Davydov Collective Vibrational Modes and Infrared Spectrum Features

Aug 3, 2017 - Intermolecular interactions have significant influences on molecular crystals, oligomers, and various van der Waals clusters. They are e...
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Davydov Collective Vibrational Modes and Infrared Spectrum Features in Aniline Crystal: Influence of Geometry Change Induced by van der Waals Interactions Yuan Kong,† Dong Hou,† Hou-Dao Zhang,*,† Xiao Zheng,†,‡ and Rui-Xue Xu*,† †

Department of Chemical Physics and Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China ‡ Guizhou Provincial Key Laboratory of Computational Nano-Material Science, Institute of Applied Physics, Guizhou Normal College, Guiyang, Guizhou 550018, China S Supporting Information *

ABSTRACT: Intermolecular interactions have significant influences on molecular crystals, oligomers, and various van der Waals clusters. They are essential in determining the quantum optics, quantum transport, and chemical properties of complex molecular systems. In this work, we investigate the infrared spectra of aniline crystal via the density functional theory. Then we identify four intriguing collective modes that are featured by NHHN wagging vibrations and four other collective modes that are featured by NH2 wagging vibrations. All these eight collective modes are due to Davydov splitting. To clarify the origin of such vibrational pattern, we further simulate aniline molecule and oligomers, and thoroughly analyze the spectra differences on some key vibrational modes, such as N−H wagging and torsional vibrations. Our results reveal that the chain structure of aniline crystal significantly enhances the van der Waals forces among adjacent molecules, and the intermolecular interactions are responsible for those NHHN wagging collective modes. Our study provides insights in intermolecular interactions and collective motions in aniline crystal and also establishes a standard protocol for the theoretical investigation of other van der Waals clusters.

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INTRODUCTION Molecular crystals and aggregates are formed by hydrogen bonds and other intermolecular interactions. Among them, collective motions due to interactions over distant molecules are of particular interest. They are dictated by the details of molecules in aggregation, supported by the structurally ordered hydrogen bonds,1−4 π−π stacking,5−7 delocalized excitonic interactions,8−12 and so on. Collective intermolecular interactions play important roles in quantum optics,13−17 in quantum transport,18−23 and in determining the chemical24−29 and biological30−32 properties of complex molecular systems. Recently, the scanning tunneling microscope induced luminescence method has made it possible to probe coherent dipole− dipole interactions at the atomic level.33−36 However, it is still difficult to observe collective intermolecular motions in molecular crystals or oligomers directly in experiments. That is because the collective intermolecular interactions in molecular crystals or oligomers are more delicate than the dipole−dipole interactions in the organic macromolecules. A comprehensive interpretation of the subtle relation between collective motions and intermolecular interactions calls for theoretical modeling and simulations, based on such as the density functional theory (DFT) calculations. In this work, we investigate the collective motions in the aniline crystal, by studying its infrared (IR) spectra via DFT calculations. To account for the van der Waals (vdW) interactions, we adopt the DFT-D2 method,37−42 which © XXXX American Chemical Society

comes up with a semiempirical dispersion potential correction to the conventional DFT energy. We choose the Perdew− Burke−Ernzerhof (PBE) exchange correlation functional for electronic structure calculations. We list out our basic findings as follows: (1) There are eight aniline molecules per unit cell in aniline crystal. (2) The N−H wagging modes in the aniline molecules exhibit collective vibrational behavior in the crystal. (3) The total eight modes aggregate into NHHN and NH2 wagging subbands due to Davydov splitting,43,44 with each subband consisting of four modes. The general Davydov splitting is known as the splitting of bands in the electronic or vibrational spectra of crystals due to the presence of more than one interacting molecular entity in the unit cell, and this splitting is quite common in molecular crystals.45−48 (4) The four vibrational modes in the XNHHN wagging subband show that half of the adjacent hydrogen atoms in the NH2 ends quench their motions, whereas those four in the XNH2 wagging subband show synergistically vibrational motions for all the adjacent hydrogen atoms in the NH2 ends. (5) Theoretical studies on the vibrational modes of similar molecular crystals such as acetanilide, furan, and pyridine have also been carried out. However, none of them exhibits such intermolecular collective behavior as the XNHHN wagging subband here. (6) Received: March 27, 2017 Revised: August 1, 2017 Published: August 3, 2017 A

