The influence of geometry relaxation in solution on the first hyperpolarizability of mesoionic compounds

Chemical Physics Letters 736 (2019) 136798

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Research paper

The influence of geometry relaxation in solution on the first hyperpolarizability of mesoionic compounds

T

E.M. Torresa, L. Adriano Juniorc, H.C. Georgb, M.A. Castrob, T.L. Fonsecab,

⁎

a

Campus de Ciências Exatas e Tecnológicas, Universidade Estadual de Goiás, 75.132-903 Anápolis, Goiás, Brazil Instituto de Física, Universidade Federal de Goiás, 74690-900 Goiânia, Goiás, Brazil c Pró-Reitoria de Pesquisa e Inovação, Universidade Federal de Goiás, 74690-900 Goiânia, Goiás, Brazil b

HIGHLIGHTS

electric properties of mesoionic rings in solution are presented. • MP2 geometric changes results in marked reductions of β . • Solvent-induced • β changes can be rationalized in terms of changes in the electronic structure. HRS

HRS

ABSTRACT

Theoretical results for the linear and nonlinear properties of mesoionic compounds in solution are presented. The electronic properties in solvents were determined by carrying out Sequential QM/MM calculations by means of the average solvent electrostatic configuration (ASEC) and the Free Energy Gradient (FEG) methods. The results illustrate the role played by geometry relaxation in the electronic properties of mesoionic rings in environments. It is found that environment-induced geometric changes impact on the molecular electronic structure of the mesoionic ring. MP2/aug-ccpVDZ results for the first hyperpolarizability obtained in solution are substantially smaller than the gas phase results.

1. Introduction The development of organic materials for nonlinear optical (NLO) applications has attracted considerable attention because the flexible chemical synthesis may result in materials with large molecular hyperpolarizability, low optical absorption, chemical and thermal stabilities, etc. [1–3]. Thus, the NLO properties of π-conjugated organic molecules are currently being investigated with particular emphasis on relationship between molecular structural features and the resultant microscopic properties. There has been a focus of attention on the electronic contribution to the NLO properties of mesoionic compounds. In particular, results of the nonlinear absorption cross-sections obtained from the nonlinear measurements emphasize the large potential of mesoionic compounds for optical limiting applications and optical data storage [4–6]. These push-pull systems have been postulated as cyclic dipolar structures in which the positive and negative charges are both separated and delocalized on two regions separated by two single bonds [7]. Previous semiempirical theoretical calculations have been performed to determine the nonlinear optical properties of mesoionic compounds [8,9]. In Ref. [8], Moura et al. showed that the intrinsic

⁎

push-pull characteristics of mesoionic rings can be enhanced varying the strength of the donor and acceptor moieties properly replaced and that can be of use for the design of compounds with large second order NLO effects. In another study, Moura and Simas explored the process of absorption of two photons of a series of homologous compounds and showed that quadrupolar organic molecules containing mesoionic rings present large two-photon absorption cross-sections [9]. Although there is considerable accumulated and important knowledge of these earlier studies, one aspect that remains unexplored is an analysis of the secondorder nonlinear response of these compounds in solvents of different polarities, where the NLO enhancement mechanism can be further tuned by solvation effects [10–19]. More recently [20], the hyperRayleigh scattering tecnique has been used to determine the first hyperpolarizability of 1,3‐thiazolium-5-thiolates mesoionic compounds in solution. Over time, the experimental investigations concerning the NLO properties of mesoionic compounds have been carried out in solution. Thus, an appropriate description of the solvent effects is particularly important for a direct comparison between experiments and theoretical predictions. There has been a continuous effort to develop and improve

Corresponding author. E-mail address: [email protected] (T.L. Fonseca).

https://doi.org/10.1016/j.cplett.2019.136798 Received 15 August 2019; Received in revised form 24 September 2019; Accepted 25 September 2019 Available online 26 September 2019 0009-2614/ © 2019 Elsevier B.V. All rights reserved.

