Article pubs.acs.org/JPCA
Molecular Dynamics Simulations and Electronic Excited State Properties of a Self-Assembled Peptide Amphiphile Nanofiber with Metalloporphyrin Arrays Tao Yu, One-Sun Lee, and George C. Schatz* Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208-3113, United States S Supporting Information *
ABSTRACT: We have employed molecular dynamics simulations and quantum chemistry methods to study the structures and electronic absorption properties of a novel type of photonic nanowire gel constructed by the self-assembly of peptide amphiphiles (PAs) and the chromophore-(PPIX)Zn molecules. Using molecular dynamics simulations, structures of the self-assembled fiber were determined with atomistic detail, including the distribution of chromophores along the nanofiber and the relative distances and orientations of pairs of chromophores. In addition, quantum chemistry calculations were used to determine the electronic structure and absorption properties of the chromophores in the fiber, so as to assess the capabilities of the nanofiber for photonics applications. The calculations show that the PA nanofiber provides an effective scaffold for the chromophores in which the chromophores form several clusters in which nearest neighbor chromophores are separated by less than 20 Å. The calculations also indicate that the chromophores can be in both the hydrophilic shell and hydrophobic core portions of the fiber. There are only small spectral shifts to the B-band of the porphyrins arising from the inhomogeneous microelectronic environment provided by the fiber. However, there are much stronger electronic interactions between nearby pairs of chromophores, leading to a more significant red shift of the B-band that is similar to what is found in the experiments and to significant excitonic coupling that is seen in circular dichroism spectra. This electronic interaction between chromophores associated with the PA nanofiber structure is crucial to future applications of these fibers for light-harvesting applications.
I. INTRODUCTION The supramolecular structures formed from self-assembled peptide amphiphiles (PAs) have been used to make promising soft gel materials, which now play important roles in many research areas. These materials have attracted lots of experimental1−3 and theoretical4−13 attention including a number of applications for biomedical purposes,1,2,14−17 use as templates for nanomaterials synthesis,18 and use as lightharvesting materials19 and nanoreactors.20 Of particular interest are PA cylindrical micelles reported by Stupp and coworkers1−3 that have been utilized to promote the growth of blood vessels and heal bones. These fibers consist of a hydrophobic core associated with the alkane part of the PA and a hydrophilic outer shell that comes from the peptide part of the PA. Recently, a novel nanofiber structure was reported that involved integrating dye chromophores with self-assembled PAs.21 This fiber possesses properties that are a hybrid of both PA and dye molecules and could potentially be used as a type of photonic nanowire material for light harvesting in solarenergy conversion processes. In particular, a chromophore-PA self-assembled photonic nanowire was synthesized by loading a number of metalloporphyrins into a solution containing the PAs during the self-assembly process. Here, the PA molecule consists of a hydrophobic tail made by an alkane chain and a peptide segment with the amino acid sequence of AHLLLKKK. © XXXX American Chemical Society
The metalloporphyrin was selected as the zinc protoporphyrin IX ((PPIX)Zn), a dye molecule widely used for light-harvesting applications. UV/visible and circular dichroism (CD) spectroscopic measurements revealed some aspects of the structure of these fibers. However, limitations of the experimental studies failed to provide more detailed (atomic level) structural information about the photonic nanowire. Missing, for instance, was significant information about how the metalloporphyrins organize relative to each other and relative to the structure of the fiber. As a result it was not clear what controls optical properties of the PAs such as the ∼20 nm shift in the B-band of the porphyrin in the fiber relative to the porphyrin in solution and the presence of a nonzero CD signal for optical transitions associated with the achiral porphyrin. Such types of structural insights are crucial for designing useful nanowire photonic devices, because both the arrangement and environment of the chromophores directly determine their functions for light harvesting. Indeed, the arrangement of chromophores in a complex environment plays a major role in applications ranging Special Issue: A. W. Castleman, Jr. Festschrift Received: March 11, 2014 Revised: April 15, 2014
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Figure 1. (a) The PA molecule used in MD simulations, where the PA sequence is AHLLLKKK. (b) The metalloporphyrin, (PPIX)Zn, used in the MD simulations. (c) The initial structure of the PAs and (PPIX)Zns for MD simulations. Six PAs are placed radially in the first layer (red) where their tails are pointing inward. The second layer also has six PAs (blue) and is rotated by 30° relative to the first layer. The angle between neighboring PAs is 60°, and the distance between layers is 5 Å. Twelve molecules of (PPIX)Zn are placed in the space between PA molecules.
