Model systems for the investigation of the Opsin shift in Bacteriorhodopsin

Article abstract of DOI:10.1021/jp904132f

Donor-acceptor substituted styrenes and phenylbutadienes with substituents varying in donor and acceptor strength and as reconstituted chromophore-protein complexes were investigated as model compounds for the protonated Schiff base chromophore in bacteriorhodopsin (bR) both experimentally and theoretically. Charge distribution, donor-acceptor strength, and the shift of the absorption energy are correlated. The effect of the external electrostatic field was tested with a compound carrying an additional nonconjugated charge. The concept of overpolarization by the external charge, that is, the reversal of the relative importance of the two main resonance structures in S₀ and Si ₁, has been emphasized and related to a simple qualitative 2 × 2 interaction model. The variable donor approach is a new way for a better understanding of the Opsin shift in Bacteriorhodopsin.

Full text of DOI:10.1021/jp904132f

J. Phys. Chem. A 2010, 114, 2179–2188
2179
Model Systems for the Investigation of the Opsin Shift in Bacteriorhodopsin
Lars Lasogga and Wolfgang Rettig*
Institut fu¨r Chemie, Humboldt-UniVersita¨t zu Berlin, 12489 Berlin, Germany
Harald Otto and Ingrid Wallat
Institut fu¨r Experimentalphysik, Freie UniVersita¨t Berlin, 14195 Berlin, Germany
Julia Bricks
Institute of Organic Chemistry NASU, KieV 02094, Ukraine
ReceiVed: May 4, 2009; ReVised Manuscript ReceiVed: NoVember 16, 2009
Donor-acceptor substituted styrenes and phenylbutadienes with substituents varying in donor and acceptor
strength and as reconstituted chromophore-protein complexes were investigated as model compounds for
the protonated Schiff base chromophore in bacteriorhodopsin (bR) both experimentally and theoretically.
Charge distribution, donor-acceptor strength, and the shift of the absorption energy are correlated. The effect
of the external electrostatic field was tested with a compound carrying an additional nonconjugated charge.
The concept of overpolarization by the external charge, that is, the reversal of the relative importance of the
two main resonance structures in S0 and S1, has been emphasized and related to a simple qualitative 2 × 2
interaction model. The variable donor approach is a new way for a better understanding of the Opsin shift in
Bacteriorhodopsin.
Introduction
the H-bond network is of minor importance as concluded in
refs 4, 5, and 11.
One of the most discussed questions in the mechanism of
vision is the reason for the bathochromic shift in the spectra of
the chromophore: whereas the unbound free chromophore has
an absorption maximum near the blue end of the visible
spectrum, the absorption maximum is red-shifted for the
chromophore bound to the protein via a protonated retinal Schiff
base linkage (PRSB). Recently, X-ray structural data1-3 have
been determined for the visual chromophore Rhodopsin (Rh)
and its closely related bacterial variant Bacteriorhodopsin (bR)
to a sufficient accuracy such that the role of the different amino
acids in the protein backbone and their effect on the absorption
spectra could be simulated by quantum chemical models (see,
e.g., refs 4 and 5). In spite of that, the relative importance of
the different factors determining the Opsin shift, that is, the
absorption difference between the chromophore in solution and
embedded in the protein, is still a matter of controversy.
These factors which are most discussed for the Opsin shift4-6
are (i) the counterion near the Schiff base nitrogen, (ii) the
electrostatic field induced by further charged residues or dipolar
groups within the protein, (iii) the twisting of the chromophore,
and (iv) H-bonding networks.
By following the most important factors (i) and ii), we are
lead to an early model, the so-called external point-charge
model. It postulates that the wavelength shift is induced by an
external charge; that is, charges or dipoles in the surrounding
protein are thought to modify the absorption spectrum.12-15
Many experimental efforts have been devoted to this question,
mostly regarding proteins reconstituted with artificial chro-
mophores related to PRSB. Bridged chromophores were also
used to block some of the important photochemical pathways,16
as well as polar fluorescent probes17 which can yield information
on the electrostatic field within the binding pocket of bR and
Rh.
Especially relevant for the interpretation of the Opsin shift
is the observation of the absorption energy of PRSB in the gas
phase which is red-shifted with respect to that in the protein.18
This indicates that the role of the negative counterion in the
neighborhood of the chromophore is of great importance.
Not only the theoretical understanding of the Opsin shift in
bR and in Rh but also the color shift in the visual color cones
of Rh which discriminate different parts of the visual spectrum
19-22
are intricate problems to solve.
Here, a further parameter
As investigated previously, factor (i), the counterion influence,
seems to be the most important one.4,7-9 It is suggested that
additional ions such as Na+ are possibly playing a role.2 In this
context, factor (ii), the possible negative or positive charges
due to protonation of amino end groups in the surrounding
protein environment, also has to be taken into account.5,9 By
contrast, factor (iii), the twisting, plays a less important role in
bR as indicated by the nearly planar chromophore found for
bR in the X-ray and electron crystallography structure.10 Also
was found to be important. Resonance Raman measurements
indicate that for the blue, green, and red pigments, the
chromophore vibrations correlate with the absorption energy.20,23
A similar correlation is also found when several intermediates
of the reaction cycle are compared.24 The electronic absorption
energy ∆E01 can be correlated with the so-called bond length
alternation (BLA),9 that is, the deviation from the ideal cyanine
behavior where all bonds are of equal length. The correlation
between ∆E01 and BLA is direct evidence for the change of
the electronic distribution induced by the electrostatic field of
* Corresponding author.
10.1021/jp904132f  2010 American Chemical Society
Published on Web 01/19/2010

2180 J. Phys. Chem. A, Vol. 114, No. 5, 2010
Lasogga et al.
TABLE 1: General Structures and Abbreviations of the
Donor and Acceptor Groups of the Model Chromophoresa
a For our study, the compound series n ) 2 was investigated
experimentally (see Table 2a parts 1 and 2).
TABLE 2A: List of Compounds Investigated Both
Experimentally and Theoretically
Figure 1. General structure of the investigated compounds with the
disection into donor and acceptor unit. For the abbreviation of the
substituents, see Table 1.
1. Compounds to Investigate the Influence of Protein Matrix
HPhs2-CHO
HPhs2-SBP+
HPhs2-SBH+sbO
MPhs2-SBH+sbO
HOPhs2-SBH+sbO
MOPhs2-SBH+sbO
DMAPhs2-SBH+sbO
MPhs2-CHO
HOPhs2-CHO
MOPhs2-CHO
DMAPhs2-CHO
MPhs2-SBP+
HOPhs2-SBP+
MOPhs2-SBP+
DMAPhs2-SBP+
the surrounding or of the equivalent effect of donor-acceptor
substituents on the chromophore.25
An open point in the relation of X-ray structures and protein-
induced fields is the presence of water molecules close to the
chromophore.2 They can lead to protonation or deprotonation
of amino acids in the neighborhood, and the X-ray studies may
be subject to some uncertainty regarding the ionization state of
the relevant amino acids.
