ARTICLE pubs.acs.org/JPCA
Ab Initio Study of the Anomalous Solvatochromic Behavior of Large Betaines Jose Maximiano F. Pinheiro, Jr. and Celso P. de Melo* Departamento de Física, Universidade Federal de Pernambuco, 50.670-901 Recife PE, Brazil ABSTRACT: The structure and spectroscopic properties of a diluted compound can be deeply affected by its interaction with the neighboring molecules of the solvent, and the associated solvatochromism is an effect that becomes more noticeable with the increase in both the dipole moment of the solute and the polarity of the medium. The correct description of the complex set of interactions that prevail in the solvation process remains a challenge for theoreticians not only when interpreting an observed behavior but also when considering the possible existence of novel properties in untested solute solvent systems. On the basis of an ab initio study, we examine here how the presence of solvents of different polarities should affect the electronic properties of a family of molecules, formally related to Betaine-30 (aka Reichardt’s dye), whose donor (D) and acceptor (A) groups are terminally connected to conjugated chains of different sizes. Because these molecules exhibit elevated ground-state dipole moment that should strongly interact with molecules of a polar solvent, a large hypsochromic shift is predicted for them. However, in a recent gas-phase study of these molecules, we have established the existence of an “inversion” in the spatial localization of their frontier orbitals when the size of the conjugated bridge connecting the D and A groups is progressively increased. This fact has led us to suggest that the increase in size of dissolved betaines should be accompanied by a large variation in their solvatochromic properties. In this work, we first use the self-consistent reaction field approach at the configuration interaction level to estimate the expected bathochromic shift in the absorption spectra (positive solvatochromism) in the largest members of the investigated betaine family when dissolved in different low polarity solvents and then discuss the conformational changes as a consequence of the solutesolvent interactions. We then use these results to interpret the observed solvatochromic properties of pushpull molecules of varying size and discuss the corresponding implications on their photochemical properties.
1. INTRODUCTION The exquisite sensitivity of enzymes1 and proteins2 to the surrounding environment can be taken as an iconic example of the importance of solventsolute interactions in controlling the occurrence of reactions in aqueous solutions. Also, “solvatochromism” is a well-known effect in which changes in the polarity of the medium can substantially affect the photophysical properties of betaines, merocyanines, and other dyes,3 leading to modifications in the shape, position, and intensity of the absorption spectra of these molecules. Suggestions of practical applications of this effect include the development of filters for specific wavelengths based on the tuning of the absorption of a given chromophore in an appropriate environment.4 In that regard, special interest has been devoted to the Betaine-30 or Reichardt’s dye (2,6-diphenil-4-(2,4,6-triphenil-N-pyridinium)phenolate), in which the intramolecular charge transfer from the phenolate to the pyridinium ring corresponds to a well-defined transition in a position very distinct from all others in the visible spectrum.5 Because of the zwitterionic nature of the Betaine-30 ground state,6 this S0 f S1 dominant π f π* electronic transition is very sensitive to the polarity of the medium. It has been suggested that the nonlinear solvent response of Betaine-30 would be a consequence of the reversal in the direction of the dipole moment r 2011 American Chemical Society
of the (first singlet) excited state (μe) relative to that of the fundamental configuration (μf).7 In any effect, because the molecular dipole is greatly reduced upon excitation, the frequency of the S0 f S1 transition increases in a remarkable manner with the polarity of the solvent in which the betaine is dispersed. This strong hypsochromism has led Reichardt to propose the ET(30) scale,6,8 an empirical ranking of the polarity of different solvents based on the comparison of their observed solvatochromic shift to that of Betaine-30. Reichardt’s dye belongs to the more general class of pushpull D-π-A molecules, in which an electron-donor group (D) is connected to an electron-acceptor group (A) through a π-conjugated bridge. The π-bridge-mediated interaction between the terminally substituted D and A groups can be strong enough to confer opposite net charges to them, leading to a zwitterionic nature of the molecule. It is worthwhile to note that the large variation of the molecular dipole in zwitterionic pushpull conjugated molecules upon absorption or emission of a photon has made this class of molecules subject of special Received: December 31, 2010 Revised: May 3, 2011 Published: June 16, 2011 7994
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The Journal of Physical Chemistry A interest for the development of nonlinear optical (NLO) devices.9,10 In fact, ionic and zwitterionic organic chromophores are considered to be an important class of materials for application in second-order NLO.11 However, whereas most π-conjugated organic molecules crystallize in centrosymmetric space groups (resulting in a vanishing second-order bulk susceptibility χ(2)), for the development of practical NLO devices, it is necessary to disperse the active molecules in a polymeric matrix or crystallize them in a noncentrosymmetric manner, chemical environments where their NLO response can be very different from that observed when in solution.12,13 Whereas a common approximation is to consider the S0 f S1 transition energy of these dyes equal to their HOMOLUMO energy gap, the agreement between predicted theoretical results for the electronic properties of these molecules when isolated in vacuum and those obtained from actual experiments in solution is generally rather poor.14 However, more recently several theoretical models have been proposed to describe in progressively better quantitative manner the microscopic mechanisms involved in the solutesolvent interactions.12,1522 For instance, Lipinski and Bartkowiak performed a detailed ab initio study of a series of D-π-A compounds and have verified by the discrete quantum-mechanical Langevin dipoles/Monte Carlo approach that the first- and second-order NLO coefficients of chromophores are very sensitive to the characteristics of the solvent, especially for the case of compounds where a large intramolecular charge transfer was observed.14,20 Continuum solvation models have also been successfully used to investigate the NLO properties of pushpull chromophores, with the corresponding results showing good agreement with available experimental data.23 Using time-dependent density functional theory (TD-DFT) methods coupled to the polarizable continuum model (PCM) approach, Ray has examined the influence of solvents upon the hyperpolarizabilities of merocyanine dyes and concluded that the NLO properties of these compounds could be optimized by a convenient choice of solvent.12 Considering isolated (i.e., gas-phase) molecules, we have recently shown24 that the electronic properties of certain betaine types of D-π-A compounds could be surprisingly altered when the length of the π-conjugated bridge that connects the D and A groups is progressively increased. Here in a more realistic framework we will examine how the solvatochromic shifts of these D-π-A compounds will be affected by the combined effects of change of solvent and increase in the length of the conjugated bridge.
