Enhancement of Twist Angle Dependent Two-Photon Activity through

Jul 10, 2012 - Herein, we show that the two-photon (TP) transition probability (δTP) of o-betaine system will reach its maximum value at a twist angl...
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Enhancement of Twist Angle Dependent Two-Photon Activity through the Proper Alignment of Ground to Excited State and Excited State Dipole Moment Vectors Md. Mehboob Alam, Mausumi Chattopadhyaya, and Swapan Chakrabarti* Department of Chemistry, University of Calcutta, 92 A. P. C. Road, Kolkata 700009, India S Supporting Information *

ABSTRACT: Herein, we show that the two-photon (TP) transition probability (δTP) of o-betaine system will reach its maximum value at a twist angle around 65°. However, the potential energy scan with respect to the twist angle between its two rings indicates that the molecule in its ground state is quite unstable at this twist angle. Out of the different possibilities, the one having a single methyl group at the ortho position of the pyridinium ring is found to attain the optimum twist angle between the two rings, and interestingly, this particular substituted o-betaine has larger δTP value than any other substituted or pristine o-betaine. The twist angle dependent variation of δTP has been explained by employing the generalized-few-state-model formula for 3D molecules. The results clearly reveal that the magnitude of ground to excited state and excited state dipole moment vectors as well as the angle between them are strongly in favor of maximizing the overall δTP values at the optimum twist angle. The constructive interference between the optical channels at the optimum twist angle also plays an important role to achieve the maximum δTP value. Furthermore, to give proper judgment on our findings, we have also performed solvent phase calculations on all the model systems in nonpolar solvents, namely, cyclohexane and n-hexane, and the results are quite consistent with the gas phase findings. The present study will definitely offer a new way to synthesize novel two-photon active material based on obetaine.

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dye.22,23 The study17 reveals that channel interference and the net TPA process in 3D molecules are much more complicated than their 2D analogue since six different angles between various transition moment vectors are associated with the net TP transition probability (δTP) of a 3D molecule. In this regard, the major challenging task is to control these angles in favor of a strong constructive interference that eventually maximizes the δTP of the system. Earlier, the variation of δTP with the twist angle between pyridinium and phenolate ring of p-betaine at the two-state model level of theory was studied by Zaleśny et al.,24 and they found that δTP would have a maximum value at a certain twist angle between the two rings of p-betaine. Pati et al.25 also studied the twist angle dependent enhancement of δTP of the quinopyran system. However, none of these works have tried to address the twist angle dependent modulation of the dipole alignment and the channel interference effect and their roll in controlling the net TPA activity of a molecule or material. In this article, we predict for the first time that the twist angle has profound impact on the alignment of different transition moment and dipole moment vectors and hence on their

INTRODUCTION Although more than 80 years of the first theoretical prediction1 of two-photon absorption (TPA) process has been elapsed, the research in this field is still very relevant, both from the fundamental as well as practical perspective. The main reason of search for the two-photon (TP) active materials is their applications in various domains of real life.2−6 Owing to their potential application in diverse areas, the main focus of synthetic chemists in this field is to synthesize more and more efficient TP active materials. However, to set up a proper design strategy of synthesizing efficient TP active material, it is found that theoretical studies are extremely helpful. This is only because the theoretical/computational studies give us an indepth view and help understand the TPA process at the molecular level. So far, quantum chemical studies indicate that solvent polarity,7 dimensionality of charge transfer network,8 vibronic coupling,9 length of conjugation,10 through space charge transfer,11−15 channel interference,16−21 etc. are very important in determining the net TP activity of a material. The effect of channel interference was first studied by Cronstrand et al.16 However, it was restricted to two-dimensional systems only. In a very recent work, Alam et al.17 extended the channel interference effect to three-dimensional systems and derived a new generalized few-states model (GFSM) formula and applied it to explore the TP activity of the simplest form of Reichardt’s © 2012 American Chemical Society

