Molecular Origins of the High-Performance Nonlinear Optical

Article pubs.acs.org/JPCC

Molecular Origins of the High-Performance Nonlinear Optical Susceptibility in a Phenolic Polyene Chromophore: Electron Density Distributions, Hydrogen Bonding, and ab Initio Calculations Tze-Chia Lin,† Jacqueline M. Cole,*,†,‡,§ Andrew P. Higginbotham,† Alison J. Edwards,∥ Ross O. Piltz,∥ Javier Pérez-Moreno,⊥ Ji-Youn Seo,# Seung-Chul Lee,# Koen Clays,⊥ and O-Pil Kwon# †

Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge, CB3 0HE, U.K. Department of Physics, University of New Brunswick, P.O. Box 4400, Fredericton, E3B 5A3, Canada § Department of Chemistry, University of New Brunswick, P.O. Box 4400, Fredericton, E3B 5A3, Canada ∥ Bragg Institute, Australian Nuclear Science and Technology Organisation, New Illawarra Road, Lucas Heights, NSW 2234, Australia ⊥ Department of Chemistry, University of Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium # Department of Molecular Science and Technology, Ajou University, Suwon 443-749, Korea ‡

S Supporting Information *

ABSTRACT: The molecular and supramolecular origins of the superior nonlinear optical (NLO) properties observed in the organic phenolic triene material, OH1 (2-(3-(4hydroxystyryl)-5,5-dimethylcyclohex-2-enylidene)malononitrile), are presented. The molecular charge-transfer distribution is topographically mapped, demonstrating that a uniformly delocalized passive electronic medium facilitates the charge-transfer between the phenolic electron donor and the cyano electron acceptors which lie at opposite ends of the molecule. Its ability to act as a “push−pull” π-conjugated molecule is quantified, relative to similar materials, by supporting empirical calculations; these include bond-length alternation and harmonicoscillator stabilization energy (HOSE) tests. Such tests, together with frontier molecular orbital considerations, reveal that OH1 can exist readily in its aromatic (neutral) or quinoidal (chargeseparated) state, thereby overcoming the “nonlinearity-thermal stability trade-off”. The HOSE calculation also reveals a correlation between the quinoidal resonance contribution to the overall structure of OH1 and the UV−vis absorption peak wavelength in the wider family of configurationally locked polyene framework materials. Solid-state tensorial coefficients of the molecular dipole, polarizability, and the first hyperpolarizability for OH1 are derived from the first-, second-, and third-order electronic moments of the experimental charge-density distribution. The overall solid-state molecular dipole moment is compared with those from gas-phase calculations, revealing that crystal field effects are very significant in OH1. The solid-state hyperpolarizability derived from this charge-density study affords good agreement with gas-phase calculations as well as optical measurements based on hyper-Rayleigh scattering (HRS) and electric-field-induced second harmonic (EFISH) generation. This lends support to the further use of charge-density studies to calculate solid-state hyperpolarizability coefficients in other organic NLO materials. Finally, this charge-density study is also employed to provide an advanced classification of hydrogen bonds in OH1, which requires more stringent criteria than those from conventional structure analysis. As a result, only the strongest OH···NC interaction is so classified as a true hydrogen bond. Indeed, it is this electrostatic interaction that influences the molecular charge transfer: the other four, weaker, nonbonded contacts nonetheless affect the crystal packing. Overall, the establishment of these structure−property relationships lays a blueprint for designing further, more NLO efficient, materials in this industrially leading organic family of compounds.

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INTRODUCTION Organic nonlinear optical (NLO) materials have received considerable attention in recent years due to numerous potential photonic applications; for example, optical switches, frequency converters, electro-optic modulators, as well as terahertz (THz) and spectroscopy applications.1−4 Conjugated organic molecules containing electron-donating and -accepting groups can exhibit higher second-order nonlinearity, lower dielectric constants, faster optical response times, and higher optical thresholds than their inorganic counterparts. These superior properties of organic materials can be attributed to the © 2013 American Chemical Society

different mechanisms that give rise to the nonlinear polarization components in inorganic and organic materials. Inorganic materials rely on suitable geometric perturbations of the key ions within a solid-state crystalline structural framework of the compound, whereas organic materials rely on the transfer of electronic charge across the molecule.5 The optical response of NLO-active organic compounds is therefore much faster than Received: January 19, 2013 Revised: April 11, 2013 Published: April 12, 2013 9416

dx.doi.org/10.1021/jp400648q | J. Phys. Chem. C 2013, 117, 9416−9430

The Journal of Physical Chemistry C

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Recently, Kwon and co-workers reported a new series of organic NLO chromophores which are based upon a conjugated triene chain that acts as the charge-transfer bridge. Two six-membered rings are embedded at both ends of the chain to form a “configurationally locked polyene” (CLP) framework (see Figure 2).12 One of these CLP compounds,

that of inorganic compounds. Organic compounds are also attractive due to their versatility in synthetic design, as molecules can be “tailor-made” to suit a desired optical application. The best-known example of an industrially successful organic NLO compound is 4′-dimethylamino-N-methyl-4-stilbazolium tosylate (DAST) which exhibits a large second-order nonlinearity: approximately ten times larger than that of the inorganic NLO standard reference material, LiNbO3.6 DAST is an organic salt consisting of a stilbazolium cation and a tosylate anion. It is the Coulomb forces between the cation and anion that give DAST its noncentrosymmetric packing in the crystalline state, an essential feature for applications that employ bulk crystals. Despite its industrial success as an NLO material, DAST suffers from modest thermal stability.6−9 Improved thermal stability in organic NLO compounds is possible by incorporating aromatic rings within the conjugated π-bridging part of an organic molecule, between the electronic donor and acceptor groups.10 However, this chemical insertion frequently comes at the cost of inhibiting the intramolecular charge transfer characteristics of a compound since the aromatic ring lies along its primary electron-transfer pathway. The addition of an aromatic ring to improve thermal stability at the expense of such charge-transfer inhibition is known as the “nonlinearity-thermal stability trade-off” for organic NLO materials.11 This trade-off has long been known as a key inhibiting factor for the widespread adoption of organic NLO materials in industry. Nevertheless, it is possible to facilitate efficient charge transfer across the aromatic ring if the molecule can exist in both the neutral and charge-separated resonance forms at comparable energies (see Figure 1(a) and (b)). This is achievable by appropriate ortho or para substitution of the aromatic ring,5 resulting in a reduction of the aromatic stabilization energy and enabling the ring to interconvert between the two forms.

Figure 2. Plot of the triene bond distances from the selected CLP compounds, which shows an overall bond-length-alternation (BLA) decrease from electron donor to acceptor groups. The bond distances were retrieved from the structural data reported in the Cambridge Structural Database.

OH1 (2-(3-(4-hydroxystyryl)-5,5-dimethylcyclohex-2enylidene)malononitrile), has shown particular promise as a next-generation organic NLO material, displaying comparable second-order nonlinearity to DAST but with superior thermal stability. A summary of the optical and NLO properties of OH1 can be found in the literature.13 Low driving-voltage electrooptic waveguide modulators14 and efficient THz generators15 based on OH1 have also been successfully demonstrated. Furthermore, OH1 has recently become a commercially available product.16 The superior thermal stability of OH1 is due, in part, to its all-trans triene backbone that is stabilized by a configurationally locked cyclohexene ring. A 30−80 °C improvement in the thermal decomposition temperature has been reported previously in similarly established configurationally locked structures.10 This enhanced thermal stability is also likely to be due to the embedding of a phenyl ring at the electron-donating site. But can the electronic nature of the phenyl ring overcome the “nonlinearity-thermal stability tradeoff”? This study seeks to answer this question by probing the electronic structure of OH1, using high-resolution X-ray singlecrystal diffraction and complementary ab initio electron density calculations. The effect of the aromatic ring in OH1 on its molecular charge-transfer characteristics can then be understood, including its propensity to overcome intrinsic chargetransfer inhibition, pending that it can exist in both aromatic and quinoidal resonance forms. Prior to this study, the structure−property relationships associated with CLP-framework compounds have not been examined at the molecular scale in any great detail. This is despite the fact that the NLO properties of organic molecules are known to be highly influenced by the nature of their electronic charge-transfer and electron density distributions.5

