ARTICLE pubs.acs.org/JPCC
Quantum Chemical Evaluation of Ionic Nonlinear Optical Chromophores and Crystals Considering the Counteranion Effects Jongtaek Kim,† O-Pil Kwon,*,‡ Mojca Jazbinsek,§ Young Choon Park,† Jung-In Seo,† and Yoon Sup Lee*,† †
Department of Chemistry, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 305-701, Republic of Korea Department of Molecular Science and Technology, Ajou University, Suwon 443-749, Republic of Korea § Rainbow Photonics AG, CH-8048 Zurich, Switzerland ‡
bS Supporting Information ABSTRACT: The direction and the magnitude of the first hyperpolarizability are investigated by the finite field (FF) method for organic nonlinear optical ionic chromophores and crystals with an isotropic counteranion, either a point charge or hexafluorophosphate. Simple model compound 4-aminopyridinium and DAPSH (N,N-dimethylamino-N0 -phenyl-4-stilbazolium hexafluorophosphate) crystal with the highest quadratic optical nonlinearities measured to date in organic crystals, as well as stilbazolium derivatives having heteroaromatic and/or bulky aromatic rings, are investigated. Calculations indicate that the extrinsic isotropic point-charges or anions almost have no effect on the direction of the intrinsic first hyperpolarizability of the cation chromophores, and induce a limited increase of the magnitude smaller than ∼15% due to their asymmetric distribution with respect to the pyridinium nitrogen atom. This finding enables one to simply approximate the first hyperpolarizability of ionic crystalline systems having 1D intramolecular charge transfer character by considering only the cation. In addition, the heteroaromatic or bulky aromatic substituents at the end of the pyridinium acceptor intrinsically do not affect the direction and only moderately affect the magnitude of the first hyperpolarizability of stilbazolium salts. These results are potentially useful for molecular design and crystal engineering of ionic organic materials, where the magnitude and the direction of first hyperpolarizability as well as the shape of the ionic chromophore are of great importance.
1. INTRODUCTION Quantum chemical calculations can provide valuable information for screening of promising organic nonlinear optical materials from the step of molecular design to evaluate their microscopic and macroscopic nonlinearities, as well as electronic and other physical properties.1 Theoretical studies on second-order nonlinear optical materials have been dealing mainly with gas phase,2 solution,3 and polymeric systems,4 but with crystalline systems only to a limited extent.5 In addition, they have been mainly devoted to the magnitude of first hyperpolarizabilty represented as β but not its direction. In gas phase and in solution and polymeric systems without electric field as in the conditions in hyper-Rayleigh scattering (HRS) measurements,6 the consisting molecules have random orientation. Therefore, the absolute direction of β does not matter in such system: only its magnitude is important. With an electric field applied as for the electric-field induced second-harmonic generation (EFISH) measurement in solution7 and the well-known poled polymeric systems,4c the consisting molecules are aligned with uniaxial, i.e., one-dimensional (1D) ordering. In such cases the direction of the polar axis is along the direction of the applied electric field, and therefore, mostly the component of β along the static dipole moment μ of the molecule gives an effective contribution. Crystalline systems have a 3-dimensional (3D) ordering of the r 2011 American Chemical Society
consisting molecules, which results in more complex contributions to the diagonal and off-diagonal macroscopic susceptibilities than in poled polymer systems.8 For correct evaluation of crystalline systems, not only the magnitude of β, but also its direction in the crystalline lattice, is very important.9 Among various quantum chemical calculation methods, such as finite field (FF) approaches,10 response theory,11,12 sum-overstates (SOS) methods,13 and two-state model,14 the FF method is useful to obtain simultaneous information on the magnitude and the direction of β, since it gives the details of the full 3D (zero-frequency) tensor of β. Recently, we have performed quantum chemical FF calculations considering both the direction and the magnitude of β for nonionic nonlinear optical crystals.1518 This allowed us to evaluate the effective macroscopic nonlinearities of crystals with all diagonal and off-diagonal tensor components by considering the orientation of the consisting molecules.15,16 In addition, we have shown that the β values are significantly changed by the change of molecular conformation17 and variation of intermolecular interactions.18 Using FF calculations for nonionic nonlinear optical crystals significantly simplifies the evaluation of most promising crystals Received: May 6, 2011 Revised: October 20, 2011 Published: November 07, 2011 23535
dx.doi.org/10.1021/jp204218t | J. Phys. Chem. C 2011, 115, 23535–23542
The Journal of Physical Chemistry C for applications, which otherwise require very time-consuming investigations ranging from the high-quality crystal growth and sample preparation using crystal cutting and polishing, to many optical and nonlinear optical characterization experiments. Moreover, the information from quantum chemical calculations is important for the selection of a starting point for various crystal engineering techniques as well as molecular design. Organic stilbazolium-salt crystals exhibit extremely large macroscopic optical nonlinearities. For example, crystals of DAST (N,Ndimethylamino-N0 -methyl-stilbazolium p-toluenesulfonate)19,20 and its derivatives2124 including DSTMS (N,N-dimethylamino-N0 -methyl-stilbazolium 2,4,6-trimethylbenzenesulfonate),22 and DAPSH (N,N-dimethylamino-N0 -phenyl-4-stilbazolium hexafluorophosphate),23,24 exhibit the largest diagonal quadratic susceptibility of up to χ(2)(2ω, ω, ω) = 580 pm/V at 1.9 μm.24a Although stilbazolium crystals possess great optical nonlinearities1924 and many practical applications have been successfully demonstrated for integrated photonic devices25 and THz generation and detection,26 quantum chemical calculations have been rarely reported especially for ionic organic crystals considering the influence of counteranions on the nonlinearity in the crystalline state5a,cf and relating the microscopic nonlinearity to the macroscopic nonlinearity.9b,27 In ionic organic crystals consisting of cation and anion species, a cation chromophore such as stilbazolium is exposed to the average electric field exerted by anions and other cations. The surrounding counteranions with shortest distance to a cation may strongly affect the β characteristics of the cation chromophore. There have been a few theoretical studies on