Mechanochemical Tuning of Pyrene Absorption Spectrum Using Force

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Mechanochemical tuning of pyrene absorption spectrum using force probes Miguel Angel Fernández-González, Daniel Rivero, Cristina García-Iriepa, Diego Sampedro, and Luis Manuel Frutos J. Chem. Theory Comput., Just Accepted Manuscript • DOI: 10.1021/acs.jctc.6b01020 • Publication Date (Web): 12 Jan 2017 Downloaded from http://pubs.acs.org on January 13, 2017

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Journal of Chemical Theory and Computation

Mechanochemical tuning of pyrene absorption spectrum using force probes. Miguel Ángel Fernández-González,1,‡ Daniel Rivero,1,‡ Cristina García-Iriepa,1,2 Diego Sampedro,2 Luis Manuel Frutos1,* 1

Química Física, Universidad de Alcalá, E- 28871 Alcalá de Henares, Madrid, Spain.

2

Departamento de Química, Centro de Investigación en Síntesis Química (CISQ), Madre de Dios, 53, E-26006, Logroño, Spain. KEYWORDS. Mechanochemistry, mechanophotochemistry, tuning spectra, optomechanics, pyrene. ABSTRACT: Control of absorption spectra in chromophores is a fundamental aspect of many photochemical and photophysical processes as it constitutes the first step of the global photoinduced process. Here we explore the use of mechanical forces to modulate the light absorption process. Specifically, we develop a computational formalism for determining the type of mechanical forces permitting a global tuning of the absorption spectrum. This control extends to the excitation wavelength, absorption bands overlap and oscillator strength. The determination of these optimal forces permits to rationally guide the design of new mechano-responsive chromophores. Pyrene has been chosen as the case study for applying these computational tools since significant absorption spectra information is available for the chromophore as well as for different strained derivatives. Additionally pyrene presents large flexibility, which makes it a good system to test the inclusion of force probes as the strategy to exert forces on the system.

1. INTRODUCTION. Control of light absorption and emission properties has received a lot of interest in the recent years. For 1 instance, in organic light emitting diodes (OLEDs) , it is desirable a more efficient primary color emission. The control of the absorption spectra is a key point to 2 improve the selectivity in E/Z photochromic switches 3 (i.e. azobenzene and stilbene derivatives ): a larger separation between absorption bands of both isomers could increase the photoconversion extent. Also, control of light absorption finds application in medicinal chemistry, for example, in the design of new photo4 sensitizing agents for photodynamic therapy (PDT). Here, excitation with low energy radiation (i.e. near infrared light), where the tissue penetration is maxi5 mum is an essential requirement . A common strategy for achieving this control is the chemical modification of the studied system. It has been shown, for instance that electroluminescent properties of organic dyes are influenced by electronic 6 donor/acceptor groups. Regarding biological applications, a lot of work has been done to red-shift the absorption spectrum of azo-derivatives through the addi7 tion of electron donor substituents at key positions. Another prominent example is the design of new cell

imaging probes, where low energy radiation in both, absorption and emission processes is mandatory in 8 order to avoid photodamage in biological systems. In addition, mechanochemistry (i.e. chemical reactivity fostered by mechanical forces) has emerged in recent years as a powerful strategy for modulating different 9 chemical properties, especially on molecular systems. In this context, techniques such as atomic force mi10 11 croscopy (AFM), sonication or molecular force probes (i.e. molecular fragments that covalently attached to the reacting system induce a controlled me12 chanical force) allow controlling the applied forces at a molecular level. All these mechanochemical techniques have been intensively applied to the study of the mechanical control of thermodynamics and kinet13,14 ics in ground state processes. Nevertheless, in spite of the potential utility of mechanochemistry in controlling also excited state properties and reactivity, only few studies exist in this context. For instance, AFM-based techniques allowed to perform optomechanical switching cycles of azobenzene 15 derivatives incorporated in a polymer chain. Moreover, the modification of the non-radiative deactivation rate of molecular rotors by the environment viscosity is

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widely used to measure the diffusion and viscosity for 16,17 instance in live cells. Also, several works show the ability of stiff-stilbene based molecular force probes to exert mechanical forc18 es upon photoisomerization. Additionally, azobenzene photoisomerization was proved to be partially 19 suppressed by mechanical forces. Other relevant examples such as the study of how maximum absorption wavelength and shape of the absorption bands 20 change in a photoswitch under external forces, or the stress-induced chemiluminescence in a dioxetane21 based polymer, prove that mechanical forces can modulate or even induce photochemical reactivity. Few works exists contributing to develop a theoretical framework to understand how photoreactivity is affected by mechanical forces. In this regard, it has been proved that topology of conical intersections (CIs) becomes affected by mechanical forces, altering ulti22 mately the photoreactivity. Also, it has been developed a computational methodology aimed to identify efficient forces tuning the excitation energy in chor23 mophores. The aim of the present work is to develop a new computational methodology able to provide guidelines for the mechanochemical control of the entire absorption spectrum of a chromophore in terms of excitation energy, intensity and absorption bands overlap by application of external forces. This formalism is applied to pyrene (Figure 1) as a case study, as this chromophore presents several experimentally well-defined UV-vis absorption bands not only for the pyrene itself but also for different strained derivatives. Moreover, pyrene shows enough molecular flexibility to explore the effect of different types of mechanical forces (including out-of-plane deformations) in its absorption spectra. The obtained results for pyrene serve ultimately to guide molecular design towards the inclusion of molecular force probes tuning the absorption spectra. These molecular force probes will imply the analysis of both in-plane and out-of-plane forces and consequently in-plane and out-of-plane distortions.