2. Compounds to Investigate the Influence of an Additional
Nonconjugated External Charge
MOPhs1-SBP+
MOPhs1-SBPip+
MOPhs1-SBPip+2
TABLE 2B: List of Additional Compounds Investigated
Theoretically
Instead of X-ray-based quantum-chemical calculations, ex-
periments on reconstituted protein complexes can yield a more
direct answer of the in vivo situation. An early study uses the
fluorescence probe PRODAN and compares the results for the
protein complex to the spectra of model compounds carrying
an additional nonconjugated charge, allowing in principle a
direct access to the effective field by comparing the spectral
shifts.17
Related to this study, we use synthetic chromophores here
to create reconstituted Bacterioopsin complexes. In addition to
the approach of Sheves et al.17 which uses model compounds
with external charges, we also change the donor-acceptor
properties of the chromophores. Comparison to solution spectra
and to quantum chemical calculations allows us to understand
the observed shifts on the basis of electrostatic fields induced
by the surrounding and by the donor-acceptor substituents. The
quantum-chemical results enable the analysis of the charge
distribution and indicate that some of the observed spectral shifts
are connected with a reversal of the original charge distribution,
explainable with the exchange of the leading resonance struc-
tures in the ground and excited states.
1. Compounds of the n ) 2 Series with Respect to Table 2a Part 1
HPhs2-SBPip+
MPhs2-SBPip+
HOPhs2-SBPip+
MOPhs2-SBPip+
HPhs2-SBPip+2
MPhs2-SBPip+2
HOPhs2-SBPip+2
MOPhs2-SBPip+2
DMAPhs2-SBPip+ DMAPhs2-SBPip+2
2. Compounds of the n ) 1 Series with Respect to Table 2a Part 2
HPhs1-SBP+
HPhs1-SBPip+
MPhs1-SBPip+
HOPhs1-SBPip+
DMAPhs1-SBPip+
HPhs1-SBPip+2
MPhs1-SBPip+2
HOPhs1-SBPip+2
DMAPhs1-SBPip+2
MPhs1-SBP+
HOPhs1-SBP+
DMAPhs1-SBP+
Synthesis
The aldehydes listed in Table 2a were synthesized according
to the general approach described in ref 26.
In some cases, protecting groups had to be used as described
in detail in ref 27. The corresponding SBP+ salts were prepared
by reacting the substituted aldehydes with pyrrolidine perchlo-
rate in isopropanol.
SBPip+ compounds were prepared by reaction of substituted
aldehydes with commercially available 1-Boc-piperazine (tert-
butyl piperazine-1-carboxylate) followed by cleavage of the
resulting Boc-protected SBPip+ compounds with trifluoroacetic
acid yielding the corresponding SBPip+2 derivatives.
All compounds were purified by column chromatography and/
or recrystallized before use, and their structure was confirmed
by NMR. The synthetic details are described in ref 27.
Experimental Part
A series of donor-acceptor polyenes were synthesized, with
increasing donor strength and some variation of the acceptor
(Figure 1, Table 1). Our study focuses on model chromophores
for protonated Schiff bases with two double bonds in the chain
(n ) 2). The experimental results are contrasted to quantum-
chemical studies which yield the distribution of the positive
charge along the backbone of the chromophores.
A model compound with an additional nonconjugated external
positive charge was also investigated experimentally in order
to analyze more directly the point charge effect, both in an
experimental and a theoretical way.
Spectroscopy
For experimental solution spectra, we used ethanol, DMSO,
THF, and acetonitrile from Merck (Uvasol grade). Absorption
spectra were measured on a Unicam UV4 spectrometer.

Investigation of the Opsin Shift in Bacteriorhodopsin
J. Phys. Chem. A, Vol. 114, No. 5, 2010 2181
The SBP+ compounds are not stable in solution and convert
to the aldehyde. To get more information on this effect, we
investigated the SBP+ compounds by time-resolved absorption
measurements in two solvents (DMSO and THF). The conver-
sion times turned out to be in the order of many hours, whereas
the measurement of spectra took less than 10 min, during which
the conversion changes can be neglected. The time when half the
conversion had occurred was about 5 h in the fastest case.
The fit of the absorption spectra which were corrected for
the solvent background was done by a PeakFit auto fit routine
with a log-normal-4 function.28 For the protein-reconstitution
experiments, Bacterioopsin was harvested from halobacterial
strain JW5 (the retinal deficient mutant) in water29 and regener-
ated at room temperature in the dark with the model chro-
mophores dissolved in ethanol. The reconstitution spectra were
measured on a Shimadzu UVPC 2102 spectrometer. The
reproducibility of the spectra was tested and was satisfactory.
The absorption spectra of the chromophore-protein com-
plexes were evaluated in the following way. The spectra at t0
) 0 were subtracted from the measured spectra at later times,
and the resulting (negative) signals of the time-dependent
difference spectra clearly showed the increasing signal of the
chromophore bound to the protein and the decreasing signal of
the corresponding unbound aldehydes. Fitting was done with
the log-normal-4 function. For detail, see Figure S1 in the
Supporting Information.
It can be deduced from a competition experiment with the
model chromophor MOPhs2-CHO that the binding to the
protein occurs at the binding site of the native chromophore,
and we assume that this also holds for the other model
compounds. For the competition experiment, the chromophore
MOPhs2-CHO was added to the protein in the ratio 1:1. After
the regeneration of the chromophore-protein complex, the
native retinal was added in the ratio 1:1. Therefore, it could be
observed that the model chromophore was replaced by the native
retinal as deduced from the appearance of the spectra of bR
(see Figure S2 in the Supporting Information).
Figure 2. Comparison of the longest-wavelength absorption bands of
the chromophores RDsPhs2-RA with the aldehyde (RA ) CHO, solid
line) and the SBP+ (RA ) SBP+, dashed line) model compounds and
spectra of the reconstituted Bacterioopsin-dye complexes (RA
)
SBH+-bO, dotted line) recovered from a PeakFit analysis for various
donor and acceptor end groups RD and RA. The experiments were done
in EtOH for the CHO and SBP+ compounds and in water for bO. In
the latter case, EtOH is only present in a very small amount.
TABLE 3: Experimental Absorption Maxima of the n ) 2
Series with Neutral and Charged Acceptor Groups RA and
Donors RD of Increasing Atrength and Acceptor End
Groups in Solution and in Protein Matrixc
The reconstitution kinetics were measured for about 72 h.
