Noncovalent interaction and its influence on excited-state behavior: A theoretical study on the mixed coaggregates of dicyanonaphthalene and pyrazoline

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Noncovalent interaction and its inﬂuence on excited-state behavior: A

theoretical study on the mixed coaggregates of dicyanonaphthalene and pyrazoline

Yulan Dai

a

_{, Meiyuan Guo}

a

_{, Jingdong Peng}

a,⇑

_{, Wei Shen}

a

_{, Ming Li}

a,b

_{, Rongxing He}

a,b,⇑

_{, Chaoyuan Zhu}

c

_,

Sheng Hsien Lin

c

a

School of Chemistry and Chemical Engineering, Southwest University, Chongqing 400715, China

b_{Education Ministry Key Laboratory on Luminescence and Real-Time Analysis, Southwest University, Chongqing 400715, China} c

Department of Applied Chemistry, Institute of Molecular Science and Center for Interdisciplinary Molecular Science, National Chiao-Tung University, Hsinchu 300, Taiwan

a r t i c l e

i n f o

Article history: Received 9 October 2012 In ﬁnal form 22 November 2012 Available online 3 December 2012

a b s t r a c t

In the present letter we investigate the noncovalent interactions in the mixed coaggregates of 1,3,5-tri-phenyl-2-pyrazoline (TPP) and 1,4-dicyanonaphthalene (DCN) and their inﬂuence on the excited-state properties of the TPP–DCN. The theoretical results show that thep–pstacking interactions play an impor-tant role in the noncovalent interactions of the TPP–DCN coaggregates. The effect of thep–pinteractions on the excited-state properties of the TPP–DCN is also fully investigated, and the results indicate that the TPP and DCN do not form an intermolecular charge-transfer complex in the ground state, whereas they form an exciplex in the excited state.

1. Introduction

Noncovalent interactions play a crucial role in many areas of chemistry, biology, and materials science [1–3]. As one of the principal nocovalent interactions, the

p

–

p

stacking is essential to understand and explain many supramolecular organization and recognition processes [4,5], such as nucleic acids[6,7], porphy-rin-like aggregates [8] and macromolecular structures [9,10]. Because of their importance for the design of novel supramolecular systems and nanomaterials, the

p

–

p

stacking interactions have been studied extensively in the past decades . In order to understand the nature of the

p

–

p

stacking interactions, the benzene dimer was investigated experimentally and theoretically as one of the simplest prototypes of

p

–

p

stacking interactions [11–15]. Theoretical computations indicated that the displace-stacked and T-shaped (edge-to-face) structures of the benzene dimer are the most stable ones because of the quadrupole– quadrupole interactions. However, only the T-shaped conﬁgura-tion was observed experimentally [11]. For the substituted benzene dimer, the situation is different from that of the benzene dimer due to the inductive effect of substituent group which alters energy landscape[16]. In some cases of given systems, the stacked conﬁgurations are predicted to be more stable than the T-shaped one because the dipole–dipole attractive interactions overwhelm the quadrupole–quadrupole repulsive interactions. Actually, the

nature of the

p

–

p

stacking interactions is still a matter of debate [17,18]. Hobza et al.[2,3,19]and Improta et al.[20–22]performed a series of theoretical studies to explore the nature of noncovalent interactions and to explain their influence on the ground and excited states of given systems, such as nucleic acids and dye aggregates. They studied the electronic state, decay rate and quantum dynamics of nucleic acids using the intermolecular charge transfer (CT) character in the density functional theory (DFT) framework. These theoretical works provided a step forward to understand the nature of noncovalent interactions and photoin-duced charge transfer (PCT) process. In general, the interaction energies between two molecules include the electrostatic interac-tions, induction interacinterac-tions, dispersion interactions and repulsive interactions. The central issue is to make clear the extent of these components contributing to final interaction enthalpy in the ground state. For the excited state, ones focus their efforts to the influence of weak interactions on ionization energies, decay rate and quantum dynamics.

