(x) R(x - ν) dx
(5)
0
0
•+
The value of H (the average full-width at half-maximum)
for G was obtained by iterative reconvolution of the observed
(3) is λ , and the energy difference between (4) and (2) is λ .
The latter parameter is compared to experimentally derived

ET Reorganization Energies of Organic Molecules
J. Phys. Chem. A, Vol. 106, No. 33, 2002 7597
TABLE 3: Vibrational Frequencies (cm-1) and Quantum-Mechanical Reorganization Energies (meV)
mode
ν(obsd)a
ν(calcd)b
ν(obsd)c
Sd
λQM
1
2
22a
0a
20a
1
1
1
379 ( 34
1455 ( 34
420 ( 34
1461 ( 34
1415 ( 34
632 ( 34
1357 ( 34
405
1426
408
1450
1406
632
408/398
1431
408
1444
1403
0.692 ( 0.020
0.636 ( 0.020
0.75 3( 0.016
0.706 ( 0.015
0.387 ( 0.008
0.334 ( 0.014
0.393 ( 0.015
33 ( 3
115 ( 4
39 ( 3
128 ( 4
68 ( 2
26 ( 2
66 ( 3
1
8
a
1
3
4
5a
g
31a
6a
1
1
1
1372
1360
a
This work. b Calculated using B3LYP/6-31G(d,p). c See Table 2. d The values of S were obtained according to the expression: S ) (I
1
(
∆
I
1
)/(I ( ∆I ), where ∆I is the square root of I
0
0
n
n
.
TABLE 4: Experimental and Calculated Reorganization
Energies (meV)
accord with calculated and experimental frequencies for the
neutral molecules (Table 2). The frequency of the 22a1 mode
in the spectrum of 1 is in excellent agreement with gas-phase
IR data and DFT calculations. The high-frequency vibrational
spacing corresponding to the 10a1 mode also accords with
experimental results and calculations.
Since the only difference between 1 and 2 is the presence of
nitrogen atoms in ring positions 1 and 10, it is reasonable to
expect that similar vibrational modes will be observed in the
spectra of these molecules. Indeed, the 20a1 mode in the
spectrum of 2 corresponds to the 22a1 mode of 1. Moreover,
the observed frequency is in good agreement with experimental
and computational results. The high-frequency progression in
molecule
λQM
λSC
λ
λ•+ λ0 λtotal
2λa
20
1
2
3
4
5
6
149 ( 5 21 ( 1
167 ( 5 13 ( 1
68 ( 2 22 ( 1
170 ( 5 107 105 212
180 ( 5 129 143 272
340 ( 5
360 ( 5
180 ( 2
316 ( 4
90 ( 2
54 77 131
57 65 122
92 ( 4 66 ( 1
154 ( 4
b
b
71 76 147 (e254 ( 9)b
61 60 121 (e232 ( 1)b
(e100) 27 ( 9 (e127 ( 9)
b
b
(e100) 16 ( 1 (e116 ( 1)
a
Twice the observed reorganization energy for the self-exchange
b
reaction. Tentative assignment.
-
1
2
is spaced by 1461 ( 34 cm , which is in excellent agreement
with the 8a1 experimental and calculated vibrational frequencies
Table 2). The vibrational frequency of the 9a1 mode of 2,
however, corresponds to the observed 10a1 mode in the spectrum
(
2
1
-1
of 1. The experimental frequency of 9a1 in 2 is 1404 cm
the calculated value is 1387 cm ). Given the relative error in
-
1
(
the spacing of the high-frequency progression in the spectrum
of 2, the assignment to 9a1 is tentative. Unlike the 10a1 mode
-
1
of 1, however, there is only a 2 cm difference between
calculated 9a1 vibrational frequencies for the neutral and cation
states of 2 (Table 2). For the 8a1 mode of 2, the difference
-
1
between neutral and cation states is 34 cm . On the basis of
these observations, we assign the observed high-frequency
progression in the spectrum of 2 to 8a1, even though it does
not correspond to the 10a1 mode of 1.
