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Theoretical Study of the Optical Properties of Artificial Self-Assembled Zinc Chlorins† Sameer Patwardhan,‡ Sanchita Sengupta,§ Frank Wu¨rthner,§ Laurens D. A. Siebbeles,‡ and Ferdinand Grozema*,‡ Optoelectronic Materials Section, Department of Chemical Engineering, Delft UniVersity of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands, and Institut fu¨r Organische Chemie, UniVersita¨t Wu¨rzburg, Am Hubland, 97074, Wu¨rzburg, Germany ReceiVed: July 30, 2010; ReVised Manuscript ReceiVed: September 10, 2010
The optical properties of the supramolecular aggregates formed by semisynthetic 31-methoxy zinc chlorins were studied theoretically using an exciton theory description. The exciton coupling between the chromophores was calculated using a transition density formalism, making it possible to distinguish stereochemical differences that arise from the facial orientations of the chiral zinc chlorin molecules in the aggregate. It is shown that the precise stereochemical orientation of the molecules inside the stack strongly influences the observed optical properties. These calculations point to a structure with alternating twist angles along the stack, suggesting a different orientation of neighboring molecules. This study is the first step to systematically investigate the optical properties of chlorophyll aggregates, to unveil the supramolecular organization, and to correctly describe the energy transport processes. 1. Introduction Green sulfur and green nonsulfur photosynthetic bacteria have unique chlorosomal antenna systems to harvest sunlight. The chlorosomes have an ellipsoidal shape that consists only of selforganized bacteriochlorophyll (BChl) pigments enclosed in a lipid-protein membrane.1-9 This is in contrast to photosynthetic antenna complexes in plants where the individual pigments are embedded in a protein matrix. The excitonically coupled BChl pigments collect energy from sunlight and achieve ultrafast energy transfer directed toward a reaction center that is located in the cytoplasmic membrane.10-12 This extraordinary architecture is responsible for the survival of some of these bacteria under extremely low light illumination at depths up to 2300 m below the surface of the water.13,14 A solid understanding of the self-organization and photophysical properties of these antenna systems can provide us with valuable design principles that can be used to achieve artificial light harvesting, for instance, in bulk heterojunction dye-sensitized solar cells. The BChl pigments that are involved in the formation of the antenna systems are primarily BChls c, d, and e.7,15 It has been shown that the self-organization of these pigments in vitro is similar to that in vivo in chlorosomes, which suggests that selforganization is solely due to pigment-pigment interactions, without assistance of the membrane proteins.16 The size of the antenna complex and the constituent pigments have been shown to depend on the growth conditions.17 Furthermore, the composition of the BChl aggregates is very similar for different species of bacteria grown under similar light conditions.18,19 This indicates that the same design principles are operative in various species to build the antenna system. The self-organization of BChl is controlled by various bonding and nonbonding interactions between the constituent pigments, leading to the formation of complex structures.20,21 †
Part of the “Mark A. Ratner Festschrift”. * To whom correspondence should be addressed. E-mail: f.c.grozema@ tudelft.nl. ‡ Delft University of Technology. § Universita¨t Wu¨rzburg.
