Kaspars
Traskovskis
*a,
Arturs
Bundulis
b and
Igors
Mihailovs
ab
aRiga Technical University, Faculty of Materials Science and Applied Chemistry, 3/7 Paula Valdena Street, Riga LV-1048, Latvia. E-mail: kaspars.traskovskis@rtu.lv; Tel: +371 29148070
bInstitute of Solid State Physics, University of Latvia, 8 Kengaraga Street, Riga LV-1063, Latvia
First published on 29th November 2017
One of the strongest known electron-accepting fragments used in the synthesis of organic dyes for applications in nonlinear optics (NLO) is 1,3-bis(dicyanomethylidene)indane (BDMI). By studying a benzylidene-type push–pull chromophore bearing a 5-carboxy-BDMI electron-acceptor and 4-(dimethylamino)aniline donor fragment, we demonstrate that this class of compounds can show unusual response to the polarity of the surrounding medium. The combined results of UV-Vis absorption spectrometry, NMR experiments and computational modeling indicate that the studied compound undergoes a geometrical transformation that involves an increase in the torsion angle ω between the aniline and indane ring systems with the rise of the polarity of the surrounding medium. This process is partly facilitated by an increased rotational freedom around ω in more polar solvents, as detected experimentally by NMR and predicted by calculations. Regarding the practical application aspects, computations predict that the solvent-polarity-induced increase of torsion ω would lead to a notable decrease in the first hyperpolarizability (β) value. This was detected experimentally, as hyper-Rayleigh scattering (HRS) data showed a drop in the compound's NLO activity from βHRS(532) = 513 × 10−30 esu in toluene to βHRS(532) = 249 × 10−30 esu in acetonitrile. This places limitations on the NLO applications of the studied compound and its structural analogues, as the surrounding medium (solvent of polymer matrix) with the lowest possible polarity needs to be used to maximize their NLO efficiency.
According to the two-state model,9,10 the electronic ground state of a conjugated π-electron system can be expressed as a combination of two limiting classical (Lewis) structures (or basis states): the neutral (push–pull) one and the charge-separated (zwitterionic) one, thus describing an actual partially ionic electronic structure (an intermediate of both). Depending on the prevalence of one or the other state, the nonlinear optical characteristics of the dipolar π-electron systems can change drastically, and maximal β is usually attained when the molecule assumes a configuration that lies between push–pull and cyanine-like (i.e., centrosymmetrical) structure.11 The charge distribution, bond configuration and consequentially NLO characteristics of chromophores can be significantly altered by the polarity of the surrounding medium (e.g. solvent, polymer matrix).12–14 For example, two-fold increase in β for some push–pull chromophores has been reported by increasing the solvent polarity.15 This means that a complete understanding of the molecule's interaction with the medium is needed to evaluate the results of experimental NLO measurements reliably and to maximize the performance of the developed materials.
One of the strongest known electron-accepting fragments used in high-performance NLO-active chromophores is 1,3-bis(dicyanomethylidene)indane (BDMI).16–21 The low cost and high chemical and thermal stability of the corresponding compounds makes BDMI a promising structural building block. In our previous study we presented an improved chemical design of BDMI by attaching a carboxyl group to its 5 position (5A-BDMI) with the intention to introduce a chemically linkable fragment for subsequent attachment of solubility-enhancing or site-isolating functional fragments.22 As it was found, reactions of 5A-BDMI with different 4-aminobenzaldehydes yielded only E-configuration benzylidenes, providing an additional tool of structural control over the geometry of the NLO active molecules. In this study we take a closer look at the solvent-polarity dependence of the molecular geometry, and linear and nonlinear optical properties in 5A-BDMI-based benzylidene IND-1 (Fig. 1). By analyzing UV-Vis, NMR, and hyper-Rayleigh scattering (HRS) data as well as carrying out quantum chemical modeling to explain the experimental observations, we demonstrate that BDMI-based chromophores can show unusual responses to the surrounding medium that need to be taken into account to maximize their molecular and macroscopic NLO efficiency.
