Article pubs.acs.org/JPCC
Vibrational Characterization of Two-Dimensional Graphdiyne Sheets Juan Zhao† and Jianping Wang*,†,‡ †
Beijing National Laboratory for Molecular Sciences; Molecular Reaction Dynamics Laboratory, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, P. R. China ‡ University of Chinese Academy of Sciences, Beijing 100049, P. R. China
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S Supporting Information *
ABSTRACT: Graphdiyne is formed by two acetylene bonds conjugatively connecting two phenyl rings, which then extend to a sizable two-dimensional structure. In this work, a molecular sizedependent CC stretching vibrational transition intensity is predicted by density functional theory in graphdiyne; in particular, the strongest infrared-active transition is enhanced in intensity by a factor of as high as 2190 from phenyl-acetylenic dimer to graphdiynic 46-mer, showing ca. 300 times enhancement per acetylene bond on average, examined at the level of B3LYP/6-31G*. Such an enhancement of vibrational transition intensity is caused by intramolecular electronic delocalization that gives rise to an enlarged transition dipole moment as well as by intramolecular vibrational delocalization that gives rise to intensity borrowing in such two-dimensionally conjugated graphdiyne molecular sheets. The enhancement is found to be diminished in defected graphdiynes. The results suggest that the periodically appearing CC bond may be used as a vibrational spectroscopic marker for assessing the size of perfect graphdiyne oligomers, and the characteristic CC stretching absorption can potentially be used to differentiate perfect graphdiyne sheets from defected ones.
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INTRODUCTION Three well-known fundamental hybridization states of carbon,1−7 sp, sp2, and sp3, are the reason for various carbon−carbon bonding types and for the formation of many carbon allotropes, such as diamond (sp3), graphite (sp2), fullerence (sp2),6 carbon nanotube (sp2),3 and graphene (sp2),4,7 to exist. Among these species, the carbon−carbon triple bond (CC) via the sp hybridization forms a unique linear and highly conjugated structure. In recent years, considerable efforts have been devoted to obtaining new carbon allotropes containing the sp-hybridized state that form a two-dimensional (2D) conjugated structure. Theoretical studies suggest that sp−sp2 carbon materials have potential applications.2,8−12 Graphdiyne (GDY), containing both sp- and sp2hybridized carbon atoms, was proposed first13 and synthesized shortly after.14−18 Being composed of diacetylenic bond units that are conjugated with benzene rings, this type of graphdiyne forms a two-dimensionally networked, sizable, and chemically stable structure. Recent theoretical and experimental works have been mostly focused on exploring electronic structures and potential applications of GDY. It has been predicted that GDY has many interesting electronic properties, including semiconductor-like band gap,19−22 electron-transporting ability,21 optical susceptibility,23 and thermal resistance and stiffness.24,25 Very recently, GDY-based materials have found novel applications in water-splitting photoelectrochemical cell,26,27 hydrogen-evolution reaction,28 and DNA29 and formaldehyde30 detections. However, the structural details of chemically synthesized graphdiyne sheets remain an elusive picture. For example, © 2017 American Chemical Society
whether the synthesized bulk GDY material is composed of homogeneous and large-scaled multilayered sheets or formed by defected sheets or oligomers and how these structural aspects affect the optical and mechanical properties of GDY sheets have not yet been understood at the molecular level. Recent molecular dynamics simulations31predicted the formation of twisted and partially defected regions in GDY at very high temperature. Presumably, the chemical composition will influence or even dedicate the electronic structure and potential applications of this type of planar material. Thus, it is of great importance to explore structure-sensitive tools that can be used to characterize and understand the structures of various graphdiynes and their derivatives. Vibrational spectroscopy, such as infrared and Raman, in principle, has been known as an effective tool to characterize molecular structures at the chemical-bond level, for biomolecules32−40 and also for carbon-based materials.41 In graphdiyne, the CC group is the key unit and periodically appears throughout the entire two-dimensional frame of a given singlelayered sheet. Recent experimental studies showed two weak Raman signals in graphdiyne films14 and in ordered graphdiyne stripes,42 and two weak infrared signals in the latter case, both in the 5 μm wavelength region, which have been assigned to the CC stretching modes. In simple isolated acetylenic compounds (e.g., in the form of R1CCR2), the carbon−carbon triple bond is usually IR-inactive or weakly Received: June 29, 2017 Revised: September 14, 2017 Published: September 15, 2017 21430
DOI: 10.1021/acs.jpcc.7b06390 J. Phys. Chem. C 2017, 121, 21430−21438
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Figure 1. Graphdiyne structures with varying size. The number of CC groups changes from 2 in GDY2 to 46 in GDY12. A red arrow indicates the direction of transition dipole moment of the strongest low-frequency CC stretching vibration mode in each case, while a green arrow in GDY12 indicates that of a weak high-frequency CC stretching mode. The angle between the transition dipole and one of the linear chemical-bond chains is marked in GDY6, GDY8, and GDY12. GDY8′ is a defected GDY9 but has the N/n ratio identical to GDY8.