gradients for the different transitions were determined numerically by using our own developed code, checking in all cases the stability of the obtained vector by using different time-steps for numerical differentiation (see Supporting Information for further details). All the calculations were performed with Gaussian09 suite of programs (see Supporting Information for complete references). 2.2. Analytical determination of optimal mechanical forces tuning the maximum absorption wavelength. Absorption spectrum tuning by mechanochemistry means implies knowing how the excitation energies and oscillator strength respond to the action of mechanical forces. It is therefore necessary to obtain expressions relating, with the highest possible generality, the external mechanical forces and the corresponding electronic energies and oscillator strengths variations. In order to do that, a quadratic approach of the potential energy surfaces (PESs) has been used for all the electronic states, which computationally implies the determination for each state energy gradient (𝐠) and hessian (𝐇). C2 (transverse)

C2 (longitudinal)

Figure 1. Chemical structure of pyrene and its numbering. The two in-plane C2 axis (transverse and longitudinal) are also indicated.

Let us consider therefore the PES of the ground state (𝐸0 ) within a quadratic approximation expanded from the equilibrium structure: 1

2. METHODS

𝐸0 (𝐪) = 𝐪𝐓 𝐇0 𝐪

2.1. Electronic structure methods. The vertical excitation energies of pyrene have been computed at the TD-DFT level of theory. Specifically, we have selected 24 the B3LYP functional with a 6-31+G** basis set, chosen after calibration with experimental data (see results sections, and Figure S1 and S2 in the Supporting Information). Analytical energy gradients and hessians were performed at the same level of theory for ground and excited states. Additionally, the oscillator strength

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2

(1)

Consequently, the square of the energy gradient is: |∇𝐸0 (𝐪)|2 = 𝐪𝐓 𝐇02 𝐪

(2)

This magnitude is crucial in predicting the mechanical response of the molecule to an external force, as it provides the magnitude of the external force as a function of the induced geometrical distortion (q). We are interested, in the most general case, in the mechanical tuning of the relative energy difference

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between two electronic states, even if none of them corresponds to the ground state. This means that in a broad sense we are interested in controlling by the action of external forces the absorption wavelength of the bands corresponding to two generic transitions: E0→E1 and E0→E2, being E1 and E2 the first (lower in energy) and the second electronic states. Once again, using a second order approach of the PES for the excited states E1 and E2: 1

𝐸1 (𝐪) = 𝐸1 (𝟎) + 𝐪𝐓 𝐠1 + 𝐪𝐓 𝐇1 𝐪

(3)

𝐸2 (𝐪) = 𝐸2 (𝟎) + 𝐪𝐓 𝐠 2 + 𝐪𝐓 𝐇2 𝐪

(4)

2 1 2

Where 𝐸1 (𝟎) and 𝐸2 (𝟎) are the relative vertical energies to the ground state equilibrium structure (𝟎). The optimal mechanical action (minimal external force) provoking an extremal change (i.e. maximum or minimum) in the energy difference between E1 and E2 is given by performing a constrained optimization of the internal force magnitude, where energy difference is kept constant (see Supporting Information for details): 𝐅𝑒𝑥𝑡,𝑜𝑝𝑡 (𝐪) = −𝐇0 𝐇 −1 ∆𝐠 (5) 2

Being: 𝐇 ≡ 𝐇02 + ∆𝐇, with ∆𝐇 ≡ 𝐇2 − 𝐇1 , ∆𝐠 ≡ 𝐠 2 − 𝜆 𝐠1 , and λ a Lagrange multiplier. By setting different values for λ, a different set of optimal forces and corresponding structures is obtained. For the special case of a planar system (as is the case of pyrene, Figure 1), the constrained optimization can be split in two sets of equations, one corresponding to the in-plane forces and the other to the out-of-plane forces. Concretely, the structural changes induced by the optimal external force are: 𝐶

𝑠 𝐪𝑜𝑝𝑡 = −𝐇 −1 ∆𝐠

(6)

for the in-plane (Cs) case, while the out-of-plane optimal distortions (C1) are the solution of the eigenvalue problem: 𝐶

2 𝐶

𝐶

1 1 −2 (∆𝐇 𝐶1 )−1 (𝐇01 ) 𝐪𝑜𝑝𝑡 = 𝜆𝐪𝑜𝑝𝑡

(7)

Concluding, Eqs. 6 and 7 provide the structural changes induced by optimal forces (i.e. minimal force magnitude) provoking the largest possible variation of the energy difference between states 1 and 2. 2.3. Analytical determination of the optimal mechanical forces tuning the oscillator strength. Let us consider a first order approach for the oscillator strength (f) as a function of the coordinates: 𝑓(𝐪) = 𝑓(𝟎) + ∇𝑓 𝐓 𝐪

(8)

where the oscillator strength gradient, ∇𝑓, is determined numerically for each optical transition at the ground state energy minimum (see Supporting Information for details).

The optimal external force (i.e. with the lowest possible module) provoking a given oscillator strength variation is given by solving the constrained optimization equation: 𝜆∇𝑓 = −2𝐇02 𝐪, where λ is a Lagrange multiplier. Therefore, the structural change produced by this optimal force is given by: 𝜆

𝐪𝑜𝑝𝑡 = − 𝐇0−2 ∇𝑓 2

(9)

Where, as a result, the optimal external force is given by: 𝜆

𝐅𝑒𝑥𝑡,𝑜𝑝𝑡 = 𝐇0−1 ∇𝑓 2

(10)