Received: May 8, 2012 Revised: July 10, 2012 Published: July 10, 2012 8067

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contribution to the net TPA process of o-betaine molecule. We have noticed that the most contributing terms appearing in GFSM become maximum at twist angles around 65−70° and this requisite twist angle can be achieved by incorporating one methyl group at the suitable ortho position of the pyridinium ring of o-betaine molecule, which ultimately maximizes the δTP of the material. For checking the reliability of our results and making it more feasible in terms of real experiments, we have also calculated the δTP of the optimized unsubstituted and substituted o-betaine in two solvents, namely, cyclohexane and n-hexane. Similar results are obtained in both the solvents, i.e., the value of δTP is maximum for the o-betaine having one methyl group on the ortho position of its pyridinium ring. The present finding will definitely help us understand the controlling mechanism of the alignment of different transition moment vectors that paves the way to synthesize novel TP active materials in the future.

The justification of using CAMB3LYP functional in this study is that this functional has already proved its worth in reproducing excitation energies in a number of previous works.13,27,28 In this case too, the CAMB3LYP functional along with the aug-cc-pVDZ basis set satisfactorily reproduces17 the experimental25 excitation energy of o-betaine in the CH3CN solvent. We must also admit here that, in the case of water, there is a difference between experimental29 and theoretical17 values, but this value is mainly related to the well-known limitation of PCM model, which is not able to account for the specific interactions like hydrogen bonding. For this reason also, we have used nonpolar solvents in this work. In the present study, we have used cc-pVDZ as the basis set and calculated the one-photon excitation energy of o-betaine at this level of theory and found that the calculated excitation energy in the CH3CN solvent is 2.55 eV, which is very close to the experimental29 value of 2.6 eV. Such a nice agreement between theoretical and experimental results justifies the use of the CAMB3LYP/cc-pVDZ level of theory in this study. After the calculation of OPA and TPA parameters for different twist angles, the δTP of all the optimized substituted and unsubstituted o-betaine molecules have been computed in both the gas and solvent phases at the same level of theory. It is worth mentioning that o-betaine has sufficient zwitterionic character in the ground state, and in the presence of a polar solvent, indirect contribution to the net TP activity will be significant,30 which ultimately will complicate the comparison of TP activity of the model systems in different solvents. To minimize the indirect contribution effect, we have selected nonpolar solvents like cyclohexane and n-hexane for the solvent phase response calculations. For solvent phase calculations, we have employed the nonequilibrium formulation of response theory31,32 within the polarizable continuum model (PCM) as implemented in the DALTON26 suite of programs. However, we must also mention here that the electrostatic PCM model we have employed does not include the dispersion term for solute−solvent interaction and that this may become important in the case of nonpolar solvents.

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COMPUTATIONAL DETAILS At first, we have optimized the ground state structures of the unsubstituted and substituted o-betaine molecules in the gas phase and two solvents namely, cyclohexane and n-hexane, at the CAMB3LYP/6-311++G (d, p) level of theory, and the calculations are performed in the DALTON26 program package. The gas phase optimized structures are shown in Figure 1. It is worth mentioning that, in an earlier work,17 it was

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RESULTS AND DISCUSSION The TP activity of a molecule is measured in terms of δTP which in turn is related to the TPA tensor elements (Sαβ). For an excitation by a single beam of linearly polarized light, the relationship between δTP and Sαβ is given by33 au δ TP = 6(S2xx + S2yy + S2zz ) + 8(S2xy + S2yz + S2xz )

+ 4(Sxx Syy + Syy Szz + Sxx Szz )

(1)

TPA tensor elements are related to the various transition dipole moment vectors and the excitation energies by the equation34

Figure 1. Optimized ground state structures of unsubstituted (a) and substituted (b−f) o-betaine in the gas phase.

Sαβ =

shown that the optimized geometry of a similar system (pbetaine) obtained from the CAMB3LYP/6-311++G(d,p) level of theory is in nice agreement with the available X-ray crystallographic data. We have also carried out the frequency calculation on the optimized geometries, and no imaginary frequency has been found. After geometry optimizations and frequency check, we have evaluated the various one- and twophoton absorption parameters of o-betaine by changing the twist angle from 0° to 180° between the pyridinium and phenolate rings, at CAMB3LYP/cc-pVDZ level of theory.