the hyperpolarizability of organic cations in solution3a and film.5b,c However, for an ionic crystalline system, to the best of our knowledge, there are no systematic quantum chemical calculations of anionic environmental effect on optical nonlinearities considering both the direction and the magnitude of β. We think that the interaction behaviors between a cation and anions for ionic organic crystals are substantially different from those in solutions or films to warrant the new investigation. In solution, it seems that a counteranion (e.g., I) exists around the positive part of a cation such as a pyridinium moiety. The first hyperpolarizability of the cation increases as the anion is getting away from the cation. The enhanced positive charge on the acceptor pyridinium lowers the intramolecular charge transfer energy, finally leading to the maximum value of the free cation.3a In film, an anion existing between cation layers, situating on top of the cation, exerts a significant influence on the π-electron cloud of the cation leading to considerable β variation of the cation.5b,c In crystalline state, the structures of ion pairing are different from solution and film in that a cation has multiple surrounding anions in or out of plane of the cation. For organic crystals such as the DAPSH crystal, the positions, distances, and distribution ratio of the PF6 anions in the vicinity of the cation can affect the hyperpolarizability of the cation differently depending upon whether they are around the donor or the acceptor site. In this work, we examine systematically the effect of counteranions on optical nonlinearities of a cation in order to expand the quantum chemical FF calculation to ionic organic crystalline systems. A simple model compound 4-aminopyridinium, which is the simplest possible π-conjugated molecule as an analogue of the benchmark stilbazolium salts, as well as the more complex DAPSH crystal with the highest optical nonlinearity measured for organic crystals have been chosen. The electrostatic perturbation effect of the environmental point-charges or anions on the β of a cation was investigated by considering their relative positions, distances, and distribution ratio around the donor
ARTICLE
and the acceptor sites. In order to remove the size and shape effect of counteranions,3a which may be dealt with in the future theoretical work, we used small isotropic counteranions, either negative point charges or hexafluorophosphates. In addition, a series of newly designed stilbazolium derivatives having heteroaromatic rings are also investigated theoretically. The heteroaromatic rings can affect the magnitude of hyperpolarizability, but cannot change the direction originating from the strong electron accepting cationic pyridinium group.
2. COMPUTATIONAL DETAILS All calculations were performed using Gaussian 0328 with the B3LYP hybrid functional29 and different basis sets, the 6-31+G(d) and/or 6-311+G(d) for the model compound 4-aminopyridinium, DAST, DAPSH, and the stilbazolium derivatives having heteroaromatic rings. The molecular geometries were fully optimized (so-called OPT geometries) except for DAPSH with hexafluorophosphate anions, for which the geometries from the crystal structure determined by the X-ray measurements were considered (EXP geometries).23b,15 Vibrational frequencies were calculated for all molecules for the optimized molecular structures (OPT) to verify that no negative frequencies exist for the obtained minimum on the potential energy surface. The finite-field (FF) method was used to get the information for both the direction and the magnitude of the first hyperpolarizability (β) which is important in crystalline systems with 3D ordering of chromophores, rather than the TD-DFT method which yields only the magnitude. The β of the DAPSH ionic crystal used in this work is expected to be involved in the electrostatic perturbation rather than the intermolecular charge transfer from the counteranion PF6 to the cation (vide infra section 3.2.2). The weak intermolecular charge transfer, in contrast to the cases of π-stacked neutral chromophores, is not directly reflected into the two-state model evaluating first hyperpolarizability. Therefore, the FF method was selected for the β calculation. The point charge in the FF calculation was described as an external charge with respect to a cation, meaning that the charge transfer from the point charge into the cation does not occur and hence the total charge of the cation is maintained during calculation. The FF method using an electric field step 0.001 a.u. calculates the hyperpolarizability tensor components (βijk) in the molecular system xyz. For these calculations, the origin of the Cartesian coordinate was located on the center of mass of each target molecule. The Cartesian axes were arbitrarily set because the dipole moment μ direction cannot be properly defined in charged molecular systems unlike nonionic systems where the dipole moment μ direction is usually set along the z direction.15 The calculated βijk tensors were appropriately transformed to obtain the maximal first hyperpolarizability hereafter denoted as βmax (i.e., the hyperpolarizability component along the main charge-transfer direction).15 The obtained βmax has directional information (Φ, θ) based on the arbitrarily set coordinates xyz of the molecular system. In order to compare the βmax direction among different molecular systems, we define the directional angle θN2fN1, which is the angle between the βmax direction and the direction along the two nitrogen atoms in the investigated chromophores: N2 stands for the nitrogen atom in the amine or amino donor and N1 for the one in the pyridinium acceptor. 23536
dx.doi.org/10.1021/jp204218t |J. Phys. Chem. C 2011, 115, 23535–23542
The Journal of Physical Chemistry C
ARTICLE
Figure 1. Molecular system of the model compound p-amino-pyridinium for βmax calculations. Point-charge effect is considered in terms of the direction and distance of the negative point charge around the cation chromophore. Gray area represents the electrostatic potential (ESP) of the cation. Dipole moment is calculated at the center of mass (COM) of the cation, and the z-axis is oriented along the dipole moment direction (μg = μz).
Figure 3. Molecular system of the real DAPSH ion pairs considering the first neighboring PF6 anions (110). Anionic effect on βmax is considered in terms of positions (e.g., direction and distance) of the PF6 anions around the cation chromophore (0).
Figure 2. βmax depending on the direction and distance of the negative point charge around the model cation chromophore. The point-charge distances denoted as e-Hx are positioned within 9.0 Å from the hydrogen atoms at the end of each C/NH bond or from the midpoints between two neighboring hydrogen atoms as seen in Figure 1.