The calculation of intermolecular energies is one of the difﬁcult tasks in today’s computational chemistry[23]. To describe exactly the intermolecular energies, many theoretical efforts have been performed [24–31]. Highly accurate coupled cluster methods (CCSD(T)) are available for small molecular systems [27]. For supermolecule, however, this methodology is not appropriate be-cause of the expensive computational cost, which makes people to use more suitable methods, such as the DFT method. Unfortu-nately, the traditional DFT (such as B3LYP) methods generally show a dramatic underestimation of the weak interactions for non-covalent systems. In the last decade, scientists have developed a series of new DFT methods including the dispersion correction 0009-2614/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved.

http://dx.doi.org/10.1016/j.cplett.2012.11.061

⇑Corresponding authors at: School of Chemistry and Chemical Engineering, Southwest University, Chongqing 400715, China. Fax: +86 23 68254000 (R. He).

E-mail addresses:hxpengjd@swu.edu.cn(J. Peng),herx@swu.edu.cn(R. He).

Contents lists available atSciVerse ScienceDirect

Chemical Physics Letters

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term, such as the M0X (X = 5, 6) family[28], the dispersion-cor-recting atom-centered potentials (B3LYP-DCPs)[29]and the Grim-me’s DFT-D [30] method. These methods have an outstanding performance to describe the

p

–

p

stacking interactions, especially the

x

B97XD functional of Grimme’s DFT-D[31]method.

The PCT process is a primary step in photophysical, photochem-ical as well as photobiologphotochem-ical processes. The PCT process can be intermolecular CT in which an electron is transferred from donor to acceptor. In earlier PCT studies, the covalent linked and hydro-gen-bonded donor–acceptor self-assembled aggregates were inves-tigated mainly. Since the PCT process in coaggregates (one of kinds of aggregates) was found occasionally by Janssen and co-workers [32], the research of coaggregates has made great progress, espe-cially in the area of supramolecular engineering of functional dyes. The most attractive features of dye aggregates are their emerging new functionalities which are not given in individual molecule but arisen upon in aggregation due to the electronic coupling of

p

-systems[33]. These functionalities render dye aggregates have the possibilities of application in novel technological areas, such as nanomaterials, organic semiconductors and solar cells[32–35].

Yao et al.[36]studied the PCT process of the mixed coaggre-gates TPP–DCN containing 1,3,5-triphenyl-2-pyrazoline (TPP) and 1,4-dicyanonaphthalene (DCN) both in experiment and theory. In the TPP–DCN, the TPP group acts as an electron donor and the DCN moiety is used as an electron acceptor. As reported in Ref. [36], for the ground state of the TPP–DCN, the pyrazoline ring of the TPP and the naphthalene ring of the DCN are in a face-to-face stacking mode. Through analyzing the properties of experimental spectra, they considered that the

p

–

p

stacking has effect on the electron transfer process, and an intermolecular charge-transfer complex between the TPP and DCN groups should be formed in the excited state but not in the ground state (S0). Recently, Chen

and his co-workers [37] investigated the PCT process and ex-cited-state properties of the TPP–DCN using the TDDFT method. They concluded that the PCT mechanism for the TPP–DCN was the mixture of intermolecular and intramolecular CT in the vertical absorption process. The phenyl group of the TPP monomer plays a role of electronic donor both in intramolecular and intermolecular CT processes. These studies provided a well explanation for the CT processes of the TPP–DCN. However, the nature of the

p

–

p

stacking interactions in the TPP–DCN is important to understand the PCT mechanism [37]. To our best knowledge, the theoretical studies on the

p

–

p

stacking interactions of the TPP–DCN coaggregates and their inﬂuence on the excited-state properties are still not re-ported. Moreover, the B3LYP functional is not suitable to describe the

p

–

p

stacking interactions, because it is defective in the descrip-tion of the dispersion interacdescrip-tions[2].