Calculations
For the quantum-chemical calculations, the GAUSSIAN 03
package was used.30 At first, the molecular structure was
optimized in the ground state by using the AM1 method and
the DFT method. Three sets of calculations were done: (a) the
entire molecule, (b) the donor moiety (D) with the acceptor unit
substituted by H, and (c) the corresponding acceptor moiety
(A) with the donor unit substituted by H (see Figure 1). From
the donor moiety (b) and the acceptor moiety (c), the energies
of the frontier orbitals HOMO(D) and LUMO(A) were taken.
The difference of these two energies was defined as the
donor-acceptor strength ∆EDA of the entire molecule, ∆EDA
) EHOMO(D) - ELUMO(A). The so defined ∆EDA is a theoretically
derived value to measure the strength of a donor-acceptor
complex. It is equivalent to the difference of ionization potential
and electron affinity of the moieties.
a The Opsin shift is the difference of absorption wavenumbers of
the SBP+ compound in solution and of the SBH+sbO complex.
b With maximal 0.5% EtOH, see spectroscopy part. c For some
donors, the protonated n-butyl complexes were also synthesized.
The experimental spectra do not differ significantly. Furthermore,
calculations of spectra with the GAUSSIAN 03 ZINDO/S routine
give the same result for both n-butyl complexes and SBP+
compounds.
when either donor or acceptor strength are increased. In every
case, the spectra of the Bacterioopsin complexes are most red-
shifted. On the basis of the red shift of the model compounds
in solution, these spectra of the Bacterioopsin complexes indicate
that the chromophore in the protein behaves as if the donor
and the acceptor are stronger than in the corresponding SBP+
derivatives in solution.
Figure 3 shows that the calculated absorption energies of the
chromophores correlate approximately linearly with the calcu-
lated fraction of positive charge located on the donor groups of
increasing strength. In solution, polarizability effects are active,
increase QD, and reduce the absorption energy because the
counterion and/or the polar solvent will tend to shift the positive
charge toward the acceptor end, quite similar to the effect of
increasing donor strength of the model compounds used here.
This leads to an increase of QD and to a red shift for the
The optimized structures from (a) were taken to calculate the
Franck-Condon transition energies by using the ZINDO/S
method and the TDDFT method embedded in GAUSSIAN 03.
Results
The absorption spectra of the uncomplexed aldehydes, of the
SBP+ model compounds, and of the protein complexes, after
the PeakFit analysis, are displayed in Figure 2, and their
absorption maxima are given in Table 3. A red shift is observed

2182 J. Phys. Chem. A, Vol. 114, No. 5, 2010
Lasogga et al.
can be done for QD from Figure 3, and the values are included
in Table 4. The increased ∆EDA for the protein complex leads
to a significant increase of the charge on the donor unit.
Discussion
A. Correlation of Chemical Structure, Absorption Maxima,
and Chromophore Charge Distribution. Consequences of the
Polymethine Model. The absorption maxima of the chro-
mophores in the Bacterioopsin complexes are red-shifted with
respect to the solution spectra of the ionic model compounds
(acceptor ) SBP+) in all cases. This shows that, for example,
the effective donor strength in the protein complex DMAPhs2-
SBH+sbO is considerably larger than that for DMAPhs2-SBP+
in polar solution. The apparently larger donor strength cannot
be due to bulk polarity effects of the surrounding medium,
because ionic compounds such as DMAPhs2-SBP+ with two
nitrogens at either end show little solvatochromy, similar to
closely related other ionic donor-acceptor compounds.31
A vectorial electrostatic field can, however, be induced by
the protein surrounding, yielding spectral shifts also for these
ionic compounds, similar to those for the neutral dipolar
compounds, as long as the charge distribution is different for
the S0 and S1 states. In our case, the protein spectra are all red-
shifted with respect to the solution spectra indicating that the
S1 is more stabilized by the field than the S0 state.
Alternatively, the red-shifted absorption spectra can be
described by the so-called polymethine or cyanine model which
predicts that the most symmetric electronic structure and charge
distribution lead to the lowest absorption energy for linear
cyanines and that asymmetric charge distributions lead to blue-
shifted spectra.32
The basic mechanism responsible for the cyanine model can
be found in the interaction of the two possible resonance
structures for symmetric as well as asymmetric cyanines, as for
example discussed in refs 33-37. The absorption is of lowest
energy when the contribution of the two resonance structures
is equal (so-called cyanine limit, CL). For our case, an example
for the two resonance structures is given in Figure 5.
Figure 3. Fraction of the positive charge QD (for the optimized ground-
state geometry) located on the donor unit of the SBP+ compounds (as
defined in Figure 1) plotted versus the absorption energy. The calculated
gas-phase absorption shifts to the red, and the charge localized on the
donor (QD is given in units of the elementary charge) increases as a
function of the donor strength (approximately linear correlation as
shown). Strong polarization effects especially for the DMA donor lead
to a red shift of the gas-phase absorption (O for TDDFT [b3lyp/6-
31G**]) for the solution surrounding (9, in Ethanol solvent) and the
protein surrounding (f). This red shift is indicated by arrows A. The
corresponding increase of QD (charge shift toward the donor D) due to
the surrounding is indicated by arrows B. The experimental absorption
of the chromophore-Bacterioopsin complex yields an approximate
value for the effective charge distribution QD of the DMA model
chromophore inside the protein (arrow C). The effective QD values are
collected in Table 4.
experimental points with respect to the calculated ones. This
effect is larger for the DMA compound than for the H compound
because of the larger electronic polarizability. In fact, the nearly
identical calculated and measured absorption energies for the
H to the MO donors yield an identical correlation line and
indicate that polarizability effects are weak in this case. The
extrapolation of the correlation line to the DMA compound
together with the experimental absorption energy allows us to
determine the effective QD in solution including polarizability
effects (Table 4; see also caption of Figure 3).
A significant change of the relative weight of the two possible
resonance structures can be induced either by changing the donor
and/or acceptor strength or by the influence of external charges.
In early work, the strongly red-shifted absorption spectra of the
proteins (Rh or bR) have been explained within this external-
charge model by negative charges placed along the retinal Schiff
base chain, far away from the Schiff base nitrogen, with an
additional negative charge due to the counterion near the Schiff
base end.4,12,13 In our charge-shift-model compounds, donors
shift better the positive charge away from the Schiff base
nitrogen and shift the spectra to the red (Figure 3). This
corresponds to a more symmetric charge distribution. A similar
charge shift and accompanying absorption red shift would be
induced by placing a positive charge in the neighborhood of
the end of the chromophore with surplus positive charge (Schiff
base nitrogen) or by placing a negative charge near the opposite
end as assumed in the external-charge model. In both cases,
the consequence will be a more symmetric charge distribution,
closer to that of symmetric cyanines, and the absorption will
therefore shift to the red.32 The opposite effect will result from
a negative charge near the Schiff base nitrogen or a positive
one at the other end.
