M = Li+, Na+, and K+ - American Chemical Society

J. Phys. Chem. C 2009, 113, 3339–3344

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Role of Metal Ions (M ) Li+, Na+, and K+) and Pore Sizes (Crown-4, Crown-5, and Crown-6) on Linear and Nonlinear Optical Properties: New Materials for Optical Birefringence Ayan Datta* School of Chemistry, Indian Institute of Science Education and Research ThiruVananthapuram, College of Engineering Technology Campus, ThiruVananthapuram-695016, Kerala, India ReceiVed: NoVember 20, 2008; ReVised Manuscript ReceiVed: January 4, 2009

Density functional theory (DFT) calculations are performed on Li+, Na+, and K+ complexes of crown-4, crown-5, and crown-6, respectively. Calculations show that, for all three structures, the rings are puckered to maintain the staggered conformations along the C-C dihedral angles. The Li+, Na+, and K+ are deflected from the center-of-mass of the crown ethers by 0.82, 0.98, and 0.33 Å, respectively, toward the surface more exposed to O atoms. These M+ complexes have different linear (R) and nonlinear (β) polarizations on the top and bottom surfaces for equal distortions on either surface. The variation in R and β is also studied with respect to the movement of the cations along the pore of the crown ether. The inherent asymmetry in the in-plane (Rip) and out-of-plane (Rop) components of the polarizations leads to a single-humped profile of optical birefringence with respect to the motion of the M+ ion along the pore. Our calculations show that the optical birefringence for these molecules, in their equilibrium geometry, is very close to their maximum possible theoretical limit. Introduction Ionophores like crown ethers,1-3 cryptands,4,5 and calixarenes6-8 are molecules of major interest because of their wide range of applications in molecular recognition, drug delivery, siteselective binding, nanocatalysis, and enzymes. Crown ethers are macrocyclic molecules, which, in their simplest form, are cyclic oligomersofdioxanesandhaveageneralformulaof(-CH2CH2O-)n.9,10 Macrocycles with n ) 4, 5, and 6 are called crown-4, crown-5, and crown-6, respectively. Larger crown-n-ethers are difficult to synthesize because of the large entropy of activation for the formation of these molecules from dioxane units. Thus, crown4, crown-5, and crown-6 can be considered as good general models for these classes of molecules. One of the most interesting properties of crown-n-ethers is their ability to selectively bind to ions depending on their pore size and, thus, “n”. Crown-4-ether selectively binds to Li+, crown-5-ether to Na+, and crown-6-ether to K+. The effective charge transfer from the lone pair of electrons on oxygen to the metal ions leads to large linear (R) and nonlinear optical (β) (NLO) polarizations in this class of molecules.11,12 There has been a sustained interest in designing molecules and aggregates that have large NLO responses for applications in all optical devices, advanced lasers, frequency doublers, and optical rectifications.13 A very effective strategy to increase NLO responses of molecules is through the functionalization of molecules with D(donor)-π-A(acceptor) systems that increase the charge-transfer ability of the systems.14 However, a very important bottleneck of this strategy arises from the fact that these molecules, being dipolar in the ground state, lead to antiparallel packing in the aggregates like thin films and single crystals, thereby effectively canceling out the NLO response of the material.15 An effective strategy to overcome this * To whom correspondence [email protected].

should

be

addressed.

E-mail:

Figure 1. Schematic representation of the in-plane and out-of-plane polarizations in a crown ether with respect to the movement of the cation (M+) along the center-of-mass of the system; +d and -d represent the distance (in Å) above and below the center-of-mass.

limitation is through the use of weak intermolecular forces like H-bonding that can effectively stitch these molecules in a pseudo 1-D system and thereby increase the response of the material.16 However, the use of other weak intermolecular forces like cation-π interactions, cation-alkyl interactions, and van der Waals forces has been rarely investigated in the literature, though there have been recent attempts.17,18 To the best of our knowledge, this work is the first ab initio calculation that systematically studies the cation-crown ether interactions for advanced material applications. The disklike nature of these molecules also ensures that binding on metal ions leads to nonisotropic polarizations in these systems with a large difference between the in-plane (ip)/ ordinary and out-of-plane (op)/extraordinary polarizability components. Figure 1 schematically shows this orientation. An even larger anisotropy can be created by the movement of the