To further understand the PCT process, in the present letter we investigated the nature of the

p

–

p

stacking interactions and their inﬂuence on the excited-state behavior of the TPP–DCN coaggre-gates. As mentioned above, in this letter the ground- and excited-state geometries of the TPP–DCN are optimized with the new DFT methods, such as the

x

B97XD functional. Then the spectral properties, charge-transfer character and

p

–

p

stacking interactions of the TPP–DCN are investigated in detail based on the optimized geometries.

2. Computational details

All calculations are performed with the GAUSSIAN09 program

[38]. The monomer geometries optimized at the B3LYP/6-311++G (d,p) level are used to construct the stacking mode of the TPP– DCN. In order to ensure the optimized geometries of the TPP– DCN are reasonable, the traditional (B3LYP and PBE0) and new (

x

B97XD, M06-2X and B3LYP-DCP) functionals are used and their

results are compared with each other and with the previous theo-retical data. It is notable that the traditional functionals give the displace-stacked and T-shaped structures of the TPP–DCN, while the new functionals only provide the displace-stacked conﬁgura-tion. Considering the outstanding performance of the new func-tional to describe the

p

–

p

stacking interactions and our main purpose, only the displace-stacked configuration is discussed in the present letter. Frequency calculations at the same levels are performed to confirm each stationary point to be a true energy minimum. According to the results of potential energy curves (PECs) (Fig. S1 and Table S1), the new functionals do provide well-defined minima of the TPP–DCN with the equilibrium dis-tances 3.6–3.7 Å between the TPP and DCN. Based on the optimized geometries, the TDDFT with the 6-311++G(d,p) basis set is used to predict vertical excitation energies (VEE). The excited-state structure of the TPP–DCN is optimized using the smaller basis set (6-31G(d)) due to the expensive computational cost of the ex-cited-state frequency calculation. Solvent effects on the geometries and on the excited-state properties have also been included by using the Polarizable Continuum Model (PCM)[39](in water). As is well known[36], the planarity and hydrophobic property can encourage the formation of

p

–

p

stacking in polar solvents.

The Multiwfn 2.3 program[40]is used to perform the charge transfer analysis. In addition, this code can provide information about the characteristic of

p

–

p

stacking interactions and molecular orbital (MO) compositions. A graphical representation of charac-teristic is displayed using the VMD 1.9[41]and Molekel programs [42]. The Huang–Rhys (HR) factors are calculated based on the optimized geometries and the vibration-normal-mode frequencies of the ground and the ﬁrst excited states with our own code.

3. Results and discussion

3.1. Geometry structures of the coaggregates

The optimized geometries of the monomers and the TPP–DCN coaggregates are shown inFigure 1. Their ground-state structures are calculated at the

x

B97XD/6-311++G(d,p) level, while the ex-cited-state geometry of the TPP–DCN is optimized at the

x

B97XD/6-31G(d) level. Some important structural parameters characterizing relative difference between the monomers and stacked complex are deﬁned and listed in Table 1. In the DCN, the dihedral angle D1 (N16–C15–C14–13) and D2 (N12–C11– C10–C9) are both almost 180°, while in the TPP–DCN they are about 89.04° and 75.63°, respectively. This indicates that the dis-tortion of DCN in the TPP–DCN is due to the steric hindrance and electrostatic repulsion. In the TPP, the dihedral angle D3 (C1–N2– N3–C4) is deﬁned to describe the coplanarity of pyrazoline ring. The calculations show that the change of D3 is small when the TPP–DCN is formed (the value is 9.36° and 7.16° in the TPP–DCN and the TPP monomer, respectively). Obviously, the neglectable change of D3 indicates an excellent coplanarity of pyrazoline ring, which is favorable to form the TPP–DCN stacking system due to the

p

–

p

stacking interactions between the TPP and DCN. In the TPP– DCN, the stacking distance d1 between the TPP and DCN calculated at the

x

B97XD/6-311++G(d,p) level is about 3.34 Å (the B3LYP dis-tance is 3.9 Å[36]). The accurate description of the stacking dis-tance is beneﬁcial to understand the inﬂuence of the

p

–

p

interactions on the electron transfer mechanism. We believe that the present results are more reasonable than the previous theoret-ical calculations because the

x

B97XD functional includes the dispersion correction term.