structure of porphyrin aggregates relative to the PA fiber are also characterized. This information determines the microenvironment of the metalloporphyrins, providing important insight into interactions between the metalloporphyrins and PAs and within clusters of the metalloporphyrins. With the quantum calculations we have determined UV/ visible absorption spectra for snapshots of the MD structures, and the results provide important insights about optical experiments that were presented in the Fry et al. work.21 It is found that there are only small (∼1 nm) spectral shifts in the Bband absorption associated with the local electronic environ-
from the light-harvesting complex in biology22,23 to recently developed metal organic framework light-harvesting materials.24 In the present work, we use molecular dynamics (MD) simulation methods in combination with quantum mechanics to determine the structural and optical properties of the metalloporphyrin-PA fibers. With MD we use atomistic force fields to simulate fiber formation, and from this we visualize the distribution and orientation of the corresponding metalloporphyrins along the PA nanofiber structure. Other significant geometric aspects, such as the relative distance and orientation between nearby pairs of metalloporphyrins, and the B
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production period. Full electrostatics was employed using the particle-mesh Ewald method38 with a 1 Å grid width. Nonbonded interactions were calculated using a group-based cutoff with a switching function and were updated every 10 time steps. Covalent bonds involving hydrogen were held rigid using the SHAKE algorithm,39 allowing a 2 fs time step. Atomic coordinates were saved every 10 ps for the trajectory analysis. II. 3. Calculation of Electronic States and Absorption Spectra. Following the MD simulations, the atomic coordinates of the hybrid nanofiber structure were saved and used in electronic structure studies using the ZINDO-S40−43 and CIS44 methods as implemented in the quantum chemistry package ORCA.45 The calculations included the following: (1) determination of the excitation energies and absorption spectra for each chromophore in vacuum; (2) spectra of individual molecules including explicit surrounding atoms in the nanofiber structure within 5 Å of any atom in each chromophore (Note: if the selected surrounding atoms based on this criterion belong to another chromophore, these atoms are not included in these calculations; also, whenever covalent bonds are cut by this procedure, the atoms with dangling bonds are hydrogenated); and (3) spectra including nearest neighbor pairs of chromophores.
ment that the chromophores experience due to nearby PAs and solvent molecules. However, the porphyrins are found to readily form clusters, and there is a more significant red shift in the B-band associated with these clusters, as well as excitonic interactions that cause the observed CD spectra. This combination of chromophore clusters, and strong intermolecular electronic coupling25−27 is an important issue in determining energy migration for light harvesting.
II. COMPUTATIONAL DETAILS II. 1. Construction of Photonic Nanowire Structure. Atomistic structures of the PA (Ala-His-Leu-Leu-Leu-Lys-LysLys) and metalloporphyrin used in the simulations are shown Figure 1a, b. To be consistent with experiments, where the optimum concentration ratio of PA to metalloporphyrin is 6:1, we employed 72 PA molecules and 12 (PPIX)Zn units in the simulations. The starting structure of the backbone of each PA is assumed to be an extended conformation. The fiber selfassembly simulations followed a protocol28 previously defined for assembly in the absence of the chromophores that simulates the final stages of assembly starting from a “seeded” initial structure (as has been justified using coarse-grained simulations29). To define the initial fiber structure, six PAs are radially placed on a plane with the tails pointing inward (Figure 1c). The angle between adjacent PAs is 60°. The second layer is taken to be identical to the first layer but rotated by 30° relative to the first layer and with the distance between layers taken to be 5 Å. A total of 12 layers that alternate between first and second layers are placed along the fiber axis to define the complete structure. For assembly simulations that include the porphyrins, 12 (PPIX)Zn molecules are placed in the space between the PA molecules. The 12 (PPIX)Zn molecules are helically placed using a space filling