Second-Order Nonlinear Optical Susceptibilities of Metal–Organic

Article pubs.acs.org/JPCC

Second-Order Nonlinear Optical Susceptibilities of Metal−Organic Frameworks Using a Combined Local Field Theory/Charge Embedding Electrostatic Scheme Tomasz Seidler*,†,‡ and Benoît Champagne*,† †

Laboratoire de Chimie Théorique, Unité de Chimie Physique Théorique et Structurale, University of Namur, rue de Bruxelles, 61, B-5000 Namur, Belgium ‡ Faculty of Chemistry, Jagiellonian University, Romana Ingardena 3, 30-060 Kraków, Poland S Supporting Information *

ABSTRACT: The linear (χ(1)) and second-order nonlinear (χ(2)) optical properties of metal−organic frameworks (MOFs) have been evaluated and interpreted by employing the combined local field theory/charge embedding approach. Three MOFs have been selected, the isostructural bis{4-[2-(4-pyridyl)ethenyl]benzoato}-zinc(II) (PEB-Zn) and bis{4-[2-(4pyridyl)ethenyl]benzoato}-cadmium(II) (PEB-Cd) and bis{4-[3-(4pyridyl)ethenyl]benzoato}-cadmium(II) (PEB′-Cd). The simulations, employing the Møller−Plesset second-order perturbation theory level to describe the ion properties, conclude that (i) χ(2) of PEB-Zn (∼60 pm/V at 1064 nm) is about 10% larger than that of PEB-Cd, (ii) χ(2) of PEB′-Cd attains 100 pm/V at 1064 nm [i.e., twice more than that of PEB-Cd or an amplitude similar to that of the 4-(N,N-dimethylamino)-3-acetamidonitrobenzene (DAN) molecular crystal] and (iii) the change of crystal structure accompanying an increase of temperature from 173 to 298 K leads to a decrease of χ(2) by ca. 10%. For the isostructural PEB-Zn and PEB-Cd, the outcome of Kurtz-Perry SHG powder method has been simulated as a function of the grain size, demonstrating that differences between the two MOFs only show up for room temperature structures. A value of 1.29 was estimated for the PEB-Zn/PEB-Cd contrast ratio, in qualitative agreement with experiment (1.16). This work opens the way toward a theoretically based design of MOFs with outstanding second-order nonlinear optical responses.

1. INTRODUCTION The local field theory (LFT) developed by Munn, Bounds, and Hurst1−4 has been successfully applied to evaluate the linear (χ(1)) and nonlinear (χ(2)) optical susceptibilities of a broad range of organic crystals, including 3-methyl-4-nitropyridine N-oxide (POM) and m-nitroaniline (mNA),5−7 where the molecules have a relatively small dipole moment. For molecules with larger dipole moments, such as, for instance, 2-methyl-4nitroaniline (MNA), the in-crystal molecular properties [the polarizability (α) and the first hyperpolarizability (β)] are strongly modified by the electric field created by the neighboring molecules and, subsequently, the linear and second-order nonlinear optical (NLO) susceptibilities.8−10 Related works on embedding effects have evidenced the polarization role of the surrounding on structural, energetic, electronic, and magnetic properties.11−17 The reliability of this approach combining the in-crystal field with LFT to evaluate χ(1) and χ(2) has been substantiated by several studies on organic crystals,18 including ionic crystals such as DAST, DSTMS, and DAPSH,19,20 but one can wonder whether this approach can be applied to other NLO materials, including hybrid, organic−inorganic, ones. Among these, metal−organic frameworks (MOFs) constitute a class of crystalline hybrid materials characterized by a very © XXXX American Chemical Society