According to the optimized geometries, several important changes going from the S0to the ﬁrst excited state (S1) should be

noted. The dihedral angle D6 (N2–N3–C9–C10) describing the

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relative location of the TPP and DCN, has the largest change by comparing the S0and S1. As shown inTable 1, D6 is about 78.18°

in the S0state, while it is only 48.80° in the S1state. In addition,

the distortion of the DCN is very large as displayed by the change of D1 and D2 (they are 89.04° and 75.63° for S0state, 92.30° and

58.21° for S1 state). These suggest that the Huang–Rhys factors

should be very large. However, the planarity of the pyrazoline ring is still retained very well (D3 changes from 9.36° to 4.42°), which is important to form the

p

–

p

stacking TPP–DCN coaggregates regard-less of the S0and S1states. Further, we ﬁnd that the change of the

distance d1 is also very small (changes from 3.34 Å of the S0to

3.28 Å of the S1). Besides, to check how the solvent effect on the

geometries, we also optimize the TPP–DCN structure in gas phase. The change trend of the stacking structures in vacuum is similar to those in solution (seeTable S2 in SI). These changes of geometries of the S0and S1states can enhance our understanding of the

stack-ing effects on the excited-state properties of the TPP–DCN. 3.2. The noncovalent interactions in the coaggregates

A visualization analysis of the noncovalent interactions is made to understand the nature of nonbonded interactions in the TPP– DCN coaggregates. Yang and his co-workers[43]developed an ap-proach to detect the noncovalent interactions in real space, based

on the electron density (

q

) and its derivatives. In the present letter we utilize this approach to identify the type of the nonbonded interactions in the TPP–DCN, which is important to reveal the nat-ure of the analogous mixed coaggregates. Our calculated results are shown inFigure 2A, in which the vertical coordinate represents the reduced density gradient (RDG), and the horizontal coordinate is sign(k2). RDG is a fundamental dimensionless quantity coming

from the density and its ﬁrst derivative (RDG ¼ 1=ð2 ð3

p

^2_Þ ^ð1=3Þ_Þj_r

_q

ð

c

Þj=

q

^ð4=3Þ_{, and sign(k}

2) is deﬁned as a physical quantity

that the electron density multiplies by the sign of the second Hes-sian eigenvalue k2. For the details that how to distinguish different

types of noncovalent interactions, ones are encouraged to recourse the Ref.[43].

As shown inFigure 2A, we ﬁnd that two low-density, low-gra-dient spikes are very close to zero in the plot of RDG vs. sign(k2)

q

for the TPP–DCN coaggregates. According to the conclusions pre-sented in Ref. [43], the low-density, low-gradient spike with slightly negative value indicates weak attractive interactions (>0.010 a.u.). Conversely, the low-density, low-gradient spike re-mains at a slightly positive value indicates a weak repulsion inter-actions (<0.010 a.u.). For the ﬁrst case, the weak attraction interactions should be the key factor to form the TPP–DCN. As we know that the intermolecular weak interactions include the hydrogen bonds, stacking interactions, electrostatic interactions and hydrophobic interactions[2]. Therefore, we are very curious to know which force will be dominant to form the TPP–DCN coag-gregates. Considering the geometries of the monomers of TPP and DCN, we can easily ﬁnd that both of them have aromatic structures with conjugated

p

electrons. This implies the

p

–

p

stacking effect should be strong when the TPP closes to the DCN in a parallel man-ner. In other words, the main composition of noncovalent interac-tions in the TPP–DCN should be the

p

–

p

stacking interactions. The plot of RDG vs. sign(k2) provides a rich visualization of this weak

