Solvatochromism in a Pyridinium Cyclopentadienylide: Insights from a

Article pubs.acs.org/JPCB

Solvatochromism in a Pyridinium Cyclopentadienylide: Insights from a Sequential Car−Parrinello QM/MM and TD-DFT/Semicontinuum Approach N. Arul Murugan* Division of Theoretical Chemistry and Biology, School of Biotechnology, Royal Institute of Technology, SE-10691, Stockholm, Sweden S Supporting Information *

ABSTRACT: Understanding the working mechanism and establishing structure−property relationships for optical probes is an essential step to develop design principles for novel molecular probes. Here we study optical properties of a small-sized dielectric probe, namely, 4-carbamido pyridinium cyclopentadienylide (CPYC) in benzene and in water solvents using a sequential approach. In particular, the structure modeling has been carried out using a Car−Parrinello hybrid QM/MM molecular dynamics approach, while the excitation energies were computed using time dependent density functional theory. To incorporate the solvent effect either a polarizable continuum model or a semicontinuum description was employed. The molecular dipole moment of CPYC in water is more than two times larger than in benzene solvent. The positive and negative charges tend to accumulate on pyridinium and cyclopentadienylide rings, respectively, with increasing solvent polarity. Significant solvent-induced geometrical changes have been reported in CPYC and this contributes to a significant red shift in spectra. Even though the absorption maxima for CPYC in benzene and water solvents were underestimated, the solvatochromic shift has been reproduced in good agreement with experiments. We also report that CPYC can be used as a two photon probe.

1. INTRODUCTION Many organic molecules with characteristic structure having electron donor, π, acceptor groups in conjugation are known to display a shift in their absorption and emission spectra with a change in the dielectric nature of their environment.1 The phenomenon is referred to as ”solvatochromism” when the spectral shift occurs due to change in solvent polarity and this has its origin in the relative stabilization of the ground and excited states of the solute molecules by the solvents.1−3 When the ground state of the molecule is more polar than the excited state, the ground state is stabilized to a larger extent in polar solvents leading to a blue shift in spectra, and these molecules are referred to as negative solvatochromic.1−3 In the case of positive solvatochromic molecules, the excited state is more polar and the relative stabilization of this state leads to a red shift in the observed spectra.1−3 As the measured absorption maximum can be used as a polarity indicator,4 these molecules can be potentially used to characterize the nature of the microenvironment in reverse micelles, nanotubes, zeolites, and protein binding sites,5−7 and so they are referred to as ”optical probes”.1−3 Thus, the information obtained about the dielectric nature of the microenvironments in proteins, fibrils, and other biostructures can be used for designing target-specific binder molecules and optimizing catalytic reactions. This also has diagnostic value in the case of so-called conformational diseases.8−11 The dielectric nature of the bioenvironment © 2014 American Chemical Society

depends on the conformational states (such as native, partially folded, and misfolded states) of proteins and so the optical probes can be used to identify the conformational nature of proteins. The properties of optical probes such as their size, binding affinity, and target-specificity in absorption or emission spectra tailor them for use in a particular probing application. For example, in identifying fibril formation, the optical probes should have affinity for these biostructures and should exhibit fibril-bound state specific absorption or emission properties when compared to fibril-free conditions.12 Sometimes the probes are too large in size, which limits them to use in studying the small binding sites in proteins. For example, the volume of the binding site in haloalkane dehalogenase protein13 which is involved in the hydrolysis of dichloromethane is only 23 Å3. Many optical probes such as nile red or Reichardt’s dye suffer due to their relatively larger molecular size.1−3 So, it would be useful to design smaller molecular probes with larger solvatochromic shift for the protein characterization applications. In this regard, theoretical modeling approaches can be advantageous and can be used cost-effectively. Received: November 4, 2013 Revised: June 3, 2014 Published: June 6, 2014 7358