Chemical Physics Letters 736 (2019) 136798

E.M. Torres, et al.

been successfully applied to optimize the structure of molecular systems in solution [27]. Using this combination, we have shown that solventinduced geometrical changes in protic environment play an important role in the determination of the second-order NLO response of the phenol blue [17]. In this study we present the second-order Møller–Plesset Perturbation Theory (MP2) results for the first hyperpolarizability of mesoionic compounds in the aprotic solvent (chloroform, acetonitrile) and protic solvent (methanol, water). Fig. 1 shows the molecular structure of the mesoionic compounds considered here, indicating the functional groups added in the cyclic structure as reported in previous works [4,28]. The solvent effects on the geometry and electronic properties were included using the Sequential QM/MM methodology and the ASEC-FEG method. The absorption spectrum of these compounds is also presented, considering that an important characteristic of these compounds is their intense absorption in the ultraviolet–visible region. For comparison, we also study the role of solvent-induced electronic polarization in the context of the model of non-relaxed geometry. 2. Computational details In the Sequential QM/MM methodology [21,22], the classical simulations were performed using the Monte Carlo (MC) method with the DICE program [29]. The Metropolis MC simulations were carried out in the NPT ensemble, at T = 25 °C and P = 1 atm, for a system composed by one solute molecule surrounded by a number of solvent molecules that assured a shell with minimum thickness of 12 Å. Solvent molecules were treated as rigid structures. The intermolecular interactions were modeled by the standard Lennard-Jones (LJ) plus Coulomb potential. For the mesoionic compounds, the LJ parameters were taken from the optimized potential for liquid simulation (OPLS) force field [30]. CHELPG atomic charges [31] for the solute were fitted to reproduce the same electrostatic potential as that obtained with the MP2/ aug-ccpVDZ model. For solvents, the force fields used were obtained from Ref. [32] (chloroform), from Ref. [33] (acetonitrile), and from Ref. [30] (methanol). For water the TIP3P model from Ref. [34] was used as force field. In this series of simulations, the energy autocorrelation function [35] was used to select 400 uncorrelated configurations (with statistical correlation less than 14%) to generate the average solvent electrostatic configuration (ASEC) [23], where solvent molecules treated as simple point charges describing an electrostatic embedding. The charges of this single configuration were then normalized by the number of selected configurations. The geometry optimization of solute in solution was performed by combining the ASEC solvation model and the Free Energy Gradient method [24–26] iteratively resulting in the ASEC-FEG methodology [27]. This methodology performs a quasi-Newton optimization to obtain the closest minimum energy structure in the free energy hypersurface. The electronic polarization of the solute is monitored by its dipole moment in solution [36] at each step of the optimization. It is assumed as a reasonable approximation that the solvent polarization by the solute is taken into account in the solvent model. At each step of the optimization, a new conformation is obtained and then new atomic charges are calculated, and both geometry and charges are updated for a new MC simulation. The iterative process is repeated until the solute dipole moment and geometric parameters converge. During the iterative process, the QM calculations of the structural and electronic properties were performed at the MP2/aug-cc-pVDZ level. This iterative procedure has been applied recently in the calculation of the first hyperpolarizability of phenol blue in solution, it has reproduced satisfactorily the experimentally observed trends [17]. A more detailed description of the iterative scheme, in which the solute is permitted to relax both its geometry and charge distribution in the presence of the solvent molecules, is given elsewhere [37].

Fig. 1. Chemical structure of the mesoionic compounds. Carbon (grey), hydrogen (white), nitrogen (blue), sulfur (yellow), chlorine (green) and oxygen (red). We have maintained the same labels of Refs. [4,28]. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

the models that account for the environment in second-order nonlinear response calculations of molecular chromophores. From the previous studies that have appeared in the literature, it clearly comes out that the sequential quantum mechanical/molecular mechanical (QM/MM) solvation model [21,22] represents an adequate procedure whenever polarity effects are dominant in determining the NLO property. In this atomistic methodology, the coupling between the QM and the MM subsystems provides an accurate description of solvent effect, although the solvent is represented in terms of an electrostatic embedding. The combination of the average solvent electrostatic configuration (ASEC) [23] and the Free Energy Gradient (FEG) [24–26] approaches have 2

Chemical Physics Letters 736 (2019) 136798

E.M. Torres, et al.