Figure 1. (a) Schematic representation of the limited resonance structures of normal polyenes; (b) configurationally locked polyenes (e.g., OH1); (c) the HOMO and LUMO of OH1, which were calculated based on the experimentally derived (neutron) geometry using the B3LYP/6-311++G** level of theory. 9417



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its decomposition into its full tensorial components have only recently been shown to be possible. Experimental chargedensity studies are the basis of this derivation22 with results showing success for relatively homogeneous (organic) molecules, as illustrated via the application of experimental chargedensity data for the organic NLO materials DED-TCNQ23 and MBADNP.24 A comparison of the gas-phase and solid-state charge-density results therefore provides a unique insight into the crystal field effects in OH1. This is highly pertinent given the previous finding that hydrogen bonding influences significantly the NLO origins of OH1.25,26 Indeed, the supramolecular chemistry of OH1 is likely to be dictated by intermolecular hydrogen bonds, as opposed to Coulomb-force interactions that feature in DAST owing to its ionic nature. Several short intermolecular contacts in the OH1 crystal have been proposed as hydrogen bonds, based on the crystal structure determined from room-temperature X-ray diffraction data.25−27 A single-crystal neutron diffraction study of OH1 is also presented herein, in order that this hydrogen-bonding network could be further investigated. The neutron diffraction data are also shown to aid the charge-density study.

We refine the high-resolution X-ray diffraction data of OH1 within a multipolar model (MM) formalism17 that models the electron density using atom-centered spherical harmonics and Slater-type radial functions. The use of this formalism is required for highly polarizable molecules such as organic NLO compounds since the independent atom model (IAM), conventionally used for structure refinement, does not account for the electron density perturbations due to bonding effects such as polarization. The implicit relationship between spherical harmonics and bond orbital topologies within the MM formalism also allows the partitioning of electron distributions into distinct orbital representations and the calculation of atomic charges. The charge-density distribution of OH1 could therefore be analyzed in this study. This employed the Quantum Theory of Atoms in Molecules (QTAIM),18,19 which creates deformation electron-density maps and their associated Laplacian maps, and these, respectively, portray the bonding electron density within a molecule and the extent of local concentration or depletion of electronic charge. The QTAIM also permits the determination of electrostatic moments and atomic-basin integration for atomic property evaluations. Overall, a quantitative examination of the nature of the chemical bonding in OH1 is therefore possible, along with the determination of the electronic chargetransfer characteristics that underpin the structural origins of the NLO phenomenon. A theoretical complement to this experimental chargedensity study is also presented using theoretical structure factors that are generated by DenProp,20 based on the gasphase density-functional-theory (DFT) wave function, and refined within the multipole formalism; a gas-phase chargedensity study is afforded. The charge transfer and charge distribution of OH1 for the experimentally determined crystalline solid could then be compared with that of the DFT-calculated gas phase. Such a comparison is important since it allows the separation of molecular and supramolecular effects and the role that each contributes to the overall NLO activity of OH1 in its single-crystal state, the form of its primary industrial application. In addition, the gas-phase and solid-state charge-density distributions of OH1 are herein employed to calculate its NLO properties, via its molecular polarization. Indeed, the electronic polarization of a molecule in an electric field, E, is related to the nonlinear optical susceptibility of a molecule by the power series Pi = μi + αij Ej + βijk EjEk + γijkl EjEkEl + ...

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EXPERIMENTAL AND COMPUTATIONAL METHODS Both the X-ray and neutron diffraction data were collected at 120 K. High-resolution X-ray data were acquired in-house using a Rigaku Saturn 724+ CCD single-crystal X-ray diffractometer, which houses a molybdenum X-ray tube (Mo Kα: λ = 0.71073 Å) with focusing Rigaku SHINE optics for X-ray radiation intensity enhancement. The neutron diffraction experiment was carried out using the KOALA Laue diffractometer at the Bragg Institute, ANSTO, Australia.28 Since OH1 crystallizes in a noncentrosymmetric space group and contains oxygen as its heaviest element, the correct absolute structure cannot be determined unambiguously from Mo Kα radiation data. Consequently, a supplementary X-ray diffraction data set was collected on OH1 using Cu Kα radiation (Agilent SuperNova Dual single-crystal diffractometer). The crystal information and experimental conditions of the Mo Kα/Cu Kα X-ray and neutron experiments are summarized in Tables S1−S3 (Supporting Information). Conventional (IAM model) and multipole (MM model) refinements were employed using SHELX29/WinGX30 and XD200631 software packages, respectively. Prior to the multipole refinement, the LSDB32,33 code was applied for atomic local axes and symmetry assignment. All the ab initio calculations were performed with Gaussian0934 software. Other details about the sample preparation, diffraction data refinement and associated data analysis, ab initio calculations, and hyper-Rayleigh scattering measurements are available in the Supporting Information.

(1)

where μi is the dipole moment of the molecule, αij the molecular polarizability, βijk the first molecular hyperpolarizability, γijkl the second molecular hyperpolarizability, and so on. The first hyperpolarizability, βijk, is commonly used as the figure-of-merit for second-order nonlinear optical susceptibility. The first three terms of eq 1 are calculated for OH1 using both the gas-phase and solid-state charge-density distributions. The results are compared with ab initio Hartree−Fock (HF) and DFT calculations. An experimental measure of βijk obtained using hyper-Rayleigh scattering (HRS)21 is also compared to these charge-density-derived results for corroboratory purposes. Gas-phase (mostly calculated) and solution-based (mostly experimental) derivations of μi, αij, and βijk in NLO materials are somewhat commonplace. However, it is noteworthy that the solid-state experimental derivation of βijk for a material and

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RESULTS AND DISCUSSION A. Quantification of Molecular Charge Transfer. The neutron-derived structure of OH1 is given in Figure 3(a); associated bond geometry is available in the Supporting Information (Tables S4 and S5). Charge transfer in OH1 can be best assessed by considering this molecular structure in three constituent parts: its phenolic group (1) and two cyano groups (2), which act as the electron-donating (D) and electronaccepting (A) groups, respectively; D and A are connected to opposite ends of a π-electron conjugated hexatriene moiety (3)

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which mediates charge transfer across the molecule, resulting in a D···A “push−pull” system. These three molecular parts, when combined, form an almost perfectly planar system (mean plane deviation of all non-hydrogen atoms involved is 0.052 Å), demonstrating highly delocalized π-conjugation throughout the molecule. Such extensive delocalization is also evidenced via the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs), as calculated by DFT (see Figure 1c). The proclivity to π-conjugation is demonstrated by the abundance of electron-rich p-orbitals throughout the molecule, as represented by the dumbbell shapes projecting from alternating phases of electron density above and below the molecular plane. Molecular charge transfer is therefore achieved readily. These phases essentially switch between the HOMO and LUMO, demonstrating the conversion from a predominantly neutral (HOMO) to charge-separated (LUMO) resonance state when transiting from the ground to excited state. The ability of OH1 to interconvert between resonance states within a two-state system is therefore revealed. This finding that OH1 can indeed exist in the neutral and charge-separated state is encouraging, as this implies that charge transfer is not inhibited significantly by the phenyl ring. As the NLO properties of OH1 are known to be very promising, this structural confirmation might be expected. However, one can go a step further by quantifying the extent of electronic delocalization in OH1, using calculations that apply the “strength−length” structural relationship in bond geometry. 1. Quantifying the Extent of Aromatic versus Quinoidal Bonding Character. Despite the need for a high-resolution diffraction study to model the electronic distribution of highly polarizable organic molecules, e.g., NLO materials, the chemical-bond “strength−length” relationship can nevertheless be applied to a sufficiently accurate conventional IAM structure determination of a molecule. In the case of OH1, this enables one to assess the extent of aromatic versus quinoidal character in its phenolic ring; i.e., it offers insight into the tendency for OH1 to form neutral versus charge-separated resonance states, respectively. The 120 K neutron-derived structure of OH1 realized by this study was employed for this analysis since its bond geometry is much more accurate than a roomtemperature X-ray diffraction study, to which the previously reported structure of OH1 pertains.25−27 Two types of empirical calculations were performed to quantify the extent

Figure 3. OH1 crystal structure and packing: (a) a 50% probability atomic displacement ellipsoid plot of the neutron-derived structure (the five potential hydrogen bonds and the atomic labeling convention are also presented here); (b) the crystal packing diagram projected on the crystallographic bc plane showing the polar molecular layer and the two Csp3H···N(1) short contacts; (c) the crystal structure viewed along the b-axis which displays the primary intermolecular interaction (OH···N(2)) and Csp2H···N(2)/Csp2H···O(1) short contacts.

