Evaluating Charge Transfer in Epicocconone Analogues: Toward a

Article pubs.acs.org/JPCA

Evaluating Charge Transfer in Epicocconone Analogues: Toward a Targeted Design of Fluorophores Olga A. Syzgantseva, Vincent Tognetti,* Agathe Boulangé, Philippe A. Peixoto, Stéphane Leleu, Xavier Franck, and Laurent Joubert Normandy University, COBRA UMR 6014 & FR 3038, Université de Rouen, INSA Rouen, CNRS, 1 rue Tesniére 76821 Mont St Aignan, Cedex, France S Supporting Information *

ABSTRACT: Through-space charge transfers upon photon absorption in aminated epicocconone analogues, which serve as promising proteins markers, are investigated within time-dependent density functional theory using total densities differences and various point-charge models (with a special emphasis on Bader’s atoms-in-molecules theory). In particular, the distances and the amounts of charge transfer, as well as the transition dipole moments, are discussed from a methodological point of view, and their values are subsequently linked with the chemical structures of these efficient fluorophores. Finally, on the basis of these theoretical findings, several hints for the future improvement of the photochemical properties of these analogues are advanced.

1. INTRODUCTION Epicocconone is a water-soluble and cell-permeable natural protein marker,1,2 which, upon binding with primary aminogroups, becomes highly fluorescent, notably displaying a large Stokes’ shift (∼100 nm).3−5 Due to these properties, it finds large applications in protein identification and separation,6−9 and is commercialized as an efficient protein sensor.10,11 However, the necessity to improve its spectroscopic characteristics, while conserving its inherent advantages, has been stimulating the research on the design of analogue compounds for the last 10 years. Recently, the synthesis and the determination of the photochemical behaviors of two families of epicocconone derivatives, represented in Figure 1, were reported by our groups.12−15 The absorption and the fluorescence properties of these new compounds were notably shown to be dependent on the nature of the side-chains. Presumably, these substituents are expected to be responsible for the modulation of through-space charge transfers (CTs), which are among the most ubiquitous and fundamental processes occurring during photon absorption with wide applications in chemistry and material physics.16,17 We thus believe that owing to the considerable importance of such molecules in biochemistry and their potential use in protein stain,18−20 the rationalization of these effects, and more generally a thorough understanding of the relationships between the structure, the charge transfer, and the spectroscopic properties of these molecules, are essential for the future design of novel fluorescent compounds.21 From our viewpoint, it is appealing to tackle such a characterization from a theoretical perspective, and we aim to provide here a reliable methodology suitable to deal with the © 2014 American Chemical Society

following general issues: To what extent do the side functional groups affect the CT properties (1)? How does the protonation state influence the properties of analogues (2)? Although a complete investigation of these issues certainly goes beyond the scope of this present study, we will nevertheless try to provide useful hints and methods to answer these questions. To this aim, we will calculate and compare the CT characteristics for a series of epicocconone derivatives, in continuation of our previous paper.15 In particular, throughspace charge transfers upon electronic excitation will be evaluated applying the two methodologies recently proposed by Le Bahers22 and Jacquemin,23 whose use has been recently assessed for the characterization of organic dyes and push−pull molecules.24−30 However, from the best of our knowledge, no methodological study has been carried out to quantitatively evaluate such phenomena occurring in proteins markers. It can be particularly stressed that these tools enable one to go beyond the most widespread approach used to deal with electronic transition based on the qualitative (but nonquantitative) inspection of the shapes of the involved molecular orbitals. Then, with the help of these results, we will analyze the relationships between the structure of the fluorophores, their protonation state, and their CT characteristics, and trace their evolution throughout the series of the reported synthetic analogues. Finally, the analysis of these data will suggest some Received: October 21, 2013 Revised: January 3, 2014 Published: January 21, 2014 757

dx.doi.org/10.1021/jp410407u | J. Phys. Chem. A 2014, 118, 757−764

The Journal of Physical Chemistry A

Article

Figure 1. Chemical structures of aminated epicocconone analogues.

proposals for a future in silico design of novels compounds with predetermined spectroscopic features.