∑ i

μα0i μβif + μβ0i μαif ΔEi

(2)

where ΔEi = ω0i − ω0f/2 and αβ ={x, y, z}. μ̂α is the αth component of dipole moment operator, and μpq α is the αth component of transition moment integral for transition from pth state to qth state. ω0i and ω0f are the excitation energies for transition from ground to ith and f th states, respectively. The summation in eq 2 runs over all the states, including the ground and the final states. The inclusion of the ground and final states gives rise to the dependence of Sαβ on the dipole moment 8068

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difference between the ground and excited states. The one- and two-photon parameters can be extracted from the residues of linear and quadratic response functions, respectively. The other alternative for evaluating the δTP and Sαβ is the few-states model (FSM) in which a limited number of intermediate states are involved in a calculation. Although FSM is computationally cheap, one must keep in mind that the reliability of this approach is limited to the involvement of effective states in the calculations. The beauty of this FSM approach lies in the fact that it can be reduced to the expressions containing angles between different transition moment vectors, which provide a better understanding of the TPA process. According to Alam et al.,17 the overall δTP of a 3D system within GFSM can be written as17 δ TP =

∑ δ ij = ∑ i,j

i,j

8|μ0i ||μ0j ||μif ||μ jf | ij X ΔEiΔEj

Figure 2. Variation of μ01 and μ11 (in au) with the twist angle (in deg) of unsubstituted o-betaine.

(3a)

where ij

X = cos

θ0ifi

cos

θ0jfj

+ cos

θ00ij

cos

θifjf

+ cos

θ0jfi

cos

extracted from the quadratic response theory, δresp, against the twist angle. The corresponding plot is shown in Figure 3

θ0ifj (3b)

θrspq

is the angle between the corresponding transition moment vectors μ⃗pq and μ⃗ rs. Here, the indices i and j runs over the intermediate states including the final state. The involvement of the final state in this summation results in the appearance of the quantum pathway involving the dipole moment difference between the ground and the final states. μif, for i ≠ f, represents the transition moment vector for i ↔ f transition, and for i = f, it is the difference in dipole moment vectors (μff − μ00) between the ground and the final states. In the present work, we have studied the variation of δTP and the interference term with the twist angle between the pyridinium and phenolate rings of o-betaine. The twist angle is varied from 0° to 180° at an interval of 5°, and for each twist angle, all the one- and twophoton parameters for the first excited state have been calculated and then plotted against these angles. The transition probability for one-photon absorption is measured by the oscillator strength (δOPA), which is related to the excitation energy (ω0i) and the transition dipole moment (μ0i) by the following relationship35 δOPA =

2ω0i 3

∑ |⟨0|μα̂ |i⟩|2 α

Figure 3. Variation of δresp, δ3SM, and δ11 (all in au) with the twist angle (in deg) of unsubstituted o-betaine.

and different TPA parameters are supplied in Table ST2 of the Supporting Information. It is evident from Figure 3 that the value of δresp at first increases with the increase in twist angle and reaches its maximum value at 70°, then, with further increase in the angle, a sharp decrease in the δresp value is observed. It is worth commenting that Zaleśny et al.24 also found a similar curve with a peak at 80° for p-betaine and that Pati et al.25 found a maximum at 76° for the quinopyran system. At this stage, it is very crucial to check whether the geometry of o-betaine at the twist angles at which δresp reaches its maximum value is stable. For this purpose, we have plotted (Figure 4) the SCF energy of unsubstituted o-betaine (in gas phase) against the twist angle. The plot dictates that the geometry of o-betaine around the twist angle 70° is energetically unstable. Earlier, Niewodniczański et al.37 have also studied the potential energy curves (PEC) of o-betaine at the HF and MP2/6-31G(d) levels of theory, and they obtained a similar feature, although the PEC was relatively flat in comparison to the present one. The twist angle of the solvent phase optimized geometries of unsubstituted o-betaine are also