Figure 2. Size-dependent IR spectra of the CC stretching mode in the GDYs. (a) Calculated transition intensities in sticks and corresponding Lorentzian function (with full width at half-maximum set to 8 cm−1) broadened IR spectra for each case. The baseline of each spectrum is vertically shifted for better view. (b) Average transition intensity (I)̅ as a function of the ratio of the CC bond number vs aromatic ring number (N/n). (c) Relationship between I ̅ and average participation ratio (P̅), and that between the intensity of the mostly enhanced transition (Imax) and its participation ratio (Pmax). Dashed lines in panel b and c only show the trends of change. The defected GDY8′ is not included in panel c. See text for details.
active43 and would only show an extremely weak IR signal if neither R1 nor R2 is aromatic. In this case, the molecular absorption coefficient of the CC stretching vibration is very small (only ca. one tenth of the C−H stretching mode).44,45 However, because graphdiyne is a conjugated planar system with variable size, the infrared vibrational property of the CC stretching is expected to be different from that in the nonconjugative system. A very early study46 has showed a lowered CC stretching vibrational frequency with somewhat increased intensity in a small conjugated molecule containing the CC, CO, and CC groups, as also shown in a recent computational work.41 Therefore, it is of fundamental importance from a theoretical aspect to obtain a better understanding of the CC vibrational signature in largely conjugated GDY structures, as well as in defected GDY structures. In this work, typical substructures of graphdiyne were chosen as model systems with varying molecular size (Figure 1), in order to understand how the conjugative effect influences the properties of the CC stretching mode. In these structures, as the molecular size increases, the ratio of the CC bond number (N) vs the benzene ring number (n) increases. Here,
the N/n ratio is used as a measure of the density of the CC bond in the network of the aromatic groups. In particular, as shown in Figure 1, GDY8′ is a defected GDY9 but has the same N/n value as GDY8. The harmonic frequency and vibrational transition intensity of the CC stretching for these GDY systems were examined using density functional theory (DFT) at the level of B3LYP with the 6-31G* basis set. The DFT method has been known to be very useful in predicting vibrational properties, including transition frequency and intensity for small molecules.47−49
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RESULTS AND DISCUSSION Computed Infrared Spectra of Graphdiyne with Varying Size. The calculated IR spectra of the CC stretching modes for these structures are shown in Figure 2a, with the frequencies scaled by a factor of 0.953.50 Two major groups of IR-active peaks are shown, one strong component located at the low-frequency side (ωL, near 2135 cm−1) and one weak component located at the high-frequency side (ωH, near 2200 cm−1). The frequency separation between these two absorption peaks is ca. 65 cm−1, while that between the highestfrequency mode and the lowest-frequency mode in GDY12 is 21431
DOI: 10.1021/acs.jpcc.7b06390 J. Phys. Chem. C 2017, 121, 21430−21438
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The Journal of Physical Chemistry C ca. 83 cm−1. This is similar to a recently reported experimental result,42 in which two very weak IR peaks were observed at 2122 and 2207 cm−1 respectively. Our simulation results show that these low-frequency modes are mainly due to the antisymmetric CC−CC stretching, while the highfrequency modes are mainly due to the symmetric CC− CC stretching. On the other hand, for these 2D sheets, the low-frequency and high-frequency modes can be termed as the longitudinal and transversal CC vibrational modes, because the former contains a large amount of CC species and has its dipole moment roughly parallel to its longer dimension in these 2D molecular frames, and the latter has its transition dipole moment roughly perpendicular to the longitudinal mode. This would be more strictly defined in the case of a graphdiyne stripe with limited width but infinite length. This can be verified by the DFT computations; the computed angle between the transition dipole moment