Table 1. Calculated BLA, the Phenyl-Ring Quinoidal Contribution to the Ground-State Derived from the HOSE Method, Reported Melting Point (°C), Thermal Decomposition Temperature (°C), and the Peak Absorption Wavelength (nm) with the Solvent Used for the Measurement of the CLP Compounds compound ID (CCDC No.) OH1 OH3 DAT1 DAT2 DAT3 DAV1 DAM1b PyT1 PyM3 a

neutron HF/6-311++G** B3LYP/6-311++G** (No. 682357) (No. 278086) (No. 278087) (No. 278088) (No. 621008) (No. 278089) (No. 293252) (No. 286962)

BLA

quinoidal contribution (%)

melting temp. (°C)a

decomposition temp. (°C)a

λabs(nm)/solvent, εa

0.0730 0.1150 0.0712 0.0809 0.0332 0.0855 0.0763 0.0781 0.0770 0.0781 0.0787

34.90 31.24 36.52 34.12 40.14 40.24 41.03 36.02 36.85 39.85

212

325

424/CH3OH, 33

283 205 235 174 220 218 178 213

310 275 293 313 278 290 290 270

424/CH3OH, 33 482/CHCl3, 4.81 502/CHCl3, 4.81 498/CH2Cl2, 4.81 505/CHCl3, 4.81 498/CHCl3, 4.81 521/CHCl3, 4.81 503/CHCl3, 4.81

Data acquired from refs 12 and 13. bThe reported X-ray structure is disordered. 9419



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(b). Harmonic-Oscillator Stabilization Energy (HOSE) Calculations. Given the importance of the phenyl ring in this study, the relative contribution of aromatic versus quinoidal character in the phenyl ring of OH1 was quantified explicitly; in effect, the associated contribution of the neutral versus chargeseparated resonance forms in these compounds is synonymous. Accordingly, an empirical harmonic-oscillator stabilization energy38,39 (HOSE) model was applied to OH1. This parallels the recent successful application of this model to quantify the para-quinoidal contributions of coumarin-based laser dyes40,41 in relation to their spectroscopic properties. The method also corresponds to the modulated conjugation concept.42,43 The HOSE model describes the energy by which a molecule is more stable than its Kekulé structure, and it can be extended to compute the relative contribution for each of the resonance states in benzene derivatives. Here, it was employed to calculate the quinoidal contribution of the phenyl ring in OH1 and, thence, to derive the relative contribution of its associated charge-separated state. Analogous calculations were also performed on the other “configurationally locked” hexatrienebased compounds in this series (see Table 1). The calculated contribution of the quinoidal resonance form correlates well with the reported UV−vis absorption peak wavelength (λmax) of this series of CLP framework compounds. For example, the calculated quinoidal contributions for OH1 and OH3 (2-(3-(4-hydroxystyryl)cyclohex-2-enylidene)malononitrile) are 34.9% and 34.1%, respectively, while λmax ∼ 424 nm for both OH1 and OH3;27,44 in contrast, the larger quinoidal contributions of DAT2, DAT3 (2-(3-(4(diethylamino)styryl)-5,5-dimethylcyclohex-2-enylidene)malononitrile), 12 PyM3 (2-(3-(4-(2-(hydroxymethyl)pyrrolidin-1-yl)styryl)-5,5-dimethylcyclohex-2-en-1-ylidene)malononitrile),45 and DAV1 (2-(4-(4-(dimethylamino)styryl)6,6-dimethylbicyclo[3.1.1]hept-3-en-2-ylidene)malononitrile)46 (40.1%, 40.2%, 39.9% and 41.0%, respectively) are associated with a more significant charge-separated resonance form of the molecules; this leads to a red-shift in λmax, with corresponding values of 502, 498, 503, and 505 nm, respectively. These slight shifts in the peak-absorption wavelengths may also be attributed, in part, to the different solvent polarities that were used for the UV−vis absorption spectroscopy (see Table 1). Nevertheless, this finding of a structure−property relationship is beneficial toward enabling a tunable UV/vis absorption peak wavelength material-design protocol. 2. Atomic Charges from Experimental Electron-Density Distributions. The modeling of electron density in a molecule, by assuming a spherical harmonic topology about each atom, enables the assignment of atomic charge according to the electron occupancies of the representative orbitals, as defined by the various refined multipolar populations. Assuming this pseudoatom method of atomic partitioning, the net charge on each atom is represented by the monopolar (spherical) populations of each atom (qmono). Accordingly, these net charges provide further insight into the charge-transfer properties of OH1. The majority of the negative and positive (i.e., gain and loss of electrons) net charges in the experimental charge-density study, MM_exp, is distributed around the cyano and phenolic fragments indicating that molecular charge transfer is dominated by these fragments. Table 2 shows that the phenol group consistently donates around 0.35e to the charge-transfer bridges, while the two cyano groups accept electrons at a level which renders the entire −C(CN)2 group with a total net charge of 0.21e (see also Table S7 (Supporting

to which the phenolic ring displays aromatic (neutral) versus quinoidal (charge-separated) character. (a). Bond-Length-Alternation (BLA) Calculations. The favored structural form of π-conjugation within a “push−pull” donor-to-acceptor organic molecule can be evaluated by a bond-length-alternation (BLA) parameter.35 BLA is defined as the difference between the averaged sum of all single C−C and double CC bond distances. The ideal situation for efficient molecular charge transfer would be a zero BLA value, calculated over all π-conjugated carbon-to-carbon bonds between the electron donor and acceptor, since this would correspond to perfectly delocalized π-conjugation. In practice, a completely null BLA (the cyanine limit) is prohibited owing to Peierls distortion,36 so a BLA value of 0.04 is generally considered to be optimal for organic NLO molecules.35,37 In contrast, a high BLA value indicates that one of the extreme canonical resonance forms dominates the ground-state structure; in the limit, the bond geometry of a molecular structure would resemble that of a wholly quinoidal or wholly aromatic canonical form. The BLA calculation for OH1 yielded a value of 0.0730. To understand the direct influence of the phenolic ring in OH1 upon this parameter, the corresponding BLA values of the closely related CLP-framework compounds were also calculated (see Table 1 and Table S6, Supporting Information). For example, the BLA calculated from previous reported structural data12 of DAT1 (2-(3-(2-(dimethylamino)vinyl)-5,5-dimethylcyclohex-2-enylidene)malononitrile) and DAT2 (2-(3-(4(dimethylamino)styryl)-5,5-dimethylcyclohex-2-enylidene)malononitrile) are 0.0332 and 0.0855. DAT2 differs from OH1 only by the presence of an −NMe2 group in place of the −OH group attached to the phenyl ring in OH1. DAT1 differs from DAT2 in that it does not contain a phenyl group and so is in effect a conjugation-truncated version of DAT2. The much lower BLA value for DAT1 supports the empirical reasoning that the phenyl-ring substitution does inhibit charge delocalization to some extent. Meanwhile, the nature of the parasubstituent on the phenyl group (−OH and −NMe2 for OH1 and DAT2, respectively) has a small but observable effect. Extending this BLA analysis to other phenyl-containing CLPframework compounds that feature different electron-donor groups (Figure 2) resulted in BLA values that lie in the range 0.07−0.09 (Table 1 and Table S6, Supporting Information). Closer scrutiny of the pattern of individual bond-length alternation across the triene charge-transfer bridge that stems from the phenyl ring in these compounds (Figure 2) reveals a consistent, progressively decreasing BLA across the triene moiety, proceeding from the electron donor to acceptor. OH1 fits into this observed trend, suggesting that the electrondonating “pushing power” of the para-phenyl terminal group is being “screened” by the presence of the phenyl ring. Meanwhile, the cyclohexene substitution has a negligible effect on the electron-acceptor “pulling” strength; this stands to reason since cyclohexene behaves essentially as a polyene chain in terms of its π-contribution to charge transfer. Thus, despite the electron-donating “screening” effect of the phenyl ring in OH1, its overall configurationally locked skeleton nonetheless has the ability to mediate the intramolecular charge-transfer process, mainly due to the strong electron-pulling effect of the unperturbed acceptor. This structural finding is corroborated by the outstanding performance of OH1 in both NLO response and thermal stability. As such, the nonlinearity-thermal stability trade-off in OH1 is somewhat defeated. 9420



