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Intra- and Inter-Molecular Charge Transfer in a Novel Dimer: Cooperatively Enhancing Second-Order Optical Nonlinearity Feng-Wei Gao, Rong-Lin Zhong, Hong-Liang Xu, and Zhongmin Su J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b08172 • Publication Date (Web): 30 Oct 2017 Downloaded from http://pubs.acs.org on October 31, 2017

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The Journal of Physical Chemistry

Intra- and Inter-molecular Charge Transfer in a Novel Dimer: Cooperatively Enhancing Second-Order Optical Nonlinearity

Feng-Wei Gao,1 Rong-Lin Zhong,2 Hong-Liang Xu1* and Zhong-Min Su1*

1

Institute of Functional Material Chemistry, National & Local United Engineering Laboratory for Power Batteries, Department of Chemistry, Northeast Normal University, Changchun 130024, People’s Republic of China.

2

Institute of Theoretical Chemistry, Jilin University, Changchun 130023, People’s Republic of China.

Abstract

Based on s-indaceno[1,2,3-cd;5,6,7-c′d′] diphenalene (1) consisting of two phenalenyl moieties, the monomer 2 and its dimer 22 are designed by boron and nitrogen atoms substituted the central carbon atoms of phenalenyl moieties. Calculated energy decompose analysis (EDA) shows that the orbital interaction for 22 possesses large attractive contributions of -18.31 kcal mol-1, which is dominated by the π-π stacking interaction between the upper and the lower π-conjugated units. Interestingly, the natural population analysis (NPA) charge and the transition density matrix (TDM) show that both of intra- and inter-molecular charge transfers (CT) exist in 22. Further, the first hyperpolarizability (βtot=4.56×104 au) of 2 with intra-molecular CT is greatly larger than that of reported molecule 3 (5.45×103 au) with inter-molecular CT. Significantly, 22 exhibits the largest βtot value to be 1.42×105 au, which is caused by the combining the intra- and inter-molecular CT transitions (βx=1.40×105 and βz=2.27×104 au). Correspondingly, HOMO→LUMO (intra-molecular CT) in the low-energy electronic transition of 22 is 68%, while HOMO→LUMO+1 (inter-molecular CT) is 18%, which demonstrates that intra-molecular CT

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effect on the βtot value is stronger than the case of inter-molecular CT effect. The present work might provide rich insight to design and develop the potential second-order optical nonlinearity materials with inter- and intra-molecular CT characters. 1. INTRODUCTION Since Franken et al. observed the phenomenon of second-harmonic generation (SHG) for the first time in 1961,1 Nonlinear optical (NLO) materials have received considerable interest due to wide variety of applications in the field of photonics, nanophotonics and optoelectronics.2-13 Consequently, how to design new NLO materials with large SHG response is of profound significance. So far, the development of organic NLO materials is on the ascendancy, owing to their larger nonlinearity, better processability and superior chemical flexibility, etc.14 Organic molecules with donor−acceptor (D−A) framework are promising building blocks for advanced functional materials, due to their intra-molecular charge transfer (CT) process in response to an external stimulus. Relevant materials are of interest for a variety of applications, including semiconductors, bio-imaging, sensing, solar cells, OLED, nonlinear optics, etc.15-22 On the other hand, the concept of inter-molecular CT electronic transition was introduced by Mulliken in 1952 and has remained a widely studied subject.5,23-29 Recently, Guasch and co-workers have exhibited that new materials present a coupling of intra- and inter-molecular CT, which are particularly promising to obtain materials for the design of future molecule-based spin-electronic devices.30 However, general organic complexes with intraand inter-molecular CT properties can hardly be predicted, designed and investigated theoretically because of the complicated and anisotropic inter-molecular interactions. Design of a regular dimer with intra- and inter-molecular CT is very important for understanding the nature of the performance of relevant materials.