(4)

where α ={x, y, z}. Figure SF1 in the Supporting Information shows the variation of δOPA associated with the S0−S1 transition of obetaine. The data containing different OPA parameters are supplied in Table ST1 of the Supporting Information. It is clear from the plot that δOPA gradually decreases with the increase in the twist angle and shows a minimum at 90°. In order to explain this behavior, we have plotted μ01 and ω01 against the twist angle. The relevant plots are shown, respectively, in Figure 2 and Figure SF2 of the Supporting Information. These plots demonstrate that, as we increase the twist angle, both μ01 and ω01 decreases continuously, which in turn is responsible for the net decrease of δOPA with the twist angle. Similar variations of oscillator strength for the p-betaine molecule, with minima at 90°, were obtained by Zaleśny et al.24 using the GRINDOL method and also by Fabien et al.36 at the ab initio CIS level. After analyzing the variation of oscillator strength, we have investigated the variation of TP transition probability as 8069

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case, within GFSM,17 the overall δTP (we represent it as δ3SM), as suggested by eq 3a, is given by δ 3SM = δ11 + δ 22 + 2δ12

(5)

Here, δ and δ terms are given by the expression 11

22

17

⎛ μ0i μif ⎞2 ⎟ (2 cos2 θ0ifi + 1) δ ii = 8⎜ ⎝ ΔEi ⎠

(6)

Equation 6 clearly indicates that the δ and δ terms will always have positive values because these involve only the square terms and hence are always constructive in the sense that they always tend to increase the overall value of δ3SM. The δ12 term, which, as suggested by eqs 3a and 3b, is given by17 11

Figure 4. Plot of SCF energy of unsubstituted o-betaine as a function of twist angle.

δ12 =

22

8μ01μ11μ02 μ21 11 21 02 × (cos θ01 cos θ02 + cos θ01 cos θ1121 ΔE1ΔE2 21 11 + cos θ01 cos θ02 )

(7)

This term depends on the orientations (given by the different angles, θ) of different transition moment vectors with respect to each other. Depending on these angles, δ12 may have either a positive or a negative value, which means it can either increase or decrease the overall δ3SM value. This dual nature δ12 (or in general δij with i ≠ j) is termed as the interference term.16,17 Therefore, in our case, i.e., the 0−1 transition, the only interference term that arises is δ12. The values of different δ terms as calculated using our model are plotted in Figures 3 and 6. Figure 3 suggests that the

far from the required value, which indicates that it is not possible for unsubstituted o-betaine to achieve the optimum twist angle to maximize the TP transition probability either in the gas phase or in solvents. To check the role of the basis set on TP activity, we have also evaluated the δresp of o-betaine at the CAMB3LYP/aug-cc-pVDZ level of theory and noticed that the nature of the variation of δresp with twist angle is quite similar to that obtained from the CAMB3LYP/cc-pVDZ level of theory and that both results give the same range of twist angle for maximum δresp values. Since in this work we are mainly concerned with the range of twist angle at which δresp becomes maximum and as both the cc-pVDZ and aug-cc-pVDZ basis sets give us the same range of twist angle, we have performed all the calculations with the smaller basis (ccpVDZ). It provides a good compromise between the computational cost and the accuracy of the results. The δresp result with aug-cc-pVDZ basis set is depicted in Figure SF3 of the Supporting Information. For explaining the variation of δresp in our case, we have applied the three-level model within GFSM17 and re-evaluated all of the δ terms appearing in eq 3a. Before going into details about our results, it is important to explain the mathematical model used for this work. In this work, we have considered the first excited state as the final state, and both the first and second excited states are taken as the intermediates. A pictorial representation of the model used is shown in Figure 5. In this

Figure 6. Variation of δ22 and δ12 (all in au) with the twist angle (in deg) of unsubstituted o-betaine.

variations of δ11, δ3SM, and δresp with twist angle are similar in nature. The plots for the three δs (Figure 3) show a crest at a twist angle of 70° and a trough at 90°. However, Figure 6 indicates that the variation of δ22 is a bit different. The δ22 term shows a sharp increase with the twist angle and reaches a peak at around 30−35°, and then, it decreases continuously until we arrive at the twist angle 90°. However, δ12 reaches its maximum value at and around 65−70°, and again the minimum value of δ12 is found at 90°. It is interesting to note that δ11 and the interference terms show maximums and minimums at almost the same point where the overall δ3SM and δresp have their respective maximum and minimum values. We must also admit here that the value of δ12 is not very large as compared to the overall δ3SM or δ11.

