Dynamic Stacking Pathway of Perylene Dimers in Aromatic and

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Dynamic Stacking Pathway of Perylene Dimers in Aromatic and Nonaromatic Solvents Manuel Hollfelder and Stephan Gekle* Physics Department, University of Bayreuth, D-95440 Bayreuth, Germany S Supporting Information *

ABSTRACT: Using molecular dynamics simulations, we elucidate in detail the dynamics of the π−π stacking process of a perylene bisimide (PBI) dimer solvated in toluene. Our calculations show that the transition from the open (unstacked) to the stacked configuration is hindered by a small free energy barrier of approximately 1kBT in toluene but not in the nonaromatic solvent hexane. A similar effect is observed tor two non-covalently linked monomers. The origin of this barrier is traced back to π−π interactions between perylene and the aromatic solvent which are very similar in nature to those between two PBI monomers. The stacking process proceeds in three phases via two well-defined transition states: (i) in the first phase, the two PBI molecules share part of their respective solvation shells forming the first transition state. Further approach needs to squeeze out the shared solvent layer, thus creating the energy barrier. (ii) After removal of the separating solvent, the two PBIs form a second transition state with one monomer located at a random position in the other’s solvation shell. (iii) Finally, the two PBIs slide on top of each other into their final stacked position.

1. INTRODUCTION

A systematic investigation of the dynamic transition pathway from the open (unstacked) to the stacked state, however, has not been conducted so far. Here, we investigate the transition dynamics considering a perylene bisimide dimer solvated in toluene by molecular dynamics (MD) simulations. The investigated structure consists of two perylene bisimide monomers (PBM) and is shown in Figure 1a. Both monomers are connected by an alkane chain containing furthermore oxygen, nitrogen, and two aromatic rings. On the other side of the PBM, two C7H15 chains are present. We consider two different solvents: toluene representing a prototypical aromatic solvent and hexane as a nonaromatic solvent. Our main focus is on the toluene-solvated system, as this has recently been investigated by fluorescence spectroscopy.31,32 The unstacked (OPEN) and stacked (STACK) configurations are well reproduced by our MD simulations, as shown in Figure 1b and c. We find the distance of the planes defined by the (almost perfectly) planar PBMs to be 0.36 nm which is in good agreement with values obtained from X-ray experiments29 and earlier MD simulations.19 The remainder of the paper is organized as follows. After introducing briefly the methods in section 2, we use section 3.1 to characterize the structure of the toluene solvation shell around a single PBM. In section 3.2, we then present the free energy profiles for the dimer solvated in toluene and hexane which govern the stacking transition. In toluene, we observe an energy barrier with a height of approximately 1kBT separating the OPEN

Molecules based on derivatives of perylene are a widely used material for many different purposes: they have useful optical properties because their emission color can be adjusted over a wide range of the visible spectrum,1−3 they are used as highly sensitive sensors,4,5 and they show n-type conduction6 making them suitable for organic transistors7−9 and optoelectronic devices in general.10 Furthermore, molecules based on perylene derivatives are considered a promising candidate for building highly efficient organic solar cells.11−14 Given these numerous applications, perylene derivatives have been intensively investigated both experimentally and computationally in the recent past. One of their salient characteristics is a tendency to form large tower-like aggregates (stacks) of molecules, as has been demonstrated by X-ray diffraction experiments,15,16 fluorescence spectroscopy,17 nuclear magnetic resonance,18 as well as classical19−22 and ab initio23 molecular dynamics simulations. This stacking behavior can be traced back to the interactions of the π-orbitals and has a great influence on the properties of the materials as it dramatically changes, e.g., the efficiency of energy and charge transfer processes.14,15,21,24−28 The static structure of these stacks has been well characterized: in the stacked state, the perylenes remain mostly planar with the distance between the two planes being around 0.35 nm;15,19,29 the perylene axes are tilted by approximately 45° with respect to each other,19 and the free energy gained from stacking is of the order of 15 kJ/mol depending on the exact chemical structure of the perylene derivative as determined by linear free energy relationships in conjunction with UV/vis spectroscopy.30 © 2015 American Chemical Society

Received: April 15, 2015 Revised: July 10, 2015 Published: July 17, 2015 10216

DOI: 10.1021/acs.jpcb.5b03612 J. Phys. Chem. B 2015, 119, 10216−10223

Article

The Journal of Physical Chemistry B

Figure 1. (a) Chemical structure of the investigated perylene bisimide dimer molecule. (b) Snapshot of an unstacked (OPEN) state. (c) Snapshot of a stacked (STACK) configuration. The solvent toluene is omitted for clarity.