ρ

d±⃗ =

2. COMPUTATIONAL DETAILS 2.1. General Details on the Excited States Modeling. Consistently with our previous study,15 calculations were performed with the Gaussian09 program,31 using the CAMB3LYP32 range-separated hybrid functional, Pople’s 6-31+ +G(d,p) basis set, while solvent (acetonitrile) effects were included in an implicit way within the IEFPCM33 solvation model, without state specific solvation. The optimized ground state geometries, in the appropriate conformations, were taken from our previous study.15 Vertical excitations (corresponding to absorption) were described within time dependent density functional theory (TDDFT),34−36 taking into account the 20 lowest excited states. We refer the interested reader to ref 15 for more details about our calculation protocol. Density grids were generated using the cubegen standard utility using the default parameters, as done and validated in ref 22. All CT calculations based on the density approach were carried out using the program developed and distributed by Le Bahers and co-workers.37 The obtained results were compared with the ones obtained using the following atomic charge models: Mulliken,38 Merz−Kollman,39 ChelpG,40 Hirshfeld,41 and Bader,42−44 the last ones being computed with the AIMAll software using very fine basin integration procedure.45 These charges can be classified into wave function partitioning (Mulliken), electron density related (Hirshfeld, Bader), and electrostatic potential fitting (MK, CHelpG). All post-treatments involving PAC were done using a homemade program. We now review the theoretical background used to describe through-space CT. 2.2. The Full Density Treatment of Charge Transfers upon Photon Absorption. Photon absorption can be primarily characterized by the variation of the molecular dipole moment between the ground state (GS) and the considered excited state (ES): δμ ⃗ = μ ⃗

ES

− μ⃗

GS

∫ ρ± ( r ⃗) rd⃗ 3r ∫ ρ± ( r ⃗)d3r

(3)

so that the effective charge transfer vector is evaluated by (we note that other metrics devoted to CT for excited states have been proposed; see, for instance, refs 47 and 48) ρ

ρ

ρ

⃗ = d+⃗ − d−⃗ dCT

(4)

Similarly the amount of charge transfer is simply defined by ρ qCT =±

∫ ρ±( r ⃗)d3r

(5)

The transition dipole moment then reads μCT ⃗ρ =

∫ (ρ+( r ⃗) + ρ−( r ⃗)) rd⃗ 3r

ρ = qCT

=

⎛ ρ ( r ⃗) r ⃗

∫ ⎜⎜ ∫+ρ ( r ⃗) − ⎝

+

ρ ⃗ρ qCT dCT

⎞ ρ− ( r ⃗) r ⃗ ⎟ 3 dr ∫ ρ−( r ⃗) ⎟⎠ (6)

Equations 2−6 constitute what we will call the “density viewpoint” for charge transfer. 2.3. The QTAIM Approach to Charge Transfers at the Excited State. Alternatively, we proposed in ref 49 an adaptation of this strategy in the framework of Bader’s Quantum Theory of Atoms in Molecules (QTAIM),42,43 based on the so-called intra-atomic dipole moment generated by the anisotropy of the electron density inside an atomic basin Ωi. For a given (ground or excited) state, the barycenter of the negative charge for each atom is in general distinct from the corresponding nucleus, and can be located according to ri ⃗ =

(1)

1 pi

∫Ω ρ( r ⃗) rd⃗ 3r i

(7)

where pi denotes the electronic basin population. Adding the positive charge carried by the nucleus, the total atomic dipole moment (a concept that does not exist if one considers point charges) is equal to

The reference values will be the ones provided by Gaussian09 and then thus be labeled δμ⃗G09. Following Le Bahers et al.,22 local electron density increase (ρ+(r)⃗ ) or decrease (ρ−(r)⃗ ) due to absorption can be quantified by (where θ denotes the Heaviside step function, and Δρ(r)⃗ = ρES(r)⃗ − ρGS(r)⃗ is also known as the first state-specific dual descriptor46):

μ⃗i GS,ES = qiR⃗ i − pi ri ⃗

(8)

where R⃗ i is the nucleus position, and qi = Zi − pi is the atomic charge. The variation of the total molecular dipole moment can be then approximated by a first order linearization,49 being conveniently expressed by separating positive and negative atomic charge variations:

Then, the associated barycenters are determined by 758



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Table 1. Charge Transfer Descriptors in Epicocconone Analogues Using Various Point Charges Schemes (Mulliken, MerzKollman, CHelpG, Hirshfeld) and Density-Based Models at the TD-CAMB3LYP/6-31++G(d,p)/noneq-PCM Level of Theorya epi ia ib ic id ie if ig ih ii ij ik il im in io ip a

qMull CT

qMK CT

qChelpG CT

qHirsh CT

qρCT

dMull CT

dMK CT

dChelpG CT

dHirsh CT

dρCT

μMull CT

μMK CT

μChelpG CT

μHirsh CT

μρCT

δμG09

0.40 0.45 0.49 0.45 0.45 0.49 0.43 0.49 0.51 0.38 0.38 0.39 0.41 0.41 0.39 0.38 0.41