10.1021/jp810198n CCC: $40.75  2009 American Chemical Society Published on Web 02/04/2009

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metal ion across the center-of-mass from the top to the bottom surface. Such a large anisotropy in polarization leads to differential refractive indices (η)19,20 along the ordinary and the extraordinary axes of polarizations, thereby creating optical birefringence. Whereas a significant amount of research has been devoted toward designing molecules with large linear and nonlinear polarizations, modeling optical birefringence at the molecular scale has not received much attention inspite of its potential applications. Our calculations for the minimal energy conformations in the crown ethers, as well as the M+ · · · crown ethers, show that the rings are puckered, and the M+ binds to the surface of the crown ethers, which have the O atoms more exposed toward the metal ions. Thus, the binding of the metal ion to the crown ether is surface-specific. We have performed extensive calculations to study the variation in R and β with the change in distance of the metal ions from the center-of-mass along both the top and the bottom surfaces of the crown ether. In the following sections, we discuss the computational approach and present and explain the results of our calculations. Finally, we conclude the paper with inferences and future prospects. Computational Techniques

Figure 2. Optimized minimum energy geometries for (i) crown-4ether, (ii) Li+ · · · crown-4-ether, (iii) crown-5-ether, (iv) Na+ · · · crown5-ether, (v) crown-6-ether, and (vi) K+ · · · crown-6-ether.

The geometries for all the structures have been optimized using the Becke three-parameter Lee-Yang-Parr (B3LYP)21 hybrid density functional theory (DFT) at the 6-31G(d) level of basis set.22,23 Additional frequency calculations were performed on the minimum energy structures to confirm that these structures belong to local energy valleys. Different possible orientations of the rings and the chelated complexes were considered, and those reported here are the minimal energy ones. The coordinate systems for these geometries were modified so that the centers-of-mass for the systems have Z axes perpendicular to the plane of the molecule. Starting from the minimal energy geometries of the M+ · · · crown ether, the distance of the M+ ion from the center-of-mass of the rings (d) is increased along both the upper plane (+d), as well as the bottom plane (-d), along the Z axis. The linear and nonlinear polarizations are calculated for each of these geometries. The overall rotational invariant polarizabilities and hyperpolarizabilities (isotropic averages) are reported as

1 Rin-plane ) (Rxx + Ryy) 2 Rout-of-plane ) Rzz βav ) √B

(1) (2) (3)

where B ) (βxxx + βxyy + βxxy)2 + (βyyy + βyzz + βxxy)2 + (βzzz + βxxz + βyyz)2 We have calculated these responses at a frequency of 0.0429 AU, corresponding to 1064 nm of the Nd:YaG laser using the polarization response formalism proposed by Snijders and Baerends.24 All the frequency-dependent polarizabilities and hyperpolarizabilities are computed using the ADF package at the PW91/TZP level.25 The calculated molecular polarizabilities are used to calculate the refractive indices (η) using the wellknown Lorentz-Lorenz relationship26

η2(ω) - 1 4π ) NR(ω) 3 η2(ω) + 2

Figure 3. Plots for electron localization functions along the mean macrocyclic ring plane for (a) Li+ · · · crown-4-ether, (b) Na+ · · · crown5-ether, and (c) K+ · · · crown-6-ether.

η(ω)in-plane as the refractive index at the molecular plane of the crown ether and η(ω)out-of-plane as the component along the perpendicular axis, we define the optical birefringence as

δ ) |η(ω)in-plane - η(ω)out-of-plane |

(5)

Results and Discussion

(4)

where N is the average number of molecules per unit volume, and R(ω) is the mean polarizability of the molecule. Defining

In Figure 2,the optimized ground-state geometries for the crown ethers and the M+-chelated crown ethers are shown (see Supporting Information for coordinates). There are several interesting features in these structures. The (CH2CH2O)n rings

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Figure 4. Variation in energy (in kcal/mol) with respect to the movement of the M+ ion (in Å) out-of-plane of the crown ether along the surface more exposed to O atoms (+d) and less exposed to O atoms (-d) for (i) Li+ · · · crown-4-ether, (ii) Na+ · · · crown-5-ether, and (iii) K+ · · · crown6-ether.

