Testing Computational Models of Hyperpolarizability in a Merocyanine

Article pubs.acs.org/JPCA

Testing Computational Models of Hyperpolarizability in a Merocyanine Dye Using Spectroscopic and DFT Methods Matthew E. Reish,† Andrew J. Kay,‡ Ayele Teshome,§ Inge Asselberghs,§ Koen Clays,§ and Keith C. Gordon*,† †

MacDiarmid Institute for Advanced Materials and Nanotechnology, Department of Chemistry, University of Otago, P.O. Box 56, Dunedin, New Zealand 9054 ‡ Photonics, Industrial Research Ltd., P.O. Box 31-310, Lower Hutt, New Zealand 5040 § Department of Chemistry, University of Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium ABSTRACT: The structural and electronic properties of a highly solvatochromic merocyanine dye, 2-(3-cyano-5,5-dimethyl-4-(3-(1-octadecylpyridin-4(1H)-ylidene)prop-1-enyl)furan-2(5H)-ylidene)malononitrile (pyr3pi), have been investigated using UV−vis, NMR, hyper-Rayleigh scattering, and Raman spectroscopies and further interpreted using computational chemistry. Spectroscopic data indicate that pyr3pi exists in its zwitterionic form even in low polarity solvents with electronic absorption spectra showing a hypsochromic shift with an increase in solvent polarity and NMR experiments indicating an increasingly zwitterionic structure in chloroform as the temperature is lowered. Raman spectra in increasingly polar solvents show small variations of the structure that are consistent with a change toward a structure with more zwitterionic character. However, comparison of the calculated and experimental vibrational energies and intensities and comparison of NMR coupling constants with calculated bond order indicate that calculations underestimate the amount of charge separation seen in low polarity solvents. Although for this system density functional theory (DFT) calculations and the two-state model qualitatively reproduce negative solvatochromism, they fail to reproduce the trends in hyperpolarizability seen experimentally. This is attributed to solvent field DFT calculations underestimating the degree of charge separation in reaction fields representing low polarity solvents.

■

INTRODUCTION Pronounced solvent effects in merocyanine push−pull chromophores are an indication of their large response to changing external electric fields. It is this property that makes them good candidates for use in nonlinear optics and photonics but also complicates the classification of their structural and electronic properties.1−3 Research into the perturbation of the ground- and excited-state structures and electronics of push− pull chromophores in changing molecular environments (i.e., solvent effects) is extensive.3,4 Even so, the description of the solvent effect on the electronic properties remains an active area of research.5 The conventional interpretation of the origin of solventdependent spectroscopic changes in push−pull dyes is illustrated in Figure 1.4 The structure of highly solvatochromic merocyanine dyes varies on a continuum between the neutral polyene structure (Figure 1I), the cyanine limit (Figure 1II), and the zwitterionic polymethine (Figure 1III). Initially researchers attributed solvatochromism to the intuitively appealing notion that the ground-state structure varies greatly between the limiting structures noted in Figure 1. While this is now accepted as being qualitatively correct, it must be noted that the degree of solvent-related ground-state geometric distortion is limited.6−8 With the advent of organic nonlinear optical materials, research into the electronics of these dyes has gained even more attention.9,10 In the search for dyes with © 2012 American Chemical Society

higher optical nonlinearities, it has been hypothesized that the hyperpolarizability reaches a maximum when the electronic structure of a dye lies approximately halfway between the polyene and the cyanine limit, that it reaches zero at the cyanine limit, and reaches a maximum of opposite sign between the cyanine limit and the polymethine. It was also found that varying the strength of the donor and/or acceptor moieties on the ends of the π-conjugated interconnect also greatly affects the degree of polyene and polymethine character.11−15 To assign dyes to a position on the continuum between polyene and polymethine, the concept of bond length alternation (BLA) can be applied. This permits dyes to be ascribed a position on the continuum by taking the difference in the average single bond and double bond lengths of the neutral canonical form of the structure.12−16 This approach allows one to readily classify dyes on the scale but inherently relies on computational methods to calculate the bond lengths, and experimental verification of the calculated BLAs is difficult to accomplish. The degree of ground-state structural change based on solvent interactions has been questioned, but the method of calculating BLA remains an important technique for classifying highly solvatochromic molecules computationally. To establish Received: February 13, 2012 Revised: May 15, 2012 Published: May 16, 2012 5453

dx.doi.org/10.1021/jp301455r | J. Phys. Chem. A 2012, 116, 5453−5463

The Journal of Physical Chemistry A

Article

Figure 1. Canonical structures of pyr3pi that are commonly used to describe the highly polarizable structure of merocyanine dyes. (I) The ideal, neutral polyene state of the molecule. (II) The cyanine limit where BLA is minimized and hyperpolarizabilty theoretically drops to zero. (III) The ideal zwitterionic polymethine state of the dye. Negatively solvatochromic dyes such as pyr3pi lie structurally between (II) and (III). This structural change can be seen in the UV−vis spectra, which show how the wavelength of the absorption maximum increases as the polarity of the solvent decreases ((A) DMSO, (B) acetonitrile, (C) acetone, (D) pyridine, (E) dichloromethane, (F) chloroform).

either H-aggregation, which is noted by a hypsochromically shifted peak for which it is named, or J-aggregation, which is noted by a bathochromically shifted shoulder and named after Jelley, who observed the phenomenon on the 1930s.3 The most commonly used spectroscopic technique to identify the presence of these dimers is UV−vis spectroscopy. Dimer formation is indicated by the emergence of a shoulder on the main charge-transfer (CT) bands of push−pull chromophores.31,35 For pyr3pi, aggregation is shown be limited to dimerization by the presence of an isosbestic point in the temperature-dependent UV−vis. The origin of this hypsochromic peak can be explained using the excitonically coupled dimer model.36,37 This method works well to explain the origins of the splitting of the lowest energy absorption band.31 NMR can also be used to clarify the ground electronic state. In contrast to UV−vis, the information obtained using NMR is decoupled from the excited state, and this makes it useful for classifying the ground state in terms of both the solventdependent BLA and the solvent-dependent charge distribution. Relative bond length alternation can be extracted from the coupling constant between the protons along the π-chain as protons vicinal to a double bond will have a greater coupling constant than those vicinal to a single bond.4 Chemical shifts indicate the charge density around the atoms, and the impact of various solvents on these can also be measured using NMR.6,38,39 In addition to complications due to dimerization, pyr3pi can exist as one of two stable rotamers, and these give different spectral responses. Predicting the relative concentrations of the rotamers is important in computational modeling, and NMR has been successfully applied to measure the relative concentration of each rotamer.40 Raman spectroscopy is a method that can be used to gauge solvent-induced structural changes. Shifts in Raman bands in a range of solvents were taken by Marder et al. as confirmation of predicted shifts in BLA.26 Selective enhancement of Raman modes is also seen as function of the conjugation in π-chains. This conjugation will be directly indicative of BLA, and changes in intensity patterns in Raman and IR measurements have been used to calculate higher order hyperpolarizabilities by Del Zoppo and others.13,41 Hyper-Rayleigh scattering (HRS) can be considered as one of the most important experimental techniques in molecular

