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Phenalenyl #-Dimer under the External Electric Field: Two-Electron/12Center Bonding Breaking and Emergence of Electrostatic Interaction Feng-Wei Gao, Rong-Lin Zhong, Hong-Liang Xu, and Zhong-Min Su J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b11732 • Publication Date (Web): 07 Feb 2017 Downloaded from http://pubs.acs.org on February 11, 2017

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The Journal of Physical Chemistry

Phenalenyl π-Dimer under the External Electric Field: Two-Electron/12-Center Bonding Breaking and Emergence of Electrostatic Interaction

Feng-Wei Gao, Rong-Lin Zhong, Hong-Liang Xu* and Zhong-Min Su*

Institute of Functional Material Chemistry, National & Local United Engineering Laboratory for Power Batteries, Department of Chemistry, Northeast Normal University, Changchun 130024, China. Abstract Phenalenyl π-dimer (PLY2) has recently attracted intensive research interest due to its unique structure and binding characteristics (two-electron/12-center bonding). The directional transfer of electron or electron pair under the external electric field can produce new structure with interesting properties. In the present work, we investigate for the first time effect of the external electric field along the main molecule axis on PLY2. Two unpaired electrons between two layers are gradually shifted to the upper layer with increasing of the external electric field strength (Fext): weaker the two-electron/12-center bonding and stronger the electrostatic interaction between two layers. Significantly, a small increment of Fext makes a big difference: the interlayer distance in the PLY2 is sharply elongated from 3.241Å (Fext = 203×10-4 au) to 3.485 Å (Fext = 204×10-4 au), which leads to the two-electron/12-center bonding breaking at 204×10-4 au. Therefore, the Fext = 204×10-4 au is regarded as the critical electric field. In this case, the interaction between two layers in PLY2 is exclusively governed by the electrostatic interaction. Besides this, the effect of the external electric field brings some distinctive changes in its diradical character (y0), the Wiberg bond index (WBI), the interaction energy (Eint) and the frontier molecular orbital (FMO)

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that can be used to explore the conversion between bonding and electrostatic interactions. This study can deepen understanding for the effect of external electric field on structures and electric properties for molecule and open a door for the discovery and development of new switching devices. 1. Introduction Phenalenyl (PLY) is a neutral odd-alternant hydrocarbon radical, which can be viewed as the most fundamental triangular unit arising from three hexagon rings. The unpaired electron is evenly delocalized over the six α-carbon sites in the singly occupied molecular orbital (SOMO) of PLY.1-5 Significantly, theoretical and experimental studies demonstrated that PLY has the ability to form stable dimers (PLY2)6-13: the interlayer distance of staggered PLY2 dimer is about 3.2 Å,11 which is longer than the 1.54 Å of conventional covalent C–C bond, but shorter than the typical C–C van der Waals distance (about 3.40 Å). It is found that PLY2 can form π−π stacking bonding, which presents unique characteristic of the two-electron/12-center (2e/12c) bonding by effective π−π interactions between the SOMO-SOMO.12,13 Very recently, PLY2 derivatives become an important consideration, owing to their unusual binding characteristics.12,14-22 Our group designed a novel 2e/12c bonding by substituting both central carbon atoms of PLY2 with boron/nitrogen.21 Different from the pure PLY2, a fascinating interlayer charge-transfer character is exhibited in PLY2 after the boron/nitrogen substituting, and it is a promising candidate for electro-optical materials. Ribas-Arino’s group in 2015 presented that ethyl-spiro-biphenalenyl π-dimers undergo switching between bonding and electrostatic interactions under the influence of temperature. Below 140 K, two unpaired electrons are localized in the superimposed PLYs directly involved in π-dimer. Conversely, above 140 K, two unpaired electrons are localized in the nonsuperimposed PLYs not directly involved in π-dimer.19 An interesting question arises: Is there an effective strategy to stimulate the interlayer charge–transfer and achieve the conversion between bonding and electrostatic interactions for pure PLY2? The external electric field may be a good choice.