0.89 1.06 1.08 1.04 1.05 1.10 1.04 1.08 1.12 0.85 0.87 0.90 1.04 1.14 0.90 0.90 0.90

0.90 1.09 1.08 1.11 1.10 1.09 1.08 1.14 1.11 0.94 0.94 0.94 1.10 1.10 0.97 0.95 0.95

0.27 0.30 0.30 0.30 0.30 0.31 0.30 0.31 0.31 0.27 0.27 0.28 0.28 0.28 0.28 0.27 0.28

0.60 0.64 0.65 0.63 0.64 0.65 0.64 0.66 0.65 0.60 0.60 0.60 0.60 0.60 0.61 0.60 0.61

2.16 2.64 2.65 2.32 2.60 2.61 2.45 2.92 2.54 3.27 3.17 3.07 1.81 1.75 3.48 3.30 3.43

1.05 1.23 1.24 1.27 1.26 1.23 1.23 1.34 1.21 1.51 1.48 1.52 0.97 0.87 1.61 1.49 1.65

1.04 1.20 1.24 1.19 1.20 1.24 1.18 1.27 1.22 1.37 1.38 1.44 0.91 0.91 1.49 1.41 1.57

3.44 4.29 4.35 4.36 4.36 4.36 4.22 4.60 4.36 4.75 4.76 4.90 3.60 3.57 5.10 4.89 5.21

1.58 2.04 2.07 2.07 2.07 2.06 1.96 2.20 2.08 2.15 2.14 2.26 1.63 1.64 2.39 2.25 2.45

4.18 5.70 6.25 5.06 5.58 6.16 5.11 6.91 6.27 5.95 5.84 5.81 3.57 3.44 6.57 6.11 6.70

4.49 6.29 6.44 6.34 6.37 6.46 6.13 6.95 6.52 6.15 6.23 6.55 4.83 4.78 6.98 6.46 7.19

4.49 6.29 6.44 6.34 6.37 6.46 6.14 6.95 6.52 6.15 6.23 6.55 4.83 4.78 6.98 6.46 7.19

4.48 6.22 6.38 6.25 6.31 6.41 6.05 6.88 6.44 6.13 6.20 6.51 4.81 4.76 6.93 6.43 7.15

4.58 6.24 6.43 6.29 6.39 6.42 6.04 6.93 6.49 6.16 6.17 6.54 4.73 4.74 6.96 6.49 7.18

4.49 6.29 6.44 6.34 6.37 6.46 6.14 6.95 6.52 6.15 6.23 6.55 4.84 4.78 6.98 6.46 7.19

Charges in electrons, distances in angstroms, and dipole moments in Debye.

δμ ⃗QTAIM ≈

∑

δqi(R⃗ i + ri ⃗) +

δqi > 0

−

∑

⎧ ⎪Q i + = ΔQ i if ΔQ i > 0 ⎨ , ⎪ = 0 if ΔQ i < 0 ⎩

δqi(R⃗ i + ri ⃗)

δqi < 0

∑ pi δ ri ⃗

(14)

(9)

i

The charge transfer is evaluated similarly as in eq 10:

We now define the QTAIM charge transfer amount by QTAIM qCT =

∑

pc qCT =

δqi

δqi > 0

=

∑ δqi > 0

QTAIM d−⃗

=

∑

∑

δQ i (15)

δQ i > 0

(10)

Then, new points are located by

In analogy with eq 3, the two following vectors are defined: QTAIM d+⃗

⎧ ⎪Q i − = ΔQ i if ΔQ i < 0 ⎨ ⎪ = 0 if ΔQ i > 0 ⎩

pc

d±⃗ =

δqi

(R⃗ i + ri ⃗), QTAIM

qCT

1 pc qCT

∑

Q i ± R⃗ i

i

(16)

so that a new charge transfer vector can be considered:

|δqi|

QTAIM δqi < 0 qCT

pc

(R⃗ i + ri ⃗) (11)

QTAIM

+ δμpol ⃗QTAIM

(12)

(17)

pc

where: QTAIM QTAIM ⎧ ⃗ QTAIM = d+⃗ − d−⃗ ⎪ dCT ⎨ QTAIM = −∑ pi δ ri ⃗ ⃗ ⎪ δμpol ⎩ i

pc

This scheme can be seen as the coarse grain (discrete) version of the one based on the electron density (which embodies the continuous point of view of CT). The associated dipole moment then reads

so that: QTAIM ⃗ δμ ⃗QTAIM ≈ qCT dCT

pc

⃗ = d+⃗ − d−⃗ dCT

pc pc ⃗ μ⃗CT = qCT dCT

(18)