DOI: 10.1021/acs.jpcc.7b02862 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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Figure 1. (a) Unit cell of the aniline crystal. (b) Vibrational pattern of mode X1 (588 cm−1) in the relaxed geometric structure. The eight benzenes within one unit cell are labeled as “1” to “8”, and the dihedral angles between these benzene ring planes are 152.1°(12), 150.2°(34), 147.1°(56), 150.5°(78), ° , 150.3(35) ° , 148.6(57) ° , and 148.5(71) ° , respectively. The eight vibrational vectors along with their associated hydrogen atoms are labeled as “a” to 152.1(13) “h”, and the angles between these vectors are 88.2°(ab), 91.1°(bc), 87.1°(cd), 89.2°(da), 87.5°(ef), 89.4°(fg), 90.2°(gh), and 89.3°(he). The distances between two neighboring hydrogen atoms are 2.48 Å(ab)(cd)(ef)(gh) and 2.24 Å(bc)(da)(fg)(he). (c) Vibrational patterns of modes X1 (588 cm−1), X2 (586 cm−1), X3 (585 cm−1), and X4 (584 cm−1) in the simplified diagrams.

potentials with an energy cutoff of 600 eV. A single crystallographic unit cell was used for all calculations, with the reciprocal lattice being sampled using k points 6 × 9 × 2. To obtain the IR spectroscopy intensities, we switch on the density-functional perturbation theory vibrational analysis. This approach enables us to calculate the Born effective charge tensors after structural optimization. Applications of this method can be found in some earlier researches.56−59

Both XNHHN and XNH2 subbands are blueshifted in the crystal infrared spectra.

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COMPUTATIONAL DETAILS Nowadays, DFT methods39−42 have been very popular for electronic structure calculations in solid-state physics and quantum chemistry. It is very convenient to utilize these methods in aniline crystal or aggregates.49,50 In this work, we adopt the Vienna ab-initio simulation package (VASP) codes for the modelization and simulation of aniline monomer, oligomers, and crystal. To consider the vdW effect, the DFTD2 method of Grimme38,51 is used in simulating the aniline dimer, trimer and crystal IR spectroscopy in this paper. We have verified our relaxed structure by other DFT methods with dispersion correction, such as vdW-DF52,53 and DFT-D3.54,55 In the structural optimizations, we use the Perdew−Burke− Ernzerhof exchange-correlation functional and PAW pseudo-

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RESULTS AND DISCUSSION Figure 1a presents the unit cell that consists of eight aniline molecules. The crystal structure is first deduced from the experiment.60 The lattice parameters and atom coordinates are then relaxed to their equilibrium values, and to obtain the stable structure for IR spectra calculations without imaginary frequencies. We present the relaxed structure in Figure 1b, with the geometric details being referred to the figure caption. B

DOI: 10.1021/acs.jpcc.7b02862 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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Figure 2. (a) Vibrational pattern of one selected mode from XNH2 subband in aniline crystal. (b) Vibrational pattern of one selected mode from band 35 in aniline crystal.

