Tuning ultrafast time‐evolution of photo‐induced charge‐transfer states: A real‐time electronic dynamics study in substituted indenotetracene derivatives

Photo‐induced charge transfer (CT) states are pivotal in many technological and biological processes. A deeper knowledge of such states is mandatory for modeling the charge migration dynamics. Real‐time time‐dependent density functional theory (RT‐TD‐DFT) electronic dynamics simulations are employed to explicitly observe the electronic density time‐evolution upon photo‐excitation. Asymmetrically substituted indenotetracene molecules, given their potential application as n‐type semiconductors in organic photovoltaic materials, are here investigated. Effects of substituents with different electron‐donating characters are analyzed in terms of the overall electronic energy spacing and resulting ultrafast CT dynamics through linear response (LR‐)TD‐DFT and RT‐TD‐DFT based approaches. The combination of the computational techniques here employed provided direct access to the electronic density reorganization in time and to its spatial and rational representation in terms of molecular orbital occupation time evolution. Such results can be exploited to design peculiar directional charge dynamics, crucial when photoactive materials are used for light‐harvesting applications.

In particular, in this article, we focus on the capability of RT-TD-DFT in describing, simulating and interpreting on the molecular scale the ultrafast charge recombination, and more in general photo-induced charge dynamics of photo-active molecules that have large potential in organic photovoltaic (OPV) applications.It is, indeed, necessary to acquire a deeper understanding of photo-induced ultrafast CT dynamics to have full control of the molecular processes underlying their functioning.[37] Their peculiar and electronic properties derive from the possibility of using a very large range of differently functionalized molecules to modify the temporal evolution of the electronic charge and to simplify the modeling and the fine tuning of the: (i) electronic layout (i.e., the energy displacement and character of the electronic states), (ii) bad-gap, (iii) crystalline structure, (iv) solubility, (v) photo-stability.In recent years, research has put efforts to boost OPV performances by exploiting also the creation of multiexcitons (a bound coupled excited electron and an associated hole) generation from single photon absorption.A wellknown photophysical process which typically occurs in crystalline materials, [38][39][40][41][42][43][44] known as singlet fission, 36,45,46 can come in handy in this field.Concerning the photophysical pathway, singlet fission is a spinallowed phenomenon that involves at least two chromophoric units, but experimental and theoretical evidence concerning single molecules, such as carotenoids [47][48][49][50] and oligomers, 36,[51][52][53] have been collected in the recent years.
The model systems investigated belong to the class of alternant hydrocarbons, promising as n-type compounds which can exploit photoinduced CT states to potentially undergo also singlet fission.We investigated photoinduced CT states of recently introduced asymmetrically substituted indenotetracene (ASI) molecules, which have been proposed to replace fullerene in OPV devices. 54,55The cases study are two substituted diarylindenotetracene molecules bearing two methyls side of the indenotetracene scaffold, as reported in Figure 1.These systems have been previously synthesized and their optical absorption and electrochemistry have been characterized as well, as promising candidates for singlet fission applications. 54[62][63][64][65][66][67][68][69] While in the actual device multiple monomeric units are arranged in a crystal or semicrystal manner, the characterization of the excited states and their ultrafast dynamics in the monomeric units is the first mandatory and crucial step to understand CT dynamics in the ultrafast time scale of the photoactive material.In this respect, an accurate ab initio modeling strategy is required to understand the ultrafast photoinduced temporal evolution of the electronic density and to rationalize the effects induced by different functional groups.
To this aim, we first exploit linear response TD-DFT (LR-TD-DFT) formalism to characterize excitation energies and spacing among electronic levels (the electronic layouts).Then, to understand the ultrafast (subpicosecond) charge dynamics on the molecular scale, we rely on the non-perturbative mean-field quantum ED via real-time timedependent density functional theory.RT-TD-DFT has been vastly employed in the past to model charge transfer and excitation dynamics directly and precisely in several donor-acceptor systems 15,17,64,[70][71][72] and to provide the molecular interpretation of the interaction between initial photoexcited states, 16,17,34,63,[73][74][75][76] exciton and polaron formation, 64,[77][78][79][80] including relativistic effects. 81,82e nature of the energy shift for several electronic transitions was unveiled by correlating the electron-donor properties of the substituent with the spatial distribution of the molecular orbitals (MOs) and their dynamical involvement in the CT.Larger effects of the substituents were noticed in the electronic layout of the CT transitions, where the effect of the methoxy group resulting in a shifting of the charge transfer transition at lower energy values for the methoxy-if compared to the Methyl ASI.
ED simulations revealed that is clear that the substituent has a role in the directionality of the recombination dynamics in the ultrafast regime (i.e., the Methoxy ASI shows a more complex and directional behavior while the methyl shows a quite symmetric rearrangement).Such results