2. REVERSE PHOTOINDUCED CHARGE TRANSFER IN LARGE BETAINES Existence of a Critical Length for Charge Transfer Inversion. In our previous study of the electronic structure of betaines,24 we did an extensive ab initio investigation of the D-(π)n-A molecules, where the number n of double bonds in the π-conjugated bridge connecting the donor (Dtimidazole) and acceptor (Atpyridine) groups was progressively increased. Our results have indicated the existence of a critical length ncrit (typically of the order of three double bonds) above which an interchange of the HOMO and LUMO spatial localizations would occur. Specifically, for the largest members of the family of betaines analyzed, the LUMO was preferentially localized in the donor moiety (imidazole plus neighboring region of the π-bridge), whereas the HOMO
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appeared as more localized in the acceptor part (pyridine plus neighboring region of the π-bridge) of the molecule. As a consequence, for these large betaines, a reverse photoinduced charge transfer was predicted, namely, that an electron flow would be favored from the acceptor to the donor regions of the molecule. We have shown that this unusual phenomenon is also manifested in the structural and electronic parameters of the system, in such a manner that at the critical n value both the bond-length alternation (BLA) parameter25 and the difference between the dipole moments of the (FranckCondon) first-excited state and the ground state (Δμ = μe μf) would change sign. Hence, we are justified in expecting that the reactivity and the spectroscopic properties of these D-(π)n-A compounds would have different characteristics accordingly to the value of n relative to ncrit. Effect of the Solvent Polarity upon the Critical Length for Charge Transfer Inversion. Within the assumption that the S0 f S1 transition energy corresponds to the HOMOLUMO energy gap, it is easy to understand that when the polarity of the solvent is increased, the absorption maximum of these D-(π)n-A betaines will be red [blue] shifted if the dipole moment of the first excited state is larger [smaller] than that of the ground state: when μf > μe for a given chromophore, then the corresponding optical gap (ΔEHOMOLUMO) will increase with the polarity of the solvent used, leading to a hypsochromic displacement of the absorption band. Naturally, a bathochromic behavior must be observed for the opposite situation, when μe > μf. Several experimental and theoretical studies have been devoted to examine how the electronic and NLO properties of pushpull D-π-A chromophores are affected by changes in the surrounding chemical environment. Note, however, that in the case of merocyanines, a rather puzzling solvatochromic behavior has been identified.26 For these compounds, a change in their absorption characteristics is observed with the use of different solvents; for instance, a negative solvatochromism (i.e., bathochromic shift) registered in the presence of polar solvents reverts to a positive solvatochromism (hypsochromic shift) when these molecules are dissolved in less polar solvents. Also, a similar reversion in the relative position of the absorption energies of isomeric vinylogous pyridone dyes with increasing solvent polarity27 has been observed. The existence of these three types of solvatochromisms (negative, positive, and inverted) in phenolate betaine dyes has led Domínguez and Rezende to propose recently28 a working model based on the gas-phase calculation of the chemical hardness of donor and acceptor fragments of these chromophores. We have previously used robust quantum chemical methods to confirm the existence of an anomalous variation on the spatial localization of the frontier orbitals of large conjugated betaines. It is now fit to examine how this unusual behavior would affect the solvatochromic properties of these compounds: hence, in the present work, we will present results from an ab initio investigation performed within the continuum model of solvation of the possible effects that different solvents could exert upon the electronic structure and absorption spectrum of a series of molecules related to Betaine-30. All molecules in the PBP family analyzed (Figure 1) have in common the presence of a negatively charged Phenolate group, a well-known electron donor, connected through conjugated (C2H2)n Bridges of increasing size to a positively charged Pyridine group, a standard electron acceptor. Consistent with our previous findings, we will show that the largest members of the PBP family are predicted to exhibit an “inverse solvatochromism” (i.e., bathochromism). The simplicity of 7995
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Figure 1. Phenolate pyridinic betaine (PBnP) family of molecules investigated in this work, where 0 e n e 10 is the number of double bonds in the conjugated bridge.
experimentally determining the presence of such effects for chromophores dissolved in solvents of increasing polarity suggests a direct and practical method of confirming the existence of an “inverse” photoinduced electron transfer (PIET) in large conjugated betaines of these type once they have been synthesized.