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In 2005, Kubo et.al. have reported the inter-molecular interaction and semiconductive behavior of a delocalized singlet biradical hydrocarbon (1), which consists of s-indacene-like moiety and two phenalenyl (PLY) moieties,31 as shown in the scheme 1. Interestingly, a combined intra- and inter-molecular interaction of the unpaired electrons presents in its dimer (12). It is worthy of note that the directional aggregation of 1 is dominated by the orbital overlap interaction of PLY moieties. Recently, many studies have highlighted the fascinating π-π stacking interactions (2-electron, 12-center (2e/12c) bonding character, etc) of the PLY dimer derivatives.32-36 Our previous work shows a polar 2e/12c bond could be induced by the orbital overlap of boron/nitrogen substituted PLYs.5 The corresponding molecule framework might open a new perspective for studying stacked complexes with fascinating inter-molecular CT characters.

Scheme 1. The intra- and inter-molecular interactions of the unpaired electrons in 1 and 12. In this work, 2 with an intra-molecular CT is designed by substituting the central carbon atoms of the two PLY moieties of 1 with boron/nitrogen atoms. As discussed in our previous work, the diverse feature of 3 is the uneven charge distribution in the two layers, which could induce a long-range inter-molecular CT. It is worthy of note that, the charge distribution of 3 though a polar 2e/12c bond is larger than that of 2. To gain a deeper insight into aggregation of complex, 22 is designed by directional stacking 2. Our investigation is focused on the structures, interaction energies and CT properties of complexes. The π-conjugated donor−acceptor dipolar molecules, have high performance for nonlinear optical properties. Therefore, we further analyze the relationships between charge transfer and the nonlinear optical properties of the special 22.



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2. COMPUTATIONAL DETAILS As proposed in previous works, coupled-cluster with singles, doubles, and perturbative triples (CCSD(T))37 calculation stands as the “golden-standard” in quantum chemical calculations38-40 of relatively weak interactions but the large computational cost limits it applications for large systems. In recent years, much progress has been made in developing density functional theory (DFT) method that performs well in understanding the π-π stacking interaction.36,41-45 According to Truhlar and Zhao’s investigations, the hybrid meta generalized gradient approximation (M06-2X)41,42 has excellent performance for aromatic-aromatic stacking interactions. On the other hand, Grimme suggested that DFT-D with additional dispersion type corrections is typically applied where the dispersion is not fully covered by the scaled down perturbation theory contribution.46,47 On the basis of previous work, the interlayer distance of 3 was 3.139 Å by the M06-2X functions,5 which is very close to experimental value of 3.201 Å.34 This suggests that the M06-2X functional is an efficient and reliable functional to study π-dimer. Therefore, geometrical structures of present system were optimized at the M06-2X/6-31G** level of theory. Further, Natural Population Analysis (NPA) charge was investigated using M06-2X with 6-31G** basis set. In order to understand the nature of π-dimer, the interaction energy was calculated by a series of density functionals (M06-2X, ωB97XD, B3LYP-D3 and CAM-B3LYP-D3) with 6-31+G** basis set. Results show the interaction energies of 3 and 22 are close to each other as shown in Table S1 of the Supporting Information, which is independent on the selected functionals. The test calculation confirms that the interaction energy calculated by the M06-2X is suitable to further discussion. To correct the basis set superposition error (BSSE), the counterpoise (CP) procedure was used in the calculation of interaction energy (Eint).48,49 The Eint was calculated as the difference between the energy of complex substances and the sum of the energies of monomers by the following formula (1):


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Eint (AB)  E (AB) AB  [ E (A) A B  E (B) AB ] Furthermore, the binding interactions were analyzed by utilizing the energy decompose scheme of Amsterdam density functional (ADF)50-52 at the M062X/TZ2P level of theory, which was originally developed by Morokuma53 and later modified by Ziegler and Rauk.54,55 The interaction energy can be divided into three main components by the following formula (2): Eint  Eelstat  EPauli  Eorb

