Classical Approaches for the Modeling of Solvation

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Polarizable QM/Classical Approaches for the Modeling of Solvation Effects on UV-Vis and Ffluorescence Spectra: an Integrated Strategy Daniele Loco, Natalia Gelfand, Sandro Jurinovich, Stefano Protti, Alberto Mezzetti, and Benedetta Mennucci J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b10463 • Publication Date (Web): 13 Dec 2017 Downloaded from http://pubs.acs.org on December 13, 2017

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The Journal of Physical Chemistry

Polarizable QM/Classical Approaches for the Modeling of Solvation Effects on UV-Vis and Ffluorescence Spectra: an Integrated Strategy Daniele Loco,† Natalia Gelfand,‡ Sandro Jurinovich,† Stefano Protti,¶ Alberto Mezzetti,§ and Benedetta Mennucci∗,† †Department of Chemistry, University of Pisa, via G. Moruzzi 13, 56124, Pisa, Italy ‡School of Natural Sciences, Far Eastern Federal University, ul. Sukhanova 8, Vladivostok 690950, Russia ¶PhotoGreen Lab, Department of Chemistry, University of Pavia, V.le Taramelli 12, 27100, Pavia, Italy §Laboratoire de Réactivité de Surface, UMR CNRS 7197, UPMC Univ Paris 06, Sorbonne Universités, 4 Place Jussieu, F-75252, Paris, France E-mail: [email protected]

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Abstract Hybrid methods combining quantum chemistry and classical models are largely used to describe solvent effects in absorption and emission processes of solvated chromophores. Here we compare three different formulations of these hybrid approaches, either using a continuum, an atomistic or a mixed description of the solvent. In all cases mutual polarization effects between the quantum and the classical subsystems are taken into account. As a molecular probe, the 3-hydroxyflavone has been selected due to its rich photophysics which involves different tautomeric and anionic forms. We show that a clear assignment of the measured spectroscopic signals to each specific form can be achieved by combining the different solvation models into an integrated and cost-effective strategy. Previously proposed mechanisms for the excited-state proton transfer (ESIPT), specific solvent perturbation effects on ESIPT, and solvent-assisted anion formation are also validated in terms of short and long range solvation effects.

1

Introduction

examples in this direction have been presented so far in the literature, applying a variety of approaches, such as fluctuating charges, 9,10 Drude oscillators 11,12 or induced dipoles 13–23 . In the years, QM/classical approaches have been extended to excited state calculations especially in combination with the Time Dependent Density Functional Theory (TDDFT) due to its computational effectiveness. Within this framework, continuum models have shown to be extremely successful strategies as they generally give a good estimation of solvation effects at a computational cost which is very similar to that required for the isolated system. This effectiveness is mainly due to the fact that a statistical sampling of the solvent is not required as implicitly included through the macroscopic properties used to describe the solvent response. On the contrary, when an atomistic picture of the solvent is used, the sampling has to be explicitly included with a simultaneous increase in the computational cost and a decrease of the easiness of the computational strategy. This is even more delicate when an emission process has to be simulated. In that case, in fact, the common sequential strategy which combines classical molecular dynamics simulations for sampling the solvent and QM/MM calculations on different snapshots is not easy to apply. In any case, when either a continuum or an atomistic polarizable embedding is used, another specificity in addition to the sampling has to be properly considered. In the TDDFT formulation the whole spectrum of the excitations of interest is determined

The idea of combining a Quantum Mechanical (QM) description with a classical one is not new in the field of Molecular Science; the first examples date back to the end of the seventies and beginning of the eighties of the previous century. 1,2 Since then, many different research groups have made important contributions to the development and implementation of alternative formulations of these original ideas and nowadays many different flavors of hybrid QM/classical approaches are available 3–8 . In literature, they are commonly divided in two big families, namely those using an atomistic description of the classical part of the system, and those introducing a continuum dielectric approximation. Among the possible formulations of continuum models, in quantum chemistry the most popular one is the so-called “apparent surface charge” (ASC) approach where the response of the dielectric is expressed in terms of an induced charge distribution on the surface of the cavity which embeds the QM subsystem 7 . In the case of atomistic descriptions instead, a Molecular Mechanics (MM) Force Field (FF) is generally the selected formulation in combination with the electrostatic embedding. Within this framework, the QM calculation is performed in the presence of the FF atomic charges representing the atoms of the classical environment. In recent years, however, many efforts have been devoted to improve both the efficiency and the applicability of the socalled polarizable embedding QM/MM. Many