Various spectroscopic and microscopic studies have been performed to investigate the supramolecular organization, including Raman spectroscopy,22 (solid-state) NMR,23,24 (cryo)electron microscopy,25-28 single-molecule fluorescence,29 electron paramagnetic resonance,30 X-ray scattering,27,28 and circular and linear dichroism.31 This has led to the proposal of a variety of supramolecular structures, including single- and doublewalled rods,24,32 lamellar,27,28 fibril-like,25 rolled-up sheets,26 and multilayered cylindrical structures.26 To date, there is no consensus on the actual supramolecular structure of BChls. Natural photosynthesis, using zinc-containing BChl a instead of magnesium, was first discovered in an acidophilic bacterium Acidiphilium ruburm.33 Owing to the stronger binding of zinc ions compared with magnesium ions, these zinc chlorins are chemically more stable and can exist at higher temperatures and more acidic conditions. For this reason, they are preferred in semisynthetic BChl model systems that are most commonly synthesized from natural chlorophylls by relativey simple modifications. These semisynthetic compounds can be tailored for different modes of organization in different solvent environments.34-37 The major advantage of the zinc chlorin model compounds over the native BChls lies in their easy semisynthetic accessibility and their higher chemical stability. Therefore, these compounds are of interest not only to improve our understanding of the natural systems but also to use them for photovoltaic applications.38 The zinc chlorin model compounds considered here (see Figure 1) have been designed for self-organization in nonpolar solvents.34-36 The formation of aggregates is due to four types of noncovalent intermolecular interactions: (1) π-π interactions between tetrapyrrole rings, (2) coordination between a central metal ion and the oxygen atom of the 31-hydroxy/methoxy group, (3) hydrogen bonding between the 31-hydroxy and 131keto groups (for 1a), and (4) interactions between the side chains. Compounds 1a and 1b can form stacked structures by intermolecular coordination between zinc and the 31-oxygen. Compound 1a has the additional possibility to form hydrogen bonds to 131 carbonyl groups of neighboring stacks. Conse-
10.1021/jp107184y 2010 American Chemical Society Published on Web 10/08/2010
Optical Properties of Self-Assembled Zinc Chlorins
Figure 1. Chemical structures of natural BChl c (left) and zinc chlorin model compounds (right).
quently, several coordinated stacks can join together into higherorder structures, for example, a rodlike conformation.34 Compounds 1a and 1b give stable aggregates that remain in solution in nonpolar solvents.35,36 Moreover, the self-assembled π-stacked structures in solution are also observed on a substrate.35 The presence of a structure where consecutive molecules in the zinc-oxygen coordinated stack are arranged in antiparallel manner has been suggested for both 1a and 1b in the microcrystalline solid-state by magic-angle spinning (MAS) NMR spectroscopy in conjunction with X-ray scattering measurements and DFT calculations.20 Interestingly, a similar model was suggested for natural BChl c aggregates in the solid state where antiparallel stacks are formed by π stacking of closed dimers.39 These results have provided some clues to understand the precise self-organization of BChl aggregates. The formation of self-assembled structures in solution can be detected by changes in the optical properties, for example, absorption and circular dichroism (CD) spectra. The formation of aggregates of compounds 1a and 1b in n-hexane/THF (1%) is accompanied by a bathochromic shift of the Qy band from 646 to 740 and 727 nm, respectively. This large bathochromic shift (70-110 nm) is a typical feature in the absorption spectra of the BChl molecules in chlorosomes.40-44 Similarly, distinct differences are observed in the CD spectra at the Qy transition. Compound 1a gives a positive bisignate curve, whereas compound 1b shows a strong Cotton effect with two positive and one negative maximum. Interestingly, the amplitude of the excitonic CD signal for 1b (∼8000 L mol-1 cm-1, g714 ) 3.3 × 10-2) is 10 times larger than that for 1a (∼580 L mol-1 cm-1, 2.5 × 10-3).35 These differences provide a clear indication of the differences in the packing and helicity of the chiral aggregates formed by these molecules.34-36 Self-assembly from monomers up to mesoscopic structures can be observed in temperature-dependent measurements of UV/ vis and CD spectra.36 The effect of increasing temperature is to break the excitonically coupled aggregated chromophores into smaller aggregates and eventually into isolated chromophores. As a result, the intensity of both the absorption and the CD spectra reduces on increasing the temperature. Interestingly, the shape and the position of CD spectra do not change with temperature. This indicates that the spectral shift and shape are not sensitive to the size of the aggregates or the supramolecular
