TICT Molecules with Accessible Conical Intersections - ACS Publications

Oct 8, 2015 - A theoretical investigation based on DFT, TD-DFT, and CASSCF/CASPT2 methods has been carried out to elucidate the photophysics of two ...
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Anilino-Substituted Multicyanobuta-1,3-diene Electron Acceptors: TICT Molecules with Accessible Conical Intersections Filippo Monti,†,§ Alessandro Venturini,*,† Artur Nenov,§ Francesca Tancini,‡ Aaron D. Finke,‡ François Diederich,*,‡ and Nicola Armaroli*,† †

Istituto per la Sintesi Organica e la Fotoreattività, Consiglio Nazionale delle Ricerche, Via P. Gobetti 101, 40129 Bologna, Italy Dipartimento di Chimica “G. Ciamician”, Università di Bologna, Via F. Selmi 2, 40126 Bologna, Italy ‡ Laboratorium für Organische Chemie, ETH Zürich, Vladimir-Prelog-Weg 3, 8093 Zürich, Switzerland §

S Supporting Information *

ABSTRACT: A theoretical investigation based on DFT, TD-DFT, and CASSCF/ CASPT2 methods has been carried out to elucidate the photophysics of two anilinosubstituted pentacyano- and tetracyanobuta-1,3-dienes (PCBD and TCBD, respectively). These molecules exhibit exceptional electron-accepting properties, but their effective use in multicomponent systems for photoinduced electron transfer is limited because they undergo ultrafast (∼1 ps) radiationless deactivation. We show that the lowest-energy excited states of these molecules have a twisted intramolecular charge-transfer character and deactivate to the ground state through energetically accessible conical intersections (CIs). The topology of the lowest-energy CI, analyzed with a linear interpolation of the two branching-space vectors (g and h), indicates it is a sloped CI, ultimately responsible for the ultrafast deactivation of this class of compounds.

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INTRODUCTION Multicyanobuta-1,3-dienes are potent electron acceptors that can serve as interesting alternatives to commonly used quinone-, perylenediimide-, and fullerene-based acceptors in multicomponent systems featuring photoinduced electron transfer.1 Recently, the photophysical properties of several dyads and triads based on a Zn(II) porphyrin electron donor and mono- and dianilino-substituted pentacyano- and tetracyanobuta-1,3-dienes acceptors (PCBD2,3 and TCBD,4 respectively, see Chart 1) were investigated.1 Chart 1. Anilino-Substituted Multicyanobuta-1,3-dienes Investigated in the Present Work Figure 1. Ultrafast transient absorption spectrum of PCBD in toluene solution at 298 K. The ubiquitous intense negative signal at 560 nm is due to laser excitation (λexc = 560 nm, optical density at λexc = 0.3). Inset: decay kinetics recorded at 520 nm.

A CI is a funnel that can either direct a photochemical process to specific photoproducts or, alternatively, induce an ultrafast internal conversion back to the ground state. Therefore, it ultimately defines the photostability of a molecule.5

PCBD and TCBD exhibit interesting electrochemical and optical properties, but they are not luminescent.1 Ultrafast transient absorption experiments carried out in toluene solutions show that the lowest singlet excited state (S1) of PCBD and TCBD decays monoexponentially to the ground state (S0) within ∼1 ps (Figure 1).1 Such a fast nonradiative deactivation process might indicate the presence of an accessible conical intersection (CI) between S1 and S0.5−9 © XXXX American Chemical Society

Received: September 23, 2015 Revised: October 8, 2015

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DOI: 10.1021/acs.jpca.5b09291 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

space orbitals depicted in Figure S2. All of the calculations indicate that the two conformers are virtually isoenergetic (ΔE < 0.017 eV), justifying the presence of both isomers in the crystal lattice. Ground-State Characterization. Both PCBD conformers adopt a ground-state geometry where the anilino substituent is slightly tilted with respect to the adjacent dicyanovinyl moiety. Experimentally, this torsion angle (i.e., α in Figure 2) is the

The development of increasingly powerful computational methods has made it clear that CIs can occur more frequently than it was expected in the past.10 Herein, we present the rationalization of the photophysical properties of PCBD and TCBD using theoretical methods, with the aim of identifying energetically accessible S1/S0 CIs and rationalizing the ultrafast radiationless decay that is experimentally observed. Such a rapid excited-state deactivation can be a significant drawback for the implementation of anilino-substituted multicyanobuta-1,3dienes as electron acceptors in organic photovoltaic devices. In fact, fast internal deactivations strongly compete with chargeseparation processes that are the first step to generate the photoinduced current. Therefore, a deeper understanding of the photophysics may have a remarkable practical relevance.