Fig. 3 (a) IND-11H-NMR spectra of representative aromatic signals in solvents of different polarity; (b) IND-113C-NMR spectral region showing broadening of the C8 signal in CDCl3. |
Solvent-dependent variations in composition of the electronic ground state in IND-1 can be examined by measuring the vicinal coupling constant 3JH9–H8 at the proton signal H9. During the push–pull-type charge transfer, the electron-donating aniline fragment of a chromophore molecule undergoes a transformation of its double bond configuration from mostly aromatic to mostly quinoidal. It is expected that with more pronounced quinoidal nature the constant 3JH9–H8 would increase, as the C–C bond between the corresponding carbon atoms shortens in this process.23 Looking at the obtained 3JH9–H8 values (Fig. 3a), the push–pull charge transfer level of IND-1 is not linearly dependent on solvent polarity. A predictable increase of aniline ring quinoidality is observed in the solvent sequence C6D6 → CDCl3, indicated by a coupling constant change from 8.2 to 9.2 Hz. However, with the further medium polarity increase in CD3CN and (CD3)2SO, the 3JH9–H8 value does not increase and even starts to drop, from 9.2 to 8.9 Hz. This indicates that push–pull electron transfer in strongly polar solvents becomes obstructed, most likely by an increased torsion angle ω (C14–C5–C6–C7).
Medium | ω [°] | ISDIb [°] | BLA(1)c | MK charge on indaned | APT charge on indaned | λ S1 [nm] | f S1 | λ S2 [nm] | f S2 | β HRS(0),g 10−30 esu | β HRS(532),h 10−30 esu |
---|---|---|---|---|---|---|---|---|---|---|---|
a Torsion angle C14–C5–C6–C7. b ISDI (indane-system deformation index) parameter is calculated as the sum of indane ring deformations (higher value corresponds to a more deformed structure). ISDI = (360 – bond-to-bond angle sum at atom C5) + |torsion angle C13–C12–C4–C3| + |torsion angle C19–C18–C14–C15| + |torsion angle C18–C14–C5–C4|. c BLA parameter calculated following path C3–C4–C5–C6–C7–C8–C9–C10. It perfectly correlates with BLA of C5–C6–C7. d Including the anhydride part; the rest of the molecule was considered the aniline region (with complimentary positive total charge). e Wavelength of the corresponding transition. f Oscillator strength of the corresponding transition. g Calculated molecular static first hyperpolarizability, averaged over components as to be comparable with HRS experimental data.31 h Experimentally determined values; these are resonance-enhanced due to proximity of the second-harmonic scattering wavelength to those of optical transitions. Zero frequency extrapolation was avoided to prevent an underestimation of the parameter. | |||||||||||
Vacuum | 10.69 | 55.41 | 0.041 | −0.598 | −0.873 | 465 | 0.40 | 416 | 0.37 | 48 | — |
Toluene | 10.66 | 50.08 | 0.038 | −0.680 | −0.945 | 487 | 0.32 | 435 | 0.39 | 59 | 513 ± 52 |
CHCl3 | 11.75 | 50.39 | 0.037 | −0.676 | −0.982 | 489 | 0.32 | 438 | 0.40 | 66 | 497 ± 40 |
DCM | 11.11 | 52.84 | 0.036 | −0.675 | −1.025 | 488 | 0.33 | 439 | 0.42 | 72 | — |
MeCN | 11.35 | 52.70 | 0.035 | −0.668 | −1.053 | 491 | 0.32 | 441 | 0.43 | 76 | 249 ± 23 |
DMSO | 12.03 | 49.48 | 0.035 | −0.707 | −1.025 | 493 | 0.33 | 442 | 0.46 | 73 | — |
In agreement with the predictions based on analogous structures, the indane ring system generally becomes less deformed during the change of ω, as is shown by ISDI (most planar in DMSO, least planar in vacuum; toluene point is an outlier). The calculated bond-length alternation (BLA) parameter values show a steady exponential drop with increasing solvent polarity (dependent not on either ω or ISDI but rather on some intricate combination of them). However, in DMSO the value of BLA is still relatively large and positive, indicating a strong neutral ground-state character.25 The charge separation level in IND-1 increases with solvent polarity (except for DMSO, where it drops; probably the reason is that the increase in indane planarity outweighs the increase in the value of ω). Note that the reverse but very weak behavior is observed in the case of Merz–Singh–Kollman26,27 (electrostatic-potential-derived) charges, even if using a 64× denser grid than the Gaussian 09 default to ensure trend consistency.