3. RESULTS AND DISCUSSION 3.1. Negative Point-Charge Effect in Model Compound. A simple model compound of p-aminopyridinium cation with C2v symmetry is employed here (see Figure 1), which reduces the computational cost for the β calculation of different cation-point charge pairs by symmetry considerations. The structure of optimized p-aminopyridinium cation is retained for the β calculation including a point negative charge, since the central cation in real crystals has a fixed structure due to the average crystal field exerted by surrounding counteranions and other neighboring cations. For this model compound, we have chosen the Cartesian axis so that the z axis is along the N2 f N1 direction and the y axis is in the plane of the pyridinium ring. On the half side of the yz molecular plane bisected by the principal z-axis, the negative point charges denoted as e-Hx are positioned within 9.0 Å from
the hydrogen atoms at the end of each C/NH bond or from the midpoints between two neighboring hydrogen atoms (see Figure 1). Considering the positions and distances of these point-charges around the donor and acceptor groups, we have calculated the βmax for cation-point charge pairs and compared it with that of the p-aminopyridinium cation itself. The external field resulting from a negative point charge outside the molecular system exerts only the electrostatic perturbation effect on the cation chromophore without inducing the charge transfer. The βmax of the model compound is categorized into three parts according to the negative point-charge effect: high, low, and similar with respect to that of the p-aminopyridinium cation itself (see Figure 2). The point charge around the electron-withdrawing pyridinium group denoted as e-Ha, e-Hab, and e-Hb reduces the βmax of the cation, whereas the point charge around the electron-donating amine group denoted as e-Hc, e-Hd, e-Hde, and e-He increases the βmax of the cation. Such a trend can be understood from the reduced electron accepting ability of the pyridinum cation due to the electron repulsion effect of the vincinal negative point charge, whereas the increased electron donating ability of the amine group can be understood from the electron push effect by the neighboring point charge.5a On the other hand, the point charge denoted as e-Hbc, which is approximately in the middle between the electron donor and acceptor groups and hence perpendicular to the electron transfer direction, does practically not affect the βmax of the cation (see Supporting Informaion). This implies that the distribution of point charges may affect the βmax of the cation chromophore through electrostatic perturbation effect. As the point charge recedes from the neighboring hydrogen atoms, the βmax shows an asymptotic behavior and thus leads to that of the cation chromophore itself.3a,5a Interestingly, when the point charge is located much closer to the amino donor group, within 2 Å from hydrogen atoms, a catastrophe in the βmax is encountered. This extremely lowered βmax might be due to the 23537
dx.doi.org/10.1021/jp204218t |J. Phys. Chem. C 2011, 115, 23535–23542
The Journal of Physical Chemistry C
ARTICLE
Table 1. Point-Charge Position Effect on the βmax (1030 esu) of the DAPSH Cation Calculated at the B3LYP/6-31+G* Level with Point Charge Centered on Each Phosphorus Atom cation/e
0/1
0/2
0/3
0/4
0/5
0/6
0/7
0/8
0/9
0/10
Æ0/jæa
0
0/jallb
μtotal
6.2
5.4
5.1
2.8
4.4
5.9
4.7
3.0
3.2
4.3
4.5
0.6
1.8
βxxx βxxy
1.4 1.5
0.5 2.0
1.4 2.7
2.7 3.4
1.6 3.1
2.2 3.0
2.3 2.0
1.3 2.3
2.4 2.5
2.8 2.6
1.9 2.5
1.9 2.5
2.1 2.7
βxyy
1.9
2.3
3.2
4.4
3.3
3.6
3.0
3.6
4.0
3.8
3.3
3.4
3.7
βyyy
0.7
2.4
4.4
5.8
5.7
5.5
2.0
3.7
4.0
4.3
3.9
3.9
5.2
βxxz
5.5
5.9
7.0
8.8
8.6
8.4
6.6
8.0
8.8
8.7
7.6
7.8
8.5
βxyz
8.6
9.8
11.8
14.1
12.6
12.3
10.6
13.0
13.1
12.2
11.8
12.1
13.4
βyyz
10.8
13.1
16.6
20.4
19.5
19.0
14.1
19.1
19.7
18.4
17.1
17.4
20.6
βxzz
27.3
29.5
34.6
40.9
35.8
34.9
32.2
37.2
37.6
36.2
34.6
35.4
40.1
βyzz βzzz
44.4 127.7
50.3 141.2
59.4 163.4
69.1 186.9
62.6 165.0
60.7 160.2
52.2 147.0
63.8 173.9
63.8 171.8
60.7 164.6
58.7 160.2
60.0 163.8
68.7 183.9
βmax
159.0
176.9
206.7
238.8
212.6
206.4
185.2
221.1
220.1
210.4
203.7
208.3
235.3
Φc
237
239
239
239
239
239
237
239
239
238
239
238
239
Θc
21
21
22
22
23
23
22
22
23
23
22
22
22
θN2fN1d
0.6
0.9
0.6
0.6
1.6
1.6
0.7
0.6
1.6
1.5
1.0
0.6
0.6
βoff‑diagonal
3.8
3.7
3.6
3.5
3.2
2.9
3.5
3.6
3.3
3.1
3.4
3.5
4.4
Mean values from 0/1 to 0/10 pairs. b Values considering all surrounding point charges. c βmax directions in the Cartesian xyz coordinates. d βmax directional angle against the N2 f N1 direction shown in Figure 3. a
Table 2. Anion Position Effect on the βmax (1030 esu) of the DAPSH Cation Calculated at the B3LYP/6-31+G* Level cation/PF6
0/1
0/2
0/3
0/4
0/5
0/6
0/7
0/8
0/9
0/10