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Table 2. Sum of Net Charges of the Selected Functional Groups Derived from Three Partitioning Methodsa MM_exp

a

MM_theo

group

qmono

qHirshfeld

qQTAIM

qQTAIM

∑q(OH) ∑q(Ph−OH) ∑q(CN)C(13)N(1) ∑q(CN)C(14)N(2) ∑q(C(CN)2) [∑q(−CH3)]average [∑q(>CH2)]average [∑q/∑Z]all

0.130 0.356 −0.134 −0.135 −0.208 −0.086 −0.049 0.000%

0.181 0.323 −0.095 −0.108 −0.151 −0.080 −0.054 −0.001%

−0.258 0.377 −0.168 −0.149 −0.189 −0.087 −0.043 0.015%

−0.087 0.321 0.041 −0.025 0.144 −0.031 −0.090 −0.093%

Unit: electrons.

Information) for the net charge of each individual atom). A similar trend is also observed for the MM_theo model. These findings correspond well to our initial postulate about the nature of the charge-transfer process; i.e., the phenol and the cyano group act as the primary electron donor and acceptor, respectively. Furthermore, a slightly asymmetric charge distribution was calculated between the two cyano groups where the charge transfer seems to tend more toward the −C(2)N(14) group. This can be rationalized by the observation that the N(14) atom acts as a hydrogen-bond acceptor of the primary intermolecular interaction, OH···N, the existence of which has been reported previously;25 this hydrogen bond will lead to an increase in electronegativity of the −C(2)N(14) group relative to that of the other cyano group. Table 2 also presents net charges for various functional groups of OH1 using two other atomic partitioning methods commonly employed in charge-density studies: the Stockholder and QTAIM methods. The associated net charges, qHirshfeld and qQTAIM, respectively, depict the same trends as described for qmono. The essential derivation of net charges for these three different atomic partitioning methods is given in the Supporting Information. 3. Topographical Analysis of Electronic Structure. The topography of the experimentally determined electronic charge distribution throughout OH1 is represented by the static model electron deformation density map, ρMM−ρIAM. Such maps are displayed for the phenol electron donor, the triene backbone, and the cyano electron acceptors of OH1 in Figure 4(a), (c), and (e), respectively. Analogous plots were also computed based on the theoretical charge density (MM_theo) model, for the purposes of comparison (see Figure 4(b), (d), and (f)). These plots reveal the nature and extent of the bonding electron density and polarization of the covalent bonds within the OH1 molecule. Bond (3,−1) critical points were also analyzed: these are the points of minimum electron density along the bond path of two bonded atoms, with local maxima of electron density in the two orthogonal dimensions to the bond direction. Owing to the nature of bonding, there must always be a critical point between any two bonded atoms. All bond (3,−1) critical points of the covalent bonds within the OH1 molecule were found in both experimental and theoretical charge-density models; this corroborates the strength of the models. Table 3 summarizes the topological properties at these bond critical points, which include the location of the bond critical point, bond electron density, ρ, the Laplacian of the electron density, ∇2ρ, and the ellipticity, ε. (Note that Table 3 only summarizes the values for the bonds on the main charge-

Figure 4. Static model deformation density maps of OH1 derived from MM_exp (left column) and MM_theo (right column) models with contour level at 0.05 e Å−3. (a) and (b): phenol; (c) and (d): triene; (e) and (f): two cyano groups (red solid lines: positive; blue dash lines: negative; black dotted lines: zero).

transfer path; Table S8 (Supporting Information) displays the full set of data for all bonds.) The first striking feature from the electron deformation density maps is that both of the lone-pair electrons of the oxygen (Figure 4(a) and (b)) and nitrogen (Figure 4(e) and (f)) atoms can be seen clearly, despite the fact that the peaks in the MM_theo maps are more pronounced. The peaks of the lone-pair electrons can also be identified in the associated Laplacian maps (∇2ρ) as shown in Figure S3 (Supporting Information). In Figure 4(e) and (f), both the experimental and theoretical deformation maps illustrate the high level of triple-bonded character in each cyano group. The aforementioned chargetransfer asymmetry (see Table 2) between the two cyano groups is also evident in the experimental deformation map (Figure 4(e)) but not in its theoretical counterpart (Figure 4(f)); this stands to reason since only the experimental chargedensity distribution will incorporate intermolecular effects, thereby corroborating hydrogen bonding as the probable origin of this charge asymmetry. The bond (3,−1) critical points of the two CN bonds lie very close to the carbon atoms, reflecting substantial electronic polarization from the more electronegative nitrogen atom. Electron density distributions in the adjoining C(12)−C(13) and C(12)−C(14) bonds appear to be polarized toward each cyano group, as expected from the similar electronegativity arguments. The slight displacement of the corresponding bond (3,−1) critical points from the bond9421



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Table 3. Summary of OH1 Topological Properties at Selected Conjugated Bonds (MM_exp: Upper Row; MM_theo: Lower Row)a ρ O(1)−C(1) C(1)−C(2) C(1)−C(6) C(2)−C(3) C(6)−C(5) C(4)−C(3) C(4)−C(5) C(4)−C(7) C(7)−C(8) C(8)−C(9) C(9)−C(10) C(10)−C(11) C(11)−C(12) C(12)−C(13) C(12)−C(14) N(1)−C(13) N(2)−C(14) O(1)−H(1A)

O(1)H(1A)···N(2) C(2)H(2A)···N(2) C(5)H(5A)···O(1) C(15)H(15A)···N(1) C(19)H(19C)···N(1)

MM_theo MM_exp

1.947 1.977 2.140 2.067 2.085 2.083 2.075 2.056 2.010 2.048 2.064 2.009 2.074 2.017 1.824 1.832 2.205 2.165 1.846 1.858 2.136 2.145 1.921 1.912 2.104 2.105 1.913 1.826 1.917 1.822 3.156 3.263 3.107 3.286 2.079 2.340 0.158 0.047 0.053 0.043 0.034

∇2ρ −15.68 −17.69 −18.15 −16.34 −18.83 −17.00 −15.91 −15.41 −17.45 −15.24 −16.34 −15.20 −17.14 −15.77 −11.38 −12.42 −20.19 −16.77 −12.81 −12.79 −17.86 −16.93 −14.07 −13.46 −18.07 −16.70 −13.42 −11.56 −14.23 −11.35 −24.22 −27.82 −9.39 −27.61 −27.47 −33.12 intermolecular interactions 2.515 0.673 0.975 0.641 0.505

Rij

d1

d2

ε

1.363 1.359 1.399 1.396 1.406 1.396 1.394 1.386 1.389 1.388 1.407 1.406 1.408 1.406 1.460 1.454 1.355 1.358 1.450 1.447 1.371 1.367 1.435 1.431 1.381 1.376 1.428 1.427 1.428 1.427 1.157 1.158 1.160 1.155 0.971 0.992

0.781 0.834 0.743 0.726 0.744 0.732 0.689 0.682 0.665 0.685 0.715 0.691 0.704 0.701 0.710 0.708 0.686 0.699 0.737 0.704 0.705 0.706 0.710 0.686 0.683 0.692 0.686 0.677 0.690 0.670 0.721 0.721 0.744 0.720 0.762 0.729

0.582 0.525 0.656 0.670 0.662 0.664 0.705 0.704 0.724 0.703 0.692 0.716 0.704 0.705 0.750 0.745 0.669 0.658 0.713 0.743 0.667 0.662 0.724 0.745 0.698 0.684 0.742 0.750 0.738 0.756 0.436 0.437 0.417 0.435 0.210 0.263