3. COMPUTATIONAL DETAILS We have used the Gaussian03 program29 to determine the spectroscopic and electronic properties of the 11 smallest members of the PBP family of compounds shown in Figure 1. The type of basis set to be adopted was chosen by taking into account both the fact that the molecules to be investigated are of varying sizes and the overall limits of computational resources available. In this manner, for each structure examined, the molecular wave function of the fundamental state was determined at the restricted HartreeFock (RHF) level by use of a double-ζ 6-31G basis set with one additional polarization function.3032 Solvent effects upon the RHF wave function, which are of fundamental importance to our study, were included via the self-consistent reaction field (SCRF) formalism;33 however, because of the fact that (especially for the larger members of the PBP family) the molecules tend to occupy a cylindrical cavity (Figure 2), we have adopted the PCM originally proposed by Tomasi.18,34,35 In this method, the 3D interface between the solute and the continuum medium representing the solvent (and which defines the solute cavity) is generated by a superposition of van der Waals spheres centered at atomic positions of the molecule of interest, such that the reaction field is obtained by placing point charges on the surface formed. Each of these spheres was drawn by taking the corresponding atomic radius as that of the united atom model for HartreeFock (UAHF), a choice recommended36 whenever the calculation of the solvation free energy is of interest. Within the PCM model, we formally describe the solute solvent system as consisting of a single molecule immersed in an infinite reservoir representing the solvent, which is approximated as a continuum medium of uniform dielectric constant: the reaction field.17 Following this approach, we have optimized the geometry of each one of the 11 molecules of the PBP family embedded in low polarity media, whose relevant chemical characteristics (e.g., density and solvent radius) correspond to those of five different solvents:29 cyclohexane (ε = 2.023), ether (ε = 4.335), chloroform (ε = 4.9), aniline (ε = 6.89), and tetrahydrofuran (ε = 7.58). This model implies that the detailed description of the solvent is omitted in favor of a very accurate (at a quantum level) description of the nonspecific interactions between solute and solvent. The influence of the solvent upon the wave function of the PBP molecules was implicitly included through the use of the PCM model within the configuration of interaction with single substitutions level of treatment (SCRF-PCM/CIS).37 For each
Figure 2. Surface accessible to the solvent molecules as calculated for n = 0 (a) and n = 8 (b) members of the PBP family.
solvent considered, the lowest energy molecular wave function of the different PBP molecules (corresponding to the ground state of the dissolved species) was used as an initial guess in a CIS calculation to determine the energies of the vertical electronic transitions (except for the ether case, for which convergence problems were experienced and only ground-state properties could be determined). In this simple procedure, we neglect relaxation effects in both solute and solvent molecules after excitation. The electronic and spectroscopic properties of interest were obtained by adopting the same basis set used during the optimization process, that is, 6-31G(d).30,31 In all SCRF-PCM/ CIS calculations performed for the 11 PBnP molecules of Figure 1 when in the presence of each one of the solvents examined, we have considered a total of 30 excited states to determine the corresponding electronic absorption spectrum. Afterward, by adopting Gaussians with an average width of 5500 cm1, we have used the program SWizard38,39 to calculate the SCRF-PCM UV/ visible spectra. An advantage of the SCR-PCM/CIS approach is that other observables related to the FranckCondon excited state (such as dipole moment and free energy) are well-described, provided that a sufficiently good basis is chosen to represent the ground state. Although this method produces results in good agreement with experiment for aprotic solvents,40 one should keep in mind the fact that a simple CIS calculation overestimates the electronic transition energies and tends to blue-shift the overall spectrum.41
4. RESULTS Localization of the Molecular Orbitals and Solvatochromism. Despite the fact that the molecular orbitals are not
univocally determined, it is possible to obtain relevant physical information and even predict the chemical reactivity of molecules on the basis of the analysis of the spatial localization of the HartreeFock canonical orbitals.42 Recently, we have verified that the frontier molecular orbitals HOMO and LUMO of members of a family of pyridinic betaines switch their spatial localization once the size of the conjugated backbone reaches a 7996
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upon the acceptor [donor] group and along part of the conjugated chain. The presence of polar solvent molecules in the immediate neighborhood would tend to stabilize even more the excited state of the PB8P molecule, and, hence, an “inverse” PIET is to be expected in this case. As a consequence, we see that when solvent effects are included via continuum solvation models, the existence of an anomalous charge transfer is predicted for the largest members of the PBP family, exactly as we have previously suggested to occur for these molecules in the gas phase. Furthermore, by examining how the use of solvents of increasing polarities would affect the spatial localization and the HOMO LUMO separation, one could attain a better understanding of the corresponding changes in the spectroscopic properties of dissolved PBnP molecules. First, we note that although it is visually possible to identify the general trend that the use of solvents of higher dielectric constant tends to increase the localization of the FMOs in opposite parts of the molecule, the corresponding degree of localization can be quantitatively assessed by introducing Γ matrices that represent the projections of the molecular electronic distribution in selected parts of the molecule.24 If we formally divide each PBP molecule into two equal sized fragments, one corresponding to the “extended donor” moiety (ED, phenolate ring plus half of the conjugated chain) and the other corresponding to the “extended acceptor” (EA, the remaining of the molecule), then we can compare the amount of localization in molecules of different sizes. For this, we write the molecular orbitals Ψi of a given PBP molecule (M) in the form M
Figure 3. -Solvent effects on the electronic contour maps of the HOMO and LUMO and respective RHF energy levels for n = 0 (a) and n = 8 (b) members of the PBP family.