Figure 5. Variation in polarizability (in AU) with respect to the movement of the M+ ion (in Å) out-of-plane of the crown ether along the surface more exposed to O atoms (+d) and less exposed to O atoms (-d) for (i) Li+ · · · crown-4-ether, (ii) Na+ · · · crown-5-ether, and (iii) K+ · · · crown6-ether.

in all systems are puckered to maintain a staggered conformation across the individual -CH2-CH2 dihedral angles. The binding of cations to all of the crown ethers is found to be exothermic with ∆E binding (defined as Ecomplex - Ecrown ether - Ecation) calculated as -98.03, -71.105, and -75.05 kcal/mol for crown4-ether · · · Li+, crown-5-ether · · · Na+, and crown-6-ether · · · K+, respectively. The average distance of the M+ ion from the

oxygen atoms is 1.95, 2.38, and 2.78 Å, respectively, for (ii), (iv), and (vi). Thus, increasing the pore size of the crown ether increases the distance between the cation and the electronegative O atoms, thereby decreasing the stability of the M+ complexes. However, it is interesting to note that the behavior is not monotonic as the binding energy of the crown-6-ether · · · K+ complex is 4.0 kcal/mol more than that for the crown-5-

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Figure 6. Variation in second-harmonic generation (SHG) and electro-optic Pockel effect (EOPE) (βav, in AU) and average dipole moment (|µ|, in Debye) with respect to the movement of the M+ ion (in Å) out-of-plane of the crown ether along the surface more exposed to O atoms (+d) and less exposed to O atoms (-d) for (i) Li+ · · · crown-4-ether, (ii) Na+ · · · crown-5-ether, and (iii) K+ · · · crown-6-ether.

ether · · · Na+ complex, even though the distance between the O atoms and the metal ions increases for the K+ complex. This can be understood by comparing the distance of the M+ ion from the center-of-mass of the ring. The Li+, Na+, and K+ ions are deflected from the centers-of-mass of the crown-4, crown5, and crown-6 rings by +0.88, +0.98, and +0.38 Å along the Z axis, respectively. Note that we consider the convention of positive displacement of the M+ ion from the center-of-mass as movement along the surface more exposed to the O atoms and vice versa for the negative. Thus, the crown-5-ether · · · Na+ faces the maximal puckering strain, which explains its lowest stability in the series. Also, the fact that the deflection of all the M+ ions is positive along the Z axis suggests that the interaction between the M+ ion and the crown ethers is essentially ionic in nature. This is clearly understood from the plots of the electron localization functions (ELF)27 for the complexes along the mean plane of the ligand, as shown in Figure 3. For all three complexes, there is no intermixing of electrons between the ligand and the M+ ions, and electrons are localized on the ligands with very little electron density between the ligand and the M+. The importance of M+ · · · O atom interactions can also be understood on the basis of asymmetric potential energy profiles of binding of the M+ ion to the crown ether along the top and the bottom surfaces, as shown in Figure 4. It is clearly seen from the plots that the M+ ions are more favorably bound to the surface more exposed to the O ends rather than to the hydrocarbon ends for the same amount of displacement along both surfaces. Increasing the displacements ((d) from the centers-of-mass destabilizes all the systems as that decreases

