Designing Efficient Azobenzene and Azothiophene Nonlinear Optical

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Designing Efficient Azobenzene and Azothiophene Nonlinear Optical Photochromes Titouan Jaunet-Lahary, Agisilaos Chantzis, Kathy J. Chen, Adèle D. Laurent, and Denis Jacquemin J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp510581m • Publication Date (Web): 12 Nov 2014 Downloaded from http://pubs.acs.org on November 18, 2014

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The Journal of Physical Chemistry

Designing Efficient Azobenzene and Azothiophene Nonlinear Optical Photochromes Titouan Jaunet-Lahary†, Agisilaos Chantzis†,*, Kathy J. Chen†, Adèle D. Laurent†, and Denis Jacquemin†,‡,* †

Laboratoire CEISAM-UMR CNR 6230, Université de Nantes, 2 rue de la Houssinière, BP

92208, 44322 Nantes Cedex 3, France. ‡Institut Universitaire de France, 103 bd Saint-Michel, F75005 Paris Cedex 05, France. Corresponding Author *

Tel (D.J.): +33 2 51 12 55 64 *Email: [email protected];

[email protected]

Abstract. The present contribution constitutes an extensive Density Functional Theory (DFT) investigation of the nonlinear optical (NLO) properties of a large number of molecules belonging to the azobenzene and azothiophene families of photochromic compounds which can act as NLO switches. Towards the design of systems simultaneously presenting both large total nonlinear response βtot values and large contrast, βratio, between the cis and trans isomers, we have focused on the monomers and azobenzene dimers, the latter containing two N=N bonds along the molecular backbone. Having established that the inclusion of implicit solvation is not important in drawing qualitative conclusions on the NLO switching ability for the investigated systems, gas

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phase calculations have shown that for the asymmetric push-pull azobenzene and azothiophene candidates, the combination of strong donating groups such as NPh2, N(Ph-OMe)2 and N(PhNMe2)2 with the dicyanoethene group CH=C(C≡N)2, as an acceptor delivers large βtrans (150217x10-30 esu) and non-negligible βcis (18-55x10-30 esu) values as well as substantial contrast, βratio (3.9-8.7). For the investigated double azobenzenes, it is found that, with a careful choice of donor and acceptor groups, the contrast βratio can be significantly increased compared to the monomers while maintaining large β values that facilitate their detection with standard experimental techniques (e.g. electric-field induced second harmonic generation). Our results set the stage on which further theoretical and experimental studies can be based, in the search for efficient

and

versatile

NLO

switches.

KEYWORDS. Photochromism, NLO, Azobenzene, Azothiophene, Switches

I. Introduction. Nowadays, the theory of nonlinear optical (NLO) properties of matter has reached an unprecedented level of maturity, offering a solid basis for the interpretation of experimental findings.1-8 Moreover, when combined with the modern arsenal of computational methods it can efficiently guide the design of novel materials with large NLO responses for applications in information processing,9,10 data storage11-13 and optical limiting.14-16 Related to the ongoing need to rapidly and efficiently store and retrieve data are the intense theoretical and experimental investigations, on novel molecular systems that can serve as efficient switches,17-21 i.e. systems that can convert between two or more different isomers having different properties (absorption spectrum, refractive index, NLO response…). In the field of NLO switches the objective is to synthesize structures that exhibit large first hyperpolarizabilities (βtot) so that the different isomers can be detected using standard techniques, e.g. electric-field-induced second


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harmonic generation (EFISHG), while maintaining a large contrast between the NLO responses (βratio) of the isomers for efficient switching.22-25 Over the years several compounds belonging to the diarylethene,26-30 spiropyrane/merocyanine,31-34 fulgide35,36 and azobenzene37,38 families as well as organometallic derivatives 23,24,39,40 have been investigated for their ability to act as NLO switches and an account summarizing the latest findings in this field has been published recently.41 From the aforementioned families of compounds, azobenzenes besides interesting applications in the fields of supramolecular organization,42,43 manipulation of biological systems using light,44,45 photoorientation of materials and conversion of light into mechanical energy,46 have also attracted considerable attention in the field of NLO properties due to the high nonlinear response obtained when adding active end groups to the azobenzene core.25,47-54 Strangely enough their efficiency in acting as NLO switches has been the subject of only a few investigations 33,37,38,55-57 and it is the major goal of the present contribution to offer a systematic study of NLO properties for this class of molecules. In this contribution we bring forth an extensive DFT quantum mechanical investigation on the NLO switching efficiency of a large panel of azobenzene and azothiophene derivatives by systematically i) varying the acceptor (A) and donor (D) groups at the ends of the π-conjugated bridge (Scheme 1) and ii) modifying the bridge itself by considering double azobenzenes, i.e. systems containing two N=N bonds along the bridge (Scheme 2). The strategy of incorporating two photochromes in a single system results in more cis-trans isomers, therefore in principle leading to more chances of achieving larger NLO contrast than their respective monomers (Scheme 2). We have therefore considered the relative stability of the different structural isomers in the multiple photochromes. The list of the different acceptor/donor groups R1 and R2 used in this work for both azobenzene and azothiophene bridges is given in Scheme 3. In total the study


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extends to a number of 124 molecules, making it possible to determine reliable structureproperty relationships so as to guide future purpose oriented syntheses towards the most interesting systems.