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in a single step calculation by solving for the poles of the proper response function. When the same problem is formulated within a polarizable embedding, an additional contribution has to be taken into account, namely the dynamic response of the polarizable environment. Such explicit response is calculated through the transition densities corresponding to the different excitations. This formulation of a classical but polarizable embedding within TDDFT (also known as “Linear Response” (LR) model) has been shown to properly describe the dynamic environment effect in excitations involving bright states characterized by a large transition dipole moment 24 . The same formulation, however, lacks the capability of describing the relaxation of the environment in response to the changes in the QM density upon excitation: it is therefore not suitable to model excitations involving large changes such as Charge–Transfer (CT) like excitations. To overcome this shortcoming, various models have been introduced to recover a state–specific (SS) description of the environment response both within a continuum 25–27 or an MM formulation. 20,23 Due to the different physical nature of the interactions described by the LR and SS models, their combination has been proposed to achieve a more complete description of environment effects on electronic excitation processes of solvated (or more in general embedded) systems. 28–30 This combined approach is also used here both in its continuum and atomistic formulation to investigate absorption and emission properties of 3-hydroxyflavone (3HF), a synthetic compound belonging to the class of flavonols. Since the seminal work of Sengupta and Kasha in 1979, 31 the photophysical properties of 3HF have attracted the attention of several research groups. In particular, 3HF has been largely studied as a model compound in the investigation of Excited State Intramolecular Proton Transfer processes (ESIPT) 32–34 . The intramolecular hydrogen bond between the 3hydroxyl (3OH) group and the C=O carbonyl moiety in 3HF is considered to play a key role in proton-transfer occurring from the excited state of 3HF (N*), to form the excited tautomer (T*,

scheme Fig. 1). Whereas emission at ca. 520540 nm from T* is observed in apolar solvents, a dual emission, with a fluorescence band around 400 nm (from N*) in addition to the predominant tautomeric band at longer wavelengths (from T*), is observed in polar and H-bonding solvents. Such peculiar photophysics has been tentatively explained by two types of solute/solvent interactions, namely specific hydrogen-bonding interactions 36 and longer range solvent polarization interactions 37 . In the former case, solute-solvent hydrogen-bonding interactions causes a perturbation (and in some cases, the disruption) of the intramolecular C=O–H-O hydrogen bond across which proton transfer occurs, thus changing the reaction dynamics and leading to both emissions. 38,39 Furthermore, the molecular environment can also induce partial ground-state deprotonation of 3HF to give the corresponding anion whose absorption and emission properties are completely different from those of neutral 3HF. 35,40–43 This richness of forms and species leads, as predictable, to an extremely high sensitivity of the photophysical properties of 3HF and its analogues to the physical and chemical properties of the surrounding (micro)environment. Despite the experimental efforts and the theoretical analyses presented so far, 42,44–47 a complete rationalisation of such solvent tuning is still not available. Here, by comparing and integrating solvation models of increasing complexity, we identify a cost-effective computational strategy able to assign all the main spectral signals of 3HF to the different tautomeric and anionic species and to explain their spectral position in terms of the specific nature of the solvent such as its polarity and the hydrogen-bonding and proton-transfer capacities.

2 2.1

Computational details QM calculations

To elucidate the effect of the solvent on the electronic transitions of 3HF, we applied three different QM/Classical approaches: (i) a fully


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(a) O

H O

+

O

O

-

OH

O

O

O

A

OH

N

(c) N* T*

-

+

T

Absorbance

(b)

Energy

3HF @ DMSO 3HF @ CHCl3

0.8

0.6

0.4

0.2 0

(d)

N

3

3.5

4

4.5

120 100

T

I (a.u.)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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80 60 40 20 0 2

2.4

2.8

3.2

Energy (eV)