METHYL ASI METHOXY ASI
F I G U R E 1 Ball and stick representations of the Methoxy ASI (left) and Methyl ASI (right) systems.Oxygen in red, hydrogen in white, and carbon in gray.can be used as grounds to design peculiar photo-active materials, employed for light-harvesting applications.

| METHODOLOGY
The crystallographic structures of both Methoxy ASI and Methyl ASI were retrieved from Reference 54 and then atomic positions of the monomeric units were refined by gas-phase geometry optimization.

| Excited state layout via linear response (LR-) TD-DFT
Vertical excitation energies and oscillator strengths are obtained by relying on methods rooted in time-dependent DFT in the linear response formalism (LR-TD-DFT), 23,25,30 using B3LYP with the Coulomb-attenuating approach (CAM-B3LYP) with 6-31g(d,p) basis set.8][119][120] In this work, we focused on the first four singlet excited states for both the Methoxy ASI and Methyl ASI to better understand the role of the substituent on the most experimentally relevant transitions and the resulting electronic layout ruling the photophysics of these systems.This preliminary characterization is mandatory for investigating the photo-induced charge dynamics described by real-time ED, as explained in the following section.

| Ultrafast electronic dynamics via real-time (RT-)TD-DFT
The real-time time-dependent DFT approach to many-electron dynamics has been proven to be very powerful in describing, simulating, and interpreting on the molecular scale the ultrafast charge recombination and, more in general, photo-induced charge phenomena, since via real-time methods we can explicitly propagate in time the electronic density by evolving the time-dependent Schrödinger equation. 20,21Herein, we present a brief description of the technique.
Given an initial condition, the electronic density matrix is propagated according to the TD-DFT equation, reported here, in atomic units.
where P and K are density and Kohn-Sham matrices on an orthonormal basis.By the use of a modified midpoint unitary transformation algorithm, 74,121 Equation ( 1) is numerically integrated.The density matrix is propagated by exploiting a unitary time evolution opera- to obtain the time evolution operator, given a time step as Δt: where eigenvectors Cðt n Þ and eigenvalues ϵðt n Þ are retrieved from the Kohn-Sham matrix at time t n .It must be emphasized that, since the nature of the wavefunction is precisely a superposition of relevant many-body states of the system like that observed immediately after the photo absorption, this dynamics is representative of the motion of a localized wave packet in a symplectic electronic parameter phase space. 121nce we are interested in the low-lying optically accessible states, we first characterize the Methoxy ASI and Methyl ASI electronic layout by performing LR-TD-DFT calculations, as discussed in the result section.To perform RT-TD-DFT ED, the initial electronic density to propagate is prepared, promoting an electron from a selected occupied MO to an unoccupied one ("Koopman excitation"-orbital population swap) according to the electronic transition of interest between the singlet ground state (S 0 ) and the nth singlet excited state (S n ), whose main orbital contributions are resolved using preliminary frequency domain LR-TD-DFT calculations.According to a well-established procedure, the "Koopman excitation" step creates a non-stationary electron density that is representative of a coherent superposition of the ground and excited states of interest. 21,62,64,80,122Since we are not allowing the nuclei to move (fixed nuclei approximation, by starting from a minimum geometry), this procedure can be used as a reasonable approximation of a vertical excitation in the Franck-Condon region in the ultrafast regime ( ≤ 50 fs).In such short simulated time, indeed, it could be assumed that the effect of nuclear vibrations is still limited.Therefore, the "fixed nuclei" approximation implied in these purely ED is reasonable.
To better characterize the excited state time evolution, the electronic density in orthonormal basis is transformed back in atomic orbital (AO) basis by the Löwdin scheme, and the time-dependent density in this AO basis, P 0 ðtÞ, is projected into the ground state MO space giving: where n i is the effective occupation number of the ground state orbital C 0 i ð0Þ in the AO basis.The time-dependent dipole moment μðtÞ is also computed at each step from the following: where D' is the electric dipole momentum operator in AO basis.A 1.0 attosecond time step was used when integrating the TD-DFT equation of motion.All RT-TD-DFT calculations were performed with the same level of theory of LR-TD-DFT computations and employing a modified development version of Gaussian. 123| RESULTS AND DISCUSSION