Scheme 1. General structure for the azobenzene (left) and azothiophene (right) derivatives bearing different substituents R1 and R2

Scheme 2. Possible isomers for the double azobenzenes in their: trans-trans (top left), trans-cis (top right), cis-trans (bottom left) and cis-cis (bottom right) conformations. Code I II III

Electron Donors NH2 NMe2 Cl

Code a b c

IV

Br

d

Electron Acceptors C≡N NO2 CF3 CH=C(C≡N)2

Benzothiadiazole V

OMe

e Azobenzothiadiazole

VI

NPh2

f

N(Ph-OMe)2 VII

Azocyanobenzothiadiazole g


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VIII

N(Ph-NMe2)2

Scheme 3. Electron donor and acceptor groups used in this work. For the bulky acceptors the chemical structures are also shown. Note that in the two last electron acceptor groups, one of the two phenyl rings linked to the azo group has been substituted by a benzothiadiazole moiety. The halogens Cl and Br obviously have a dual nature (can act as donor or acceptor groups) and we have included them as donors just conventionally.

II. Computational Details. The ground state (GS) geometries of all systems reported herein have been optimized at the DFT ωB97X-D58/6-311G(d,p) level of theory with the BernyGEDIIS59 algorithm and utilizing tight convergence criteria (10–5 a.u. for the RMS force). The respective minima were characterized as true minima (no imaginary frequencies) by performing harmonic frequency analysis at the same level of theory. The calculations of static polarizability α(0;0) and first hyperpolarizability β(0;0,0) tensor components as well as the frequency dependent ones (ω=1907 nm, 0.65 eV) relevant to the electrooptical Pockel’s effect βEOPE(ω;ω,0) and second the harmonic generation βSHG(-2ω;ω,ω) were performed analytically solving the coupled-perturbed Kohn-Sham equations60 at the ωB97X-D/6-311++G(d,p) level of theory. The aforementioned range-separated hybrid was used since it is well established that functionals with a correct asymptotic behavior are mandatory for obtaining accurate NLO properties.61-63 The average polarizability αave and the total first hyperpolarizability βtot have been determined by,64 1 ≡ ave =

+ +

3 1 ⁄ ≡ tot = + + 5


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= + +

where i and j denote the Cartesian axes of the molecule-fixed coordinate system. While the majority of calculations were performed in the gas phase, we have also employed the popular Polarizable Continuum Model (PCM) in its IEF-PCM variant65 to model the bulk solvation effects of solvents of different polarity: n-hexane (HEX), tetrahydrofuran (THF) and N,N-dimethylformamide (DMF). All NLO properties in solution were computed using optimized geometries in the presence of solvent. Both equilibrium (eq) and non-equilibrium (neq) PCM solvation have been used since it is intuitively difficult to characterize the interaction of a solute with a laser field in solution as a steady-state or dynamic effect.66 All calculations reported employed the pruned “ultrafine” (99,590) Euler-Maclaurin-Lebedev integration grid which consists of 99 radial and 590 angular points per atom while strict criteria of at least 10–9 a.u. were used to monitor SCF convergence. All calculations were carried out using the Gaussian 09.D01 suite of programs.67 III. Results. A. Solvents Effects. Since the purpose of the present study is to be as general as possible in its conclusions, it is important to demonstrate that the first hyperpolarizability values as well as their ratio are, for all practical purposes, insensitive to the particular solvent used. Therefore in this Section the effect of aprotic solvents of varying polarity (HEX, THF and DMF) on the first hyperpolarizability of four symmetric (R1=R2=H, NO2, MNMe2 and CF3) and six asymmetric (R1≠R2) azobenzene and azothiophene derivatives which are representatives of the whole set of molecules investigated is studied. Both the equilibrium (eq) and nonequilibrium (neq) limits of


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PCM solvation have been used since, as already stated, the electric polarization in solutions cannot be unambiguously classified as a static or dynamic phenomenon. The results are summarized in Tables S-1 to S-4 of the Supporting Information (SI). Starting from an evaluation of the effect of employing the eq and neq limits on the calculated absolute β values (of course all static properties are identical for the two limits since they are evaluated at zero frequency), it becomes clear that they are slightly different. This is of course expected since in the eq case both the electronic and nuclear degrees of freedom of the solvent are equilibrated with the solute’s instantaneous charge density whereas in neq solvation only the electronic degrees of freedom of the solvent are in full equilibrium. What is of importance is that the frequency-dependent βratio values differ only by an order of 0.2 ratio units for the eq and neq solvation limits; differences that can be considered negligible considering the range of ratio values obtained in the present work. There is, however, one exception to this aforementioned trend that merits further discussion. For the case of the azothiophene with R1=NMe2 and R2=NO2 the difference of the βratio for the eq and neq limits is not negligible for the case of polar solvents. In THF differences of 0.56 ratio units between βratio(-ω;ω,0) (eq) and βratio(-ω;ω,0) (neq) and of 1.21 between βratio(2ω;ω,ω) (eq) and βratio(-2ω;ω,ω) (neq) are observed while in DMF the difference becomes even more pronounced, reaching 1.95 ratio units for the case of βratio(-2ω;ω,ω) (eq) and βratio(-2ω;ω,ω) (neq). This system possesses a large dipole moment in the first excited state, rendering it extremely susceptible to the solvation model used, which in turn explains the discrepancies between eq and neq βratio values observed in polar solvents. On the contrary, for the case of the azobenzene with the same ligands (namely R1=NMe2 and R2=NO2) such discrepancies are not observed since its smaller dipole moment makes it less susceptible to the solvation effects. Having established the near equivalence of the equilibrium and nonequilibrium limits of PCM