{R}

Figure 1: (a) Tautomeric equilibrium between normal (N) and tautomeric (T) forms of the 3HF, and formation of its anionic (A) form.(b) Graphical representation of the photophysics of 3HF: in the GS the N form is more stable than the T one; after excitation, the N* form undergoes a fast excited state proton transfer giving the stable T* form. Experimental absorption (c) and emission (d) spectra of 4.2×10−2 M solutions of 3HF in DMSO and chloroform. 35 continuum description of the solvent by means of the polarizable continuum model (PCM) 7 in its integral equation formalism (IEF) version, 48,49 (ii) a completely atomistic approach using a polarizable MM embedding, and (iii) an intermediate approach where the solute and one solvent molecule (i.e. a minimal environment) are treated at QM level while the rest of the solvent is treated at continuum level (QM(ME)/PCM). As it regards the polarizable embedding QM/MM, the AMOEBA 50 formulation of the induced dipole model has been used in the implementation recently done by some of the authors. 23 We will refer to this approach as QM/AMOEBA. Two solvents were considered, namely, dimethyl sulfoxide (DMSO, = 46.70) and chloroform ( = 4.71). All the geometry optimizations were performed in the presence of the solvent modeled by means of PCM. The ground state (GS) optimizations were performed at B3LYP/6–31G(d,p) level of theory whereas for the ES, geometry optimizations were performed at TDB3LYP/6–31G(d,p) within an equilib-

rium approach for the continuum solvent. Excitation and emission energies were calculated using a TDDFT approach and two different functionals, namely B3LYP 51 and CAM– B3LYP, 52 with both the 6–31G(d,p) and 6– 31+G(d,p) basis sets. As the best agreement with the experimental results was found with the B3LYP/6–31+G(d,p) level of theory, only this set of data will be presented and discussed in the main text while the results obtained with the other functional and basis set are reported in the Supporting Info. For all the QM calculations we used a locally modified version of Gaussian16 53 .

2.2

Classical MD

Classical Molecular Dynamics (MD) simulations were performed on the N form of 3HF in DMSO by means of the AMBER suite 54 . The force field for the DMSO solvent, not available in the standard package, was taken from literature 55 . For the 3HF molecule the General Amber Force Field (GAFF) 56


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was employed, but improving some dihedral parameter through a fitting on a QM reference (see Supporting Info). The atomic charges were obtained from a RESP 57 approach using the HF/6-31G(d) level, performed on the B3LYP/6-31G(d)/PCM(DMSO) optimized geometry. The system was prepared by placing the solute in the centre of a 64˚ A x 59˚ A x 57˚ A box containing 1781 solvent molecules of DMSO. A minimization of the solvent molecules, with the 3HF geometry kept frozen, was initially run followed by a heating step from 50 K to 300 K in a short run of 100 ps, with an integration time step of δt = 2 fs with the SHAKE algorithm to constrain hydrogen atoms. After these two steps the system was equilibrated for additional 100 ps in the NPT ensemble at 300 K, controlled with a Langevin thermostat, in order to equilibrate the density of the solution. The production run was started from this point for a total simulation time of 20 ns, saving the coordinates from the trajectory every 4 ps. The first 10 ns has been discarded, considered as part of the equilibration of the system, keeping the last 10 ns for the production. In order to investigate the effect of the solvent on the fluorescence of the anionic form of 3HF, we applied the same strategy on a frozen anion in the geometry optimized at TD-B3LYP/631G(d,p) level in DMSO, described at PCM level. We kept the same Lennard–Jones parameters used for the GS simulation while we recalculated RESP charges for the excited state of interest, to describe in a satisfactory way the electrostatic interaction with the solvent.

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nm. In literature, this was assigned to the anionic (A) form of 3HF produced by solventinduced ground state deprotonation of the 3OH group. A study using a more concentrated solution of 3HF in DMSO has also revealed that this band is formed by two bands, one peaked at 428 nm (weak) and another centered at ca. 485 nm (very weak). The interpretation of these two bands has been given in terms of a “free” anionic 3HF− and a complex formed by the anion and a protonated DMSO molecule, 3HF− · · · DMSOH+ . 42 To validate this interpretation, we have calculated the two lowest excitations for the N form and the lowest one for the T and A forms. In Fig. 2 we report the molecular orbitals (MO) involved in each of the investigated excitation. For all the three forms, the lowest transition is a HOMO–LUMO ππ ∗ transition, whereas the second one for the N form is an HOMO-1– LUMO transition, also with a ππ ∗ character, partially mixed with a charge transfer to the hydroxyl group.

Results and Discussions

Figure 2: Representation of the MOs involved in the bright transitions for the three 3HF forms: a) the lowest HOMO – LUMO and the second HOMO-1 – LUMO transitions for the N form; b) HOMO – LUMO of the T form; c) HOMO – LUMO of the A form. The MOs are computed in DMSO at B3LYP/6–31+G(d,p).