Where the ΔEelstat is the electrostatic interaction energy between the fragments, the ΔEPauli corresponds to the repulsive interaction between the fragments and the ΔEorb describes the orbital interaction between the fragments. According to previous investigations, the M06-2X functional with the 6-31G** basis sets is adapted to evaluating the first hyperpolarizabilities (βtot) for π-dimer systems. In addition, the CAM-B3LYP and the BHandHLYP functionals are applied to compute the βtot values. The results show that three functionals obtained very close βtot values. The first hyperpolarizability was determined as the following formula (3):

 tot  (  x2   y2   z2 )1/2 where βi is defined as:

 i  iii   ijj   ikk (i, j, k  x, y , z ) All of the calculations were performed with Gaussian 09 program package except for special emphasis.56 The charge density difference maps (CDDMs) and the transition density matrix (TDM) (at the M06-2X/6-31G** level) were obtained by employing the Multiwfn version 3.3.8 software.57 The reduced density gradient (RDG) is plotted using VMD 1.9.3.58

3. RESULTS AND DISCUSSION In this work, we design 2 with boron and nitrogen atoms substituting the central carbon atoms of the two PLY moieties of 1, which consists of s-indacene linkage and two PLY derivative moieties (B-PLY and



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N-PLY). Inspired by the forming 3, the directional stack of 2 is capable of forming π-dimer (22) with superimposed B/N-PLYs in Figure 1. Full geometry optimizations are performed for 2, 3 and 22. It is find that the interlayer distance (3.111 Å) of superimposed B/N-PLYs for 22 is slightly smaller than 3.139 Å of 3 in optimized structures. In order to evaluate the thermal stability of 22, thermodynamic property at 298.15 K is investigated. Calculated enthalpy value (ΔH) for the formation of 22 is negative value (a detail of calculated enthalpy is presented in Table S2).

Figure 1. The geometry structures of complexes. In order to identify charge transfer (CT) characters, we focus on NPA charges, which are graphically presented in Figure 2a. The result indicates that 2 presents intra-molecular CT and the electron transfer from the N-PLY (0.18) to the s-indacene linkage (-0.09) and B-PLY (-0.09). Contrastively, inter-molecular CT from B-PLY to N-PLY is 0.33 in 3, which shows that the magnitude of inter-molecular CT (0.33) of 3 is larger than that of 2 (0.18). More interesting is 22 that charge of N-PLY in the upper layer is 0.16 and the s-indacene linkage is -0.12, indicating that magnitude of intra-molecular CT from B-PLY to N-PLY is 0.04. Note that the calculated NPA shows that the charge of B-PLY in the upper layer is -0.28, indicating that electrons transferred from N-PLY in the lower layer to B-PLY in the upper layer is 0.24. Therefore, 22 possess intra- and intermolecular CT characters, and inter-molecular CT (0.24) is larger than intra-molecular CT (0.16) in 22. The physical and chemical properties of complexes are significantly


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dependent on the NPA charge distribution. Corresponding the dipole moments induced by intra- and inter-molecular CT in 2, 3 and 22 are show in Table S3. Furthermore, the analyses of electrostatic potential (ESP) on the van der Waals (vdW) surface for 2, 3 and 22 give an intuitional impression of charge distribution in Figure 2b. It can be seen that the B-PLY and N-PLY represent quite different electrostatic potential characters. The important region of more negative potential (red regions) is mostly located on the B-PLY, whereas the N-PLY presents the net positive potential (blue regions) for 2 and 3 and 22, which is in line with NPA analysis. Significantly, superimposed B/N-PLYs in 22 presents the opposite potential (more negative potential is mostly located on B-PLY in the upper layer, whereas the N-PLY presents the net positive potential in the lower layer), which shows that the interaction between two layers presents electrostatic attraction.