Figure 5. Pictorial representation of the few-state model used in this work. 8070

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The variation of these δ-terms can be explained by considering the variation of other terms involved in their expressions (i.e., μ, ω, and Xij). From eq 3a, it is obvious that the δ12 term (in three-level model) depends on the four transition moment vectors, two energy terms and six angle terms, whereas δ11 depends only on two μ terms (μ01 and μ11), the angle between them, and an energy term. We have calculated all these terms by changing the twist angle, and the results are depicted in Figures 2 and 7. We have noticed that

of twist angle on X11, X22, and X12, we have calculated these parameters in the entire range of the twist angle, and the relevant results are depicted in Figures 7 and SF5 of the Supporting Information. Interestingly, X12 attains significantly large positive values in the angle range 65−80°, and a similar kind of variation is also observed for X11, which in fact is associated with the highest contributing term, δ11. It is very interesting to note that the value of X22 is close to the maximum value (+3) for the entire range of angles (except for 90°). However, this large value of X22 is eclipsed by the small magnitudes of related transition moment vectors, and hence, the overall contribution of δ22 is very small. The above discussion clearly reveals that the large value of δ3SM around 65−70° twist angle arises from the very large contribution of δ11 and δ12, which ultimately comes from a combined effect of the magnitudes of different transition moment vectors (mainly μ01 and μ11) and their alignment with respect to each other. From the above analyses, one can easily anticipate that, if somehow the twist angle between the two rings of o-betaine can be restricted around 65−70°, the system will show very large TP activity. As mentioned earlier, this target angle cannot be achieved with o-betaine because the system at such a twist angle is energetically unstable, and the angle between the two rings of optimized geometry is 36° only. However, the accomplishment of this target angle is not a very difficult task. One possible way to increase the twist angle between the rings of o-betaine is to exploit the method of substitution(s) at the remaining three ortho positions of o-betaine. On the basis of this strategy, we have considered five model systems (Figure 1b−f) in which the hydrogen atoms at the ortho positions of o-betaine were substituted by one, two, and three methyl groups. It is worth commenting that, in the case of substitutions by one methyl or two methyl groups, simultaneously, there are two distinct possibilities in each case. For one methyl group substitution, CH3 can be placed on the ortho position of either pyridinium ring (Figure 1b) or the phenoxide ring (Figure 1c). Similarly, for two methyl groups substitution, the two possibilities are one in which both the methyl groups are attached to the pyridinium ring (Figure 1d) or, in the other case, each ring of o-betaine contains one methyl group (Figure 1e). The only possibility for trimethyl substituted o-betaine is shown in Figure 1f. After optimizing the geometry of all these model systems, we have evaluated the δresp at the CAMB3LYP/cc-pVDZ level of theory. The twist angle between the rings of the model systems including o-betaine, and the δresp of all the systems are presented in Table ST3 of the Supporting Information. It is evident from this table that the highest δresp (1.49 × 105 au) is obtained with the system as depicted in Figure 1e, where the twist angle between the rings is around 65°. It is also important to note that almost the same value for δresp (1.47 × 105 au) is obtained for the monosubstituted o-betaine (where the CH3 group is on the ortho position of the pyridinium ring). For this system, the twist angle is 60.5°. However, trimethyl substituted o-betaine (Figure 1f) has a twist angle around 80°, and it has more than 20 times lower δresp with respect to that of the model systems shown in Figure 1b,e. All the above-mentioned calculations have been performed with the gas phase optimized geometries. To verify the robustness and reliability of the gas phase results, it is always instructive to repeat these calculations in solvent phases too. For this purpose, we have also optimized all the substituted and unsubstituted o-betaine molecules in two different solvents, namely, cyclohexane and n-hexane, and calculated their δresp with the corresponding solvent phase