large porosity and a highly developed internal surface. Therefore, these materials find applications in gas storage, separation by selective gas adsorption, catalysis, drug storage/delivery, and as templates for the synthesis of new materials.21−27 From the viewpoint of engineering noncentrosymmetric crystalline phases, MOFs present a large design flexibility. By following an appropriate strategy (i.e., by selecting organic anions with large β together with cations driving the coordination geometry), many examples of second harmonic generation (SHG)-active MOFs have been prepared.28 The d10 ions of Zn2+ and Cd2+ are especially suitable as inorganic linkers due to the improved transparency in the visible range (no d-d transitions), good chemical stability with respect to redox conditions, and the possibility of preparing structures of various dimensionalities.29 The most promising types of crystal lattices are the diamondoidal 3-dimensional structures, among which bis{4-[2-(4-pyridyl)ethenyl]benzoato}-zinc(II) (PEB-Zn) and bis{4-[2-(4-pyridyl)ethenyl]benzoato}-cadmium(II) (PEB-Cd) were found to exhibit powder SHG efficiencies of 400 and 345 Received: January 8, 2016 Revised: February 17, 2016

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The Journal of Physical Chemistry C with respect to α-quartz.30 Another promising class contains 2-dimensional structural motifs, which is achieved by the use of bent organic anions of the m-pyridinecarboxylate type. In this class, the highest SHG powder efficiencies have been reported for bis{3-[2-(4-pyridyl)ethenyl]benzoato}-cadmium(II) (PEB′Cd) and Zn4{3-[2-(4-pyridyl)ethenyl]benzoate}8·{3-[2-(4pyridyl)ethenyl]benzoic acid}·(H2O) and amount to 800 and 400 relative to α-quartz, respectively.28,31 For comparison, the SHG powder efficiencies of 2-methyl-4-nitroaniline (MNA), 4-N,N-dimethylamino-4′-N′-methyl-stilbazolium tosylate (DAST), and 4-N,N-dimethylamino-4′-N′-phenyl-stilbazolium hexafluorophosphate (DAPSH), materials possessing exceptionally large NLO activities, are of the order of 180,32 550, and 47033 times the value of urea, respectively. Note that the original work of Kurtz and Perry describes urea as 400 times better at powder SHG efficiency than α-quartz.34 However, it should be noted that this value has recently been reassessed to 4.9 relative to KDP,35 and it was proved that these results depend strongly on the experimental conditions, generally not sufficiently described. The above qualitative comparison points out that the design of MOFs could provide materials with very high second-order nonlinearities combined with very good transparency and mechanical stability. Moreover, MOFs have been shown to be NLO-switches,36 and their NLO properties can be modulated by guest molecules as well as by doping their structure.37 In addition to the aforementioned properties, some of the noncentrosymmetric phases could also exhibit reactivitybased properties and other properties as, for instance, ferroelectricity.38−40 Thus, the design of NLO hybrid crystalline phases could result in obtaining multifunctional materials. In the current contribution, we employed our previously developed method8,18−20 to the characterization of the linear and nonlinear optical susceptibilities of two isomorphic MOF materials displaying a diamondoid lattice, PEB-Zn and PEB-Cd, as well as one example of material with 2-dimensional structural motif, PEB′-Cd. These MOFs were selected because of their high SHG activity, as discussed above, and their well-defined crystal structure (no disorder and/or disordered solvent molecules). Their structures have already been investigated experimentally, while their NLO properties have been characterized using the Kurtz-Perry powder technique.30,31 Moreover, a first theoretical investigation of the NLO responses of PEB-Zn and PEB-Cd has recently been reported by one of us,41 adopting the so-called cluster approach.42,43 The main limitation of this approach is the size- and shape-dependence of the cluster linear and nonlinear optical responses. In addition, contrary to molecular crystals, building MOFs clusters necessitates to cut bonds between cations and anions, which in some cases leads to charged clusters and also to different strategies to saturate or not the atoms at the periphery by hydrogen atoms. Indeed, the cluster charge and the presence of saturating H atoms have generally a non negligible impact on the (hyper)polarizabilities. To the best of our knowledge, there have been yet neither theoretical nor experimental assessment of the full χ(1) and χ(2) tensors for hybrid organic−inorganic systems. Indeed, computational investigations have concentrated on the hyperpolarizabilities of molecules and clusters,41,44−47 whereas the oriented electron gas model was the only method for interrelating β with χ(2).48 Therefore, the main objective of this contribution is to provide a first assessment of the full χ(1) and χ(2) tensors for these three representative NLO MOFs within the combined local field-charge embedding electrostatic scheme approach. The paper is organized as

follows. Section 2 describes the theoretical and computational aspects of our multiscale approach. Section 3 is devoted to the Kurtz-Perry method. Then, section 4 presents and discusses the results before conclusions are drawn in section 5.