Which is the analogous of Eq. 5 for the case of oscillator strength. Concluding, the above derived equations provide information on how to tune different properties of the absorption spectra (i.e. the excitation energy, energy band separation or oscillator strength) with mechanical forces. More specifically, the obtained forces are the optimal ones (i.e. those provoking the largest response of the property with the minimal force magnitude). These forces are obtained based on first and second derivatives of the energy and oscillator strength of the involved electronic states, and therefore the methodology is universally applicable and valid as long as the quadratic approximation on the potential energy surface remains valid. In this case we have chosen pyrene as a case study for its interesting properties and the available experimental information as explained above. 3. RESULTS. The methodology described above for quantifying the mechanical response of absorption spectra can be applied to any molecular system, including planar systems. In the following we apply this methodology to pyrene which is, as has been mentioned above, a good candidate for exploring different types of forces. The obtained results are then used for guiding molecular modeling of force-probes-mediated strained pyrenes with tuned absorption spectrum. 3.1. Model system: pyrene absorption spectrum. In order to study the mechanical tuning of pyrene absorption spectrum, we first consider it in the absence of any force. The experimental spectrum of pyrene con25,26 sists of four bands. These bands are commonly 27 referred by the nomenclature as suggested by Clar, which is based on their behavior with temperature and solvent changes. When recording the absorption spec26 trum in diethyl ether, the weakest band located at -1 -1 372 nm (𝜀 = 510 mol cm L) is called the 𝛼 band. The second and third bands, p and  respectively, are of -1 -1 comparable absorption intensities (ε = 55800 mol cm -1 -1 L and ε = 53600 mol cm L, respectively), appear at

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336 and 273 nm, and present a regular vibrational structure. Finally, the fourth band, ’ , corresponds to a -1 -1 strongly allowed transition (ε = 88400 mol cm L) and its maximum absorption wavelength is 242 nm. In the following, we refer to these three bands (i.e. p,  and ’), corresponding to the low-lying bright states, by their respective electronic transition nature, as shown in Table 1. Table 1. Electronic transition, computed excitation energies and oscillator strengths of the considered absorption bands. The excitation energies and oscillator strengths are compared with the experimental data. TD-DFT B3LYP/6-31+g** Bands

Experimental f

24

ε (mol1 -1 cm L)

Electronic Transition

Excitation Energy, eV (nm)

p

S0S1

3.65 (340)

0.277

Excitation Energy, eV (nm) 3.69 (336)



S0S4

4.56 (272)

0.276

4.54 (273)

53600

'

S0S11

5.34 (232)

0.800

5.12 (242)

88400

55800

The selected functional for determination of vertical 24 transition energies, B3LYP, has been widely applied before for the study of the absorption spectrum of pyrene because it shows a good agreement with the 28 experimental data, especially for p,  and  ’ bands. In contrast, the excitation energy corresponding to the α band is overestimated when using this functional (i.e. being higher than the p band). The experimental order 29 is reproduced when using the CAM-B3LYP functional, but the excitation energies of the other bands become notably higher than the experimental values (see Supporting Information). Considering that in this study we are focused on the modulation of the most intense absorption bands (i.e. the p,  and  ’ bands), we have selected the B3LYP functional with the 631+G** basis set (see Supporting Information for further details). 3.2. Mechanical tuning of the maximum absorption wavelength of pyrene. Regarding to the mechanochemical control of the chromophore absorption spectrum, the first aspect to be considered is the maximum absorption wavelength of each transition. Following the methodology developed above, Eq. 5 provides the general expression for determining the optimal forces controlling the excitation energy. More specifically for molecules with Cs symmetry, Eq. 6 and 7 provide the corresponding in-plane and out-of-plane contributions to the forces respectively. Nevertheless, in case of no symmetry considerations, Eq. 6 could be used directly. In this case, since we are using cartesian

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coordinates for energy gradients and hessians, it is necessary to separate both set of coordinates. This formalism is based on the validity of the approximate potential energy surfaces. Within the considered external force magnitudes (up to ca. 2 nN) it can be proven that the second order approach in the potential energy surfaces provides, in general, excellent results in the prediction of energies and geometries, which have at least a qualitative validity if not quantitative (see Supporting Information for further details). According to pyrene symmetry, in the following we firstly study the optimal in-plane forces controlling the excitation energy and secondly the corresponding analysis for the out-of-plane ones. In-plane external forces. As discussed above, Eq. 5 provides the force vector that modulates the excitation energy more efficiently, while the corresponding structural distortion induced by this force is given by Eq. 6. In fact, this equation has, for a given force magnitude, two solutions corresponding to the positive and negative value of the Lagrange multiplier λ, related to a decrease and increase of the excitation energy. In the following the analysis will be made by considering the vectors which shift the energy differences to higher values (∆Eexc > 0). Nevertheless, it should be noted that the vectors providing the decrease of the energy difference (∆Eexc < 0) are simply the opposite vectors as those drawn in the corresponding figures. The structural distortions (Eq. 6) optimally modifying the excitation energies for the three optically active states are shown in Fig. 2a. As it is apparent from this figure, the displacement vectors involve concerted movements of groups of opposite atoms, mainly involving pulling the molecule apart from the two possible opposite sides (top-down and left-right, see Figure 2a). The analysis of the optimal in-plane force tuning the excitation energy, allows also predicting the mechanical sensitivity of the chromophore, i.e. the maximum change in the excitation energy per force unit. As can be seen in Figure 2b, the maximum absorption wavelengths for S0→S1 and S0→S11 can be tuned with a ratio -1 of ca. 1.5 kcal·mol /nN while the S0→S4 band responds to the external force with a ratio of ca. 1.0 kcal·mol 1 /nN, showing therefore less in-plane sensitivity than the other two bands. Moreover, the in-plane response of the excitation energy to the external forces is somehow modest, considering that 2nN can be considered an upper limit for the applied forces range. Therefore, it is not possible to have a relevant control of the three excitation energies by exerting in-plane forces, since taking into account this upper limit for the force magnitude, the largest possible variation of the absorption