J. Phys. Chem. C, Vol. 114, No. 48, 2010 20835 structure but only depend on the primary structure that consists of a coordinated stack of zinc chlorin molecules. Previous theoretical investigations of the optical properties of BChls in chlorosomes have primarily focused on tubular cylindrical aggregates as they were considered, until recently,26-28 to be the main components of the antenna system.11,45-47 In this previous work, the point dipole approximation was used to describe the excitonic coupling, despite the fact that this model is known to give a rather poor description for closely spaced molecular aggregates. In these calculations it has also not been possible to account for the stereochemical information contained within the BChl molecule. Finally, it was shown that a variety of structures can give similar optical properties, making it difficult to draw conclusions about the supramolecular structure of the aggregates.31 Therefore, a more systematic and more detailed theoretical study is needed in order to understand the optical properties and the supramolecular organization. In this work, we have used exciton theory to establish the relationship between the optical properties and the supramolecular organization for the model BChl 1b aggregates. Calculations of exciton coupling matrix elements using atomic transition densities allow a determination of the precise stereochemical orientation of BChl molecules in the microstructure. The experimental shape of the CD spectra can be reproduced by assuming an antiparallel stacked structure with alternating twist angles between neighboring molecules. It is shown that the stereochemical orientation is very important to correctly interpret the experimental CD spectra. 2. Theory In this work, we use exciton theory48-52 to study the relationship between the structure and optical properties of selfassembled zinc chlorin 1b molecules. This section gives a detailed description of the theoretical methodology used here to calculate the absorption and CD spectra. It has been arranged as follows: Section 2.1describes the exciton Hamiltonian and all the integrals that have to be evaluated in order to obtain the matrix elements. In section 2.2, the equations to calculate various integrals are discussed. Section 2.3 describes the equations for calculating absorption and CD spectra from the eigenstates of the exciton Hamiltonian. 2.1. The Exciton Hamiltonian. The delocalized excited states (or excitons) in an aggregate of chromophores can be written in terms of the singly excited states localized on the ˆ ) has the constituent monomers. The exciton Hamiltonian (H form Nmol
ˆ ) H
∑
Nmol
∑
1 εmBˆm† Bˆm + Jml(Bˆ†1Bˆm + Bˆm† Bˆ1) 2 m)1 m,l)1
(1)
m*l
where Bˆ†m and Bˆm are the creation and the annihilation operators of the exciton on molecule m, εm is the site energy, Jml is the exciton coupling between molecules m and l, and Nmol is the total number of monomers in the aggregate. In a matrix representation, εm and Jml would be the diagonal and the offdiagonal matrix elements of the Hamiltonian matrix, respectively. The diagonal (site energy) terms consist of several contributions:
εm ) ∆εm + Jmm + δm + d0
(2)
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The first term on the right (∆εm) represents the excitation energy of molecule m in vacuum. The second term (Jmm) is called the displacement energy that accounts for the change in monomer excitation energy due to the presence of other molecules. The term δm takes into account the random fluctuations in the monomer excitation energy due to molecular distortion and interaction with solvent molecules. This term δm can be modeled by random selection of energies from a Gaussian distribution. The last term d0 is the bathochromic shift due to the zinc-oxygen coordination. The excited-state wave function of the aggregate is written as a linear combination of localized molecular excited-state functions, Ψme
∑ CmΨme
Ψexciton )
(3)
The localized functions Ψme are antisymmetrized products of the wave functions of the individual monomers Nmol
Ψme
)
Aψme
∏ ψgk
(4)
k*m