model as shown in Figure 1c. The distance from the center of the PA fiber to the zinc atom of each metalloporphyrin is 24 Å, the angle between neighboring (PPIX)Zn molecules is 30°, and the azimuthal distance between zinc atoms along the fiber is 5 Å. The system was solvated in a water box using the SOLVATE module30 implemented in VMD.31 Periodic boundary conditions were used in the simulations, using a box of dimensions of 108 × 108 × 56 Å3. This box was filled with 16 687 water molecules based on the modified TIP3P potential.32,33 To neutralize the system, 130 Cl− ions are added. A 1000 step energy minimization was applied to the solvated system to remove the high-energy contacts. II. 2. MD Simulations. Three independent molecular dynamics simulations were carried out using NAMD2.34 The force field for the Zinc porphyrin came from the work by Marques and Cukrowski.35 An annealing molecular dynamics protocol was applied to the system using a NVT ensemble. The temperature, initially set at 800 K, was lowered by 200 K after every 1 ns, until it reached 400 K. During the annealing simulation, the movement of the terminal carbon of each PA tail to the direction normal to the PA fiber is restrained to maintain the fiber structure. This annealed structure is used as a starting configuration for a subsequent production molecular dynamics simulation. In the production period, the system was simulated for 10 ns using the NPT ensemble and Langevin dynamics36 at a temperature of 300 K with a damping coefficient g = 5 ps−1. Pressure was maintained at 1 atm using the Langevin piston36,37 method with a piston period of 100 fs, a damping time constant of 50 fs, and piston temperature of 300 K. No atomic coordinates were constrained during the
III. RESULTS AND DISCUSSION To construct reasonable structures of the metalloporphyrin-PA nanofibers using MD techniques, we considered two different strategies, adding the porphyrins after the fiber is assembled or including them directly during the self-assembly. In the first approach, the metalloporphyrin molecules were added at the interface between the PA fiber and the surrounding solvent molecules and then several cycles of annealing (heating-up and cooling-down steps in the MD simulations) were performed. We expected to observe that the metalloporphyrins could embed themselves into a portion of the PA fiber and thus the hybrid nanofiber structure would be generated. However, this procedure was not successful and the metalloporphyrins still remained near the surface of the PA fiber after the MD simulations. This result demonstrates that there exists a large enough free energy barrier that blocks the metalloporphyrins from transferring into the nanofiber, even when relatively hightemperature simulation steps are included. The failure of this postloading strategy is consistent with what has been found in the experiments, where the hybrid nanofiber can only be synthesized by adding metalloporphyrins into the mixture of PAs before the nanofibers are generated. The second strategy to create the hybrid nanofiber structure is to directly put the metalloporphyrins inside the PA fiber at the initiation of selfassembly. During the annealing process, the metalloporphyrins are subjected to considerable perturbation and can access configurations with relatively low free energies. After several cycles of annealing, configurations close to the global freeenergy minimum are expected to be obtained. Finally, further MD simulations at room temperature are conducted to equilibrate configurations for another 10 ns. Figure 2 shows a representative structure of the hybrid nanofiber (based on a calculation in which the porphyrins are added at the beginning) after one of the MD simulations. Highlighted in the figure are the 12 (PPIX)Zn molecules that have undergone significant rearrangement compared to their initial structure in Figure 1. Figure 3 highlights the distribution and labeling of the (PPIX)Zn after the other two MD simulations. Figure 2 shows that the fiber diameter is around C
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Figure 4. A distribution of the secondary structure, beta-sheet (in closed circle) and the turn (in open circle), of the PA-nanofiber along the peptide sequence: AHLLLKKK.
Figure 2. A representative snapshot of the structure of the (PPIX)ZnPA hybrid nanofiber structure obtained by a 10 ns MD simulations. The (PPIX)Zn molecules are labeled from 1 to 12 and the blue lines represent the hydrophobic core of the PA nanofiber.