Æ0/jæa
0
0/jallb
μtotal
49.0
40.3
26.9
21.6
35.6
50.1
35.6
22.3
31.2
43.9
35.6
0.6
5.0
βxxx
1.4
0.2
1.4
3.1
0.8
2.2
2.7
1.1
2.6
3.8
1.9
1.9
1.3
βxxy
1.4
2.3
2.8
3.6
3.1
3.2
1.6
2.3
2.3
2.8
2.5
2.5
2.9
βxyy
1.9
2.0
2.7
4.6
3.1
3.9
3.3
3.6
3.9
4.0
3.3
3.4
4.4
βyyy
0.1
2.5
4.5
6.3
6.6
6.6
1.8
3.3
2.7
3.9
3.8
3.9
3.2
βxxz
5.2
5.9
7.2
8.6
7.9
8.6
6.2
8.4
8.9
10.0
7.7
7.8
7.7
βxyz βyyz
8.5 9.9
10.0 12.7
11.7 14.3
13.9 20.0
12.2 20.7
12.9 21.2
10.6 14.7
13.5 20.1
12.8 18.4
12.8 18.0
11.9 17.0
12.1 17.4
14.2 20.5
βxzz
27.1
30.1
35.6
40.5
33.6
35.8
31.6
37.2
37.6
39.1
34.8
35.4
41.6
βyzz
43.3
50.1
58.3
68.1
64.5
65.1
53.2
64.0
61.9
60.4
58.9
60.0
72.6
βzzz
125.9
141.8
166.5
182.4
166.0
169.3
148.0
168.8
171.3
167.8
160.8
163.8
190.6
βmax
156.4
177.6
208.1
234.0
214.1
218.7
186.6
217.8
217.5
214.5
204.5
208.3
244.9
Φc
237
238
237
238
242
240
238
239
238
236
238
238
239
Θc
21
21
21
23
23
23
22
23
22
23
22
22
23
θN2fN1d βoff‑diagonal
0.6 4.0
0.5 3.7
0.6 3.9
1.5 3.5
2.1 3.3
1.7 2.7
2.0 3.5
2.2 3.9
2.0 3.3
3.1 2.9
1.6 3.5
0.6 3.5
2.2 5.8
Mean values from 0/1 to 0/10 pairs. b Values considering all surrounding PF6 anions. c βmax directions in the Cartesian xyz coordinates. d βmax directional angle against the N2 f N1 direction shown in Figure 3. a
electron repelling effect exerted by the point charge too close to the donor group.5a However, this kind of catastrophe is not likely to be observed in most real crystals where the closest distances of counteranions to nearest neighboring atoms are larger than 2 Å. The βmax direction of the cation and point-charge pairs in the model compound are practically identical to that of the cation within θN2fN1 = 2 for any location of the point charge. The βmax direction of the cation is therefore along the z axis, which corresponds to the charge transfer (CT) direction from the N2 atom in the amine donor to the N1 atom in the pyridinium acceptor (i.e., N2 f N1). We have found from this point-charge perturbation effect that the point charge may only affect the
magnitude of βmax but not its direction. For this model compound, the perturbation due to counterions was considered only in 2D (i.e., in-plane arrangement) and not above or below the main plane of the model molecule. For real crystals, 3D effects (i.e., in-plane and out-of-plane arrangements) should be considered and will be discussed in the following section. The main conclusion here is that the effect of the in-plane point charges on βmax is essentially 1-dimensional along the main charge transfer direction, but not perpendicular to it. 3.2. Anion Effect in DAPSH Crystal. To investigate the anionic environmental effect on the βmax in real crystalline systems, we extend the point-charge concept of FF calculation 23538
dx.doi.org/10.1021/jp204218t |J. Phys. Chem. C 2011, 115, 23535–23542
The Journal of Physical Chemistry C to the DAPSH crystal,23b which is the organic crystalline material with the highest nonlinear optical properties measured to date.24a The DAPSH crystal is composed of N,N-dimethylamino-N0 phenyl-4-stilbazolium chromophore and hexafluorophosphate (PF6) counteranion species. The counteranions PF6 in the first neighboring positions of the cation, which is expected to properly represent the electronic environment of the cation in DAPSH, were included as a negative point charge or a whole molecule for the FF calculation of the stilbazolium-type cation. Not only the electrostatic perturbation effect but also the intermolecular charge transfer effect of PF6 anions on the βmax of the cation is investigated by considering their positions, distances, and distribution around the cation. For consistency, the same Cartesian coordinate system as in the cation was used for all calculations with DAPSH. 3.2.1. Point-Charge Effect. The negative point charges of the surrounding PF6 anions are described as sitting at the position of each phosphorus atom in the experimental DAPSH crystalline structure (see Figure 3).23b The βmax of the N,N-dimethylaminoN0 -phenyl-4-stilbazolium cation is 208.3 1030 esu with directional angle of θN2fN1 = 0.6, i.e., practically along the N2 f N1 direction. As listed in Table 1, the βmax magnitudes of the cationpoint-charge pairs change in the range 159.0238.8 1030 esu corresponding to 76115% of that of the cation which is on the same order of magnitude as the experimental values measured in solution.23 Compared to the case of the model compound, the direct comparison among the βmax values listed in Table 1, depending on the relative positions around the
Figure 4. Anion distance effect on the βmax of the DAPSH cation (0), depending on the distance between the pyridyl nitrogen atom (N1) and the phosphorus atom (P1) of the anion 1 as shown in Figure 3. Values with the bold symbols for the experimental results.