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wavelength is ca. 10nm for S0→S1, and 6nm for both S0→S4 and S0→S11 bands.

previously (Figure 2). Moreover it can be seen that simple force pairs reduce the optimal response of the excitation energy up to ca. 0.53, 0.41 and 0.59 kcal/mol for S0→S1, S0→S4 and S0→S11 respectively. -0.53

S0 → S 1

0.29

-0.41

S0 → S4

0.19

-0.59

S0 → S11

0.36

S0 S1

S0 S4

S0 S11

3 2

-1

Eexc (kcal·mol )

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


1

S0SS1→ - S11 S0 → 0 S0 → S S0S4→- SS44 S0 → S110 -S S0S→ S11 11 0

0.53 (kcal/mol)/nN

0 -1 -2 -3 0.0

0.5

1.0 |F| (nN)

1.5

2.0

Figure 2. a) Optimal displacement vectors for each studied transition of pyrene spectrum (vectors decreasing ∆Eexc are displayed, being equal but opposite to those that increase ∆Eexc). On the right the corresponding qualitative structural modifications are shown. b) Vertical excitation energy variation as a function of the obtained optimal force (calculated using Eq. 6).

Even though the response of excitation energy to external in-plane forces is low, it may be interesting to analyze the most efficient force pairs tuning this property. Force pairs are a common way to induce strain into a molecule (e.g. by means of including it into a polymer chain). Therefore, identification of the most efficient force pairs should provide valuable information in the design of new mechanoresponsive materials. In this regard, using quadratic approximations for the ground and excited state PESs and following a 23 formalism previously developed, we have computed all the possible force pairs and their corresponding effect on the excitation energy for each active transition. The results are shown in Figure 3, where it can be confirmed that the most efficient force pair patterns are in agreement with the most efficient forces found

0.41 (kcal/mol)/nN

0.59 (kcal/mol)/nN

Figure 3. Excitation energy variation matrix for each possible force pair (i.e. applied in each pair of carbon atoms) in pyrene for the three existing bright transitions. Each square of the matrix (row index “i” and column index “j”) corresponds to the variation of the energy gap (numerical values are displayed with a color-scale) when the force pairs are applied in the carbon atom “i” and “j”. The highest response is marked in the corresponding matrix with circles (two circles define a force pair) and the corresponding vector is shown below with arrows in the pyrene model. Note that there is an equivalent matrix for each transition (not shown in the figure) when we consider compressing pair of forces. Their elements are equal -1 in magnitude but with opposite sign (e.g. -0.53 kcal·mol /nN in the S0→S1 transition achieved with the force vector shown -1 in the figure, becomes +0.53 kcal·mol /nN for equivalent vector but with opposite direction, i.e. compression force).

The developed formalism also permits to study the mechanical response of energy absorption band separation. To this end, we analyzed the results for the energy differences between all the possible combinations of excited states. Thus, Figure 4a shows the optimal mechanically induced structural displacements modifying the band separation between each pair of transitions. As it can be seen from inspection of displacement vectors, the energy separation between two states involves a more complex contribution of all the atoms. Moreover, it is found that all the displacement vectors are quite similar for each pair of bands. This qualitative result implies that it would not be possible to change the separation between a given pair of bands without affecting another pair. Also, it is worth noting that the mechanical sensitivity to in-plane forces for separating each pair of bands is higher than it is for individual bands (Figures 2b and 4b). This means that in principle, with in-plane forces,

5


Journal of Chemical Theory and Computation it is more feasible the energy band separation tuning than absorption energy tuning. Figure 4b shows that the mechanically induced separation between S0→S1 and S0→S11 (i.e. S1-S11 energy difference) is tuned with a -1 maximum ratio of ca. 2.3 kcal·mol /nN, on the other hand, S4-S11, and S1-S4 band separation energy has a -1 -1 mechanical response of ca. 1.3 kcal·mol nN in both cases.

a)

magnitude. It has to be noted that for all the out-ofplane forces, there is a previous in-plane distortion given by the branching point where the in-plane and out-of-plane curves bifurcate, otherwise, the direct application of the out-of-plane force is not optimal. This come from the fact that Eqs. 6 and 7 are coupled and therefore the optimal forces have both components: in-plane and out-of-plane. Nevertheless, for the most efficient out-of-plane forces the corresponding in-plane component of the distortion is almost vanishing in comparison to the out-of-plane counterpart (Figure 5).

S1-S11 S4-S11

-1

84

0.5

1.0

1.5

2.0

80

Figure 5 shows the out-of-plane optimal forces that allow for the most efficient control of the excitation energy for each transition. The in-plane variation of the energy gap as a function of the force magnitude previously described (Figure 2b) is represented with black lines, whereas the colored lines show the out-ofplane variation obtained with Eq. 7. The out-of-plane distortions induced by the optimal forces are also shown in Figure 5 along with the energy-gap response of the different excitations as a function of the force

0.5

S0 → S4

1.0 1.5 FS0 (nN)

2.0

2.5

v6 (S0 → S1)

104

v3

102

v1

100

126 -1

0.0

0.0

0.5

v8 v6 v4 v5 v7

v2 1.0 1.5 FS0 (nN)

2.0

v1 (S0 → S4), v1 (S0 → S11)

2.5

S0 → S11

v2 (S0 → S1), v2 (S0 → S4), v2 (S0 → S11)

124 122 120 118

v2

116

v1

114 0.0

Out-of-plane external forces. The eigenvalue problem of Eq. 7 can be solved in order to find the out-of-plane forces and distortions that optimally control the energy gap separation between two states. Each out-ofplane force is found when the eigenvalues and eigenvectors of the corresponding C1 submatrix given in Eq. 7 are determined. The Lagrange multiplier obtained on Eq. 7 for a given particular eigenvalue determines the in-plane forces according to Eq. 5. Therefore, the complete set of optimal forces (i.e. in-plane and out-ofplane contributions) are established.