Figure 7. Variation of X11 and X12 (all in au) with the twist angle (in deg) of unsubstituted o-betaine.

the two energy terms (ω 01 and ω 02 ) are decreasing continuously with the increase in twist angle and reaches a minimum at 90°. A closer inspection of all the μ plots reveals that, out of the four transition moment vectors, the contribution of μ11 is much higher than the other three. Moreover, Figure 2 clearly indicates that, while the peak in the variation pattern of μ11 has appeared at the twist angle 90°, μ01 shows just the opposite trend, that is, it has the minimum value at 90° twist angle. As a consequence, this particular twist angle (90°) should not be a good choice to maximize the δTP of the system. However, the two μ curves, namely, the twist angle dependent variations of μ11 and μ01, meet at an angle 65° with moderate values, and therefore, the product of μ11 and μ01 will have a maximum value at this point. The value of ω01 is also sufficiently small at 65° angle. This explains the highest contribution of the δ11 term. The contribution of the other two μ terms, namely, μ12 and μ02, are rather very small (Figure SF4 of the Supporting Information) in the entire range of the angle variation, and hence, the corresponding contribution from δ22 is also very small. Apart from the magnitude of the various transition moment vectors, the contribution, Xij, that comes from the angles between these vectors and hence the channel interference term may play an important role in determining the net δTP of the system. Therefore, it is highly instructive to check the variation of Xij with the twist angle. Within 3SM, the Xij should have three different components, namely, X11, X12 and X22 of which X11 and X22 are associated with δ11 and δ22 and always have positive values. On the contrary, the cross-term, X12 may have both positive and negative values in the range {−3 to +3}. The sign of this cross-term will ultimately dictate the nature of the channel interference, and it is always a difficult task to find out the means of controlling its sign. As stated earlier, we have found constructive channel interference for o-betaine, or in the other words, the value of X12 is positive. To examine the effect 8071

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optimized geometries. The solvent phase δresp values are supplied in Table ST3 of the Supporting Information, and the corresponding TPA cross-sections (in Göppert-Mayer unit) are depicted in Figures 8, 9, and SF9 of the Supporting

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CONCLUSIONS In conclusion, we have studied the variation of TP transition probability with the twist angle between the two rings of obetaine using both quadratic response theory and recently developed GFSM. The GFSM analysis clearly explains that the term δ11 together with the channel interference (δ12) have dominant contribution to the overall TP transition probability of the system and that these terms become maximum in the twist angle range of 65−70°. In this range of twist angle, the magnitude of ground to excited state transition moment (μ01), excited state dipole moment (μ11), and the angle between these vectors are in favor of maximum δTP. We have also shown that the required optimum twist angle can be achieved by introducing one methyl group at the ortho position of the pyridinium ring of o-betaine. To be more realistic, we have also calculated the TP transition probability of all possible ortho substituted o-betaine model systems in two solvents, namely, cyclohexane and n-hexane. We have found that the monosubstituted o-betaine (where one CH3 group is on the ortho position of pyridinium ring) has a twist angle very close to the optimum value and also has larger TP transition probability than other model systems. To the best of our knowledge, this is the first successful attempt to control the alignment between different transition moment vectors with respect to twist angle and hence to control the TPA process of a 3D system.

Figure 8. Plot of TPA cross-section (in GM unit) against wavelength, λ (in nm), for unsubstituted and substituted o-betaine in gas phase.