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COMPUTATIONAL DETAILS We have adopted an integrated approach using both density functional theory (DFT and TD-DFT)11−15 and multiconfigurational methods (CASSCF/CASPT2).16−21 The former affords a preliminary description of the potential-energy surfaces (PESs), while the latter enables a deeper examination of the ultrafast internal-conversion, corroborating DFT predictions. DFT and multiconfigurational calculations were carried out using the Gaussian 0922 and Molpro23 quantum chemistry packages, respectively. In our previous paper,1 we used the PBE024,25 and the CAMB3LYP26 functionals in combination with the 6-31G(d) basis set27,28 to get a basic insight into the electronic properties of both PCBD and TCBD acceptors, and we ensured the quality of our theoretical methods by comparing the computed vertical excitations (calculated in vacuum) with the experimental absorption spectra in toluene solution at 298 K (Figure S1).1 Here we use the 6-31G(d) basis set for the computationally demanding CASSCF and CASPT2 methods, and to establish a more accurate approach, we added the more flexible cc-pVTZ basis-set29 to the previously mentioned DFT functionals. We also tested the effect of toluene solvation by means of the polarizable continuum model (PCM) in CAM-B3LYP/ccpVTZ calculations.30−32 TD-DFT calculations used to compute the lowest vertical electronic transitions and to perform S1 geometry optimizations were carried out with a total number of 12 roots for both PCBD and TCBD. On the contrary, in the case of multireference methods, vertical excitations were calculated using a state-averaged wave function weighted on the lowest five states, while excited-state geometry optimizations were carried out considering only S0 and S1 states. Because PCBD and TCBD display very similar photophysical properties, we will predominantly focus on the smaller PCBD molecule to assess the presence of accessible CIs, using multiconfigurational methods. Afterward, we will move to the bigger TCBD, which can only be investigated by DFT methods due to its larger molecular size.

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Figure 2. Superimposition of the X-ray structures and ground-state optimized geometries (calculated at different levels of theory) for both t-PCBD (a) and c-PCBD (b). The structural overlap is calculated by minimizing the root-mean-square deviation of all atomic positions, except hydrogen atoms.

same for both t-PCBD and c-PCBD isomers (i.e., 9.3°). Gasphase DFT methods overestimate α (22 ± 4° for t-PCBD and 26 ± 3° for c-PCBD). It should be stressed that short-range intermolecular interactions are known to play an important role in PCBD crystals, probably affecting its molecular geometry.3,33 The CASSCF computations show α angles of 48.3° for tPCBD and 47.7° for c-PCBD, which are virtually identical however much larger than the DFT results. This discrepancy is a consequence of the different treatment of the correlation at DFT and CASSCF levels,34 with the former predicting a stronger π-conjugation between the aniline and butadiene moieties, implying smaller α angles. As shown in Figure 2, the entire percyano-butadiene scaffold is highly not planar and the dihedral angle between the dicyanovinyl and the tricyanovinyl moieties (β) strongly differs depending on the two isomers. In the case of t-PCBD, X-ray data indicate a β angle of 107.8°, while both CASSCF and DFT methods with the large cc-pVTZ basis-set estimate a β angle of (98 ± 1)°. On the contrary, for the c-PCBD isomer, the butadiene moiety displays a β angle of 78.0° in the crystal, which is estimated to be 73.4° by CASSCF in gas phase or (68 ± 2)° by DFT methods, regardless of functionals and basis sets used. Solvation does not significantly affect the ground-state geometry of PCBD. For example, α and β angles, calculated in toluene using PCM-CAM-B3LYP/cc-pVTZ for t-PCBD, are 19.8 and 101.0°, respectively, to be compared with 22.4 and 99.1° computed in vacuum at the same level of theory.