2. THEORETICAL AND COMPUTATIONAL ASPECTS Starting from X-ray diffraction data of the low-temperature (LT) phases (T = 173 K) of PEB-Zn and PEB-Cd (C2 space group)30 as well as from the structures of PEB-Zn49 (C2 space group) and PEB′-Cd (Fdd2 space group),31 obtained at room temperature (RT), the geometry was optimized with the CRYSTAL14 package50,51 using periodic boundary conditions (PBC). These optimizations were carried out at the DFT level with the B3LYP exchange-correlation (XC) functional and with the LANL2DZ effective core potential (ECP) for Zn and Cd together with the 6-31G(d,p) basis set for the other atoms. Only the fractional coordinates were optimized while the cell parameters were kept frozen to their experimental values. The RT structure of PEB-Cd was estimated by considering the same breathing effect as in PEB-Zn, that is, the lattice parameters and unit cell volume were scaled according to RT LT dPEB − Cd = dPEB − Cd

RT dPEB − Zn LT dPEB − Zn

(1)

where d stands for the a, b, and c lattice parameters as well as the unit cell volume. The β angle was adjusted to match these breathings. The calculations of molecular properties, α and β, were performed for the individual cations (+2 charge) and anions (−1 charge) within their embedding electric field. This field was simulated by a 100 Å radius sphere of Mulliken point charges, calculated using the PBC/B3LYP method on the crystal-optimized geometries. We have recently discussed the adequacy of this choice of charge definition.52 The static (λ = ∞) responses were evaluated at the second-order Møller− Plesset method (MP2) level. To estimate dynamic MP2 responses (vide inf ra), the DFT/B3LYP method was used to evaluate the static and dynamic properties. At both levels, the basis set consists in the LANL2DZ effective core potential (ECP) for the Zn and Cd cations and the 6-311++G(d,p) basis for the anion atoms. All the molecular property calculations were performed with Gaussian09.53 The frequency dispersion of the molecular properties was described by employing a modified multiplicative scheme, where the static MP2 values are combined with the static [α(0;0)] coupled-perturbed Kohn−Sham (CPKS) and dynamic [α(−ω;ω)] time-dependent DFT (TDDFT) tensors evaluated using the B3LYP XC functional. First, the static (MP2 and CPKS/B3LYP) polarizability tensors were diagonalized separately with the aid of the transformation matrices X ′ and X ″, respectively. Using the X ″ matrix, the TDDFT/B3LYP polarizabilities are then transformed to the eigenaxes system of the CPKS/B3LYP polarizability tensor. Finally, the dynamic MP2 polarizability tensor components are obtained according to the formula αij′ MP2( −ω; ω) = αij′ MP2(0; 0)

α″B3LYP ( −ω; ω) δij α″B3LYP (0; 0)

+ [(1 − δij)αij″ B3LYP(−ω ; ω)]

(2)

The static [β(0;0,0)] hyperpolarizability tensors are transformed to a reference frame minimizing most of the off-diagonal B

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3. KURTZ-PERRY METHOD Kurtz-Perry method is the usual technique to characterize the SHG effects of powders.34 It is one of the methods providing an answer to the crystallographer’s question about the noncentrosymmetricity of the phase. It is also a fast screening tool to assess the NLO responses of just-synthesized materials. Kurtz-Perry method has recently received a revived interest, and it was revisited by Aramburu et al.54 The full expression for the SHG signal intensity is provided in refs 35 and 54, under the following form:

components (using the transformation matrices Y ′ and Y ″ for MP2 and B3LYP, respectively). These transformation matrices are built such that (1) the z axis is chosen parallel to β (0;0,0) [of which the components are given 1 by βi = 5 ∑j (βijj + βjij + βjji))]; (2) the x axis is as much parallel as possible to the direction of the lowest eigenvalue of the static polarizability tensor [the z-component of this direction vector is removed using the Gram-Schmidt orthogonalization method)]; and (3) y is orthogonal to x and z (y = z × x). In order to approximate the MP2 second harmonic generation (SHG) dynamic [β(−2ω;ω,ω)] first hyperpolarizability, the multiplicative scaling procedure is performed for every component separately if