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ASSOCIATED CONTENT

S Supporting Information *

Data for the plot of oscillator strength, ω01, ω02, μ01, μ11, μ02, and μ12 against the twist angle of unsubstituted o-betaine molecule; data for the plot of different δ-terms against the twist angle of unsubstituted o-betaine molecule; twist angle and corresponding TP transition probability of different substituted and unsubstituted o-betaine molecules in gas and solvent phases; twist angle and corresponding TP transition probability of different substituted and unsubstituted p-betaine molecules in gas phase; variation of oscillator strength with twist angle in unsubstituted o-betaine molecule; variation of excitation energies with twist angle in unsubstituted o-betaine molecule; variation of δresp with the twist angle of unsubstituted o-betaine molecule; variation of μ02 and μ12 with the twist angle in unsubstituted o-betaine molecule; variation of different Xij terms with twist angle of unsubstituted o-betaine molecule; molecular orbital pictures of unsubstituted, disubstituted,and trisubstituted o-betaine molecules; optimized geometries of different substituted and unsubstituted p-betaine molecules; variation of X12 and X22 with twist angle of unsubstituted pbetaine molecule; plot of TPA cross-section of different substituted and unsubstituted o-betaine molecules against the twist angle in cyclohexane solvent. This material is available free of charge via the Internet at http://pubs.acs.org.

Figure 9. Plot of TPA cross-section (in GM unit) against wavelength, λ (in nm), for unsubstituted and monosubstituted o-betaine in nhexane phase.

Information. The TPA cross-sections are evaluated considering 0.1 eV width of the spectra. These two figures clearly elucidate that the value of δresp in both solvents is maximum for monosubstituted o-betaine having a −CH3 group on the ortho position of the pyridinium ring where the twist angle is very close to 65°. For other substituted o-betaines, in particular, for the trisubstituted system, the twist angle between the rings is very close to 90°, and as a consequence, the δresp of this system is sufficiently small. We have also performed similar calculations with the substituted p-betaine (in the gas phase), and the results are presented in Table ST4 of the Supporting Information. In this case, the effect of the twist angle is even more prominent. The substituted p-betaine with three methyl groups at the ortho positions (Figure SF7 in Supporting Information) has more than 105 times higher δresp than that of its tetra-substituted analogue. Finally, we believe that the present investigation will attract the attention of the experimentalist to synthesize new TPA active material based on substituted o-betaine.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS S.C. wishes to convey his special thanks to Professor Antonio Rizzo of Consiglio Nazionale delle Ricerche−CNR, Italy, for 8072

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(33) McClain, W. M. J. Chem. Phys. 1971, 55, 2789. (34) Shen, Y. R. The Principles of Nonlinear Optics; Wiley: New York, 1984; pp 23−25. (35) Hilborn, R. C. Am. J. Phys. 1982, 50, 982. (36) Fabian, J.; Rosquete, G. A.; Montero-Cabrera, L. A. J. Mol. Struct. 1999, 469, 163. (37) Niewodniczański, W.; Bartkowiak, W. J. Mol. Model. 2007, 13, 793.

allowing us to use his code for generating TPA spectra. M.M.A. thanks the Council of Scientific and Industrial Research (CSIR) for his Senior Research Fellowship. M.C. thanks the Centre for Research in Nanoscience and Nanotechnology (CRNN) for her fellowship. S.C. acknowledges the CRNN for research funding.