3. RESULTS AND DISCUSSION 3.1. Charge Transfer upon Excitation: Methodological Aspects. The first excited state, corresponding mainly to the HOMO→LUMO transition, is investigated in epicocconone and a set of 16 synthetic analogues (following our recent theoretical work15) as represented in Figure 1. These compounds can be separated in two groups: first and second generations (see Figures S1−S2 in the Supporting Information for the detailed structures). The difference between them resides, respectively, in a simple keto- or a 1,3-diketo-group of the side chain part connecting the molecular scaffold with its substituent. It must be stressed that only the aminated forms (derived from butylamine, as this alkylamine is frequently used in practice) are examined because these compounds become

(13)

The first term on the right-hand side describes interatomic charge transfer, while the second one is related to the intraatomic polarization change (electron reorganization inside the basin). It should be noticed that this formula is exact as long as first-order linearization is valid. 2.4. The Pure Point Charges Approach to Charge Transfers at the Excited State. The last framework that we will investigate is the “point charges” one, as developed by Jacquemin and co-workers.23 Given point charges (whatever their origin) Qi, in the same spirit as in eq 2, two new functions are defined depending on their variations between the ground and excited states: 759



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fluorescent (and thus present a biochemical interest) only once they are bound to the terminal NH2 group of the target protein. We will first assess the ability of the atomic charge models to reproduce the variation of the molecular dipole moment. As it can be easily reckoned from Table 1, all models, except Mulliken charges, succeed quite well in reproducing ∥δμ⃗ G09∥. The mean absolute errors (MAE) for the whole series are 0.59 D (Mulliken) and 0.05 D for Hirshfeld. The corresponding mean signed values (MSE) are respectively equal to −0.59 D and −0.05 D, proving that both schemes always underestimate the transition dipole moments. For MK and CHelpG schemes, as the dipole fitting procedure was switched on, they obviously reproduce the Gaussian09 values. It can be noticed that not only are Mulliken charges unable to provide accurate values, but they are also not linearly correlated to the reference ones, as evidenced by the very low R2 value (0.56). Conversely, the Hirshfeld description, which is already excellent, can be improved to compensate the observed underestimation by multiplying the values by 1.01 (R2 > 0.99, MAE = 0.02 D). Obviously, this correction may be only suitable for molecular structures closed to the studied ones. The dipole moments obtained within Bader’s theory (see Table 2 for the corresponding values) now deserve special

ones given by Gaussian09, an expected result as QTAIM is solely based on the electron density. The intra-atomic dipole moments, which are sometimes overlooked when QTAIM charges are compared with PAC, are thus fundamental to correctly describe CT upon photon absorption. For the studied fluorophores, the average value for ∥δμ⃗ QTAIM ∥ is 0.20 D, the minimal and maximal ones being pol equal to 0.16 and 0.30 D, respectively. This last number deserves a further attention since it corresponds to the only natural product, the epicocconone, which actually reveals to be the molecule in which the intraatomic polarization variation is the most considerable. Interestingly, for this compound, ∥qQTAIM d⃗QTAIM ∥ is equal to CT CT QTAIM 4.38 D, while ∥δμ⃗ ∥ is 4.49 D. The difference between these two last values is only 0.11 D, and thus only represents one-third of ∥δμ⃗QTAIM ∥. This proves that the qQTAIM d⃗QTAIM and pol CT CT δμ⃗QTAIM vectors are not parallel. pol More precisely, we can calculate the angle, denoted φ, between them. For instance, φ = 0 for ih, the two contributions being “in phase” (with ∥qQTAIM d⃗QTAIM ∥ = 6.31 D, ∥δμ⃗ QTAIM ∥= CT CT pol 0.21 D, ∥δμ⃗ QTAIM∥ = 6.52 D). More generally, the average φ value calculated for all compounds equals 39° (with a large standard deviation: 20°), the maximum being reached, once more, for epicocconone (70°). However, in any case, it is lower than 90°, showing that the two contributions (qQTAIM d⃗QTAIM CT CT QTAIM and δμ⃗ pol ) are globally cumulative, even if this combination can be far from being optimal. This cumulative “efficiency” of intra-atomic polarization change can be evaluated by the cos(φ) quantity. For instance, it equals 100% for ih, but only 34% for epicocconone. As a final remark on this QTAIM description of transition dipole moments, we notice that the evaluation of the polarization contribution requires an additional computational step with respect to the calculation of the atomic populations. Nonetheless, it is actually possible to skip it using the following linear regression (with R2 > 0.99):