The donor and acceptor strength and their combined influence
can be quantified by the parameter ∆EDA. The latter is derived
from the HOMO and LUMO energies of the donor and acceptor
units (Figure 1, Table 4) as described in the Experimental Part.
Figure 4 reveals that the absorption energies correlate with the
donor-acceptor strength ∆EDA. As discussed below (see eq 4),
the correlation is expected to follow a parabola, but because of
the small range in the experimental case, it can be approximated
by a linear fit.
The SBP+ derivatives (Figure 1) are a good model for the
chromophore in the Bacterioopsin complex as long as the protein
surrounding is not considered. Consequently, both chromophores
differ little in ∆EDA values in vacuum, but anisotropic medium
effects such as the protein can change this value. The additional
red shift for the Bacterioopsin complex as compared to ethanol
solution is therefore due to medium-difference effects: ethanol
versus protein matrix. This medium influencesas discussed in
Figure 8scan be determined quantitatively. From the experi-
mental absorption maximum of the Bacterioopsin complexes,
the protein-induced change of ∆EDA can be determined from
the correlation yielding an effective ∆EDA for the protonated
Schiff base chromophore embedded in the protein. For example,
for RD ) DMA, ∆EDA shifts from ∆EDA ≈ -2,7 eV for the
SBP+ derivative to ∆EDA ≈ -0,7 eV for the Bacterioopsin
complex corresponding to an effectively increased donor-acceptor
strength, induced by the protein matrix. A similar extrapolation
By applying this point of view to the observed absorption
data of protonated retinal Schiff base in vacuum (610 nm)38
and methanol solution (440 nm)39 as well as in bR (570 nm),40
we can interpret the strong blue shift from vacuum to the

Investigation of the Opsin Shift in Bacteriorhodopsin
J. Phys. Chem. A, Vol. 114, No. 5, 2010 2183
TABLE 4: Summary of the Calculated Donor-Acceptor Strength ∆EDA (Derived from the HOMO Energy of the Donor
a
Moiety (D) and the LUMO Energy of the Acceptor Moiety (A)) and Transition Energy ∆E01
b
b
c
calc d
exp e
f
g
molecule
EHOMO(D)
ELUMO(A)
∆EDA
∆E01
∆E01
QD
∆EDA
HPhs2-SBP+
-9.653
-9.330
-9.114
-9.004
-8.274
-5.560
-5.560
-5.560
-5.560
-5.560
-4.093
-3.770
-3.554
-3.444
-2.714
3.239
3.280
13
16
26
23
39
-3.952
-3.516
-2.281
-2.700
-0.701
MPhs2-SBP+
HOPhs2-SBP+
MOPhs2-SBP+
DMAPhs2-SBP+
3.043
2.974
2.896
2.705
3.171
2.863
2.952
2.130
a All values are given in eV. As can be seen, an increasing (less negative) ∆EDA leads to a decreasing transition energy. b Calculated by
GAUSSIAN 03. c Calculated difference EHOMO(D) - ELUMO(A) d Calculated excitation energy by TDDFT (b3lyp/6-31G**). e Experimental
.
excitation energy in EtOH. f Fraction of positive charge on the donor unit for the corresponding bO complex with respect to the polarization
effects, derived from a linear fit of Figure 3 (in percent). g Donor-acceptor strength ∆EDA for the bacterioopsin protein complex with respect to
the polarization effects, derived from Figure 4.
CL. The similar energies for resonance structures A and B
implies that their weight in the wave function (AB of the
molecular system with resonance between the two structures A
and B) is 50%. This can be expressed by the condition c2 )
0.5 for the CL in eqs 1 and 2. For unsymmetric cases (compound
2), the contribution of the resonance structures becomes unequal,
and the S0 - S1 energy difference increases, Figure 6.
ψ
AB(S0) ) cψA + (1 - c2)0.5ψB
AB(S1) ) (1 - c2)0.5ψA - cψB
(1)
(2)
ψ
For the general case, the value of the transition energy ∆E01
can be obtained by solving the 2 × 2 secular determinant (eq
3) involving the interaction energy F as off-diagonal element
and the energy difference b ) bA - bB of the resonance
structures,34 resulting in eq 4. This energy difference b is equal
to the donor-acceptor strength ∆EDA of the molecule as defined
in the calculation section above; therefore, we can write b )
∆EDA. The consequences of this model can be visualized for
different values of F and b (Figure 7).
Figure 4. The calculated donor-acceptor strength ∆EDA plotted versus
the calculated (0 O) and experimental (9) absorption maxima of the
n ) 2 SBP+ compounds. Experiments are done in EtOH solvent.
Polarization effects are analogous to those in Figure 3. The red shift is
indicated by arrows A. Polarization also leads to a shift of the
donor-acceptor strength indicated by arrow B. The experimental
absorption of the chromophore-Bacterioopsin complex yields an
approximate value for the effective donor-acceptor strength of the
DMA model chromophore inside the protein (arrow C). For the protein
data points, it was assumed that the theoretical correlation line is
applicable for deriving the effective ∆EDA valid for the protein
surrounding (see text). The ∆EDA values are collected in Table 4.
E - bA
0.5F
0.5F
E - bB
) 0
(3)
(4)
|
|
2
2
√
∆E01 ) F + b
solution spectrum as introduced by the negative counterion
located near the positively charged Schiff base end. In the
protein, there is a similar counterion close to the Schiff base
end. Additional charges in the protein complex can induce the
red shift with respect to the solution spectrum according to the
external-charge model,4,12,13 fully consistent with our qualita-
tive model (see discussion in Figure 8).
The same applies to the compounds like DMAPhs2-SBP+
measured here. There will be a counterion in both solution and
in the protein, but the protein around the DMAPhs2-SBH+sbO
complex may create an additional anisotropic electric field
leading to a more symmetric charge distribution than in solution
and yielding a possible explanation for the observed absorption
red shift as compared to the solution spectra.
Equation 4 allows to predict that for F . b, the effect on
∆E01 by a change of b (corresponding to the variation of
substituents DMA to H) will be very small. The contrary is
observed (Figure 3), and we can conclude that F is small and
the effect of b prevails. Quantitative determination of b and F
is however not possible within the accuracy of our data (see
Figure 4).