critical limit.24 As a consequence, we have predicted that an anomalous intramolecular charge transfer would occur in the largest members of this family of compounds because a direct optical transition would involve transferring electronic density from the acceptor side to the donor side of the molecule. However, because the above results were obtained for molecules in the gas phase, it would be of utmost relevance to examine if the behavior predicted was robust enough to be observed in the more practical case of betaine molecules in solution. The confirmation that this is in fact the case can be seen by analyzing the data presented in Figure 3, where we show the changes that occur both in the energy levels and in the spatial localization of the HOMO and LUMO of the n = 1 and 8 members of the PBP family (PB1P and PB8P, respectively) as a result of the interaction with the different solvents. In the case of PB1P molecule (Figure 3a), for instance, one can see from the represented electronic isosurfaces that these frontier orbitals are spatially distributed along the molecule in the usual manner; that is, if we formally divide the molecule in two fragments of almost equal size, the HOMO [LUMO] will be more localized in the left [right] fragment, the one containing the donor [acceptor] group. In this manner, upon absorption of an incident photon by the PB1P molecule, the extra charge originally present in the donor (phenolate) is transferred in the normal direction toward the side where the acceptor (pyridine) is located. For the PB8P molecule (Figure 3b), the spatial localization of the HOMO and LUMO is already reversed, with the HOMO [LUMO] mainly concentrated
ED
EA
∑μ cμi χμð Br Þ ¼ ∑μ cμi χμ ð Br Þ þ ∑μ cμi χμð Br Þ
Ψi ð B rÞ ¼
ð1Þ
where χμ represents the corresponding atomic orbitals. Then, the degree of localization Γi of a given molecular orbital Ψi in each one of the two halves of the molecule can be defined as ΓED ¼ i
ED
ED EA
EA ED
∑μν cμi Sμν cνi þ 2 ð∑μ ∑ν cμi Sμνcνi þ ∑μ ∑ν cμi Sμνcνi Þ 1
ð2aÞ and
1 EA ED ¼ ð c Sμν cνi þ ΓEA i 2 μ ν μi
∑∑
ED EA
EA
∑μ ∑ν cμi Sμν cνi Þ þ ∑μν cμi Sμν cνi ð2bÞ
EA where S is the overlap matrix of the atomic orbitals and ΓED i þ Γi = 1.
As expected, for the PB1P molecule in the presence of hexane, EA the degree of localization ΓED HOMO [ΓLUMO], which is on the order of 70% [77%], increases to 77% [80%] when this molecule is dissolved in THF. As for the case of the PB8P molecule, a larger member of the PBP family for which the reversal of localization of the FMOs has already occurred, the corresponding figures are ED 94% [80%] for ΓEA HOMO [ΓLUMO] in presence of hexane and 93% [84%] in the case that THF is used as solvent. Hence, when the polarity of the solvent increases, the HOMO and LUMO wave functions become more localized (and further apart) along the molecule. However, it is well-established in the condensed matter literature that the probability of charge transfer between localized states in amorphous systems decreases exponentially with their separation43 (a result that, with some reserves, has been recently confirmed in the case of disordered polymers44). Then, we will take these facts as suggestive that a reduction in the 7997
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oscillator strength for the direct HOMO f LUMO transition must also be observed (with a consequent decrease in the intensity of the absorption band of the chromophores). This conclusion is in general agreement with what is observed for the UV/visible absorption band of dye betaines.45 Bathochromism of Larger Betaines. We now examine how the energy of the FMOs is affected by a change in the solvent used. Two different situations can then be identified, depending on whether or not the size of the conjugated bridge of the conjugated molecule considered is smaller than the critical length, the one for which the “inversion” in the spatial localization of the HOMO and LUMO occurs for the PBP family in the presence of the solvent considered. In fact, whereas for small members of this family of betaines the dipole moment of the ground state must be higher than the dipole moment of the excited state, the reverse is true for the larger molecules where the HOMOLUMO inversion has taken place. In this manner, we observe (Figure 3a) that for the PB1P molecule in the presence of polar solvents, whereas the HOMO is stabilized by the solventsolute interaction, the LUMO energy is slightly
Figure 4. Change of permanent dipole moment (Δμ = |μe| |μf|) as a function of n for the PBP molecules in different solvents.