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In recent studies, the effect of external electric field growing attention has been directed toward organic conductors,23 hydrogen bonding complexes,24 nanotubes,25-28 graphenes29-31 and so on. The effect of external electric field modulate structure and chemical bonding is still the subject of extensive investigations.32-38 Dating back to 1960s, the experiments have been conducted to investigate the effect of electric field on water structures actually 39,40

(they first observed protonated water clusters in field ionizations by mass spectrometers).

In the past decade,

theoretical studies have been devoted to rationalize the formation of water whiskers under the influence of external electric field.35,37,41 The chain-length of water whiskers depended on the critical electric field (for example, the critical electric field strength Fc = 535×10-4 au for two water whiskers).35 On the other hand, the external electric field can control the proton transfer from acid (HCl) to base (NH3/H2O) (the critical electric fields strength Fc = 54×10-4 au).24 The donor–acceptor bond (B–N bond) breaking at Fc = 321×10-4 au36 in BH3NH3 and the H-Ar bond in HArF was the shortest at Fc = 189×10-4 au.37 In the present work, structures and electronic properties of pure PLY2 are investigated to explore the interlayer charge-transfer and the conversion between bonding and electrostatic interactions under the external electric field (see Scheme 1). The natural bond orbital (NBO) analysis shows that a fascinating interlayer charge-transfer is induced by the external electric field, which leads to change of the 2e/12c bonding. Furthermore, the frontier molecular orbital analysis can well explain that the 2e/12c bonding is weakened and two unpaired electrons are pushed to the upper layer. This study demonstrates that the external electric field is able to control and modulate two-electron/multicenter bonding and provide important directions for further applications in switching devices.



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Scheme 1. Illustration of bonding orbital (HOMO) in PLY2 under the external electric field. 2. Computational details All calculations are performed based on density functional theory (DFT) with the Gaussian 09 suite of programs (the external electric field strength, 1 au = 5.142 × 109 V/cm).42 In recent years, the previous theoretical calculations of π-dimers widely used the hybrid meta exchange−correlation functional M06-2X,20,21,43 which was proposed by Truhlar and Zhao’s.44,45 In this work, the optimized geometric structures of PLY2 were obtained using the M06-2X method with the 6-31+G** basis set under the external electric field (ranging from 0 to 210 × 10-4 au). On the other hand, a broken-symmetry spin-unrestricted method46 performs well for such systems, because PLY is the open-shell electronic structure and its dimer presents the nature of diradicaloid. We find that the optimized structures by UM06-2X method are more stable than that of M06-2X method. Correspondingly, comparison of the total energy (Etot) is discussed in the Supporting Information (in Table S1). So we chose the results of UM06-2X method for further discussion. In order to further analyze the effect of external electric field on electronic properties of molecule, the natural bond orbital (NBO) analysis and the Wiberg bond index (WBI)47 at the M06-2X level are investigated without and with external electric field. In this work, M06-2X method is also employed to calculate the interaction energy (Eint). To correct the basis set superposition error (BSSE), the counterpoise (CP) procedure is used to calculate the interaction energies qualitatively.48,49 The Eint is calculated using the following formula: Eint (AB) = E (AB) AB − [E (A)AB + E (B)AB]

(1)

where the Eint is the difference between the energy of PLY2 π-dimer (AB) and the sum of the energies of PLY monomers (A, B). In addition, the diradical character (y0) is a significant chemical index for evaluating the nature of diradical