Additionally, we have also included the electronic polarization of the solute due to the solvent in the context of the non-relaxed solute geometry through an iterative procedure. In this context, the geometries used during the MC simulations were optimized in the gas phase at the MP2/aug-cc-pVDZ level. This approach has been successfully employed in previous studies in which the first hyperpolarizability of organic molecules was investigated in different solvents [16,38]. In this case, the process is iterated until it reaches the convergence of the solute dipole. The components of the first hyperpolarizability (βijk) were calculated by numerical differentiation of the analytical polarizabilities in relation to the electric field, as implemented in GAUSSIAN 09 package [39]. The MP2/aug-cc-pVDZ model has been employed in the calculations of this electric property. It is known that the reliable computation of molecular (hyper)polarizabilities requires the use of basis sets appropriately designed for this purpose, specially for small molecules, as shown by Maroulis [40–42]. However, the choice of the basis set used in the present work represents a good compromise between computational cost and accuracy, although the results could be undoubtedly improved by using a more extended basis set [43,44]. Here, we have calculated the average the quantity sampled in the hyper-Rayleigh scattering intensity for the plane polarized incident light, and the associated depolarization ratio (DR) which are given by HRS

=

2 ZZZ

+

2 ZXX

Table 1 MP2/aug-cc-pVDZ bond lengths (Å) for MI-1, MI-2 and MI-3 obtained in gas phase and in aprotic and protic solvents using the ASEC-FEG method. CFM = chloroform; ACN = acetonitrile; MET = methanol and WAT = water. MI-1

2 ZZZ 2 ZXX

C2-N3

N3-N4

N4-C5

C5-S6

C2-C6

Gas Phase CFM ACN MET WAT

1.651 1.669 1.681 1.691 1.711

1.378 1.367 1.361 1.356 1.349

1.334 1.341 1.346 1.347 1.352

1.362 1.357 1.352 1.351 1.351

1.717 1.714 1.711 1.710 1.711

1.823 1.806 1.796 1.786 1.769

C2-S1

C2-N3

N3-N4

N4-C5

C5-S6

C2-C6

1.647 1.660 1.673 1.675 1.703

1.384 1.374 1.367 1.365 1.352

1.327 1.333 1.339 1.340 1.348

1.368 1.361 1.355 1.355 1.351

1.723 1.721 1.718 1.718 1.716

1.824 1.810 1.800 1.795 1.774

C2-S1

C2-N3

N3-N4

N4-C5

C5-S6

C2-C6

1.652 1.670 1.681 1.690 1.716

1.380 1.367 1.360 1.355 1.344

1.333 1.342 1.349 1.350 1.357

1.360 1.352 1.348 1.348 1.346

1.721 1.719 1.718 1.717 1.718

1.821 1.805 1.798 1.788 1.770

Gas Phase CFM ACN MET WAT

MI-3

Gas Phase CFM ACN MET WAT

(1)

(2)

with the PCM method [28]. Additionally, we have also analyzed the environment-induced geometric changes on the bond order (BO) of the C2-S1, C2-N3, N3-N4 and N4-C5 bonds. The BO values have been calculated at the Hartree-Fock (HF) level by employing the Wiberg bond order [47] with Natural Atomic Orbitals (NAOs) [48] as the orthogonalized basis set, therefore assuring positive values for the calculated bond orders. The results for the BO of MI-1, MI-2 and MI-3 in aprotic and protic solvents for both non-relaxed and relaxed situations are presented in Table 2. One can see that with increasing solvent polarity the C2-S1 bond elongates and the bond order decreases systematically, changing from 1.5 in gas phase to 1.2 (close to a single bond) in water. The reverse trend is observed for the N3-N4 bond which decreases with the solvent polarity, the bond order becoming 1.5 in water. This contrasts with the results obtained with the non-relaxed solvation model which indicate that the presence of the electrostatic embedding almost does not affect the molecular electronic structure of the compounds in both aprotic and protic solvents. As expected, the nature of the functional group added to the mesoionic ring can also affect the bond orders of its conjugation. Thus, the substitution of the phenyl ring by the 5-NO2-2-furanyl ring gives rise to less alternated structures; in water, for the relaxed situation, the BO values for C2-N3 and N4-C5 bonds are smaller (around of 0.02) than the corresponding BO ones of MI-1. Unlike what is observed for the bond orders, the intrinsic charge separation of mesoionic rings is little affected by the geometry relaxation in solution. Table 3 presents the MP2/aug-cc-pVDZ results for CHELPG partial atomic charges of the mesoionic compounds in solution. To analyze the redistribution of partial charges in solution, we reported results for the liquid charges of the groups of atoms (N4C5S6) and (S1C2N3) and of the S1 atom. Both non-relaxed and relaxed solvation models indicate that in the mesoionic ring the group N4C5S6 forms a region of positive liquid charge whereas the group S1C2N3 forms a region of negative liquid charge. This intrinsic charge separation is enhanced with increasing solvent polarity. For the relaxed situation, for example, the charge of the group S1C2N3 increase from 25 to 44% in aprotic solvents to 43–77% in protic solvents, when compared to the corresponding gas-phase results. At the same time, there is