p

–

p

attraction, which is showed as a spike at the bottom-left point inFigure 2A where sign(k2) is about 0.002 a.u. To conﬁrm the

validity about the nature of noncovalent interactions, we calculate the low-gradient (RDG = 0.6 a.u.) isosurfaces which subjects to the constraint of low density for the TPP–DCN, and the result is Figure 1. Optimized structures of the monomers and coaggregates. (a) DCN; (b) TPP; (c) ground state and (d) excited state of the TPP–DCN coaggregates. The vertical distance between TPP and DCN is described as d1. The geometry of ground state of the mixed coaggregates is optimized at thexB97XD/6-311++G(d,p) level and that of the excited state is obtained atxB97XD/6-31G(d) level.

Table 1

Selected geometrical parameters of monomers and the TPP–DCN coaggregates calculated by the xB97XD theoretical level. The atom numbering is showed in

Figure 1. Parameters TPPa _DCNa _TPP–DCN(S 0)a TPP–DCN(S1)b D1(N16-C15-C14-C13) 180 89.04 92.30 D2(N12-C11-C10-C9) 180 75.63 58.21 D3(C1-N2-N3-C4) 7.16 9.36 4.42 D4(N3-N2-C5-C6) 0.87 7.53 3.07 D5(N3-C4-C7-C8) 5.49 8.83 3.56 D6(N2-N3-C9-C10) 78.18 48.80 d1 3.34 3.28 a

Calculated by thexB97XD/6-311++G(d,p) theoretical level.

b

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displayed inFigure 2B. In the plot of low-gradient isosurfaces, a density cutoff of

q

< 0.05 a.u. is chosen since it encapsulates the interesting noncovalent interactions region (see Figure 2A). Obviously, in the TPP–DCN, there is an area of nonbonded overlap located at the whole molecular planes of the TPP and DCN moieties, particularly at the centers of ring III (pyrazoline) of the TPP and ring I (benzene) of the DCN. This area of low-gradient iso-surface is colored as green1_{(links the spike at the bottom-left point}

inFigure 2A by using black arrow) according to the corresponding values of sign(k2)

q

. The

p

–

p

stacking interactions are manifested

by the isosurface ﬁlling the space between the molecular planes of the TPP and DCN groups. For the second case, the weak repulsion interactions (as shown by the spike at the bottom-right point in Fig-ure 2A where sign(k2)

q

is about 0.002 a.u.) between the TPP and

DCN also can be pictured by the same method. When the TPP grad-ually closes to the DCN, the repulsion force will become larger until it ﬁnally equals to the

p

–

p

attraction force. We consider that this equilibrium leads to the formation of the stable TPP–DCN coaggre-gates. In addition, almost no blue or even cyan isosurfaces can be observed, indicating that the dimeric stablization is dominated by

p

–

p

stacking interactions rather than hydrogen bonds. Noted that the red isosurfaces at the centers of molecular rings denote the steric repulsion, which is linked to the plot of RDG vs. sign(k2)

q

with a blue

arrow.

Let us now analyze the results related to the

p

–

p

stacking inter-actions in the TPP–DCN coaggregates. In this letter the electrostatic potential surfaces of the TPP, DCN and TPP–DCN are also calcu-lated, and the maps are shown inFigure 3. The red areas indicate more negative electron density, while blue areas denote more

positive electron density. Inspection of the maps shows that the negative charge is centered on the ring I of the DCN and the ring VI of the TPP, while the positive charge is concentrated on the side of the DCN and the ring III of the TPP. Apparently, the electrostatic attraction mainly take place between the ring I of the DCN and ring III of the TPP. As a composition of the

p

–

p

stacking interactions, the electrostatic interactions play an important role in the formation of the

p

–

p

stacking TPP–DCN coaggregates.