RESULTS AND DISCUSSION

X-ray diffraction data show that PCBD adopts two different geometries in the crystal that depend on the percyanobuta-1,3diene transoid or cisoid conformation, leading to t-PCBD and c-PCBD isomers, respectively.3 Using these two structures as initial guesses, we fully optimized both conformers in vacuum using the PBE0 and CAM-B3LYP functionals with different basis sets (6-31G(d) and cc-pVTZ) and a single-state CASSCF(12,11)/6-31G(d) calculation selecting the activeB

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The Journal of Physical Chemistry A Table 1. TD-DFT, CASSCF, and CASPT2 Vertical-Excitation and Excited-State Energies (in electronvolts) of PCBD Conformers, Relative to Each S0 in its Minimum-Energy Geometrya S0→S1 vert. exc. (osc. strength) CAM-B3LYP/6-31G(d) CAM-B3LYP/cc-pVTZ CASSCF(12,11)/6-31G(d) CASPT2b

2.60, 2.70, 3.40, 2.72,

(0.053) (0.033) (0.023) (0.018)

[2.62, [2.68, [3.51, [2.63,

(0.059)] (0.052)] (0.035)] (0.026)]

S0→S2 vert. exc. (osc. strength) 3.53, 3.47, 4.18, 3.00,

(0.670) (0.712) (0.552) (0.396)

[3.62, [3.57, [4.30, [3.06,

(0.682)] (0.688)] (0.614)] (0.437)]

S1 min. 1.72 1.78 2.49 1.46

[1.95] [1.98] [3.02] [1.44]

a

Data in square brackets refer to c-PCBD conformer. All CASSCF and CASPT2 data were obtained using equally weighted state-averaged calculations with five roots in the case of vertical excitations and only two for S1 geometry optimizations. bCASPT2 single-point calculations performed with CASSCF(12,11)/6-31G(d) optimized geometries.

Vertical Excitations. To rationalize the photophysical properties of PCBD, the energies associated with the two lowest-energy vertical excitations (S0 → S1 and S0 → S2) are reported in Table 1. All methods validate the hypothesis that the S0 → S1 transition is charge transfer in nature and involves the transfer of one electron from the HOMO, centered on the aniline moiety, to the π* LUMO, which is located on the pentacyanobutadiene subunit (Figure S3). On the contrary, the stronger absorption band experimentally observed in the UV− vis spectrum of PCBD (λmax = 440 nm, Figure S1) is associated with the S0 → S2 excitation. Such transition involves the promotion of one electron from the HOMO to the LUMO+1, which is mainly centered on the pentacyanobutadiene moiety, like the LUMO, with an additional contribution from the anilino π* orbitals (Figure S3). Accordingly, also this transition exhibits a strong charge-transfer character, but because of the better overlap between the π and π* orbitals of the aniline subunit, a higher oscillator strength is observed (Table 1). Remarkable discrepancies are found between CASSCF and TD-DFT results because CASSCF normally tends to overestimate charge-transfer excitation energies and dynamic correlation (single-point CASPT2/CASSCF) is needed to have a better description of this type of transitions.35,36 After CASPT2 corrections, multireference results virtually converge to those obtained using CAM-B3LYP with the large cc-pVTZ basis set (e.g., 2.63 vs 2.68 eV for c-PCBD, Table 1). If solvent effects are considered, the S0 → S1 excitation preserves the same nature, but its energy is lowered by ∼0.2 eV (e.g., 2.46 vs 2.70 eV, for t-PCDB at the CAM-B3LYP/cc-pVTZ level of theory with and without PCM, respectively). Anyway, the S0 → S1 vertical excitation energy computed taking into account solvation effects still overestimates the experimental absorption maximum (1.99 eV).1 Also, in the case of the S0 → S2 transition, all calculated excitation energies are still overestimated, but, remarkably, the CASPT2 results show the best agreement with experimental data (i.e., 3.03 vs 2.82 eV, see Table 1). On the contrary, the best estimate achieved with a TD-DFT method is again obtained if solvent effects are considered (e.g., 3.22 eV for t-PCDB at the PCM-CAMB3LYP/cc-pVTZ level of theory). All of these results are in line with a recent study, which demonstrates that the rough comparison between absorption maxima and vertical transition energies induces systematic overestimations of the experimental data by approximately 0.1 to 0.3 eV.37 Lowest Excited-State Relaxation. Because in our previous paper1 the PCBD molecule was experimentally excited at 550−560 nm (i.e., an energy well below the one required for the S0 → S2 excitation) in this section we will only consider the relaxation of the lowest singlet excited-state (S1). Starting from the Franck−Condon region (FC), both TD-DFT and CASSCF methods find a minimum along the S1 potential

energy surface of both PCBD conformers. Notably, the chargetransfer transition induces significant geometrical changes in the molecule, and a twisted intramolecular charge-transfer (TICT) state is formed. This is particularly evident in the S1 minimum-energy geometry of t-PCBD, where, according to all computational methods, the pentacyanobutadiene moiety becomes essentially planar (β 180 ± 1°) and perpendicular (α = 89 ± 1°) to the anilino subunit (Figure 3.a). It is worth