of the low-frequency strong transition (the longitudinal mode) and one of the linear chemical-bond chains is marked in GDY6, GDY8, and GDY12. The angle is quite small in larger sheets (for example, being 0° in GDY9 and 7.9° in GDY12). However, for those smaller GDY structures considered in this work, the transition dipole shown in Figure 1 is not necessarily parallel to any of the backbones. For the transversal mode, one of such modes is illustrated in Figure 1 by a green arrow for its transition dipole direction in the case of GDY12. This mode is found to be 2191.1 cm−1 in frequency and 9.85 KM/mol in intensity. Figure 2a shows that as the molecular size increases, the vibrational intensity of the CC stretching increases dramatically, especially for the ωL-component. The enhancement is found to be nearly 2190 times for the strongest vibrational mode at the theoretical level (B3LYP/6-31G*) used in this work, as the molecular system changes from GDY2 to GDY12. The transition intensity of the strongest mode in each molecule is listed in Table S1 of the Supporting Information. The defected case, GDY8′, which has the same N/n ratio as GDY8, on the other hand, shows the maximum intensity that is lower than either GDY9 or GDY8 (also see Table S1 for more detailed vibrational characteristics of all the systems considered in this work), suggesting the enhancement is closely associated with 2D-conjugated effect. To justify the transition intensity enhancement of the strongest component from GDY2 to GDY12, computations at two theoretical levels (B3LYP/6-31+G* and B3PW91/631G*) for GDY2, GDY4, and GDY12 were also carried out, and the results are listed in Table S2 in the Supporting Information. The strongest intensity increases by 1228 and 723 times respectively at these two theoretical levels, when the size of graphdiyne increases from dimer to 46-mer. In the meanwhile, the average intensity also increases ca. 175 and 104 times from GDY2 to GDY 12, respectively. Thus, the enhancement is confirmed, even though the enhancing factor depends on the level of theory. To quantify the size dependence of the intensity enhancement, the average transition intensity of all the CC stretching modes, which is defined as
transition intensity of GDY2 was set to 1. Thus, it is clear that the average transition intensity of the CC stretching increases substantially as the N/n value (or the density of the CC bond in the network of aromatic ring) increases. Note that the I ̅ value in GDY8′ is much lower than that in both GDY9 and GDY8, again clearly indicating the conjugationdefect effect. In addition, several other defected GDY structures (GDY6′, GDY8″, and GDY12′, Figure S1) were also considered to examine the conjugation-defect effect. The computed transition intensities of the CC stretching modes in these structures are shown in Table S3. Clearly, as long as there are defects in such conjugated structures, by missing either an aromatic ring or a CC unit, the computed CC stretching intensities for the averaged and for the strongest mode will decrease significantly. To concentrate on the properties of the perfectly conjugated structures, in the rest of this work, we ignore the case of GDY8′ and other defected structures. On the other hand, the predicted slight frequency red-shift (from 2140.8 to 2128.4 cm−1, see Table S1) is due to the bond lengthening and force constant increasing effect of the CC group (as summarized in Table S1), which will be further discussed later in this work. Examination of Infrared Enhancement. To characterize the computed vibrational intensity enhancement, we first examined the vibrational delocalization degree of the CC stretching vibration in these GDY substructures. Under the vibrational exciton approximation,51 a set of the CC stretching oscillators (chromophores) can form a collection of excitonic state |i⟩ through a linear combination in the form of N
|i ⟩ =
k
∑ Ii/N i=1
(2)
where |k⟩ is the CC stretching site state, N is the total number of the CC chromophores in a given system, and qik is the expansion coefficient of the kth site state in the ith excitonic state. The participation ratio Pi can be defined for each excitonic state |i⟩52−54
Pi =
∑ qik4 k
(3)