the reliability of these calculations, it is necessary to validate computational work using experimental data. The spectroscopy of highly solvatochromic dyes is inherently complex as variations in spectroscopic properties can depend on many different solvent parameters. For example, there remains some ambiguity about whether donor−acceptor chromophores can pass through the cyanine limit.6,7,17−22 In the case of Brooker’s merocyanine, several authors conclude by computation and UV−vis spectroscopy that there is a solventdependent switch from polyene to polymethine accompanying the inverted solvatochromism.19,20,22 However, other researchers have taken the opposing view and conclude from NMR and UV−vis spectroscopic studies that any inverted solvatochromism is a result of either vibrational splitting of electronic levels, protonation, or aggregation.6,17 The main spectroscopic methods used for the determination of electronic and structural properties of push−pull chromophores are UV−vis,23 electro-optic absorption (EOA),7,24 hyper-Rayleigh scattering (HRS),14,25 NMR, and vibrational spectroscopies such as Raman and IR.13,26−30 In this work, we focus on the use of UV−vis, Raman (HRS), and NMR to give insight into the varying structural and electronic properties of a merocyanine dye with a very high hyperpolarizability. Each technique provides different information about the nature of solvent-induced changes in the molecule. UV−vis gives direct information about the excitation energy, and early interest in the merocyanine dyes was due to their large solvent-dependent UV−vis response.26 There are a number of reasons for solvatochromic behavior that are not directly related to changes in the ground-state structure (Figure 1).6,7 For example, aggregation of NLO chromophores is a significant issue and can be detected via the appearance of concentration- and/or temperature-dependent shoulders in UV−vis spectra.31 The use of negatively solvatochromic dyes for photonics applications has been limited by their aggregation in low polarity media. For organic NLO materials to exhibit a macroscopic response, the chromophores need to be aligned noncentrosymmetrically in a matrix, and this ordering must be maintained over time. This ordering can be both difficult to attain and maintain in the presence of significant aggregation, something that has been highlighted in the literature.32−34 For negatively solvatochromic merocyanines, dimerization can be 5454



Article

⎛ ⎞ ⎛ 24π 4 ⎞⎜ (ν0 − νj)4 ⎟⎛ h ⎞ ⎟Sj =⎜ ⎟⎜ ⎟⎜ ∂Ω ⎝ 45 ⎠⎜ 1 − exp⎡ −hcνj ⎤ ⎟⎜⎝ 8π 2cνj ⎟⎠ ⎣⎢ kT ⎦⎥ ⎠ ⎝

second-order nonlinear optics. It can be used to determine the molecular second-order nonlinearities (molecular first hyperpolarizability, β). HRS has also proven to be a very powerful technique to determine molecular and supramolecular symmetries. HRS experiments are performed by measuring the frequency doubled (2ω) incoherent light scattered from a liquid sample, irradiated by laser light at frequency ω. This technique relies on orientational fluctuations of asymmetric molecules in solution, which gives rise to an average symmetry in an isotropic liquid.42 The calculation of nonlinear optical figures of merit is a useful tool in both understanding the origin of large higher order polarizabilities and designing molecules to maximize these.43 The work of Marder, Gorman, and others in the early 1990s using point charges to simulate varying molecular environments showed great insight into the molecular origins of hyperpolarizability.12,15 However, these computational studies reinforced the erroneous view that large changes in ground-state structure accompanied solvation with different solvents.18 With the publication of in-depth description of theory and method along with the increasing availability of QM software packages, the calculation of molecular polarizabilities has become a tool available to many researchers.44 However, it has been shown that for the compound studied herein, the calculation of higher order polarizabilities should be interpreted with caution as the agreement between experimental hyperpolarizability and that calculated by the two-state model can be achieved fortuitously, and under closer examination it is noted that calculated results do not correlate well with experimental results.6,8,45 This finding is important because, if it occurs more generally for other systems, the use of DFT calculations and continuum solvation models for guiding molecular design may create misleading design guidelines and poor optimization of macroscopic properties.

∂σj

where ν0 is the laser excitation frequency and νj is the frequency of the jth mode. FT-Raman spectra were obtained using a Bruker Equinox 55 interferometer coupled with a FRA-106 Raman module and a D418T liquid-nitrogen-cooled Germanium detector, controlled by the Bruker OPUS v5.5 software package. A Nd:YAG laser operating at 1064 nm and 120 mW of power was used. The spectra were acquired with a resolution of 4 cm−1. The powdered samples were dispersed in KBr and pressed into a disk to minimize laser heating. The 350.7 nm line of a continuous-wave Innova I-302 krypton-ion laser (Coherent, Inc.) was used to generate resonance Raman (RR) scattering when pyr3pi was dissolved in toluene and acetonitrile. A Pellin-Broca prism was used to separate Kr+ plasma lines, and laser power was adjusted to 30 mW at the sample. Further details of the RR experimental setup have been described several times previously.53,54 Absorption spectra in each solvent were recorded on a Varian Cary 500 scan UV−vis−NIR spectrophotometer utilizing Cary Win UV Scan Application software. Spectra were recorded from 300 to 800 nm. Variable-temperature absorption spectra were obtained using the Varian 6 × 6 block peltier temperature controller accessory. Solutions were typically 10−6 mol L−1 and were contained in a 1 cm cell. Fluorescence spectra in each solvent were measured at concentrations of around 10−6 mol L−1 with a Perkin-Elmer luminescence spectrometer LS50B with FL Winlab v. 4.00.02. The excitation wavelengths were determined by the absorbance maximum obtained in the previously described absorption measurements, and emissions were scanned from 300 to 800 nm. 1 H and 13C NMR spectra and two-dimensional (COSY, ROESY) spectra were collected on a 500 MHz Varian UNITY INOVA spectrometer with a variable-temperature probe. All nonlinear optical experiments were performed at room temperature using the frequency-resolved hyper-Rayleigh scattering (HRS) technique at 800 nm. The apparatus and experimental procedures used for the femtosecond HRS studies with high frequency demodulation of multiphoton fluorescence were exactly as described previously.55 Crystal violet (CV) dissolved in methanol was used as an octupolar external reference (βxxx = 338 × 10−30 esu). The solvent dependency studies were performed in dimethyl sulfoxide (DMSO), dimethylformamide (DMF), acetonitrile (ACN), methanol (MeOH), acetone, dichloromethane (DCM), tetrahydrofuran (THF), chloroform (CHCl3) and 1,4-dioxane. For each sample, a diluted concentration series was measured and compared to the reference concentration series. To correct for the difference in solvent between the chromophores and the reference compound, the local field correction factors were applied ((n2 + 2)/3)3, where n is the refractive index of the solvent at the sodium D line, n(DMSO) = 1.48, n(DMF) = 1.43, n(ACN) = 1.344, n(MeOH) = 1.32, n(acetone) = 1.359, n(DCM) = 1.424, n(THF) = 1.41, n(CHCl3) = 1.44, and n(1,4-dioxane) = 1.422. The calculations of the dynamic first hyperpolarizabilities were made by taking the ratio of the slopes of the sample to the reference compound and considering the appropriate tensor components (dipolar βzzz for the unknown versus octupular