The computational analysis of the electronic transitions reveals that the lowest-energy absorption band of the studied chromophores consists of two transitions, S1 ← S0 and S2 ← S0, in which electron density shifts from the aniline ring to the region of indane, centered around one or the other of the two dicyanomethylene groups (Fig. 4). As is expected from the results of structural optimizations, the slow change in molecular geometry with the increase in solvent polarity determines a slow change in spectral properties (Table 1). Correlation can be drawn between the transition energy and some combination of ω and BLA: in general, weakly bathochromic solvatochromism is predicted for IND-1. No notable band shape and intensity transformations are present, as indicated by oscillator strength values; the intra-band weight, however, shifts gradually from S1 ← S0 to S2 ← S0 transition, producing some faint negative solvatochromism, as is also observed in experiments. It is interesting to note that the transition energies computed are off from the experimental band maximum even by as much as 0.6 eV. This is rather unusual, as range-separated DFT usually yields better transition wavelengths than the global hybrids (which provide better results in the absolute values in our case) specifically by making these wavelengths shorter.28,29 On the other hand, in particular cases like cyanines29 and condensed heteroaromatics29,30 modern TD-DFT implementations still happen to produce errors of the scale mentioned.
It is obvious therefore that the previously discussed results of quantum chemical modeling do not give a consistent explanation to the observed NMR data, and linear and especially (as discussed latter) nonlinear optical properties. It must be taken into consideration that those calculated values represent a static structure in its optimized, lowest-energy state, so any possible effects of structural dynamics are being ignored; as are specific solvent effects due to the use of PCM. Hence, in an actual medium the molecule can have rather different value of average ω, being in addition surrounded by available internal-rotational (vibrational) states. As this torsion is probably the most significant coordinate of thermal motion, we a performed potential energy surface (PES) scan for IND-1 by setting the torsion ω to various values and optimizing the rest of the molecule in the corresponding medium (Table 2; see Table S1 in ESI† for additional ω values). Although it is usually advised to use meta functionals for barrier studies,32–34 and we also found that M06-2X Gibbs energy barriers are more consistent than those computed with CAM-B3LYP, we have faced considerable convergence problems with the meta functionals (see the Experimental section), and decided to use CAM-B3LYP for scan-relevant computations, as range-separated hybrid functionals also do perform fairly well for barriers.32,33,35 Conformations explored range from the almost planar E-isomer to the fully twisted (ω = 90°) structure to the Z-isomer. As is predicted, with increased torsion ω the value of the ISDI parameter steeply falls, and at 90° the indane ring assumes the most planar configuration. The calculated BLA parameter values in the ω = 11–40° range are typical for those of the neutral ground state structures.25 Starting from ca. 55°, these become negative, indicating the dominance of the zwitterionic resonance form. The increased charge separation is also reflected by both charge types, which increase in absolute value in the range of negative BLA. Before that, MK charges are just oscillating, whereas the APT ones are decreasing (probably attributable to different vibration modes of classical and zwitterionic forms).