0.17 0.11 0.24 0.21 0.42 0.21 0.19 0.21 0.39 0.21 0.15 0.19 0.26 0.20 0.23 0.13 0.24 0.25 0.14 0.15 0.26 0.24 0.16 0.14 0.22 0.27 0.13 0.12 0.13 0.14 0.00 0.05 0.00 0.03 0.03 0.01

1.955 2.721 2.407 2.706 2.788

0.698 1.165 0.983 1.093 1.150

1.257 1.556 1.424 1.613 1.638

-

ρ is the electron density at bond critical points (e Å−3); ∇2ρ is the Laplacian of the electron density (e Å−5); Rij is the length of the bond path between atoms (Å); d1 and d2 are the distances between the critical point to the first and second atom specified in the bond column respectively (Å); ε is the ellipticity. a

significant π-bonding character in these bonds. Furthermore, the electron density in each bond of the triene charge-transfer bridge is distributed almost equally between the bonding atoms. Most of the C C bond critical points within the triene bridge lie close to the centers of each respective bond, except for the C(4)−C(7) bond, in which it lies slightly closer to the C(7) atom. No obvious electronic polarization was found within this fragment, and all bond ellipticities are typical for a delocalized π-bonded system, thus indicating that the triene moiety acts as a passive medium for transferring charge across the molecule, as anticipated. The triene-conjugating system may even extend further to the bonds vicinal to the CN groups, as judged by the slightly

distance midpoint toward the C(12) atom further supports this observation. The ellipticity, which is defined by ε = (λ1/λ2) − 1 (where λi are the eigenvalues of the Hessian matrix), is used to evaluate the amount of π-bonding character present in the bond; for example, ε = 0 pertains to no π-bonding electron density, as in the case of the σ bonds, whereas a large value of ε denotes a substantial amount of π-bonding present, as in the case of an aromatic ring or other conjugated olefinic chemical moieties. The average ellipticity of the C C bonds in the triene fragment is 0.20 from the MM_exp model, while a slightly lower ε of 0.15 corresponds to the average over all bonds emanating from C(12). This all indicates that there is 9422



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longer bond lengths of the two CN bonds. This comparison was revealed by a survey of all published CN bond distances under different chemical environments (see Table S9, Supporting Information) affording average CN bond distances of 1.136 Å (from 3383 total counts) and 1.142 Å (from 6023 total counts) for Csp3 and Csp2 hybridization, respectively; this compares with 1.1537(9) Å and 1.1589(9) Å (from the MM_exp model, see Table S4, Supporting Information) in OH1 for C(13)−N(1) and C(14)−N(2) bonds, respectively. The zero ellipticity values for both CN bonds (Table 3) are typical of triple bonds and are a simple consequence of the orthogonal nature of the two electron-rich π-orbitals in the bond cross-section of a triple bond, resulting in equal eigenvalues, λ1 and λ2. Substantial π-bonded character was also confirmed within the phenyl ring, as judged by the high ellipticities of all its C C bonds. The electron density distribution of the entire ring seems slightly polarized away from its hydroxyl substituent, which may be attributed to the electronic push effect from the donor side. A ring (3,+1) critical point was located at the center of the phenyl ring, positioned at 1.366, 1.437, 1.457, 1.461, 1.365, and 1.319 Å from atoms C(1) to C(6), respectively. The local depletion of charge at this center is 3.10 e Å−5, which is typical for a conjugated ring critical point. Finally, the ellipticity values associated with C(4) and C(7) are significant; since these atoms link the triene and phenyl groups, this shows that the π-orbital conjugation of both moieties extends each to the other, forming a fully delocalized π-bonding system. Overall, this topographical analysis shows that electronic delocalization propagates throughout the planar parts of the OH1 molecule. The phenol and two cyano donor and acceptor substituents are conjugated or partially conjugated to the triene bridge, invoking the “push−pull” effect. Meanwhile, the triene bridge acts as a uniformly delocalized passive electronic medium to facilitate the charge-transfer process. B. Determining Solid-State Electronic Moments and Nonlinear Optical Coefficients from Molecular Electron Density Distributions. The multipolar modeling of the electron density distribution of OH1 provides direct access to its electronic moments via the electron occupancy levels of a specific multipole on a given atom. Accordingly, the molecular moments of OH1 can be ascertained up to the order of spherical harmonics by which the multipoles were refined for all atoms, i.e., l = 3, the octupolar term. These moments can be used to derive all solid-state tensorial components of the molecular dipole, μi, linear polarizability, αij, and first hyperpolarizability, βijk, coefficients via empirical calculations.22 1. Molecular Dipole Characteristics. Within Bader’s QTAIM theory, the computation of the electrostatic moments is defined as a volume integral of the desired property density, i.e., the electron density multiplied by a specific geometrical expression, over the basin, Ω. For example, the atomic zerothorder moment (the monopole) is an integral of the electron density ρ over the atomic basin (see Supporting Information). Similarly, the first-order atomic moment (the dipole), which measures the extent and direction of the electronic charge cloud shifted with respect to its nucleus, is defined by the integration of the electron density multiplied by the radius vector (r) over the atomic basin Ω μ(Ω) = −

∫ ρ(r)rΩdr

Since Bader’s atom is additive, the total molecular charge is the sum of the individual atomic charges. Accordingly, the total dipole moment of the system (molecule or fragment) is defined as a sum over the net-charge contributions and the first-order moments of all atoms in the system μtot =

∑ [qΩi X i + μi (Ω)] i

(3)

The vectorial components of the solid-state molecular dipole moment for OH1 are derived from MM_exp via Bader’s and Hirshfeld’s partitioning methods, as illustrated in Figure 5. As

Figure 5. Molecular unabridged moments derived from theoretical calculations (LC-BLYP, CAM-B3LYP, B3LYP, and HF) and chargedensity studies (MM_theo and MM_exp). The moments are in Debye·Å(l−1) unit, where l = 1, 2, and 3 stand for first-order (a), second-order (b), and third-order (c) unabridged moments, respectively.

discussed further in the Supporting Information, the differences in the individual atomic charges integrated by the Stockholder and QTAIM methods are solely due to the different partitioning schemes. As a result, the dipole moments computed from these partitioning methods are almost identical. Complementary gas-phase ab initio calculations of the dipole moment for OH1 using Hartree−Fock and DFT methods are also provided for comparison. This demonstrates a significant enhancement of the dipole moment (by 7−8 D) from the gas to solid state, which is presumably due to crystal field effects. This presumption is corroborated by a secondary comparison of the ab initio results with the molecular dipole moment derived from the theoretical charge-density model (MM_theo). In contrast to MM_exp, the MM_theo electron density distribution contains no crystal field effects since it was calculated from the isolated-molecule wave function, while μi from both ab initio and MM_theo results agree well with each other. Considering the individual vectorial components of μi for MM_exp in comparison to the gas-phase calculations, it is evident that the solid-state enhancement of OH1 essentially arises from the μz direction. This crystal field effect anisotropy can be explained via an analysis of the crystal packing of OH1 which shows that the molecules form a head-to-tail sequential chain due to the strong OH···N intermolecular hydrogen bonding, and the main molecular charge-transfer direction is closely aligned with the z-direction (∼ ± 22° projected onto the bc plane).13 To further support the conjecture that this

(2) 9423



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OH···N hydrogen bond is the primary cause of the crystal field effects, DFT calculations were carried out on a series of dimer, trimer, tetramer, and pentamer clusters of OH1 molecules, using the B3LYP functional and both 6-31++G**/6-311+ +G** basis sets. These calculations realized an enhancement of ∼5 D between the dipole moment of the largest cluster relative to that of the isolated molecule (see Figure 6(a)); these findings are in line with the results obtained from the solid-state experimental charge-density study.