dx.doi.org/10.1021/jp410854b | J. Phys. Chem. B 2014, 118, 7358−7366

The Journal of Physical Chemistry B

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long time scale processes, while the hybrid QM/MM technique can be limited to capturing the molecular processes happening on the time scale of a few tens of picoseconds. However, this approach has an advantageous feature that it is force-field free and can account for the environmentally induced geometrical changes in solutes and also the polarization of solute by the solvents, which cannot be captured by standard force-field molecular simulation techniques. In particular, for the optical probes, the solvent or environmentally driven structural modifications are reported to be quite substantial,25,26 and for the accurate modeling of properties accounting this would be very important. So, here we have used the hybrid QM/MM molecular dynamics for modeling the structure. In the case of property modeling too there are various approaches that differ in how they treat the interaction between solute−solvent subsystems. A few of these approaches can be listed as follows: (i) TD-DFT/polarizable continuum model (PCM);27,28 (ii) TD-DFT/semicontinuum model;29 (iii) hybrid QM/MM response approaches.30,31 The former one has limitations in accounting for site-specific hydrogen bonding interactions between the solute and polar solvents, and this can be overcome by using a semicontinuum model that also includes a few “influential” solvents in the QM region29 while the solvent effect from the remaining remote solvents can be incorporated from continuum description. There are also sophisticated approaches that account for various interactions between solute−solvent subsystems using an effective Hamiltonian, and these are referred to as hybrid QM/MM approaches.30,31 In this study, for property modeling we have used TD-DFT within polarizable continuum and semicontinuum models. Overall, for modeling the absorption spectra, we have used sequential Car−Parrinello and time dependent density functional theory (TD-DFT) approaches. First, Car−Parrinello hybrid QM/MM molecular dynamics simulations32,33 were carried out for CPYC in benzene and in water solvents. Then, the absorption spectra calculations for CPYC in water were carried out using TD-DFT with the Coulomb attenuated B3LYP (CAM-B3LYP) functional34,35 including the solvent molecules through polarizable continuum or semicontinuum approaches. In the case of benzene solvent, only a polarizable continuum model27,28 has been employed since this has been reported to be sufficient for a nonpolar solvent. The intramolecular structure, charge distribution, and molecular dipole moment of CPYC in polar, nonpolar solvents have been analyzed. The solute−solvent radial distribution functions for both CPYC−solvent systems have been computed. The contributions from solvent-induced geometrical changes and solvent effect to the excitation energies of CPYC have been analyzed. Finally, the two photon absorption (TPA) cross sections for CPYC probe in both solvents (described using a PCM model) are computed using quadratic response TD-DFT and using a two state model to explore the possibility of this probe to be used as a two photon probe.16−18

In this article, we have studied a small sized molecular probe, 4-carbamido pyridinium cyclopentadienylide (will be referred as CPYC) in polar and nonpolar solvent environments. Refer to Figure 1 to see the molecular structure of CPYC. This molecule

Figure 1. Molecular structure of CPYC along with the numbering of atoms.

has been reported to be a probe for studying the dielectric nature of enzyme active sites.14 As we have mentioned the molecular size of CPYC is comparably smaller than other optical probes and so appears to be a promising probes to study such small active sites in enzymes. There are experimental reports on the absorption spectra of CPYC in different solvents.14,15 In a nonpolar solvent like benzene, the CPYC has an absorption maximum at 562 nm and it blue shifts to 518 nm in water solvent. Interestingly, going from water solvent to the binding site of horse-liver alcohol dehydrogenase protein, the absorption maximum shifts to 597 nm which reveals the hydrophobic nature of the active site.14 The CPYC is considered to be negative solvatochromic and it is suggested that the intramolecular-charge transfer absorption band is associated with the solvatochromic shift. The scope of the present work is to model the structure and optical property of CPYC in benzene and water solvents and to establish its working mechanism as optical probe. We also aim to investigate the contribution from solvent-induced geometry (indirect solvent effect) and the direct solvent effect on the excitation energy and to characterize the nature of the solvatochromic band. Finally, we study whether this optical probe can also be used as a two photon probe.16−18 Below, we quickly review the existing tools for modeling optical properties of molecules in solvents and explain the reasons for choosing sequential Car− Parrinello and time dependent density functional theory (TDDFT)/semicontinuum approach for studying the optical property of CPYC. Modeling the properties of molecules in solvents had been always challenging due to the necessity to include the small and large time scale processes and also the need to account for all important interactions such as electrostatic and polarization between the solute−solvent subsystems in the structure and property modeling. To overcome these difficulties associated with the wider time scale and length scale and in addition the need for treating explicitly electronic degrees of freedom of solute−subsystems in the property calculations, many sequential approaches have been proposed and used in the literature.19−24 Such an approach involves sequential modeling of structure and property of molecules in solvents.19−24 For modeling the structure, molecular dynamics, Monte Carlo, ab initio, or hybrid QM/MM molecular dynamics approaches are usually employed. The first two approaches when compared to the latter have the advantage that they can be used to model the