ω [°] | ISDI [°] | BLA(1) | APT charge on indane | MK charge on indane | ΔEa [kcal mol−1] | ΔEb [kcal mol−1] | λ S1 [nm] | f S1 | λ S2 [nm] | f S2 | β HRS(0), 10−30 esu |
---|---|---|---|---|---|---|---|---|---|---|---|
a Relative energy of conformation from the bottom of the E isomer well. b The same parameter but calculated for the corresponding conformations in benzene. c E isomer. d Z isomer. | |||||||||||
11.3c | 52.70 | 0.035 | –1.05 | –0.67 | 0.00 | 0.00 | 507 | 0.32 | 458 | 0.43 | 76.2 |
30.1 | 41.35 | 0.023 | −1.15 | −0.76 | 0.98 | 1.08 | 508 | 0.46 | 466 | 0.33 | 69.6 |
50.1 | 26.75 | 0.005 | −1.22 | −0.80 | 3.84 | 4.16 | 526 | 0.53 | 474 | 0.20 | 51.6 |
70.0 | 23.41 | −0.014 | −1.25 | −1.05 | 8.24 | 8.94 | 573 | 0.42 | 478 | 0.20 | 29.9 |
90.1 | 7.27 | −0.056 | −1.04 | −1.34 | 14.44 | 16.03 | 848 | 0.02 | 493 | 0.26 | 25.8 |
110.4 | 9.00 | −0.014 | −1.29 | −0.85 | 8.84 | 9.60 | 588 | 0.35 | 486 | 0.20 | 25.1 |
130.1 | 23.07 | 0.011 | −1.22 | −0.64 | 3.77 | 3.97 | 517 | 0.51 | 484 | 0.19 | 51.6 |
150.2 | 47.65 | 0.030 | −1.09 | −0.71 | 0.65 | 0.66 | 479 | 0.29 | 494 | 0.43 | 69.3 |
157.7d | 53.69 | 0.034 | −1.05 | −0.66 | 0.41 | 0.32 | 478 | 0.29 | 492 | 0.42 | 73.2 |
Regarding the calculated electronic transitions S1 ← S0 and S2 ← S0, a notable nonlinearity can be observed in the response to increasing ω. This is best rationalized by plotting all three PES together (example for chloroform given in Fig. 5, demonstrating the close qualitative resemblance of situations in all three solvents). Initially (until approximately ω = 40° in all solvents considered) all three states are developing in the same direction, with most quickly rising for S0 (hence the small bathochromic shift for both transitions, somewhat larger for S2 ← S0). Then, however, states S1andS0 start approaching one another, resulting in plummeting energy of the first transition (shift ca. 5× that for S2 ← S0, in energy dimension). The oscillator strength (f) of the first transition is climbing, but that of the second one is descending until ω = 40°, with the sum of both remaining nearly constant; this can be rationalized through planarization of the indane 5-membered ring, increasing quantum interference effects on the efficiency of both transitions. Both transitions are inherently asymmetric due to non-equality of both dicyanomethylene groups (one is in-plane with the rest of the molecule, another one is not), but this cannot explain the increase in asymmetry when this sterically induced bias is removed by increasing ω. The difference in quantum interference patterns, the true cause of the increasing asymmetry, is caused by an electron-accepting carboxylic group in 5A-BDMI, which by cross-conjugation stabilizes the charge transfer involving the C4-centered dicyanomethylene group. Beginning with ω = 40°, fS2 stabilizes while fS1 drops down to almost zero at ω = 90°. In this region, as revealed by NTO plots, S2 ← S0 starts to localize on the indane part of the molecule, while its counterpart withdraws to aniline; yet both transitions spread over both structural regions until the very adjacency of the turning point at ω = 90°. This is caused by the loss of the conjugation between the aniline and indane π-electronic subsystems. In this region, transition S1 ← S0 displays a characteristic saw-tooth, which means that the real rotation path in the first excited state is more complicated than just the change of a single dihedral;36 this is obviously linked to the considerable non-planarity of the 5-membered ring of indane. As the second transition is much less affected by the change of the dihedral, it also shows almost no sign of such ‘saw-tooth’, following the pattern in the ground state. Seeing no ‘saw-tooth’ for the ground state, we reckon that the change in ω represents the real internal rotation path sufficiently well. In the region of the Z-isomer, it is observed that λ and f oscillate for both transitions, as the S1 and S2 states approach each other and mix together. We have also performed a less detailed scan with the same CAM-B3LYP on TPSSh-optimized geometries, because this functional provided the largest range of dihedral values during the full optimization study in various solvents. However, no notable differences in trends of electronic states were observed (see Fig. S5 in the ESI†).