■

EXPERIMENTAL SECTION The synthesis of pyr3pi and many similar right-hand-side chromophores is described by Kay et al.46,47 Pyr3pi was shown by NMR to be pure and was not purified further. All solvents used were spectroscopic or HPLC grade from Merck and Sigma-Aldrich. Deuterated DMSO and chloroform were supplied by Cambridge Isotope Laboratories. Geometry optimizations, vibrational frequency calculations, and electronic excitation calculations using time-dependent methods were performed using density functional theory with the B3LYP functional and the 6-31G(d) basis set. All calculations were carried out using the Gaussian 09 software package.48 For solvent field calculations, we used the integral equation formalism polarizable continuum model (IEFPCM)49,50 self-consistent reaction field (SCRF)1,2 with default solvent parameters provided by the Gaussian program. For theoretical Raman vibrational energies, a scale factor of 0.967 was determined by minimizing mean absolute deviation (MAD) between calculated and experimental modes and was found to be similar to recent recommendations.51 Intensity correction for calculated spectra was applied to convert the Raman activity given by the Gaussuian 09 program to Raman scattering cross sections.52 The differential Raman cross section of the jth mode, ∂σj/∂Ω, is related to the Raman activity, Sj, given by the Gaussian 09 frequency calculation (Gaussian keyword: Freq=Raman) as follows: 5455



Article

Table 1. Solvent-Dependent Linear Optical Properties of pyr3pi dielectric

absorption energy

emission energy

intensity/bandshape

solvent

relative permittivity

λmax (nm)

νmax (cm−1)

λmax (nm)

νmax (cm−1)

∫ ε dν (106 L mol−1 cm−2)

fwhm (Δν cm−1)

dioxane toluene CHCl3 THF DCM pyridine acetone acetonitrile DMF DMSO

2.2 2.3 4.8 7.5 9.1 12.3 21.1 36.7 37.5 46.7

632.0 648.1 632.1 598.8 619.3 602.4 584.8 573.8 573.1 566.5

15 820 15 430 15 820 16 700 16 150 16 600 17 100 17 420 17 450 17 650

666 673 662 654 655 652 639 637 634 635

15 000 14 840 15 110 15 280 15 260 15 340 15 650 15 700 15 770 15 750

15.3 14.5 14.6 16.3 14.3 14.1 16.7 16.5 16.4 14.5

1383 941 1223 1528 1406 1903 2161 2557 2586 2857

βxxx for the CV reference compound). The static first hyperpolarizability is derived from the simple two-level model as described by Oudar et al.10

■

RESULTS AND DISCUSSION Electronic Spectroscopy. The solvatochromic response of pyr3pi (Table 1) in a wide range of aprotic solvents shows a hypsochromic shift of the lowest energy transition with increasing solvent polarity. This is indicative of the ground state being more polar than the excited state; that is, the ground state is zwitterionic (Figure 1III).4 Figure 2 shows the

Figure 3. Relationship between the solvent dipole moment and the absorption and emission maxima. The solvatochromic shift of the absorption maximum responds linearly to the dipole moment of the solvent. The decrease in Stokes shift in lower polarity solvents can also be seen. This is an indication that the molecule is closer to the cyanine limit in low polarity solvents.

that approaches the cyanine limit (Figure 1II). The reduced Stokes shift in low polarity solvents is consistent with this (Figure 3). The presence of aggregation was confirmed by the appearance of a concentration-dependent blue-shifted shoulder. This type of behavior has been seen before for this system and other negatively solvatochromic merocyanines.31,35,56 In low polarity solvents, such as toluene and dioxane, dimerization occurs readily, and a small, temperature-dependent shoulder is observed in these solvents in solutions as dilute as 10−6 M. All observed aggregation appears to be limited to a one equilibrium process such as dimerization (as opposed to higher order aggregation) consistent with the presence of a single isosbestic point in the UV−vis spectrum with changing temperature (Figure 4). While dimer formation is seen in several solvents, it is notably absent in both acetone and DMSO and was determined not to be purely dependent on solvent polarity as aggregates are present in acetonitrile solutions at 3 × 10−3 M, while similar concentrations in acetone were shown by short path-length UV−vis to be dimer-free. NMR. 1H and 13C NMR spectra were recorded in both chloroform and DMSO. At suitable concentrations for NMR (5 × 10−3 M), the chloroform solution was shown to have an appreciable concentration of dimer by UV−vis, although the amplitude of the dimer peak was around one-half of the

Figure 2. Absorption maxima plotted against solvent dielectric. Small variation in dielectric is generated by temperature variation. (A) Toluene, 0 to 80 °C, (B) CHCl3, −10 to 30 °C, (C) CH2Cl2, −10 to 25 °C, (D) pyridine, 25 °C, (E) acetone, −10 to 40 °C, (F) acetonitrile, 15 to 35 °C, (G) DMSO, 10 to 45 °C.

dependence of λmax on the polarity of the solvent dielectric. Varying solvent temperature allows for a small adjustment of the dielectric of the solvent, which is also seen in Figure 2. The fluorescence of pyr3pi also shifts with solvent but to a lesser degree than the absorption, and we therefore see a greater Stokes shift in higher polarity solvents (Figure 3). The profiles of the absorption spectra provide insight into the structural changes between the ground state and excited state. The data presented in Figure 1 show that as the dipole moment of the solvent is reduced, the band shape narrows and red-shifts. The narrowing the band shape implies smaller structural distortions between the ground and excited states, and such behavior is often attributed to a ground-state structure 5456