v5

v2

106

128 Eexc (kcal·mol )

Figure 4. a) Optimal displacement vectors for tuning separation between each pair of bands. b) Frank-Condon energy difference between excited states as a function of the optimal force, providing the separation energy between the two bands (e.g. S1-S4 indicates the separation between S0→S1 and S0→S4 bands).

v3 v4

v1

78

98

|F| (nN)

v1 (S0 → S1)

82

108

0.0

v6

S0 → S1

86

76

-1

-1

S1-S4


b)

S4 – S11

S1 – S11

S1 – S4 5 4 3 2 1 0 -1 -2 -3 -4 -5


88

E (kcal·mol )

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

Page 6 of 13

0.5

1.0 1.5 FS0 (nN)

v7 v3 v4 v6 v5 2.0

2.5

v3 (S0 → S1), v4 (S0 → S4), v4 (S0 → S11)

Figure 5. Left column: the corresponding electronic transition between S0 and the rest of the states (S1, top; S4, middle; S11, bottom), where the black line indicates the in-plane contribution to F and ΔE properties, and the colored lines the out-of-plane component with their own sensitivities. Right column: the most relevant out-of-plane distortions for the three transitions induced by the corresponding vectors “v” (see Supporting Information for other distortions).

Most of the out-of-plane forces only permit the reduction of the excitation energy. Only in the case of S0→S1 transition it has been found a distortion permitting the increase of the excitation energy. Therefore, in the case of pyrene, it is apparent that mechanical blue-shift of excitation energies is almost limited to the less efficient in-plane forces. The most efficient vectors for reducing the energy gap in the three cases (v1 vector in Figure 5) is related to simple bending of the molecular plane. Concretely, the distortions are basically characterized by the transverse (short C2 axis, Figure 1) in the case of S0→S1 exci-

6


The energy gap response is represented in Figure 6 along with the main structural distortions modifying (increasing and decreasing) the energy difference between each band. Similarly to the in-plane case, the structural distortions become more complex in the case of energy difference between two bands than in the case of excitation energy modulation. Additionally, several ways to increase and decrease the energy difference between bands are possible. There are two main distortions induced mechanically that can be highlighted in this case. On the one hand, the longitudinal (large C2 axis) distortion (related to v1, see Figure 6) is responsible for the reduction of the energy differences between all the bands. On the contrary, a bowltype distortion is responsible for the most efficient energy increase between bands (see Figure 6).

22

50

v7 -1

v6

20

v1

18 16 14

0.0

0.5

22

1.0 1.5 (nN) F|F| S0

2.0

2.5

v5

v4

v3

20

v5 v4 v3

v2

S1 – S4

ES1-S11 (kcal·mol )

24 -1

The same behavior was found for band separations. The out-of-plane distortions can modulate the energy gap more efficiently than the in-plane counterpart. In all the studied cases, there are out-of-plane distortions which can increase or decrease the band separation, and their corresponding response to mechanical stimulus are larger than the in-plane forces. This outof-plane response of the excitation energy (or energy band separation) is ultimately due to the significant flexibility of the chromophore, together with the fact that one or several low-frequency coordinates permitting this flexibility also provoke a large variation of the energy difference between the two electronic states.

In this way, the obtained optimal displacement vectors (i.e. structural changes that modify the oscillator strength more efficiently, given by Eq. 9) are shown in Figure 7a. Following this, in the right-side of Figure 7a the structural modifications that should be induced mechanically to modify the oscillator strength (i.e. intensity) are shown for a given transition. Each one of these structural changes defines the corresponding mechanical sensibility of the oscillator strength (Figure 7b). Interestingly, the S0→S11 band shows higher sensi-1 tivity (ca. 0.062 nN ) than the remaining two bands -1 (ca. 0.013 – 0.023 nN ).


tation, and a mixture of longitudinal (large C2 axis) and transverse distortions in the case of S0→S4 and S0→S11 excitations. The out-of-plane forces increasing the energy gap are restricted to the S0→S1 excitation and are characterized by longitudinal distortions (see Figure 5).

-1

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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v6

45

v5

v7

40 35 30 25

v2 S1 – S11 0.0

0.5

v4 v3

v1 1.0 1.5 F |F| (nN) S0

2.0

2.5

18 16

v1

14

v2

12 10 8

v1 (S1 – S4), v1 (S1 – S11), v1 (S4 – S11)

S4 – S11 0.0

0.5

1.0 1.5 FS0(nN) (nN) |F|

2.0

2.5

v6 (S1 – S4), v5 (S1 – S11), v3 (S4 – S11)

Figure 6. The corresponding band separation (ΔE) between S1 and S4 (top-left), S1 and S11 (top-right), S4 and S11 (bottomleft). Black lines indicate the ΔE with in-plane forces, and the colored lines the corresponding out-of-plane forces. Bottomright: the most efficient force induced out-of-plane distortions in changing the band separation energy. See Supporting Information for other distortions.

3.3. Mechanical tuning of the band intensity. It is well known that band intensity can be expressed in terms of the oscillator strength, f (which is close to unity for an intense band), for the respective electronic transition. In this context, the developed methodology was applied in order to find the optimal forces for tuning band intensities. As stated above, a first order approximation is employed for f, which proved to be accurate in the studied force range, up to 2nN (see Supporting Information for further details). In order to do this, numerical oscillator strength gradients were computed for the three different transitions (see Supporting Information for further details). Following a similar procedure to the one described in the previous subsection, Eq. 10 is used to obtain the optimal forces for tuning the intensity of a given band.