where and are the orientationally averaged hyperpolarizabilities, whose expressions are given in Ref. [45]. All MP2 calculations are carried out within the frozen core approximation. The vertical electronic excitation energies were calculated using the TD-DFT method with the long-range corrected CAM-B3LYP [46] functional. In this functional the asymptotic behavior of the exchange interaction is improved partitioning it into short- and long-range components. The 6-311+G(2d,p) basis has been adopted in all TD-DFT calculations [28]. The QM calculations were performed with the GAUSSIAN 09 package [39]. 2 ZZZ

C2-S1

MI-2

and

DR =

Environment

2 ZXX

3. Results and discussion We have iteratively applied the ASEC-FEG method to optimize the geometry of each mesoionic compound in chloroform, acetonitrile, methanol and water. MP2/aug-cc-pVDZ results (average over the last five steps of the iterative process) for a set of selected geometric parameters of MI-1, MI-2 and MI-3 in solution and in gas phase are shown in Table 1. The convergence criteria in the optimizations were the maximum and RMS forces with thresholds of 15 × 10−4 and 5 × 10−4 hartree/bohr, respectively, which are very reasonable values for non-gas phase calculations. For all optimized geometries, solvent effects lead to a reduction of the C2-N3, C2-S6, C5-S6 and N4-C5 bonds and an elongation of the N3-N4 and C2-S1 bonds compared to the results of the gas phase. In particular, a considerable geometric change is observed for the C2-S1 bond. It is observed for all compounds that the values of the C2-S1 bond length increase with increasing polarity of the medium, indicating a marked influence of the specific interactions of the solvent molecules with the exocyclic sulfur atom. For compound MI-2, for example, this length is increased from 0.056 Å in going from the gas phase (1.647 Å) to the water (1.703 Å). Taking as reference the geometric parameters of MI1, we note that the substitution of one of the phenyl rings by the 5-NO22-furanyl (MI-2) ring or furanyl (MI-3) ring can affect the conjugation of mesoionic ring. The ASEC-FEG method predicts optimized structures in solution in which the terminal rings are twisted with respect to the plane of the mesoionic ring (see Fig. 1), in agreement with the results obtained 3

