Nonlinear Optical Molecular Switches for Alkali Ion Identification

This work demonstrates by means of DFT and ab initio calculations that recognition of alkali cations can be achieved by probing the variations of the second-order nonlinear optical properties along the commutation process in spiropyran/merocyanine systems. Due to the ability of the merocyanine isomer to complex metal cations, the switching between the two forms is accompanied by large contrasts in the quadratic hyperpolarizability that strongly depend on the size of the cation in presence. Exploiting the nonlinear optical responses of molecular switches should therefore provide powerful analytical tools for detecting and identifying metal cations in solution.


Introduction
For a few years now, the design of molecular switches with large nonlinear optical (NLO) contrasts has been the focus of a lot of experimental and theoretical investigations [1][2][3][4]. These systems, characterized by their ability to alternate between two or more different chemical forms displaying contrasts in one of their NLO properties, are of particular interest in the development of new photonic technologies including frequency doublers, space communications or biomedical imaging [5,6]. The commutation can be triggered by using various external stimuli such as a variation of pH [7][8][9], OPEN ACCESS temperature [10], light [11][12][13], redox potential [14][15][16], or solvent polarity. At the molecular scale, the property to optimize is usually the first hyperpolarizability (β), which is defined as the secondorder response of the electric dipole moment (μ) to an external electric field, whereas a few studies have reported molecules with second hyperpolarizability (γ) contrasts [17]. A wide variety of NLO switches have been proposed, based e.g., on the indolino-oxazolidine [7][8][9]18,19], anil [11,[20][21][22][23] or spiropyran [24] moieties, in which the amplitude of the β contrasts can be modulated by structural modifications and chemical functionalizations, i.e., by varying the nature and length of the π-conjugated backbone, and/or the nature and position of donor and acceptor substituents.
Recently, we demonstrated by means of ab initio calculations that NLO switches based on the merocyanine/spiropyran equilibrium could also be exploited for selective identification of metal ions, thanks to the ability of the merocyanine form to complex cationic species such as alkali, alkaline earth, or transition metal ions. The design of molecular sensors able to recognize cations is of technological relevance with respect to many ecological, toxicological, or chemical issues [25,26]. In merocyanine/ spiropyran systems, the commutation processes were shown to induce large NLO contrasts that depend on the nature of the cation involved, providing therefore a powerful detection tool [27] complementary to standard techniques based on variations in the absorption or fluorescence spectra [28,29]. In this paper, we pursue our seminal investigation on a spiro[indoline-8-(benzothiazol-2-yl)-benzopyran] derivative (Scheme 1), whose metallochromic properties [30,31] and β contrasts [24,27] were previously reported, by analyzing its effectiveness to recognize alkali ions by means of variations in its linear and second-order nonlinear optical properties. In addition, we also concentrate on the thermodynamics of the cation complexation. Scheme 1. Equilibrium between the spiropyran form and the merocyanine form complexing an alkali ion.

Molecular Structures and Thermodynamic Analysis
Representative bond lengths and torsion angles of the structures optimized in acetonitrile at the M06/6-311G*/Stuttgart1997 level are gathered in Table 1 for the spiropyran, the merocyanine, and the merocyanine complexing alkali ions. The largest variations appear for bonds 12-13 and 13-14 (ligand-metal, d O-M and d N-M distances) as well as 12-14 (claw opening distance), which evolves in parallel to the cation size, i.e., Li + < Na + < K + < Rb + < Cs + . Note that the d O-M distance is systematically shorter than the d N-M one, due to the generally larger negative charge on the oxygen (q O ϵ [−0.47, −0.54]) compared to the nitrogen (q N ϵ [−0.41, −0.54]), where q O has been obtained from Mulliken population analysis. The reverse trend is observed for the 11-12 and 14-15 bond lengths, which get slightly smaller (and the bond stronger) when the cation is larger, evidencing a weaker complexation effect. The cation complexation has also an impact on the bond length alternation [BLA = ½ (d 2-3 + d 4-5 − 2d 3-4 )] along the vinylic bridge linking the two aromatic moieties, which decreases from 0.039 Å for Li + to 0.021 Å for Cs + . Indeed, a stronger complexation by the ligand induces the lengthening of the O-C bond, which then reduces the donor character of the ligand moiety (towards the accepting ring) and therefore increases the BLA. Owing to these π-conjugation effects and their modifications upon cation complexation, most bond lengths display systematic variations as a function of the cation size. Though the merocyanine moiety is planar, the θ 11-12-13-14 dihedral angle increases significantly from Li + (13.1°) to Rb + (69.1°), which is related to the growing size of the cation and the need for a wider opening of the ligand claw. The global charge of the different fragments (S i ) of the compounds were then computed at the M06/6-311G*/Stuttgart1997 level using the Mulliken approximation (Table 2). Upon complexing Cs + the modification of the charge distribution is mostly located on the nearby ligands, of which the electron density increases. Then, going towards smaller cations, this charge transfer effect is enhanced and the ligands get more negative while the cations get less and less positive. As a matter of fact, the resulting excess positive charge is distributed over the rest of the system, and particularly on the two closer aromatic rings (S 5 and S 9 ) but also, to a lower extent, on the merocyanine part. Switching between the spiropyran and merocyanine forms is also characterized by charge reorganizations, resulting from the opening of the spiro function.  Table 3 summarizes the main thermodynamic data for the complexation reaction of the alkali ion by the merocyanine form. The most exothermic reaction is the complexation of the largest cations (Rb + and Cs + ). The enthalpy of reaction evolves non-monotonically with the cation size, decreasing (in absolute value) from Li + to K + , and then increasing to similar values for Rb + and Cs + . To some extent, the Gibbs free energies behave similarly with the cation size, with however a more pronounced difference in the complexation energy of Li + compared to that of the largest cations. This is attributed to the larger amplitude of the entropy in the case of Li + , due to the fact that the ligands are more tightly bound to the alkali atom. Indeed, the complexation reaction is accompanied by a decrease of the entropy and the amplitude of that reduction tends to increase as a function of the covalent character of the cation-ligand bonds. Table 3. Enthalpy, entropy, and Gibbs free enthalpy of reaction (kcal mol 1 except the entropies in cal mol 1 K 1 , at 298.15 K and 1 atm) for the complexation reaction calculated at the M06/6-311G* level in acetonitrile for different alkali cations.
Selected vibrational frequencies calculated at the M06/6-311G* level in acetonitrile are listed in Table 4. Those around 1,600 wavenumber correspond to CO stretching vibrations and display a strong IR intensity. The frequency of these vibrational modes increases with the size of the cation. Indeed, smaller cations lead to a larger covalent character of the oxygen-metal bond, which translates into a smaller CO bond strength (as indicated by the increase of the CO bond length, see Table 1) and therefore into a smaller vibrational frequency. An opposite behavior is observed for the low frequency mode (684-495 cm 1 ), which presents a strong O-cation and N-cation stretching character. In this case, the smaller the cation, the stronger the covalent bonds and the stronger the bond strengths.