Table 2. Charge Transfer Descriptors in Epicocconone Analogues in Bader’s QTAIM Framework at the TDCAMB3LYP/6-31++G(d,p)/noneq-PCM Level of Theorya epi ia ib ic id ie if ig ih ii ij ik il im in io ip

qQTAIM CT

dQTAIM CT

qQTAIM dQTAIM CT CT

δμQTAIM pol

δμQTAIM

δμG09

0.22 0.28 0.28 0.27 0.28 0.29 0.28 0.28 0.29 0.23 0.24 0.24 0.25 0.25 0.24 0.24 0.24

4.21 4.57 4.58 4.69 4.67 4.57 4.41 4.93 4.56 5.35 5.34 5.55 3.88 3.89 5.97 5.61 6.17

4.38 6.14 6.28 6.17 6.23 6.29 5.96 6.76 6.31 6.03 6.10 6.43 4.71 4.66 6.85 6.37 7.09

0.30 0.16 0.19 0.19 0.16 0.19 0.16 0.23 0.21 0.18 0.19 0.19 0.19 0.19 0.22 0.19 0.23

4.49 6.30 6.45 6.35 6.37 6.46 6.11 6.95 6.51 6.15 6.23 6.56 4.83 4.78 6.97 6.47 7.19

4.49 6.29 6.44 6.34 6.37 6.46 6.14 6.95 6.52 6.15 6.23 6.55 4.84 4.78 6.98 6.46 7.19

QTAIM

QTAIM ⃗ || δμmodel dCT ⃗QTAIM || = 1.02 || qCT

||

(19)

The MAE using this model is 0.03 D, a sufficient accuracy for most applications (provided that molecules similar to these analogues are studied). Note that this model does not depend only on QTAIM charges, since the CT distance vectors include the ri⃗ terms (see eq 7), which represent the distance between the nucleus and the barycenter of the negative charge inside the atoms. However, it is worth mentioning that if one calculates QTAIM ⃗ QTAIM ∥qCT dCT ∥ neglecting these ri⃗ contributions, almost identical values (the differences being about 0.01 D in magnitude) are obtained. With such an approximation, eq 19 can be rewritten only with QTAIM charges (this is actually exactly identical to eq 18 if the corrected coefficient is disregarded):

a

Charges in electrons, distances in angstroms, and dipole moments in Debye.

attention since two contributions are involved: the interatomic charge transfer and the intra-atomic reorganization. Let now consider the first one: ∥qQTAIM d⃗QTAIM ∥. If only this term was CT CT included, the MAE and MSE would be equal to 0.14 D and −0.14 D, respectively. This means that ∥qQTAIM d⃗QTAIM ∥ always underestimates the CT CT transition dipole moment, confirming our previous observations49 on α,ω-nitro,amino-polyphenylene oligomers and diketopyrrolopyrrole dyes. It also follows from data in Table 2 that one cannot neglect the polarization term δμ⃗ QTAIM . When pol we include this physical effect (due to the anisotropy of the charge distribution), the resulting QTAIM transition dipole moments are strictly equal (within numerical accuracy) to the

δμ ⃗QTAIM = 1.02( ∑ δqiR⃗ i + δqi > 0

∑ δqi < 0

δqiR⃗ i) (20)

We now turn our attention to the deviations of qCT and dCT with PAC models with respect to qρCT and dρCT (Table 1). For the amount of charge transfer (in electrons), the mean absolute deviations (MAD, we here privilege the term “deviation” rather than “error” for a reason that will appear below) are respectively equal to 0.19 (Mulliken), 0.38 (MK), 0.41 (ChelpG), and 0.33 (Hirshfeld). It is informative to compare 760