2. COMPUTATIONAL DETAILS We have carried out Car−Parrinello hybrid QM/MM (CPMD QM/MM) molecular dynamics32,33,36−38 calculation to model the structure of CPYC in benzene and water solvents. The affordable total time scale for such hybrid QM/MM molecular dynamics (MD) is a few tens to hundreds of picoseconds. So, we pre-equilibrate solute−solvent systems by employing a force-field MD. In the MD run, we have used B3LYP/6311+G(d,p) optimized molecular structure for CPYC in the 7359



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respective solvents (using Gaussian 09 software39) and GAFF force-field40 to describe the interaction with solvents. The charges for CPYC were obtained by fitting to molecular electrostatic potential using the CHELPG procedure as implemented in Gaussian 09.39 For water and benzene solvents, we have used TIP3P41 and GAFF40 force fields, respectively. The simulation for CPYC in water solvent included a single CPYC molecule and 9704 solvent molecules. The simulation box was orthorhombic with dimensions 66.0, 71.1, and 62.9 Å. In the case of CPYC in benzene, the simulation box dimensions were 62.4, 58.7, and 49.9 Å and included a single CPYC molecule along with 1128 benzene molecules as solvent. The MD simulations were carried out in an isothermal−isobaric (NPT) ensemble using Amber11 software.42 In the MD simulations the temperature and pressure are controlled by connecting the system to Nóse thermostat43 and Barendsen barostat44 with week-coupling scheme. The time step for the integration of equation of motion was kept as 1 fs. The total time scale for the MD runs was around 1 ns. Since the simulations are carried out in NPT ensemble, both the solute− solvent systems evolve to appropriate density independent of the initial box dimensions. The final equilibrated solute−solvent structure has been used as the initial configuration for the subsequent CPMD-QM/MM calculation. In this set of calculations the CPYC is treated at the density functional theory level, while the description of solvents is based on molecular mechanics force-field. The QM/MM implementation36−38 interface accounts for the interaction between the QM and MM subsystems which involves electrostatic, short-range repulsion and long-range dispersion interactions. This takes into account the polarization of the QM region due to the instantaneous electric field generated by the atomic charges of MM atoms. In our present calculations, for the description of QM region we have used the Becke, Lee, Yang, and Parr (BLYP) gradient corrected functional45,46 and the Troullier-Martins norm conserving pseudopotentials.47 The electronic wave function is expanded in a plane wave basis set and the number of plane waves is dictated by the energy cutoff which here is set to 80 Ry. We have used 5 au as the time step for the integration of the equation of motion and 600 amu as the fictitious electronic mass. The CPMD calculations are initiated with a quenching run carried out for the configuration from pre-equilibrated MD and subsequent scaling and Nóse runs were carried out to bring the system temperature to 300 K. In the Nóse run, the solute−solvent system samples the canonical ensemble. The total time scale for the production run is around 30 ps in the case of both CPYC−solvent systems. The absorption spectra for CPYC in water were computed for 70 configurations picked at equal intervals from the total CPMD-QM/MM trajectory. The absorption spectra calculations were carried out at the CAM-B3LYP34,35 level of theory using the TZVP basis set.48 We have shown in our earlier reports that such a combination of theory and basis set is the most suitable for modeling the optical property of solvatochromic molecules.24 For the trajectory of CPYC in water, four sets of absorption spectra calculations were carried out using Gaussian 0939 software; the first set of calculations were carried out for CPYC molecule and by treating the solvents using a polarizable continuum model.27,28 These results will be referred to as MM1. A second set of calculations were carried out for CPYC in water by treating solvents using a semicontinuum approach29 and the results obtained will be referred to as MM2. In this approach, the solvent molecules involved in hydrogen