In Figure 1b, we also show the vibrational pattern of mode X1. Clearly, this vibrational mode is dominated by the collective movement of the adjacent hydrogen atoms in the NH2 ends. These hydrogen atoms, with the same labels from “a” to “h” as their individually associated vibrational vectors, constitute a peculiar chain in the aniline crystal. We denote these hydrogen atoms as type-1. In comparison, the rest hydrogen atoms of NH2 ends are less active in mode X1, and attributed to type-2. In fact, the four collective modes are nearly degenerate, with almost the same frequency (from 584 to 588 cm−1) and similar vibrational patterns, see the simplified sketches in Figure 1c. The above findings indicate that all these collective modes originate from the same vibrational mode in the aniline monomer. Moreover, they constitute a single XNHHN wagging subband in the crystal IR spectra. In analogy to XNHHN wagging subband, the four modes of XNH2 wagging subband are also nearly degenerate and share similar vibrational patterns. In Figure 2a, we therefore only show one case for illustration. Comparing the vibrational pattern of mode X1 in Figure 1b to that in Figure 2a, we find the movements of Type-2 hydrogen atoms are quenched during the crystallization, while those of Type-1 hydrogen atoms are enhanced in mode X1. However, in the vibrational mode of Figure 2a, the synergistically vibrational motions of eight molecules in one unit cell indicate the vibrational structure of mode 32 in the monomer is preserved in the crystal. Therefore, we denote the subband that consists of modes X1,2,3,4 as XNHHN wagging subband, and the other as XNH2 wagging subband throughout this paper, respectively. Parts a and b of Figure 3 present the IR spectra of an isolated aniline monomer and the aniline crystal, respectively. For the aniline crystal simulation in Figure 3b, we adopt the PBE functional with the DFT-D2 dispersion potential correction.38,51 To investigate the vdW interaction effects, we further present in Figure 3c the IR spectra of a reference aniline crystal, where the DFT-D2 dispersion correction is not considered in both the structure optimization and IR spectra calculation. Therefore, we denote this reference model as the pseudocrystal in the rest of this paper. It is worthy to note that the crystal and

Figure 3. Comparison of calculated IR spectra of (a) aniline monomer in the gas phase; (b) aniline crystal with DFT-D2 correction; (c) aniline reference crystal model without DFT-D2 correction. The inset presents the vibrational pattern of mode 32, which becomes the XNHNH and XNH2 subbands in the crystal, due to the combined effects of the Davydov splitting and the vdW dispersion relaxation.

the “pseudo”-crystal have quite different geometric structures after the relaxation. These structural differences further lead to significant frequency shifts and intensity variations of several vibrational modes in the IR spectra. In the aniline crystal and the “pseudo”-crystal simulations, each unit cell contains eight molecules. Therefore, a single vibrational mode in isolated monomer would transform into a band of eight modes in the crystal. In our paper, the index number of the mode refers to that of isolated monomer or the band consisting of two subbands in the crystal. To further investigate the IR spectra differences among the isolated aniline monomer, the crystal and the “pseudo”-crystal, C

DOI: 10.1021/acs.jpcc.7b02862 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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Table 1. Comparison of the Vibrational Frequencies of Some Representative Modes in Aniline Crystal and Monomera crystal (“Pseudo”-crystal) index

name

monomer

1 2 32 35

antisymmetric N−H symmetric N−H wagging N−H torsional N−H

3615 3509 461 325

−66 (−40) −61 (−43) 206 (183)* 165 (185)

−87 (−53) −120 (−61) 125 (129)** 145 (165)

The frequency shifts of the subband centers of the crystal from the monomer references are reported, and the “pseudo”-crystal results are listed in parentheses. The XNHHN and XNH2 subbands are labeled with * and **, respectively.

a

interactions are not as evident as band 32, and intermolecular subband like XNHHN does not emerge. The large red shifts and splitting of vibrational spectra of crystals in modes of type 1 and 2 are listed in Table 2. We depict vibrational patterns of antisymmetry mode 1a and mode 1b in Figure 4, parts a and b, and vibrational patterns of symmetry mode 2c and mode 2d in Figure 4, parts c and d.