It is worth highlighting that since charge-density experiments probe crystal structure data, this method uniquely enables a solid-state evaluation of all tensorial coefficients of αij and βijk, whereas all experimental property measurements that derive αij and βijk are based on the characterization of a material in the liquid, solution, or gaseous phase. The molecular moments (second- and third-order unabridged moments) acquired from both MM_exp and MM_theo models, using the center of charge as the origin, are shown in Figure 5. In common with the dipole moment, the high-order molecular moments derived from Stockholder and QTAIM methods are consistent with each other. When comparing the second- and third-order moments from MM_exp with those of the theoretical predictions (i.e., MM_theo model and HF/DFT calculations), marked differences are only found in Qzz, Oxxx, Oxxz, Oxzz, and Ozzz, which are all the tensorial components that contribute to the overall x,zdirection (hyper)polarizability. Such disparities parallel those of the dipolar case and are not surprising since the second- and third-order moments of MM_exp will be equally affected by crystal-field forces, while those of MM_theo reflect OH1 in its isolated molecular form. The molecular moments calculated from the MM_theo model are slightly smaller than those predicted directly from the B3LYP wave function. The MM_theo model was refined against theoretical structural factors that were generated based on the same B3LYP wave function, but this difference is presumably a result of inadequate fitting owing to the truncated nature of the multipole expansion of the present model. Overall, the fact that the molecular moments acquired from both charge density analyses (MM_exp and MM_theo) agree fairly well with those of ab initio predictions is encouraging since a similar trend may be expected from the (hyper)polarizability values derived from these moments via eqs 4 and 5. Considering that both MM_exp and MM_theo were modeled based on the multipole formalism, the full set of tensorial components for αij and βijk for these two models was first compared via Figure 6(b)−(d). In common with the molecular moments, the αij and βijk from MM_exp and MM_theo are consistent with each other, as expected. Since the focus on OH1 concerns its second-order nonlinear optical properties, which pertain to the first hyperpolarizability at the molecular scale, the moments-derived βijk tensor was further studied; corresponding evaluations of βijk are summarized in Table 4. These are presented in terms of the associated static (zero frequency) hyperpolarizability, β0, and the vector

Figure 6. (a) Theoretical estimate of the increasing dipole moment enhancement of OH1 across a series of molecular clusters (from dimer to pentamer), involving the OH···N hydrogen bond as the principal intermolecular interaction. (b−d) Molecular polarizability (αij) and hyperpolarizability (βijk) coefficients for OH1, as derived based on eqs 4 and 5 from MM_exp (dark color) and MM_theo (light color) models.

2. Molecular (Hyper)polarizability Coefficients. In the same way that the first-order dipolar electronic moment of the charge distribution relates to the molecular dipole moment, the second- and third-order moments can be directly related to the linear polarizability, αij, and first-order hyperpolarizabilty, βijk.47 Since αij and βijk are related to the optical refractive index and the second-order nonlinear optical process, respectively, it is pertinent to study the molecular moments of OH1. Early attempts to evaluate αij and βijk from molecular moments derived from experimental electron density distributions resulted in values that were orders of magnitude different from those determined by optical measurements.48 However, following Robinson, Zyss, and others (see ref 22 and references therein), under the Unsöld approximation, and subsequently introducing a correction factor to account for the total electron number of the subject molecule, we recently found that αij and βijk can be evaluated reliably from these charge-density-derived ground-state molecular moments for relatively homogeneous molecules,22 according to 2 αxy ,0 = (Q xx + Q yy)Q xy (4) n

Table 4. Comparison of the Static First Hyperpolarizabilties Derived from Experimental and Theoretical Methods unit: 10‑30 esu MM_exp MM_theo

and ⎛2⎞ ⎜ ⎟ (Q Q + Q yyQ zz + Q xxQ zz)Oxyz xx yy ⎝n⎠

HF DFT

2

βxyz ,0 =

(5) EFISH

where Qij and Oijk refer to the second and third Cartesian unabridged moments of the molecular charge distribution, respectively.

HRS 9424

Stockholder QTAIM Stockholder QTAIM B3LYP CAM-B3LYP LC-BLYP in chloroform in dioxane in methanol

|β0|

|βμ|

46 39 39 38 45 97 83 70 110 ± 30

45 38 37 37 28 73 62 52 139 69 -

values were derived according to eqs 4 and 5

from ab initio calculations

see ref 16 this work



Article

Table 5. Summary of the Geometrical (Bond Lengths/Angles) and Bond-Energy (Local Kinetic, Potential, and Total Energies) Properties of the Potential Hydrogen Bonds Attained from Neutron-Derived and MM_exp Structure potential HBs

O(1)H(1A)···N(2)

sum of VdW, Å d(H···A), Å d(D···A), Å ∠(D···H···A), ° ∠(H···A···Y), ° Sym. Opt.

2.75 1.945(3) 2.915(2) 177.2(3) 174.7(1) 3/2 − x −1/2 + y −3/2 + z

G(rBCP), kJ·mol−1 V(rBCP), kJ·mol−1 EHB, kJ·mol−1 H(rBCP), kJ·mol−1 |V(rBCP)|/G(rBCP)

60.11 −51.72 25.86 8.39 0.86

C(2)H(2A)···N(2)

C(5)H(5A)···O(1)

C(15)H(15A)···N(1)

geometrical properties from neutron-derived structure 2.75 2.72 2.663(3) 2.377(4) 3.469(2) 3.360(2) 130.5(2) 149.3(3) 126.4(1) 118.5(2) 3/2 − x 1−x −1/2 + y −y −3/2 + z 1/2 + z hydrogen-bond energies derived from topological descriptors 14.14 20.04 −9.94 −13.53 4.97 6.77 4.20 6.51 0.70 0.68

C(19)H(19C)···N(1)

2.75 2.672(3) 3.715(2) 158.1(2) 89.6(1) 3/2 − x −1/2 + y −1/2 + z

2.75 2.745(4) 3.685(2) 143.7(3) 98.6(1) 3/2 − x −1/2 + y −1/2 + z

13.29 −9.12 4.56 4.17 0.69

10.29 −6.82 3.41 3.47 0.66

term with its x and y cross terms, βyzz and βxzz, being secondary. βxxx and its z cross term, βxxz, are also significant. The preponderance of the in-plane βzzz term is also evidenced by the overall dominance of the reduced vectorial component, βz. These conclusions provide good consistency, although one must bear in mind the large experimental errors associated with the optical measurements and the significant assumptions involved in the derivation of a solid-state value of βijk from the experimental charge-density distribution. It is, however, very encouraging that the latter derivations correlate well with theory and compare with the optical measurements within an order of magnitude; indeed, this level of agreement is considered to be good, in relation to that demonstrated for other organic nonlinear optical materials.22−24 C. Supramolecular Considerations for Nonlinear Optical Properties. The optical coherence length of an organic material typically spans a number of molecules. Therefore, the nonlinear optical properties of an organic molecule can be strongly influenced by its supramolecular environment, as we have already observed via crystal field effects. Hydrogen bonding can have a particularly marked supramolecular impact on NLO properties53,54 since these are the strongest type of intermolecular interaction and they are highly directional. In particular, the nature of intermolecular interactions can influence (1) molecular charge transfer where electron donors or acceptors are involved in hydrogen bonding especially within a layer of planar organic molecules; (2) the angle between the molecular charge-transfer axis and the crystallographic polar axis, i.e., the NLO phase-matching angle, which is ideally 0° for an orthorhombic crystal system55 as per the symmetry of OH1; and (3) the overall crystal packing efficiency which governs all sorts of crystal field forces and, consequentially, the level of thermal stability of a molecule. Therefore, it is important to understand the nature of the hydrogen-bonding network in OH1, in the context of these three NLO-related aspects. The previous report on the crystal structure of OH1 from room-temperature X-ray diffraction25−27,56 suggested that five intermolecular interactions were present; tentative hydrogen-bond separations were given, although X-rays cannot locate hydrogen accurately. In contrast, the neutron-derived crystal structure of OH1, reported herein, gives an accurate measure of hydrogen