which is a measure of delocalization degree of the ith mode; Pi = 1 indicates a completely localized state and Pi = 1/N indicates a completely delocalized state. The relationship between the intensity of the mostly enhanced transition (Imax) and its participation ratio (Pmax) is shown in Figure 2c. Figure 2c also shows the relationship between the average vibrational transition intensity (I)̅ and average participation ratio N
P̅ =
∑ Pi /N i=1
(4)
for the CC stretching mode in each system. As can be seen, even though Pmax varies from molecule to molecule, the general trend of the two curves in Figure 2c is quite similar. Further, Figure 2c shows that neither P̅ nor Pmax reaches the completely delocalized case except the phenyl-acetylenic dimer, but the delocalization degree is still quite high at larger molecular sizes, as is demonstrated further in the later section of this work. Thus, even though the molecular symmetry of these graphdiyne structures is high (e.g., D2h for GDY9) and the total electric dipole moment of each of these molecules is zero (data not shown), the transition dipole moment of the CC stretching
N
I̅ =
∑ qik|k⟩
(1)
is plotted as a function of the N/n ratio for these structures and is shown in Figure 2b, where the averaged CC vibration 21432
DOI: 10.1021/acs.jpcc.7b06390 J. Phys. Chem. C 2017, 121, 21430−21438
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bonds, which are electron-withdrawing groups with respect to the benzenic CC groups in these GDYs. Due to these conjugative influences, both the CC group and CC of the benzene unit on the peripheral regions of GDY are consequently less affected. π-Electron Delocalization. Electron localization function (ELF) is a very useful real-space function to measure the electron localization.59−61 A spatial region with high ELF value is a region where electrons are highly localized. As we discussed above, the conjugative effect in GDY molecule is mainly caused by the π-orbitals electrons; thus, only the ELF of these GDY structures due to the π-orbitals electrons (ELFπ) was examined. Figure 3c shows the ELFπ isosurface for GDY12 structure with the isovalue of 0.745. The results of all the conjugated GDY structures are given in Figure S5. It is clear that at this isovalue the reducible domain connected by the π-electrons is just to be decomposed into irreducible domains on certain CC bonds (labeled by arrows) above and below the benzene unit in these GDY structures (expect GDY2). These positions labeled by the red arrows are referred to as bifurcation point.62,63 Topological analysis of ELFπ gives the exact bifurcation value for different reducible domain. Figure S6 shows the ELFπ given for the C C bond of benzene unit in these GDY structures. It is clear that ELFπ reducible domain breaks down early for the CC bonds of the benzene unit that connects more CC bonds, indicating the π-electrons are easier to delocalize to other domains. The average bifurcation ELFπ values of benzene unit for these GDY structures are shown in Figure S7a. The result shows that as the molecular size increases, the average bifurcation ELFπ value of benzene unit decreases linearly with the N/n ratio, which is consistent with the average MCBO result. Indeed, a linear relationship between the average MCBO and the average bifurcation ELFπ value was predicted by our computation (data not shown). However, as the molecular size increases, the ELFπ value between the two carbon atoms of the CC bond (see Figure S8) only changes to some extent, indicating that the πelectrons are relatively more localized on the CC bonds than on the benzene unit, and the conjugative effect is mainly caused by the π-electrons of the benzene units. This is also in agreement with the conventional understanding that CC bonds are generally electron-attracting groups. Bond Length Analysis. Next, to examine the conjugative effect from the structural aspect, we also analyzed the bond parameters of these graphdiyne structures. The averaged bond lengths for CC, CC, and the single C−C bond length between the two CC bonds for these molecules are shown in Figure 3, panel d, e, and f, respectively. Generally, a linear relationship between bond length and the value of N/n is shown, owing to the stronger conjugative effect at larger molecule size. The triple and double bonds become lengthened while the single bond is generally