ARTICLE
donor and the acceptor sites, may be complicated because of the different 3D arrangements of the point charges relative to the cation molecular plane (i.e., in-plane or out-of-plane) as well as their different distances to the vicinal hydrogen. For example, around the donor group, the point-charge position 4 gives the highest value of 238.8 1030 esu due to the in-plane character. The point-charge position 5 shows lower value of 212.6 1030 esu due to the out-of-plane character although the position 5 is closer to the donor group. The point charge position 1 at the tail of acceptor group gives the lowest value of 159.0 1030 esu due to the in-plane and close distance character. Therefore, it can be thought that the individual point charge can increase or decrease the βmax of the cation, depending on the relative arrangements around the donor and the acceptor sites. The averaged βmax values of all the cationpoint-charge pairs denoted as Æβmaxæ is 203.7 1030 esu which is similar to the value of the cation 208.3 1030 esu. To account for the averaged negative point-charge effect in a more realistic way, we have also investigated the model in which all 10 point charges of the first-neighboring anions are present around the cation. The obtained βmax is 235.3 1030 esu, about 15% larger than that of the bare cation. We note that this increase is impossible in solution.3a This result can be understood from the asymmetric distribution in which more anions are around the donor site than the acceptor site.5ac The asymmetric distribution of the anions is expected to increase the βmax by inducing electron push effect as suggested in the model compound. The βmax direction does not change appreciably for any of the cases (e.g., systems of one cation, one cation and one point-charge pairs, and one cation and 10 point charges), and stays within θN2fN1 < 1.6 regardless of the surrounding anion point charges. The electronic perturbation effect is found to be small in the offdiagonal components of the βijk tensor, whose values are within 2.4% of the βmax. Therefore, we suggest that the cation chromophore itself can be used as a target system for FF calculation of ionic nonlinear optical crystals with essentially 1D intramolecular charge transfer character. 3.2.2. Isotropic Counteranion Effect. The FF calculation including counteranions is performed to investigate intermolecular charge transfer effect of the surrounding PF6 anions on the βmax of the stilbazolium-type cation. As listed in Table 2, the individual values are very similar to those of the point-charge FF calculation (see Table 1). The similar results that are rather unexpected can be understood from the fact that the isotropic anions PF6 having zero dipole moment and small polarizability weakly interact with the cation in the distances 2.472.96 Å
Figure 5. Investigated stilbazolium derivatives with heteroaromatic or bulky aromatic rings. 23539
dx.doi.org/10.1021/jp204218t |J. Phys. Chem. C 2011, 115, 23535–23542
The Journal of Physical Chemistry C
ARTICLE
without π-electron overlap except for the 0/7 pair. The βmax of the cation in the DAPSH crystal seems to be affected mainly by the electrostatic perturbation from the anions which act as the external electric charges, rather than by the intermolecular charge transfer. To evaluate the electrostatic perturbation effect on the βmax depending on the distances between the PF6 anion and the cation, we have performed FF calculation by elongating the distance of the PF6 at the 0/1 ion pair with respect to the N1 atom in the pyridinium acceptor (see Figure 3), and the results are shown in Figure 4. The distance of PF6 at the original position 1 is around 8 Å. As shown in Figure 4, below 8 Å, the counteranion reduces the βmax because of increased electron repulsion effect caused by closer distance to the pyridinium Table 3. Heteroaromatic or Bulky Aromatic Effect on the βmax (1030 esu) of the Stilbazolium Derivative Cations Calculated at the B3LYP/6-311+G* Level DAST
JH1
HS1
HS2
HS3
HS4
HS5
βmax
158.8
193.2
174.4
176.3
150.1
162.7
160.6
θN2fN1
0.4
1.3
1.5
0.6
0.7
1.5
1.0
βoff‑diagonal
4.8
4.9
3.0
4.9
5.5
4.9
4.2
HS6
HS7
HS8
pMPS
mMPS
oMPS
oPPS
βmax θN2fN1
172.6 1.0
114.3 0.3
161.5 0.6
183.2 0.3
194.2 0.4
192.0 1.3
196.1 1.3
βoff‑diagonal
3.5
4.0
2.4
5.0
4.8
4.8
4.4
acceptor. As the anion distances increase beyond 8 Å, the βmax of the cationanion pair leads to that of the cation,3a,5a whereas the dipole moment considerably increases in proportion to the distance. This asymptotic behavior is quite different from that of a small ionic molecule like LiF for which βmax would strongly depend on the interatomic distances. The large π-conjugated anisotropic cation has the respectable hyperpolarizability 208.3 1030 esu as itself and the small non-πconjugated isotropic anion imposes only a secondary electrostatic perturbation on its inherent nonlinearity. The βmax direction is maintained within θN2fN1 = 3.7 irrespective of the distance, which is in agreement with the N2 f N1 direction. Therefore, the extremely large cation species in the DAPSH crystal compared with the small counteranion mainly determines both the magnitude and the direction of βmax. Especially, this finding is valid when considering all counteranions arranged roughly symmetrical to the center of mass of a cation (see Figure 3). By including an anionic environmental effect in the FF calculation for both the model and the real ionic chromophore systems, we have found that the first hyperpolarizability of ionic nonlinear optical materials can be reasonably approximated by that of a cation, which can be utilized in the design of ionic-type nonlinear optical materials. This hypothesis may be valid for ionic organic crystals with isotropic or monoatomic anions which are expected to have weak interactions in plane with the large anisotropic cations. In the current model, anions are located at the distances 2.472.96 Å. Further studies are needed in the future for other crystals having anionic environments different from the DAPSH crystal.