Figure 2. NPA charges (a), and the electrostatic potential (ESP) of studied complexes (red regions represent negative charge, while blue regions represent positive charge) (b). What is the interaction between two layers? We perform an energy decompose analysis (EDA)59,60 method to analyze the physical origin of the interaction between the two layers. As for interaction energy, the ΔEPauli is the crucial factor for determining molecular geometries is the valence shell electron pair repulsion scheme. In contrast, the ΔEorb and the ΔEelstat provide the crucial factors for stabilizing energy. Results in Table 1 show that the ΔEint of 3 (-21.59 kcal mol-1) and 22 (-21.10 kcal mol-1) are close to each other. This trend of ΔEint is in accordance



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with the corresponding ΔEint in Gaussian (see Table 1). Further, the different contributions of the ΔEint can be quantified. We find that the ΔEorb values for 3 (-18.29 kcal mol-1) and 22 (-18.31 kcal mol-1) are very close each other, which shows that the strong attractions in 3 and 22 are originated from the overlap of the orbitals between two layers. On the other hand, 3 possess relatively larger the ΔEint value because the ΔEelslat (-13.68 kcal mol-1) make a major contribution to the ΔEint, indicating that the strong interaction in 3 is mainly attributed to orbitals and the electrostatic attraction. It is worth noting that the ΔEelstat for 22 possesses higher attractive contributions of -24.30 kcal mol-1 compared with 3. However, the ΔEint of 22 is close to that of 3, which is caused by the increment of valence shell electron pair repulsion (ΔEPauli = 21.51 kcal mol-1). Further, the reduced density gradient (RDG) map is an important tool to distinguish three different types of weak interactions (hydrogen binding, van der Waals interaction, and steric hindrance) for the dimers, detailed analysis is shown in Figure S1.61 Table 1. Decomposition energies (kcal mol-1) of the complexes obtained by ADF program.

ΔEelstat

ΔEPauli

ΔEorb

ΔEint

3

-13.68

10.38

-18.29

-21.59(-21.46)*

22

-24.30

21.51

-18.31

-21.10(-21.19)

*The interaction energies are calculated in Gaussian 09. By virtue of its unique electronic properties, intra- and inter-molecular CT play a crucial role in nonlinear optics research. We investigate the first hyperpolarizability (βtot) by three popular DFT functionals (M06-2X, CAM-B3LYP and BHandHLYP) to examine the reliability on βtot of studied complexes, and corresponding results are listed in Table 2. Different functionals obtain same trend in the βtot value, so we chose the results of the M06-2X functional for further discussion. The order of βtot value from M06-2X


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functional is 1.42×105 (22) > 4.56×104 (2) > 5.45×103 au (3). Obviously, the βtot value of 2 mainly contributed by βx (4.56×104 au), which is caused by intra-molecular CT in the direction of the x coordinate axis. The βtot value of 3 mainly contributed by βz (5.45×103 au), which is caused by inter-molecular CT in the direction of the z coordinate axis. Surprisingly, 22 obtains an impressively large βtot value and its value is mainly contributed by βx (1.40×105 au) and βz (2.27×104 au), which is reasonably due to the combination of the intra- and inter-molecular CT transitions. In addition, the contribution of βx value to 22 is significantly three times larger than that of 2, indicating that inter-molecular CT promotes intra-molecular CT transition, and the contribution of βz value to 22 is significantly four times larger than that of 3, indicating that intra-molecular simultaneously promotes inter-molecular CT transition. Therefore, we can draw the conclusion that the influence of intra- and inter-molecular on the βtot is to promote each other. Table 2. First hyperpolarizabilities of studied complexes by the M06-2X, CAM-B3LYP and BHandHLYP functionals.

M06-2X

CAM-B3LYP

BHandHLYP

2

3

22

βx

4.56×104

-6.07

1.40×105

βy

1.80×102

16.23

1.98×102

βz

0.15

5.45×103

2.27×104

βtot

4.56×104

5.45×103

1.42×105

βx

4.14×104

-0.80

1.15×105

βy

1.32×102

1.68

1.15×102

βz

0.14

5.93×103

2.07×104

βtot

4.14×104

5.93×103

1.17×105

βx

4.27×104

-0.80

1.26×105



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βy

2.13×102

1.68

3.15×102

βz

0.13

5.93×103

2.21×104

βtot

4.27×104

5.93×103

1.28×105

Further, the βtot values are determined as the approximately two-level expression proposed by Oudar.62,63