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systems.50 The electronic structures of open-shell singlet systems have been classified into three categories: y0 = 0, 0 < y0 < 1, and y0 = 1, representing closed-shell, intermediate diradical and pure diradical systems, respectively.51,52 On the basis of ab initio configuration interaction (CI) calculations,53-55 the diradical characters for PLY2 are estimated at a complete active space with two electrons and two orbitals CAS (2, 2)/6-31+G** level under the external electric field. 3. Results and Discussion 3.1 Geometric structures and 2e/12c bonding In order to explore the effect of external electric field on structure for PLY2, we applied the external electric field along the main molecule axis, which is parallel to the 2e/12c bonding (In Figure 1). Firstly, the geometric structures for eclipsed and staggered PLY2 have been optimized by using UM06-2X/6-31+G** method without the external electric field. We find that the upper layer occur parallel movement for eclipsed PLY2 (see in Figure S1 in the Supporting Information). Therefore, Our present work only focuses on staggered configuration to illustrate the effect of the external electric field on structure and properties of PLY dimer. Secondly, the geometric structures for staggered PLY2 are optimized under the external electric field with selected the external electric field strengths (Fext) ranging from 0 × 10-4 to 210 × 10-4 au (per Fext = 10×10-4 au). We mainly focus on discussing the interlayer distance variation (the interlayer distance is the distance between the central atoms of two layers) for PLY2 under different external electric field, and the corresponding results are listed in Figure 2. In the absence of external electric field, PLY2 presents a short interlayer distance of 3.108 Å, showing unique 2e/12c π-π bonding. With increasing of Fext, the interlayer distance is elongated, which shows that the 2e/12c π-π bonding becomes weaker. When Fext increases from 0 to 200×10-4 au, the interlayer distance is slightly elongated from the 3.108 to 3.214 Å. However, the interlayer distance is sharply elongated when Fext increases from 200×10-4 to 210×10-4 au, and it is suddenly elongated to 3.518



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Å at Fext = 210×10-4 au, which is larger than the C–C van der Waals (vdW) distance (about 3.40 Å). We initially speculated that the 2e/12c π-π bonding breaking. Further, the Fext of 200 – 210×10-4 (per Fext = 1×10-4 au) are investigated with a smaller increments (Figure 2). The interlayer distance is slightly elongated from 3.214 Å (F = 200×10-4 au) to 3.241Å (F = 203×10-4 au) and its average increment is only 0.01 Å per Fext = 1×10-4 au. Significantly, a small increment of the external electric field makes a big difference: the interlayer distance for PLY2 is sharply elongated (0.244 Å) from 3.241Å (F = 203×10-4 au) to 3.485 Å (Fext = 204×10-4 au) which is larger than the C–C vdW distance. This sudden change suggests that the 2e/12c π-π bonding breaking at 204×10-4 au. Therefore, we draw a conclusion that the 2e/12c π-π bonding becomes weaker with increasing of Fext, and Fext = 204 × 10-4 au is regarded as the critical electric field (Fc) of the “ 2e/12c π-π bonding breaking” for PLY2.

Figure 1. Optimized structure of PLY2 under the external electric field (Fext = 1 × 10-4, au).

Figure 2. The interlayer distances [Å] of PLY2 under the external electric field (Fext = 1 × 10-4, au ). To provide insight into the interaction between two layers for PLY2 under the external electric field, the Wiberg bond index (WBI) values of PLY2 are investigated and the results are shown in Figure 3. The WBI is found to decrease with increasing of Fext, showing that the 2e/12c π-π bonding becomes weaker. From Figure 3, in the region


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of Fext (0 – 203×10-4 au), the WBI is slightly decreased (0.300 – 0.143). It is surprising to find that the WBI is sharply decreased (0.093) at Fext = 204×10-4 au. According to the above analysis, the effect of external electric field can modulate the structure and weaken the 2e/12c π-π bonding in PLY2 until it breaks.