the energy difference between these excited states (∆E). In BChl, ∆E ) 1 eV between the Soret and the Qy band, and ∆E ) 0.67 eV between the Qx and Qy bands, whereas the exciton coupling is of the order of 0.01 eV. Therefore, neglecting the contributions of higher excited states is justified in this case, and only the Qy state is considered into exciton theory calculations. Test calculations have shown that the mixing with these higher-lying states is indeed negligible. The calculated excited-states properties of the BChl molecule are provided in the Supporting Information. 2.2. Evaluation of Integrals. An accurate estimate of the diagonal (eq 7) and off-diagonal (eq 6) Coulomb interaction terms is the central task in exciton theory. The most commonly used way of determining the off-diagonal interaction terms is the point dipole approximation. The accuracy of this approach is known to be limited for closely spaced chromophores, and therefore, a more accurate way of calculating the exciton coupling using atomic transition densities is used in this work.54,55 This formalism takes the spatial extent of transition densities into account. A similar approach can be used for calculation of displacement energy Jmm. The integrals appearing in the equations of the exciton coupling (eq 6) and the displacement energy (eq 7) can be expressed in terms of these densities as49,56,57
where molecule m is in the excited state and all other molecules are in the ground state. Similarly, the collective ground-state wave function Ψg can be written as
Jml )
1 4πε0
Nm
Nl
i
j
∑ ∑ (Rm - Rl)
Nmol
Ψg ) A
∏ ψgk
(5)
k
Here, ψgk and ψek are the many-electron wave functions of molecule k in the ground and the excited state, respectively. The most challenging part of exciton theory is to evaluate the exciton coupling Jml and the displacement energy Jmm that can be written in terms of the full antisymmetric wave function, but, after neglect of the exchange part, also in terms of the monomer orbitals and the Coulomb operator.53
ˆ |ψle〉 ) 〈ψme ψlg |Vˆml |ψmg ψle〉 Jml ) 〈ψme |H
(6)
Nmol
Jmm )
∑ (〈ψme ψlg|Vˆml|ψme ψlg〉 - 〈ψmg ψmg |Vˆml|ψmg ψmg 〉)
l*m
(7) In the above equation, the Coulomb operator, Vml, between electrons of molecules m and l is given by
Vˆml )
1 4πε0
nm
nl
i
j
2
∑ ∑ (ri -e rj)
(8)
where ri and rj are positions of the ith and jth electrons on molecules m and l, respectively. nm is the total number of electrons on molecule m. The two-state model (one ground and one excited state for each constituent molecule) that is presented above is valid only when excited states are well separated in energy. Mixing between the lowest excited state and higher lying ones is not significant when the exciton coupling (J) is small compared with
Nmol Nm
Jmm )
Nl
∑∑∑
1 4πε0 l*m
i
j
qitqjt
[
i
qieqjg (Rim - Rjl)
(9)
j
-
qigqjg (Rim - Rjl)
]
(10)
where Rmi is the position of an atom i on molecule m and Nm is the total number of atoms on molecule m. The integrals in eqs 9 and 10 depend on the atomic transition densities qti, the excitedstate atomic charge densities qei , and the ground-state atomic charge densities qgi . The atomic (transition) densities of the isolated chromophores were obtained from singly excited configuration interaction (CIS) calculations based on a INDO ground-state wave function.58 The excited-state basis function ψme in eq 6 is written in terms of the singly excited CI configurations as
ψe )
∑
AijΦij
(11)
conf(i,j)
In eq 11 and below, the subscript m is dropped for simplicity because these equations only concern a single molecule. Φji is the CI determinant that accounts for excitation of an electron from occupied orbital φi to unoccupied orbital φj, and Aij is the corresponding CI coefficient. The molecular orbital basis (φk) is written as
φk )
∑ cpk χp b
AOpb
b
(12)
where χp is an atomic orbital basis function and b is an index that runs over all atomic orbitals centered on atom p. The atomic orbital and CI coefficients that are obtained from the INDO/CIS calculation can be used to obtain the atomic
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transition densities, ground-state densities, and excited-state densities using following equations unocc occ
qtp ) √2e
∑ ∑ ∑ Aijcip cjp b
b
j
(13)
b
i
occ
qgp ) qcore - 2e p
∑ ∑ cip cip b
b
qep
)
qcore p
-e
[
i
unocc occ j
i
cpk bcpk b
+
k
cjpbcjpb - cipbcipb
}
]
fi )
∑
Nm
qtp ) 0;
p)1
∑
Nm
qgp ) 0;
p)1
∑
Nm
qep ) 0; f µ)
p)1
∑ qtpbRp
p)1
(16) where b Rp is the position of atom p with respect to an arbitrary origin. 2.3. Absorption and Circular Dichroism Spectra. Calculation of the matrix elements of the exciton Hamiltonian requires atomic details of the structure of the aggregate under investigation. The energies Ei and eigenvectors are obtained by diagonalizing the exciton Hamiltonian matrix:
(
ε1 l JNmol1
)( ) ( )
... J1Nmol Ci1 Ci1 ·· l ) Ei l l i CNi · · · εNmol CN ·
2 me ED 3 p2 i i
(20)
(15)
In these equations, qpcore is the charge on the core (nucleus + inner shell electrons) on atom p. The electronic densities mentioned above satisfy the following identities for the (transition) densities and transition dipole moment
Nm
Figure 2. The R/β nomenclature for describing the diastereotopic ligation of metal-chlorin: the zinc chlorin 1b is shown with IUPAC numbering.