| Electronic layout characterization
In the present work, the characterization of the low-lying electronic transitions via LR-TD-DFT calculations has been extended beyond the S 1 state (this last one was studied in details in Reference 54) by analyzing the higher energy singlet transitions to locate the lowest energy CT states.Thus, the effects of different substituents on the electronic layout and, above all, on higher energy states (important for photoinduced charge-dynamics) of the indenotetracene scaffold can be better understood.We now analyze the main differences in terms of MOs isosurfaces to emphasize the role of the substituents on the aforementioned transitions.First, a very close electronic density distribution is observed for both Methoxy ASI and Methyl ASI LUMOs.Consequently, the origin of the red-shift for the methoxy derivative requires the comparison of the HOMO and the HOMO-1 respectively for S 1 S 0 and the S 2 S 0 transitions.For the S 1 case, the main difference between the two HOMOs regards a larger electronic density rearrangement on the substituent group for the Methoxy ASI with respect to the Methyl ASI.
Since methoxy is a better electron-donor group and HOMO has a non-negligible isodensity on this moiety (while the LUMO has an almost null contribution on it), we can say that this tendency leans toward destabilizing the HOMO more for the Methoxy ASI with the subsequent larger decrease in the HOMO-LUMO energy gap, resulting in the observed red-shift.Such findings are in perfect agreement with the similar trend observed trough cyclic voltammetry measurements. 54The S 2 S 0 transition involves the HOMO-1 that shows a different nature for the Methyl ASI case, where it is more delocalized also on the entire indenotetracene scaffold as in the LUMO, while for the Methoxy ASI, the substituent region plays a larger role in percentage.Such a difference can explain (i) the different nature of these transitions, still alternating bond for Methyl ASI (as for the first one) and CT for Methoxy ASI (different from the first one), (ii) the larger red-shift observed with respect to the S 1 S 0 , given the HOMO-1 of  ASI and Methyl ASI, the S 3 S 0 transition can be considered slightly allowed (f=0.069 and 0.073, respectively) and almost similar in excitation energy (À0.01 eV from Methyl ASI to Methoxy ASI), their character can be expressed by two very similar hole-electronNTOs pairs (see Figure 3, bottom panel).Regarding the NTO pair with the highest contribution ($0.7), in both cases, the hole is delocalized along the entire indenotetracene scaffold with a non-negligible contribution of all peripheral phenyl rings and oxygen lone pairs (both the sides of the scaffold).The electron NTO, instead, is less symmetrically distributed on the phenyl rings, thus, suggesting a CT nature for S 3 S 0 transition (from left to right in the figure) for both systems.In both cases, the hole-1 electron+1 pair (contribution to the transition $0.3) can be described by an alternating bond redistribution.
The S 4 S 0 transition can be conveniently represented by a single NTO pair (contribution to the transition close to 1.00) for both systems.This time in both derivatives the transition probability is very low (f < 0.001) and a marked red-shift of À0.25 eV is observed from the Methyl ASI to Methoxy ASI.In both cases, the hole is asymmetrically localized on one side of the system (mostly the two phenyl substituent groups on the left in Figure 3 and partially on the tetracene portion).Upon excitation, the density reorganizes towards the indenotetracene moiety (electron), revealing a strong CT character for this state.From this analysis, it is clear that the substituent plays a larger role in this transition, explaining the larger red-shift observed this time, since methoxy is a better electron-donor group and can more destabilize the hole.One interesting result is the role of different substituents in inducing changes to the indenotetracene electronic layout.
In particular, the substituent nature can affect the order of the first charge transfer transition, which is observed in the S 3 S 0 in the case of Methyl ASI while is the S 2 S 0 for the Methoxy ASI.
Similar substituent modulation of the electronic properties for other highly conjugated molecular systems used as dyes in dye-sensitized solar cells, mainly π linkers in triphenylamine, has also been predicted in previous studies. 126To have a deeper understanding of ultrafast CT dynamics we will examine the charge recombination dynamics through RT-TD-DFT electron dynamics and by focusing on the first optically active CT transitions just discussed, namely, the S 2 S 0 for the Methoxy ASI and the S 3 S 0 for the Methyl ASI, respectively.