sheets,46−48 thus they contribute the most to this type of secondary structure. Next we consider the relative geometries of the 12 (PPIX)Zn molecules in each of the three MD simulations with respect to the PA nanofiber structure. Figure 5 displays the distribution of the (PPIX)Zn molecules along the fiber based on the result of the first MD simulation, characterized by the distance of the metal Zn with respect to the center-axis of the fiber cylinder. The results demonstrate that the relative distance spans a broad range from 9 to 30 Å. Note that the radius of the hydrophobic core of the fiber is around 18 Å and the hydrophilic peptide shell occupies radii between 18 and 40 Å. It is found that five of the Zn centers in the metallophorphyrins (numbered 1, 7, 10, 11, and 12), belong to the hydrophobic core, while another six of the Zn centers in the metallophorphyrins (2, 3, 4, 5, 8, and 9) are located in the hydrophilic shell. The remaining Zn center in the metallophorphyrin 6 is at the interface between the core
8.1 nm, which agrees very well with the experimental measurements. Concerning the secondary structure, it was demonstrated in the experiments21 that although most of the peptides in the nanofiber display a random coil structure, there exist ordered secondary structures, that is, beta-sheet and turn, in the fiber structure. This is consistent with the simulation results for which the distribution of secondary structures is displayed in Figure 4. Here it is seen that beta-sheet structures contribute a small portion of the total secondary structure, and they are inhomogeneously distributed across the peptide sequence AHLLLKKK, being mostly found in the middle part of the sequence, with negligible beta-sheet character in the C- and N-terminals. Meanwhile, as expected, the leucine residues have a considerable propensity to form beta-
Figure 3. The representative snapshot of the structure of the (PPIX)Zn molecules in the second (left) and third (right) simulations. In each snapshot, the (PPIX)Zn molecules are labeled from 1 to 12. D
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Table 1. Number of Surrounding PA Residues Defined As the Closest Neighbors within 5 Å with Respect to Each Atom of the 12 Individual (PPIX)Zn Molecules simulation 1 1 2 3 4 5 6 7 8 9 10 11 12
Figure 5. Radial distance of each Zn center with respect to the center axis of the PA-nanofiber cylinder (based on the first MD simulation). The horizontal lines stand for the boundary of the core (blue) and peptide shell (red) in the PA-nanofiber structure.
1 2 3 4 5 6 7 8 9 10 11 12
and shell. This inhomogeneous distribution of the metalloporphyrins comes from a converged simulation of the metalloporphyrins in the PA nanofiber (although we note that diffusion effects at >10 ns time scales are not described), so apparently both hydrophobic and hydrophilic environments are possible. Similarly, tracking the results in the other two simulations, it is found that the zinc center of metalloporphyrins 2, 6, 7, 8, and 10 were located in the hydrophobic portion of the fiber, and 1, 3, 4, 5, 9, 11, and 12 were distributed in the hydrophilic shell. In the third simulation, the zinc center of the metalloporphyrins 3, 5, 8, 9, 10, 11, and 12 were located in the hydrophobic core, and 1, 2, 4, 6, and 7 were distributed in the shell. To further explore this we characterize the microenvironment surrounding each metalloporphyrin molecule in the fiber, here determining the most probable residues within 5 Å of each atom in the metalloporphyrin. The results for the three simulations are listed Table 1. The simulations that give the same results within statistical uncertainty, show that each (PPIX)Zn molecule is surrounded by more than 10 residues from different PA molecules in the nanofiber structure, in addition to water molecules. Note that on average for those (PPIX)Zn whose Zn centers are located within the core or at the core−shell interface, there are more ALA and less LYS residues than the neighbors. In contrast, the (PPIX)Zn whose Zn centers are located within the shell are more LYS but less ALA. This result is reasonable because ALA is the N-terminal residue, which is therefore closest to the core of the fiber, while LYS is the C-terminal residue, which is farthest