bonding and charge transfer were treated using a discrete approach and are explicitly included in the QM region. The remaining solvents were treated using a polarizable continuum model. In particular, the solvent molecules up to the second solvation shell in the solute-all-atoms and solvent center of mass (g(rX‑COM)) radial distribution function (rdf) (see Figure 1sa of Supporting Information) are included explicitly. In this rdf, all the solvent molecules involved in the hydrogen bonding with the polar groups of CPYC appear below a distance, r = 2.9 Å. Refer to a shoulder appearing at this distance in Figure 1sa. It has been previously reported49,50 that for the property calculations the solvation shells based on g(rX‑COM) rdf are highly desirable and convenient when compared to those obtained from usual solute−solvent center of mass rdf. The number of solvent molecules in the first hydration shell of CPYC varies between 0 and 5 and the average number of solvent molecules is approximately 2 (see Figure 2sb of Supporting Information). The number of solvent molecules in the second solvation shell varies between 8 and 19 and the average number of solvent molecules in this shell is 14. We have included all the solvent molecules up to second solvation shell explicitly in the absorption spectra calculations. Figure 3s of Supporting Information shows a snapshot of CPYC and solvent molecules included up to second solvation shell for both solute−solvent systems. We have also investigated the effect of microsolvation of specific hydrogen bond donor and acceptor groups of CPYC (namely, NH2 and CO) in its optical property. In the excitation energy calculations only those solvent molecules that are involved in the microsolvation of these groups are explicitly treated while the remaining solvent effect is described using the continuum model. In particular, this set of calculations were performed for the two groups, namely, NH2 and CO of CPYC. These results will be referred to as N-MM2 and O-MM2, respectively. These four sets (MM1, N-MM2, O-MM2, MM2) of calculations provide insight into different contributions to the absorption spectra of CPYC in water. The MM1 results include the contributions from solvent-induced geometrical changes and from solvent effect included using a continuum approach. So, this does not account for the contributions from hydrogen bonding and intermolecular charge transfer effect which have been accounted for in the MM2 results. The N-MM2 and OMM2 results provide the contributions coming from the solvents involved in the microsolvation of hydrogen bond donor and acceptor groups. Overall, the MM2 calculations with a semicontinuum approach provide more accurate and realistic description of solvents, since we define the influential solvent molecules using the discrete approach (by explicitly including in the QM region) while the remaining solvents (which are not in immediate contact and direct interaction with solute) are treated using a continuum approach which is a sufficiently good approximation. Moreover, for CPYC in benzene the MM-1 set of calculations were carried out for 70 configurations extracted from the CPMD-QM/MM trajectory. Benzene, being a nonpolar solvent, is not involved in any hydrogen bonding interactions with solute, and so the continuum approach based calculations are sufficient to model the solvent effect on the optical properties. Moreover, the calculations with an explicit solvent model for CPYC in benzene will be computationally very demanding since there are as many as 20 benzene solvent molecules in the solvation shell (refer to Figure 2sa of the Supporting Information). On the contrary, water can be involved in hydrogen bonding with solute and the models 7360



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how the direct and indirect solvent effect contributes to the solvatochromic shift.1 As we have reported in the case of quinolinium betaine, these two effects oppose, and in this case the indirect solvent effect leads to a red-shift while the direct solvent effect leads to a blue shift. Ultimately, the relative contributions of these direct and indirect effects should dictate the solvatochromic nature. With this background on the molecular structure and solvatochromic shift, we will investigate the solvent-dielectric dependent structure of CPYC. The CPYC is reported to be negative solvatochromic14 and so it would be interesting to study its ground state structure and the solvent influence. Here, we have studied the average molecular structure of CPYC in solvents using average bond lengths of a few important bonds and the average twist angle between the two aromatic moieties. Figure 2 shows three

referred to as O-MM2, N-MM2, and MM2 in fact account for this. There are detailed studies in the literature49,51 that discuss the importance of explicit solvent models for the optical property calculations of polar solute molecules. Along with these various sets of calculations based on CPMD-QM/MM trajectory, as a reference excitation energy calculations for the optimized geometry of CPYC in respective solvents were carried out using PCM model and these results will be referred to as ”static” in the following discussion. In the PCM model to define the cavity of CPYC solute, UAHF based radii were used which are only defined for heavier atoms like C, N, and O. In fact, this value corresponds to zero temperature while the results from other sets correspond to finite temperature. The two photon absorption properties of CPYC were computed using the quadratic response time dependent density functional theory52 where the solvent effect is accounted through the polarizable continuum model.