Article

Figure 4. The UV−vis spectra of pyr3pi in toluene as a function of temperature. The increase in the height of the blue-shifted peak at lower temperatures indicates the presence of a dimer. The dimer peak also increases as the concentration is increased.

amplitude of the monomeric peak. The presence of dimerization was neglected in the interpretation of the NMR spectrum for several reasons. First, there was neither distinct line broadening nor the existence of separate monomer and dimer peaks. Second, temperature variation (which was shown to change the amount of aggregation in solution by UV−vis) showed only small changes that were consistent with those seen in DMSO where it was determined that there was no dimer present. Third, NOESY and COESY experiments showed no through space Overhauser coupling between the protons of the dimeric system that would be expected should the dimeric species be present. NMR indicates that there are two rotamers of pyr3pi present in solution (Figure 5). The amount of each rotamer present is dependent on solvent polarity. Integration of the peaks due to the cis- and trans-isomers shows that the percentage of cisrotamer in DMSO is 53 ± 1%. In chloroform, the percentage of cis-isomer is 85 ± 1%. DFT calculations using different PCM solvent fields confirmed that the relative energy of the two rotamers is closer in DMSO (2.46 kJ/mol) than in chloroform (5.9 kJ/mol). Furthermore, a Boltzmann distribution of the rotamers at 298.15 K based on the energies found in the DFT calculations matches well with experimental concentrations found for each rotamer (Figure 6). The calculated fraction of cis-isomer in a solvent field approximating DMSO is 0.545, while the fraction of cis-isomer in a solvent field approximating chloroform is 0.910. The larger deviation between calculated and experimental values for the lower polarity solvent is consistent with the trend we see for other molecular properties calculated in lower dielectric fields where the molecule has been shown experimentally to maintain more zwitterionic character in low polarity solvents than is suggested by calculations. A change in the chemical shifts of the 1H NMR spectra indicates variations in the electronic shielding present in the molecule as a function of different solvents (Figure 7 and Table 2). The solvent-dependent shifts are the result of two effects. First, the variation in electron densities between the cyanine limit and the charge-separated zwitterionic state (Figure 1II and III) creates different electronic environments, and, second, the varying polarity of the solvent shell creates variations in local electronic shielding. These two effects are difficult to decouple, but a comparison of the chemical shifts of protons 4,5 and 6,7 in both solvents with the equivalent protons in pyridine shows

Figure 5. NMR spectra in both CDCl3 and DMSO-d6. The pyridyl protons, especially those α to nitrogen (6 and 7), vary greatly depending on solvent polarity. Both the cis- and trans-rotamers are present. In DMSO-d6, the cis- and trans-rotamers are present in near equal concentrations, while in CDCl3 the cis-rotamer is the dominant species.

Figure 6. Fraction of cis-isomer as a function of solvent dielectric. Red circles indicate experimental values determined by peak heights in the NMR spectra, while the calculated values are determined by a Boltzmann distribution with single point energy values of each rotamer calculated using DFT.

that the changes for pyridine are much smaller than those found for pyr3pi. For pyridine, the change of the chemical shift for the protons α to the nitrogen is less than 0.02 ppm when changing from CDCl3 to DMSO-d6, while for pyr3pi the shifts are 0.75 ppm (cis) and 0.59 ppm (trans). Therefore, most of this change in pyr3pi is presumed to be generated by variation in electronic structure of pyr3pi. However, as the solvent shell in pyr3pi is also more polarized than in pyridine, this could create a larger variation in the local environment. Consequently, a better indicator of any variation in structure is 5457



Article

CDCl3 (d6-DMSO, J23 = 14.7 Hz, J21 = 12.2 Hz; CDCl3, J23 = 14.2 Hz, J21 = 12.5). However, the change is much less than expected from calculation as BLA in CDCl3 is expected to be only one-half that in DMSO. This is consistent with other data collected (HRS and Raman) that suggest that calculations underestimate the amount of the charge separation in low polarity solvents.6 Raman Studies. Raman spectroscopy may be used to probe solvent-dependent structural changes as measurements can be taken in solvents of different polarities. Raman spectra were recorded in solutions with a range of dielectric constants from toluene (εr = 2.4) to DMSO (εr = 46.7). Shifts indicating changes in bond strength (order) and changes in the relative intensities of different modes are dependent on the solvent polarity (Figures 8 and 9). DFT calculations including a solvent

Figure 8. Raman spectra in solvents of varying dielectric. In all solvents except for toluene and acetonitrile, the Raman excitation wavelength was 1064 nm. To limit dimerization, spectra in toluene and acetonitrile were taken at lower concentrations at resonant Raman excitation wavelengths. 351 nm was used for the acetonitrile solution, while 488 nm was used for the toluene solution. This allows accurate energies to be obtained, but the intensities vary with resonance effects. (* denotes a solvent band.)

Figure 7. Solvent-dependent shift of protons of the cis-rotamer for (a) protons 4 and 5, and (b) protons 6 and 7. The low dielectric solvent is CDCl3, and the high dielectric solvent is d6-DMSO. Small changes in solvent dielectric were attained by changing the temperature at which the spectra were recorded.

Table 2. Solvent-Dependent 1H NMR Chemical Shifts chemical shift (ppm) solvent

isomer

H1

H2

H3

H4,5

H6,7

d6-DMSO

cistranscistrans-

5.73 5.66 5.84 5.39

8.36 7.63 8.54 7.44

6.27 6.33 5.94 5.96

7.52 8.48 7.26 7.76

8.56 7.87 7.81 7.28

CDCl3

likely to be gained from an examination of changes in coupling constants along the π-chain as a function of solvent. Coupling between the protons on the π-conjugated interconnect can give an indication of variations to the bond order along the chain as a function of different solvents.6,12,48 In pyr3pi, the values of J21 and J23 are informative as the magnitudes for both should be similar at the cyanine limit, but J23 should be greater than J21 as the structure becomes more zwitterionic due to the greater degree of bond alternation. Thus, low polarity solvents should generate coupling constants that are similar in magnitude, while polar solvents should generate greater differences. Analyzing the coupling constants shows the expected bond order, with J23 being higher than J21, and the expected changes due to solvent are also seen as the difference in coupling constants is greater in d6-DMSO than in

Figure 9. Solvent dependence of the Raman shift of the cyano stretching mode (a) and of several skeletal carbon modes (b−d). 5458