Figure 3. The Wiberg bond index (WBI) of PLY2 under the external electric field (Fext = 1 × 10-4, au ). The above discussion indicates that the structure in PLY2 can be successfully modulated by the external electric field. The effect of the external electric field on electron transfer will be investigated in the following content. 3.2 Natural Bond Orbital (NBO) and Diradicals Characteristic (y0) Under the external electric field, the Natural Bond Orbital (NBO) variations for PLY2 are investigated, and selected results are shown in Table 1 and Figure 4. There is no interlayer charge–transfer in the absence of electric field. Under the external electric field, the NBO charges have obvious change: the NBO charges on the upper layer (qU) show negative and the NBO charges on the lower layer (qL) show positive, indicating that the direction of electron transfer is from the lower layer to the upper layer along the main molecule axis. The negative charges on the upper layer are slightly increased from 0 to -0.699 and the positive charges on the lower layer are slightly increased from 0 (Fext = 0 au) to 0.699 (Fext = 200×10-4 au), which shows that the electrostatic interaction between two layers is slightly enhanced with increasing of Fext. However, the NBO charges are sharply increased (0.699 – 0.841) when Fext increases from 200×10-4 to 210×10-4 au. Further, Fext of 200 – 210×10-4 (per Fext = 1×10-4 au) are investigated with a smaller increments (Figure 4). The NBO charges are sharply increased (0.812) when Fext increases to 204×10-4 au. Fc



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is also found at 204×10-4 au, and the interaction between two layers in PLY2 is exclusively governed by the electrostatic interaction.

Figure 4. The NBO charges of PLY2 under the external electric field (Fext = 1 × 10-4, au ). In order to obtain a more detailed NBO analysis, we investigate the NBO charge difference (∆q) between the NBO charge without external electric field and the NBO charge with external electric field, and the corresponding results are provided in Table 1 and Figure 5. It is generally known that PLY2 consists of four types of carbon atom: six Cα, three Cβ, three Cγ and one central carbon atom. It is noteworthy that the ∆q-Cα account for about 90 % of the total NBO charges of each layer. For example, the ∆q-Cα is 0.764, accounting for 94.1 % of the 0.812 at Fc = 204×10-4 au. This indicates that the radical electron close to the lower layer is mainly transferred to the Cα atoms of the upper layer under the external electric field.

Figure 5. The NBO charges difference (∆q: Cα, Cβ and Cγ) between the NBO charge without external electric field and the NBO charge with external electric field (Fext = 1 × 10-4, au ). Further, the diradical character (y0) variations in PLY2 are investigated under the external electric field. The y0


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values for PLY2 by the CAS (2, 2) method are shown in Table 1. In the absence of electric field, as seen from the y0 = 0.137 in PLY2, possessing a weak diradical character. With increasing of Fext, the y0 is decreased until decreased to 0, which is regarded as an almost significant closed-shell character. According to above investigation, the external electric field effect can control two unpaired electrons between two layers gradually shifted to the upper layer and finally result in the disappearance of diradical character and emergence of closed-shell character. Table 1. The Natural Bond Orbital (NBO) charges, the NBO charge difference (∆q), the diradical characters (y0) and the interaction energies (Eint, kcal mol-1) of studied PLY2 under the external electric field (Fext = 1 × 10-4, au).

NBO

qU

0

100

200

203

204

210

0

-0.331

-0.699

-0.719

-0.812

-0.841

-0.287

-0.649

-0.670

-0.764

-0.793

0.330

0.699

0.720

0.812

0.841

0.292

0.648

0.665

0.781

0.789

∆q-Cα qL

0

∆q-Cα y0

0.137

0.098

0

0

0

0

Eint

16.799

-21.337

-72.292

-71.001

-65.394

-63.248

∆q as the difference between the NBO charge without external electric field and NBO charge with external electric field. 3.3 Interaction Energy (Eint) and Frontier Molecular Orbital (FMO) Interaction energy (Eint) with CP correction is considered under the external electric field to systematically understand the nature of dimer, and the corresponding results are presented in Table 1. With increasing of Fext, the interaction energy between two layers is increased, in which the bonding component of the Eint between two layers becomes smaller (the interlayer distance is elongated), but the attractive electrostatic interaction between two layers