Figure 2. Average density of the solvent toluene around one PBM of the dimer during the OPEN state. The density is illustrated as colored plots over planar cuts through the PBM center of mass along the xy (a), yz (b), and xz (c) plane with the legend of the plots in part d. The PBM’s carbon, oxygen, and nitrogen atoms are depicted in gray, red, and blue, respectively. In part e, the distances of the density’s contour areas above 13 nm−3 from the center of mass of the PBM are shown. In part b, A marks a special point which is referred to during the stacking mechanism in section 3.3.1.

and the STACK configuration. This barrier is not present in the nonaromatic solvent. In section 3.3, we describe the full stacking pathway which proceeds from the OPEN to the STACK state via two well-defined transition states in toluene whereas in hexane only a single transition state is identified. Finally, in section 3.4, we compare the free energy profiles of the dimer to similar profiles for two non-covalently linked perylene bisimide

monomers confirming the existence of a free energy barrier in toluene but not in hexane.

2. SIMULATION METHODS Classical molecular dynamics simulations are run with Gromacs33 and the Gromos 53a634 force field. The structure 10217

DOI: 10.1021/acs.jpcb.5b03612 J. Phys. Chem. B 2015, 119, 10216−10223

Article

The Journal of Physical Chemistry B

similar in nature to the π−π interaction in perylene stacks. This interaction strongly influences the stacking dynamics as we will show further below. A similar analysis of the static solvation shell for the solvent hexane can be found in the Supporting Information. 3.2. Free Energy of Stacking. As a first step toward understanding the stacking pathway of the dimer in aromatic solvent, we present in Figure 3 the free energy profile as a

file for the perylene bisimide dimer and monomer was built with JME35 and Avogadro.36 The force field topologies were calculated using Automated Force Field Topology Builder (ATB) and Repository.37 The corresponding files are stored in the ATB database for the dimer38 and the monomer.39 The force field file for the solvent toluene was calculated using PRODRG,40 and the force field for hexane is taken from the ATB database.41 Unitedatom force field topologies were used for the simulations. The visual analysis of the molecular structure files and trajectories was carried out using VMD.42 For the simulations, the dimer was solvated in a rectangular box with 1000 toluene and 900 hexane molecules, respectively. Two monomers were solvated in 1100 toluene molecules and in 900 hexane molecules. After energy minimization and NVT equilibration, the final runs were simulated as NPT ensembles at 300 K and 1 bar. In order to investigate the general behavior and stacking of the dimer, simulations were started with different starting configurations of the atoms’ positions and velocities. Every simulation was stopped as soon as stacking occurred. For the dimer, 36 simulations were conducted in total for toluene and 36 for hexane. Further settings and options for the final runs can be found in the Supporting Information. For the free energy calculations in section 3.2, we use umbrella sampling43 where the distance between the centers of mass of the PBMs was chosen as a reaction coordinate and different states along that coordinate were created using the Gromacs pull code. The distances between the molecules were evaluated with the Gromacs tool g_dist/gmx distance. After equilibration, the simulations were simulated as NPT ensembles for each window at 300 K and 1 bar. For the bias potential, the umbrella potential implemented in the Gromacs package was used and simulations with different spring constants were started. The free energy profile was calculated using the Weighted Histogram Analysis Method implemented in Gromacs as g_wham.44 The spacing of the reaction coordinate, the different spring constants, and further information for the different solvents and the dimer/ monomers can be found in the Supporting Information.

Figure 3. Free energy change as a function of the center of mass (COM) distance between both PBMs of the dimer for the solvents toluene (red) and hexane (green). The states STACK/OPEN and the energy barrier for toluene are marked, and the energy profiles are shifted against each other for clarity.

function of the distance between the COMs of the two monomers for toluene and hexane. The profiles are calculated using umbrella sampling as described in the Simulation Methods section. Any stacking pathway needs to proceed from the plateau region at the right of Figure 3 corresponding to the OPEN state toward the minimum located at 0.38 nm corresponding to the STACK state at the very left. Note that the distance between the COM considered here is slightly larger than the plane−plane distance of 0.36 nm in the STACK state due to the tilting of the monomers with respect to each other.19,32 We start by considering the dimer solvated in toluene (red curve). There is a clear energy barrier with a height of approximately 1kBT separating the STACK and OPEN states from each other. The barrier is rather broad, starting at 1.40 nm and extending down to 0.8 nm. From the top of the barrier, the free energy drops sharply toward its minimum. Around 0.50 nm, we observe a turning point marking a change in the curvature of the free energy curve. Finally, for distances smaller than 0.38 nm, the free energy rises steeply, which is caused by unfavorable squeezing of the PBMs during the stacked state. The free energy difference between the minimum identified with the STACK state and the OPEN state with constant free energy for distances beyond 1.40 nm is approximately 5.2kBT corresponding to 13 kJ/mol. This is in good agreement with values obtained from UV/vis experiments for the aggregation of perylene bisimide: for a slightly different structure of the PBMs (two additional benzene molecules and no connecting carbon chain), the free energy change was obtained as 15.8 kJ/mol for the solvent toluene.30 The density profiles of the toluene solvation shells around the monomers (Figure 2) allow a physical interpretation of the distinct features observed in the free energy profile in the transition region between 1.4 and 0.8 nm. Noting from Figure 2b