1 3


ny ∼ nz. Going from LT to RT, the χ(1) tensor components decrease, though by less than 0.1. A similar reduction is achieved when going from PEB-Zn to PEB-Cd, in particular for the χ(1) 33 component and nz. The situation is different in PEB′(1) Cd, where two χ(1) tensor components dominate [χ(1) 11 and χ33 ]. In this case, nx ∼ nz > ny. The MP2-based wavelengthdispersion curves of the refractive indices, plotted in Figure 3, show that these relationships between the refractive indices hold for wavelengths ranging from 2000 to 650 nm. The χ(2) tensor components have opposite signs in PEB-Zn and PEB-Cd because their structures are related more or less by inversion symmetry (disregarding the cations). At λ = 1064 nm, (2) the dominant χ(2) tensor component [χ(2) 112 and χ211 ] of the PEB compounds ranges from 50 to 63 pm/V. For the linear response, going from LT to RT these dominant components decrease, whereas a similar effect (on the absolute values) is observed when substituting the Zn cations by Cd cations. For PEB′-Cd, the χ(2) responses are larger and attain 100 pm/V for (2) value for PEB′-Cd than in χ(2) 333 at λ = 1064 nm. This larger χ the case of the PEB compounds originates from a smaller angle between the β vector and the crystal axes (Table 4), which overcompensates the smaller βtot of the PEB′ anion. Owing to these χ(2) responses going up to 100 pm/V MOFs belong to the same category of NLO materials as 4-(N,N-dimethylamino)-3-acetamidonitrobenzene (DAN), of which the dominant

Figure 3. Wavelength dispersion of the refractive indices of PEB-Zn (LT structure), PEB-Cd (LT structure), and PEB′-Cd (RT structure) determined at the MP2 level of approximation.

χ(2) tensor component, as estimated at the same level of approximation and wavelength, attains 121 pm/V.18 Still, their performances are smaller than those of MNA (−363.3 pm/V) and stilbazolium-based organic crystals like DAST (480 pm/V at 1542 nm). Kurtz-Perry Responses for PEB-Zn and PEB-Cd. The outcome of the Kurtz-Perry experiment is simulated in Figure 4 as a function of the grain size. An experimental I2(PEB-Zn)/ I2(PEB-Cd) contrast ratio of 1.16 (= 400/345) was measured at RT for grain size of 76 ± 13 μm.30 With the assumption that this contrast originates from differences in their g(r) values, averages over the grain size have been calculated using their χ(1) and χ(2) tensor components. g(r) contrast ratios of 0.98 ± 0.25 and 1.29 ± 0.33 were obtained for the LT and RT structures, respectively. In fact, upon increasing the temperature from LT to RT, the structural changes lead only to a minor increase of g(r) of PEB-Zn, whereas g(r) of PEB-Cd drops clearly. This is consistent with the slightly larger decrease of the χ(2) tensor F

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PEB-Zn is about 10% larger than that of PEB-Cd, (ii) χ(2) of PEB′-Cd, which is about 100 pm/V or twice larger than that of PEB-Cd, is similar to that of 4-(N,N-dimethylamino)-3acetamidonitrobenzene (DAN), though still a step smaller than that of MNA or DAST, and (iii) the change of crystal structure accompanying an increase of temperature from 173 to 298 K leads to a decrease of χ(2) by ca. 10%. For the isostructural PEB-Zn and PEB-Cd, the outcome of Kurtz-Perry SHG powder method has then been simulated as a function of the grain size, demonstrating that differences between the two MOF’s only show up for room temperature structures. A contrast ratio of 1.29 was estimated, in qualitative agreement with experiment. Together with a previous investigation on MOFs clusters,41 this work opens the way toward a theoretically based design of MOFs with outstanding second-order nonlinear optical responses. The progress goes in parallel with improving the comparison between the experimental and numerical simulations results of the Kurtz-Perry SHG intensities. The proposition of Aramburu et al.35 goes in this direction. It consists of using glass spheres and small concentration of the NLO-active materials to better control critical factors such as the volume packing fraction and the scattering function.