This model predicts that for linear ideal cyanines like structure
1 (Figure 5), the absorption energy becomes 0 (infinite absorp-
tion wavelength) for F ) 0 but cannot become 0 for F of finite
size. This is relevant for the prediction of the absorption energy
(wavelength) for n toward infinity, for example. in conjugated
polymers. Simple cyanine models predict an infinite absorption
wavelength for this condition,41,42 whereas experimentally, the
absorption energy converges to a finite nonzero value,43 which
moreover depends on the nature of the end groups, and this is
correctly described by the above equations for F * 0 even for
n tending toward infinity and by other more refined models.44,45
The absorption shifts with increasing donor-acceptor dif-
ference can be understood on the basis of changes in b if the
coupling F of the two main resonance structures is kept constant
starting from the CL (b ) 0, c2 ) 0.5). The spectra will blue-
shift in both directions of increasing |b|, with b > 0 being the
normal region (structure A more stable) and b < 0 being the
region where structure B is more stable than structure A (we
What is new in our study compared to the previous external-
charge studies12-14 is that we apply a variation of the donor
strength, and the external-charge influence on the charge
distribution induced by the same external field can be different
(see below Section B).
As mentioned, Fo¨rster’s resonance model34 which was later
refined by Platt35 as well as the cyanine model of Da¨hne32,36,37
predict that the absorption energy of a simple unsymmetric
cyanine is lowest for an approximately evenly distributed
positive charge and for resonance structures A and B in Figure
5 of similar energy (compound 1). This situation is called the

2184 J. Phys. Chem. A, Vol. 114, No. 5, 2010
Lasogga et al.
Figure 5. Lowest energy resonance structures of symmetric and unsymmetric cyanines. Without external field effects, the resonance structure B
is of equal (1) and higher energy (2) than A. The symmetric 1 (Pyrrolidinosn-SBP+) and the unsymmetric 2 (DMAPhsn-SBP+) are given as
examples. For the nonsymmetric case 2, mesomeric coupling between structures A and B leads to a larger weight of structure A in the ground state
and a surplus of positive charge at the molecular end as given in structure A. An external charge will influence the relative energy of these two
structures and hence change their contribution in the wave function as well as in the charge distribution.
Figure 6. Schematic energy dependence of S0 and S1 states of
unsymmetric cyanines and merocyanines on the energy difference of
the resonance structures A and B, which determine the mixing
coefficient c. For c2 ) 0.5, the two resonance structures have equal
energy, and the energy gap ∆E01 is due to the interaction matrix element
F and is smallest (CL, region II). In range I, structure A is more stable,
and in range III, structure B is more stable. In both cases, the absorption
energy increases. The transition from region I to II to III can occur by
donor and acceptor substituents or by external charges (see below).
The thickness of the lines indicates the relative contribution of resonance
structure B in the wave function of the molecule.
Figure 8. Influence of external positive or negative charges on the
distribution of the positive charge along an unsymmetric cyanine (e.g.,
for DMAPhs2-SBP+). A more ground-state-extended charge distribu-
tion leads to an absorption red shift, and a more narrow one leads to
a blue shift. In every case, the charge distribution in the excited state
is opposite to that in the ground state.
Figure 7. Model calculations for unsymmetric cyanines regarding the
dependence of the absorption energy (in a.u.) on the coupling strength
F and on the energy difference b (in a.u.) of the two main resonance
structures according to eqs 3 and 4. F2 values of 0, 10, 100, and 1000
are chosen as an example. ∆EDA ) bA - bB ) b is the energy difference
between the two resonance structures in Figure 5.
at the CL and the charge is approximately evenly distributed,
the longest-wavelength absorption will be present, and distur-
bance by a positive or negative charge at either end will lead to
a blue shift. Applied to the compounds investigated here, a
strong electrostatic field or an external charge which shifts the
majority of the positive charge from the Schiff base to the donor
end and thus reverts the original charge distribution, where the
majority of the positive charge is located close to the Schiff
base nitrogen, will cause overpolarization, that is, inversion of
the charge distribution. Examples showing the above ideas are
given in Figure 8. In cases where the switching from region I
to III (Figure 6 and cases 3 and 4 in Figure 8) caused by
overpolarization is symmetric, no shift is expected, whereas the
strongest shift is expected for changes within regions I and II
connected with a relative large slope in Figure 7 (cf. also Section
B below).
call it overpolarized case for unsymmetric compounds containing
an aromatic ring like 2 in Figure 5 because the quinoid structure
is normally the less stable one).
If a compound is close to CL (c2 ) 0.5), the effect of an
external field will be smaller than for a compound with less
evenly distributed positive charge (see also Figure 7). We can
observe this effect for the methoxy donor (MOPhs2-SBP+, with
a strongly asymmetric charge distribution, Figure 3, and
MOPhs2-SBH+sbO). The MO-derivative shows an Opsin shift
(2310 cm-1) larger than the compound with the stronger donor
(DMAPhs2-SBP+ and DMAPhs2-SBH+sbO, 1770 cm-1,)
see Table 3, because MOPhs2-SBP+ is further away from the
CL (less evenly distributed charge density). If a compound is
The influence of an electrostatic field in region I is connected
with a strong slope, that is, leads to a strong red shift and can
yield an explanation for the Opsin shift of the chromophore in

Investigation of the Opsin Shift in Bacteriorhodopsin
J. Phys. Chem. A, Vol. 114, No. 5, 2010 2185
TABLE 5: Calculated and Experimental Absorption
Maxima for MOPhs1-RA
TABLE 6: Percentage of Charge Located on Donor and
Acceptor Moieties, Together with Transition Energies,
Donor-Acceptor Strength ∆EDA, and Charge-Distribution
Enhancement as Determined from ZINDO/S Calculations
a
b
c
molecule
∆EDA (eV) QD QA ∆E01 (eV) QED
For n ) 1 Compounds
HPhs1-SBP+
-4.093
-3.770
-3.554
-3.444
-2.714
-4.059
-3.736
-3.520
-3.410
-2.680
-0.163
0.160
17
18
19
21
28
17
18
20
21
28
36
41
45
48
62
83
82
81
79
72
83
82
80
79
72
64
59
55
52
38
3.206
3.057
2.996
2.965
2.691
3.200
3.051
2.991
2.959
2.685
3.068
2.965
2.924
2.905
2.805
MPhs1-SBP+
HOPhs1-SBP+
MOPhs1-SBP+
DMAPhs1-SBP+
HPhs1-SBPip+
MPhs1-SBPip+
HOPhs1-SBPip+
MOPhs1-SBPip+
DMAPhs1-SBPip+
HPhs1-SBPip+2
MPhs1-SBPip+2
HOPhs1-SBPip+2
MOPhs1-SBPip+2
DMAPhs1-SBPip+2
19
23
26
27
34
0.376
0.486
1.216
the bR environment. With respect to Figure 8, we explain the
Opsin shift in the protein by three possibilities: (a) additional
positive charge at the acceptor end of the chromophore, (b)
additional negative charge at the donor end of the chromophore,
or (c) increased distance of the counterion in the protein.
B. Investigation of Model Compounds with External
Nonconjugated Charges. In order to study the polarization
effect induced by external charges in more detail and to simulate
an anisotropic electric field related to the field in the bR protein,
we experimentally investigated a derivative of MOPhs1-SBP+
with an additional nonconjugated positive charge and performed
detailed quantum-chemical calculations for comparison.