| Electronic tuning effects of methyl and methoxy groups
Before moving to CT dynamics, we elucidate the relationship between the electron-donating ability of methyl and methoxy groups on the energy of MOs involved in the electronic transition reported in Table 1, please see Figure 4.The MOs eigenvalues of the two ASI dyes are compared to the unsubstituted homologue and are reported, along with their isodensity representations, in Table S1 and in Figure S1, respectively.
Concerning the S 1 S 0 transition, by direct comparison, the LUMO is more energetic than the non-substituted indenotetracene (0.07 eV for Methoxy ASI and 0.06 eV for Methyl ASI).The same energy difference (0.01 eV) is observed for the HOMO of methoxyand methyl-functionalized derivatives, which are, respectively, 0.08 and 0.07 eV above the HOMO of the unsubstituted molecule (À5.99 eV).The patterns found, in agreement with previous theoretical and experimental results, 54 are directly comparable with the orbital contours presented in Figure S1, which show to have similar contributions on the same atoms.We investigated the energetic alignment of the occupied orbitals just below HOMO given their crucial importance for photo-induce CT dynamics.It is important to underline that the occupied orbitals at lower energy present more marked energetic differences and better emphasize the degree of electron donation of the two substituents.
The HOMO-1 of Methoxy ASI and Methyl ASI is 0.31 and 0.11 eV above the orbital of the non-substituted indenotetracene (À6.85 eV).
Consequently, the observed redshift for the S 2 S 0 transition (0.12 eV) can be explained by assuming that the p-methoxyphenyl group provides electron density only to a portion of the indenotetracene, leading to a slight energetic destabilization of HOMO-1 since it is not completely delocalized as in the case of Methyl ASI.
Concerning HOMO-2 for diarylindenotetracene, the electronic density is distributed between the peripheral phenyl rings and the tetracene core (left panel of Figure S1), whereas for the two derivatives,

| Real-time TD-DFT electronic dynamics
Initial conditions for resembling the CT electronic transitions of interest are prepared according to the orbital swap procedure explained in the methods and by exploiting the results of the previous sections.
We focused here, given their potential role in light harvesting phenomena, on the lowest (in energy) charge transfer transitions from the ground to the S 3 for the Methyl ASI (initial state prepared as HOMO-3 to LUMO swap) and the S 2 for the Methoxy ASI (initial state prepared as HOMO-1 to LUMO swap) (see Table 1).We first analyze in Figure 5  In summary, the Methoxy ASI appears to have a multi-directional charge transfer dynamics while the Methyl ASI privileges the direction orthogonal to the indenotetracene scaffold and connecting the phenyl substituents (x direction in Figure 5).These results can be obtained only by directly observing the ED via RT simulations.This technique can provide direct access to the electronic density reorganization in time and to its spatial and rational representation in terms of MO occupation time evolution, indeed.