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solvation for the properties of interest one can now move to the influence of the nature of solvent. First it can be noted that the β values in solution are generally larger than their gas phase counterparts for both azobenzene and aziothiophene derivatives and are sensitive to the polarity of the employed solvent. This emerges as a general trend for the cis-trans azobenzene and azothiophene derivatives for the static as well as the dynamic β values. Taking the static hyperpolarizability β(0;0,0) of the azobenzene NMe2-NO2 derivative as an example, one can note the following trend for the various solvents; β(0;0,0)gas < β(0;0,0)HEX (+13%) < β(0;0,0)THF (+33%) < β(0;0,0)DMF (+42%) clearly demonstrating the capacity of polar solvents to stabilize strongly dipolar species, eventually leading to a higher nonlinear response. For the βratio(0;0,0) values of the asymmetric azobenzene systems (indicated inside parentheses) the following trends emerge: Gas: NO2-CF3 (2.25) < NMe2-H = H-NO2 (2.45) < NMe2-CF3 (2.82) < NMe2-NO2 (3.21) < H-CF3 (3.22)

HEX: NO2-CF3 (2.22) < NMe2-H (2.42) < H-NO2 (2.49) < NMe2-CF3 (2.77) < H-CF3 (3.25) < NMe2-NO2 (3.33)

THF: NO2-CF3 (2.16) < NMe2-H (2.27) < H-NO2 (2.50) < NMe2-CF3 (2.62) < H-CF3 (2.64) < NMe2-NO2 (3.45)

DMF: NO2-CF3 (2.12) < NMe2-H (2.20) < H-CF3 (2.37) < H-NO2 (2.50) < NMe2-CF3 (2.54) < NMe2-NO2 (3.47)

Between the gas phase values and those obtained in HEX and THF, the ordering remains unchanged, except for H-CF3 and NMe2-CF3 which present similar ratios. When going to DMF, an extra inversion with H-NO2 is noted, but again for compounds of similar βratio. For the azothiophene systems, the trends emerge as follows: Gas: H-CF3 (1.24) < NO2-CF3 (1.85) < H-NO2 (2.18) < H-NMe2 (2.25) < N-Me2-CF3 (2.93) < NMe2-NO2 (4.18)


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HEX: H-CF3 (1.45) < NO2-CF3 (1.91) < H-NMe2 (2.36) < H-NO2 (2.39) < NMe2-CF3 (3.12) < NMe2-NO2 (4.78)

THF: H-CF3 (1.42) < NO2-CF3 (1.93) < H-NMe2 (2.45) < H-NO2 (2.61) < NMe2-CF3 (3.21) < NMe2-NO2 (5.67)

DMF: H-CF3 (1.42) < NO2-CF3 (1.92) < H-NMe2 (2.46) < H-NO2 (2.67) < NMe2-CF3 (3.18) < NMe2-NO2 (5.91)

Again, going from gas to the condensed phase does not significantly modify the “chemical ordering”. Indeed, the only change in the relative ordering of the βratio for this series is that HNMe2 and H-NO2 are interchanged by passing from the gas phase to HEX; an observation that is of no significant importance since their gas phase values are highly similar (2.25 vs 2.18). In addition, an obvious trend emerges: solvation increases the βratio as the β increase is larger for the trans than for the cis isomers. It can be seen that there is larger range of ratio values for the substituted azothiophenes (1.42-5.91 in DMF) than for the corresponding azobenzenes (2.123.47 in DMF). It is possible to extract two major conclusions from the study of the influence of the solvent on the calculated β and βratio values. On the one hand, it has been demonstrated that for both the azothiophene and azobenzene derivatives the limit chosen for the solvation calculations (eq vs neq) does not affect significantly neither the absolute values nor their ratio. On the other hand, for the influence of the solvent itself, it has been shown that although the absolute hyperpolarizability values greatly depend on the solvent’s polarity, the cis-trans ratio as well as the ratio ordering for different choices of substituents R1 and R2 remain practically unchanged. Therefore, all necessary comparisons can be made in the gas phase without loss of generality and in what follows all data pertain to the gas phase unless stated otherwise. B. Symmetric Systems. In this Section results on the static first hyperpolarizability β(0;0,0) of the cis isomers of symmetrical systems with R1=R2 are reported. The naming convention is that


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of Scheme 3. For completeness the Gibbs free energies ∆G between the cis and trans isomers as well as the total polarizability α and its cis/trans ratio are reported in Tables S-5 and S-6 of the ESI for the azobenzenes and azothiophenes, respectively. Obviously for the trans symmetrical systems the second order response vanishes due to their centrosymmetry and therefore only the substituent effects on the absolute β values will be discussed. In total, 28 systems were investigated and the main results are summarized in Table 1 and Table 2 for azobenzenes and azothiophenes, respectively. Clearly the Cl and Br substituents give rise to low values of β. The comparison between systems Isym, IIsym and Vsym shows that, as expected, the amine groups are much stronger electron donors than the alkoxy group, a difference that manifests itself in the ordering of their β values: NMe2 > NH2 > OMe for both azobenzenes and azothiophenes.