Article

were used to identify the normal modes of pyr3pi and to gain a greater insight into the effects that solvent has on the molecular structure as reflected by Raman energies. Dimerization of the chromophores was observed in acetonitrile, chloroform, dichloromethane, and toluene and was noted by a shift in “backbone” modes to lower Raman shifts. Dimerization was eliminated by lowering the concentration in all solvents except for toluene. In toluene, at the lowest concentration at which a usable resonance Raman spectrum could be recorded, there is still an appreciable amount of dimer. To ensure that vibrational energies in toluene were not greatly affected by dimerization, spectra were recorded at high temperature (65 °C). No appreciable change could be seen, although UV−vis of the same solution showed a large change in the proportion of monomer and dimer as the temperature was increased from 20 to 55 °C. This was taken as an indication that the transition between monomer and dimer in low polarity solutions has a negligible effect on the structure. This, however, is not the case in higher polarity solvents. In acetonitrile, large changes in vibrational energy are noted between the high (3 × 10−3 M) and low concentration (3 × 10−5 M) solutions, indicating a change in bond order between the dimer and the monomer. In both toluene and acetonitrile, acceptable spectra could not be collected using FT-Raman, and resonance Raman spectra were taken to obtain solventdependent vibrational energies (Figure 8). The energy of the various skeletal modes was tracked in varying solvents (Figure 9), and it was found that the energy of various modes shows a positive correlation with solvent polarity. This is consistent with the increasing bond order that is expected in higher polarity solvents. These shifts in energy are difficult to correlate with BLA as the vibrations that are described are delocalized across the conjugated chain and therefore may not vary uniformly with changing single or double bond character. However, changes in the intensity pattern of skeletal modes have been to correlate well with conjugation and therefore BLA (see below).13,41 The lowering of the energy of the cyano stretches (Figure 9) is also consistent with an increasingly charge-separated structure as the negative charge can be shared across the two cyano groups, thereby decreasing the bond order of the two cyano groups and lowering their frequency. Cyano stretches are known to be solvatochromic but to a lesser degree than that seen in pyr3pi. In acetonitrile, there is ∼5 cm−1 variation between acetonitrile dissolved in CCl4 and acetonitrile dissolved in DMSO, while for pyr3pi a variation of ∼8 cm−1 between CHCl3 and DMSO solvation is observed.57 Raman intensities can also be correlated with BLA and hyperpolarizability;13,41 a selective enhancement of “backbone” modes correlates with an increase in BLA. The increase in intensity can be quantified by taking the ratio of the mode that is enhanced, as with the mode around 1150 cm−1 (Figure 8), and a mode that is largely unaffected by the change in BLA, such as the cyano stretch.13 In pyr3pi it is seen that the ratio of the mode at the 1150 cm−1 to that of the cyano stretch increases as a function of solvent polarity, indicating an increase in BLA (Figure 10). Using this ratio and calibrating it by fitting the calculated ratio plotted against the calculated BLA, it is possible to estimate the amount of BLA seen experimentally. This relies on the DFT model accurately describing the relationship between mode intensities and calculated bond length alternation, and at present we have no way of checking this value experimentally. Using this method, the BLA of pyr3pi

Figure 10. The ratio of the intensity of cyano stretch to the intensity of the prominent carbon−carbon stretching mode around 1150 cm−1.

in chloroform is estimated to be −0.039 Å, which would agree well with the experimental maximum in hyperpolarizability occurring in chloroform. Hyper-Rayleigh Scattering Studies. The experimental static first hyperpolarizability of pyr3pi in different solvents has been measured using fundamental excitation at 800 nm, and the results are given in Table 3. In agreement with our previous Table 3. Experimental and Calculated Nonlinear Optical Properties of pyr3pi in Differing Solvents solvent

dielectric

calc (two-state) (βzzz,0 (10−30 esu))

dioxane toluene CHCl3 THF DCM pyridine acetone acetonitrile DMF DMSO

2.21 2.38 4.8 7.5 9.1 12.3 21.19 36.78 37.5 46.7

127 131 130 135 135 147 144 142 152 148

calc (finite field) (βzzz,0 (10−30 esu))

exp (HRS) (βzzz,0 (10−30 esu))

65 72 155 214 235 279 313 341 366 361

250 ± 1056 470 ± 4056 370 ± 1556 460 ± 15 345 340 330 260

± ± ± ±

15 15 1056 10

reports,47,56 the first hyperpolarizability values for the merocyanine compound are dependent on the polarity of the surrounding medium. One way solvent polarity can influence the values of the first hyperpolarizability of solute merocyanines is by affecting the extent of molecular aggregation.31 It follows from this that the molecular merit |μβ| is highly dependent on merocyanine concentration in low polarity solvents,58,59 as the concentration-dependent value for the first hyperpolarizability was observed in 1,4-dioxane for this compound. At high concentrations, centrosymmetrical aggregate formation lowers the retrieved value. Indeed, a higher value is deduced in the low-concentration limit for detection. No concentration dependence for the first hyperpolarizability was found in the other more polar solvents (within a concentration range from 10−4 to 10−7 M).56 More importantly, there is a trend toward an increase in first hyperpolarizability upon lowering the solvent polarity (although not in 1,4-dioxane). This is in accordance with negative solvatochromism and is rationalized by the transition energy dependence in the two-level model. That means that solvent polarity can affect the β value of merocyanines by modifying the electron distribution within the conjugated bridge between the electron donor and acceptor groups in the 5459