shortened. More surprisingly, we note that the C−C bond length between the two adjacent CC bonds is always shorter than that of the benzene CC bond (panel e vs f), suggesting the conjugative effect occurring among the CC, CC, and C−C bonds. In addition, the finding of the shorter bond length for the CC bonds on the edge of the graphdiyne molecule (Figure S9) is consistent with the higher FBO value for the same CC bonds on the edge (Figure S3); both are due to less conjugative effect on the peripheral regions. In addition, computations at other levels of theory were also carried out to evaluate the variation of the bond length. For example, at the B3LYP/3-21G* level, the average CC bond length from GDY2 to GDY12 increases in
normal mode becomes very large (Table S1) because of the mode delocalization, which leads to the enhanced vibrational intensity for this mode (Figure 2a). Bond Order Evaluation. As a conjugative system, graphdiyne has its π-electrons delocalized onto the entire molecular frame, and the distribution of electron density may vary with the size and shape of molecule. Thus, due to the conjugative effect, the bond properties would be different. Bond order can be used to measure the degree of electron delocalization between two atoms. Figure 3a presents the
Figure 3. Dimension-dependent bond order and bond length. (a) Average FBO of CC bond. (b) Average MCBO of benzene unit. (c) ELFπ isosurface for GDY12 structures at isovalue of 0.745. The red arrow indicates the bifurcation point. (d) Average CC bond length. (e) Average CC bond length in benzene ring. (f) Average C−C single bond length between the two CC bonds. Dashed lines in panels a, b, d, e, and f are linear fits. See text for details.
relationship between the average fuzzy bond order (FBO)55 of the CC bond and the N/n ratio in these structures. On the other hand, in these GDY structures, the electron delocalization of the benzene ring differs as the structural dimension changes. Therefore, we also examined the electron delocalization of the aromatic unit, using the multicenter bond order (MCBO).56,57 MCBO is usually used to measure the extent to which the electrons are delocalized among a set of atoms, which is also useful in measuring the aromaticity of conjugated molecules such as benzene. Figure 3b shows the average MCBO of benzene unit as a function of N/n. It is clear that both FBO and MCBO values are linearly anticorrelated with the N/n ratio, showing that as the molecule size increases, the electrons, especially the π-electrons (see Figure S2 in the Supporting Information), are no longer confined within the two carbon atoms of the CC bond and the benzene rings but are more delocalized on the entire molecule. Furthermore, the average MCBO of benzene units decreases more significantly than the FBO of CC bond (38.8% vs. 2.2%) from GDY2 to GDY12. This is perhaps due to the electron-withdrawing ability of the acetylenic group. In addition, bond polarity is also known to be anticorrelated with bond order;58 thus, the results in Figure 3a suggest that as molecular size or the N/n ratio increases, the CC bond polarity increases. Moreover, both the FBO value of the CC bond and the MCBO value of the benzene unit show an edge effect: the FBO and MCBO values on the edge are significantly larger than those of the insiders (Figures S3, S4). This is because on the edge the benzene units connect fewer CC 21433
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Figure 4. Two-dimensional potential energy distributions of the CC stretching mode of the low-frequency strongest mode in GDY2, GDY3, GDY4, GDY6, GDY8, GDY9, and GDY12 (a−g) and that of one of the high-frequency modes in GDY12 (h) and GDY4 (i). The PED values are normalized in each case.
Figure 5. Quantum connectedness length as a measure of the CC stretching vibrational state delocalization for the GDYs considered in this work. (a) QCL vs average pairwise CC distance. (b) QCL vs maximum pairwise CC distance. (c) Peak position of the fitted low-frequency component (ωL, Figure 2) as a function of the maximum pairwise CC distance. A previous experimental result (indicated by a red dot)42 is also shown, for which a 10 (number of phenyl units) by 10 graphdiyne sheet is assumed, and the maximum pairwise CC distance of ca. 180 Å is used.