Table 1. Electric hyperpolarizabilities of the cis symmetric azobenzene derivatives calculated at the ωB97X-D/6-311++G(d,p) level of theory. Molecule Isym IIsym IIIsym IVsym Vsym VIsym VIIsym VIIIsym asym bsym csym dsym esym fsym gsym

R1=R2 NH2 NMe2 Cl Br OMe NPh2 N(Ph-OMe)2 N(Ph-NMe2)2 C≡N NO2 CF3 CH=C(C≡N)2 Benzothiadiazole Azobenzothiadiazole Azocyanobenzothiadiazole

β(0;0,0)cis(10−30 esu) 6.03 9.51 3.07 2.59 5.15 7.54 16.43 20.53 0.42 3.84 1.23 10.07 3.51 0.59 0.70


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Table 2. Electric hyperpolarizabilities of the cis symmetric azothiophene derivatives calculated at the ωB97X-D/6-311++G(d,p) level of theory. Molecule R1=R2 Isym NH2 IIsym NMe2 IIIsym Cl IVsym Br Vsym OMe VIsym NPh2 VIIsym N(Ph-OMe)2 VIIIsym N(Ph-NMe2)2 asym C≡N bsym NO2 csym CF3 dsym CH=C(C≡N)2 esym Benzothiadiazole a Unstable form, cis isomer return to the trans conformation.

β(0;0,0)cis(10−30 esu) 6.86 10.15 5.74 4.39 4.25 5.11 12.13 17.47 3.30 5.60 2.70 a 11.66

For the phenyl family of donors, an increase of the β values is observed by passing from VIsym to VIIsym and VIIIsym. For example, an almost threefold increase is observed for the case of azobenzenes: VIsym (7.54x10-30 esu) < VIIsym (16.43x10-30 esu) < VIIIsym (20.53x10-30 esu). A similar trend holds for azothiophenes. It becomes evident that in the case of strong donors as well, the value of β is proportional to the electron donating ability of the substituent: addition of NMe2 on the diphenylamines results in a larger nonlinear response compared to the addition of OMe. This latter observation is in line with our previous one. For the derivatives bearing electron donating groups, the hyperpolarizability values are much lower than the corresponding ones bearing acceptor groups. For the azobenzene family the presence of the dicyanoethene group (dsym) gives the largest β(0;0,0)cis value, namely 10.07x10-30 esu which is at least one order of magnitude larger than the rest of the series. For the azothiophenes it is the benzothiadiazole group (esym) derivative that attains the largest β(0;0,0)cis value, which is one order of magnitude larger than all the rest. As a general conclusion, it can be surmised, from the contents of Tables 1 and 2, that the electron donating groups result in higher nonlinear responses than the corresponding electron accepting ones for both families of switches. This trend is to be expected since enriching the central bridge (azobenzene and azothiophene) with electrons results in more


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(hyper)polarizable systems. Moving to a comparison between the corresponding azobenzene and azothiophene derivatives, we pinpoint that for the case of the strong donating groups (VIsym, VIIsym and VIIIsym), the azobenzene derivatives develop larger hyperpolarizability values compared to the azothiophene ones, while the reverse holds in the case of weak donors and acceptors. Moreover, for the electron donating groups, both families give rise to nonlinear responses of the same order of magnitude. On the contrary, for the case of derivatives bearing electron accepting groups, large discrepancies can be found between the two families for asym and esym. Since the origin of these differences is not obvious, we have studied the issue in detail, taking the benzothiadiazole derivatives as examples. For these azobenzene and azothiophene derivatives the electron density differences, ∆ρ, between the ground and the first singlet excited state are shown in Figure 1. It becomes evident that for the case of the azothiophene derivative the reorganization of the density extends over the whole molecule while for the azobenzene it is much more localized. In order to rationalize the differences between the two geometries and their influence on the calculated β we have disrupted the ground state optimized geometry of the azobenzene system firstly by changing the dihedral angle between the benzothiadiazole and the nearby ring from the initial value of ~ 40° to 20°; the latter value being the one found between the benzothiadiazole ring and the nearby thiophene ring in the azothiophene molecule. This changes the β(0;0,0)cis only slightly, from 3.51x10-30 esu to 4.74x10-30 esu. Apparently, the large difference in the nonlinear response of the two systems is not due to the relative orientation between the substituents and the adjacent rings. On the contrary, by only changing the relative orientation of the two phenyl rings of the azobenzene derivative so as to match the orientation of the two azothiophene rings found to its azothiophene counterpart results in a huge 134% increase of β(0;0,0)cis attaining a value of 7.97x10-30 esu. It is thus the orientations of the rings vicinal to


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the N=N bond that play the most important role in explaining the different responses of the azobenzene and azothiophene systems.

Figure 1. Electron density differences ∆ρ between the first excited singlet state and the ground state calculated at the ωB97XD/6-311++G(d,p) level of theory for the azobenzene (left) and azothiophene (right) substituted by two benzothiadiazoles . The blue regions imply a depletion of density while the red ones imply an increase of density upon excitation. A isovalue of 0.0004 a.u. has been used.

C. Asymmetrical Systems: Push-Pull Molecules. For the case of asymmetrical systems of push-pull character the first hyperpolarizability of the trans isomers is no longer zero and the βratio value can be defined as βratio ≡ βtrans/βcis. Again, the naming convention of Scheme 3 is adopted. A particular system is specified by reporting a roman number (donor, R1), a letter (acceptor, R2) and the type of the bridging moiety (AZB for azobenzenes and AZT for azothiophenes). Thus AZB-V-c stands for an azobenzene molecule having the OMe group as a donor (V) and CF3 as an acceptor (c).