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them with the corresponding MSD: −0.19 (Mulliken), 0.38 (MK), 0.41 (ChelpG), and −0.33 (Hirshfeld). It results that the Mulliken and Hirshfeld schemes always give lower values than the density approach, while MK and ChelpG systematically provide higher values. The correlation ρ coefficients R2 between these qpc CT and qCT are respectively equal to 0.87 (Mulliken), 0.46 (MK), 0.52 (ChelpG), and 0.92 (Hirshfeld). These discrepancies can be enlightened by looking at compounds ii, ij, ik, il, im. For these five molecules, the same qρCT value is obtained (0.60), while the range predicted by ChelpG is [0.94; 1.10]. Let now focus on QTAIM charge transfers: first of all, they are almost equal to Hirshfeld ones (so QTAIM tends to underestimate them), a result that may be surprising as the two frameworks considerably differ, but that has already been observed, as discussed more in details in ref 50. However, as for the other schemes, the QTAIM values are not correlated to qρCT (R2 = 0.86). In fact, in general, they have to be different. Indeed, qQTAIM CT only evaluates the charge that a given atom looses or gains. On the contrary, qρCT sums the variations at any point. In other words, qQTAIM only includes charge transfers between atoms, CT while qρCT takes into account interatomic charge transfers and intra-atomic reorganization on the same footing. From this and qρCT should be seen as conveying useful viewpoint, qQTAIM CT complementary information about charge transfers. Now, as a consequence of the reported qCT values, the CT distances are greater using Mulliken, Hirshfeld, and Bader charges, than the ones obtained from the pure electron density perspective, while MK and CHelpG give low values in comparison with the density approach. The average values for ρ the dpc CT/dCT ratios are respectively equal to 1.31 (Mulliken), 0.63 (MK), 0.61 (ChelpG), 2.15 (Hirshfeld), and 2.37 (Bader). In summary, the overall conclusion of this assessment is similar to the one expressed in Jacquemin’s pioneer work23 on this matter: if several PAC models succeed in well estimating the transition dipole moments (MK, CHelpG, Hirshfeld, and Bader, this last scheme being exact), none of them reproduce the qρCT and dρCT values. In the case of QTAIM, we highlighted the reasons why the two schemes must in principle provide different values and why both could be usefully applied in theoretical studies of charge transfer phenomena in protein markers. 3.2. Charge Transfer upon Excitation: Comparing the Various Analogues. As it can be deduced from the data collected in Table 1, the amount of charge transfer in the compounds of first-generation (compounds ia−ih) is found to be slightly higher than for second generation (ih−ip), whatever the scheme used for their evaluation. Indeed, the actually qCT averages are equal (in electrons) to 0.47 and 0.39 (Mulliken), 1.07 and 0.94 (MK), 1.10 and 0.99 (ChelpG), 0.30 and 0.28 (Hirshfeld), 0.28 and 0.24 (Bader), and 0.65 and 0.60 (full density approach). On the contrary, the charge separation distance dCT is higher for the second generation, the average being respectively equal (in angstroms) to 2.59 and 2.91 (Mulliken), 1.25 and 1.39 (MK), 1.22 and 1.31 (ChelpG), 4.36 and 4.60 (Hirshfeld), 4.62 and 5.22 (Bader), 2.07 and 2.11 (density approach). It can be noticed that the fact that all schemes are consistent the one with the other is rather appreciable, so that they can be used to qualitatively compare different molecular families. As a consequence, the corresponding transition dipole moments for the first and the second generations are quite

close to each other and belong to the 6−7 D range. The only exceptions are the nonenolizable il and im compounds with δμG09 ∼ 4.8 D. Surprisingly, δμG09 for epicocconone is also substantially smaller than that of synthetic compounds (4.49 D). This difference is ascribable to the smaller CT distance rather than to the transferred charge. Indeed, qρCT is equal to 0.60 e for epicocconone, a value that is very close to the one reported for the synthetic analogues. Meanwhile, dρCT equals 1.6 Å for epicoccone, whereas it is almost always higher than 2.0 Å for the synthetic molecules. Interestingly, the two generations can be discriminated by their ∥δμ⃗QTAIM ∥ values: they belong to the [0.27 D; 0.29 D] pol range for the first generation, while they lie in the [0.23 D; 0.25 D] one for the second generation. The differences are even more prominent when concentrating on the φ angle: lower than 35° for the first generation (with an average equal to 21°), higher than 47° (average: 54°). These results can be translated in terms of the intra-atomic charge reorganization efficiency, measured by the cos(φ) factors: its average is equal to 90% for the first generation and to 59% for the second one. It can then be concluded that intra-atomic polarization is more intense for the first generation, being at the same time greater in magnitude and more parallel to the interatomic CT direction. Additionally, remarkable characteristics are observed for ig, in, and ip structures. The first one displays the highest values for μρCT, qρCT, and dρCT within the molecules of the first generation, while the last ones also feature particularly high μρCT and dρCT values. Interestingly, the main differentiation between the whole set of compounds stems once more from the CT distance (up to 50% of variation) rather than from the transferred charge (8% of variation at most). Another way for unraveling the nature of such transitions is to scrutinize the position of the barycenters corresponding to the electron density increase and electron density decrease ⃗ vector. upon light excitation, as well as the direction of the dρCT In first-generation compounds, both barycenters almost coincide with some atomic positions (as epitomized by ia, see Figure 2), namely, the ring carbon atom C* in the O = C− C*=C−NH moiety and the sp2 carbon at the junction of the five-membered and six-membered cycles. As for compounds of second generation, the position for the decrease barycenter typically displaces toward the center of the six-membered ring, while the zone of density increase also shifts toward the diketogroup (as pictured in Figure 2 for the representative ik molecule). Here, as well, nonenolizable im and il molecules constitute an exception, the CT vector being