The resulting behavior of the composite band is an initially small bathochromic shift with hyperchromism, as the energetic gap between both bands narrows until ω = 40° while the combined f value also slightly increases (from 0.75 to 0.81). After the 40° mark, the bands begin to separate, with the total intensity dropping noticeably. The same parabolic behavior of the absorption intensity can be observed in the solvatochromism experimental data, where similar changes in ε values of IND-1 were detected depending on solvent polarity. In fact, the evolution of bands can also explain the perceived negative solvatochromism in the most polar solvents: as the medium polarity grows, the higher-energy transition gains a little in intensity, while the lower-energy one loses it considerably. In addition, both transitions show only a marginal red shift in this range of polarity. As a result, the maximum of the band formed by both transitions should shift to higher energies – which is actually observed experimentally. This suggests that in the response to growing polarity of the surrounding medium the dominating conformational population of the molecules assumes gradually larger values of torsion angle ω.
It should be mentioned that absolute transition energy values that are similar to those observed in the experiments appear only at the very proximity to the saddle point. In the absence of some multi-molecular processes unaccounted for it seems highly improbable for IND-1 to remain steadily in such a geometry; possibly part of this discrepancy is explained by the aforementioned inaptitude of range-separated density functionals.
Another argument that speaks in favor of this hypothesis is provided by comparison of E/Z-isomerization barriers in solvents of different polarity. Table 2 presents electronic energies of different conformations, while in Table 3 the barriers calculated from the more reliable Gibbs free energies are given. A notable deviation in ΔE between the two solvents can be observed starting from ω = 30°, where the computed structure in benzene is of slightly higher relative energetic cost; this comes to a significant difference at ω = 90°. According to the Eyring–Polanyi transition state theory, under room temperature conditions this would lead to an E/Z-isomerization rate constant difference of several orders (103 s−1 in MeCN vs. 10−1 s−1 in benzene). Such a difference in the time scale of the process is in accordance with NMR data, where both isomers were detected in C6D6, in contrast to more polar solvents. As a consequence, it can be assumed that it is less likely for IND-1 to assume conformations with higher ω in low-polarity solvents.
Medium | CAM-B3LYP/6-311G(d,p) | M06-2X/6-311G(d,p) | ||||||
---|---|---|---|---|---|---|---|---|
ΔG‡antia [kcal mol−1] | ΔG‡synb [kcal mol−1] | k anti [s−1] | k syn [s−1] | ΔG‡antia [kcal mol−1] | ΔG‡synb [kcal mol−1] | k anti [s−1] | k syn [s−1] | |
a Gibbs activation free energy and the corresponding force constant from the side of the E isomer. b Same from the side of the Z isomer. c Unfortunately, we could not converge the minimum geometry of the syn isomer. | ||||||||
Benzene | 18.00 | 15.86 | 0.2 | 7 | 16.85 | —c | 1 | —c |
Toluene | 15.70 | 12.64 | 9 | 1669 | 16.39 | 13.79 | 3 | 240 |
CHCl3 | 15.09 | 16.24 | 26 | 4 | 15.47 | 14.02 | 14 | 163 |
MeCN | 13.02 | 13.71 | 874 | 273 | 14.09 | 12.18 | 143 | 3627 |
The Gibbs energy (hence the population) of the Z-isomer in benzene (toluene) has significantly higher values (ΔG) in comparison with their E-counterparts, and at the lowest energy configuration the difference is slightly above 2 (3) kcal mol−1. This is in an agreement with the X-ray structural analysis of IND-1 that shows the presence of only the E-isomer. While a slight population of Z-isomer is expected to be present in solutions of the compound, the slow process of crystallization apparently causes a selective precipitation of the compound in its more stable form. Again, the difference between both isomers is rationalized by the quantum interference, for in the case of the E-isomer the carboxylic-group-promoted conjugation path runs along the more coplanar of the two regions around the dicyanomethylene groups, the one centered around C4.
As is clear from the previous discussion, the results of the calculations for energetically optimized structures are not consistent with experimental observations; the twist around torsion ω needs to be taken into account to model the solvatochromic response of IND-1 accurately. The results of this modeling (Table 2 and Fig. 6) indicate a steady drop of βHRS with increasing ω, as it is expected, due to the loss of conjugation between the aniline and indane fragments. At the 80° mark the orientationally averaged βHRS(0) value is expected to drop by 62% (β0 even more so). The predicted temporary increase in hyperpolarizability in the 80°–90° range is in accordance with the three-level model proposed by Kuzyk et al.37 This model suggests that the first hyperpolarizability becomes larger when the target energy level of the first electronic transition lowers and at the same time increasingly departs from the rest of the excited states. This requirement is met by the behavior of steeply falling S1 ← S0 and relatively steady S2 ← S0 transition.