3. RESULTS AND DISCUSSION 3.1. Solvent Dependence of Structure of CPYC. In general, the organic molecules with donor, π, acceptor groups in conjugation can be referred to as ”molecular chameleons”53 since they have a tendency to change their absorption spectra (or color) depending upon the nature of the environment.1,2,4 The change in color is due to the change in molecular and electronic structure by the environment and these media effects are generally discussed in terms of direct and indirect contributions.1,2 In particular, the latter arises from the solvent-induced geometrical changes in solute. The conjugated molecules with strong push−pull groups such as polymethine, merocyanine, and betaines have a larger tendency to change the ground state electronic structure depending upon the polarity of the solvents.1 Usually, in a nonpolar solvent environment they tend to have a neutral ground state, and this changes to zwitterionic ground state in a polar solvents.1 We need to have a polar solvent to stabilize the zwitterionic state of a molecule, and naturally, it appears that no negative solvatochromism should be observed for solvatochromic molecules in nonpolar solvents or in less polar solvents. In line with this hypothesis, many negative solvatochromic molecules tend to become positive solvatochromic in nonpolar solvents, and this phenomenon is referred to as “solvatochromic reversal”.54 However, when the solute molecular structure has an interlocked donor and acceptor group without a spacer group in between them, it seems to have a tendency to retain the charge separated form even in a nonpolar or gas phase environment and such molecules exhibit negative solvatochromic behavior independent of solvent polarity. The molecules such as ortho-betaine50,55 and Reichardt’s dye1 appear to belong to such a category. As discussed above there is a strong correlation between the ground state molecular structure and the solvatochromic behavior. In order to reproduce the solvatochromic shift correctly, we should be able to model the solvent-dependent molecular geometry in these solvatochromic molecules. The hybrid QM/MM modeling technique that we have used in fact can successfully account for the solvent-induced geometrical changes in solute. Second, the solute−solvent interactions also contribute to the solvatochromic shift which arises from relative stabilization of ground and excited states of solute due to ion−dipole and dipole−dipole interactions. When the excited state is stabilized relative to ground state there is red shift in the spectra, while the blue shift is observed when the reverse is true. It is also interesting to see

Figure 2. Dihedral angle distributions of CPYC in (a) benzene solvent and in (b) water solvent. The three dihedral angles were computed for the set of atoms, 1−2−6−7, 3−2−6−11, and 13−15−16−23.

different twist angle distributions for CPYC in water and benzene solvents. The three dihedral angles describe the relative orientation of two aromatic rings, and the orientation of CNH2 and CO groups relative to the pyridinium ring. Respectively, these three dihedral angles were computed for the set of atoms, 13−15−16−23, 3−2−6−11, and 1−2−6−7. For labeling of atoms, refer to Figure 1. The results show that the two aromatic moieties on average are in the same plane, even though the twist angle between these two aromatic moieties varies between ±70° suggesting that the instantaneous conformational geometry can also be twisted. The dihedral angle distribution for CNH2 and CO groups shows a bimodal distribution in water solvent, while in benzene it appears to be a unimodal distribution. This shows that the carbamide group conformation is twisted with respect to the pyridinium group in water solvent, while in benzene it is in the same plane as this aromatic ring. Such dramatic solvent-induced geometrical changes are also seen in betaines where the twist angle between the aromatic groups increases in polar solvent.50,55 The difference in the molecular dipole moment of these conformational states appears to be quite different and this has been the origin for such solvent-induced conformational changes. The dipole moment of a twisted conformation is relatively larger when compared to planar conformations and such conformers can be stabilized in polar solvents, so the population of such twisted molecular conformations increases in polar solvents. 7361



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and donor groups and so a larger polarizing ability of this solvent. 3.2. Absorption Spectra and Solvatochromic Shift of CPYC. The analysis of one photon absorption spectra for CPYC in solvents included the six lowest states. However, as we will see, only the first two excitations contribute to the solvatochromic band and were considered for the following detailed analysis. The results on vertical excitation energies56,57 for these two states are presented in Table 3. The first two

The average bond lengths for some of the bonds in the conjugation pathway are shown in Table 1. It shows signatures (the CO and CN bonds tend to have single and double bond characters) of neutral ⇒ zwitterionic transition when going from nonpolar to polar solvent. Table 1. Average Bond Lengths Average bond length, Å pair

in benzene

in water

O1−C2 C3−N3 C2−C6 N15−C16

1.24 1.39 1.49 1.39

1.26 1.35 1.50 1.41

Table 3. Average Excitation Energy (in nm) and Solvatochromic Shifta system Static MM1 N-MM2 O-MM2 Full-MM2 Expt14

In order to understand the solvent influence on the charge distribution we have computed group charges for amide, pyridinium, and cyclopentadiene groups and the results are shown in Table 2. The atomic charges used for this analysis are

Static BenzeneMM1-WaterMM1 BenzeneMM1-WaterMM2 BenzeneMM1-WaterO−MM2 BenzeneMM1-WaterMM2 Expt.

group charges, q/e group

in benzene

467 (0.01) 476 (0.20)

CPYC in water 468 493 491 510 469 518

(0.70) (0.48) (0.46) (0.42) (0.48)

437 448 445 467 421

(0.01) (0.14) (0.15) (0.23) (0.09)

solvatochromic shifts

Table 2. Average Group Charges and Molecular Dipole Moment

Amide −0.07 Pyridinium 0.33 Cyclopentadienyl −0.26 molecular dipole moment, Debye 3.98