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the protic solvents. The converged MP2/aug-cc-pVDZ results for the dipole moment in aprotic and protic solvents are also quoted in Table 3. There is a marked effect of the solvent polarization on the dipole moment values in relation to the gas phase results, with the results for μ obtained in the nonrelaxed geometry situation being slightly smaller in protic solvents. While in aprotic solvents the polarization effect produces increases of 21–53%, in protic ones the increases are 47–101%. For comparison, the corresponding increases obtained with the method PCM at the MP2/6311+G(d,p) level for these compounds in DMSO are 63–72% [28]. The protic nature of methanol increase the µ values of MI-1 and MI-3 by 8 and 5%, respectively, compared to the results obtained in acetonitrile. For MI-2 there is no significant difference. Fig. 2 shows the first hyperpolarizability behavior of the mesoionic rings with increasing polarity of solvent. MP2/aug-cc-pVDZ results obtained in the gas phase and in solution with the non-relaxed and relaxed solvation models are gathered in Table 4. For the relaxed situation, βHRS is very sensitive to solvent effects, with significant reductions in both protic and aprotic solvents. In aprotic solvents, the βHRS values of MI-1 and MI-3 decrease considerably. From gas phase to chloroform it is reduced by 46 and 49% and from chloroform to acetonitrile, the hyperpolarizability decreases further by 27 and 31%. On the other hand, for MI-2, the decreases of βHRS in aprotic environments, in relation to the gas phase, are smaller (8% for chloroform and 17% for acetonitrile). In protic solvents the effect in the hyperpolarizability for MI-1 and MI-3 is even larger. For methanol the reductions in βHRS values are of 69 and 65%, respectively, in relation to gas phase values. In water, the corresponding reductions are of 57 and 36%. It is also observed that the effect of the change from methanol to water decreases the value of βHRS of MI-2 (33%), but it increases the values of βHRS of MI-1 of 40% and of MI-3 in 80%. In addition, the comparison between the results obtained in acetonitrile and in methanol shows a significant influence of the solvent nature on βHRS. The protic nature of methanol leads to a decrease in the βHRS values of all compounds. For the depolarization ratios (Table 4), a certain solvent dependence of DR is observed for MI-1 and MI-3 with decrease between 34 and 45% in chloroform, acetonitrile and methanol and increase between 27 and 46% in water. For MI-2, in contrast, the solvent effects on DR are small,

Table 2 HF/aug-ccpVDZ Wiberg bond orders for the C2-S1, C2-N3, N3-N4 and N4-C5 bonds optimized in solution. Results for non-relaxed situation are given in brackets. CFM = chloroform; ACN = acetonitrile; MET = methanol and WAT = water. MI-1 Environment

C2-S1

Gas Phase CFM ACN MET WAT

1.505 1.410 1.357 1.300 1.229

C2-N3 [1.507] [1.507] [1.506] [1.506]

1.366 1.425 1.458 1.491 1.531

[1.365] [1.365] [1.365] [1.366]

N3-N4

N4-C5

1.127 1.112 1.104 1.105 1.098

1.373 1.382 1.390 1.387 1.382

[1.127] [1.127] [1.127] [1.127]

[1.373] [1.373] [1.372] [1.374]

MI-2 C2-S1 Gas Phase CFM ACN MET WAT

1.536 1.450 1.389 1.369 1.251

C2-N3 [1.535] [1.535] [1.540] [1.538]

1.326 1.381 1.424 1.435 1.510

[1.327] [1.327] [1.323] [1.325]

N3-N4

N4-C5

1.161 1.142 1.127 1.126 1.112

1.344 1.357 1.368 1.366 1.367

[1.161] [1.160] [1.163] [1.162]

[1.344] [1.344] [1.344] [1.344]

MI-3 C2-S1 Gas Phase CFM ACN MET WAT

1.502 1.398 1.352 1.295 1.210

C2-N3 [1.500] [1.500] [1.506] [1.504]

1.364 1.436 1.471 1.505 1.557

[1.365] [1.365] [1.361] [1.363]

N3-N4

N4-C5

1.126 1.103 1.092 1.091 1.081

1.350 1.354 1.357 1.351 1.339

[1.126] [1.125] [1.127] [1.126]

[1.350] [1.350] [1.351] [1.351]

a negative charge accumulation on S1 that becomes larger as the solvent polarity increases as a result of the decrease in electron density mainly of the functional groups connected to the mesoionic ring, which are positively charged, emphasizing the electronic donor character of these groups. Note that there is a reduction of the donor character due to the presence of an acceptor group in one of the rings (MI-2). It is expected that the accumulation of negative charge on S1 favors the formation of specific bonds between the sulfur atom and molecules of

Table 3 MP2/aug-cc-pVDZ results for partial atomic charge (in a.u.) and dipole moment (in Debye) of MI-1, MI-2 and MI-3 compounds in gas phase and in aprotic and protic solvents. Results for non-relaxed situation are given in brackets. CFM = chloroform; ACN = acetonitrile; MET = methanol and WAT = water. MI-1 Environment

q(N4C5S6)

q(S1C2N3)

q(S1)