(D2) or in atomic units (1D ) 0.393 au). The dipole strength is related to the oscillator strength (fi, a dimensionless quantity) by the following expression.
occ
∑ ∑ ∑ AijAij{2 ∑ b
(14)
b
(17)
2.4. Calculation of Spectra. The structure of 1b was optimized with density functional theory (DFT) in the Gaussian03 package using the B3LYP exchange correlation functional and the 6-311G(d,p) basis set.59 The excited-state calculation was performed for the optimized geometry using the singly excited configuration interaction (CIS) method with a reference wave function calculated at the semiempirical level (INDO).58 To construct the CI wave function, single excitations from the highest 20 occupied orbitals into the lowest 20 unoccupied orbitals were included. The excitation energy, transition dipole vector, and the atomic ground-state, excited-state, and transition densities were extracted from this calculation. 3. Results and Discussion 3.1. Stereochemistry of Zn Chlorin Stacks. The central zinc atom of molecule 1b is a stereocenter that can bind to a ligand (in this case, a 31-oxygen of another molecule) from two sides of the chlorin plane. Following the nomenclature by Balaban et al., the R- and β-coordinated diastereomers can be identified, as shown in Figure 2.60,61 The R-coordination side of the chlorin plane is denoted by face R (FR), whereas the β-coordination side of chlorin plane is denoted by face β (Fβ). In nonpolar solvents, compound 1b forms extended aggregates. The primary force leading to this aggregation in the form of long
The dipole strength of the ith excitation (Di) for obtaining the absorption spectrum is given by
|∑ | Nmol
Di )
k
Nmol
Nmol
Cikf µk 2 )
∑
f |2 + (Cik)2 |µ k
k
∑ CikCli*(µfk ·fµl)
k,l
k*l
(18) For calculating the circular dichroism (CD) spectra, the rotational strength of the ith excitation (Ri) has to be evaluated. This is given by
Ri ) -
π 2λi
Nmol
∑ CikCli*(Xbkl ·fµk × fµl)
(19)
k,l
where λi is the wavelength associated with the ith eigenstate. The dipole strength can be expressed either in Debye-squared
Figure 3. Different possible stacked conformations formed by zinc chlorins.
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stacks is the intermolecular coordination between zinc and the 31oxygen (Figure 3). A stack formed in this way can be seen as a one-dimensional system. On one side of the molecular plane of the chlorin, the zinc atom attaches to the 31-oxygen of the neighboring molecule, whereas on the opposite side, the 31-oxygen coordinates with the zinc center of the next molecule. The zinc atom of a molecule in the stack can be coordinated in two ways (R and β). Therefore, there are three possible conformations of the stacks, taking into account the stereochemical orientation of chlorin planes and the (R-/β-) coordination at zinc atoms:
Patwardhan et al.
Figure 4. Exciton coupling between zinc chlorin molecules for dimers in different conformations.
Conformation A: FRFβ f FRFβ f FRFβ f FRFβ f FRFβ....... Conformation B: FβFR f FβFR f FβFR f FβFR f FβFR....... Conformation C: FRFβ f FβFR f FRFβ f FβFR f FRFβ.......