| CONCLUSIONS
A comprehensive study of photo-induced charge-transfer states as well as the dynamics of a transferring electron in time has been conducted.

Methoxy 68 F
ASI more localized in percentage on an electron-donating substituent; (iii) the dissimilarity in transitions brightness, given that the Methoxy ASI HOMO-1 has a different symmetry of the Methyl ASI HOMO-1, slightly allowing S 2 S 0 transition in the first case.Now we move to the higher energy transitions.For both S 3 S 0 and S 4 S 0 , multiple pairs of canonical MOs with comparable CI coefficients participate in defining the nature of these transitions.To provide an easier molecular picture, we computed natural transition orbitals (NTOs) 124 which have proved useful to better analyze and visualize the electronic redistribution in such cases in terms of a reduced number of hole-electron pairs (see Figure 3). 65,66,125A close inspection of Figure 3 reveals several differences between the starting hole NTOs for Methoxy ASI and Methyl ASI regarding both electronic transitions, showing interesting features due to the different involvements of the alkoxy and alkyl substituents, while negligible differences between the electron NTOs are observed, instead.Fort both Methoxy METHYL ASI METHOXY ASI F I G U R E 2 CAM-B3LYP/6-31G(d,p) isosurfaces (isovalue = 0.02) of the frontier MOs mainly responsible (see Table 1) in the S 2 S 0 (top) and S 1 S 0 (bottom) transitions of Methoxy ASI (left) and Methyl ASI (right).I G U R E 3 Isosurface (isovalue = 0.01) of NTOs.Hole/hole-1 and electron/electron+1 pairs for the S 3 S 0 (bottom) and S 4 S 0 (top) transitions calculated at the TD-CAM-B3LYP/6-31G(d,p) level of theory are reported for the Methoxy ASI (left) and Methyl ASI (right).The contribution to the transition of each NTO pair is shown on top of each arrow connecting them.
the tetracene is less involved (central and right panels of FigureS1in ESI).The higher degree of electron donation of the alkoxy group leads to a significant increase in energy (0.51 eV) compared to the Methyl ASI case (0.14 eV) and to the non-functionalized indenotetracene, whose HOMO-2 is at À7.60 eV.The negligible red-shift computed for the S 3 S 0 transition (0.01 eV) is in agreement if it is considered that the arrival electronic state is severely combined with other orbital pairs (see CI coefficients in TableS1), including LUMO+1 and LUMO +2 located at 0.57 and 0.75 eV for Methoxy ASI and 0.53 and 0.74 eV for Methyl ASI that thus align the resultant energy gaps.Two orbital pairs, HOMO-2-LUMO and HOMO-3-LUMO, characterize the nature of the S 4 S 0 electronic transition.Since for Methoxy ASI and Methyl ASI the isodensity of the target orbital is very similar, the observed red-shift (0.25 eV) may result from the mixing of HOMO-2 and HOMO-3 which have different energies.Specifically, for the HOMO-3 of the methyl derivative the electron density on the ring containing the -CH 3 group is responsible for the lower energy increase (0.02 eV) with respect to the Methoxy ASI case (À7.66 eV) for which the electronic density is mainly confined on the tetracene moiety.Given that materials based on photoactive indenotetracene scaffolds are also promising for photovoltaic devices in the field of solar cells, a detailed comprehension of the ultrafast photo-induced charge transfer dynamics on the molecular scale represent a key element for the development of improved materials to boost novel technological applications (Figure 4).