increased: as a result, an increase of 0.44 eV in the HOMO LUMO gap of this molecule is predicted when the solvent used changes from cyclohexane (ε = 2.023) to tetrahydrofuran (ε = 7.58). This corresponds to the characteristic blue shift of the absorption spectrum commonly observed in zwitterionic systems.40,46,47 For the PB8P molecule, one can observe in the energy levels diagram shown in Figure 3b that the LUMO is the FMO stabilized by the progressive increment in the polarity of the solvent, whereas a small increase is observed in the HOMO energy; as a consequence, an unusual red shift resulting from a decrease of 0.13 eV in the HOMOLUMO gap is predicted for the larger betaines, under the same change of solvents as previously discussed. However, we note that because these calculations were performed at the HartreeFock level, which does not account for a good description of the virtual states, one should take the above results only as a good indication of the existence of the identified behavior rather than attach special relevance to the exact amount of the estimated spectroscopic shifts. Naturally, these results may be improved via inclusion of electron correlation effects by describing the wave function of the dissolved PBP molecules at the configuration interaction (CI) level, as we will discuss later, after we examine how solvents of different polarities will affect the charge distribution and the dipole moments of small and large members of the PBnP betaines. Dipole Moments and Structural Characteristics. We have calculated the dipole moments μf and μe of each one of the molecules of the PBP family in the presence of the chosen solvents. In Figure 4, we show the corresponding differences Δμ = |μe| |μf| for three of these solvents, where one can note that in a similar manner to what was observed in gas phase24 at a certain ncrit a discontinuity exists for Δμ, which changes sign because of the onset of an inverse PIET as the size of the conjugated bridge increases. However, the value of ncrit is bigger for the dissolved betaines than for the isolated molecules and increases with the polarity of the solvent. For a solvated betaine, a combination between the intramolecular interactions within the solute molecules and the polarization effect induced on them by the solvent must occur. In smaller betaines, both effects contribute to stabilize the charge separation characteristic of the ground state of these molecules. However, once the size of the conjugated bridge reaches its critical value, this stabilization will be larger for the first excited state, leading to a discontinuity in the behavior of Δμ as a
Table 1. Mulliken Net Charges (au) at the Oxygen and Nitrogen Atoms and Bond Length Alternation (BLA) Value of the 0 e n e 10 Members of the PBP Family As Calculated for RHF-Optimized Geometries in Three Different Solvents aniline n
QO (e)
QN (e)
c-hexane
chloroform BLA
QO (e)
QN (e)
BLA
QO (e)
QN (e)
BLA
0
0.831
0.622
0.789
0.619
0.723
0.698
1
0.807
0.609
0.085
0.757
0.598
0.078
0.698
0.579
0.042
2
0.809
0.612
0.075
0.757
0.601
0.066
0.680
0.571
0.010
3
0.816
0.620
0.081
0.764
0.608
0.069
0.655
0.560
0.026
4
0.827
0.627
0.091
0.779
0.617
0.082
0.629
0.545
0.064
5
0.836
0.631
0.100
0.792
0.624
0.094
0.618
0.538
0.084
6 7
0.674 0.668
0.544 0.538
0.081 0.092
0.650 0.641
0.554 0.545
0.085 0.094
0.612 0.610
0.535 0.533
0.094 0.100
8
0.666
0.535
0.098
0.631
0.535
0.100
0.608
0.532
0.104
9
0.665
0.534
0.102
0.630
0.534
0.103
0.607
0.532
0.106
10
0.664
0.533
0.105
0.629
0.534
0.106
0.606
0.531
0.108
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The Journal of Physical Chemistry A function of n, an effect that should be more pronounced for solvents of higher polarity. The higher level of interaction between the dipole moments of the solute and the molecules of more polar solvents would account for the dependence of ncrit with the polarity of the solvent considered. The analysis of the Mulliken charges in the heteroatoms of the donor and acceptor groups (oxygen and nitrogen, respectively) shown in Table 1 reinforces this interpretation: for the PBP molecules, whereas the charge in these atoms becomes more negative when the solvent used is of higher polarity, the difference between them initially increases with the size of the conjugated chain but experiences a sudden decrease at the point where the inversion of the HOMOLUMO spatial localization occurs and then approaches a limiting value for very large values of n. A convenient way to look at the changes in the electronic distribution induced by the solventsolute interactions is to examine how the bond length alternation (BLA) of the conjugated chain is affected by the polarity of the medium.48 BLA, which can be defined as the average difference between the length of double and single bonds,49 can be understood as a measure of the relative weight of the neutral and zwitterionic resonance forms, the two extreme resonant forms of the system.22,50 Adopting the convention that positive values of BLA correspond to zwitterionic ground-state structures, we see from the data shown in Table 1 that use of solvents of increasing polarity contributes to the stabilization of charge separation in the fundamental state, especially for small members of the PBP family, and that for a given solvent an increase in the size of the conjugated chain leads to a progressive decrease in the value of the BLA, which becomes negative for the largest molecules considered. Hence, for PBP molecules of increasing sizes, the electronic distribution of the molecular ground state evolves from an essentially zwitterionic (or cianine-type, for the cases of solvents of low polarity) limit to a neutral polyenic structure after the HOMOLUMO “inversion” has taken place. Note, however, that the critical size for which the BLA changes sign depends on the polarity of the solvent considered: whereas ncrit = 5 for aniline and chloroform cases, ncrit = 2 for cyclohexane. Naturally, the above results are in general agreement with the expected inversion in the solvatochromic behavior for large members of the PBP family of betaines. Also, the same trend must be observed for the variation in the dipole moment, Δμ. From the plot shown in Figure 4, one can see that a change in the sign of Δμ occurs for values of ncrit progressively higher as solvents of increasing polarity are used: note, for example, that ncrit goes from 3 to 5 when aniline is used instead of cyclohexane. One should note, however, that most of the small betaines already synthesized are not easily soluble in solvents of low polarity; this fact may explain why the reversal of the solvatochromic properties has been observed more as an exception than as a rule.26,27,51 Also, we can use the original ideas of Bayliss and McRae,52,53 who suggested that the influence of the solvent upon the electronic spectrum of organic molecules could be interpreted in terms of both the polarity of the solvent used and the relative difference between the dipole moments of the ground state and of the first excited state. Then, if we confine ourselves to low dielectric constant media, when using solvents of increasing polarity, the absorption spectrum of the PBP molecules will be affected in two different manners, accordingly to the case in which: (a) Δμ < 0, that is, for those molecules with n < ncrit, when the ground state has a more zwitterionic character than the
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Figure 5. SCRF-PCM/CI simulated absorption spectrum of the (a) n = 1(PB1P) and (b) n = 10(PB10P) members of the PBP family in the presence of three different solvents.