7



(Fig. 8A) and in-plane forces (Fig. 8B) controlling the S0→S1 excitation energy. As has been argued, it is apparent that in-plane forces do not significantly affect the absorption spectrum, while out-of-plane forces have a relevant impact on it.

A

S0 S4 ε (L·mol-1·cm-1)

S0 S11

B

261

30000

232

25000 20000

312

404

15000

340 272

10000 5000

20000

342

340 272

10000

0.8

0.6

0.6

0.4 0.2 0.0

0.06 0.04

-S SS 0→ 0 S11 SS S44 -S 0→ 0 SS S11 S 0→ 11 0

272

15000

1.0

0.8

F(nN)

b)

232

25000

5000

1.0

0.08

232

30000

ε (L·mol-1·cm-1)

S0 S1

500

450

400

350

λ(nm)

300

250

200

F(nN)

0.4 0.2 0.0

500

450

400

350

300

250

200

λ(nm)

Figure 8. Mechanically affected absorption spectrum of pyrene when the applied force is defined by (A) v1 vector for the S0→S1 transition (see Figure 5) and by (B) S0→S1 most efficient force pairs (see Figure 3). The molar absorptivity is plotted as a function of the wavelength (nm) and the applied force magnitude (in nN) including the single deconvoluted bands. Maximum wavelength for 0.0 nN and 1.0 nN are numerically indicated for each band.

0.02

f

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

Page 8 of 13

0.00 -0.02 -0.04 -0.06 -0.08 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

|F| (nN)

Figure 7. a) Predicted optimal displacement vectors tuning the oscillator strength (i.e. band intensity) to higher, or lower values. b) Oscillator strength variation with respect to the predicted optimal force modulus (calculated using Eq. 10).

3.4. Pyrene absorption spectra under mechanical stress. With all the previous results in mind, we can establish some general trends in the mechanical response of the pyrene absorption spectrum. (i) In-plane forces are much less efficient in tuning both, excitation energy and energy difference between two bands. (ii) There is a relatively modest tuning of the oscillator strength with in-plane forces, although differentiated for each transition. (iii) The optimal outof-plane mechanically induced distortions for tuning the excitation energy as well as the band separation are almost restricted to three type of distortions: the longitudinal and transverse (around the two in-plane C2 axis) bending and a bowl-type distortion. From the quantitative information obtained of the mechanically affected pyrene absorption spectrum, it is possible to construct the bidimensional absorption spectrum (i.e. molar absorptivity as a function of two variables: the wavelength and the magnitude of the applied force). There is one bidimensional spectrum for each considered force type. Figure 8 shows those spectra for the most efficient out-of-plane force pair

In order to go to specific real molecular systems with specific tuned absorption spectrum, in the following we introduce new pyrene derivate systems where forces are included via force probes. Moreover, since inplane forces are much less efficient that out-of-plane forces, we will focus on the design of derivatives presenting out-of-plane distortions induced by same type of forces.

3.5. Pyrene absorption spectra using molecular force probes. It has been shown that using the developed methodology it is possible to understand the mechanical response of the absorption spectrum of pyrene in terms of in-plane and out-of-plane external forces. This information becomes extremely useful for molecular design purposes as it provides a guide for straining the chromophore using different strategies as its inclusion in a polymer matrix or by adding a force probe (i.e. a strained molecular fragment, usually cyclic chain). While in the case of polymer stretching, the exerted forces are basically restricted to in-plane type, molecular force probes are mostly dominated by outof-plane forces. We have followed the latter strategy, i.e. tuning the absorption spectrum of pyrene by straining the chromophore by means of molecular force probes. In order to define specifically what kind of molecular probes

8


would be explored as well as their linking positions, we have tried to mimic the most efficient out-of-plane distortions found in previous sections, i.e. vectors v1, v2 and v3 corresponding to S0→S1 transition (see Figure 5). These vectors provide the larger response of the excitation energy for a given mechanical force magnitude (see Figure 5). Since v1, v2 and v3 correspond to out-of-plane distortions reducing the excitation energy in all the three bright transitions, the designed strained pyrene systems are expected to present redshifted absorption bands. It has to be noted that for pyrene we are focusing on rationally design strained pyrenes with force probes modifying the excitation energies for different transitions and studying the response of the rest of the properties. Nevertheless, other approaches could be investigated as, for instance, the variation of a specific band separation energy, which falls out of the scope of the present case study. According to this choice, it is possible now to define more precisely the proposed systems in order to imitate the distortions given by v1, v2 and v3. To conform the molecular force probes we have chosen aliphatic carbon chains of variable length (see Figure 9). This choice is based on two main reasons: i) the simple chemical structure of the probes and ii) in most cases experimental absorption spectra are available for these systems, making possible to verify the theoretical predictions. More in detail, all the force probes studied are attached (head and tail of the chain) to pyrene in two single centers, corresponding to positions (see Figure 1 for numbering) 2-7 where oxygen atoms are the linkers (A in Figure 9), and positions 2-7, 1-8 and 16 where the aliphatic chain is directly linked to pyrene (B, C and D respectively in Figure 9).

strained systems (see Figure 9). Concretely, 2-7 linking would correspond to v1, and 1-6 type to v2, while the more complex 1-8 would be related mainly to a combination of v1 and v3 for S0→S1 transition and v1 and v4 for the other two transitions. In addition, in the specific case of S0→S1 transition for 2-7 linking, v6 deformation seems to have also some minor contribution (Figure 5). The calculated spectra of the designed systems A, B, C and D (Figure 9), are summarized in Figure 10, where the maximum absorption wavelength is plotted against the available experimental data, showing a good agreement between theoretical and experimental val25-27,30 ues. In order to understand the effect of the chain length in the absorption spectrum, it is necessary to determine the strength and nature of the forces exerted by each molecular force probe. These forces have been computed by removing the aliphatic chain on the optimized structure and evaluating the force pairs on each carbon atom after adding a relaxed hydrogen atom saturating the linking positions (see Supporting Information for further details). The analysis of the forces shows that the shorter the chain length the larger the exerted force as it would be expected. This is also apparent from the pyrene structure linked to molecular force probes, which presents larger out-of-plane deformation for shorter chain lengths. An (S0-S1)