Figure 4. g(r) Kurtz-Perry function for PEB-Zn and PEB-Cd as obtained at the MP2 level of approximation.

components from LT to RT for PEB-Cd than PEB-Zn, though this is not the only factor due to the nonlinearity of eq 4 of ref 54. The RT calculations are in good qualitative agreement with the experiment because they predict a larger response for the Zn derivative for any grain size. An insight into the nature of the SHG signal might also be given from the calculations. The percentages of types I (interaction of two slow beams at ω, described by refractive index n+ω with fast beam at 2ω described by refractive index n−2ω; for brevity: ++ → −) and II (interactions of slow, n+ω, and fast, n−ω, beams at ω with fast beam at 2ω, n−2ω; for brevity: +− → −; for a more detailed description see ref 55) phase matchings (PM) are presented in Table 5. Interestingly, our calculations

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S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b00217. Lattice parameters, optimized fractional coordinates, and atomic charges of PEB-Zn, PEB-Cd, and PEB′-Cd structures; static (λ = ∞) and dynamic (λ = 1064 nm) polarizability α and first hyperpolarizability β tensor components (PDF)

Table 5. Contribution (in %) of Type I (++ → −) and Type II (+− → −) Phase Matchings as Obtained for r = 76 μm Using the Local Field/Charge Embedding Method PEB-Zn PEB-Cd

LT RT LT RT

type I

type II

98 99 74 77

0 0 24 22

ASSOCIATED CONTENT

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. Tel: (+32) 081 724554. *E-mail: [email protected]. Tel: (+32) 081 724554. Notes

The authors declare no competing financial interest.

predict that the nature of the KP signal differs between the two compounds. For PEB-Zn, type I PM is largely dominant, whereas in the case of PEB-Cd up to 22−24% come from type II PM.

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ACKNOWLEDGMENTS

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REFERENCES

This research was supported in part by PL-Grid Infrastructure as well as by the Belgium government (IUAP N°P7/05, Functional Supramolecular Systems). T.S. acknowledges the financial support of IUAP N°P7/05 for his postdoctoral grant. The calculations were performed on the computers of the Consortium des Equipements de Calcul Intensif and mostly those of the Technological Platform of High-Performance Computing, for which we gratefully acknowledge the financial support of the FNRS-FRFC (Convention nos. 2.4.617.07.F and 2.5020.11) and of the University of Namur.

5. CONCLUSIONS In this paper, we have presented the first application of the combined local field theory/charge embedding approach to the evaluation and interpretation of the linear (χ(1)) and secondorder nonlinear (χ(2)) optical properties of metal−organic frameworks. Three MOFs have been selected, bis{4-[2-(4pyridyl)ethenyl]benzoato}-zinc(II) (PEB-Zn), bis{4-[2-(4pyridyl)ethenyl]benzoato}-cadmium(II) (PEB-Cd), and bis{4[3-(4-pyridyl)ethenyl]benzoato}-cadmium(II) (PEB′-Cd). The second harmonic generation performances of PEB-Zn and PEB-Cd have been previously characterized experimentally using the Kurtz-Perry powder method and amount to 400 and 345 with respect to α-quartz (contrast ratio of 1.16),30 whereas PEB′-Cd is made of a similar anionic ligand, but its crystal structure is different. The simulations, based on second-order Møller−Plesset property calculations, conclude that (i) χ(2) of

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DOI: 10.1021/acs.jpcc.6b00217 J. Phys. Chem. C XXXX, XXX, XXX−XXX