The experimental hyperpolarizability values were determined by the HRS technique in toluene (εr = 2.4), CHCl3 (εr = 4.8) and ACN (εr = 37.5) (Table 1). The acquired βHRS(532) values demonstrate a medium-polarity response that is in full agreement with the assumption that in more polar solvents IND-1 populates states with larger value of torsion ω (either by wider conformational freedom or by more pronounced influence of solvent-specific effects). The highest βHRS was measured in toluene, while in CHCl3 it dropped by 4% and in ACN by 52%. Assuming that in toluene the structure is maximally planar, a rough estimate of the actual ω value in the other two solvents can be made using the model outlined in Fig. 6. Multiplying the experimental value of toluene by the coefficient of the computed βHRS ratio for E-isomers in both solvents, then normalizing the βHRS torsion-angle dependence to this value, we can conjecture that the dominating conformational population of IND-1 resides at around the 37° mark in CHCl3 and around the 80° mark in ACN. The last figure seems quite improbable, in particular because there is no associated major change in electronic transitions observed experimentally; we can at least rule out the influence of the Z-isomer, as the ω-dependence of βHRS(0) is rather symmetric around the ω = 90° point. It is probably also not the effect of decomposition due to laser radiation, as absorption spectra taken after measurements did not show any remarkable change. On the other hand, it is known that in “wet” ACN (and in other hydrogen-bond-donating media, as alcohol solutions) the IND-1 absorption peak features major hypochromism with the addition of band splitting, resembling the spectrum of the 5A-BDMI anion (i.e., indicating totally split conjugation, as around the ω = 90° point). Although no such changes were found in absorption spectra of ACN solutions used for HRS, they may occur locally at the focal point of the laser beam. This is one probable reason for the unexpectedly small values of βHRS observed in acetonitrile. Another one is connected with the inability of CAM-B3LYP to predict absolute values of electronic transition energies for IND-1 (vide supra). As hyperpolarizability is intrinsically a property of the same nature, we can expect the lesser performance of this functional also for β values. It would be expected, however, that it underestimates β, as the electronic transition energies are overestimated (see ref. 37). This confirms that some unexplored molecular-level processes take place at the focal point of the laser beam.
The following assumptions can be made about the conformational changes and solvatochromism of IND-1:
(1) A greater twist of torsion ω between the planes of indane and aniline corresponds to greater contribution of the zwitterionic structure to the ground state. Thus, in polar solvents, which favor a charge-separated state over the mostly-neutral one, the twist must become more pronounced. To some extent the increase in ω can be facilitated by specific solvent interactions and photochemistry in high-intensity optical fields.
(2) The experimentally observed nonlinear behavior of the UV-Vis absorption band of IND-1 is in agreement with computational modeling predictions, which are as follows. Initially, in response to increasing ω different evolution of the two lowest-energy transitions leads to an initial intensification and moderate bathochromic shift of the combined band. In the ω > 40° range, with the intensity difference now in favor of the higher-energy transition, this leads to the perceived reversal of solvatochromism and drop of intensity.
(3) The calculations and NMR data show that the energy of the rotational barrier between the planes of indane and aniline in IND-1 notably decreases with increased polarity of the surrounding medium, thus favoring the probability of the twisted conformations. This provides evidence for the theoretical reasoning outlined in the first point.