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REFERENCES

(1) Mayer, M. G. Ann. Phys. 1931, 9, 237. (2) Parthenopoulos, D. A.; Rentzepis, P. M. Science 1990, 245, 843. (3) Kawata, S.; Sun, H. B.; Tanaka, T.; Takada, K. Nature 1990, 412, 697. (4) Tutt, L. W.; Boggess, T. F. Prog. Quantum Electron. 1993, 17, 299. (5) Ehrlich, J. E.; Wu, X. L.; Lee, L. Y. S.; Hu, Z. Y.; Rockel, H.; Marder, S. R.; Perry, J. W. Opt. Lett. 1997, 22, 1843. (6) Arnbjerg, J.; Jiménez-Banzo, A.; Paterson, M. J.; Nonell, S.; Borrell, J. I.; Christiansen, O.; Ogilby, P. R. J. Am. Chem. Soc. 2007, 129, 5188. (7) Luo, Y.; Norman, P.; Macak, P.; Ågren, H. J. Phys. Chem. A 2000, 104, 4718. (8) Norman, P.; Luo, Y.; Ågren, H. J. Chem. Phys. 1999, 111, 7758. (9) Luo, Y.; Ågren, H.; Knuts, S.; Jørgensen, P. Chem. Phys. Lett. 1993, 213, 356. (10) Albota, M.; Beljonne, D.; Brédas, J. L.; Ehrlich, J. E.; Fu, J.; Heikel, A. A.; Hess, S. E.; Kogej, T.; Levin, M. D.; Marder, S. R.; McCord-Maughon, D.; Perry, J. W.; Rö ckel, H.; Rumi, M.; Subramaniam, G.; Webb, W. W.; Wu, X.; Wu, C. Science 1998, 281, 1653. (11) Chakrabarti, S.; Ruud, K. Phys. Chem. Chem. Phys. 2009, 11, 2592. (12) Chakrabarti, S.; Ruud, K. J. Phys. Chem. A 2009, 113, 5485. (13) Alam, M. M.; Chattopadhyaya, M.; Chakrabarti, S. Phys. Chem. Chem. Phys. 2011, 13, 9285. (14) Chattopadhyaya, M.; Alam, M. M.; Chakrabarti, S. J. Phys. Chem. A 2011, 115, 2607. (15) Alam, M. M.; Chattopadhyaya, M.; Chakrabarti, S.; Ruud, K. J. Phys. Chem. Lett. 2012, 3, 961. (16) Cronstrand, P.; Luo, Y.; Ågren, H. J. Chem. Phys. 2002, 117, 11102. (17) Alam, M. M.; Chattopadhyaya, M.; Chakrabarti, S. Phys. Chem. Chem. Phys. 2012, 14, 1156. (18) Drobizhev, M.; Meng, F.; Rebane, A.; Stepanenko, Y.; Nickel, E.; Spangler, C. W. J. Phys. Chem. B 2002, 110, 9802. (19) Jagatap, B. N.; Meath, W. L. J. Opt. Soc. Am. B 2002, 19, 2673. (20) Jagatap, B. N.; Meath, W. L. Chem. Phys. Lett. 1996, 258, 293. (21) Delysse, S.; Raimond, P.; Nunzi, J.-M. Chem. Phys. 1997, 219, 341. (22) Reichardt, C. Chem. Rev. Soc. 1992, 21, 147. (23) Paley, M. S.; Meehan, E. J.; Smith, C. D.; Rosenberger, F. E.; Howard, S. C; Harris, J. M. J. Org. Chem. 1998, 54, 3432. (24) Zaleśny, R.; Bartkowiak, W.; Styrez, S.; Leszczynski, J. J. Phys. Chem. A 2002, 106, 4032. (25) Pati, S. K.; Marks, T. J.; Ratner, M. A. J. Am. Chem. Soc. 2001, 123, 7287. (26) DALTON, A Molecular Electronic Structure Program, 2011; see http://www.kjemi.uio.no/software/dalton/dalton.html. (27) Peach, M. J. G.; Cohen, A. J.; Tozer, D. J. Phys. Chem. Chem. Phys. 2006, 8, 4543. (28) Peach, M. J. G.; Benfield, P.; Helgaker, T.; Tozer, D. J. J. Chem. Phys. 2008, 128, 044118. (29) González, D.; Neilands, O.; Rezende., M. C. J. Chem. Soc., Perkin Trans. 2 1999, 713. (30) Murugan, A. N.; Kongsted, J.; Rinkevicius, Z.; Aidas, K.; Mikkelsen, K. V.; Ågren, H. Phys. Chem. Chem. Phys. 2011, 13, 12506. (31) Mikkelsen, K. V.; Ågren, H.; Jensen, H. J. A.; Helgaker, T. J. Chem. Phys. 1988, 89, 3086. (32) Mikkelsen, K. V.; Cesar, A.; Ågren, H.; Jensen, H. J. A. J. Chem. Phys. 1995, 103, 9010. 8073

dx.doi.org/10.1021/jp304456w | J. Phys. Chem. A 2012, 116, 8067−8073