For each pair of coordinated molecules in the conformations above, there are four possible facial orientations: FRFβ f FRFβ, FβFR f FβFR, FRFβ f FβFR, and FβFR f FRFβ. The arrow (f) indicates the coordination of the 31-oxygen of the former molecule to the zinc atom of the latter. The neighboring faces of the BChl are underlined in this notation. In conformations A and B, all zinc atoms are R- and β-coordinated, respectively. As a result, all molecules in conformations A and B are equivalent. On the other hand, in conformation C, zinc atoms of alternate molecules are R- and β-coordinated (Figure 3). Therefore, because of the difference in stereochemistry, the alternate molecules in conformation C are nonequivalent. The presence of intense features in CD spectra generally indicates an ordered structure in which the transition dipoles have a single-handed helical orientation. Therefore, helical conformations were generated by introducing a rotational twist around the coordination bonds into the antiparallel structure with the 31-oxygen pointing to opposite sides of the stack (see Figure 3). As a convention, an anticlockwise rotation around an oxygen-zinc coordination bond is indicated as positive. The rotational freedom for the four coordinated facial dimers varies because of the steric hindrance imposed by either the 171-side chain or the 181-methyl group. As a result, the rotational flexibility in the different conformations varies. The allowed rotational angles for the four coordinated dimers taking these steric restrictions into account are as follows: FRFβ f FRFβ (0-180°), FβFR f FβFR (-145° to 35°), FRFβ f FβFR (-145° to 35°), and FβFR f FRFβ (0-180°). 3.2. Calculation of the Spectra for Aggregates. Using the theoretical methodology outlined in section 2, the ground- and excited-state densities and transition densities were obtained. These densities were used together with the geometry of a selfassembled aggregate to calculate the absorption and CD spectra of the aggregate. A helical stack structure was generated by defining the following parameters: the conformation (A, B, or C), the number of molecules in the stack, and the twist angles as described in the previous section. The structural parameters (atomic coordinates) together with the parameters obtained from a CIS calculation were used to calculate the diagonal and off-diagonal elements of the exciton matrix, as described in section 2.2. The exciton Hamiltonian matrix (eq 17) is then formed for a stack of N molecules, from which the eigenvectors and eigenvalues were obtained after diagonalization.
The current methodology to calculate absorption and CD spectra explicitly accounts for stereochemical differences. As a result, the site energy and exciton coupling values are very sensitive to the facial orientation of BChl molecules in the stack (Figure 2). The exciton coupling as a function of twist angle is plotted in Figure 4 for the different facial orientations of BChl molecules in a coordinated dimer. This clearly shows that there are distinct differences in the exciton coupling for the different conformations of the stack. 3.3. UV/vis and CD Spectra: One Twist Angle. The purpose of this section is to demonstrate the dependence of the UV/vis and the CD spectra on the twist angle for stacks in which the average twist angle is the same everywhere. The diagonal site energy terms were fixed at the monomer excitation energy of 1.9 eV, and only the exciton coupling elements are being evaluated explicitly. The spectral properties were calculated without disorder first. The exciton coupling is sensitive to the twist angle, as shown in Figure 4, which means that the UV/ vis and CD spectra will also depend on the twist angle. The CD and absorption spectra for a twist angle of 45° for a stack in conformation A are plotted in Figure 5. The UV/vis and CD spectra for different angles and conformations are provided in the Supporting Information. The excitonic interaction between neighboring molecules leads to a bathochromic shift in the absorption and CD spectra of up to 52 nm, depending on the twist angle. Interestingly, only a single bisignate curve in the CD broadened spectra and a single maximum are obtained in the broadened UV/vis spectra for all twist angles. Note that all the off-diagonal exciton coupling matrix elements are the same because all molecules are equivalent in these two conformations (A and B), as discussed above. The effect of disorder in the twist angles on the optical properties was studied by introducing random disorder in the twist angles sampled from a flat distribution. The spectra were averaged over several hundreds of realizations of the disordered stacks. As an example, in Figure 6a,b, the UV/vis and CD spectra are plotted for conformation A with an average twist angle of 45° and random disorder in the range of (45°. The spectra without random disorder are also shown. Similarly, in Figure 6c,d, the same is shown for twist angles between 80 and 160° (with an average of 120°). In both cases, the changes in the UV/vis spectrum are small; only a slight broadening is observed. In the CD spectrum, the effect is much more pronounced, especially the intensity. This is evident in Figure 6b for an average twist angle of 45°, whereas for a twist angle of 120°, the change in the intensity is much smaller. This is closely related to the dependence of the CD spectrum on the twist angle. The sign of the bisignate curve in the CD spectrum changes between positive (+/-) and negative (-/+) in the interval of [0-90°], whereas it does not change sign in the interval of [80-160°]. As a result, very low CD intensities are
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Figure 5. Spectral properties for a stack of 100 molecules with a twist angle of 45° in a “stick” representation (a, c) and broadened by a Gaussian function with a width of 0.02 eV (b, d).