Figure 6. Heteroaromatic or bulky aromatic effect on the βmax (red dotted arrow) of the stilbazolium derivatives calculated at the B3LYP/6-311+G* level. The origin of βmax is at the center of mass (COM) of each cation. The z-axis is arbitrarily set and not in agreement with the dipole moment (μ) direction. 23540
dx.doi.org/10.1021/jp204218t |J. Phys. Chem. C 2011, 115, 23535–23542
The Journal of Physical Chemistry C 3.3. New Stilbazolium Derivatives with Heteroaromatic Ring. We extend the approximate FF calculation above to a series
of new stilbazolium derivatives having N-substituted electronrich heteroaromatic ring at the tail of the prydinium acceptor. The molecular structure and initial geometry for calculation are based on the DAPSH cation because of its high hyperpolarizability owing to the electron delocalizing phenyl group instead of a methyl group of the widely used DAST crystals.23b The chemical structures of investigated stilbazolium derivatives with heteroaromatic ring are shown in Figure 5. The heteroaromatic thiophene, furan, and imidazole with different substituted positions are introduced (HS1HS8). Since the torsional angle between pyridinium ring and N-substituted aromatic ring may affect the characteristics of the hyperpolarizability, relatively bulky aromatic group with methyl-substituted groups are incorporated into the following cations: pMPS, mMPS, oMPS, and oPPS. As listed in Table 3, the calculations indicate that the magnitudes of βmax are similar to that of DAPSH, except for the HS7 having a much lower value of 114.3 1030 esu. The βmax directions are the same within θN2fN1 = 1.5 regardless of torsional angles of heteroaromatic rings as well as heteroatom positions as shown in Figure 6. This phenomenon can be understood from the strong electron-accepting effect of the positive nitrogen atom (N1) at the pyridinium group maintaining the hyperpolarizability direction from N2 to N1. In contrast, the hyperpolarizability direction can considerably vary in nonionic chromophores with heteroaromatic rings as large as θ = 32,17a since the electron-acceptor center can change depending on the torsional angles and heteroatom positions. Overall, the heteroaromatic rings in ionic organic materials such as stilbazolium derivatives can affect the hyperpolarizability magnitude, but not its direction. On the other hand, the heteroaromatic ring and/or bulky aromatic rings can provide new intermolecular interactions in the crystalline state and the site isolation effect.27 Without altering the large magnitude and the direction of first hyperpolarizability, heteroatoms may be introduced to the ring to open additional possibilities for crystal engineering by modifying crystal packing based on newly created intermolecular interactions.
4. CONCLUSIONS We have introduced the point charge or the counteranion concept to the FF (finite field) calculations of salt-type organic materials to investigate the anionic environmental effect on the magnitude and the direction of maximal first hyperpolarizability βmax. Our calculations lead to the following conclusions for ionic organic crystals with isotropic or monoatomic anions which are expected to have in-plane positions with respect to a cation chromophore: (i) The relative positions of isotropic anions to the electron donating and withdrawing group can change the magnitude of the βmax of a cation chromophore by a small amount, but not the direction. (ii) Treating only the cation can lead to a reasonable estimate for the relative magnitude and the direction of the βmax of ionic organic materials. (iii) The heteroaromatic and bulky substituents at the end of the prydinium acceptor do not change the direction of βmax. Therefore, by using heteroaromatic and bulky aromatic groups at the tail of the cationic acceptor group one may change the crystal packing and other crystal characteristics, without considerably changing the direction and the magnitude of the molecular hyperpolarizability.
ARTICLE
These findings are expected to contribute to molecular design of ionic organic materials for nonlinear optical applications, where both the magnitude and the direction of first hyperpolarizability are of great importance.
’ ASSOCIATED CONTENT
bS
Supporting Information. Cartesian coordinates (x, y, z) for finite field (FF) calculations were provided for the representative cases concerning the model compound and the DAPSH system. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected] (Y.S.L.);
[email protected] (O-P.K.).