In order to select an appropriate method, we compared various calculated geometry parameters of IND-1 with the X-ray analysis data. The final choice of the functional was made by considering asymptotic behavior of them in various real media (vacuum, tetrachloromethane, toluene, tetrahydrofuran (THF), dichloromethane (DCM), acetic anhydride, nitromethane, acetonitrile (ACN), dimethylsulfoxide (DMSO)), as well as (for van der Waals cavity tests, which showed very similar results) in three fictitious ones (with dielectric constants εr = 65; 81; 100 and εr∞ = 3), modeled with a simple, resource-effective conductor-like polarizable continuum model (CPCM).40,41 These dependencies were checked for up to 10 density functionals (APFD,42 B3LYP,43 TPSSh,44 M06-2X,45 LC-BLYP,46 LC-ωPBE,47 ωB97X,48 ωB97XD,49 CAM-B3LYP50 and M11;51 not all calculations converged for every solvent, especially with meta functionals) with the 6-311G(d,p)52 basis set. For the main parameter of this study, the C14–C5–C6–C7 dihedral, among the best were CAM-B3LYP and M06-2X; the largest absolute range was obtained with TPSSh and is 5.9°, 34% of the average value for this functional; the largest relative range was obtained with M11 (3.4° and 37%). Despite local functionals (incl. TPSSh) showing the broadest window of ω values, they also predict its maximum in DCM, without rise in DMSO, which triggered us to continue using CAM-B3LYP, as we also needed to obtain excited-state energies at every point, for which this functional was found to be optimal (see below). Although it is usually advised to use meta functionals for barrier studies,32–34 we faced considerable problems with converging geometry optimizations (both full and partial) for this class of functionals when they have large percentage of HF-like exchange admixed (this is the reason why we have almost no data with M06-HF but is also manifested with M06-2X, M11 and BMK, the ones we have checked for the barrier calculations). The values of barriers computed from purely electronic energies are similar between CAM-B3LYP and M06-2X, and more consistent with M06-2X when Gibbs energies are used. Hence, we have chosen M06-2X values for barriers, while the potential energy scan around the dihedral mentioned was still performed with CAM-B3LYP due to its better computational stability and because the examples in the literature show that range-separated hybrid functionals also do perform fairly for barriers.32,33,35
In addition to geometry parameters, the quality of electronic transition solvatochromism was checked for the same functionals (in the state-specific (relaxed-density) time-dependent DFT approximation), and CAM-B3LYP showed overall the best results for the combined task when compared to the experiment and some reference calculations with SAC-CI/6-31G(d′)//CAM-B3LYP/6-311G(d,p). This is illustrated in Fig. S1 and S2 in the ESI† (see also the captions of these two figures). Literature analysis also has shown that this functional is one of the best for optical transitions.29,53 Therefore, we chose to perform further calculations (LR-TD-DFT electronic spectrum and CPKS polarizabilities) at the CAM-B3LYP/6-311G(d,p)//CAM-B3LYP/6-311G(d,p) level. SAS cavity was also chosen for full and partial optimization studies, and non-electrostatic terms of dispersion, Pauli repulsion and cavity formation (nelst) were included into the model. The SAC-CI54 (see ESI† for the extended reference list) calculations were performed with full orbital window and with LevelTwo accuracy level. A relatively small basis set 6-31G(d′)55,56 from Petersson et al. was used. CBS methods for these were dictated by limited computational resources available. The CAM-B3LYP/6-311G(d,p) geometry was utilized for SAC-CI calculations to avoid high computational burden and because the effect of geometry on the shape of the predicted spectra was confirmed to be much less important than that of the functional chosen for the TD-DFT procedure.
A study considering the effect of changing dihedral C14–C5–C6–C7 was carried out as a set of partial optimizations with the dihedral mentioned frozen. For these partially optimized structures, spectra and polarizabilities were calculated. Polarizabilities calculated with 6-311G(d,p) and with 6-311+G(d,p) are almost perfectly correlated (slope 0.95, R2 = 0.999 for ACN) save the region of 89°–100°, so we chose to use the same basis for all the DFT calculations. The functional used for hyperpolarizability computations is also CAM-B3LYP, as is frequently suggested in the literature.57,58
Atomic charges were computed using the atomic polar tensor (APT) model,59 as well as the Merz–Singh–Kollman scheme.26,27 Natural transition orbital (NTO)60 difference plots were obtained using the cubegen utility of Gaussian 09 and Gabedit.61 Avogadro62 was also used for visualization.
Footnote |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/c7cp06333d |
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