(panel h) and GDY4 (panel i). Clearly, these modes are also delocalized; otherwise, it would be less likely to achieve 300 times intensity enhancement on average (Figure 2c). How far can a vibrational delocalization diffuse in these planar molecular sheets? To address this issue from a different angle, quantum connectedness length (QCL, in Å) is evaluated,65,66 which is defined as
the amount of 0.0011 Å, which is in reasonable agreement with the result (0.0015 Å, Figure 3d) obtained at the same theory level used in this work (B3LYP/6-31G*). Vibrational Delocalization. For such two-dimensional structures, we also examined the strongest component in terms of potential energy distributions (PED)64 on the normal-mode basis. The results are shown in Figure 4a−g to visualize the spatial distribution of PED in a two-dimensional fashion. It can be seen clearly that from GDY2 to GDY12, this CC stretching mode is substantially delocalized in each case. In addition, for the high-frequency weak mode, the 2D-PED shows a similar pattern, for example, in the case of GDY12
⎛ ∑ Δ r 2 ⎞1/2 kl kl ⎟⎟ QCL = ⎜⎜ kl ∑ Δ ⎝ kl kl ⎠ 21434
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delocalized π-electron in such conjugated system could serve as the driving force of the chemical enhancement of surfaceenhanced infrared spectroscopy; thus, the results in this work present a good starting point for understanding the chemical origin of surface-enhanced infrared absorption, particular for the first-layer effect.71 It is generally believed that the chemical enhancement is mode-selective and originates from the interaction of vibrations with electron−hole pairs and is restricted to the first layer of adsorbates on an enhancingsurface material such as metal.72More efforts need to be made in order to explore the potential application of such 2D carbon material as surface-enhancing material and its first-layer effect for extrinsic vibrational modes, which is, however, beyond the scope of this work.
where Δkl = R kl / R kk ·R ll , and R kl = ∑i qik2 qil2 which is the distance between kth and lth local CC bond centers. QCL describes overall how delocalized the CC stretching normal modes are in a given GDY molecule. The computed results are shown in Figure 5a, b, where QCL is plotted as a function of the average pairwise CC distance and the largest pairwise CC distance, respectively. As can be seen, as the molecular size increases, the quantum connectedness length increases linearly and nearly reaches 16 Å, indicating more connected CC stretching vibrational states, which is in agreement with the 2D PED results shown in Figure 4. However, because of the limited GDY size evaluated in this work, we do not know whether it remains a linear relationship for even larger sheets or it is the rising phase of an exponential growth. It should be pointed out that the vibrational delocalization and electron delocalization are corrected in these 2D structures. This is because the increased electron delocalization occurs at larger GDY molecules, which is shown in Figure 3 in the form of a decreased average MCBO of benzene unit, as well as in Figure S2 in the form of a decreased bifurcation ELFπ value between two carbon atoms of benzene unit. On the other hand, the vibrational delocalization can be quantified by quantum connectedness length (QCL). As shown in Figure 5b, the QCL is linearly dependent on the maximum distance between two remote CC groups, which is also a measure of the molecular size. Thus, vibrational delocalization and electron delocalization are corrected, and the correlation is shown in Figure S7b in the Supporting Information. Vibrational Frequency Shift and Transition Dipole. Finally, we have attempted to understand the frequency redshift for the fitted low-frequency peak (ωL) as a whole. Figure 5c shows the frequency change of this component taken from Figure 2a as a function of the maximum pairwise CC distance. In the simplest harmonic picture, the vibrational stretching frequency increases as the bond order increases.67 This is also what we see in these GDY molecules, with a decreasing CC bond order at increasing molecular size (Figure 3). However, as can also be seen from Figure 3, average CC bond length only increases by 0.1% from GDY2 to GDY12, which is less than the amount of frequency drop of the ωL-component (ca. 0.6%). The additional contribution must be due to the force constant, as seen in Table S1. Further, there is also a correlation between the frequency drop and molecular size, which was examined and is shown in Figure 5c. In this figure, roughly an exponentially decreased frequency pattern is shown, on which a recent experimental IR result of graphdiyne,42 was also placed as a data point. In this case, a 10 (number of phenyl units) by 10 graphdiyne sheet is assumed for the synthesized GDY sheet, which is a reasonable estimation.31 Next, it is interesting to note that the enhanced CC stretching vibration shows a quite large transition dipole moment (0.2075 D for GDY12, Table S1), which is equivalent to that of a CO stretching mode in simple organic compounds or in peptides.68 Such an enhanced signal may be regarded as a self-surface-enhancing phenomenon, where the IR-active transition with its transition dipole direction parallel to the surface (2D molecular backbone) is enhanced, showing a selection rule totally different from what was known for surfaceenhanced infrared absorption spectroscopy,69,70 where only the vibrational modes having transition dipole moments perpendicular to the enhancing-surface will be enhanced. Further, the