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The results for the average polarizability, its cis/trans ratio and the cis/trans Gibbs free energies ∆G are summarized in Tables S-7 and S-8 of the ESI for azobenzenes and azothiophenes, respectively. The first hyperpolarizability β and ratio βratio values for the cis and trans isomers are summarized in Tables 3 and 4 while the cis/trans static β(0;0,0) values are plotted in Figures 2 and 3 for the azobenzenes and azothiophenes, respectively. For the trans azobenzene and azothiophene isomers similar trends emerge: for any given acceptor group, the largest β(0;0,0)trans is achieved by using VIII as donor and the property value sequentially increases following the order III ≈ IV < V < I < II < VI < VII < VIII. Among the acceptor groups, d (dicyanoethene) provides the largest β(0;0,0)trans value irrespectively of the donor group present in the system. From a chemical point of view, the amine groups (I and II) lead to larger hyperpolarizability values than the alkoxy ones (V) while the halogens (III and IV) are the most ineffective in giving a high second-order nonlinear response; the same trends were found also for the case of the symmetrical systems. In addition, the attained βtrans values for both families of molecules are of the same order of magnitude, namely in the 2x10-30-200x10-30 esu range. For the cis isomers the maximum β values that can be achieved are much lower (54.70x10-30 esu and 24.97x10-30 esu for azobenzenes and azothiophenes, respectively) compared to those of the trans systems. In turn, this indicates a more complicated outcome: for azobenzenes the evolution βcis with respect to the selected acceptor group when VI is used as a donor is strikingly different than the rest of the systems. In fact, systems AZB-VI-d and AZB-VI-e attain βcis values of 14.37x1030

and 3.09x10-30 esu, both of which are much lower than expected based on the general trends

seen in Figure 2. On the contrary, for the aziothiophene derivatives the observed trends are much more uniform (see Figure 3).


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Table 3. Electric hyperpolarizabilities and their cis-trans ratio for different push-pull azobenzenes calculated at the ωB97X-D/6311++G(d,p) level of theory. Molecule I-a I-b I-c I-d I-e I-f I-g II-a II-b II-c II-d II-e II-f II-g III-a III-b III-c III-d III-e III-f III-g IV-a IV-b IV-c IV-d IV-e IV-f IV-g V-a V-b V-c V-d V-e V-f V-g VI-a VI-b VI-c VI-d VI-e VI-f VI-g VII-a VII-b VII-c VII-d VII-e VII-f VII-g VIII-a VIII-b VIII-c VIII-d VIII-e VIII-f VIII-g

R1 NH2 NH2 NH2 NH2 NH2 NH2 NH2 NMe2 NMe2 NMe2 NMe2 NMe2 NMe2 NMe2 Cl Cl Cl Cl Cl Cl Cl Br Br Br Br Br Br Br OMe OMe OMe OMe OMe OMe OMe NPh2 NPh2 NPh2 NPh2 NPh2 NPh2 NPh2 N(Ph-OMe)2 N(Ph-OMe)2 N(Ph-OMe)2 N(Ph-OMe)2 N((Ph-OMe)2 N(Ph-OMe)2 N(Ph-OMe))2 N(Ph-NMe2)2 N(Ph-NMe2)2 N(Ph-NMe2)2 N(Ph-NMe2)2 N(Ph-NMe2)2 N(Ph-NMe2)2 N(Ph-NMe2)2

R2 C≡N NO2 CF3 CH=C(C≡N)2 Benzothiadiazole Azobenzothiadiazole Azocyanobenzothiadiazole C≡N NO2 CF3 CH=C(C≡N)2 Benzothiadiazole Azobenzothiadiazole Azocyanobenzothiadiazole C≡N NO2 CF3 CH=C(C≡N)2 Benzothiadiazole Azobenzothiadiazole Azocyanobenzothiadiazole C≡N NO2 CF3 CH=C(C≡N)2 Benzothiadiazole Azobenzothiadiazole Azocyanobenzothiadiazole C≡N NO2 CF3 CH=C(C≡N)2 Benzothiadiazole Azobenzothiadiazole Azocyanobenzothiadiazole C≡N NO2 CF3 CH=C(C≡N)2 Benzothiadiazole Azobenzothiadiazole Azocyanobenzothiadiazole C≡N NO2 CF3 CH=C(C≡N)2 Benzothiadiazole Azobenzothiadiazole Azocyanobenzothiadiazole C≡N NO2 CF3 CH=C(C≡N)2 Benzothiadiazole Azobenzothiadiazole Azocyanobenzothiadiazole

βcis(10−30esu) 9.61 12.98 7.84 23.48 9.66 7.68 11.89 14.75 18.38 12.31 30.66 13.13 12.00 18.33 3.62 5.93 2.90 12.64 2.78 3.03 5.12 3.41 5.86 2.56 12.50 2.38 2.69 4.94 7.03 9.81 5.68 18.56 6.85 5.74 8.77 16.67 19.96 13.06 14.37 3.09 10.06 19.32 26.86 30.70 23.16 40.17 18.62 20.21 30.48 36.78 41.23 32.68 54.70 28.37 29.26 42.63