’ ACKNOWLEDGMENT This work was supported by grants (2009-0084918, 20110001213, 2010-0027743, 2010-0028294) of the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology. Computational resources were in part provided by KISTI (KSC-2011-C2-18). ’ REFERENCES (1) Papadopoulos, M. G.; Sadlej, A. J.; Leszczynski, J. Nonlinear Optical Properties of Matter: From Molecules to Condensed Phases; Springer: Dordrecht, The Netherlands, 2006. (2) (a) Hrobarik, P.; Sigmundova, I.; Zahradnik, P.; Kasak, P.; Arion, V.; Franz, E.; Clays, K. J. Phys. Chem. C 2010, 114, 22289–22302. (b) Bogdan, E.; Rougier, L.; Ducasse, L.; Champagne, B.; Castet, F. J. Phys. Chem. A 2010, 114, 8474–8479. (c) Datta, A. J. Phys. Chem. C 2009, 113, 3339–3344. (d) Coe, B. J. Acc. Chem. Res. 2006, 39, 383–393. (e) Coe, B. J.; Beljonne, D.; Vogel, H.; Garin, J.; Orduna, J. J. Phys. Chem. A 2005, 109, 10052–10057. (f) Ray, P. C. Chem. Phys. Lett. 2004, 394, 354–360. (g) Duan, X. M.; Konami, H.; Okada, S.; Oikawa, H.; Matsuda, H.; Nakanishi, H. J. Phys. Chem. 1996, 100, 17780–17785. (h) Plaquet, A.; Guillaume, M.; Champagne, B.; Rougier, L.; Mancois, F.; Rodriguez, V.; Pozzo, J. L.; Ducasse, L.; Castet, F. J. Phys. Chem. C 2008, 112, 5638–5645. (i) Geskin, V. M.; Lambert, C.; Bredas, J. L. J. Am. Chem. Soc. 2003, 125, 15651–15658. (j) Abe, J.; Shirai, Y.; Nemoto, N.; Nagase, Y. J. Phys. Chem. B 1997, 101, 1910–1915. (k) Abe, J.; Shirai, Y. J. Am. Chem. Soc. 1996, 118, 4705–4706. (3) (a) Tessore, F.; Cariati, E.; Cariati, F.; Roberto, D.; Ugo, R.; Mussini, P.; Zuccaccia, C.; Macchioni, A. ChemPhysChem 2010, 11, 495–507. (b) Inerbaev, T. M.; Gu, F. L.; Mizuseki, H.; Kawazoe, Y. Int. J. Quantum Chem. 2011, 111, 780–787. (c) Ray, P. C.; Leszczynski, J. Chem. Phys. Lett. 2004, 399, 162–166. (d) Bogdan, E.; Plaquet, A.; Antonov, L.; Rodriguez, V.; Ducasse, L.; Champagne, B.; Castet, F. J. Phys. Chem. C 2010, 114, 12760–12768. (e) Ray, P. C. Chem. Phys. Lett. 2004, 395, 269–273. (f) Abbotto, A.; Beverina, L.; Bradamante, S.; Facchetti, A.; Klein, C.; Pagani, G. A.; Redi-Abshiro, M.; Wortmann, R. Chem.—Eur. J. 2003, 9, 1991–2007. (g) Abe, J.; Shirai, Y.; Nemoto, N.; Miyata, F.; Nagase, Y. J. Phys. Chem. B 1997, 101, 576–582. (4) (a) Dalton, L. R.; Sullivan, P. A.; Bale, D. H. Chem. Rev. 2010, 110, 25–55. (b) Sullivan, P. A.; Rommel, H.; Liao, Y.; Olbricht, B. C.; Akelaitis, A. J. P.; Firestone, K. A.; Kang, J. W.; Luo, J. D.; Davies, J. A.; Choi, D. H.; et al. J. Am. Chem. Soc. 2007, 129, 7523–7530. (c) Liakatas, I.; Cai, C.; Bosch, M.; Jager, M.; Bosshard, C.; Gunter, P.; Zhang, C.; Dalton, L. R. Appl. Phys. Lett. 2000, 76, 1368–1370. (5) (a) Duan, X. M.; Konami, H.; Okada, S.; Oikawa, H.; Matsuda, H.; Nakanishi, H. THEOCHEM 2000, 531, 65–77. (b) Mestechkin, 23541
dx.doi.org/10.1021/jp204218t |J. Phys. Chem. C 2011, 115, 23535–23542
The Journal of Physical Chemistry C M. M. Opt. Commun. 2001, 198, 199–206. (c) Dibella, S.; Fragala, I.; Ratner, M. A.; Marks, T. J. Chem. Mater. 1995, 7, 400–404. (d) Nunzi, F.; Fantacci, S.; Cariati, E.; Tordin, E.; Casati, N.; Macchi, P. J. Mater. Chem. 2010, 20, 7652–7660. (e) Vijayakumar, T.; Joe, I. H.; Nair, C. P. R.; Jayakumar, V. S. THEOCHEM 2008, 877, 20–35. (f) Nunzi, F.; Fantacci, S.; De Angelis, F.; Sgamellotti, A.; Cariati, E.; Ugo, R.; Macchi, P. J. Phys. Chem. C 2008, 112, 1213–1226. (g) Terenziani, F.; D’Avino, G.; Painelli, A. ChemPhysChem 2007, 8, 2433–2444. (h) Hamada, T. J. Phys. Chem. 1996, 100, 8777–8781. (6) Clays, K.; Persoons, A. Phys. Rev. Lett. 1991, 66, 2980–2983. (7) Levine, B. F.; Bethea, C. G. J. Chem. Phys. 1975, 63, 2666–2682. (8) Zyss, J.; Oudar, J. L. Phys. Rev. A 1982, 26, 2028–2048. (9) (a) Bosshard, C.; Spreiter, R.; Gunter, P. J. Opt. Soc. Am. B 2001, 18, 1620–1626. (b) Silva, P. S. P.; Cardoso, C.; Silva, M. R.; Paixao, J. A.; Beja, A. M.; Garcia, M. H.; Lopes, N. J. Phys. Chem. A 2010, 114, 2607–2617. (c) Skwara, B.; Bartkowiak, W.; Leszczynski, J. Struct. Chem. 2004, 15, 363–368. (d) Wu, K. C.; Snijders, J. G.; Lin, C. S. J. Phys. Chem. B 2002, 106, 8954–8958. (10) (a) Kurtz, H. A.; Stewart, J. J. P.; Dieter, K. M. J. Comput. Chem. 1990, 11, 82–87. (b) Cohen, H. D.; Roothaan, C. C. J. J. Chem. Phys. 1965, 43, 34–39. (11) Olsen, J.; Jørgensen, P. Time-dependent response theory with applications to self-consistent field and multiconfigurational self-consistent field wave functions. In Modern Electronic Structure Theory, Part II; Yarkony, D., Ed.; World Scientific: Singapore, 1995; pp 857990. (12) Olsen, J.; Jorgensen, P. J. Chem. Phys. 1985, 82, 3235–3264. (13) (a) Orr, B. J.; Ward, J. F. Mol. Phys. 1971, 