Figure 6. UV/vis and CD spectra for aggregates of zinc chlorin with equilibrium twist angles of 45° (a, b) and 120° (c, d) with and without disorder.
observed in the disordered stack in the first interval (45 ( 45°) where the intensities are canceled due to a change in the sign of the bisignate curve. In the second case (120 ( 40°), an appreciable CD intensity is retained. The smaller sensitivity of UV/vis spectra to disorder can be understood because the total oscillator strength is constant, which is equal to the sum of the oscillator strengths of all the constituent molecules. 3.4. UV/vis and CD Spectra: Two Twist Angles. The calculated CD spectra for conformations A and B at a single equilibrium twist angle consist of a single bisignate curve that is either positive (+/-) or negative (-/+). Therefore, conformations A and B cannot account for the experimentally observed CD spectra, which have two positive and one negative extremum, as shown in Figure 7. In conformation C, the physical and chemical environment for consecutive neighbors is different (section 3.1). As a result, it is expected that the equilibrium
twist angle can be different between molecules of consecutive neighbors. Therefore, it is of interest to investigate the spectral properties for the stack by assigning two different twist angles
Figure 7. Experimental CD spectrum of a 1.7 × 10-5 M solution of zinc chlorin 1b in cyclohexane/n-hexane (1:1) at 7 °C.35
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Figure 8. Absorption and CD spectra of the zinc chlorin stacks composed of 100 molecules with alternating twist angles of 10° and 70° in stick (a, c) and broadened (b, d) representations.
Figure 9. Effect of equilibrium twist angle (a) (fwhm of rotational disorder, 20°; fwhm of diagonal disorder, 0.2 eV) and rotational disorder (b) (fwhm of diagonal disorder, 0.2 eV) on the CD spectra.
to consecutive neighbors. Interestingly, on introducing two twist angles, the UV/vis spectrum splits into two parts that have appreciable oscillator strength, as shown, for example, in the stick spectrum in Figure 8a. Both of these parts give rise to a bisignate curve in the CD spectrum. Four different combinations of two bisignate curves are possible, depending on the two angles along the stack: (+/- and +/-), (+/- and -/+), (-/+ and -/+), and (-/+ and +/-). The splitting of levels in the UV/vis spectrum is relatively small and disappears when broadening the spectrum; however, in the CD spectrum, it is largely retained because of the change in the sign. In Figure 8, results are plotted for alternate twist angles of 10° and 70°. In this figure, the twist angles were chosen such that the experimental shape is reproduced but angles close to these give similar results. The relative intensities of the maxima and minimum in the CD spectrum can be tuned somewhat by changing the twist angles. From these simulations, it is concluded that a conformation with two alternating twist angles, such as conformation C, is a likely model for zinc chlorin aggregates. To compare the experimental CD spectra to calculated spectra, more elaborate calculations were performed that take into account the effect of disorder in twist angles and disorder due to solvent molecules. Moreover, the disorder in the site energies was included, as mentioned in section 2.2. It should be noted that this way of including the disorder in the site energy does not include polarization effects, but the main contributions are accounted for.