βtrans(10−30esu) 29.01 39.58 21.67 68.74 25.18 26.19 45.40 45.30 58.98 34.75 99.51 42.34 41.87 70.74 10.78 18.47 7.46 29.06 1.97 9.11 18.29 11.44 19.48 7.87 30.61 1.87 9.52 19.67 21.24 30.29 15.66 51.69 15.86 18.95 32.97 62.90 79.51 48.18 129.04 49.47 55.88 99.88 83.68 103.11 65.97 166.43 73.31 76.97 129.74 108.27 132.40 86.35 215.26 99.92 101.76 170.80

βratio 3.02 3.05 2.76 2.93 2.61 3.41 3.82 3.07 3.21 2.82 3.25 3.23 3.49 3.86 2.97 3.12 2.57 2.30 0.71 3.01 3.57 3.35 3.32 3.08 2.45 0.78 3.54 3.98 3.02 3.09 2.76 2.79 2.31 3.30 3.76 3.77 3.98 3.69 8.98 16.02 5.56 5.17 3.12 3.36 2.85 4.14 3.94 3.81 4.26 2.94 3.21 2.64 3.94 3.52 3.48 4.01

Table 4. Electric hyperpolarizabilities and their cis-trans ratio for different push-pull azothiophenes calculated at the ωB97XD/6-311++G(d,p) level of theory. Molecule I-a I-b I-c I-d I-e II-a II-b II-c II-d

R1 NH2 NH2 NH2 NH2 NH2 NMe2 NMe2 NMe2 NMe2

R2 C≡N NO2 CF3 CH=C(C≡N)2 Benzothiadiazole C≡N NO2 CF3 CH=C(C≡N)2

βcis(10−30esu) 8.29 11.65 6.93 21.97 16.13 10.44 13.67 9.15 24.75

βtrans(10−30esu) 24.54 41.49 18.16 70.40 35.65 35.60 57.07 26.85 97.33

βratio 2.96 3.56 2.62 3.20 2.21 3.41 4.17 2.93 3.93


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II-e III-a III-b III-c III-d III-e IV-a IV-b IV-c IV-d IV-e V-a V-b V-c V-d V-e VI-a VI-b VI-c VI-d VI-e VII-a VII-b VII-c VII-d VII-e VIII-a VIII-b VIII-c VIII-d VIII-e

NMe2 Cl Cl Cl Cl Cl Br Br Br Br Br OMe OMe OMe OMe OMe NPh2 NPh2 NPh2 NPh2 NPh2 N(Ph-OMe)2 N(Ph-OMe)2 N(Ph-OMe)2 N(Ph-OMe)2 N(Ph-OMe)2 N(Ph-NMe2)2 N(Ph-NMe2)2 N(Ph-NMe2)2 N(Ph-NMe2)2 N(Ph-NMe2)2

Benzothiadiazole C≡N NO2 CF3 CH=C(C≡N)2 Benzothiadiazole C≡N NO2 CF3 CH=C(C≡N)2 Benzothiadiazole C≡N NO2 CF3 CH=C(C≡N)2 Benzothiadiazole C≡N NO2 CF3 CH=C(C≡N)2 Benzothiadiazole C≡N NO2 CF3 CH=C(C≡N)2 Benzothiadiazole C≡N NO2 CF3 CH=C(C≡N)2 Benzothiadiazole

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17.58 5.93 8.78 4.80 15.94 9.32 5.96 8.73 4.87 16.28 9.02 7.39 10.68 5.98 19.94 14.48 15.90 17.78 14.04 18.13 12.06 16.76 15.86 16.94 21.47 17.81 21.46 21.09 21.49 24.97 20.59

(a)

55.44 12.06 24.51 8.39 37.44 6.50 13.19 26.37 9.16 40.40 6.75 19.75 34.52 14.34 57.41 24.32 61.15 89.87 46.70 150.41 73.17 74.97 107.10 59.22 177.03 104.83 93.29 131.31 74.52 216.90 139.75

3.15 2.03 2.79 1.75 2.35 0.70 2.21 3.02 1.88 2.48 0.75 2.67 3.23 2.40 2.88 1.68 3.84 5.06 3.33 8.29 6.07 4.47 6.75 3.49 8.25 5.89 4.35 6.23 3.47 8.69 6.79

(b)

Figure 2. Evolution of the absolute β(0;0,0) values for different donors as a function of the acceptor group for trans (a) and cis (b) azobenzenes calculated at the ωB97X-D/6-311++G(d,p) level of theory.

(a)

(b)


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Figure 3. Evolution of the absolute β(0;0,0) values for different donors as a function of the acceptor group for trans (a) and cis (b) azothiophenes calculated at the ωB97X-D/6-311++G(d,p) level of theory.