the electrostatic interactions. However, such a simplistic explanation does not account for the fact that the M+ ions are deflected by +0.88, +0.98, and +0.38 Å along the Z axis for (i), (ii), and (iii), respectively, in their optimized geometries. Such deflections can be understood from the fact that, for d ) 0.00 Å, the M+ · · · O distances become lower than the average bond lengths, thereby destabilizing the systems. For example, at d ) 0.00 Å, one of the M+ · · · O bonds becomes as small as 1.63, 1.96, and 2.62 Å for crown-4-ether · · · Li+, crown-5ether · · · Na+, and crown-6-ether · · · K+, respectively. To study the variation in the polarizability (both in-plane and out-of-plane components) with such a movement of ions across the crown ether, frequency-dependent calculations are performed at ω ) 0.049 AU. In Figure 5, the profiles are shown for all the systems. There are two major inferences from the plots. The first one being that the in-plane component of R (Rip) is greater than the out-of-plane component (Rop) for distortions ((d), which can be understood from the fact that the major interactions between M+ and the crown ether are along the pseudoplane where O atoms are located, which is perpendicular to the movement of the ion. Distortions more than 3.5 Å are not physically meaningful as they lead to destabilization of the system by ∼50 kcal/mol (see Figure 4), and even polar solvent cages would be insufficient to stabilize such unstable geometries. The other major conclusion from Figure 5 is that the maximum difference between Rip and Rop is created for d ) 0 to (1 Å and decreases with further increases in d. We believe that this is a significant result as d for the optimized geometries for all the complexes is less than 1 Å. Thus, the equilibrium

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Figure 7. Variation in refractive index (η) and optical birefringence (δ) with respect to the movement of the M+ ion (in Å) out-of-plane of the crown ether along the surface more exposed to O atoms (+d) and less exposed to O atoms (-d) for (i) Li+ · · · crown-4-ether, (ii) Na+ · · · crown5-ether, and (iii) K+ · · · crown-6-ether.

geometries are predicted to have a very large anisotropy in polarization between the in-plane component and out-of-plane component. The movement of the M+ ion across the pore also leads to a change in the first hyperpolarizability, β. In Figure 6, we show the variation in two typical nonlinear polarizations, the secondharmonic generation, βav(-2ω;ω,ω), and also in the electrooptic Pockels effect ( EOPE), βav(-2ω; 2ω,0), with increasing the distance ((d) between the ion and the crown ether. Both SHG and EOPE are minimal at the equilibrium geometries and increase with an increase in the separation distance. Such a trend in β can be readily understood from the similar variation in the ground-state dipole moment, [|µ| ) (µx2 + µy2 + µz2)1/2], where d is minimum at the equilibrium geometries. It is important to note that, since equilibrium geometries are noncentrosymmetric, the dipole moments, as well as first hyperpolarizabilities, are nonzero. For example, |µ| and (βSHG and βEOPE) are 1.46 D and (34.92 and 34.73 AU), 1.75 D and (61.03 and 59.62 AU), and 0.51 D and (15.64 and 13.48 AU) for Li+ · · · crown-4-ether, Na+ · · · crown-5-ether, and K+ · · · crown-6-ether, respectively. Thus, metal-ion-complexed crown ethers are NLO-active molecules. However, the NLO activity is least at the equilibrium geometries, though small distortions that would increase d will lead to an increase in the SHG and the EOPE efficiencies. The other interesting result from these calculations is that both |µ| and βav are greater for -d than +d for the same d. This can be readily understood from the fact that the extent of charge separation is greater in the -d axis than in the +d axis as the distance between the M+ ion and the O atoms is greater.

In Figure 7, we compute the variation in the refractive indices (η) of the three complexes with the movement of the metal ion across the pore of the crown ether. We have used densities of 1.089, 1.113, and 1.237 g/mL corresponding to the available densities of the crown-4-ether, crown-5-ether, and crown-6ether, respectively.28 Calculations show that both the in-plane and the out-of-plane components of η increase monotonically with an increase in (d. For all three complexes, the out-ofplane component of η is more sensitive to the movement of the metal ion with a ∼4% change for ∼3 Å movement of the metal ion across the center-of-mass of the crown ether. More interestingly, however, the optical birefringence (δ) for all three complexes shows an inverted U-shaped profile with maxima in the range of (1 Å and decreasing for greater (d. Even accounting for the fact that the equilibrium geometries have +d of 0.88, 0.98, and 0.38 Å, δ are 0.145, 0.147, and 0.187 for crown-4-ether, crown-5-ether, and crown-6-ether, respectively, which are within 98% of their maximal possible limit for any distortions ((d). Conclusion There are several important conclusions from our present model study on the prototypical examples of complexation of metal ions with crown ethers. For all the systems, the metal ions bind to the side more exposed to the more electronegative atoms of the crown ethers, thereby creating an asymmetric electrostatic profile for the movement of metal ions across the pore of the crown ether on either surface. Metal-ion-complexed