first FranckCondon excited state and, therefore, a progressive blue shift in the absorption spectra will be observed, configuring the well-known hypsochromism of betaines, and (b) Δμ > 0, that is, for those molecules with n > ncrit, when the first FranckCondon excited state is the one to exhibit a more zwitterionic character; for this case, we predict the appearance of a progressive red shift in the absorption spectra and that a bathochromic effect will be identified. (We point out that rather than a controversial behavior,26 this should be exactly the expected characteristic of large betaines in the presence of solvents of increasing polarity.) We now have a simple and generic interpretation of the anomalous solvatochromic of betaine molecules based on the idea that an inversion of the spatial localization of the highest occupied and lowest unoccupied molecular orbitals sets in for molecules possessing a large enough conjugated bridge. A more complete investigation of the absorption spectra of the PBP family of molecules will help in the understanding of this phenomenon. 7999
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Table 2. Estimated Changes in Intensity of the First Absorption Band Obtained by CIS Calculations of the Transition Dipole Moment and the Oscillator Strength for the 0 e n e 10 Members of the PBP Family aniline (ε = 6.89) N
chloroform (ε = 4.9)
c-hexane (ε = 2.02)
|μt|
f
|μt|
f
|μt|
f
0
1.892
0.376
1.953
0.357
3.458
0.980
1
4.049
1.386
4.261
1.415
4.729
1.580
2
4.916
1.906
5.155
1.910
5.789
2.132
3
5.594
2.381
5.876
2.357
6.665
2.628
4
6.080
2.815
6.332
2.728
7.070
2.985
5
6.481
3.248
6.626
3.075
7.248
3.248
6 7
7.549 7.500
3.347 3.408
7.532 7.572
3.483 3.622
7.375 7.470
3.454 3.607
8
7.468
3.433
7.604
3.712
7.538
3.714
9
7.442
3.439
7.627
3.769
7.585
3.788
10
7.423
3.437
7.642
3.805
7.618
3.838
Solvatochromic Shifts and Absorption Spectra. In Figure 5, we present the absorption spectrum of the n = 1(PB1P) and n = 10(PB10P) members of the PBP family calculated in the presence of three different solvents at the SCRF-PCM/CI level.37 As can be seen in Figure 5a, the calculation reproduces the intense hypsochromism of the S0 f S1 transition expected to occur in betaine molecules of small size, in which there is a large contribution of electron pushpull effects in the ground-state structure.54 The small variation in the dielectric constant of the medium when THF is used as solvent instead of cyclohexane causes a 79 nm blue shift in the main UV/visible absorption band of the PB1P molecule, a result in agreement with the fact that the corresponding Δμ is estimated to be negative in the range of the polarity of the solvents considered. Note, however, that the simulated spectra for the PB10P molecule (Figure 5b) exhibit a small red shift as solvents of higher polarity are considered, an observation again in agreement with the theoretical prediction that a bathochromic effect should now be observed. In Figure 5, one can also observe that for both molecules examined the increase in the polarity of the medium leads to a reduction in Φmax, the intensity of the maximum of the UV/ visible absorption band. In fact, as the data shown in Table 2 reveal, the following competing effects are present: (i) the intensity of the S0 f S1 transition is more affected by the change in n, that is, the size of the conjugated chain, than by variation of the polarity of the medium, and (ii) whereas the use of solvents of the increasing polarity leads to a decrease in Φmax, the S0 f S1 oscillator strength of PBP molecules of increasing size in the presence of a given solvent initially increases in a substantial manner and then approaches a limiting value for large enough conjugated bridges. (This result is naturally associated with the strong spatial localization of the HOMO and LUMO known to exist in large conjugated “pushpull” molecules,55 as discussed by Catalan and collaborators while analyzing the hyperchromic effect in large polyenes.5658) In Figure 6, we present a plot of the spectroscopic shifts (relative to the case of cyclohexane) δES0fS1 as a function of n, where the molecular geometries have been optimized for the corresponding solvents. For the case of both aniline and chloroform, the PBP molecules change from a hypsochromic to a bathochromic behavior in the 5 < n < 6 region, exactly the same
Figure 6. Calculated solvatochromic shifts relative to electronic transition S0S1 in chloroform and aniline as a function of n for the PBP molecules.