Article

molecules, thereby affecting the degree of bond length alternation (BLA). High polarity solvents generate a greater reaction electric field about the dipolar molecule than those with lower polarities. This increases the extent of charge separation (zwitterionic character), which in turn impacts on β. Therefore, the increase in β values with decreasing solvent polarity (DMSO < DMF < acetonitrile < acetone < THF < CHCl3) observed for this compound is consistent with the reported BLA values of −0.0448 Å from X-ray crystallographic data of a similar compound.60 Consequently, further tuning of the chromophore is required to afford the optimal structure. Quantum Calculations. DFT calculations give us the ability to access molecular properties that are difficult or impossible to obtain experimentally. Highly polarizable molecules represent a challenge to calculate accurately as their properties are greatly affected by their environment.44 To account for changes in electronic structure due to solvent interactions, a solvent field was employed for all calculations. This solvent field iteratively fits a field of constant dielectric to a reaction field determined by the electron density surrounding the molecule.49,50 This model neglects specific interactions between the solvent and the chromophore, and it has been noted in the literature that large shifts in UV−vis absorption energies are the result of such interactions.4 We have also attempted direct solvation modeling through the explicit use of a limited number of solvent molecules at likely sites of direct solvent interaction. In our hands, the use of direct solvation is quite unpredictable with varying trends found even though experimentally both UV−vis and vibrational energies vary predictably with variations in solvent polarity. Candidates for specific interaction in this system are hydrogen bonding through the cyano groups and the pyridyl nitrogen and hydrogen bonding through the hydrogen atoms of pyr3pi that show the highest δ1H as found by NMR. Another approach that is gaining favor is the use of molecular mechanics methods for solvent molecules to establish a full solvent shell around the compound being studied. This method suffers from increased complexity and problems with lower levels of theory not being able to correctly interpret weak bonding interactions.61,62 Because of the wide variety of specific interactions that are possible, the increased computational cost, and the lack of direct experimental evidence to check the description of weak interactions in this system, it has been decided that the use of PCM model is more general and less speculative. Furthermore, in this study, the use of aprotic and weakly electron-donating and -accepting solvents limits the specific interactions and allows for a more direct comparison between the PCM calculated and experimental values. DFT often fails in the description of systems with diffuse orbitals, so to check the reliability of DFT calculations, MP2 calculations were performed using the same basis set (631G(d)).63 MP2 geometry optimizations, when compared to DFT, show some increased response to the solvent field but do not give qualitatively different results from DFT as manifest by BLA in varying solvent fields (Figure 11). In vacuo calculations and calculations in a solvent field representing toluene at the MP2 level show greater inverted BLA than do DFT calculations, while higher permittivity solvent fields reverse this trend with increased negative BLA. In vacuo calculations give a BLA value of 0.031 Å using MP2 and 0.021 Å using DFT and a similar disparity for toluene with a value of 0.008 Å for MP2 and a value of −0.018 Å for DFT. For higher permittivity solvent fields, the trend is reversed with a solvent field

Figure 11. The average bond length alternation of the trans-rotamer calculated using DFT (B3LYP-6-31G(d), black squares) and MP2 (631G(d), red circles). The compound was calculated in vacuo and using three three different solvent dielectric values representing toluene, chloroform, and DMSO.

representing CHCl3 showing a BLA of −0.030 Å using MP2, while the equivalent calculation using DFT gives a value −0.019. In solvent fields representing DMSO, the values of BLA are −0.049 and −0.039 Å for MP2 and DFT, respectively. MP2 calculations are considerably more expensive than DFT, and solvent-dependent trends calculated using each method show little significant difference from DFT. Frequency calculations can be used as an indicator of the reliability of the calculated structure, and the use of a solvent field was shown to be very important in achieving an acceptable match of the potential energy surface with that observed experimentally64 (Figure 12). Solvent field calculations were

Figure 12. Calculated and experimental Raman spectra of pyr3pi in DMSO (bottom) and CHCl3 (top). The correlation between spectra and the corresponding solvent field is poor. However, the calculation in a solvent field representing DMSO matches well with the experimental spectrum in chloroform. This is an indication that the solvent effects are underestimated in solvent field calculations.

shown to have a large effect on the calculated geometry with in vacuo calculations underestimating the degree of charge separation seen in experiment. The calculated molecule approaches the “cyanine limit” in vacuo and in low polarity solvent fields as evidenced by the lack of any BLA. A clear change in the vibrational structure, with strong bands seen around 1140 and 1570 cm−1 decreasing in intensity, 5460



Article

Figure 13. Correlation between the relative permittivities of various solvents and the hyperpolarizability and average BLA (shown here with opposite sign for comparison with other properties). For all graphs, blue circles represent the trans-isomer, the red triangles represent the cis-isomer, and the black squares represent the weighted average of the two. Top left: Experimental HRS values of β versus solvent polarity. Top right: Calculated twostate values for β versus solvent polarity. Bottom left: Calculated FF value for β versus solvent polarity. Bottom right: Calculated BLA versus solvent.

finite-field (FF) method. These two methods have both been widely used in the literature with no clear method gaining favor even though both have been employed heavily since the early 1990s.44 The two-state model of organic D−π−A systems was introduced by Oudar and Chemla and is of great practical use as many design parameters that are controllable are represented in the basic equation for hyperpolarizability.10 In the SOS model, the hyperpolarizability is linked to the dipole change between the ground state and excited state, the oscillator strength of a transition, and the energy of the transition. It is calculated as follows:

corresponds to the loss of distinct double bond and single bond modes and therefore a reduction in the degree of BLA.13 Experimentally, there is a shift and a change in intensity of the Raman bands with a change in solvent (Figures 9 and 12), but even in low polarity solvent, such as, toluene and CHCl3, the strongest bands continue to be the main single- and doublebond centered modes observed around 1140 and 1570 cm−1, respectively. The ratio of the intensity of the CN band to the mode at 1150 cm−1 found computationally in a CHCl3 solvent field is 0.98, while experimentally this value is 0.12. In DMSO, the calculation gives a value of 0.12 with an experimental value of 0.04. Along with NMR coupling constants, this is another indication that solvent field calculations underestimated the degree of solvent polarity seen in experiment. Experiments in high polarity solvents show structural changes that indicate additional enhancement of additional single- and double-bond modes around 1300 and 1460 cm−1 (Figure 12). This enhancement pattern is presumed to indicate a structure that is more polarized than any of the structures that could be calculated using the PCM model; this is again consistent with the calculations underestimating the solvent polarity. HRS experiments support the idea of an underestimation of charge separation in the calculations, as the experimental β values are at the highest in low polarity solvents, while the finite-field calculations predict that they are higher in high polarity solvent fields (Figure 13, Table 3). There are two main classes of calculations used to estimate β computationally; these are the two-state or sum over states (SOS) method and the

β0 =

3(Mge)2 Δμ 2(hωge)2

where subscripts g and e are the ground and excited states, Δμ is the change in dipole moment, Mge is the transition dipole moment, ℏωge is the transition energy, and β0 is the frequencyindependent component of the first hyperpolarizability. This method can be performed using a frequency-dependent factor or statically as is represented above. Care must be taken to ensure that the dipolar change upon excitation is taken in the direction of maximum dipole change to be directly comparable with HRS experiments. The finite-field (FF) method is a more direct approach, which uses an electric field perturbation of the electronic wave function to gauge the dipole response to a variable electrical field.44 5461