CPYC in benzene 494 (0.80) 528 (0.53) 562

in water −0.11 0.63 −0.52

a

26 35 37 18 59 44

The numbers given in the parentheses refer to oscillator strength.

excitation energies for CPYC in benzene from static approach are 494 and 467 nm. The first excitation is the one associated with larger intensity and the second one is not very intense. For the water solvent, the predicted values of the static calculations are, respectively, 468 and 437 nm for these two excitations. The reason for analyzing only these excitations will be explained later. Due to the larger intensity associated with the first excitation, this can be compared to the experimental absorption maximum of CPYC in these solvents. The experimental absorption maximum for CPYC in benzene and water is, respectively, 562 and 518 nm, which yields a solvatochromic shift of 44 nm. When compared to this, the static approach predicted value of 26 nm is reasonably good. However, the absolute values of excitation energies for CPYC in benzene and water solvents are underestimated by 68 and 50 nm, which may partly be attributed to neglect of the difference in zero point energies of ground and excited states.56,57 For benzene solvent, the dynamic approach with a polarizable continuum model for solvent description yields values, respectively, 528 and 476 nm. The intensity of the first excitation decreases when compared to the static case, while the second excitation gains intensity. The dynamic approach for benzene solvent improves the computed excitation energy of CPYC toward the experimental value. The difference reduces to 34 from 68 by going from the static to the dynamic approach. We will now analyze how much contributions come from such explicit treatment of the solvents in the time dependent density functional theory calculations. The dynamic calculations at the MM1 level for CPYC in water solvent predict 493 and 448 nm for the lowest two excitations, which in fact is closer to the experimental value (for the first band). As seen in the case of benzene solvent, when compared to the static approach the second excitation gains intensity while the first one loses intensity. Now, we will discuss these results with explicit solvent models with solvents involved in

9.13

of the D-RESP38 type and are obtained from best fitting to the molecular electrostatic potential. As has been proposed,14 the positive charge is accumulated on the pyridinium ring and the negative charge is accumulated on the cyclopentadiene group. There is also a small negative charge on the amide group. We also see that the charges on pyridinium and cyclopentadiene groups increase 2-fold when going from benzene to water solvent. In addition, the computed molecular dipole moment is more than two times larger in water solvent when compared to benzene. The dipole moment distribution for CPYC has been calculated for various instantaneous configurations in these two solvents and the results are presented in Figure 3. The distribution curve has comparably larger width in water solvent, which is attributed to the presence of both electron accepting

Figure 3. Dipole moment distribution of CPYC in benzene and water solvents. 7362



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solvatochromic shift (which is 59 nm) for CPYC from benzene to water solvent is in good agreement with experiment, i.e., 44 nm. Given that the computed solvatochromic shift is 59 nm, the shift when going from benzene to water is 35 nm as predicted from PCM model and this amounts to more than 50% of the total solvatochromic shift. The remaining solvatochromic shift has to be attributed to the explicit inclusion of water solvent molecules and has to account for hydrogen bonding and charge transfer interaction between the probe and solvent molecules. The comparison between the static and MM-1 results shows the contributions due to finite temperature effect in the excitation energies which contributes as much as 36 and 25 nm for CPYC in benzene and water solvents, respectively. However, care should be taken that the geometries for these two sets are obtained from different functionals. To verify the convergence of the computed spectra, we have also plotted the instantaneous and N-point average of absorption wavelength for the first excitation against number of configurations. Refer to Figure 5. As can be seen, the N-point

the microsolvation of CO and NH2 groups and the whole CPYC molecule. The results are respectively presented as MM1, O-MM2, N-MM2, and Full-MM2 in Table 3. The solvents involved in the microsolvation of the NH2 group do not have substantial shift when compared to the no-explicit solvent model, i.e., the MM-1 model. On the contrary, the solvent molecules involved in microsolvation of the CO group have a substantial effect on the absorption spectra. When compared to the MM-1 model, the O-MM2 model yields 17 and 19 nm shifts in the excitation energies. Interestingly, a red shift in spectra is observed due to the explicit inclusion of solvent molecules involved in the microsolvation of the CO group while the CPYC molecule itself is negatively solvatochromic. However, explicit inclusion of whole microsolvation of CPYC yields a blue shift when compared to MM-1 results and the excitation energies are, respectively, 469 and 421 nm. The solvatochromic shifts due to MM1, N-MM2, O-MM2, and Full-MM2 models of water are, respectively, 35, 37, 18, and 59 nm when compared to the experimental value of 44 nm. Including the static model, all the models employed here reproduce the correct sign for the solvatochromic shift. The dynamic models except O-MM2 serve as better models when compared to static model in reproducing the shift. The absorption spectra for CPYC in water solvents as computed by convoluting the bands associated with six low energy excitations are shown in Figure 4. In particular, the full