A chemical way of generating a nonconjugated positive
chargenearadialkylaminogroupforacompoundlikeDMAPhs2-
SBP+ consists in the design of Schiff bases containing the
piperazinium fragment (SBPip+) instead of the pyrrolidinium
(SBP+) one. The second piperazinium nitrogen can be proto-
nated in an acidic medium, and a model compound (acceptor
end called SBPip+2) can be created with a surplus positive
charge chemically attached close to the Schiff base nitrogen of
the absorbing chromophore. Such molecules can serve as tests
for investigating external-charge effects, both with experimental
and quantum-chemical methods. Related experiments with
nonconjugated charges close to the PRSB chromophore have
been reported previously.17,46-52
For n ) 2 Compounds
HPhs2-SBP+
-4.093
-3.770
-3.554
-3.444
-2.714
-4.059
-3.736
-3.520
-3.410
-2.680
-0.163
0.160
12
13
14
15
23
12
13
15
16
23
33
38
42
46
60
88
87
86
85
77
88
87
85
84
77
67
62
58
54
40
2.762
2.653
2.616
2.591
2.367
2.756
2.648
2.611
2.586
2.361
2.687
2.630
2.610
2.608
2.586
MPhs2-SBP+
HOPhs2-SBP+
MOPhs2-SBP+
DMAPhs2-SBP+
HPhs2-SBPip+
MPhs2-SBPip+
HOPhs2-SBPip+
MOPhs2-SBPip+
DMAPhs2-SBPip+
HPhs2-SBPip+2
MPhs2-SBPip+2
HOPhs2-SBPip+2
MOPhs2-SBPip+2
DMAPhs2-SBPip+2
21
25
28
31
37
0.376
0.486
1.216
a QD ) qD/(qD + qA) in percent. b QA ) 100 - QA in percent.
c Charge-distribution enhancement: QED ) QD(RDPhsn-SBPip+2) -
QD(RDPhsn-SBP+).
counterion is substituted by the neutral but hydrophile asparagin
(N). This fits quite well with the observed 37 nm shift from
SBPip+ to SBPip+2 in ACN, see Table 5. In the dark-adapted
form of R82A and R82Q (positive arginin replaced by a neutral
residue), the absorption is blue-shifted to 547 nm. Later (1999),
it was found by X-ray crystallography3 that these residues, D85,
R82, and D212, together with some water molecules, belong
to a distributed counterion connected by hydrogen bonds where
the negative D85- exhibits the smallest distant to the protonated
Schiff base. In the triple mutant where all three charged residues
of the counterion are replaced by neutral ones, the retinal
chromophore can bind if some millimolar salt is added.7 The
color depends on the anion radius (549, 563, 573, and 580 nm
for F-, Cl-, Br-, and I-, respectively), indicating that the smaller
anions may come closer to the Schiff base generating a bigger
blue shift.
We could synthesize the doubly charged model compound
MOPhs1-SBPip+2 and compare it to MOPhs1-SBPip+. We
further have the comparison of experiment with quantum
chemical calculations, and we can model the effect of the
additional positive charge of the SBPip+2 compound on the
charge distribution along the chromophore, the donor strength
∆EDA, and the absorption maximum.
The results are summarized in Table 5.
As expected, the absorption energies, both experimental and
calculated, do not differ significantly for the singly charged
nonprotonated SBP+ and SBPip+ derivatives. This indicates that
the influence of the slightly different N-alkyl groups near the
Schiff base end can be neglected. The additional positive charge
shifts the spectra only slightly to the red, consistently for
experiment and calculation. The calculations underestimate the
observed transition energy. For bR, an absorption shift of 44
nm from 550 nm at wild-type ebR (in E-coli expressed) to 594
nm at D85N in the dark adapted state (retinal in 13 cis form)
was observed.53 For the light adapted state (retinal in all trans)
of D85N, a red shift of 33 nm compared to ebR was found.7 In
the D85N, the deprotonated negative aspartic acid (D) in the
The experimental results for MOPhs1-RA were supplemented
with the full set of calculations for a range of donors and both
series n ) 1 and n ) 2. In this way, charge distribution and
absorption energy can be contrasted.
These results are summarized in Table 6.
As can be seen, the somewhat unsymmetric charge distribu-
tion of the singly charged cations is strongly polarized by adding
an additional positive charge. The corresponding absorption
energies can be determined by quantum-chemical treatment and
compared to experiment (see Figure 3 and Table 4). Two cases

2186 J. Phys. Chem. A, Vol. 114, No. 5, 2010
Lasogga et al.
Figure 9. Fraction of the positive charge QD (left bar) located on the
donor unit and fraction of the positive charge QA (right bar) located on
the acceptor unit of RDPh-1-RA compounds with a single positive charge
(SBP+ and SBPip+ compounds) and with an additional nonconjugated
charge (SBPip+2, outermost bar at the right). The cases RD ) H, MO,
and DMA are shown.
Figure 10. Fraction of the positive charge QD (left bar) located on the
donor unit and fraction of the positive charge QA (right bar) located on
the acceptor unit of RDPh-2-RA compounds with a single positive charge
(SBP+ and SBPip+ compounds) and with an additional nonconjugated
charge (SBPip+2, outermost bar at the right). The cases RD ) H, MO,
and DMA are shown.
of overpolarization can be observed and are shown in Figures
9 and 10. For reference, SBP+ and SBPip+ derivatives are
compared, and their charge distribution differs very little, as
expected.
by the nonconjugated charge is stronger than polarization
(without the additional field) although the compound is origi-
nally in region I.
The calculations summarized in Table 6 in fact show this to
be the case. This is visualized in Figure 11, which shows that
the change of the absorption energy E01 is different for every
compound and can correspond to either a red shift (RD ) H),
As can be seen in these figures, the field of the additional
positive nonconjugated charge near the Schiff base nitrogen
polarizes the distribution of the positive charge on the molecule
in such a way that the positive charge moves away from the
Schiff base nitrogen toward the donor, as qualitatively outlined
in Figure 8. For donors RD ) H and MO, the external charge
modifies the original charge distribution but does not revert it.
In the case of the dimethylamino compounds (RD ) DMA), a
charge reversal is observed; that is, a charge distribution results
where a surplus of charge is located on the donor unit. This
corresponds to situation 4 in Figure 8, that is, to the valence
structure B being more stable than structure A (Figure 5). In
terms of the resonance model, we are in the region III (Figure
6), and the ground-state wave function carries a larger weight
of B (c2 > 0.5); hence, the unequal superposition by resonance
of the two valence-bond structures leads to a surplus of positive
charge near the aminophenyl group, resulting from structure B
(Figure 5). We call region III in Figure 6 the overpolarized
region, because the field reverts the original charge distribution.