Figure 5 )Figure 6 .Figure 5 .
Figure5) shows immediately larger and larger oscillations, reaching its maximum value after $10 fs (μ x $ 5 D).These large amplitude oscillations are present for the entire ED until the end, but around a lower final average value (μ x $ 1.2 D).In contrast, the y component starts from a value similar to the ground state (μ y (t 0 ) $ À1.5 D) and we observe small oscillations until $ 10 fs of this component.After 10 fs, large amplitude oscillations are present also for μ y , as for the x component, and its final average value decreases, although in a smaller magnitude with respect to the final x one (final μ y $ À1 D).There is no Via real-time time-dependent density functional theory ED, a molecular picture of the ultrafast (femto-second) dynamics of CT states has been unrevealed to enhance the efficiency of photo-active devices based on organic photovoltaic materials.In this work we studied the class of asymmetrically substituted indenotetracene molecules and effects of substituents with different electron-donating characters are investigated on both the overall electronic energy spacing and resulting ultrafast CT dynamics by employing both LR-TD-DFT and RT-TD-DFT based approaches.A red-shift in the vertical excitation energies of the methoxy-substituted derivative with respect to the methyl-substituted one was observed, showing the capability of different substituent groups in tuning the electronic layout and the resulting optical absorption.For each transition, the nature of the energy shift was unveiled by correlating the electron-donor properties of the substituent with the spatial distribution of the canonical MOs (or NTOs) involved.Larger effects of the substituents were noticed in the electronic layout of the charge transfer transitions, where the effect of the methoxy group resulting in a shifting of the charge transfer transition at lower energy values for the methoxy-if compared to the Methyl ASI.ED simulations allowed us to look closely at the electronic density evolution in terms of the electric dipole moment and the MO occupation evolution.In particular it is evident that the substituent has a role in the directionality of the recombination dynamics in the ultrafast regime (i.e., the Methoxy ASI shows a more complex and directional behavior while the methyl shows a quite symmetric rearrangement).Such results can be exploited to design peculiar directional charge dynamics, very important when photo-active materials are employed for light-harvesting applications.

F I G U R E 6
Time resolved molecular orbital occupation number obtained by a 20 fs RT-TD-CAM-B3LYP/6-31G(d,p) electronic dynamics, where initial conditions resemble the S 2 S 0 transition by a HOMO-1 to LUMO occupation swap (Methoxy ASI, left) and the S 3 S 0 transition obtained by a HOMO-3 to LUMO occupation swap (Methyl ASI, right).Isodensity plots of the most involved MOs are also reported.

Table 1
54mmarizes the results computed for both Methoxy ASI and Methyl ASI substituted systems.The first electronic transition is optically allowed for both ASI dyes and are computed at 2.41 and 2.44 eV for Methoxy ASI and Methyl ASI compounds, respectively, in nice agreement with previous experimental and theoretical findings by Cramer and coworkers.54Weobservedamoderatered-shiftfor the S 1 S 0 transition of À0.03 eV from Methyl ASI to Methoxy ASI, in accordance with Reference 54 and a larger one (À0.12eV)for the S 2 S 0 transition.Contour plots of MOs that mainly contribute to the first two transitions (see Table1for MOs contributions) are reported under Figure2showing a non-negligible 31G(d,p) vertical excitation energy values (eV) and the frontier orbitals that mostly contribute (h states for HOMO and l for LUMO) for the first four low-lying electronic transitions of the Methoxy ASI (left) and Methyl ASI (right).
Note: Oscillator strengths are reported in parentheses.The transition character is indicated in the χ column where AB stands for alternating bond and CT for charge transfer.In the last column we define if the transitions are predicted to be allowed (yes, f > 0.1), dark (no, f < 0.01), or slightly active (slightly, 0.01 < f < 0.1).