Figure 2. Charge transfer vector d⃗ρCT in representative synthetic analogues of the first (ia) and second generations (ik) denoted by green arrays. Red arrays for ia shows the positions of atoms, which almost coincide with d⃗ρ+ and d⃗ρ− positions. 761



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similar to the compounds of first generation. As already mentioned, epicocconone features (see upper part of Figure 3) a CT profile quite different from the synthetic analogues, mainly due to the displacement of the d⃗ρ− barycenter from the amine fragment toward the side chain.

3.3. On the Role of pH in the Absorption Features. In light of the previous remark, and even if such a study is clearly outside the scope of this paper, some interesting facts about the role of the pH can be briefly discussed. First, we can mention that the formation of anions, cations, or zwitterions leads to higher mixing of one-particle transitions for the first excited state. This is particularly the case of epicocconone and ik in its zwitterion form. Additionally, for ia in its cationic state, an inversion of the transition types order is observed, since the most intense absorption (corresponding to the HOMO→ LUMO transition) becomes third in the order. Furthermore, we observe a blue shift in the excitation wavelengths for all structures. For instance, λ = 444 nm for neutral epicocconone, λ = 413 nm when the enolate is formed, λ = 411 nm when nitrogen is protonated. For compound ik, the corresponding values are respectively equal to 437 nm, 398 nm, 357 nm. In addition, we notice a concomitant increase of the oscillator strength for cations (from 1.51 to 1.94 for epicocconone, and from 0.93 to 1.34 for ik) and a decrease for anions with respect to neutral forms (from 1.51 to 1.34 for epicocconone, and from 0.93 to 0.80 for ik). This is in line with experimental observations according to which the intensity is enhanced in the domain of acidic pH and almost disappears in basic medium.2,13,14 3.4. Toward an in Silico Design of Novel Fluorophores: The Role of the Functional Groups. We now intend to highlight how these CT descriptors can be used as valuable tools to account for the role of the various substituents entering the chemical structure of such fluorophores. All of the studied compounds share the same scaffold, in which we can distinguish between (see Figure 1) the core, formed by the junction of penta- and hexa-cycles (1); the enamine moiety (2); the right-hand aliphatic side branch, connected to the hexadienone cycle and holding alcohol groups (3); the lefthand side substituent R2 (4), linked to dihydrofuranone by the (di)keto group (5); and the methyl (6) substituent at the junctions of the two cycles. To clarify and disentangle the contribution of each of these fragments, we have chosen to analyze in details the CT characteristics in compounds obtained by incremental modifications of the aminated epicocconone (all corresponding structures having been fully reoptimized at the same level of theory). These evolutions are pictured in Figure 3. Note that in the following, only CT descriptors obtained using the full electron density approach will be reported. Thus, in order to simplify the notations, the corresponding descriptors of interest will be denoted dCT, qCT, μCT. For the butylaminated epicocconne (upper part in Figure 3), the CT distance, charge, and dipole moment are respectively equal to 1.58 Å, 0.60 e, and 4.58 D. We now substitute the butyl chain in the amine moiety by a methyl group (molecule labeled (a) in Figure 3). The new CT characteristics are 1.50 Å (dCT), 0.59 e (qCT), and 4.27 D (μCT): the charge transfer amount is thus unchanged, but the transition dipole moment is slightly decreased due to the small decrease of the CT distance. These results prove that the protein that will bind may have a noninnocent, but probably limited, impact on excited state charge transfers. Then, the R1 moiety (on the right) is removed, leading to compound labeled (b) in Figure 3, resulting in the new following values: 1.53 Å (dCT), 0.60 e (qCT), 4.41 D (μCT). The change is even weaker than at the previous step, suggesting that R1 only plays a minor role for the modulation of CT processes.

Figure 3. Evolution of the charge transfer properties upon the removal or substitution of various functional groups in aminated epicocconone.