3.3. The absorption features of the coaggregates

As mentioned in Introduction, Yao et al.[36]considered that an intermolecular charge-transfer complex between the TPP and DCN moieties should be formed in the excited state but not in the ground state. To inspect the inﬂuence of

p

–

p

stacking on spectral properties, we calculate the absorption and emission spectra of the TPP–DCN with the traditional and new DFT methods. The re-sults of these methods are almost consistent with each other although the obtained transition order from them is slightly differ-ent. For example, the most intense transitions are the second (S2)

and the third excited (S3) states for new DFT methods, but they

are S3 and S4(the fourth excited state) states for the traditional

DFT methods. Therefore, in the following only the

x

B97XD results are discussed.

The calculated UV–vis absorption spectra of the TPP–DCN, pure TPP and DCN monomers in water are shown inFigure 4a. As listed in Table 2, the theoretical absorption peak of the TPP is about 322.81 nm, the peaks of the DCN appear at 308.08 and 222.92 nm, and the bands of the TPP–DCN locate at 328.29 and 223.87 nm. These results agree well with the experimental [36] and previous theoretical counterparts [36,37], indicate that the optimized geometries of these compounds are reasonable and Figure 2. Thep–pstacking interactions in TPP–DCN mixed aggregates. Plots of the reduced density gradient vs. the electron density multiplied by the sign of the second hessian eigenvalue.

1

For interpretation of color in Figure 3, the reader is referred to the web version of this article.

DCN TPP DCN-TPP

Figure 3. Electrostatic potential maps of the monomers TPP and DCN, TPP–DCN calculated at thexB97XD/6-311++G (d,p) level in aqueous solution.

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the selected method is reliable. Further, we ﬁnd that the spectrum of the TPP–DCN is almost identical to the linear superposition of the spectra of the pure DCN and TPP monomers, and the singlet ex-cited-state energy level of the TPP (3.99 eV) lies below that of the DCN (4.06 eV). These imply that the TPP and DCN do not form an intermolecular charge-transfer complex in the mixed coaggre-gates. That is, the present calculations approve the experimental consequence that the

p

–

p

stacking interactions has no remarkable inﬂuence on the absorption spectrum of the ground state of the TPP–DCN (thus an intermolecular charge-transfer complex in ground state of the mixed coaggregates is not formed).

However, does an intermolecular charge-transfer exciplex (ex-cited-state complex) can be generated? Most importantly, how to explain the experimental results? These are very important to help ones understand the nature of PCT, which could provide insights for understanding other analogous systems. In the present letter we use the absorption spectra, emission spectra and frontier molecular orbital theory to investigate the intermolecular charge-transfer of excited state, and the theoretical results can sat-isfactorily explain the experimental details[36].

For the TPP–DCN, the calculated oscillator strengths of vertical excitation from the ground state to excited states are reported in Table 2. To obtain a sufﬁciently large pool of excited states for the relevant excitations, we calculate the ﬁrst 10 vertical excitation energies, and only four main excited states with large oscillator strengths are given inTable 2. The relative strengths are 0.0102, 0.3764, 0.4189 and 0.0395 for the excitations S0?S1, S0?S2,

S0?S3and S0?S4, respectively. The S1 is resulted mainly from

the electron excitation from the highest occupied orbital HOMO to the lowest unoccupied orbital LUMO. According to the results of the molecular orbital fragment analyses (Figure 5), HOMO is composed of 99.6% HOFO (HOMO of fragment orbital) of the TPP fragment, and LUMO is nearly formed by 98.6% LUFO (LUMO of fragment orbital) of the DCN moiety. That is, HOMO and LUMO of the TPP–DCN are

p

-type orbitals mainly located at the DCN and TPP moieties, indicating that the S1is a CT state with transition

forbidden characteristic. The two excited states, S2and S3, possess

the largest oscillator strengths among the four excited states (see Table 2). The S2is contributed mainly from HOMO to LUMO + 1,

the S3 mainly from HOMO-1 ? LUMO. As shown in Figure 5,

HOMO-1 is a

p

-type orbital located on the DCN moiety, and LUMO + 1 is also a

p

-type orbital located on the TPP group. Thus the S2and S3are local excitation (LE) states.