hyperpolarizability, βμ, the projection amplitude of β along the dipole moment direction; this form of β enables a ready comparison with optical measurements of β. The |β0| for OH1 derived from the moments-based method for the MM_exp model is ∼45 × 10−30 esu, which correlates well with the ab initio predictions. The |β0| calculated by the B3LYP functional is almost double that of the HF result, whereas the improved CAM-B3LYP and LC-BLYP functionals provide values that are in between the HF and B3LYP predictions. To further validate the moments-derived first hyperpolarizabilties, an independent optical measurement was carried out using the high-frequency demodulated hyperRayleigh scattering method.49 This afforded a βHRS signal of 1140 ± 300 × 10−30 esu at 800 nm in methanol solution, and by applying the two-level model,50−52 the static first hyperpolarizabilty, |β0,HRS|, was determined to be 110 ± 30 × 10−30 esu. The ratio of the intensities between the vertical and horizontal state of the scattered second-harmonic light was characterized as ∼3.2, which reflects the dipolar characteristic of OH1. The measured β0,HRS can be compared with results from electric-field-induced second harmonic generation (EFISH):25 βEFISH = 69 × 10−30 esu in dioxane and 139 × 10−30 esu in chloroform, respectively. Note that βEFISH is the projected component along the dipole direction and so is associated with βμ. Bearing in mind the three different solvents used for these optical measurements, and the relative ability of these solvents to undergo hydrogen bonding with an OH1 molecule, the HRS and EFISH measurements are best compared between the results from methanol and chloroform, respectively. Meanwhile, dioxane is unlikely to form hydrogen bonds with OH1; indeed, the EFISH results of OH1 in dioxane are much more akin to both gas-phase calculations and solid-state experimental chargedensity-based evaluations of |βμ|, where no solvent is present. The implied correlation between an absence of solvent···OH1 hydrogen bonding and gas-phase and solid-state |βμ| values for OH1, and that the gas-phase (Hartree−Fock) and solid-state values are similar, tends to suggest that the influence of crystal field effects is not so strong on β, in contrast to its marked effect on μ. The βijk coefficients of OH1 revealed by the solid-state charge-density derivation nonetheless demonstrate a distinct level of anisotropy which is typical for a planar organic push− pull conjugated molecule; vis a vis, βzzz is by far the dominant 9425



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neighboring layers being twisted by ∼40° in the bc plane owing to a C(5)H(5A)···O(1) short contact and steric hindrance caused by the methyl substitution (C(18)). The two methyl groups substituted onto the nonconjugating cyclohexene ring and the associated short contacts are known to dictate the crystal packing arrangement of OH1 and other similar compounds.27,44 For example, it has been reported that OH1 derivatives which differ from OH1 by the absence of either one (i.e., OH2) or both methyl groups (i.e., OH3) crystallize into monoclinic space group, Cc, rather than orthorhombic Pna21 as per OH1. By removing the steric effects of both methyl substitutions, for example, in the case of OH3, the molecules are expected to pack more closely. This empirical observation was substantiated by a calculation of the Kitaigorodskii packing index.60 The higher the value of this index, the more efficient the packing (less space between molecules). These calculations were performed using the PLATON program,61 and the packing indices at room temperature for OH1 and OH3 were found to be 66.4% and 70%, respectively. A similar trend was found in related configurationally locked compounds, such as DAT2 and DAM1 (2-(3-(4-(dimethylamino)styryl)cyclohex-2-enylidene)malononitrile).12 The former has the double methyl substitution on the nonconjugating fragment as per OH1, whereas the latter possesses no such substitution (see Figure 2 and Figure S4, Supporting Information). The packing indices for DAT2 and DAM1 are 66.1% and 69.5%, respectively; the difference in packing indices between DAT2 and DAM1 is thus similar to that of the OH compounds, i.e., averaging a 3.5 ± 0.1% enhancement of the packing efficiency in both companions. The higher packing efficiency also leads to stronger intermolecular interactions, which is reflected in OH3 by its shorter primary OH···NC hydrogen bond as well as its higher melting point when compared to OH1. 2. Advanced Hydrogen-Bond Classification via QTAIM Analysis. On the basis of all these considerations, the nature of all the hydrogen bonding in OH1 appears to influence positively all three NLO aspects outlined above. However, these considerations assume the classification of hydrogen bonds according to conventional structural criteria. One can in fact extend this classification beyond simple geometric considerations using a full QTAIM-based analysis of the potential hydrogen bonds.62−64 Thereupon, a hydrogen bond can be classified according to much more stringent criteria, using the topological analysis of the total electron density to assess whether or not these putative hydrogen bonds conform with certain expectations of a hydrogen bond in terms of charge and local kinetic and potential energy. For the QTAIM methodology, there are eight criteria that need to be fulfilled to ensure a hydrogen bond exists as proposed by Koch & Popelier;65 these comprise the existence of: a bond critical point, low bond electron density at the bond critical point, a positive value for the Laplacian of the electron density, mutual penetration of both the hydrogen and acceptor atoms, loss of charge of the hydrogen atom due to the formation of the hydrogen bond, energetic destabilization of the hydrogen atom, a decrease in the dipole moment, and a reduced volume of the hydrogen atom. The first four criteria can be taken together, according to the standard topological qualifiers for QTAIM. First of all, the bond critical points of all five short intermolecular contacts, identified via the conventional structural analysis, were located from the experimental multipole model. The topological properties at

positions and so is well suited to hydrogen-bonding characterization. 1. Conventional Hydrogen-Bond Classification via Neutron Diffraction. The five intermolecular interactions that were proposed by Kwon and co-workers25−27 (see Figure 3(a)) turned out to be the same as those identified by neutron diffraction, based on the hydrogen-bond classification criteria used in conventional structural analysis: a hydrogen bond is defined as DH···A, where “D”, “H”, and “A” stand for the proton donor, hydrogen, and proton acceptor atom for the given hydrogen bond. The initial detection of possible hydrogen bonds in this structure was performed using Mercury57 (version 3.0) based upon the following two acceptance criteria: the interatomic distance between the hydrogen and the potential hydrogen-bond acceptor (i.e., d(H···A)) is less than the sum of the van der Waals radii;58 the angle at the donor hydrogen atom (∠DH···A) is larger than 120°, as suggested by Wood et al.59 Despite the fact that the exact geometrical definition of a hydrogen bond is still debatable, the criteria applied here were derived from a database statistical analysis and interaction energy calculation, which provides a practical guideline to identify the most important interactions. Table 5 presents the associated interatomic distances, angles that subtend hydrogen atoms and hydrogen-bond donor atoms, and the corresponding symmetry operations of the identified potential hydrogen bonds. The primary supramolecular interaction in OH1 is the OH···NC linear hydrogen bond with the oxygen atom of the phenolic hydroxyl group as the donor and the nitrogen atom of the nitrile group as the acceptor. The proton donor and acceptor of this OH···NC hydrogen bond are not only located at the two geometrically opposed ends of the molecule but also overlay with the intramolecular (electronic) charge-transfer donor/acceptor groups. Thus, the intermolecular hydrogen bond may be stabilized by the intramolecular charge-transfer process. The formation of the weak CH···O (H(5A)···O(1)) and CH···N (H(2A)···N(1)) intermolecular solid-state interactions also affects the molecular charge transfer slightly since they induce torsion within the molecule; in particular, the phenol ring twists by 5.88° with respect to the mean conjugated plane which is justifiably attributed to the C(5)−H(5A)···O(1) interaction since this twist was not observed in the energy-minimized structure calculated in the gas phase (i.e., geometry optimized from HF/6-311++G** and B3LYP/6-311++G** levels of theory). Since the OH···NC hydrogen bond forms between the two opposite ends of the adjacent molecules, it assembles the molecules in the solid state as an infinite molecular polar chain. As shown in Figure 3(b), the interlaced parallel chains form a molecular layer within the OH1 crystal, with adjacent chains being separated by around 3.370 Å. Due to this directionality of the OH···N hydrogen bond and steric effects of the substituted methyl group (C(19)) on the nonconjugated cyclohexene ring, the chains form a wavelike shape, and the main charge-transfer directions (from electron donor to acceptor) of sequential molecules within this chain deviate from the overall polar chain direction by ∼22°. Two weak intermolecular interactions were identified between these adjacent chains: H(15A)···N(1) and H(19C)···N(1) short contacts (see Figure 3(c)). Overall, the three-dimensional bulk crystal packs together by the stacking of these parallel chains, with the polar directions of the chains in 9426