Figure 5. Instantaneous and N-point average of excitation energy for CPYC in benzene and in water solvents.

average appears to converge beyond 30 configurations. Overall, the experimentally reported negative solvatochromic shift has been reproduced in excellent agreement with experiments.14 Interestingly, the solvents involved in microsolvation of the CO group yield a red shift in the spectra while the inclusion of all solvent molecules up to the second solvation shell brings the correct sign for the solvatochromic shift. We have also plotted the molecular orbitals involved in the two lowest energy excitations in Figure 6. The first excitation has HOMO → LUMO character while the second excitation has HOMO−1 → LUMO character. As can be seen the first excitation is π−π* type, since the electron density is distributed over both aromatic moieties along with some intramolecular charge transfer from amide group to dienyl cyclopentadiene group, while the second excitation has intramolecular charge transfer character involving the charge transfer from cyclopentadiene group to pyridinium and amide groups. By looking into the aforementioned molecular orbitals, we can get some insight into the red shift in the excitation energy when we use the O-MM2 model. As shown in Figure 6c, the LUMO orbital of CPYC has nonzero contribution due to C O group atoms and their contributions to HOMO and HOMO−1 molecular orbitals are less significant and so the microsolvation of this group will lead to red shift in the first and second bands of the absorption spectra. This is due to relative

Figure 4. Absorption spectra of CPYC in benzene and water solvents. The spectra are obtained by convoluting the six low energy excitation bands.

width at half-maximum for plotting the band associated with each excitation is computed from its standard deviation corresponding to that specific excitation. This procedure is explained in our earlier report.25 There appears to be a single band in the spectral range 400−600 nm which has contributions from the first two excitations. The deconvolution of the first band into two Gaussians corresponding to the first two excitations is shown in Figure 4S of the Supporting Information which explains the importance of analyzing the first two excitations. As can be seen the full spectra show two bands where only the low energy band is solvatochromic. In addition to the observed blue shift there is also a decrease in the intensity of this band when going from benzene to water. The second intense band appearing in the UV region also shows a decrease in intensity and displays a small red shift. Overall, the absolute value of λmax for CPYC in benzene and water solvents are underestimated approximately by 34 and 49 nm when compared to experimental values.14 However, the computed 7363



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Here α is the fine structure constant, a0 is the Bohr radius, c is the speed of the light, Γ is the width of the Lorentzian-shape absorption profile, and ω is the energy of the photon. The σGM is the two photon absorption cross section in GM units. δau which is two photon transition probability and is calculated from two photon transition tensor elements (for the case of linearly polarized light) through the following expression 2 2 2 2 2 2 δau = 6(Sxx + Syy + Szz ) + 8(Sxy + Sxz + Syz )

+ 4(SxxSyy + SxxSzz + SyySzz)

(2)

The two-photon transition moment tensor, Sab in the above expression (where a and b refer to x, y, and z components) is defined below: Sab =

⎡ ⟨0|μ ̂ |n⟩⟨n|μ ̂ |f ⟩ a b

∑⎢ n

stabilization of LUMO when compared to HOMO and HOMO−1 molecular orbitals, since these bands have HOMO → LUMO and HOMO−1 → LUMO type character. The results in Table 3 clearly explain this. When compared to MM-1 results on the absorption wavelength for the two low energy bands, the O-MM2 results show red shift which is due to the stabilization of CO group by microsolvation of solvents. 3.3. Is CPYC a Two Photon Probe? The results shown above clearly explain the mechanism for CPYC as an optical probe since the first intense band in the absorption spectra shows solvent polarity dependent behavior. The probe exhibits as much as −59 nm solvatochromic shift (i.e., blue shift) in the first band when going from benzene to water solvent. The wavelength range of the solvatochromic band is 400−600 nm. It would be interesting to further investigate whether this probe can also act as a two photon probe in addition to its potential use as an optical probe for dielectric nature of microenvironments in solvents and in protein cavities. In this case the simultaneous absorption of two photons in IR wavelength can be used to excite the molecule. The relatively smaller size of the probe is an advantageous feature since a potential probe should not introduce any structural/conformational changes within the target biostructure. There are no experimental reports on the two photon absorption spectra of the probe molecule and this has motivated us to investigate this aspect. So, we have computed the two photon absorption cross section for the optimized geometry of CPYC in two different solvents, namely, benzene and water (the solvents are described using a polarizable continuum model) using the following expression58 (2π )3 αa05ω 2 δau cπ Γ