from the core. In addition, it is found that HIS is the residue with the least number of the neighbors, as expected because the total number of HIS in the PA sequence is the least. When normalized for the relative populations of HIS relative to LEU or LYS, HIS has about the same number of (PPIX)Zn molecules nearby as LEU and more than LYS. In contrast to speculation in the work by Fry et al.,21 we find no strong preference for the porphyrin to associate with histidine. In general, it is expected that the environment near the metalloporphyrins in the PA fiber is the result of interactions between both the metalloporphyrins and PA molecules and between metalloporphyrins and water molecules. The (PPIX)
1 2 3 4 5 6 7 8 9 10 11 12
ALA
LYS
LEU
HIS
7 1 1 2 1 5 6 1 3 4 8 6
1 2 6 4 5 2 4 4 2 0 2 1 simulation 2
3 8 6 5 9 7 4 6 5 1 3 3
0 1 0 3 2 2 2 3 2 1 1 1
ALA
LYS
LEU
HIS
2 6 2 1 3 5 7 6 0 7 2 3
2 2 4 4 2 2 2 2 5 1 5 4 simulation 3
5 6 8 6 6 2 5 3 7 3 8 6
1 2 2 0 1 1 1 2 0 1 0 1
ALA
LYS
LEU
HIS
0 3 7 2 5 0 1 8 6 7 6 8
2 3 1 4 3 2 5 1 2 3 1 2
7 6 2 7 6 7 5 2 3 5 5 2
0 2 1 2 1 0 1 2 3 2 1 1
Zn molecule has two negative N− and one positive Zn2+ in the center of the ring and two negative deprotonated carboxyl groups at the edge of the porphyrinic part. These units are expected to have significant electrostatic interactions with water molecules or with the charged LYS residues. In addition, van der Waals interactions will play important roles given the large size of the (PPIX)Zn. Note that the cavity containing the (PPIX)Zn molecules not only serves as a scaffold to stabilize the molecules in the nanofiber but it also provides a microelectronic-environment that modifies the optical properties of each (PPIX)Zn molecule, thus influencing the performance of the hybrid nanofiber used as a photonic nanowire. Another significant geometric aspect is how the (PPIX)Zn molecules organize relative to each other in the confined E
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Table 2. Distances in Å between Pairs of Zn Centers in the Hybrid Nanofiber Structure for the 12 Porphyrin Molecules simulation 1 1 2 3 4 5 6 7 8 9 10 11 12
1 2 3 4 5 6 7 8 9 10 11 12
1 2 3 4 5 6 7 8 9 10 11 12
1
2
3
4
5
35 45 44 39 30 32 33 28 52 39 11
15 22 32 36 43 58 50 43 36 40
10 26 36 46 63 59 47 44 52
16 29 39 58 55 45 43 52
16 30 46 47 47 43 49
1
2
3
4
5
39 46 55 43 41 42 40 48 25 44 9
9 28 30 29 35 49 50 42 38 30
21 28 29 39 52 55 47 46 37
18 21 37 46 55 48 59 48
4 25 29 42 32 54 38
1
2
3
4
5
52 45 50 54 65 65 50 44 30 31 23
20 22 22 48 54 40 39 44 61 46
15 10 30 36 24 27 31 49 32
12 34 45 38 41 43 60 41
27 36 29 34 40 58 41
6
7
8
9
10
11
22 21 33 27 38
16 51 42 37
41 29 28
15 53
39
7
8
9
10
11
22 18 23 38 38
27 16 54 40
27 37 46
43 25
38
6
7
8
9
10
11
16 28 38 45 61 46
22 32 40 53 43
10 23 38 30
16 31 25
18 11
21
16 30 33 42 36 40 simulation 2 6
21 26 38 29 50 36 simulation 3
12
12
12
5/6, 6/7, 8/9, and 10/11 and the clusters being the molecules 1−12, 2−3−4−5−6−7, 8−9, and 10−11. In the second simulation, 6 pairs and 6 clusters are found with the pairs 1/ 12, 2/3, 4/5, 5/6, 7/9, and 8/10 and the clusters being 1−12, 2−3, 4−5−6, 7−9, 8−10, and 11. Similarly, in the third simulation, 8 pairs and 5 clusters are found, with the pairs being 3/4, 4/5, 4/5, 6/7, 8/9, 9/10, 10/11, 10/12 and the clusters being 3−4−5, 6−7, 8−9−10−11−12, 1, and 2. The nomenclature of the pairs and clusters is displayed in Scheme 1. Note that most of the (PPIX)Zn molecules are involved in clusters with only three monomers in the three trajectories. There are 19 pair structures overall, and many of the pairs form clusters that are chains of pairs. The low probability of forming trimers can be understood in terms of interactions between (PPIX)Zn molecules and their concentration. The (PPIX)Zn molecules are negatively charged so electrostatic repulsions would tend to inhibit aggregation. In addition, the concen-