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these bond critical points for each interaction are given in Table 3. Next, local depletions of charge were revealed at the regular bond critical points of all of these short contacts as demonstrated by the low electron density and the all-positive ∇2ρ values. Positive ∇2ρ values represent an ionic (as opposed to covalent) nature of bonding, i.e., an electrostatic interaction, as exemplified by a hydrogen bond. The larger the magnitude of ∇2ρ, the stronger the electrostatic interaction; the relative magnitudes of ∇2ρ for the five intermolecular interactions are therefore consistent with the proposed relative strengths of hydrogen bonds, as classified by conventional structural criteria. The fourth criterion demands that the hydrogen and the acceptor atom penetrate each other. That is, for a given intermolecular short contact, the bonding radii for hydrogen and acceptor atom, as defined by the distances from the two nuclei to the bond critical point, are less than their respective nonbonding radii, as defined by their van der Waals atomic radii or the distances out to the 0.001 au or 0.002 au electron density contours in the gas-phase system. This criterion, to some extent, has been examined already by one of the aforementioned conventional structural tests (i.e., d(H···A) < the sum of the van der Waals radii). Nevertheless, to complete the entire analysis within the QTAIM framework, the modified standard nonbonding radii derived purely from QTAIM, as proposed by Klein,63 were used in this test. Interatomic penetrations of all the hydrogen and acceptor atoms involved in these five short contacts were revealed. However, only the O(1)H(1A)···N(2) interaction displays a significant level of penetration for both hydrogen and acceptor atoms; moderate atomic penetrations were found in the C(2)H(2A)···N(2) and C(5)H(5A)···O(1) short contacts, while the atomic penetration for the two weakest (judging by the d(H···A)) short contacts is almost negligible (see Table S10, Supporting Information). Within the scope of the QTAIM theory, the next four criteria were examined by assessing the relevant differences in the atomic properties (i.e., the integrated properties of the hydrogen and acceptor atoms) observed in an isolated molecule (via the MM_theo model) compared with those of a molecule modeled within a crystal lattice (via the MM_exp model). These results are summarized in Table S10 (Supporting Information). The atomic basin integrations for inspecting these properties were carried out using the XDPROP and TOPXD modules in XD200631 for both MM_exp and MM_theo models. Overall, while all intermolecular interactions meet the first four criteria, the QTAIM classification assessment of the last four criteria conflicts with that of the conventional structural analysis; indeed, it appears that only OH···N readily f ulf ills all of the eight criteria for a hydrogen bond, proposed by Koch and Popelier. The other four short contacts merely satisf y the criteria. 3. Calculation of Hydrogen-Bond Energies. To assess the bond energies of these short contacts, the bonding energies derived from topological descriptors were computed. Following Abramov,66 the local kinetic energy density at the bond critical point is given by G(rBCP) =

3 1 (3π 2)2/3 × ρ5/3 (rBCP) + ∇2 ρ(rBCP) 10 6

V (rBCP) =

1 2 ∇ ρ(rBCP) − 2G(rBCP) 4

(7)

The total energy H(rBCP) is then given by the sum of the local kinetic and potential energy H(rBCP) = G(rBCP) + V (rBCP)

(8)

and the hydrogen-bonding energy, EHB, can be expressed as 1 E HB = − V (rBCP) 2

(9)

As shown in Table 5, the hydrogen-bond energy of the OH···N interaction is ∼26 kJ/mol, whereas, for the other short contacts, the hydrogen-bond energies are all in the range of 3− 7 kJ/mol, which is only marginally higher than the thermal energy, RT (∼2.5 kJ/mol). When considering the energetic stabilization of this bond, the OH···N contact is, once again, regarded as a hydrogen bond, while the other intermolecular interactions are considered to be simply short contacts. The Laplacian map of this OH···N hydrogen bond is shown in Figure S5 (Supporting Information), illustrating the directional preference of the acceptor atom of this hydrogen bond: the H(1A) atom is pointing toward the lone-pair electron of the N(2) atom. A local depletion of charge is clearly visible in the region between the H(1A) and N(2) atoms, which is the typical characteristic for a hydrogen bond. Overall, this advanced classification of hydrogen bonding confirms the OH···N short contact to be a hydrogen bond, while the other four previously identified hydrogen bond candidates are best regarded as simply short intermolecular contacts. This description is consistent with the three NLO factors that are influenced by all five types of intermolecular contacts. Only the first factor requires an intermolecular interaction to be explicitly a hydrogen bond since an electrostatic interaction is needed to enhance molecular charge transfer. The second two factors concern crystal packing, and so electrostatic interactions per se are not so important intermolecular contacts can be influential on steric or other electronic grounds, to afford the required layer integration and crystal packing efficiency.

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CONCLUDING REMARKS This study has illustrated a detailed molecular and supramolecular interrogation of the organic phenolic polyene compound, OH1, which exhibits high-performance NLO activity with excellent thermal stability, such that OH1 is already being commercialized. The origins of its NLO performance from the perspective of electronic charge transfer have been established. The factors involving intermolecular interactions that influence the NLO properties on the supramolecular scale have also been assessed. The ability to calculate all solid-state first hyperpolarizability tensorial coefficients for OH1 from the experimental electron density distribution has also been demonstrated. This lends very timely support to the recently revised approach to determine this solid-state property22 and paves the way for such studies on other organic molecules to follow suit. The overall findings of this work will hopefully help to design even more promising organic NLO materials in the phenyl polyene chemical family. By considering the results for OH1 as core information about a set of molecular building blocks rather than as a unitary CLP framework, one could further employ them to inform the molecular engineering of a new chemical

(6)

and from the local virial theorem,67 the local potential energy, V(rBCP), can be derived, 9427



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Chemistry Software (NSCCS) at Imperial College London and contributions from its staff in supporting this work.

class of organic NLO materials. Such quantum-tailored molecular design lies at the center of high-throughput materials discovery efforts that are starting to emerge.68 These developments are being motivated by the rapidly increasing demand for more efficient materials for the telecommunications and data storage industries; such materials will drive down the intensifying energy consumption that is being caused by the amassing globalization and burdening upon information technology resources.

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ABBREVIATIONS NLO, nonlinear optical; CLP, configurationally locked polyene; IAM, independent atom model; MM, multipolar model; QTAIM, Quantum Theory of Atoms in Molecules; DFT, density-function theory; HF, Hartree−Fock; B3LYP, Becke three-parameter hybrid functional combined with Lee−Yang− Parr correlation functional; HRS, hyper-Rayleigh scattering; EFISH, electric-field-induced second harmonic generation; HOMO, highest occupied molecular orbital; LUMO, lowest unoccupied molecular orbital

ASSOCIATED CONTENT

S Supporting Information *

CCDC 927886-8 and CCDC 928258 contains the supplementary crystallographic data for this paper. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif. Sample preparation, X-ray and neutron diffraction experimental details and associated data analysis, ab initio calculations, and hyperRayleigh scattering measurement details are available. This material is available free of charge via the Internet at http:// pubs.acs.org.

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REFERENCES

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS TCL acknowledges the Taiwanese Government for a Studying Abroad Scholarship. JMC is grateful to the Royal Society for a University Research Fellowship, the University of New Brunswick for The UNB Vice-Chancellor’s Research Chair, and NSERC for Discovery grant, 355708. APH is indebted to the Winston Churchill Foundation of the United States for an eponymous scholarship. OPK thanks the support by the Priority Research Centers Program through the National Research Foundation of Korea (NPF) funded by the Ministry of Education, Science and Technology (2012−0006687). The OPAL reactor, ANSTO, Australia, is acknowledged for access to neutron scattering facilities via program proposal, ID 1236. The authors would like to thank Professor Chris Frampton from Pharmorphix, part of the Sigma-Aldrich Corporation, for access to a single-crystal diffractometer with a Cu Kα X-ray source and his associated assistance in realizing the absolute structure of OH1. The authors would like to thank Dr. Anatoliy Volkov from Department of Chemistry, Middle Tennessee State University, USA, for kindly providing both DenProp and WFN2SHELX codes and helpful advice on the refinement of the theoretical structure factors in construction of the MM_theo model in this work. The authors also would like to thank Dr. Katarzyna N. Jarzembska from the Chemistry Department, University of Warsaw, Poland, for kindly providing the LSDB code and useful discussions related to the constraints/restrictions assignment of the multipole refinement. The authors would like to acknowledge the use of the EPSRC UK National Service for Computational 9428



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Molecular Origins of the High-Performance Nonlinear Optical

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