 tot 

  f 0 E 3

To simplify the expressions and interpret them easily, three major influencing parameters related to the βtot value: the excitation energy (ΔE), the oscillator strength (f0), and the difference in dipole moment between the crucial transition states (Δμ) are listed in Table 3. According to the two-level model, the ΔE value at the crucial transition state is an important factor for the first hyperpolarizability (the third power of the ΔE value is inversely proportional to the βtot value). The ΔE (1.75 eV) value of 22 is the smallest with respect to 2 and 3, which may be attributed to mixture of the two transition patterns in 22. Thus, the βtot value of 22 (1.42×105 au) is the largest. In addition, the βtot value is proportional to the Δμ and the f0. Compared to 2 and 3, the βtot value (4.56×104 au) of 2 is larger than that of 3 (5.45×103 au), because Δμ (10.33 Debye) and f0 (0.61) of 2 is larger than that of 3 (2.01 Debye and 0.24). Furthermore, we also calculated the (f0·Δμ)/ΔE3 values of three molecules at the M06-2X level of theory. Their values are increased in the order of 4.19×102 (3) < 5.39×103 (2) < 1.09×104 au (22), which is consistent with the trend of βtot value. In order to further verify the two-level expression is suitable in the work, we calculate the first hyperpolarizabilities for three complexes by the sum-over-states (SOS) method.64 Moreover, the contributions of other excited states to the two-level expression are taken into account. It is found that the βtot value calculated by the SOS method is in good agreement with that of two-level expression (Table S4). For a comprehensive understanding the transition energies, Figure 3 depicts the UV-vis absorption spectra


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of 2, 3 and 22 by using the TDM06-2X. At the high-energy transition, 3 contains two absorption peaks at 218.6 and 324.7 nm. With regard to 3, two absorption peaks of 2 at 255.4 and 327.7 nm are slightly enhanced. Importantly, 22 presents a strongest absorption peak at 340.0 nm and its absorption peak is red-shifted compared to those of 2 and 3. Moreover, at the low-energy transition, the the maximum absorption wavelengths (λmax) of all complexes exhibit in the visible region and the λmax in the order of 2 (594.7) ≈ 3 (592.8) < 22 (697.9 nm), which clearly exhibits red-shifted. Above results further support the reduction of ΔE (1.75 eV) of 22. It is worth noting that positions of the λmax of 2 and 3 are close to each other, which is also one of the fundamental reasons for the two transition patterns (intra- and inter-molecular CT transitions) of the low-energy region in 22.

Figure 3. UV-vis absorption spectra of complexes. According to Kongsted et al., the charge-transfer length (Δr-index)65 of an essential excited state and the hyperpolarizability of push−pull system exist a simple power relation: β~(Δr)k.66 It is worthy of note that the increase order of βtot value is in accord with the Δr-index, 2.05 (3) < 5.19 (2) < 7.52 Å (22) (Table S5). Based on the above research, 22 has great potential for the design and preparation of highly efficient NLO materials. Table 3. The transition energies (ΔE), the oscillator strength (f0), the difference of dipole moments (Δμ, Debye) between the ground and excited states, the Δr index (Å), and major contribution of complexes.



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ΔE

f0

μg

μe

Δμ

2

2.10

0.61

7.13

17.47

10.33

3

2.09

0.24

4.16

6.17

22

1.75

1.10

11.55

18.23

  f 0 E 3

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Δr

Excitation (%composition)

5.39×103

5.19

HOMO→LUMO (83%)

2.01

4.19×102

2.05

HOMO→LUMO (98%)

6.68

1.09×104

7.52

HOMO→LUMO (68%) HOMO→LUMO+1 (18%)