As discussed in the Introduction, 3HF can exist in two tautomeric forms (N and T) due to an intramolecular proton transfer. From the analysis of the experimental absorption spectrum, two bright excitations at ca. 300 and 350 nm are observed in both solvents: in the literature they have been attributed to the N form. 42 Only in DMSO an additional red-shifted much weaker and broader band is present at λ >390

In Table 1 we compare the calculated excitation energies for the selected transitions of the three forms in the two different solvents, with


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the experimental data from the literature. 35,42 As said, the signal due to the anionic form is observed only in DMSO, and it is formed by two components at 485 and 428 nm, suggested to be due to the “free” anion and the complex of the anion with a protonated DMSO solvent molecule, respectively. In order to achieve a cost-effective approach, we first apply the fastest solvation model, namely the continuum one. From such QM/PCM results, we see that the two lowest excitations of the N form are in very good agreement with the intense peaks experimentally observed in both solvents. Instead the excitation energy of the T form is calculated to be at much lower energy and quite close to the one calculated for the “free” anion. Both values are within the experimental range measured for the weak additional band observed in DMSO. In order to have a more detailed analysis of the solvent effect, for the N form we have also applied the QM(ME)/PCM scheme, where an hydrogen-bonded DMSO molecule is introduced in the QM subsystem (see Fig. 3). From the QM(ME)/PCM optimization, we found two very close minima, differing mainly for the orientation of the QM DMSO molecule. Such a structural difference, however, does not have any relevant effect on the absorption properties and here we report only the value for one of the two structures (the results obtained for the the other structure are reported in the Supporting Information). By comparing the energies corresponding to the two transitions in the QM/PCM and the QM(ME)/PCM we can immediately see that the effect of the DMSO molecule is small (about 0.08 eV for the lowest transition and almost negligible for the second). It has to be noted that the suggested structure where a proton has been transferred from 3HF to a DMSO molecule does not correspond to a minimum in the QM(ME)/PCM optimization: without artificially constraining the proton on the DMSO molecule, it always relaxes back on the 3HF hydroxyl oxygen. Specific solute-solvent interactions, possibly involving other DMSO molecules of the solvent cage, may favour the formation of proton transfer to the solvent but this kind of analysis is beyond

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the present investigation and it will deserve further study. N

N*

T*

A*

Figure 3: QM(ME)/PCM optimized structures for the different forms of 3HF in the ground and excited state; the OH and hydrogen–bonding lengths are reported in ˚ A. As a third level of analysis, we have extended the atomistic description to the whole solvent by introducing the atomistic QM/AMOEBA approach. A set of 250 snapshots extracted from the classical MD of the N form has been used in order to get the correct sampling (see Section 2.2). In Fig. 4 the QM/AMOEBA excitation energy distributions for the two bright transitions of the N form are reported, whereas their average values are shown in Table 1. To have a more complete appreciation of these results, we recall that the MD simulation has been performed by allowing both the solute and the solvent to move. This means that the energy distribution reported in Fig. 4 is due both to internal and external (i.e. fluctuations in the solvent electrostatic and polarization response) effects. The QM/AMOEBA average results are found to be extremely close to the QM/PCM for both transitions confirming that the good agreement found with the simple continuum description was not due to a fortuitous cancellation of errors.


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Table 1: Comparison between calculated and experimental (where available) absorption energies (in eV and in the corresponding wavelengths in nm) for the three forms of 3HF. QM/PCM and QM/ME/PCM correspond to a single calculation on the optimized geometry, while for QM/AMOEBA an average value on the snapshots extracted from the classical MD is reported. All calculations refer to TDB3LYP/6–31+G(d,p). Method

Solvent

QM/PCM

DMSO CHCl3

QM(ME)/PCM

DMSO

QM/AMOEBA

DMSO

N

T

3.54 4.07 3.53 4.10 3.46 4.11 3.53 4.11

(350) 2.71 (458) (304) – (351) 2.67 (465) (302) – (358) – (302) – (351) – (302) –

3.56 4.03 3.59 4.01

(348) (308) (345) (309)

A 2.64 (470) – – – – – – –

Experiment DMSO CHCl3

The same analysis used to investigate the absorption process, has been repeated for the emission of 3HF in the two solvents. Experimentally, in CHCl3 3HF shows fluorescence only from the T* form due to a complete proton transfer in the excited state. On the contrary, in DMSO, beside the T* emission band, the fluorescence from the N* form is also observed. This finding has been interpreted as a perturbing effect on the ESIPT reaction given by the formation of a hydrogen bond between the hydroxyl group of 3HF in the T form (the donor) and the oxygen of a DMSO molecule which acts as an acceptor. 35 In addition, contributions arising from A* fluorescence are also present in solvents that favor deprotonation of 3HF, such as DMSO. As a matter of fact, two experimental values have been measured for the A form and they have been assigned to the “free” anion, and to the complex formed by the anion and a protonated DMSO molecule, respectively. In Table 2 the experimental fluorescence energies are reported together with the calculated emission energies for the different solvation schemes.