Gas-phase CFM ACN MET WAT

0.227 0.315 0.357 0.392 0.457

−0.534 −0.676 −0.744 −0.779 −0.908

−0.378 −0.511 −0.590 −0.693 −0.816

[0.277] [0.318] [0.332] [0.381]

[−0.664] [−0.701] [−0.731] [−0.842]

μ [−0.493] [−0.554] [−0.618] [−0.732]

7.8 10.5 11.9 12.9 15.7

[10.5] [11.9] [12.6] [15.1]

MI-2

Gas-phase CFM ACN MET WAT

q(N4C5S6)

q(S1C2N3)

q(S1)

0.270 0.349 0.416 0.391 0.466

−0.490 −0.613 −0.706 −0.705 −0.839

−0.315 −0.451 −0.544 −0.596 −0.775

[0.303] [0.344] [0.348] [0.380]

[−0.581] [−0.641] [−0.650] [−0.728]

μ [−0.436] [−0.509] [−0.528] [−0.596]

9.0 10.9 13.1 13.2 16.7

[11.3] [13.0] [12.9] [14.3]

MI-3

Gas-phase CFM ACN MET WAT

q(N4C5S6)

q(S1C2N3)

q(S1)

0.238 0.322 0.388 0.384 0.445

−0.526 −0.682 −0.752 −0.783 −0.931

−0381 −0.528 −0.596 −0.699 −0.854

[0.287] [0.322] [0.313] [0.372]

[−0.641] [−0.697] [−0.706] [−0.835]

4

μ [−0.502] [−0.557] [−0.611] [−0.746]

9.7 12.7 14.6 15.4 19.1

[12.8] [14.6] [14.8] [18.1]

Chemical Physics Letters 736 (2019) 136798

E.M. Torres, et al.

kept rigid during the MC simulations. For these mesoionic compounds connections are found between the reductions of the βHRS values and the solvation shifts of the absorption spectrum. We present here a brief analysis of the effects of the protic environment on the first electronic transition characterized by intramolecular charge transfer from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO). A detailed analysis based on the results obtained with PCM method for the lowest electronic transitions of these compounds in DMSO was reported in Ref. [28]. CAM-B3LYP/6-311+G(2d,p) values for the excitation energy and oscillator strength of the first electronic transition of mesoionic compounds in gas phase and in solution computed with the non-relaxed and relaxed solvation models are quoted in Table 5. For the relaxed situation, the solvent effect leads to large blue shifts for the π-π* transition of all compounds in going from gas phase to solution, especially in protic solvents. CAM-B3LYP model predicts blue shifts in going from gas phase to methanol [to water] between 0.38 and 0.75 eV [0.74–1.00 eV]. The effect of the protic nature of methanol gives blueshifted excitation energies in the range of 0.20 eV for MI-1 and MI-3 and of 0.04 eV for MI-2, relative to the results in acetonitrile. Following the two level model [49], that establishes a link between the first hyperpolarizability and a low-lying charge transfer excited state, we note that the difference in the transition energies in going from gas phase to solution is crucial factor and leads to the reductions of βHRS of the mesoionic compounds in protic and aprotic solvents. Consistently, no essential change is observed for either βHRS or electronic transitions when the solute geometries are held fixed in their vacuum structure during simulation. Our results show, in addition, that the effect of the incorporation of functional groups on the mesoionic ring can significantly increase the first hyperpolarizability, and depends on the environment. As expected, inclusion of the nitro group (electron acceptor group, MI-2) substantially increases the βHRS values, compared to the corresponding results of compound MI-3. These increments are consistent with the red shifts of the first electronic transition in gas phase and in solution when the nitro group is added (MI-3 → MI-2). It is well known that the incorporation of electron donor and acceptor groups is a generally effective procedure for obtaining large hyperpolarizabilities in conjugated organic molecules, with the charge transfer from the donor to the receptor through the conjugate segment to improve these properties. 4. Conclusions In the present work, we have obtained a valuable description of the first hyperpolarizability of mesoionic rings in chloroform, acetonitrile, methanol and water based on MP2 calculations within the Sequential QM/MM approach. Both solute electronic polarization and geometry relaxation are properly taken into account using a iterative procedure by means of the ASEC-FEG method. It turns out that the solvent-induced geometric changes in the mesoionic compounds results in marked reductions of βHRS in both aprotic and protic environments, which are consistent with changes in the molecular electronic structure. The solvent dependence of the first hyperpolarizability can be rationalized in terms of the transition energy between the ground state and the first excited state. It is also found that the calculated static result for βHRS of MI-2 in acetonitrile (17.7 × 10−30 esu) is in good concordance with experimental static results for first hyperpolarizability of 1,3‐thiazolium-5-thiolates mesoionic compounds dissolved in dimethyl sulfoxide (8.7–10.4 × 10−30 esu) obtained from hyper-Rayleigh scattering experiments performed at λ = 1180 nm, using a two-level model.