360

An (S0-S4) An (S0-S11)

340 320 300

S0-S11

Bn (S0-S11) C8 (S0-S1)

O (CH2)n

(CH2)n

An

Bn

(CH2)n

Cn

260

Figure 9. From left to right, the different pyrene derivatives with force probes corresponding to different linking points: 2-7 linking positions (numbering according to Figure 1) with oxygen atoms as linkers (A set of compounds), 2-7, 1-8 and 16 with aliphatic chain directly linked (B, C and D families of compounds respectively). The subscript n denotes the number of CH2 units. The studied systems are An=5,..,10, Bn=5,..,8, Cn=5,..,8, and Dn=5,..,8.

By simple inspection of vectors v1, v2 and v3 (see Figure 5) it is clear that their corresponding out-of-plane distortions are similar to those obtained in the proposed

288

279

270

B A A7 7 A5(S0-S11) 8 D8 A10 C8 A9 P B5(S0-S11) 276

240

260

280

300

320

282

exp (nm)

340

C8 (S0-S4)

An (S0-S1) An (S0-S4)

D8 (S0-S1)

An (S0-S11) Bn (S0-S1) Bn (S0-S4)

D8 (S0-S4)

Bn (S0-S11)

C10 (S0-S1) C10 (S0-S4)

P (S0-S1)

D10 (S0-S1) D10 (S0-S4) P (S0-S1) P (S0-S4)

P (S0-S4)

P (S0-S11)

288

P (S0-S11)

360

exp (nm)

(CH2)n

Dn

B6

S0-S4

240 O

Bn (S0-S4)

S0-S4

280

220

Bn (S0-S1)

S0-S1

TD-DFT (nm)

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


TD-DFT (nm)

Page 9 of 13

Figure 10. Theoretically predicted maximum absorption wavelength for each allowed transition versus experimental values. The included data correspond to transitions (S0→S1, S0→S4 and S0→S11) for the systems A (A5,…A10), B (B5..B7), C8, D8 and pyrene (P) for which experimental data are available.

First, the variation of the excitation energy with exerted force for each transition (Figure 11, left column) goes in line with the predictions made for the isolated pyrene analysis (Figure 5) indicating that 2-7 linking (v1 distortion) corresponding to A and B derivatives, is the most efficient in reducing the excitation energy except for transition S0→S1 as will be later discussed. The 1-6 linking (v2 distortion) corresponding to D derivatives is

9


Journal of Chemical Theory and Computation the next in efficiency, while 1-8 linking (combination of v1 and v3) corresponding to C derivatives, present a similar efficiency than 1-6 (Figure 11). 1 -1

-1

n=5

-2

An

-3

Dn

-4

Cn

-5 1.5

2.0

2.5 |F| (nN)

3.0

3.5

-2 -3 -4

ip

An

ip

Dn

ip

Cn

oop

An

oop

Dn

n=5

oop

Cn

1.0

1.5

2.0 2.5 |F| (nN)

0 -1

-2

n=5

-3 -4

An

-5

Dn

-6

Cn 1.5

2.0

0

2.5 |F| (nN)

3.0

3.5

0 -2 -4 -6 -8 -10 -12 -14 -16 0.5

-1

-6

An

-10 -12

Dn

-14

Cn 1.5

2.0

n=5

2.5 |F| (nN)

3.0

-6 -8 0.5

-4 -8

-4

An

ip Dn ip Cn oop An oop Dn oop Cn

1.0

3.0

3.5

ip

ip

-2

3.5

-2

-16

-1

0.5

-1

-7

ip

0

-5

ES0-S4 (kcal·mol )

-1


0

-1


0


-1


1


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

n=5 1.5

ip

An

2.0 2.5 |F| (nN)

3.0

3.5

3.0

3.5

ip

ip

Dn

ip

Cn

oop

An

oop

n=5

Dn

oop

Cn

1.0

1.5

2.0 2.5 |F| (nN)

Figure 11. In the left column the variation of the energy gap for the three bright states (S0→S1, S0→S4 and S0→S11 transitions) is plotted as a function of the molecular probe exerted force for the three different linking positions. The right column displays the decomposed contributions (in-plane and out-of-plane, denoted with superscript “ip” and “oop” respectively) of each kind of distortions to the energy gap variation. The strain (force) decreases from n=5 (indicated in the figure) to larger values of n (see Figure 9 caption for numbering).