Linear Optical Properties
The values of the transition energies, wavelengths, and oscillator strengths calculated at the TDDFT/ωB97X level with the 6-311G*/Stuttgart1997 basis sets are gathered in Table 5. Owing to the formation of a π-conjugated segment between the donor and acceptor moieties, the breaking of the spiro junction results in a decrease of the first excitation energy by 1.6 eV and a substantial increase of the oscillator strength. Complexing the big Cs + atom leads to a small hypsochromic shift of the S 0 → S 1 transition (7 nm or 0.03 eV) whereas going towards smaller cations, this shift increases up to 18 nm (0.11 eV), consistently with the increase of the BLA along the vinylic linker ( Table 1). Note that this hypsochromic shift goes in the opposite direction to what was observed and calculated for coumarin 343 fluoroionophores [32]. The effect of the cation size on the oscillator strengths is negligible.

Second-Order NLO Properties
Tables 6 and 7 report the static and dynamic HRS first hyperpolarizabilities (β HRS ), the depolarization ratios, as well as the β contrasts between the spiropyran and the merocyanine(-M + ) calculated in acetonitrile using different levels of approximation, namely HF, ωB97X, and MP2. The dynamic (λ = 1064 nm) MP2 values were estimated using Equation (1).
The (static and dynamic) β HRS values increase upon including electron correlation at the MP2 level, are considered as reference. Compared to HF values, this increase is of 141, 36, 147, 110, 95, 83, and 63% respectively for the spiropyran, merocyanine and the merocyanine complexing Li + , Na + , K + , Rb + , and Cs + . This results in variations of the first hyperpolarizability contrasts, in particular of the β mero /β spiro contrast that decreases by about a factor of 2. When considering the ωB97X results, the electron correlation effects are about twice smaller than with the MP2 method. Except for the merocyanine where they lead to a decrease of β HRS by 3%, the inclusion of electron correlation effects with the ωB97X functional enhances the HF β HRS by 46%, 57%, 35%, 30%, 22%, and 16% for the spiropyran and the merocyanine complexing Li + , Na + , K + , Rb + , and Cs + , respectively. These exaltation effects are much amplified when considering the dynamic β HRS values, as a consequence of the smaller ωB97X excitation energies that lead to stronger frequency dispersion.
More importantly, the MP2 calculations evidence a strong enhancement of the β HRS response of the merocyanine form upon complexation, whose amplitude increases inversely to the size of the alkali ion. With the exception of Na + and K + , which display similar NLO responses, the hyperpolarizabilities of the various merocyanine/cation complexes are significantly different, allowing unambiguous identification of the nature of the alkali metal. Similar trends are observed when using the ωB97X XC functional, whereas at the HF level the alkali complexation effects on β HRS are much smaller and mainly go in the opposite direction. Besides, whatever the nature of the alkali, the complexation process does not induce remarkable variations in the values of the depolarization ratios (DR), which remain typical of one-dimensional π-conjugated systems dominated by a single diagonal β tensor component. Table 6. Static (λ = ∞) and dynamic (λ = 1064 nm) HRS first hyperpolarizabilities, and depolarization ratios calculated at the HF, ωB97X, and MP2 levels with the 6-311+G*/Stuttgart1997 basis sets. Solvent effects (CH 3 CN) are included via the IEF-PCM scheme.