– –

2.56 (484), 2.90 (427)

If we first analyse the QM/PCM results, we see that a very good agreement with the experiments is found for both the N* and T* form in DMSO. The calculations lead to two minima for both forms also in CHCl3 and their emission energies remain extremely close to the ones calculated in DMSO. An underestimation is found instead for the emission from the A* form. In the measured fluorescence spectra, however, two maxima have been identified which have been suggested to correspond to the free anion (2.34 eV) and the complex 3HF− · · · DMSOH+ (2.47 eV). To validate this assignment we have repeated the calculations using the QM(ME)PCM model where an hydrogen-bonded DMSO molecule is introduced in the QM subsystem and the geometry of the lowest excited state of the complex has been optimized. Three stable structures have been found corresponding to the N* and T* forms, respectively and to another species where the proton has been transferred from the 3-OH to the DMSO molecule (see Fig. 3). This configuration coincides with the previously suggested complex, 3HF− · · · DMSOH+ , and it presents an emission energy (2.58 eV), which is


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Table 2: Comparison between calculated and experimental emission energies (in eV and in the corresponding wavelengths in nm) for the three forms of 3HF. QM/PCM and QM(ME)PCM correspond to a single calculation on the optimized geometry, while for QM/AMOEBA an average value on the snapshots extracted from the MD is reported. All calculations refer to TDB3LYP/6–31+G(d,p). Method

Solvent

QM/PCM

DMSO CHCl3 DMSO DMSO

3.11 (399) 2.38 (521) 2.28 (544) 3.13 (396) 2.37 (523) – 2.99 (415) 2.34 (530) 2.58 (480)a – – 2.24 (553)

DMSO

3.10 (400) 2.32 (534)

QM(ME)/PCM QM/AMOEBA

N*

T*

A*

Experiment

CHCl3

–

2.38 (521)

2.34 (530)b 2.47 (502)b –

a: This value refers to an optimized structure where the − 3HF · · · DMSOH+ complex has been formed in the excited state. b: The two experimental values have been assigned to the “free” anion, and the complex formed by the anion and a protonated DMSO molecule, respectively.

significantly higher than the one found for the free A* form at QM/PCM. The emission of this additional species energy is in agreement with the experimental value of 2.47 eV, thus confirming the previous assignment. To further analyse the effect of the DMSO solvent on the anionic form, we have also calculated the emission energy of A* with the QM/AMOEBA approach. To achieve a correct statistical sampling, we performed TD– B3LYP/6–31G(d,p) calculations using the c– LR formulation of the QM/AMOEBA approach recently presented by some of the present authors 23 on 250 uncorrelated structures extracted from the MD simulation described in Section 2.2. The distribution of the calculated emission energies, are reported in Fig.5, whereas the average value is reported in Table 2. As it can be seen, the calculated distribution is centered on an average value which is very close to that calculated with a purely continuum model (QM/PCM). By comparing with the distribution obtained for the absorption energies, we also note that now the distribution is less broad: this can be explained by the fact

that in the MD used for the excited state, the geometry of the solute is kept frozen. The resulting fluctuations of the emission energies are thus only due to solvent. Combining all the results, we can conclude that a purely continuum model captures the effects of the main solute–solvent interactions of 3HF in DMSO (and CHCl3 ), giving overall a very satisfying picture for both absorption and emission processes. The explicit treatment of the solvent through QM/AMOEBA and its sampling over configurations from a classical MD does not significantly change the picture but it allows to recover the broadening missing in the continuum model. In particular, the agreement between the average QM/AMOEBA values and the QM/PCM results for the absorption suggests that, even if H-bond interactions are present between 3HF and DMSO, they do not significantly affect the investigated transition energies. Indeed, artificially emphasizing such interactions, introducing a single, strongly interacting solvent molecule in the QM description (QM(ME)/PCM), does not lead to any improvements and can lead to a less balanced description. However, the effects of


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The Journal of Physical Chemistry 45

40

(a)

40

35 30

30

Occurrences

Occurrences

35

25 20 15

25 20 15

10

10

5

5

0 3.1

3.2

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3.9

4

0 2.05 2.10 2.15 2.20 2.25 2.30 2.35 2.40 2.45 2.50 Emission Energies (eV)

4.1

(b)

35

Figure 5: Distribution of the emission energies of the A form of the 3HF in DMSO, computed along the MD in which the solute is kept frozen in its excited state geometry. A total of 250 structures extracted every 40 ps, have been used. The lines represent a gaussian fitting.