A well-resolved vibrational progression in the spectrum of 3
corresponds to the 5ag mode. Low-frequency progressions are
also observed (Figure 5) and are used to fit the experimental
data. These vibrational lines, however, are poorly resolved and
were not used to estimate the reorganization energy.
Figure 9. Potential energy surfaces of neutral and cation states that
define λ and λ .
•
+
0
The only five-ring molecule in the series that has a well-
resolved high-frequency progression is 4. We assign this
-
1
values of λ in Table 4. The total reorganization energy, λtotal,
progression (spaced by 1357 ( 34 cm ) to the 16a1 mode,
QM
•
+
•+
•+
0
and the low-frequency progression to 31a1. We estimate λ
for the A + A a A + A process is the sum of λ and λ
Table 4).
QM
to be 92 ( 4 meV, which is lower than λ for 1 or 2. We
(
SC
SC
estimate λ to be 66 ( 1 meV, which is larger than λ for 1,
SC
2
, or 3. If λ is overestimated, it would explain the significant
Discussion
difference, 101 meV, between experimental and calculated
reorganization energies.
Excellent agreement was obtained between experimental and
calculated ionization energies for molecules 1 through 6 (Table
Since the first and second ionization bands overlap in the
QM
1). Koopmans’ theorem gives raw calculated values for the first
photoelectron spectra of 5 and 6, values of λ
were not
ionization energies that are roughly 0.1 eV lower than the
experimental results. Shifting ionization energies such that the
first experimental and calculated ionization energies are the same
and then compressing the results by the factor of 1.3 produces
excellent agreement (within 0.068-0.010 eV) with the experi-
mental values.
obtained. Semiclassical band shape analyses give 27 ( 9 meV
QM
for 5 and 16 ( 1 meV for 6. We assume that λ is not greater
than 100 meV. Therefore, we expect the total reorganization
energy for 5 or 6 not to exceed 120-130 meV.
•
+
Calculated λ values are lower than their experimental
counterparts (Table 4). The best agreement is for 3, where the
difference between experimental and calculated parameters is
only 36 meV. Computational results reproduce experimental
Quantum-mechanical analyses of the first ionization bands
QM
of compounds 1-4 gave λ
values (Tables 3 and 4). The
•
+
values for the vibrational spacings in the photoelectron spectra
trends in λ values (Table 4): λ and λ for the three-ring

7598 J. Phys. Chem. A, Vol. 106, No. 33, 2002
Amashukeli et al.
molecules are larger than those for the five-ring systems, with
(3) Miller, J. R.; Closs, G. L. Science 1988, 240, 440-447.
4) (a) Chattoraj, M.; Laursen, S. L.; Paulson, B.; Chung, D. D.; Closs,
G. L.; Levy, D. H. J. Phys. Chem. 1992, 96, 8778-8784. (b) Jortner, J.;
Bixon, M.; Wegewijs, B.; Verhoeven, J. W.; Rettschnick, R. P. H. Chem.
Phys. Lett. 1993, 205, 451-455. (c) Shou, H.; Alfano, J. C.; van Dantzig,
N. A.; Levy, D. H.; Yang, N. C. J. Chem. Phys. 1991, 95, 711-713. (d)
Brenner, V.; Millie, P.; Piuzzi, F.; Tramer, A. J. Chem. Soc., Faraday Trans.
(
the exception of 3. Ring systems containing heteroatoms exhibit
•
+
larger λ and λ values than their carbon analogues.
•
+
0
Calculated values of λ and λ are similar for 1-6 (Table
4
), indicating that curvatures of the energy surfaces are
equivalent for equilibrium geometries of neutral molecules and
cations. We assume that curvatures of experimental parabolic
surfaces for the neutral and cation species also are the same;
therefore, total reorganization energies for the self-exchange
1
997, 93, 3277-3287. (e) Tramer, A.; Brenner, V.; Millie, P.; Piuzzi, F. J.