In order to understand this behavior the ground state dipole moments of systems AZB-VI-d (βcis=14.37x10-30 esu), AZB-VII-d (βcis=40.17x10-30 esu) and AZB-VIII-d (βcis=54.70x10-30 esu) in their cis forms were compared (see Figure 4) and it was found that it is not only the magnitude of the dipole moment vector of the first compound (2.82 D) that is much lower compared to the latter two (4.26 D and 7.98 D, respectively), but also its direction. This difference in the dipole moments has prompted us to focus on the geometrical differences of the three molecules; notably it was found that the orientation of the two phenyl rings of the donor group is strikingly different in AZB-VI-d compared to AZB-VII-d and AZB-VIII-d. In the latter two compounds the phenyl rings are arranged perpendicular to each other which is not the case in the former one. As a proof of concept, we have substituted the OMe and NMe2 groups in AZB-VII-d and AZB-VIII-d with H without reoptimizing the geometries. These distorted AZB-VI-d systems attain βcis values (30.87x10-30 and 33.35x10-30 esu) that are almost twice larger than the value found when AZBVI-d adopts its equilibrium geometry (14.37x10-30 esu), thus demonstrating the important impact of the orientation of the two phenyl rings of the donor group on the calculated βcis values. The same explanation holds also for the small βcis value of system AZB-VI-e whose βratio value is irregularly high. Focusing now on the βratio values (see Figure 5), it is seen that the halogen (Cl and Br) containing azothiophenes are the worst candidates for NLO switching due to their very low βratio values irrespectively of the acceptor group used. The halogen containing systems AZBIII-d, AZB-III-e, AZB-IV-d and AZB-IV-e have the lowest βratio values among the investigated azobenzene derivatives. The best candidates bear as electron donors the groups NPh2, N(PhOMe)2 and N(Ph-NMe2)2 and the dicyanoethene group as an acceptor, except for AZB-VI-d, and


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the results are summarized in Table 5. Among the best candidates, azothiophenes have βratio values that are almost twice larger compared to azobenzenes, with AZT-VIII-d having the largest value of all.

Figure 4. Total dipole moment vectors of the cis systems AZB-VI-d, AZB-VII-d and AZB-VIII-d calculated at the ωB97X-D/6311G(d,p) level of theory.

(a)

(b)

Figure 5. Evolution of the ratio values β(0;0,0)ratio for different donors as a function of the acceptor group for azobenzene (a) and azothiophene (b) bridged system calculated at the ωB97X-D/6-311++G(d,p) level of theory.

Table 5. Results for the absolute hyperpolarizability values (in 10-30 esu) as well as the trans-cis ratios of the best push-pull candidates for NLO switching. All values pertain to the ωB97X-D/6-311++G(d,p) level of theory.

Bridge AZB AZT

Code VII-d VIII-d VI-d VII-d VIII-d

β(0;0,0)trans 166.43 215.26 150.41 177.03 216.90

β(0;0,0)cis 40.17 54.70 18.13 21.47 24.97

βtrans/βcis 4.14 3.94 8.29 8.25 8.69


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D. Double azobenzenes. For the double azobenzenes we have considered as examples the systems AZB2-VI-d, AZB2-VI-e and AZB2-VIII-d (the index 2 in AZB implies a double azobenzene and the naming convention of Scheme 3 is adopted) and their possible isomers, as shown in Scheme 2. Evidently, for R1≠R2 there are four possible isomers: trans-trans (TT), trans-cis (TC), cis-trans (CT) and cis-cis (CC). Before moving to a discussion on their hyperpolarizabilities, it is of interest to first discuss their relative stability in terms of their Gibbs free energies, ∆G, though bearing in mind that despite the thermodynamic control of the photoisomerizations, kinetic control might be also important. There are two successive photoisomerization paths that lead from the trans-trans isomers to the cis-cis ones: a) trans-trans → cis-trans→ cis-cis (TT-CT-CC) and b) trans-trans → trans-cis→ cis-cis (TT-TC-CC). For the AZB2-VI-d and AZB2-VIII-d the intermediate isomer trans-cis is more stable than the cistrans one (absolute ∆G values of 0.35 and 1.00 kcal/mol, respectively). For these molecules the path TT-TC-CC is thermodynamically more favored, although the difference of the G values between the cis-trans and trans-cis intermediate forms is very small. For the system AZB2-VI-e the isomers cis-trans and trans-cis have practically identical G values (absolute ∆G value of 0.04 kcal/mol). Let us now focus on the hyperpolarizability values of the different forms. The values of the static first hyperpolarizability β(0;0,0) of all the isomers of the double azobenzenes are gathered in Table 6. Firstly, one can remark that for the three systems the trans-cis isomers have a larger hyperpolarizability value compared to the cis-trans, differing by a factor of 1.26, 3.09 and 3.07 for systems AZB2-VI-d, AZB2-VI-e and AZB2-VIII-d, respectively. This behavior can be explained by the fact that a more efficient charge transfer takes place when the moiety that bears the donor group is planar, that is, when the configuration of the 1 and 2 cycles is in a trans conformation with respect to the N=N bond (see Scheme 2).


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Table 6. Results for the absolute hyperpolarizability values (in 10-30 esu) of all isomers of the investigated double azobenzenes as well as the trans-trans/cis-cis ratios. All values pertain to the ωB97X-D/6-311++G(d,p) level of theory. System AZB2-VI-d AZB2-VI-e AZB2-VIII-d