range of sizes for which the HOMOLUMO spatial localization inversion is predicted to occur. Possible Effects of Conformational Changes. So far, only the all-trans conformation of the each betaine molecule has been considered in this work. Upon photon absorption, a dissolved molecule should be excited in a “vertical” manner and only then reach a new equilibrium conformation in a process involving both structural relaxation and solvation dynamics;59 hence, it is important to investigate the coupling between the solvation process and the electronic reorganization in the solute molecule.60 It is known that even when a limited set of conformations is considered13,61 quantum chemical calculations of the problem correlate well with the experimental results.61,62 Theoretical studies for small betaines show that for their ground state in the gas phase, steric conflicts between ring hydrogens favor a twisted geometry for the central chromophore.59 The torsional dependence of the charge separation observed in the gas phase seems to be much weaker in the presence of polar solvents63 so that solvation rather than geometric changes may be relevant to the charge transfer process.60 In fact, it has been suggested that the reason for this would be the cancellation of the correlation energy effects and solvation free energy variation with changes in the torsion angle,63 as demonstrated by the time evolution of the spectra, which is suggestive of the dominance of electronic relaxation effects on the solvation time scale.59 Then, instead of considering torsional effects, we decided rather to perform a brief investigation on how the presence of multiple cis conforms along the conjugated bridge would affect our conclusions of a charge transfer inversion in longer betaines with respect to conformational change. The all-trans conformation corresponds to the single point of minimal energy in the phase space of all possible cis and trans planar conformations accessible to the molecule according to a Boltzman distribution at a given temperature. As an initial assessment of the effect of dihedral angle changes along the conjugated chain, we have considered the presence of one, two, and three cis bonds symmetrically disposed along the polyenic bridge of the n = 3 and 7 PBnP molecules. For all cis and trans conformers considered, the optimal geometries were determined by SCRF-PCM 8000
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Table 3. Influence of the cis Conformations on the Electronic Structure of the Solvated PB3P and PB7P Betainesa n=3
n=7
cyclohexane
cyclohexane
λmax (nm)
Δμ (D)
δEtot (kcal/mol)
λmax (nm)
Δμ (D)
δEtot (kcal/mol)
01-cis
529.10
5.889
2.67
478.56
6.3335
3.73
02-cis
498.97
3.938
7.92
463.83
3.4768
8.61
03-cis
506.34
5.164
11.82
470.76
4.104
12.36
Aniline
Aniline
λmax (nm)
Δμ (D)
δEtot (kcal/mol)
λmax (nm)
Δμ (D)
δEtot (kcal/mol)
01-cis 02-cis
420.63 438.40
15.284 12.780
16.07 23.29
500.01 475.67
6.453 4.25
14.61 19.49
03-cis
484.21
13.520
26.42
484.21
4.939
23.21
Calculated values of Δμ and (λmax(cyclohexane) λmax(aniline)) are consistent with the suggestion of the occurrence of an inversion in the HOMO and LUMO spatial localizations and consequent reversal in the direction of the photoinduced charge transfer. a
calculations using cyclohexane and aniline as solvents. The properties of the “vertical” excited states were also obtained by applying the SCRF-PCM/CIS method at the ground-state geometry. The corresponding results are shown in Table 3, where δEtot is the calculated difference in the total energy of a given conformer to that of the corresponding all-trans molecule. Regardless of the solvent used, the all-trans conformation is the most stable structure for the π-conjugated bridge. As one can observe from this exploratory calculation, in all cases, the n = 3 and 7 molecules do in fact exhibit an inversion in the value of Δμ so that we can conclude that even the presence of even multiple cis bonds along the conjugated bridge of PBP betaines does not seem to prevent the occurrence of an inversion in the HOMO and LUMO localizations and consequent reversal in the charge transfer.
5. SUMMARY AND CONCLUSIONS We have performed an ab initio investigation of the solvatochromic properties of D-(π)n-A oligomers of increasing size (molecules related to the Betaine-30 standard dye and here defined as the PBP family) in presence of a series of low polarity solvents. The solutesolvent interactions were described by the SCRF approximation within the scope of the PCM, and the different degrees of stabilization of the fundamental state and the first excited state were compared in each case. For all solvents examined, we have confirmed the occurrence of the inversion of the spatial localization of the frontier molecular orbitals (HOMO and LUMO) with the increase in n, as previously observed for large betaines in the gas phase. Although (as it could be expected) the specific value of ncrit where this inversion sets in depends on the polarity of the chosen solvent, we confirm that even when dissolved in different solvents the PBP molecules should exhibit a reversal in the direction of electron transfer, which for n > ncrit should occur from the acceptor moiety toward the donor side of the molecule. These results are consistent with previous conclusions inferred from the calculated charge distribution and dipole moments, where we have found not only that the difference between the ground state and first FranckCondon excited-state dipole moments, Δμ, evolves in a discontinuous manner from negative (for small n) to positive values beyond a certain critical size
(n > ncrit) but also that the value of ncrit is modulated by the value of the dielectric constant of the medium. Also, a short investigation of the possible effects of the presence of multiple cis bonds along the conjugated bridge has indicated that the inversion in charge transfer predicted to occur in larger PBnP molecules seems robust at least to conformational changes that retain the planar configuration of the molecule. This means that within certain limits it may be possible to control the direction of electron transfer in a given molecule by a fine-tuning of the chemical environment. In that regard, it is worthwhile to note that betaine-30 also presents thermosolvatochromism7 as a result of the increase in a solvent polarity due to the rise of its dielectric constant upon cooling to the freezing point.61 Naturally, it would be extremely desirable to dispose of several members of the PBP family or related similar betaines to effectively measure the existence of the predicted anomalous electron transfer because we have also shown that this phenomenon must be associated with a noticeable reversal from a hypsochromic to a bathochromic behavior. On that regard, the sparse experimental information so far available seems to confirm this hypothesis.26,27,51 Recent work done in our group seems to suggest that the HOMOLUMO inversion responsible for this peculiar behavior of betaine molecules of increasing size is a consequence of the progressive increase in the internal (molecular) electric field. Also, it would be worthwhile to investigate a possible relation between the reversal solvatochromic effect and the thermodynamic properties of the betaine molecules in solution through a detailed PCM study. The solvation free energy is the best parameter to this analysis because all thermodynamic quantities can be derived from the free energy. In preliminary calculations, we have verified that when n increases the solvation free energy varies in a manner similar to the behavior observed for the dipole moment (including the occurrence of a discontinuity for the same ncrit value). This is a result to be expected because electrostatic interactions must be dominant in the solvation process of zwitterionic molecules. A more detailed understanding of the corresponding thermodynamic processes involved could be reached through the analysis of the different contributions to the free energy. Eventually, the thermodynamic properties derived from continuum models should be contrasted/ combined with cluster models (e.g., QM/MM and Monte Carlo), which treat the solvent in atomic detail, to get a deep 8001
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The Journal of Physical Chemistry A insight into the effects of specific interactions on the optical properties of large betaines.64
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. Fax: 1-55-81-3271.0359.