If a field causes overpolarization from region I (polarization)
to III (overpolarization), the CL (region II) has to be crossed.
Starting from the CL, polarization toward the region I and
overpolarization toward the region III both lead to a blue shift
(Figure 8); hence, if the polarization/overpolarization is sym-
metric with respect to CL, no shift will be observed. There can
even be a blue shift induced by the charge, if overpolarization
a blue shift (RD ) DMA), or nearly constant energy (RD
)
MO). Hence, MOPhs1-SBPip+ and MOPhs2-SBPip+ in the
gas phase are nearly symmetric cases with respect to CL. We
notice that the charge distribution remains, nevertheless, biased
toward the Schiff base nitrogen. The reason for this is that the
phenyl groups possess aromatic character, and hence, the
resonance structure A (with the aromatic phenyl ring) has a
weight larger (>50%) than expected from the simplified eqs 1
and 2. This has been outlined in detail previously for the case
of stilbenes, where the weight of the aromatic structures is even
more emphasized.25,54
The ∆EDA values (see calculational part) derived from the
energies of HOMO(D) and LUMO(A) in Table 4 are related to
the energy difference b between resonance structures A and B,
and it can be seen that the external charge increases ∆EDA
toward less negative or even positive values (Table 6), that is,
toward CL (for H and MO) and beyond (region III in Figure 6
for DMA). The absorption energies (Table 6) behave according
to eq 4 and Figure 7: red shift for the weaker donors (range I),
blue shift for the strong donors (range III), and some intermedi-
ate cases with no shift (range II near CL).
This behavior is emphasized in Figure 11, which compares
the two series n ) 1 and 2. As can be seen, for n ) 2 and the

Investigation of the Opsin Shift in Bacteriorhodopsin
J. Phys. Chem. A, Vol. 114, No. 5, 2010 2187
a simple 2 × 2 interaction model (and neglecting further weaker
interactions which are also present).
The observed Opsin shifts for the chromophore-protein
complexes can be correlated with the donor-acceptor strength
and yield quantitative information regarding the placement of
the chromophores with respect to the CL.
The charge distribution of the chromophore is also linked to
the CL, and in the overpolarized case, the majority of the
positive charge is far away from the Schiff base nitrogen.
The sensitivity of this effect depends on the donor property of
the substituent and on the chain length n, being stronger for
longer chains. The new approach using variable donor-acceptor
strength of protein-embedded model chromophores can also
yield new insight into the mechanism of the Opsin shift.
Acknowledgment. We thank the International Bureaux of
the Ministry of Research and Technology (WTZ-Projekt UKR
02/004) for support of this work through a travel grant to J.B.
The authors are grateful for the support of M. Heyn and
J. Heberle, Free University of Berlin.
Supporting Information Available: This material is avail-
able free of charge via the Internet at http://pubs.acs.org.
References and Notes
(1) Palczewski, K.; Kumasaka, T.; Hori, T.; Behnke, C. A.; Motoshima,
H.; Fox, B. A.; Le Trong, I.; Teller, D. C.; Okada, T.; Stenkamp, R. E.;
Yamamoto, M.; Miyano, M. Science 2000, 289, 739.
(2) Okada, T.; Fujiyoshi, Y.; Silow, M.; Navarro, J.; Landau, E. M.;
Shichida, Y. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 5982.
(3) Luecke, H.; Schobert, B.; Richter, H.-T.; Cartailler, J.-P.; Lanyi,
J. K. J. Mol. Biol. 1999, 291, 899.
Figure 11. Calculated shift of the absorption energy with introduction
of an external positive charge near the Schiff base nitrogen as a function
of the donor strength (H, MO, and DMA compounds) and the chain
length (n ) 1,2).
(4) Sekharan, S.; Sugihara, M.; Buss, V. Angew. Chem., Int. Ed. 2007,
46, 269.
(5) Fujimoto, K.; Hayashi, S.; Hasegawa, J.; Nakatsuji, H. J. Chem.
Theory Comput. 2007, 3, 605.
(6) Kleinschmidt, J.; Harosi, F. Proc. Natl. Acad. Sci. U.S.A. 1992,
89, 9181.
(7) Marti, T.; Ro¨sselet, S.; Otto, H.; Heyn, M. P.; Khorana, H. G.
J. Biol. Chem. 1991, 266, 18674.
(8) Marti, T.; Otto, H.; Ro¨sselet, S.; Heyn, M. P.; Khorana, H. G.
J. Biol. Chem. 1992, 267, 16922.
strong donor DMA, the blue shift with introduction of the charge
and due to overpolarization is stronger for the n ) 2 series.
This indicates that for the n ) 2 series, smaller electric fields
are necessary to reach the CL or cross it to the overpolarized
region.
Table 6 also includes the charge distribution enhancement
QED, which mirrors the larger sensitivity to the additional charge
of the n ) 2 series and of the compounds with intermediate
donor strength (MOPh).
For the experimental results of the chromophore-bO com-
plexes, the shift is invariably to the red, that is, corresponding
to range I. We can thus conclude that the electrostatic field
present in Bacterioopsin is much smaller than that in our model
compound with a surplus positive charge in close proximity to
the positively charged Schiff base nitrogen. Model calculations
of the chromophores with various charges in the surrounding
should be able to reproduce the Opsin shift observed (Table 3).
This work is in progress.
(9) Hoffmann, M.; Wanko, M.; Strodel, P.; Ko¨nig, P. H.; Frauenheim,
T.; Schulten, K.; Tajkhorshid, E.; Elstner, M. J. Am. Chem. Soc. 2006, 128,
10808.
(10) See for instance pdb files 1c3w and 2at9.
(11) Aton, B.; Doukas, A.; Callender, R.; Becher, B.; Ebrey, T.
Biochemistry 1977, 16, 2995.
(12) Balogh-Nair, V.; Carriker, J. D.; Honig, B.; Kamat, V.; Motto,
M. G.; Nakanishi, K.; Sen, R.; Sheves, M.; Arnaboldi Tanis, M.; Tsujimoto,
K. Photochem. Photobiol. 1981, 33, 483.
(13) Nakanishi, K.; Balogh-Nair, V.; Arnaboldi, M.; Tsujimoto, K.;
Honig, B. J. Am. Chem. Soc. 1980, 102, 7945.
(14) Derguini, F.; Caldwell, C. G.; Motto, M. G.; Balogh-Nair, V.;
Nakanishi, K. J. Am. Chem. Soc. 1983, 105, 646.
(15) Lugtenburg, J.; Muradin-Szweykowska, M.; Heeremans, C.; Par-
doen, J. A.; Harbison, G. S.; Herzfeld, J.; Griffin, R. G.; Smith, S. O.;
Mathies, R. A. J. Am. Chem. Soc. 1986, 108, 3104–5.