3344 J. Phys. Chem. C, Vol. 113, No. 8, 2009 crown ethers are found to be excellent materials for both linear and nonlinear optics. Whereas the NLO coefficients are minimal at the equilibrium distances, thus, limiting their use for major technological applications, the anisotropy between the in-plane and out-of-plane components of the refractive indices is almost maximal at their equilibrium distances. Thus, these M+ ion · · · crown ethers are predicted to have very a large optical birefringence at their equilibrium distances. This certainly has a very large prospect for future device integration. In the ideal bottom-up approach for designing molecular materials, the critical step invariably rests in selecting the basic molecular units in its highest activity. Our calculations show that M+ · · · crown ethers are already fine-tuned to almost their maximal ability in their ground-state geometries. The fact that the movement of a small metal ion across the pore of a simple molecule like a crown ether leads to a ∼6% (ηip + ηop) change in the overall refractive index suggests a promising application of artificial ionophores, as well as Na+/K+ ion channels, for new materials for all optical devices. Acknowledgment. The calculations reported here were performed in the computing facility of IISER-Thiruvananthapuram. This article is dedicated to Professor Weston Thatcher Borden on the occasion of his 65th birthday. Supporting Information Available: Ground-state-optimized geometries, frequencies, and complete ref 23. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) (a) Liu, C.; Walter, D.; Neuhauser, D.; Baer, R. J. Am. Chem. Soc. 2003, 125, 13936. (b) Olsher, U.; Hankins, M. G.; Kim, Y. D.; Bartsch, R. A. J. Am. Chem. Soc. 1993, 115, 3370. (c) Marsella, M. J.; Swager, T. M. J. Am. Chem. Soc. 1993, 115, 12214. (d) Warshawsky, A.; Kahana, N. J. Am. Chem. Soc. 1982, 104, 2663. (2) (a) Zhang, H.; Chu, I. H.; Leming, S.; Dearden, D. V. J. Am. Chem. Soc. 1991, 113, 7415. (b) Zhang, H.; Dearden, D. V. J. Am. Chem. Soc. 1992, 114, 2754. (c) Olmstead, M. M.; Power, P. P. J. Am. Chem. Soc. 1985, 107, 2174. (d) Shinkai, S.; Nakaji, T.; Nishida, Y.; Ogawa, T.; Manabe, O. J. Am. Chem. Soc. 1980, 102, 5860. (e) Cram, D. J.; Roitman, J. N. J. Am. Chem. Soc. 1971, 93, 2231. (3) (a) Dietrich, B.; Viout, P.; Lehn, J.-M. Macrocyclic Chemistry: Aspects of Organic and Inorganic Supramolecular Chemistry; Wiley-VCH: Weinheim, Germany, 1993. (b) Pedersen, C. J. J. Am. Chem. Soc. 1967, 89, 2495. (c) Pedersen, C. J. J. Am. Chem. Soc. 1967, 89, 7017. (d) Gokel, G. W. Chem. Soc. ReV. 1992, 21, 39. (4) (a) Gokel, G. W. Crown Ethers and Cryptands; Royal Society of Chemistry: Cambridge, U.K., 1991. (b) Jones, J. W.; Zakharov, L. N.; Rheingold, A. L.; Gibson, H. W. J. Am. Chem. Soc. 2002, 124, 13378. (c) Mason, S.; Llinares, J. M.; Morton, M.; Clifford, T.; Bowman-James, K. J. Am. Chem. Soc. 2000, 122, 1814.

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