we list the calculated vibrational frequencies of some representative modes/subbands in Table 1. By studying Table 1, we find three major differences on IR spectra between the aniline crystal and isolated monomer, see also parts a and b of Figure 3 for comparison. First of all, the mode 32 that is located at 461 cm−1 in the monomer IR spectra (Figure 3a) transforms into collective XNHHN and XNH2 subbands in the crystal IR spectra (Figure 3b). The large frequency splitting (81 cm−1) between these two subbands is evident. The splitting is determined by the vdW intermolecular interactions in the unit cell, which is well-known as Davydov splitting.43,44 This enormous splitting during crystallization of band 32 suggests the band is quite sensitive to vdW interactions. Moreover, the blueshifts of XNH2 subband (206 cm−1) and XNHHN subband (125 cm−1) are quite large. The second remarkable difference comes from the vibrational mode/band 35 in the aniline monomer/crystal. In the simulated IR spectra of monomer, this mode is located at 325 cm−1, and has been attributed to the N−H torsional vibration in previous studies.61−63 Compared to the monomer result in Figure 3a, we observe large blueshift of the band 35 in Figure 3b. Besides, band 35 also contains two subbands, with frequency blueshifts being about 145 and 165 cm−1. However, the Davydov splitting between these two subbands is extremely small (20 cm−1). This observation is in consistent with the fact that the two subbands have similar vibrational patterns, quite different from the case of XNHHN and XNH2 subbands in band 32. In Figure 2b, we only depict the vibrational pattern of one mode from band 35. Apparently, all the hydrogen atoms in NH2 ends contribute to the vibrational band 35, similar to the XNH2 subband in band 32. The above observations also imply that the vdW interactions have a great influence on band 35. The last notable difference between IR spectra of aniline crystal and monomer involves the antisymmetric N−H (mode 1 in Figure 3) and symmetric N−H (mode 2 in Figure 3) vibrations. Each mode transforms into the corresponding band with two subbands in the aniline crystal, see Figure 1b. In Table. 1, the redshifts of their frequencies (61−120 cm−1 in crystal) are quite large, which indicate a weakening of the N−H bond in aniline during crystallization. Moreover, the intensities of these N−H stretching vibrations in aniline crystal are dramatically enhanced. All these observations are supported by some earlier researches.62,63 On the contrary, the splitting between two subbands is not very large (21−59 cm−1 in the crystal), compared to the high frequencies of these modes in the monomer (>3500 cm−1). Thus, the large redshifts and the enhancement of intensities of those bands indicate vdW interactions also have non-negligible influences on bands 1 and 2 during crystallization. Meanwhile, small Davydov splitting between two subbands reflects the influences of vdW

Table 2. Calculated Frequencies and Intensities of the N−H Stretching Modes in Aniline Crystala N−H antisymmetry modes

N−H symmetry modes

frequency (cm−1)

intensity

frequency (cm−1)

intensity

3550 3548a 3548 3547 3529 3528 3527 3527b

0.0 0.921 0.352 0.003 0.0 0.229 0.011 1.0

3449 3449 3448 3448c 3399 3399 3398 3387d

0.096 0.009 0.011 0.385 0.0 0.155 0.0 1.0

a

The left two columns are N−H anti-symmetric modes and the right two are the symmetric modes. Intensities of same stretching modes are normalized. Some modes marked by superscript a, b, c, and d are shown in parts a−d of Figure 3, respectively.

At this moment, we also like to point out that the modes mixing during crystallization could be analyzed via vibrational patterns that account directly for the dipole−dipole interaction. We take mode 27 (736 cm−1 in monomer) as an example. The vibrational pattern of mode 27 in monomer is illustrated in Figure S2 in the Supporting Information, which is found to have only a small change in the crystal, due to our calculation. The blue shifts of this mode are only 13−17 cm−1 during crystallization; see Table S2 in the Supporting Information. That is because in mode 27, the major contribution is from the benzene ring but not the hydrogen atoms in NH2 end which take little contribution to the vibrations. While in the NHHN and NH2 wagging modes, the hydrogen atoms in NH2 end take a major part in the vibrations. Thus, it is hardly the modes like mode 27 mix with NHHN or NH2 wagging modes since the dipole−dipole interaction between them would be too small to take effects. In the aniline crystal simulation, the intensities of all demonstrated absorption spectroscopies should have included the dipole−dipole interaction and dispersion effects. To interpret the frequency shifts observed in Figure 3b, the dipole−dipole interactions are also calculated. The dipole− dipole interaction is calculated using the following textbook equation: D

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Figure 4. (a) Details of N−H antisymmetry stretching vibration mode, marked as 3548a in Table 3. (b) Details of N−H antisymmetry stretching vibration mode, marked as 3527b in Table 3. (c) Details of N−H symmetry stretching vibration mode marked as 3448c in Table 3. (d) Details of N− H symmetry stretching vibration mode marked as 3887d in Table 3, respectively.