Figure 4. Calculated absorption and emission spectra using thexB97XD functional. (a) The absorption spectra calculated at thexB97XD/6-311++G(d,p) level. (b) The emission spectra calculated at thexB97XD/6-31G(d) level.

Table 2

Computed vertical excitation energies of monomers and the TPP–DCN coaggregates using different theoretical levels.

Energy (osc.str.) Orbitalsa TPP xB97XD/6-311++G(d,p) S1 322.81(0.5981)n365b H ? L S2 283.02(0.0677) H ? L + 1 S3 222.92(0.8142) H ? L + 2 S4 222.56(0.2284) H-5 ? L; H ? L + 3 DCN xB97XD/6-311++G(d,p) S1 308.08(0.2603)321b H ? L S2 299.31(0.0632) H-1 ? L; H ? L + 1 S3 289.96(0.0108) H-2 ? L + 1 ;H-1 ? L; H ? L + 1; H-1 ? L + 2 S4 283.59(0.0302) H-2 ? L TPP–DCN xB97XD/6-311++G(d,p) S1 418.77(0.0102) H ? L S2 328.29(0.3764) H-1 ? L; H ? L + 1; H ? L + 2 S3 305.38(0.4189) H-1 ? L; H ? L + 1 S4 282.22(0.0395) mixed ? L; mixed ? L + 2 PBE0/6-311++G(d,p) S1 621.69(0.0003) H ? L S2 373.93(0.4583) H ? L + 1 S3 346.22(0.0028) H ? L + 2 S4 337.25(0.2404) H-1 ? L; H-10 ? L M062X/6-311++G(d,p) S1 433.24(0.0105) H ? L S2 332.30(0.3773) H ? L + 1;H-1 ? L;H ? L + 2 S3 303.16(0.3692) H ? L + 1;H-1 ? L;H-2 ? L S4 289.66(0.0275) H ? L + 1; H ? L + 2 B3LYP/6-31Gb,c S1 647.24(0.0011) H ? L S2 368.62(0.4502) H ? L + 1;H-1 ? L S3 344.14(0.0017) H ? L + 2;H-1 ? L S4 341.45(0.2019) H ? L + 1;H ? L + 2;mixed ? L B3LYP/6-31+G(d,p)-DCP S1 636.27(0.0184) H ? L S2 384.86(0.1124) H-1 ? L; H ? L + 1; H ? L + 2 S3 361.81(0.1148) H-1 ? L; H ? L + 1; H ? L + 2 S4 349.81 (0.0406) H-2 ? L; H-1 ? L; H ? L + 1 a

Assignment: H = HOMO, L = LUMO, L 1 = LUMO-1, H-1 = HOMO-1, etc.

b

Ref.[36].

c

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The effect of

p

–

p

stacking on the emission spectrum is also examined by the same methods (Figure 4b). The calculated emis-sion peaks of the TPP, DCN and TPP–DCN respectively are 407.32, 367.83 and 560.53 nm (the corresponding experimental data[36] are 456, 396 and 560 nm). Evidently, the origin of the red-shifted emission at about 560 nm is neither from the TPP nor from the DCN. Further, we also calculate the ﬂuorescence spectrum of the TPP–DCN using its S1 geometry, and the band locates at about

418.77 nm. The present result indicates that the emission band of 560.53 nm does come from a new structure, which is the so-called excited-state complex (exciplex) of the TPP–DCN. As dis-cussed in Subsection 3.1, there is a large change between the geometries of the S0and S1. As we know that the structural

differ-ence will result in the redistribution of molecular charge. For the transition of S0?S1, the transferred charge amount is about 1.34

(seeTable S3 in SI) estimated at the

x

B97XD/6-311++G(d) level. This implies that the S1 is indeed a CT state due to the

p

–

p

stacking effect. In fact, the calculated dipole moment also conﬁrms the re-sult. As displayed inTable S3, the calculated dipole moment of the S0is about 5 Debye (D), but that of the S1is beyond 17 D. A

large change of dipole moment indicates a charge separation in the S1. Obviously, this result suggests that there are prominent

electronic interactions between the TPP and DCN components in the S1, which indicates that the TPP and DCN in the mixed

coaggre-gates do form an intermolecular charge-transfer complex through direct photoexcitation. Our theoretical discovery agrees well with the experimental conclusion[36].