■

The FF method gives a better match to the magnitude from experiment than the two-state model with a calculated static hyperpolarizability value of 361 × 10−30 esu when a DMSO solvent field is used, while a value 148 × 10−30 esu is calculated using the two-state model. Both models severely underestimate the experimental value of 470 ± 40 × 10−30 esu. The FF value also mirrors the calculated values of BLA much more closely than that of the two-state model. It has been shown often that the BLA is a good indicator of hyperpolarizability, and we therefore consider that the two-state model may not accurately reflect the hyperpolarizability of the calculated molecule. This suggests the correct trend in regard to experiment (Figure 13) generated by the two-state model is by chance and does not accurately reflect the calculated structure. Several other recent papers have questioned the validity of the two-state model for use with push−pull chromophores, and it is therefore suggested that the method must be applied with caution.8,45 When we consider the match of the experimental vibrational frequencies and intensities with the calculated ones and the smaller than expected change in coupling constants in π-chain protons from NMR data, the reason for the underestimation of the hyperpolarizability in low polarity solvent fields becomes clearer. The comparison of the vibrational frequency values (Figure 12) and the match of intensity ratios show that the DMSO solvent field generates a charge-separated structure that more closely resembles the structure seen experimentally in CHCl3, and when this is taken into account the values calculated for the finite field method more accurately reflect that of experiment. The underestimation of charge separation in donor−acceptor chromophores has been noted before, and here we reiterate the need to align computational data with experimental data.6

Article

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We would like to thank the University of Otago, the New Zealand Ministry of Science and Innovation, and the MacDiarmid Institute for support.

■

REFERENCES

(1) Rivail, J.-L.; Rinaldi, D. Chem. Phys. 1976, 18, 233−242. (2) Cimiraglia, R.; Miertuš, S.; Tomasi, J. Chem. Phys. Lett. 1981, 80, 286−290. (3) Mishra, A.; Behera, R. K.; Behera, P. K.; Mishra, B. K.; Behera, G. B. Chem. Rev. 2000, 100, 1973−2012. (4) Reichardt, C.; Welton, T. Solvent Effects on the Absorption Spectra of Organic Compounds. In Solvents and Solvent Effects in Organic Chemistry; Wiley-VCH Verlag GmbH & Co. KGaA: New York, 2010; pp 359−424. (5) Marder, S. R. J. Mater. Chem. 2009, 19, 7392−7393. (6) Morley, J. O.; Morley, R. M.; Docherty, R.; Charlton, M. H. J. Am. Chem. Soc. 1997, 119, 10192−10202. (7) Würthner, F.; Archetti, G.; Schmidt, R.; Kuball, H.-G. Angew. Chem., Int. Ed. 2008, 47, 4529−4532. (8) Bale, D. H.; Eichinger, B. E.; Liang, W.; Li, X.; Dalton, L. R.; Robinson, B. H.; Reid, P. J. J. Phys. Chem. B. 2011, 115, 3505−3513. (9) Williams, D. J. Angew. Chem., Int. Ed. 1984, 23, 690−703. (10) Oudar, J. L.; Chemla, D. S. J. Chem. Phys. 1977, 66, 2664−2668. (11) Marder, S. R.; Beratan, D. N.; Cheng, L.-T. Science 1991, 252, 103−106. (12) Marder, S. R.; Gorman, C. B.; Tiemann, B. G.; Perry, J. W.; Bourhill, G.; Mansour, K. Science 1993, 261, 186−189. (13) Del Zoppo, M.; Castiglioni, C.; Gerola, V.; Zuliani, P.; Zerbi, G. J. Opt. Soc. Am. B 1998, 15, 308−317. (14) Hendrickx, E.; Clays, K.; Persoons, A. Acc. Chem. Res. 1998, 31, 675−683. (15) Gorman, C. B.; Marder, S. R. Proc. Natl. Acad. Sci. U.S.A. 1993, 90, 11297−11301. (16) Meyers, F.; Marder, S. R.; Pierce, B. M.; Bredas, J. L. J. Am. Chem. Soc. 1994, 116, 10703−10714. (17) Niedbalska, M.; Gruda, I. Can. J. Chem. 1990, 68, 691−695. (18) Albert, I. D. L.; Marks, T. J.; Ratner, M. A. J. Phys. Chem. 1996, 100, 9714−9725. (19) Botrel, A.; le Beuze, A.; Jacques, P.; Strub, H. J. Chem. Soc., Faraday Trans. 2 1984, 80, 1235−1252. (20) Benson, H. G.; Murrell, J. N. J. Chem. Soc., Faraday Trans. 2 1972, 68, 137−143. (21) McRae, E. G. J. Phys. Chem. 1957, 61, 562−572. (22) Murugan, N. A.; Kongsted, J.; Rinkevicius, Z.; Agren, H. Phys. Chem. Chem. Phys. 2011, 13, 1290−1292. (23) Brooker, L. G. S.; Keyes, G. H.; Sprague, R. H.; VanDyke, R. H.; VanLare, E.; VanZandt, G.; White, F. L.; Cressman, H. W. J.; Dent, S. G. J. Am. Chem. Soc. 1951, 73, 5332−5350. (24) Beckmann, S.; Etzbach, K.-H.; Krämer, P.; Lukaszuk, K.; Matschiner, R.; Schmidt, A. J.; Schuhmacher, P.; Sens, R.; Seybold, G.; Wortmann, R.; et al. Adv. Mater. 1999, 11, 536−541. (25) Clays, K.; Persoons, A. Phys. Rev. Lett. 1991, 66, 2980−2983. (26) Marder, S. R.; Perry, J. W.; Tiemann, B. G.; Gorman, C. B.; Gilmour, S.; Biddle, S. L.; Bourhill, G. J. Am. Chem. Soc. 1993, 115, 2524−2526. (27) Kelley, A. M. J. Chem. Phys. 2003, 119, 3320−3331. (28) Leng, W.; Würthner, F.; Kelley, A. M. J. Phys. Chem. B 2004, 108, 10284−10294. (29) Leng, W.; Würthner, F.; Kelley, A. M. J. Phys. Chem. A 2005, 109, 1570−1575.