30 Occurrences

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

25 20 15 10 5

By comparing and integrating the results of the different descriptions of the solvent, a detailed interpretation of all the measured spectral signals in terms of the different anionic and tautomeric forms has been possible. In particular, the comparison between an implicit (through the continuum model) and an explicit description of the solvent molecules (either through a classical or a quantum approach) has allowed to clearly connect each signal to a specific form and explain their spectral position in terms of specific hydrogen bonding and polarity characteristics of the solvent. Intramolecular and solute-solvent excited state proton transfers have also been confirmed through the characterization of their specific spectral signatures. This study shows that solvent effects on the photophysics of molecular solutes can be accurately predicted by integrating different formulations of QM/classical approaches in a hierarchical way, namely starting from the simplest approach (here PCM) and scaling up towards more complete but also more expensive models when and where really needed. This effective strategy can open the way of their more massive use in the interpretation of experimental spectroscopic data, especially when site-specific fluorescent probes are used (see for instance Ref.[

0 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 Excitation Energies (eV)

Figure 4: Distribution of the excitation energies (eV) of the first (a) and second (b) bright state of the N form of 3HF, computed along the classical trajectory, extracting a configuration every 40 ps, for a total of 250 structures. The lines represent a gaussian fitting. such H-bonding interactions can change on the excited 3HF. This has been revealed by the QM(ME)/PCM model which has allowed us to assign the additional fluorescence signal observed in DMSO to a complex where a proton is transferred from the excited 3HF to the Hbonded DMSO molecule.

4

Summary

The solvent dependent photophysics of 3HF has been investigated by means of a hierarchy of QM/classical models going from a purely static and continuum approach up to a dynamic and fully atomistic description. In all cases, mutual polarization effects between the solute and the solvent have been included both in the ground and the excited states.


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41]). It can also help in the design of novel fluorescent probes with the desired sensitivity to the surrounding environment to be applied in several fields, ranging from biology to materials science.

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Effect in Biomolecular Systems. Chem. Rev. 2000, 100, 4187–4226. (7) Tomasi, J.; Mennucci, B.; Cammi, R. Quantum Mechanical Continuum Solvation Models. Chem. Rev. 2005, 105, 2999– 3094.

Supporting Information Available: Details about the refinement of dihedral angle MM parameters for 3HF force field; supplementary tables about absorption and emission results obtained by using different DFT functionals and basis sets; supplementary figure of QM(ME)/PCM optimized structures of 3HF in DMSO. This material is available free of charge via the Internet at http://pubs.acs.org/.

(8) Senn, H. M.; Thiel, W. QM/MM Methods for Biomolecular Systems. Angew. Chem. Int. Ed. 2009, 48, 1198–1229. (9) Bryce, R. A.; Buesnel, R.; Hillier, I. H.; Burton, N. A. A solvation model using a hybrid quantum mechanical/molecular mechanical potential with fluctuating solvent charges. Chem. Phys. Lett. 1997, 279, 367 – 371.

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(2) Miertuˇs, S.; Scrocco, E.; Tomasi, J. Electrostatic interaction of a solute with a continuum. A direct utilizaion of Ab initio molecular potentials for the prevision of solvent effects. Chem. Phys. 1981, 55, 117–129.

(11) Lamoureux, G.; MacKerell, A. D. J.; Roux, B. A simple polarizable model of water based on classical Drude oscillators. J. Chem. Phys. 2003, 119, 5185–5197. (12) Boulanger, E.; Thiel, W. Solvent Boundary Potentials for Hybrid QM/MM Computations Using Classical Drude Oscillators: A Fully Polarizable Model. J. Chem. Theory Comput. 2012, 8, 4527–4538.

(3) Tomasi, J.; Persico, M. Molecular Interactions in Solution: An Overview of Methods Based on Continuous Distributions of the Solvent. Chem. Rev. 1994, 94, 2027– 2094.

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Classical Approaches for the Modeling of Solvation

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