’ ACKNOWLEDGMENT This work was partially supported by the Brazilian agencies FINEP, CAPES, and CNPq. J.M.F.P. would like to thank CAPES for a graduate fellowship. ’ REFERENCES (1) Ben-Naim, A. Biophys. Chem. 2002, 101, 309. (2) Ben-Naim, A. J. Chem. Phys. 2006, 125. (3) Wurthner, F.; Archetti, G.; Schmidt, R.; Kuball, H. G. Angew. Chem., Int. Ed. 2008, 47, 4529. (4) Patnaik, L. N.; Sahu, B. J. Solution Chem. 1994, 23, 1317. (5) Lobaugh, J.; Rossky, P. J. J. Phys. Chem. A 2000, 104, 899. (6) Reichardt, C. Chem. Rev. 1994, 94, 2319. (7) Zhao, X. H.; Burt, J. A.; Knorr, F. J.; McHale, J. L. J. Phys. Chem. A 2001, 105, 11110. (8) Reichardt, C. Solvents and Solvent Effect in Organic Chemistry; VCH: Weinheim, Germany, 1988. (9) Bredas, J.-L.; Beljonne, D.; Coropceanu, V.; Cornil, J. Chem. Rev. 2004, 104, 4971. (10) Bredas, J.-L.; Beljonne, D.; Coropceanu, V.; Cornil, J. Chem. Rev. 2004, 104, 4971. (11) Teshome, A.; Kay, A. J.; Woolhouse, A. D.; Clays, K.; Asselberghs, I.; Smith, G. J. Opt. Mater. 2009, 31, 575. (12) Ray, P. C. Chem. Phys. Lett. 2004, 395, 269. (13) Sitha, S.; Rao, J. L.; Bhanuprakash, K.; Choudary, B. M. J. Phys. Chem. A 2001, 105, 8727. (14) Lipinski, J.; Bartkowiak, W. Chem. Phys. 1999, 245, 263. (15) Mennucci, B.; Cammi, R. Continuum Solvation Models in Chemical Physics: From Theory to Applications; John Wiley & Sons: Hoboken, NJ, 2007. (16) Cramer, C. J.; Truhlar, D. G. Chem. Rev. 1999, 99, 2161. (17) Tomasi, J.; Mennucci, B.; Cammi, R. Chem. Rev. 2005, 105, 2999. (18) Tomasi, J.; Persico, M. Chem. Rev. 1994, 94, 2027. (19) Balakina, M. Y.; Nefediev, S. E. Int. J. Quantum Chem. 2006, 106, 2245. (20) Bartkowiak, W.; Misiaszek, T. Chem. Phys. 2000, 261, 353. (21) Bartkowiak, W.; Zalesny, R.; Niewodniczanski, W.; Leszczynski, J. J. Phys. Chem. A 2001, 105, 10702. (22) Cammi, R.; Mennucci, B.; Tomasi, J. J. Am. Chem. Soc. 1998, 120, 8834. (23) Aidas, K.; Mogelhoj, A.; Nilsson, E. J. K.; Johnson, M. S.; Mikkelsen, K. V.; Christiansen, O.; Soderhjelm, P.; Kongsted, J. J. Chem. Phys. 2008, 128. (24) Pinheiro Filho, J. M.; Peixoto, P. H. R.; de Melo, C. P. Chem. Phys. Lett. 2008, 463, 172. (25) Sheng, Y. H.; Jiang, Y. S.; Wang, X. C. J. Chem. Soc., Faraday Trans. 1998, 94, 47. (26) Dasilva, L.; Machado, C.; Rezende, M. C. J. Chem. Soc., Perkin Trans. 2 1995, 483. (27) Aliaga, C.; Galdames, J. S.; Rezende, M. C. J. Chem. Soc., Perkin Trans. 2 1997, 1055. (28) Dominguez, M.; Rezende, M. C. J. Phys. Org. Chem. 2010, 23, 156. (29) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson,
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