These results go in line with the fact that out-of-plane distortions are dominant against in-plane distortions. Nevertheless, 2-7 linking for S0→S1 transition is an exception in this behavior, as previously noted. Contrary to expected, the excitation energy is blue-shifted for increasing strains. At a first sight, the S0→S1 v6 outof-plane distortion which increases the excitation energy and that is not present for any other transition, could be responsible for mixing with v1 and making the energy gap to finally increase with increasing forces. Nevertheless, this exception merits a deeper analysis. By computing the stretching/bending and torsional contributions separately, i.e. in-plane and out-of-plane force components (see Supporting information for details), it is possible to decompose the contribution of in-plane and out-of-plane distortions to the total variation of the excitation energy as a function of the force exerted by the molecular probe (Figure 11 right col-

Page 10 of 13

umn). For all the situations (i.e. for the three different probes and the three different transitions), the out-ofplane distortions are dominant in comparison to inplane distortions. In fact, the contribution of the inplane distortions to the absorption spectrum shift is always less than 1 kcal/mol while out-of-plane contributions reach maximum values close to 15 kcal/mol, and remains always higher than the in-plane counterpart. This is the general behavior except for the case of 2-7 linking in the S0→S1 transition. In this case, the out-of-plane distortion in fact reduces the energy gap slightly, but the in-plane contribution increases the excitation energy and is higher than out-of-plane counterpart, making the net effect to slightly increase the energy gap with increasing force. From the analysis of the response of pyrene absorption spectrum to mechanical forces, it is therefore possible to get a valuable knowledge of what kind of forces would permit such an optimal tuning. In fact, qualitative distortions obtained from this analysis (Figure 5) have permitted to design the corresponding force probes linked to pyrene (Figure 9) qualitatively obtaining the predicted trend. In any case, there is room for a finer design of molecular force probes, anyway guided by the general results obtained by the methodology developed in this work.

4. CONCLUSIONS. We have developed a formalism for computational identification of the optimal forces controlling the absorption spectrum of a chromophore (i.e. the highest possible response of absorption wavelength and molar absorptivity with the lowest possible mechanical force magnitude), including the absolute excitation energy and oscillator strength of each band, as well as the relative energy separation between two bands. The methodology has been applied to the study of the pyrene absorption spectrum and its modulation by external forces induced by different molecular force probes. Regarding the excitation energy tuning in pyrene, it has been found that in-plane distortions have a minor role in controlling the excitation energy, while out-ofplane forces are very efficient in decreasing this energy. On the contrary, increasing the excitation energy of the three considered bands is only possible with inplane forces except for S0→S1 transition, where an outof-plane distortion increases the gap. On the other hand, energy difference between two bands has been also analyzed, showing that in-plane forces are still modest in comparison with the tuning capability of out-of-plane forces. Two main mechani-

10


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cally induced distortions are able to increase or decrease the energy difference between two bands, a longitudinal torsion and a bowl-type distortion respectively. Additionally, the oscillator strength for each transition has a relatively small response to in-plane forces reach-1 ing a maximum ratio of ca. 0.06 nN . Once the proposed methodology was applied to analyze the mechanical response of the chromophore to external forces, the obtained information has guided the molecular design of new pyrene derivatives. Specifically, several force probes (aliphatic oligomers) have been rationally introduced in the chromophore in order to mimic the already identified optimal forces tuning the absorption spectrum. Qualitatively, the expected changes in the absorption spectrum predicted by the theoretical analysis have been confirmed for the different designed systems for which available experimental data shows a good agreement with computational results. The developed methodology may provide relevant information regarding the molecular design of mechanically stressed chromophores, permitting the computationally guided design of strained chromophores with tuned absorption spectra, avoiding a tryand-error computational strategy in favor of a rational molecular design.

ASSOCIATED CONTENT Supporting Information. Computational details and TDDFT calibration with experimental data. Determination of the numerical oscillator strength gradient vectors. Derivation of the optimal external forces using second-order PES approximation. Electronic Nature of the Vertical Excitations of Pyrene. Validation of the second-order PES approach. Outof-plane motions controlling the energy difference between states. Procedure for the determination of the mechanical forces exerted by the molecular force probes. Decomposition of in-plane and out-of-plane contributions to the total force exerted by the molecular force probes studied. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author * E-mail: [email protected]

Author Contributions ‡These authors contributed equally.

Funding Sources

This research was supported by the Spanish MIENCO (grants CTQ2012-36966, CTQ2014-59650-P and CTQ2016-80600-P) and UAH (Universidad de Alcalá) grant CCG2014/EXP-083.

ACKNOWLEDGMENT D.R. and M.A.F.-G., are grateful to the UAH and Spanish Ministerio de Educación y Ciencia (MEC) for a doctoral fellowship. C.G.-I. acknowledges MEC for a doctoral fellowship.

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25. Yoshinaga, T.; Hiratsuka, H.; Tanizaki, Y. Bull. Chem. Soc. Jpn. 1977, 50, 3096-3102. 26. Bodwell, G. J.; Bridson, J. N.; Cyrañski, M. K.; Kennedy, J. W.; Krygowski, T. M.; Mannion, M. R.; Miller, D. O. J. Org. Chem. 2003, 68, 2089-2098. 27. Clar, E. Spectrochimica Acta 1950, 4, 116-121. 28. (a) Parac, M.; Grimme, S. Chem. Phys. 2003, 292, 1121; (b) Örücü, H.; Acar, N. Comp. Theor. Chem. 2015, 1056, 1118; (c) Sharif, M.; Reimann, S.; Wittler, K.; Knöpke, L. R.; Surkus, A. E.; Roth, C.; Villinger, A.; Ludwig, R.; Langer, P. Eur. J. Org. Chem. 2011, 2011, 5261-5271. 29. Yanai, T.; Tew, D. P.; Handy, N. C. Chem. Phys. Lett. 2004, 393, 51-57. 30. Yang, Y.; Mannion, M. R.; Dawe, L. N.; Kraml, C. M.; Pascal Jr, R. A.; Bodwell, G. J. J. Org. Chem., 2012, 77, 57.

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KEYWORDS. Mechanochemistry, Mechano-photochemistry, absorption spectra tuning, molecular force probes, pyrene absorption spectrum.

30000

ε (L·mol-1·cm-1)

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


25000 20000 15000 10000 5000

Fext

1.0

Fext

0.8 0.6

F(nN)

0.4 0.2 0.0

500

450

400

350

300

250

200

λ(nm)

13


Mechanochemical Tuning of Pyrene Absorption Spectrum Using Force

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