nanofiber structure, here considering the 12 metalloporphyrins as an array or network along the fiber. In this case, we are interested in the electronic interaction between the (PPIX)Zn molecules, which is important to the light-harvesting process. To characterize these interactions quantitatively, we measured distances between pairs of Zn centers as well as their relative orientation with the latter defined in terms of the intersection angle between the transition dipole moment of each chromophore. The results of the three simulations are presented in Tables 2 and 3. Using the information in Table 2, we can organize the (PPIX)Zn molecules according to their separations. We assume a cutoff distance of 20 Å and define those (PPIX)Zn molecules whose intermolecular distance is less than the cutoff distance as a pair and then several mutually interacting pairs as a cluster. From this we find that in the first simulation there are 8 pairs and 4 clusters with the pairs corresponding to the (PPIX)Zn molecules 1/12, 2/3, 3/4, 4/5, F
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Table 3. Relative Orientation Anglesa in Degrees between Each Pair of (PPIX)Zn Molecules in the Hybrid Nanofiber Structure simulation 1 1 2 3 4 5 6 7 8 9 10 11 12
1 2 3 4 5 6 7 8 9 10 11 12
1 2 3 4 5 6 7 8 9 10 11 12 a
1
2
3
4
5
89 93 69 43 73 43 6 77 104 35 95
16 25 47 51 128 94 26 32 65 94
39 50 67 125 98 18 44 64 109
35 32 112 75 39 36 57 81
60 81 48 35 71 22 106
1
2
3
4
5
66 33 111 17 51 105 145 17 111 152 162
92 63 50 74 111 106 50 46 93 97
108 50 36 76 120 44 137 174 150
104 72 58 44 95 52 72 53
59 115 146 12 94 136 147
1
2
3
4
5
120 7 116 20 133 36 76 101 144 101 87
125 119 129 107 155 157 115 64 92 54
113 21 128 32 73 95 140 104 94
98 26 81 40 75 85 54 109
119 26 61 107 159 83 84
6
7
8
9
10
11
37 107 147 62 107
81 110 37 97
58 46 118
92 65
120
7
8
9
10
11
44 104 109 100 74
135 75 56 30
96 142 145
47 54
26
6
7
8
9
10
11
97 59 57 60 75 123
41 84 138 89 108
75 115 67 115
54 130 168
115 115
56
112 79 71 37 79 49 simulation 2 6
57 94 47 110 143 120 simulation 3
12
12
12
The relative orientation angles are calculated by considering the intersection angle between the transition dipole moment of each porphyrin.
tration of (PPIX)Zn molecules is only 1/6 that of the PA molecules (based on the experimental conditions) that one would expect would disfavor the formation of higher aggregates, yet the porphyrin is large enough that monomers are also disfavored. Different interactions seem to govern the formation of pairs depending on whether the porphyrins are in the hydrophobic or hydrophilic parts of the fiber. In the first simulation result for instance, Figure 5 indicates that the (PPIX)Zn molecules 2, 3, 4, 5, 8, and 9 are located in the hydrophilic shell of the fiber. In this configuration, there can be electrostatic attraction between the positively charged LYS of the PA and a negative-charged oxygen atom of the (PPIX)Zn. This provides the driving force for pair formation, and indeed the pairs 2/3, 3/4, 4/5, 8/9 are all in this region. Similarly, the (PPIX)Zn labeled 1, 6, 7, 10, 11, 12 are distributed in the hydrophobic core of the fiber where
interactions of the porphyrin molecules with ALA in the peptide and with the alkane tail of the PA in the fiber would be dominant. These effects can play a role in the formation of the pairs 1/12, 6/7, and 10/11. Note from Table 3 that the transition moments in pairs are broadly distributed with some angles being close to zero or 180° while others are close to 90°. All the structural insights from the hybrid nanofiber structure discussed above directly affect the optical properties of the metalloporphyrin molecules. The UV/visible absorption spectrum of the metalloporphyrin has been well studied experimentally and it is found that there is a characteristic absorption peak around 410 nm called the B-band. This band is the strongest absorption peak of the metalloporphyrin molecules, determining their color. Furthermore, the B-band is not only sensitive to the oxidation state of the metal center in the porphyrin but also sensitive to the surrounding environG
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Scheme 1. Nomenclature of the Clusters in the Three Simulationsa
a
The monomer, dimer, and trimer are recognized by having one, two, and three porphyrins (labeled by the numbers) in the green circle, respectively.
Figure 6. The nearest (within 5 Å of each atom in the metalloporphyrin-6) surrounding environment of metalloporphyrin-6 (represented in yellow) in the nanofiber structure from the first MD simulation. All of the atoms in the range selected were used for quantum calculations.