⟨0|μb̂ |n⟩⟨n|μâ |f ⟩ ⎤ ⎥ ωn − ωf /2 ⎥⎦

(3)

In the response theory formulation, the two photon transition tensors are computed as the first residue of the quadratic response function, and so the cumbersome explicit summation over excited states of the molecules is avoided.52,58 In the calculation of σGM, we have used the usually chosen value for Γ (i.e., 0.1 eV).59 The computed TPA cross sections for CPYC in benzene and water solvent are, respectively, 47 and 61 GM (corresponding to the lowest energy excitation band which is the one associated with intense two photon absorption when compared to the remaining) which appears very promising for the molecule to be used as TPA probe. Interestingly, the two photon absorption cross section shows solvent dependent behavior and so the molecule is shown to have two photon solvatochromism60,61 (as reported in the case of DANS) along with its one photon solvatochromism. However, the current study is limited to only two solvents, and so general solvent dependent behavior in TPA cross section cannot be addressed here. In order to understand the responsible intrinsic parameter for such a solvent polarity dependent behavior in TPA we have computed the value using a two state model62 as shown in the following expression:

Figure 6. HOMO−1, HOMO, and LUMO molecular orbitals involved in the two lowest energy excitations of CPYC molecule.

σGM =

⎢⎣ ωn − ωf /2

+

δ 2SM =

01 16 |μ01|2 |Δμ|2 (1 + 2 cos2 θΔμμ ) 2 15 ω

(4)

Here, μ refers to the ground to excited state transition dipole moment, Δμ refers to difference in excited and ground state dipole moments, while θ is the angle between these two quantities, and ω refers to the excitation energy. The values for δau as computed from a two state model and from response theory are presented in Table 4, and as can be seen the values are in good agreement, suggesting that the two photon absorption process only involves the ground and first excited states. Almost a 2-fold increase in the δ2SM is seen for 01

Table 4. Two State Model Analysis Parametersa system

μ01

Δμ

θΔμμ01

ω

δ2SM × 10−3

CPYC in benzene CPYC in water

3.64 3.26

1.80 2.57

0.27 0.39

0.0915 0.0980

5.884 (3.374) 11.007 (11.044)

a

All numbers are reported in au. The numbers in the last column should be multiplied by 103. The calculations are performed for the geometries of CPYC in benzene and water solvents optimized using B3LYP functional. The numbers in parentheses refer to the values from response theory calculations.

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CPYC when going from benzene to water solvent. The major factor for such an increase is the difference in dipole moment between the ground and excited states. We can tune this parameter by altering the intramolecular charge transfer through substitution of strong electron withdrawing and donating groups in CPYC which can lead to changes in two photon absorption cross section. Eventually this study shows that CPYC can be used as a potential two photon probe with some chemical modification.

4. CONCLUSIONS We have used sequential Car−Parrinello and TD-DFT continuum/semicontinuum approaches to study the structure and absorption spectra of CPYC in nonpolar and polar solvents. The structure of CPYC seems to have substantial solvent dependence where there is preference for twisted conformations in a polar solvent. The dipole moment of CPYC in water increases more than 2-fold, when compared to its value in benzene solvent. Even though the absorption maximum is underestimated in both solvents, the solvatochromic shift obtained is in good agreement with experimental results. We have also shown that this probe can be used not only as an optical probe, but also as a two photon probe with some structural modification. The current study shows that the modeling of the optical (linear and nonlinear) properties of organic molecular probes in polar solvents can be carried out successfully using sequential Car−Parrinello and TD-DFT/ semicontinuum approaches.

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ASSOCIATED CONTENT

S Supporting Information *

The solute−solvent center of mass radial distribution function for both CPYC−solvent systems are shown in Figure 1S. The time evolution of solvent molecules in different solvation shell for CPYC in benzene and water solvents are shown Figure 2S. The representative snapshot configurations for CPYC and solvent molecules up to second solvation shell are shown in Figure 3S. The deconvolution of the first band of the absorption spectra into two Gaussians corresponding to two (lowest energy) excitations is shown in Figure 4S. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 0046855378418. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by a grant from the Swedish Infrastructure Committee (SNIC) for the project ”Multiphysics Modeling of Molecular Materials”, SNIC 023/07-18.

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REFERENCES

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Solvatochromism in a Pyridinium Cyclopentadienylide: Insights from a

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