Computational Section
Geometry optimizations were performed at the density functional theory (DFT) level of approximation using the M06 exchange-correlation (XC) functional [33]. The 6-311G* basis set was used for all atoms except Rb and Cs, which were described by the Stuttgart 1997 basis set [34]. The components of the first hyperpolarizability tensor (β) were evaluated at different levels of approximation. The coupled-perturbed Hartree-Fock (CPHF) and the time-dependent Hartree-Fock (TDHF) approaches [35,36] were employed with the 6-311+G*/Stuttgart1997 basis sets to evaluate the static and dynamic (λ = 1064 nm) first hyperpolarizabilities, respectively. Secondly, in order to account for electron correlation effects, the static β components were computed by employing the second-order Møller-Plesset level (MP2) in combination with the finite field (FF) procedure [37] using the same basis sets. In these FF calculations, the higher-order contaminations were removed by adopting the usual Romberg procedure [38][39][40]. Then, the HF and MP2 results were combined in order to predict approximate dynamic MP2 values. This was achieved by using the multiplicative scheme [41][42][43], which consists in multiplying the static MP2 value by a corrective dispersion factor: Additional calculations of the first hyperpolarizability were performed at the time-dependent density functional theory (TDDFT) level with the ωB97X XC functional [44]. This functional includes 15.77% and 84.23% of exact HF exchange at short-and long-range, respectively, and is among the best XC functionals to predict the excitation energies of push-pull π-conjugated systems. Among second-order NLO phenomena, we focused on the hyper-Rayleigh scattering (HRS) response, β HRS (-2;,) = β HRS [45]. Assuming a non-polarized incident light propagating along the Y direction (in the laboratory frame), the intensity of the harmonic light scattered at 90° along the X direction and vertically (V) polarized (along the Z axis) is given by Bersohn's expression [46]: The depolarization ratio, DR, which reveals the shape of the NLO-phore, reads: where  ZZZ 2 and  ZXX 2 are orientational averages of β tensor components, which are proportional to the scattered signal intensities for vertically and horizontally-polarized incident signals, respectively. The orientational averages in Equations (2) and (3) were calculated without assuming Kleinman's conditions, i.e., without applying permutation symmetry rules on the Cartesian components of the hyperpolarizability tensor. All reported β values are given in atomic units [1 a.u. of β = 3.62 × 10 42 m 4 V 1 = 3.2063 × 10 53 C 3 m 3 J 2 = 8.641 × 10 33 esu] within the T convention of [47]. The vertical excitation energies (∆E ge ) and the corresponding wavelength λ ge were calculated at the TDDFT level using the range-separated hybrid functional ωB97X and the combination of the 6-311G(d)/Stuttgart1997 basis sets. Solvent effects on the linear and nonlinear optical properties were accounted by using the polarizable continuum model within the integral equation formalism (IEF-PCM) [48,49]. This model describes the molecular environment as a structureless polarizable continuum characterized by its macroscopic dielectric permittivity, , which depends on the frequency  of the applied electric field.

Conclusions
Structural, thermodynamical, vibrational, as well as linear and nonlinear optical properties of a spiro[indoline-8-(benzothiazol-2-yl)-benzopyran] derivative and of its merocyanine form have been evaluated by using first principles methods. In particular, calculations are used to unravel the variations of these properties that occur when the merocyanine form complexes alkali cations of increasing size, from Li + to Cs + . The following trends have been observed, (i) the complexation of smaller cations leads to the formation of stronger metal-ligand bonds, larger geometrical relaxations, and larger charge redistributions over the whole system, that result in a stronger hypsochromic shift of the first excitation energy and in a larger enhancement of the first hyperpolarizability, (ii) these structural, electronic, vibrational, and optical properties are less impacted by the complexation of larger cations, and (iii) the enthalpies of complexation show a minimum for the Na + and K + cations for which the covalent bond is weaker than in the case of Li + , whereas the opening of the claw is too large to match the cation size as in the case of Rb + and Cs + . The broad range of variation of the first hyperpolarizability as a function of the cation size confirms the potential of the second-order NLO responses of this merocyanine for detecting and identifying metal cation.

Acknowledgments
A.P. thanks the F.R.S.-FNRS for her postdoctoral researcher position. This work has been supported by funds from the CNRS, the Région Aquitaine, the F.R.S.-FNRS, the AUL (ARC TinTin), and by the Belgian Government (IUAP No. P7/5). The calculations were performed on the computing facilities of the Consortium des Équipements de Calcul Intensif (CÉCI, http://www.ceci-hpc.be), in particular those of the Plateforme Technologique de Calcul Intensif (PTCI) installed in the University of Namur, for which we gratefully acknowledge financial support of the FNRS-FRFC (Convention No. 2.4.617.07.F and 2.5020.11) and of the University of Namur.

Author Contributions
A.P. performed the calculations; A.P., B.C., and F.C. analyzed the data and wrote the manuscript.

Conflicts of Interest
The authors declare no conflict of interest.