■

CONCLUSION Structural and electronic properties relevant to nonlinear polarization of a merocyanine dye have been investigated. The negatively solvatochromic nature of the dye indicates that it is in a zwitterionic state in all solvents. Any apparent reversal in experimental solvatochromism in the dye can be explained on the basis of more specific solvent interactions in solvents of lower dielectric. UV−vis spectroscopy supports the intuitively appealing notion of a large structural change associated with changing solvent polarity; however, the use of NMR and Raman suggests that structural changes associated with large changes in absorption energy are minimal. Calculations using solvent fields show a change in the structure of pyr3pi from having vanishing BLA in low dielectric solvent fields, to having large BLA in high strength solvent fields. This supports the idea of a high degree of structural change, but again the experimental evidence refutes this. Computational data were also used to calculate hyperpolarizability using both the two-state method and the finite field method. The two-state model shows the same trend as the HRS experiment, but this is misleading and there is a contradiction between the trend in BLA and hyperpolarizability attained. The finite field method corresponds well with calculated BLA and therefore is probably a more accurate reflection of the trend in relation to the calculated structure. It is suggested that use of spectroscopic data (especially solvent dependent Raman) is a way to remedy or recognize the problem of solvent field calculations underestimating solvent effects in lieu of explicit solvent models that can be efficiently and consistently applied. 5462



Article

(30) Leng, W.; Grunden, J.; Bartholomew, G. P.; Bazan, G. C.; Kelley, A. M. J. Phys. Chem. A 2004, 108, 10050−10059. (31) Würthner, F.; Yao, S.; Debaerdemaeker, T.; Wortmann, R. J. Am. Chem. Soc. 2002, 124, 9431−9447. (32) Di Bella, S.; Ratner, M. A.; Marks, T. J. J. Am. Chem. Soc. 1992, 114, 5842−5849. (33) Robinson, B. H.; Dalton, L. R.; Harper, A. W.; Ren, A.; Wang, F.; Zhang, C.; Todorova, G.; Lee, M.; Aniszfeld, R.; Garner, S.; et al. Chem. Phys. 1999, 245, 35−50. (34) Dalton, L. R.; Harper, A. W.; Robinson, B. H. Proc. Natl. Acad. Sci. U.S.A. 1997, 94, 4842−4847. (35) Yao, S.; Beginn, U.; Gress, T.; Lysetska, M.; Würthner, F. J. Am. Chem. Soc. 2004, 126, 8336−8348. (36) Liptay, W.; Wortmann, R.; Böhm, R.; Detzer, N. Chem. Phys. 1988, 120, 439−448. (37) Kasha, M.; Rawls, H. R.; Ashraf El-Bayoumi, M. Pure Appl. Chem. 1965, 11, 371−392. (38) Abbotto, A.; Beverina, L.; Bozio, R.; Bradamante, S.; Ferrante, C.; Pagani, G. A.; Signorini, R. Adv. Mater. 2000, 12, 1963−1967. (39) Kulinich, A. V.; Ishchenko, A. A.; Groth, U. M. Spectrochim. Acta, Part A 2007, 68, 6−14. (40) Hobley, J.; Malatesta, V. Phys. Chem. Chem. Phys. 2000, 2, 57− 59. (41) Zuliani, P.; Del Zoppo, M.; Castiglioni, C.; Zerbi, G.; Marder, S. R.; Perry, J. W. J. Chem. Phys. 1995, 103, 9935−9940. (42) Verbiest, T.; Clays, K.; Rodriguez, V. Second-Order Nonlinear Optical Characterization Techniques: An Introduction; CRC Press: New York, 2009. (43) Dalton, L. R. Adv. Polym. Sci. 2002, 158, 1−86. (44) Kanis, D. R.; Ratner, M. A.; Marks, T. J. Chem. Rev. 1994, 94, 195−242. (45) Murugan, N. A.; Kongsted, J.; Rinkevicius, Z.; Ågren, H. Proc. Natl. Acad. Sci. U.S.A. 2010, 107, 16453−16458. (46) Kay, A. J.; Woolhouse, A. D.; Gainsford, G. J.; Haskell, T. G.; Wyss, C. P.; Giffin, S. M.; McKinnie, I. T.; Barnes, T. H. J. Mater. Chem. 2001, 11, 2271−2281. (47) Kay, A. J.; Woolhouse, A. D.; Zhao, Y.; Clays, K. J. Mater. Chem. 2004, 14, 1321−1330. (48) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09, revision A.02; Gaussian, Inc.: Wallingford, CT, 2009. (49) Miertuš, S.; Scrocco, E.; Tomasi, J. Chem. Phys. 1981, 55, 117− 129. (50) Tomasi, J.; Mennucci, B.; Cammi, R. Chem. Rev. 2005, 105, 2999−3094. (51) Andersson, M. P.; Uvdal, P. J. Phys. Chem. A 2005, 109, 2937− 2941. (52) Horvath, R.; Gordon, K. C. Coord. Chem. Rev. 2010, 254, 2505− 2518. (53) Walsh, P. J.; Gordon, K. C.; Lundin, N. J.; Blackman, A. G. J. Phys. Chem. A 2005, 109, 5933−5942. (54) Lundin, N. J.; Walsh, P. J.; Howell, S. L.; McGarvey, J. J.; Blackman, A. G.; Gordon, K. C. Inorg. Chem. 2005, 44, 3551−3560. (55) Olbrechts, G.; Strobbe, R.; Clays, K.; Persoons, A. Rev. Sci. Instrum. 1998, 69, 2233−2241. (56) Teshome, A.; Kay, A. J.; Woolhouse, A. D.; Clays, K.; Asselberghs, I.; Smith, G. J. Opt. Mater. 2009, 31, 575−582. (57) Eaton, G.; Pena-Nunez, A. S.; Symons, M. C. R. J. Chem. Soc., Faraday Trans. 1 1988, 84, 2181−2193. (58) Cross, G. H.; Hackman, N. A.; Thomas, P. R.; Szablewski, M.; Pålsson, L. O.; Bloor, D. Opt. Mater. 2003, 21, 29−37. (59) Sainudeen, Z.; Ray, P. C. J. Phys. Chem. A 2005, 109, 9095− 9103. (60) Smith, G. J.; Middleton, A. P.; Clarke, D. J.; Teshome, A.; Kay, A. J.; Bhuiyan, M. D. H.; Asselberghs, I.; Clays, K. Opt. Mater. 2010, 32, 1237−1243. (61) Dapprich, S.; Komáromi, I.; Byun, K. S.; Morokuma, K.; Frisch, M. J. J. Mol. Struct. (THEOCHEM) 1999, 461−462, 1−21.

(62) Vreven, T.; Mennucci, B.; da Silva, C. O.; Morokuma, K.; Tomasi, J. J. Chem. Phys. 2001, 115, 62−72. (63) Cohen, A. J.; Mori-Sánchez, P.; Yang, W. Science 2008, 321, 792−794. (64) McGoverin, C. M.; Walsh, T. J.; Gordon, K. C.; Kay, A. J.; Woolhouse, A. D. Chem. Phys. Lett. 2007, 443, 298−303.

5463


Testing Computational Models of Hyperpolarizability in a Merocyanine

Recommend Documents