Phys. Chem. A 1998, 102, 2798-2807. (f) Van Dantzig, N. A.; Shou, H.;
Alfano, J. C.; Yang, N. C.; Levy, D. H. J. Chem. Phys. 1994, 100, 7068-
7
078.
(5) Balzani, V., Ed. Electron Transfer in Chemistry; Wiley-VCH Verlag
•
+
•+
electron-transfer reaction, A + A a A + A, are 2λ (Table
). With the assumption that solvent molecules do not perturb
any of the internal modes involved in the self-exchange reaction,
λ is the same as λi. The value of 2λ for 1 is 340 meV, and λi
GmbH: D-69469 Weinheim, Germany, 2001; Vol. 3, Part 2, p 177.
(6) Lichtenberger, D. L.; Kellogg, G. E.; Kristofzski, J. G.; Page, D.;
Turner, S.; Klinger, G. Lorenzen, J. ReV. Sci. Instrum. 1986, 57, 2366.
4
(7) Renshaw, S. K. Ph.D. Dissertation, University of Arizona, 1992.
2
(8) Turner, D. W.; Baker, C.; Baker, A. D.; Brundle, C. R. Molecular
for intramolecular electron transfer between phenanthrene and
Photoelectron Spectroscopy; Wiley-Interscience: London, 1970.
(9) Jaguar Version 4.0; Schr o¨ dinger Inc.: Portland, OR, 1999.
(10) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb,
M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.;
Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A.
D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi,
M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.;
Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick,
D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.;
Ortiz, J. V.; Baboul, A. G.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz,
P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-
Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P.
M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Gonzalez, C.;
Head-Gordon, M.; Replogle, E. S.; and Pople, J. A. GAUSSIAN 98, Revision
A.9; Gaussian, Inc.: Pittsburgh, PA, 1998.
3
the biphenyl anion radical is 450 meV. Assuming that the
reorganization energy of biphenyl is not greater than that of
phenanthrene, λi for this reaction is only slightly higher than
predicted from our results.
To extend the analysis to a single-ring system, we examined
2
6
the reported He I photoelectron spectrum of benzene. Unlike
-6, benzene has degenerate HOMOs and the first ionization
energy is due to the removal of an electron from the 1e1g π
1
2
7
28
orbital. Owing to the Jahn-Teller effect, vibrational structure
in the benzene spectrum is complex: the first band exhibits a
strong adiabatic transition followed by short and weak progres-
2
6
sions, indicative of a small geometry change upon ionization.
Treating the spectrum as for 1-6, we estimate that λ does not
exceed 100 meV. Calculations of the reorganization energy of
(11) Becke, A. D. J. Chem. Phys. 1993, 98, 5648-5652.
(
(
12) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785-789.
13) There is a simple procedure for scaling the raw calculated values
(
1
Martin, J. M. L.; El-Yazal, J.; Francois, J.-P. J. Phys. Chem. 1996, 100,
5358-15367) that accounts for anharmonicities provided that no strong
•
-
benzene anion formation indicate that λ is in the range 289-
1
58 meV,29 and reported changes in the bond lengths for the
Fermi resonances exist. We use ratios of computed to experimental
frequencies of anthracene and phenanthrene as the desired scaling factors
and report that they cluster in three groups: an average ratio of 0.956 for
the C-H stretches; an estimated ratio of 0.973 for the in-plane bends; and
an average ratio of 0.987 for the low-frequency in-plane vibrations. These
scaling factors are then applied to the raw calculated frequencies of other
molecules.
2
9
negative ion are almost the same as for the positive ion,
a
•
+
•-
finding supporting the assumption that λ ≈ λ . The value of
•-
29
λ
for anthracene is in the range 67-86 meV, which agrees
•+
well with our DFT calculation of λ , 57 meV, and experimental
•
-
λ, 90 meV, of 3. Since λ for anthracene is nearly the same as
(
14) Lichtenberger, D. L.; Copenhaver, A. S. J. Electron Spectrosc. Relat.