Fig. 2. Solvent dependence of the first hyperpolarizability of MI-1, MI-2 and MI-3 in aprotic and protic solvents for both non-relaxed and relaxed situations. CFM = chloroform, ACN = acetonitrile, MET = methanol, WAT = water.

and the calculated values of 5.19–5.77 indicate large dipolar contribution to the second-order nonlinear response in both aprotic and protic environment. It should be stressed that although for non-relaxed situation the polarization effect leads to a similar intrinsic separation of charges of mesoinic ring as compared to the relaxed ones, the presence of the electrostatic embedding almost does not affect the first hyperpolarizability and depolarization ratio in both aprotic and protic solvents. This is consistent with the small bond order solvent dependence of the bonds of the mesoionic ring when the solute geometries are

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. 5

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Table 4 MP2/aug-cc-pVDZ results for the static hyper-Rayleigh scattering first hyperpolarizability (in a.u.) and depolarization ratio of MI-1, MI-2 and MI-3 in gas phase and in aprotic and protic solvents. Results for non-relaxed situation are given in brackets. CFM = chloroform; ACN = acetonitrile; MET = methanol and WAT = water. βHRS

DR

Gas

CFM

ACN

MET

WAT

Gas

CFM

ACN

MET

WAT

MI-1

543.4 2460.7

MI-3

525.5

202.9 [545.4] 2046.4 [2413.7] 195.8 [518.4]

165.8 [550.8] 1869.3 [2523.3] 185.5 [567.5]

232.8 [566.8] 1254.8 [2457.3] 334.4 [548.5]

2.94

MI-2

276.5 [549.8] 2269.0 [2447.0] 282.9 [518.4]

1.91 [2.98] 5.19 [5.18] 1.91 [3.10]

1.77 [3.03] 5.23 [5.20] 1.85 [3.17]

1.63 [3.04] 5.40 [5.22] 2.04 [3.34]

3.72 [3.12] 5.77 [5.22] 4.54 [3.31]

Table 5 Excitation energies (in eV) and (oscillator strengths) for the first electronic transition of MI-1, MI-2 and MI-3 calculated at the CAM-B3LYP/6311+G(2d,p) level in gas phase and in aprotic and protic solvents. Results for non-relaxed situation are given in brackets. CFM = chloroform; ACN = acetonitrile; MET = methanol and WAT = water. Gas

CFM

ACN

MET

WAT

MI-1

2.85 (0.15)

MI-2

2.44 (0.23)

MI-3

2.74 (0.18)

3.16 (0.19) [2.84] (0.15) 2.63 (0.32) [2.44] (0.23) 3.05 (0.26) [2.74] (0.18)

3.40 (0.20) [2.85] (0.15) 2.78 (0.35) [2.45] (0.23) 3.23 (0.31) [2.75] (0.18)

3.60 (0.22) [2.84] (0.15) 2.82 (0.35) [2.43] (0.22) 3.38 (0.33) [2.73] (0.18)

3.85 (0.30) [2.85] (0.15) 3.18 (0.44) [2.44] (0.22) 3.70 (0.46) [2.74] (0.18)

[13] [14] [15] [16]

[17]

Acknowledgments

[18]

The authors gratefully acknowledge the financial support of CNPq, CAPES and FAPEG (PRONEX) agencies (Brazil) as well as the computer resources of the LCC-UFG laboratory.

[19]

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