β(0;0,0)cis-cis 6.33 6.41 22.56

β(0;0,0)cis-trans 54.34 14.61 40.40

β(0;0,0)trans-cis 68.73 45.15 124.42

β(0;0,0)trans-trans 184.92 79.69 314.75

βratio(trans-trans/cis-cis) 29.21 12.43 13.95

Secondly, by comparing the β(0;0,0) values for the double azobenzenes in their trans-trans conformation and the corresponding values for the simple trans azobenzenes (see Table 7) it becomes evident that the addition of a second azobenzene augments the nonlinear response by a factor of 1.5 on average. This augmentation is due to the increase of the length of the π electron bridge, resulting in better electron delocalization, although, due to the nonadditive nature of the (hyper)polarizabilities, the β values of the double azobenzenes are not twice the values of their simple counterparts. Among the three investigated double azobenzenes, AZB2-VI-d has the largest contrast between the isomers trans-trans and cis-cis, attaining a βratio value of 29.21 (Table 6). Nonetheless, this system does not meet all the criteria set forth (see Introduction) for the selection of the most efficient NLO switch: the β(0;0,0) value for the cis-cis isomer is only 6.33x10-30 esu. On the contrary, system AZB2-VIII-d meets all the criteria, the β(0;0,0) value for the cis-cis and trans-trans being 22.56x10-30 esu and 374.75x10-30 esu, respectively. This latter value is the largest achieved among all the systems investigated in the present study and therefore AZB2-VIII-d is the “best” candidate for use in NLO switching. Table 7. Comparison of the absolute first hyperpolarizability values (in 10-30 esu) of the trans and trans-trans isomers of selected simple and double azobenzenes, respectively as well as their trans-trans/trans ratios. All values pertain to the ωB97X-D/6311++G(d,p) level of theory. System AZB2-VI-d/AZB-VI-d AZB2-VI-e/AZB-VI-e AZB2-VIII-d/AZB-VIII-d

β(0;0,0)trans 129.04 49.47 215.26

β(0;0,0)trans-trans 184.92 79.69 314.75

βrato(trans-trans/trans) 1.43 1.61 1.46


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Conclusions. A detailed investigation on the NLO switching capability of a large number of azobenzenes, azothiophenes and double azobenzene push-pull derivatives has been performed. The study focused predominantly on the gas phase properties, since it was proven that using implicit solvation with solvents of varying polarity did not affect the relative nonlinear responses of the investigated systems, thus allowing for general qualitative conclusions to be principally drawn from the gas phase data. With the aim of simultaneously maximizing both the total hyperpolarizabilities β of the systems as well as the contrast βratio of their cis-trans isomers we have studied a total of 15 electron donor and acceptor groups of various strength and size, making it possible to simultaneously reach high values for the nonlinear response (β > 200x10-30 esu) and large contrasts (βratio > 8). Moreover, the possibility of improving the NLO switching capability has been examined by considering some double azobenzene derivatives. Although it was shown that the incorporation of a second photochrome did not double the total first hyperpolarizability of the trans-trans isomers compared to the monomeric trans ones, an improvement of the contrast βratio between the trans-trans and cis-cis has resulted (βratio > 13) while maintaining high values of β. Our proposed strategy of designing efficient NLO switches based on double azobenzenes can pave the way for practical applications since no control on the isomerization of each subunit is necessary: the NLO switching activity is based on the fully isomerized cis-cis and trans-trans forms and not the partially isomerized cis-trans or trans-cis. It would be of great interest to pursue this strategy further by computationally investigating the NLO contrast of multiple azobenzenes in their fully trans and cis forms provided that isomerization of all subunits can be


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proven experimentally to be possible. We therefore hope that our investigation will stimulate a stronger interplay between theory and experiment in the domain of NLO switching.

ASSOCIATED CONTENT Static and frequency dependent first hyperpolarizability ratios βratio of different azobenzene and azothiophene systems in the gas phase as well in various solvents. Static and frequency dependent average polarizabilities α and first hyperpolarizabilities β of azobenzenes and azothiophenes in the gas phase and in various solvents. Relative cis/trans Gibbs free energies and electric average polarizabilities and their cis-trans ratio for the symmetric azobenzene and azothiophene derivatives. Relative cis/trans Gibbs free energies, electric average polarizabilities and their cis-trans ratio for different push-pull azobenzenes and azothiophenes. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author *

Tel (D.J.): +33 2 51 12 55 64 *Email: [email protected];

[email protected] Notes The authors declare no competing financial interests. ACKNOWLEDGMENT


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T.J.-L thanks the European Research Council (ERC, Marches-278845) for supporting his internship in the CEISAM laboratory. A.C. thanks the European Research Council (ERC, Marches-278845) for his postdoctoral grant. D.J. acknowledges the European Research Council (ERC) and the Région des Pays de la Loire for financial support in the framework of a Starting Grant (Marches-278845) and a recrutement sur poste stratégique, respectively. This research used resources of (1) CCIPL (Centre de Calcul Intensif des Pays de Loire) and (2) a local Troy cluster. REFERENCES 1. Boyd, R. W. Nonlinear Optics; Academic Press: San Diego, 2008. 2. Shen, Y. R. The Principles of Nonlinear Optics; John Wiley and Sons: New Jersey, 2003. 3. Non-Linear Optical Properties of Matter. From Molecules to Condensed Phases; Papadopoulos, M.G., Sadlej, A.J., Leszczynski, J., Eds.; Springer: The Netherlands, 2006. 4. Kuzyk, M. G.; Singer, K. D.; Stegeman, G. I. Theory of Molecular Nonlinear Optics. Adv. Opt. Photonics 2013, 5, 4-82. 5. Zyss, J.; Ledoux, I. Nonlinear Optics in Multipolar Media: Theory and Experiments. Chem. Rev. 1994, 94, 77-105. 6. Bishop, D. M. Molecular Vibration and Nonlinear Optics. Adv. Chem. Phys. 2007, 104, 1-40. 7. Kurtz, H.; Dudis, D. Quantum Mechanical Methods for Predicting Nonlinear Optical Properties. Rev. Comput. Chem. 1998, 12, 241-279.


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Designing Efficient Azobenzene and Azothiophene Nonlinear Optical

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