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CONCLUSIONS In summary, the vibrational properties of the CC stretching in graphdiyne molecules with different structural dimensions under the conjugative effect were examined by computations at the level of density functional theory. In these conjugated graphdiyne structures, the π-electrons of carbon form a delocalized π-bonding network. Such a delocalization results in increased CC and CC bond lengths and a decreased C−C bond length. In graphdiyne, acetylenic bond is an electron-attracting group in comparison to the CC group of benzene ring. Thus, the electrons are delocalized to a sizable region of such conjugative system, which is confirmed by the decreased MCBO values as well as by the ELF-π evaluation of the benzene ring at varying graphdiynic molecular size. Fuzzy bond order assessment also indicates a decreased CC bond order and an increased CC bond polarity as the size of graphdiyne increases. Thus, the CC vibration becomes significantly more IR-active at larger sheets. As the molecular size of these graphdiyne structure increases, the delocalization degree of the CC stretching vibration increases, as can be seen by the computed two-dimensional PED and quantum connectedness length. These conjugated effects cause the dramatically enhanced vibrational transition intensity of the strongest CC stretching mode, which, in each case, is found to be mainly limited to the low-frequency region, while the weak modes are found to be limited to the high-frequency region as shown in Figure 2a, which is the consequence of electronic and vibrational delocalization and also vibrational coupling. The enhancement has been confirmed by using different levels of theories and basis sets, although the enhancing factor may vary. Our results provide a vibrational spectroscopic means for understanding the structural aspect of graphdiyne oligomers, which is the chemical foundation of various applications of this type of novel material. In addition, it should be pointed out that due to the limited molecular size of GDYs examined in this work, whether the average intensity enhancement reaches a plateau at larger size cannot be predicted at this moment. More advanced computational methods should be employed to address such question. Further, it is conceivable that since perfect planar graphdiyne molecular structures show a dramatically enhanced CC stretching absorption peak but the defected graphdiynes do not (Figure 2a, b), such property can potentially be used to characterize the perfectness of GDY sheets, i.e., whether they are perfect 2D sheets or have defects. Our work also suggests that experimentally synthesized graphdiynic materials reported so far are likely to be defected, so as to show weak CC stretching absorption intensity in their infrared spectra. 21435
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The Journal of Physical Chemistry C
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Additionally, it should be pointed out that we have attempted to compute and compare the Raman scattering activity of the CC stretching mode in these GDY structures at the same level of density functional theory; however, no abnormal Raman signal intensity enhancement was observed. Since only very limited GDY structures were examined in this work, we cannot draw any solid conclusion in this regard. More work needs to be done in this direction in the future.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b06390. Average FBO of the CC bond and average MCBO of the CC bond of benzene unit as a function of the N/n ratio and their composition analyses; detailed pictures of FBO, MCBO, bifurcation ELFπ values, and their analyses; the CC bond length distributions and calculated CC stretching harmonic vibrational properties of these GDY structures (PDF)
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AUTHOR INFORMATION
Corresponding Author
*Tel.: (+86)-010-62656806. Fax: (+86)-010-62563167. E-mail:
[email protected]. ORCID
Jianping Wang: 0000-0001-7127-869X Author Contributions
J.Z. carried out computations; J.Z. and J.W. wrote the manuscript. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The work was supported by the National Natural Science Foundation of China (21603238 and 21573243). The authors thank Ms. Y. Wu and Ms. X. Dong for technical help.
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REFERENCES
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