V (r ) = − ∑ ij

2μi μj 4π ϵ0rij

3

interhydrogen interactions lead to an alternating chain structure. This structural property indicates the weak vdW forces between adjacent molecules significantly alter the lattice parameters and atomic positions, and are therefore responsible for the NHHN wagging collective modes. In this work, the aniline crystal simulation incorporate the dispersion corrections provided in the DFT-D2 method, while the “pseudo”-crystal simulation does not account for such dispersion effects. This single factor leads to significant differences on both structural and spectra properties between aniline crystal and the “pseudo”-crystal. The relaxed geometric structure of “pseudo”-crystal is quite different from that of the crystal. For instance, the distances between two adjacent type 1 hydrogen atoms in “pseudo”-crystal are 2.32 and 2.60 Å, which are larger than those in crystal. Furthermore, these geometric differences further result in the deviations in the IR spectra. By studying the details of Table 1, we find two major differences between the IR spectrum of the aniline crystal in Figure 3b and that of the “pseudo”-crystal in Figure 3c. In Figure 3c, the IR spectrum of aniline “pseudo”-crystal also has the collective wagging subband XNHHN and collective wagging subband XNH2. However, their intensities become much smaller than those in Figure 3b. Moreover, the splitting between these two subbands in the “pseudo”-crystal (54 cm−1) is much smaller than that in the crystal (81 cm−1). It is because the decrease of vdW interactions weakens the Davydov splitting

(cos θij − 3 cos θi cos θj) (1)

The above summation runs over involved dipoles of the particularly selected vibrational mode of all molecules in one cell, where ϵ0 is the permeability of space, μi and μj denote two vibrational dipoles, θij and rij are the angle and distance between them, respectively, and θi and θj are the angles formed by the two dipoles with respect to the line connecting their centers. In the equation, the distance between two dipoles is vital. Thus, we consider only the dipoles contributed from adjacent and secondary adjacent ones in our calculation. The results obtained for XNH2 and XNHHN wagging modes are 167 and 48 cm−1, respectively. The ratio between them is 3.48. While the ratio between the energy blue shifts of the two modes in the IR spectrum of Figure 3b is 1.65 (206 cm−1/125 cm−1). They are of the same magnitude. Therefore, the dipole−dipole coupling basically explains the trends of energy shifts between crystal and monomer. Among these differences in IR spectra between aniline crystal and the isolated monomer, the most evident one is the emergence of intermolecular collective modes. These collective modes aggregate into XNHHN subband in the crystal. In the relaxed aniline crystal, the distances between two adjacent type 1 hydrogen atoms are 2.24 and 2.48 Å. As we know, the vdW radius of two hydrogen atoms is 2.40 Å. Thus, the E