From a similar perspective, one can compare the molecular dipole moments in ground and excited states in order to deduce whether the molecule in the excited state is more polarized or not. First, the angle between them was investigated. We found that light absorption also involves a small rotation of the total molecular dipole moment direction according to the following statistics: 9.5° (average value), 2.6° (standard deviation), 5.3° and 13.1° (minimal and maximal values, respectively). At variance with what we observed for the variation of the polarization term, the two generations present similar properties (the average angles respectively equal 9.1° and 9.7°, for the first and second generations): this rotation angle cannot thus be used to discriminate between the analogue families. We now turn our attention to the magnitude of these molecular dipole moments for the two states. We obtained that for the whole data set of molecules in their neutral form, the dipole moment increases in magnitude upon absorption, so that it can be suggested that polar solvents may contribute to a relative greater stability of in the first excited state. It also implies that this state might be more prone to protonation, and potentially leads to fluorescence quenching. 762



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illustrated by sequential removals of chemical groups in epicocconone. More specifically, we established that the diketo moiety (that connects R2 to the core) tends to largely increase the charge transfer distance, while the R2 side-chain decreases it even more dramatically. On the contrary, the other groups have been found to have a minor impact on the charge redistribution upon excitation. Additionally, the analysis of GS and ES dipole moments, for representative compounds in different protonation states, allowed proposing a theoretical explanation for the experimentally observed trends. In particular, our calculations may rationalize the fact that the intensity becomes more intense for acidic pH and almost disappears in basic medium. Concerning the differences between the two analogues’ generations, they mainly lie in the charge transfer distances rather than in the amount of charge transfers (which is barely sensitive to the nature of the substituents). Interestingly, a clear discrimination between both families was identified in terms of intra-atomic polarization change, a contribution that is essential to accurately model charge transfers. Finally, we hope that this light cast on these charge transfer characteristics, along with the reported findings on the role of the structural fragments, may facilitate the design of novel compounds and could also be used for the fine-tuning of the spectroscopic properties of yet unsynthesized compounds.

In fact, the hydroxylated aliphatic side chain (3) in real systems plays a role of anchor. The conclusions are all the more different when considering the removal of the R2 heptatriene chain (molecule (c) in Figure 3). Although the CT amount is scarcely increased (+3%), a dramatic change in the distance is observed: +0.67 Å. As a consequence, there is a strong increase of the transition dipole moment: +2.15 D. The importance of this polyene substituent can be qualitatively illustrated through the picture of the frontier orbitals in epicocconone. Indeed, it can be inferred from Figure 4 that they are largely delocalized on the

Figure 4. Views of highest occupied (HOMO) and lowest unoccupied molecular orbitals (LUMO) of epicocconone, as well as variation of the electron density variation Δρ for the first excitation.

heptatriene side chain. Its removal triggers a displacement of the barycenter toward the 6-membered ring, so that we finally obtain a picture very close to the one for compound ia (see Figure 2). All these facts give evidence that once epicocconone looses the polyene side chain, its CT characteristics become very close to those of the synthetic analogues. The subsequent suppression of the side (di)keto-group (giving (d) in Figure 3) leads to an important decrease of dCT (−0.23 Å) while the amount of charge transfer is unchanged, so that the CT dipole moment (which rotates a little) decreases in magnitude (−0.67 D). These effects are thus opposite to the ones induced by the R2 group, but are less intense, so that they do not fully compensate the impact of the heptatriene chain. We finally checked that the substitution of the methyl group at the junction of the two cycles by a hydrogen atom has almost no influence on charge transfer upon excitation.

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ASSOCIATED CONTENT

* Supporting Information S

Chemical structures of aminated epicocconone analogues. This information is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; phone number: +33 (0)2 35 52 29 47. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge the ANR-BLAN-732-01 grant for financial support, the IDRIS, CINES and CRIHAN computational centers for providing HPC resources. V.T. and L.J. thank the Centre National de la Recherche Scientifique (CNRS) for a “Chaire d’Excellence” at the University of Rouen.

4. CONCLUSIONS In this paper, charge transfers upon photon absorption in epicocconone analogues were theoretically investigated using Le Baher’s and Jacquemin’s approaches, by focusing on the three main related parameters: variation of the molecular dipole moment, transferred charge, and charge transfer distance. It was found that the use of point charges (except Mulliken) gives satisfactory results for the evaluation of the molecular dipole moment variation, but provides charges and distances that importantly differ from the ones obtained using the full electron densities of the two states. We emphasized that Bader’s QTAIM theory not only provides exact transition dipole moments, but also enables to clearly and physically distinguish between interatomic charge transfers and intra-atomic polarization change. This scheme thus carries additional information to that obtained using the sole electron densities. For such a reason, we advocate its possible use for the optimization of charge transfers in protein markers. Then, we explored how these tools can be used to identify the main physicochemical factors ruling the absorption process. It was in particular shown that the through-space charge transfer properties depend on the nature of the substituents, as

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REFERENCES

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