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becomes stronger (The NBO charge is increased). When Fext increases to 203×10-4 au, the Eint runs up to the greatest value (-71.001, kcal mol-1), bringing the largest stability of molecule. The Eint is decreased (-65.394, kcal mol-1) at 204×10-4 au, because the 2e/12c bonding breaking. In the case, the Eint is exclusively derived from the electrostatic interaction between two layers in PLY2. Continuing to increase Fext, the attractive electrostatic interaction between two layers becomes weaker, which may be the reason for the interlayer distance is elongated. To further confirm the change of structures and electronic properties under the external electric field, the frontier molecular orbital (FMO) are investigated under the external electric field in Figure 6. The highest occupied molecular orbital (HOMO) is attributed to the SOMO-SOMO overlap between two layers of radicals. Without external electric field, two unpaired valence electrons symmetrically contribute to each monomer in the HOMO. However, under the external electric field, the HOMO shape is changed. Obviously, when Fext increases to 204×10-4 au, the SOMO–SOMO overlap between two layers of radicals is disconnected: the 2e/12c bonding breaking, and the electron density for HOMO is mainly localized on the upper layer of PLY2, thus giving rise to a larger attractive electrostatic interaction between two layers in PLY2, which related to the previous investigated electron transfer from the lower layer to the upper layer.

Figure 6. The frontier molecular orbitals of PLY2 under the external electric field (Fext = 1 × 10-4, au ).


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Overall, with increasing of Fext, the bonding component of the interaction between two layers becomes smaller and the attractive electrostatic interaction between two layers becomes stronger. At Fc = 204×10-4 au, the 2e/12c bonding converts to the electrostatic interaction. 4. Conclusions In this work, the effect of external electric field is applied along main molecule axis to drive and modulate structures and electric properties of PLY2 π-dimer for the first time with selected Fext ranging from 0×10-4 to 210×10-4 au. The main conclusions are summarized as follows: (1) With increasing of Fext, the interlayer distance of PLY2 is increased, resulting in weak 2e/12c bonding. At Fext = 204×10-4 au, the interlayer distance is sharply elongated to 3.485 Å, which is larger than the C–C van der Waals (vdW) distance (about 3.40 Å), thus the 2e/12c π-π bonding breaking. Further, the WBI is sharply decreased from 0.154 (F = 203×10-4 au) to 0.080 (Fext = 204×10-4 au). The frontier molecular orbital (FMO) well present that the SOMO–SOMO overlap between two layers of radicals is disconnected, which shows that the 2e/12c π-π bonding breaking at Fc = 204×10-4 au. (2) When the external electric field is introduced, it is possible for pure PLY2 π-dimer to come into being fascinating interlayer charge–transfer. The NBO analysis shows that the direction of electron transfer is from the Cα atoms of the lower layer to the Cα atoms of the upper layer along main molecule axis. The electron density is mainly distributed in the upper layer at 204×10-4 au, showing that the interaction between two layers in PLY2 is mainly originated from the electrostatic interaction. (3) The Eint values show that Fext = 203 × 10-4 au runs up to the greatest Eint value (-71.001, kcal mol-1), bringing the largest stability of molecule. The Eint is decreased (-65.394, kcal mol-1) at 204×10-4 au, which is exclusively governed by the electrostatic interaction between two layers in PLY2.



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According to the above investigations, the conversion between the 2e/12c bonding and the electrostatic interactions can be realized by inducting the external electric field. The critical electric field (Fc) is found at 204×10-4 au for PLY2. This work will be helpful to understand the effect of electric field on chemical bond and this system is a promising candidate for molecular conductor switching devices based on PLY2 π-dimer with fascinating 2e/12c bonding. Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: The detailed datas (per Fext = 10×10-4 au) are provided, including total energies (Etot), the layer distances (D, Å), the NBO charges, the Wiberg bond index (WBI) and the interaction energies (Eint) for PLY2 under the external electric field. Corresponding Authors *E-mail: [email protected] *E-mail: [email protected]. Acknowledgements 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 Science Foundation (2014M560227).


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