Phenom. 1990, 50, 335-352.
(15) Koopmans, T. Physica 1933, 1, 104.
•+
•-
λ
and λ of 3, and λ for benzene is slightly larger than 100
meV, our estimate of λ for benzene is reasonable. What is more,
it is consistent with resonance Raman experiments of Myers
and co-workers on the hexamethylbenzene/tetracyanoethylene
complex, where the reorganization energy of specific modes
(
16) Cornil, J.; Vanderdonckt, S.; Lazzaroni, R.; dos Santos, D. A.; Thys,
G.; Geise, H. J.; Yu, L.-M.; Szablewski, M.; Bloor, D.; L o¨ gdlund, M.;
Salaneck, W. R.; Gruhn, N. E.; Lichtenberger, D. L.; Lee, P. A.; Armstrong,
N. R.; and Br e´ das, J. L. Chem. Mater. 1999, 11, 2436-2443.
(17) Hush, N. S.; Cheung, A. S.; Hilton, P. R. J. Electron Spectrosc.
Relat. Phenom. 1975, 7, 385-400.
3
0
localized on hexamethylbenzene is estimated to be 129 meV.
(
18) Brunschwig, B. S.; Sutin, N. Comments Inorg. Chem. 1987, 6, 209-
35.
Concluding Remarks
2
(
19) Bree, A.; Solven, F. G.; Vilkos, V. V. B. J. Mol. Spectrosc. 1972,
We have shown that mode-specific quantum-mechanical and
semiclassical analyses of ionization band profiles can be used
to determine electron-transfer reorganization energies for isolated
molecules. Experimentally derived λ values for 1-6 are in the
range 90-180 meV and are on average 63 meV higher than
the DFT results. Reorganization energies of five-ring systems
are slightly lower that those for three-ring systems. Analysis of
the photoelectron spectrum of benzene yields λ e 100 meV.
4
4, 298-319.
(
20) Cane, E.; Miani, A.; Palmieri, P.; Tarroni, R.; Trombetti, A.
Spectrochim. Acta A 1997, 53, 1839-1851.
(21) Perkampus, H.-H.; Rother, W. Spectrochim. Acta A 1974, 30, 597-
6
2
10.
(
26.
22) Durnick, T. J.; Wait, S. C., Jr. J. Mol. Spectrosc. 1972, 42, 211-
(
23) Orr, S. F. D.; Thompson, H. W. J. Chem. Soc. 1950, 218-221.
(24) Ballhausen, C. J. Molecular Electronic Structures of Transition
Metal Complexes; McGraw-Hill: U.K., 1979; p 125.
25) Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T.
(
Acknowledgment. This work was supported by NSF (CHE-
Numerical Recipes, The Art of Scientific Computing, (Fortran Version);
Cambridge University Press: New York, 1989; p 383.
(26) Karlsson, L.; Mattson, L.; Jadrny, R.; Bergmark, T.; Siegbahn, K.
Phys. Scr. 1976, 14, 230-241.
0
078809: H.B.G., J.R.W.; CHE-0078457: D.L.L.) and DOE
(DE-FG03-95ER14574: D.L.L.).
(27) Hollas, J. M. Modern Spectroscopy, 3rd ed.; John Wiley & Sons
References and Notes
Ltd: Chichester, U.K., 1996; p 270.
(
1) Balzani, V., Ed. Electron Transfer in Chemistry; Wiley-VCH Verlag
GmbH: D-69469 Weinheim, Germany, 2001; Vols. 1-5.
2) Marcus, R. A.; Sutin, N. Biochim. Biophys. Acta 1985, 811, 265-
(28) Jahn, H. A.; Teller, E. Proc. R. Soc. A 1937, 161, 220-235.
(29) Klimk ja ns, A.; Larsson, S. Chem. Phys. 1994, 189, 25-31.
(30) Markel, F.; Ferris, N. S.; Gould, I. R.; Myers, A. B. J. Am. Chem.
Soc. 1992, 114, 6208-6219.
(
22.
3