ment of the chromophore. For the particular case of (PPIX)Zn, the B-band is at around 412 nm21 and red shifts to 431 nm in the PA-nanofiber, thus demonstrating the effect of the microenvironment associated with the nanofiber. Using the structure obtained from the MD simulations, we have calculated the absorption spectrum of the (PPIX)Zn molecules in various contexts, providing detailed insight on how the structural details, PA microenvironment, and nearby chromophores affect the optical properties of the chromophores. To that end, we employed the semiempirical method, ZINDO-S/CIS to obtain both the ground-state and excitedstate energy levels, and corresponding absorption spectra. Although ZINDO-S is a semiempirical method, it is parametrized by spectroscopic data;40−43 thus, it often reliable, being widely used for studying the absorption spectra of metalloporphyrins. In addition, it is computationally simple enough to allow inclusion of many surrounding residues and water molecules in the electronic structure calculation. Note that the conventional QM/MM method49 would not be an appropriate choice for this application, because it only considers polarization of the QM segment induced by the MM part and not polarization of MM part generated by QM segment in the absence of polarizable force-fields.50,51 In our calculations, for each of the three 10 ns simulations we selected 10 frames, and in each frame the 12 (PPIX)Zn molecules were considered individually and their B-band absorptions were initially calculated in the absence of nearby atoms. The average ZINDO-S/CIS B-band absorption wavelength for the three simulations is 408, 406, and 407 nm, respectively, which is consistent with experimental measurements21 where the observed wavelength is around 412 nm. In the next step, we evaluated the effect of the surrounding PA molecules on the B-band absorption in the nanofiber structure. To that end, the same 120 (PPIX)Zn molecules were considered, and for (PPIX)Zn those atoms in the surrounding PA residues and solvent molecules that are located within 5 Å of any atom in the (PPIX)Zn were added to the ZINDO-S/CIS calculations. As an example, Figure 6 displays the selected surrounding atoms with respect to the (PPIX)Zn-6 in the ZINDO-S/CIS calculation. The average wavelength of the Bband for these 120 (PPIX)Zn is around 409 nm. This shows that the surrounding PA molecules do red shift the spectra but the effect is very small.
On the basis of the experimental measurements, the B-band absorption of the (PPIX)Zn molecules displays a significant red shift, about a 20 nm, when embedded in the nanofiber structure. This indicates that there must exist another mechanism to regulate the electronic excitation properties beyond the effect of the surrounding medium. Note from our earlier discussion that the 12 (PPIX)Zn form pairs and clusters as defined by considering relative intermolecular distances less than 20 Å. In these clusters, one expects electronic coupling between the chromophores that can be described with calculations in which two or three (PPIX)Zn are combined when calculating the electronic excitations. We also considered even larger groupings (with four chromophores) for these calculations, such as porphyrins 2, 3, 4, and 5 in the cluster C1− 2 in Scheme 1; however, we found that because the larger clusters consists of pairs that are chained together, these longer range interactions are weak and do not noticeably influence the results. Considering the dimer and trimer interactions, it is found that there are two relatively strong B-bands with wavelengths of 406 and 418 nm, 399 and 415 nm, and 400 and 414 nm for our three simulations. The blue shift absorption B-bands can be attributed to H-aggregate couplings within the dimer and trimer structures as well as to distortions of the (PPIX)Zn structures away from the optimized geometry due to thermal fluctuations. The red-shifted absorption (which averages to around a 10 nm shift) can be attributed to Jaggregate coupling in the dimer and trimer structures as well as distortions due to thermal fluctuations. While the 10 nm red shift is smaller than is measured, it shows that cluster formation plays an important role in determining the observed spectra. The differences between theory and experiment might arise from several factors, including inaccuracy in the electronic structre theory, incomplete aggregation of the porphyrins that results in less than optimum orientation of the J-aggregate pairs, and the low concentration of the trimer clusters due to incomplete equilibration of the fibers. To study these questions, we consider the contribution of the trimer clusters to the redH
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shifted absorption. It is found that the averaged absorption wavelength is 426 nm based on the cluster C3−1 (Scheme 1). This is a larger shift that is close to the experimental results (around 20 nm comparing with the calculated absorption of the isolated porphyrin). On the other hand, if we consider dimers but assume perfect alignment for a J-aggregate dimer (here using the porphyrins 2 and 3 in the cluster C1−2, refer to Figure S1 in the Supporting Information), it is found that the absorption is shifted to 421 nm. Therefore, we conclude that both cluster alignment and trimer clusters are contributing reasons for differences between experiment and calculations. Independently of this, the present results show that the observed red shifts are the result of interacting pairs and trimers of chromophores, which is a mechanism whereby this type of hybrid nanofiber can function as a light-harvesting structure. In addition, the excitonic couplings between pairs provides an explanation for the observation of a nonzero CD spectrum for the B-band. Exciton-coupled CD is well-known in structures like DNA dumbbells,52 where it leads to significant CD in capping achiral chromophores as long as the chromophores are not separated by more than a few base-pairs (