It is well-known that the electronic transition characters are closely associated with the frontier molecular orbitals (FMO). Therefore, we focus on analyzing FMO of the crucial transition in the lower energy, as shown in Figure 4. The crucial transitions 2 and 3 are dominated from HOMO to LUMO. It is obvious that the B-PLY and the N-PLY contribute differently to the HOMO and LUMO for 2 and 3. The electronic distributions of HOMOs are mainly concentrated on the N-PLY and LUMOs are mainly contributed by the B-PLY in 2 and 3, which exhibits intra- and inter-molecular CT transitions, respectively. Most importantly, the low-energy electronic transitions of 22 mainly arise from HOMO→LUMO (68%) and HOMO→LUMO+1 (18%). The electronic distribution of HOMO for 22 is mainly distributed over the N-PLY in the upper and the lower layers. Correspondingly, LUMO is mainly contributed by the B-PLY in the upper and the lower layers, which is similar to LUMO of 2 in combination with the orbital shape, this reflects intra-molecular CT transition. LUMO+1 is mainly contributed by the B-PLY in the upper layer and the B-PLY in the lower layer, in which the orbital shape of superimposed B/N-PLYs is similar to LUMO of 3, this reflects inter-molecular CT transition. Remarkably, the degree of HOMO→LUMO transition (68%) is larger than that of HOMO→LUMO+1 (18%), which shows that intra-molecular CT transition contributed to overall the first hyperpolarizability is stronger than that of inter-molecular CT transition (Table 2). In-depth investigation of contributions for orbitals must be very helpful for understanding of


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these properties by using the AOMix program,67 as plotted Figure S2. The results show that 22 has intra-molecular CT transition within the two respective moieties and inter-molecular CT transition between the two fragments. In addition, the orbital overlap for HOMO reflects π-π stacking interaction between superimposed B/N-PLYs, which is conducive to intra- and inter-molecular CT transitions from B-PLY to N-PLY. Further, the transition density matrix (TDM)68,69 and the charge density difference maps (CDDMs) of dominant electron transitions are investigated for system 2, 3 and 22 (Figure S3 and Figure S4), providing valuable evidence for the above discussions.

Figure 4. The frontier molecular orbital and corresponding the major contribution of complexes. 4. CONCLUSIONS In summary, two molecules (2, and 22) are investigated based on s-indaceno[1,2,3-cd;5,6,7-c′d′] diphenalene (1) and compared with previous investigated 3 to explore intra- and inter-molecular CT characters. The NPA calculations indicate that intra- and inter- molecular CT is mainly originated by the electron transfer from N-PLY to B-PLY. Further, the transition density matrix (TDM) calculations for visual descriptors, are further used to investigate inter- and intra-molecular CT characters. Interestingly, the βtot values show that 22 obtain an impressively largest βtot value (1.42×105 au) as compared with 2 (4.56×104 au) and 3 (5.45×103 au). It was surprised to find that primary components of βx (1.40×105 au) in 22 is significantly three times larger than that of 2, and βz (2.27×104 au) is significantly four times larger than that of 3. Therefore, we can draw the conclusion that the influence of intra- and inter-molecular on the



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βtot value is to promote each other. More importantly, the FMO shows that both of HOMO→LUMO(68%) (intra-molecular CT) and HOMO→LUMO+1(18%) (inter-molecular CT) exist in the low-energy electronic transitions of 22, which demonstrate that intra-molecular CT effect on second-order optical nonlinearity is stronger than the case of inter-molecular CT effect. The calculated EDA quantificationally analyzes the different contributions of the interaction energy for 22, in which ΔEorb and ΔEelstat comprise a significant proportion of ΔEint value. With all of these unique electronic structure and photophysical properties, the stable dimer presents good π-π overlap to yield interaction between two layers, which might help to the theoretical and experimental design new molecules with intra- and inter-molecular CT characters, and open a door for the discovery and development of new functional organic materials. Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: Detailed datas are provided, including dipole moments of the ground state (μg, Debye), contributions of fragments to HOMO and LUMO, the charge density difference maps (CDDMs) and the transition density matrix (TDM) of complexes. Corresponding Author *E-mail: [email protected] *E-mail: [email protected]. ACKNOWLEDGMENTS The authors gratefully acknowledge financial support from the National Science Foundation of China (NSFC) (21473026, 21603082), the Science and Technology Development Planning of Jilin Province (20140101046JC), and H.-L.X. acknowledges support from Project funded by the China Postdoctoral


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