3. RESULTS AND DISCUSSION 3.1. Static Solvation Shell for Toluene. We first analyze the static structure of the toluene solvation shell around a single PBM of the dimer in the OPEN state. We find a clear first solvation shell whose time averaged density is, however, rather inhomogeneous, as shown in Figure 2 from different perspectives. Since the monomers are fairly stiff, they remain almost perfectly planar during the entire simulation time. In Figure 2a, which corresponds to a view from the top, alternating regions of high and low densities can be distinguished. The distance from the monomer’s center of mass (COM) to the high density spots on the y-axis is approximately 0.65 nm. Near the partially charged oxygen atoms, we observe regions of fairly low solvent density. In Figure 2b, which represents a head-on view, one can see two rather homogeneous ellipsoidal rings formed around the monomer by the solvent. The side view, Figure 2c, illustrates four clear spots of high solvent density right above and below the PBM. Figure 2e shows a contour plot of the inhomogeneous solvation shell for values above twice the bulk density (above 13 nm−3) and the distance of those spots from the PBM’s COM. The distance between the spots right above and below the PBM and the PBM itself is in z-direction 0.40 nm corresponding to the well-known stacking distance between perylene molecules. This confirms the existence of a π−π interaction between the perylene and the aromatic solvent very 10218

DOI: 10.1021/acs.jpcb.5b03612 J. Phys. Chem. B 2015, 119, 10216−10223

Article

The Journal of Physical Chemistry B

We now focus more closely on the actual stacking process illustrated using an exemplary COM distance trajectory shown in Figure 5. The most notable features are two regions of fairly

and c that the solvation shells are located at distances between 0.40 nm in the z-direction and 0.65 nm in the y-direction, the first contact of the solvation shells is expected to occur for distances between 0.8 and 1.3 nm (depending on the relative orientation of the PBMs during approach) which corresponds closely to the width and position of the energy barrier for toluene. After contact, further approach of the PBMs is only possible if (at least) one of the PBMs loses part of its solvation shell and the two PBMs further on “share” solvent molecules. Scraping off the solvation shell clearly requires energy in the case of the solvent toluene, thus explaining the observed energy barrier. For distances smaller than about 0.7 nm, the PBMs start interacting directly leading to a rapid drop toward the STACK state which represents the absolute minimum of the free energy. We now compare the free energy profile in toluene to the one observed in hexane (green curve in Figure 3). We first note that the free energy gained from stacking in the nonaromatic solvent (7kBT) is larger than that in toluene (5.2kBT). This is in good qualitative agreement with the experimental measurements of ref 30 where the free energy was found to be about 2 times larger in hexane than in toluene. An important difference between the two solvents is the disappearance of the free energy barrier which we attribute to the fact that π−π stacking between the PBM and the solvent is not possible in hexane. Thus, the binding of the PBM to its solvation shell is much less rigid. Accordingly, there is no free energy penalty when the solvation shell is removed in contrast to the toluene case described above. We note the appearance of a slight dip in the hexane free energy profile at around r = 1.1 nm which we will come back to below. 3.3. Dynamic Stacking Pathway of Perylene Bisimide Dimers. 3.3.1. Stacking Mechanism in Toluene. We now turn to the actual stacking pathway for toluene as an example of an aromatic solvent. Figure 4 shows the COM distance of the two

Figure 5. COM distance between both PBMs during the stacking process showing two plateau regions corresponding to the two transition states TS1 and TS2 for the solvent toluene.

constant distance between −780 and −400 ps and between −250 and −50 ps, respectively. These regions correspond to two welldefined transition states which we shall denominate in the following as TS1 and TS2, respectively. These transition states can be found with variable time duration in all of our simulations during the stacking process. To give a full picture, we present in Figure 6 a histogram taken over all 36 simulations during the last

Figure 6. Histogram over COM distances for the transition from OPEN to STACK in the solvent toluene. Only frames