DOI: 10.1021/acs.jpcc.7b02862 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C in “pseudo”-crystal. These results suggest the XNHHN and XNH2 collective subbands are vital to analyze the intermolecular interactions. Moreover, we use the same geometry obtained from the DFT-D2 method to calculate the infrared spectrum without the DFT-D2 method. The spectrum changes slightly compared to the infrared spectrum with the DFT-D2 method. Since geometry determines the IR spectra, as known, proper treatments of van der Waals effects in simulating molecular crystals are crucial. Thus, we find that the vdW forces affect the equilibrium geometry of the crystal, which then affects how the vibrational modes couple to each other. Therefore, it is crucial to include the vdW effects in determining the geometry and spectroscopy of crystals. Compared to the monomer results, it is clearly shown that the IR spectra of crystal and “pseudo”-crystal is altered. In forming molecular crystal, the neighboring molecules are jointed by weak vdW interactions. These long-range intermolecular interactions determine the detailed long chain structure and also alter the symmetry of the crystal field. Thus, the intermolecular interactions which are enhanced by hydrogen atoms chains are the main reasons for the large Davydov splitting between XNH2 and XNHHN subbands, and other vibrational differences during crystallization such as large blueshifts in band 32 and 35, redshifts in band 1 and 2, and the changes of their intensities. To explore the principle and mechanism of the weak interactions in aniline crystal, we also carry out calculations for molecular aniline dimer and trimer for comparison. In the dimer case, we follow previous researches64−66 and study two typical aniline dimers: the NH−NH type and the NH−π type, see the molecular structures in the right panels of Figure 5, parts a and b. The former is featured by the intermolecular NH−NH interaction, while the latter is featured by the intermolecular interaction between hydrogen atom and the center of π bonds. The situation of trimer is much more complicated, and we only investigate the NH−NH−NH type, see Figure 5c for details. For accuracy, DFT-D2 dispersion correction is used for all the oligomers calculations. After relaxing all the crystal structures to their equilibrium conditions, we obtain the IR spectrum of the NH−π type dimer in Figure 5a, the NH−NH type dimer in Figure 5b, and the NH−NH− NH trimer in Figure 5c. In Figure 5d, we repeat the theoretical IR spectrum of the isolated aniline monomer as a reference. Moreover, to further investigate details of IR spectra in aniline oligomers, we present some representative mode frequencies of the oligomers in Table 3. In Figure 5, there are two attractive features among aniline oligomers. First, all the oligomers do not have XNHHN and XNH2 subbands. To answer that, we examine the distances between two adjacent hydrogen atoms in NH2 ends. As we know, the vdW radius of two hydrogen atoms is 2.40 Å. The interhydrogen distances in the NH−NH type dimer are bigger than it, while that in the trimer are smaller than it. However, in aniline crystal, the most intriguing phenomenon is that the interhydrogen distances form an alternating chain structure in crystal, Moreover, the special hydrogen atoms chain structure enhances the vdW interactions, which leads to the large blueshifts of mode 32 and a huge Davydov splitting between two subbands during crystallization. Thus, it is the cardinal factor for the emergence of XNHHN wagging subband.

Figure 5. Theoretical IR spectra and geometry structure of aniline aggregates. (a) Theoretical IR spectrum and geometry structure of aniline NH−π type dimer, the distance between Ha and center of the π bonds is 2.26 Å. The inset presents the NH−π intermolecular vibrational mode. (b) Theoretical IR spectrum and geometry structure of aniline NH−NH type dimer, the distance between Ha···Hb is 2.56 Å and between Ha···Hc is 2.60 Å. (c) Theoretical IR spectrum and geometry structure of NH−NH−NH aniline type trimer, the distance between Ha···Hb is 2.27 Å, between Hb···Hc is 2.27 Å, and between Ha···Hc is 2.26 Å. (d) Theoretical IR spectrum and geometry structure of aniline monomer.

Table 3. Comparison of the Vibrational Frequencies of Some Representative Modes in Aniline Monomer, Dimers and Trimera index

monomer

dimer NH−π (NH−NH)

trimer

1 2 31 32 35

3615 3509 505 461 325

−20 (−42) −19 (−89) 45 (−10) 25 (191) 11 (25)

−82 −224 −4 234 55

a

The results of the NH−NH type dimer are presented in the parentheses after those of the NH−π type dimer.

Second, the blueshift of mode 32 in NH−π type dimer (25 cm−1) is much smaller than those in NH−NH type dimer (191 cm−1), the trimer (234 cm−1) and the crystal (125 and 206 cm−1). This phenomenon is explained by the fact that band 32 is significantly influenced by intermolecular interactions among adjacent hydrogen atoms in oligomers and crystal. In NH−π type dimer, the distances (>3 Å) between two hydrogen atoms in NH2 ends are much larger than other three situations (