20, 513–526. (b) Ward, J. F. Rev. Mod. Phys. 1965, 37, 1–18. (14) (a) Oudar, J. L. J. Chem. Phys. 1977, 67, 446–457. (b) Oudar, J. L.; Chemla, D. S. J. Chem. Phys. 1977, 66, 2664–2668. (15) Kwon, S. J.; Kwon, O. P.; Seo, J. I.; Jazbinsek, M.; Mutter, L.; Gramlich, V.; Lee, Y. S.; Yun, H.; Guenter, P. J. Chem. Phys. C 2008, 112, 7846–7852. (16) (a) Kwon, O. P.; Jazbinsek, M.; Yun, H.; Seo, J. I.; Seo, J. Y.; Kwon, S. J.; Lee, Y. S.; Gunter, P. CrystEngComm 2009, 11, 1541–1544. (b) Kwon, O. P.; Jazbinsek, M.; Seo, J. I.; Choi, E. Y.; Yun, H.; Brunner, F. D. J.; Lee, Y. S.; Gunter, P. J. Chem. Phys. 2009, 130, 134708. (c) Kwon, O. P.; Kwon, S. J.; Jazbinsek, M.; Brunner, F. D. J.; Seo, J. I.; Hunziker, C.; Schneider, A.; Yun, H.; Lee, Y. S.; Gunter, P. Adv. Funct. Mater. 2008, 18, 3242–3250. (d) Kwon, O. P.; Jazbinsek, M.; Yun, H.; Seo, J. I.; Kim, E. M.; Lee, Y. S.; Gunter, P. Cryst. Growth Des. 2008, 8, 4021–4025. (17) (a) Kwon, O. P.; Jazbinsek, M.; Seo, J. I.; Kim, P. J.; Choi, E. Y.; Lee, Y. S.; Gunter, P. Dyes Pigm. 2010, 85, 162–170. (b) Kwon, O. P.; Jazbinsek, M.; Seo, J. I.; Kim, P. J.; Yun, H.; Lee, Y. S.; Gunter, P. J. Chem. Phys. C 2009, 113, 15405–15411. (18) Kwon, O. P.; Kwon, S. J.; Jazbinsek, M.; Seo, J. Y.; Kim, J. T.; Seo, J. I.; Lee, Y. S.; Yun, H.; Gunter, P. Chem. Mater. 2011, 23, 239–246. (19) Marder, S. R.; Perry, J. W.; Schaefer, W. P. Science 1989, 245, 626–628. (20) (a) Pan, F.; McCallion, K.; Chiappetta, M. Appl. Phys. Lett. 1999, 74, 492–494. (b) Meier, U.; Bosche, M.; Bosshard, C.; Pan, F.; Gunter, P. J. Appl. Phys. 1998, 83, 3486–3489. (c) Marder, S. R.; Perry, J. W.; Yakymyshyn, C. P. Chem. Mater. 1994, 6, 1137–1147. (21) (a) Yang, Z.; Jazbinsek, M.; Ruiz, B.; Aravazhi, S.; Gramlich, V.; Gunter, P. Chem. Mater. 2007, 19, 3512–3518. (b) Ruiz, B.; Yang, Z.; Gramlich, V.; Jazbinsek, M.; Gunter, P. J. Mater. Chem. 2006, 16, 2839–2842. (c) Yang, Z.; Aravazhi, S.; Schneider, A.; Seiler, P.; Jazbinsek, M.; Gunter, P. Adv. Funct. Mater. 2005, 15, 1072–1076. (d) Glavcheva, Z.; Umezawa, H.; Mineno, Y.; Odani, T.; Okada, S.; Ikeda, S.; Taniuchi, T.; Nakanishi, H. Jpn. J. Appl. Phys., Part 1 2005, 44, 5231–5235. (22) (a) Yang, Z.; Mutter, L.; Stillhart, M.; Ruiz, B.; Aravazhi, S.; Jazbinsek, M.; Schneider, A.; Gramlich, V.; Gunter, P. Adv. Funct. Mater. 2007, 17, 2018–2023. (b) Stillhart, M.; Schneider, A.; Gunter, P. J. Opt. Soc. Am. B 2008, 25, 1914–1919. (c) Mutter, L.; Brunner, F. D. J.; Yang, Z.; Jazbinsek, M.; Gunter, P. J. Opt. Soc. Am. B 2007, 24, 2556–2561. (23) (a) Coe, B. J.; Harris, J. A.; Asselberghs, I.; Wostyn, K.; Clays, K.; Persoons, A.; Brunschwig, B. S.; Coles, S. J.; Gelbrich, T.; Light,
ARTICLE
M. E.; et al. Adv. Funct. Mater. 2003, 13, 347–357. (b) Coe, B. J.; Harris, J. A.; Asselberghs, I.; Clays, K.; Olbrechts, G.; Persoons, A.; Hupp, J. T.; Johnson, R. C.; Coles, S. J.; Hursthouse, M. B.; et al. Adv. Funct. Mater. 2002, 12, 110–116. (24) (a) Figi, H.; Mutter, L.; Hunziker, C.; Jazbinsek, M.; Gunter, P.; Coe, B. J. J. Opt. Soc. Am. B 2008, 25, 1786–1793. (b) Ruiz, B.; Coe, B. J.; Gianotti, R.; Gramlich, V.; Jazbinsek, M.; Gunter, P. CrystEngComm 2007, 9, 772–776. (25) (a) Mutter, L.; Koechlin, M.; Jazbinsek, M.; Gunter, P. Opt. Express 2007, 15, 16828–16838. (b) Mutter, L.; Guarino, A.; Jazbinsek, M.; Zgonik, M.; Gunter, P.; Dobeli, M. Opt. Express 2007, 15, 629–638. (c) Geis, W.; Sinta, R.; Mowers, W.; Deneault, S. J.; Marchant, M. F.; Krohn, K. E.; Spector, S. J.; Calawa, D. R.; Lyszczarz, T. M. Appl. Phys. Lett. 2004, 84, 3729–3731. (d) Kaino, T.; Cai, B.; Takayama, K. Adv. Funct. Mater. 2002, 12, 599–603. (e) Thakur, M.; Xu, J. J.; Bhowmik, A.; Zhou, L. G. Appl. Phys. Lett. 1999, 74, 635–637. (f) Pan, F.; Knopfle, G.; Bosshard, C.; Follonier, S.; Spreiter, R.; Wong, M. S.; Gunter, P. Appl. Phys. Lett. 1996, 69, 13–15. (26) (a) Schneider, A.; Neis, M.; Stillhart, M.; Ruiz, B.; Khan, R. U. A.; Gunter, P. J. Opt. Soc. Am. B 2006, 23, 1822–1835. (b) Taniuchi, T.; Ikeda, S.; Okada, S.; Nakanishi, H. Jpn. J. Appl. Phys., Part 2 2005, 44, L652–L654. (27) Kim, P. J.; Jeong, J. H.; Jazbinsek, M.; Kwon, S. J.; Yun, H.; Kim, J. T.; Lee, Y. S.; Baek, I. H.; Rotermund, F.; Gunter, P.; et al. CrystEngComm 2011, 13, 444–451. (28) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; et al. Gaussian 03, revision C.02; Gaussian, Inc.: Wallingford, CT, 2004. (29) (a) Becke, A. D. J. Chem. Phys. 1993, 98, 5648–5652. (b) Lee, C. T.; Yang, W. T.; Parr, R. G. Phys. Rev. B 1988, 37, 785–789.
23542
dx.doi.org/10.1021/jp204218t |J. Phys. Chem. C 2011, 115, 23535–23542