It was found that for alternating twist angles of 0° (FRFβ f FβFR) and 110° (FβFR f FRFβ), the relative intensities of the extrema in experimental spectra are reproduced best in the presence of disorder. These angles are somewhat different than the values of 10 and 70° mentioned above for ordered aggregates, but the general shape of the shape of the CD spectrum does not change very much. It should be noted that the relative intensities are sensitive to the way in which disorder is taken into account. Different relative intensities in the CD spectra are obtained when disorder is introduced in the site energies in the Hamiltonian rather than just broadening the spectra of the ordered stacks. The changes in site energy and the exciton coupling due to interaction with neighboring molecules results in a shift of the absorption maximum from 654 (monomer) to 694 nm (aggregate). The data obtained from the calculations presented here clearly show that two alternating twist angles are necessary along the stack of chlorins in order to account for the shape of the experimental CD spectrum. This means that subsequent chlorins in the stack should be distinct from each other, such as, for instance, in conformation C. The occurrence of conformation C over conformations A and B implies that there should be a difference in the binding constants for the two types of faceto-face contacts that are present in the π stack. A possible variation of conformation C that would be consistent with the results presented here is the initial formations of so-called closed
Optical Properties of Self-Assembled Zinc Chlorins dimers, as proposed by Nozawa and co-workers.39,62-64 This implies that dimers of two chlorins with two coordinative bonds are formed initially that assemble in a subsequent step into extended stacked structures by π-π interactions without involvement of coordinative bonds between oxygen ligands and zinc centers. Although such a conformation would be consistent with the calculations presented here, the occurrence of it is still to be established experimentally. 4. Conclusions The optical properties of aggregates of 31-methoxy zinc chlorins have been studied theoretically using exciton theory in order to establish the supramolecular organization in these aggregates. It is shown that the stereochemical orientation of the molecules inside the stack has a large effect on the optical properties. The comparison between experimental absorption and CD spectra and the results from calculations can give important information to establish the supramolecular structure of aggregates of multiple chromophores. Using this approach, it is shown that the zinc chlorins considered in this work selfassemble in solution to give a one-dimensional π stack with alternating face-to-face contacts and alternating rotational twist angles close to 0° and 110° between neighboring molecules. The alternating twist angles imply that subsequent chlorin in the stack should be distinct in orientation, for instance, as in conformation C in Figure 3. Acknowledgment. This work was supported by a VENI grant from The Netherlands Organization for Scientific Research (NWO). Supporting Information Available: The Supporting Information includes absorption and CD spectra at different stack lengths and twist angles for different conformations. The implicit origin independence of the current methodology is briefly discussed. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Cruden, D. L.; Stainer, R. Y. Arch. Microbiol. 1970, 72, 115–134. (2) Feick, R. G.; Fuller, R. C. Biochemistry 1984, 23, 3693–3700. (3) Foidl, M.; Golecki, J. R.; Oelze, J. Photosynth. Res. 1998, 55, 109– 114. (4) Golecki, J. R.; Oelze, J. Arch. Microbiol. 1987, 148, 236–241. (5) Martinez-Planells, A.; Arellano, J. B.; Borrego, C. A.; LopezIglesias, C.; Gich, F.; Garcia-Gil, J. S. Photosynth. Res. 2002, 71, 83–90. (6) Montano, G. A.; Bowen, B. P.; LaBelle, J. T.; Woodbury, N. W.; Pizziconi, V. B.; Blankenship, R. E. Biophys. J. 2003, 85, 2560–2565. (7) Taisova, A. S.; Keppen, O. I.; Lukashev, E. P.; Arutyunyan, A. M.; Fetisova, Z. G. Photosynth. Res. 2002, 74, 73–85. (8) Vassilieva, E. V.; Stirewalt, V. L.; Jakobs, C. U.; Frigaard, N. U.; Inoue-Sakamoto, K.; Baker, M. A.; Sotak, A.; Bryant, D. A. Biochemistry 2002, 41, 4358–4370. (9) Zhu, Y. W.; Ramakrishna, B. L.; vanNoort, P. I.; Blankenship, R. E. Biochim. Biophys. Acta, Bioenerg. 1995, 1232, 197–207. (10) Prokhorenko, V. I.; Holzwarth, A. R.; Muller, M. G.; Schaffner, K.; Miyatake, T.; Tamiaki, H. J. Phys. Chem. B 2002, 106, 5761–5768. (11) Prokhorenko, V. I.; Steensgaard, D. B.; Holzwarth, A. F. Biophys. J. 2000, 79, 2105–2120. (12) Savikhin, S.; Zhu, Y. W.; Blankenship, R. E.; Struve, W. S. J. Phys. Chem. 1996, 100, 3320–3322. (13) Beatty, J. T.; Overmann, J.; Lince, M. T.; Manske, A. K.; Lang, A. S.; Blankenship, R. E.; Van Dover, C. L.; Martinson, T. A.; Plumley, F. G. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 9306–9310. (14) Manske, A. K.; Glaeser, J.; Kuypers, M. A. M.; Overmann, J. Appl. EnViron. Microbiol. 2005, 71, 8049–8060. (15) Staehelin, L. A.; Golecki, J. R.; Drews, G. Biochim. Biophys. Acta 1980, 589, 30–45. (16) Miller, M.; Gillbro, T.; Olson, J. M. Photochem. Photobiol. 1993, 57, 98–102.
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