Is it reasonable that there is a large geometrical change between the S0and S1states to produce an exciplex (CT state)? To explore

this photophysical property, we calculate the Huang–Rhys (HR) fac-tor of every vibrational normal mode of the TPP–DCN. The HR facfac-tor reﬂects the degree of geometrical change along with the vibrational normal coordinates when electron transfers from one state to an-other state. For the ith mode, the HR factor can be expressed as:

Si¼

x

id 2

i=2h ð1Þ

in which

x

iis the harmonic frequency of the ith normal mode, di

denotes the displacement which can be simply calculated by

di¼ Q0i Qi¼ X j Lij q0j qj ð2Þ where q0

jand qjare the mass-weighted Cartesian coordinates at the

equilibrium geometries of the S0and S1states, and the

transforma-tion matrix L in Eq.(2), along with q0

jðqjÞ, is calculated by using

GAUSSIAN09 program package. The obtained HR factors are depicted

inFigure 6. We can see some of these modes have large HR factors, such as the mode with frequency 1492.99 cm1_{has the largest HR}

factor (260.85). According to Eq.(1), the HR factors are determined

mainly by the displacement di. Thus, the large HR factor indicates a

distinct geometrical change between the ground and excited states. Further, we ﬁnd that the mode with frequency 1492.98 cm1

corre-sponds to the rotational vibration between the TPP and DCN moie-ties in the TPP–DCN. This implies that the dihedral angle D6 should change sharply when photoexcitation occurs. Actually, the calcu-lated structural parameters have demonstrated this result (D6 changes from 78.18° (S0) to 48.80° (S1)). Therefore, it is reasonable

that there is a large geometrical change when electron transitions from the S0to S1, which leads to a charge-separated excited state.

4. Conclusion

In the present letter we optimize the geometries of the S0and S1

states of the TPP–DCN coaggregates, and investigate the nature of the

p

–

p

stacking interactions and the inﬂuence on the excited-state behavior. Our study indicates that there is a large structural change between the S0and S1states, which leads to the redistribution of

charge in the S1. This result is proved by the calculated Huang–Rhys

factors. Using the approach developed by Yang et al.[43], we detect the noncovalent interactions of the TPP–DCN in real space based on the electron density and its derivatives, and ﬁnd that the

p

–

p

attraction between the TPP and DCN is the main driving force to form the TPP–DCN coaggregates. That is, the

p

–

p

stacking interac-tions play an important role in the nonbonded interacinterac-tions. In addi-tion, we also examine the inﬂuence of the

p

–

p

stacking interactions on the excited-state behavior of the TPP–DCN. The calculated re-sults suggest that the TPP and DCN do not form an intermolecular charge-transfer complex in the ground state, whereas they form an exciplex in the excited state. The present theoretical results can satisfactorily explain the experimental details, and are ex-pected to help us understand the nonbonded interactions nature and PET process of other analogous mixed coaggregates.

Acknowledgment

This letter was supported by the National Natural Science Foun-dation of China (Nos. 20803059 and 21173169).

Appendix A. Supplementary material

Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.cplett.2012. 11.061.

Figure 5. Composition analysis of fragment molecular orbital based on the xB97XD/6-311++G(d,p) results.

Figure 6. Calculated Huang–Rhys factors vs. normal mode frequencies for the TPP– DCN coaggregates using thexB97XD/6-31G(d) level.

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