(16) Sheves, M.; Albeck, A.; Baasov, T.; Friedman, N.; Ottolenghi, M.
Retinal Proteins; VNU Science Press, 1987; pp 201-216.
(17) Baasov, T.; Sheves, M. J. Am. Chem. Soc. 1987, 109, 1594.
(18) Andersen, L. H.; Nielsen, I. B.; Kristensen, M. B.; El Ghazaly,
M. O.; Haacke, S.; Nielsen, M. B.; Petersen, M. A. J. Am. Chem. Soc.
2005, 127, 12347.
(19) Lin, S. W.; Kochendoerfer, G. G.; Carroll, K. S.; Wang, D.; Mathies,
R. A.; Sakmar, T. P. J. Biol. Chem. 1998, 273, 24583.
(20) Kochendoerfer, G. G.; Lin, S. W.; Sakmar, T. P.; Mathies, R. A.
Trends Biochem. Sci. 1999, 24, 300.
(21) Sun, H.; Macke, J. P.; Nathans, J. Proc. Natl. Acad. Sci. U.S.A.
1997, 94, 8860.
(22) Stenkamp, R. E.; Filipek, S.; Driessen, C. A. G. G.; Teller, D. C.;
Palczewski, K. Biochim. Biophys. Acta 2002, 1565, 168.
(23) Sun, H.; Macke, J. P.; Nathans, J. Proc. Natl. Acad. Sci. U.S.A.
1997, 94, 8860.
Summary
The change of the absorption energy and the charge distribu-
tion in the compounds investigated both in solution and as
chromophore-Bacterioopsin complexes have been shown to be
related to the difference of the donor and acceptor strength of
the substituents, as well as to the external electrostatic field
created by an external charge. These effects can be simulated
by quantum-chemical-model calculations, giving evidence that
in some compounds, the role of the main resonance structure is
reversed for the ground and excited states (overpolarized case).
In this context, the concept of the CL is of importance and
allows us to describe the changes in absorption energy by using
(24) van den Berg, R.; Du-Jeon-Jang; Bitting, H. C.; El-Sayed, M. A.
Biophys. J. 1990, 58, 135.

2188 J. Phys. Chem. A, Vol. 114, No. 5, 2010
Lasogga et al.
(25) Dekhtyar, M.; Rettig, W. J. Phys. Chem. A. 2007, 2035.
(26) Friedli, A. C.; Yang, E.; Marder, S. R. Tetrahedron 1997, 53 (No
8), 2717–2730.
(27) Bricks, J. In preparation.
(28) Peak Fit is a registered trademark of Systat Software Inc., www.
systat.com.
(36) Dähne, S.; Moldenhauer, F. In Progress in Physical Organic
Chemistry; Taft, W., Ed.; John Wiley & Sons, Inc., 1995; Vol. 15, pp 1-
130.
(37) Dähne, S.; Leupold, D. Ber. Bunsenges. Phys. Chem. 1966, 70,
618.
(38) Andersen, L. H.; Nielsen, I. B.; Kristensen, M. B.; El-Ghazaly,
M. O. A.; Haacke, S.; Nielsen, M. B.; Petersen, M. A. J. Am. Chem. Soc.
2005, 127, 12347.
(39) Freedman, K. A.; Becker, R. S. J. Am. Chem. Soc. 1986, 108, 1245.
(40) Lanyi, J. K. Nature 1995, 375, 461.
(41) Dähne, S.; Radeglia, R. Tetrahedron 1971, 27, 3673.
(42) Brooker, L. G. S. ReV. mod. Physics 1942, 14, 275.
(43) Tyutyulkov, N.; Fabian, J.; Mehlhorn, A.; Fietz, F.; Tadjer, A.
Polymethine Dyes. Strucutre and Properties; St. Kliment Ohridski University
Press: Sofia/Bulgaria, 1991.
(44) Dyadyusha, G. G.; Kachkovskii, A. D. Ukr. Khim. Zh. 1975, 41,
1176.
(45) (a) Dyadyusha, G. G.; Kachkovskii, A. D. Theor. Eksp. Khim. 1979,
15, 152. (b) Dyadyusha, G. G.; Kachkovskii, A. D. Theor. Eksp. Khim.
1981, 17, 393.
(46) Sheves, M.; Nakanishi, K. J. Am. Chem. Soc. 1983, 105, 4033.
(47) Baasov, T.; Sheves, M. J. Am. Chem. Soc. 1985, 107, 7524.
(48) Sheves, M.; Friedman, N. Angew. Chem., Int. Ed. Engl. 1986, 25, 284.
(49) Baasov, T.; Sheves, M. Biochemistry 1986, 25, 5249.
(50) Sheves, M. Albeck, A.; Baasov, T.; Friedman, N.; Ottolenghi, M.
Retinal Proteins; VNU Science Press, 1987; pp 201-216.
(51) Baasov, T.; Friedman, N.; Sheves, M. Biochem. 1987, 26, 3210.
(52) Albeck, A.; Livnah, N.; Gottlieb, H.; Sheves, M. J. Am. Chem.
Soc. 1992, 114, 2400.
(29) Oesterhelt, D. Methods Enzymol. 1982, 88, 10–17.
(30) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb,
M. A.; Cheeseman, J. R.; Montgomery, Jr., J. A.; Vreven, T.; Kudin, K. N.;
Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.;
Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.;
Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.;
Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li,
X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.;
Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.;
Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.;
Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich,
S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.;
Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.;
Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz,
P.; Komaromi, I.; 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.; Gonzalez, C.; Pople, J. A. Gaussian 03,
Revision D.01; Gaussian, Inc.: Wallingford CT, 2004.
(31) Solvatochromy is also nearly absent for closely related ionic
stilbazolium derivatives, see Ephardt, H.; Fromherz, P. J. Phys. Chem. 1991,
95, 6792.
(32) Dähne, S.; Hoffmann, K. In Progress in Physical Organic
Chemistry; Taft, W., Ed.; J. Wiley & Sons, Inc., 1990; Vol. 18, pp 1-
64.
(33) Lippert, E. Ber. Bunsenges. Phys. Chem. 1957, 61, 962.
(34) Th. Fo¨rster, Z. Elektrochem. Angew. Physik. Chem. 1939, 45,
571.
(53) Otto, H.; Marti, T.; Holz, M.; Mogi, T.; Stern, L. J.; Engel, F.;
Korana, H. G.; Heyn, M. P. Proc. Natl. Acad. Sci. U.S.A. 1990, 87, 1018.
(54) Rettig, W.; Dekhtyar, M. Chem. Phys. 2003, 293, 75.
(35) Platt, J. R. J. Chem. Phys. 1956, 25, 80.
JP904132F