Figure 3. Molecular geometry of t-PCBD (a) and c-PCBD (b) in their lowest excited-state (S1) minimum conformation, together with some key structural parameters. Data are computed at the TD-CAMB3LYP/cc-pVTZ level of theory.

noting that, at CASSCF level, the amino moiety in both PCBD isomers is now planar, as also predicted by TD-DFT calculations. No appreciable differences in bond lengths between the two computational methods are observed. On the contrary, in the case of c-PCBD, the steric repulsions between the cyano groups of the cisoid butadiene moiety prevent the formation of an ideal TICT state and, despite the anilino moiety being almost perpendicular to the butadiene one (α = 86 ± 1° in DFT and 71.6° in CASSCF calculation), the latter is far from planarity with a β angle of 26 ± 2° (Figure 3b). Accordingly, the stabilization energy of S1 upon relaxation is ∼0.9 eV for t-PCBD and only 0.7 eV in the case of c-PCBD. Also, in this case, solvation effects do not significantly affect the excited-state picture computed in vacuum, the only difference being a further stabilization of the TICT state (e.g., 1.62 vs 1.78 C

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The Journal of Physical Chemistry A eV, for t-PCDB at CAM-B3LYP/cc-pVTZ level of theory with and without PCM, respectively). Conical Intersections. Despite the presence of the two minima on the S1 potential energy surface of PCBD (one minimum for each conformer), emission is never observed because of the presence of accessible S1/S0 CIs, namely, crossing points close to S1 minima from which a prompt radiationless decay to the ground state can occur. Actually, in a complex molecule such as PCBD, the presence of several accessible CIs is expected and indeed we were able to characterize four of them. (See Figure S4 to compare their nature, energy, and geometry.) Because the aim of this paper is to give a general picture on the photophysics of anilinosubstituted multicyanobuta-1,3-diene electron acceptors, herein we describe in detail only the lowest-energy CI, which is related to the transoid conformer. This CI is above the S1 minimum of t-PCBD by 0.45 and 0.22 eV (i.e., 10.4 and 5.1 kcal·mol−1) at CASSCF and CASPT2/CASSCF levels, respectively (see below). In the S1/S0 CI geometry (Figure 4, top), the anilino moiety displays a strong quinoidal character with a symmetry plane that bisects the aniline ring through the (CH3)2N−C bond. Practically, the carbon atom directly linked to the butadiene moiety has a marked radical character. On the contrary, the excited electron is strongly delocalized over the whole pentacyanobutadiene moiety, as also suggested by the shortening of the Cβ−Cγ and the elongation of the Cδ−Cγ and Cβ−Cα bonds (Figure 4, top). This strong delocalization is also reflected in the fact that this part of the molecule remains planar and without any localized unpaired electron, which can lead to photochemical reactions. Consequently, the formation of a new bond is prevented, as further confirmed by the sloped topology of this CI (vide infra). The two degeneracy-lifting coordinates defining the branching-space g and h are shown in Figure 4 (middle). The g vector breaks the pseudo-Cs symmetry plan through the rotation of the anilino substituent and the deformation of the planar butadiene backbone; moreover, it induces a shortening of the anilino (CH3)2N−C bond. On the contrary, the coupling vector h tends to elongate the previously mentioned C−N bond and preserve the pseudo-Cs symmetry of the molecule. In Figure 4 (bottom) a linear approximation of the S0 and S1 potential-energy surfaces in the branching space of their CI is reported. The topography of the S1/S0 CI corresponds to a sloped CI without transition state.10,38 This topological feature is corroborated by a linear interpolation pathway connecting S1 and CI at the CASSCF level of theory (Figure S5). In line with other examples of sloped CIs, a difference in energy between S1 and CI of 6.4 kcal·mol−1 enables a fully efficient decay to the ground state through the CI funnel.39−43 Essentially, such a low energy barrier between the relaxed excited state geometry and the crossing region (i.e., < 0.4 eV after CASPT2 correction) allows the internal conversion to take place efficiently.10 In fact, when the PCBD molecule is excited to the FC region on the S1 PES, it has a sufficient excess of energy available to overcome the barrier of this sloped S1/S0 CI, leading to a fast deactivation to the ground state. This scenario is supported by the steepest slope of the ground-state PES observed for negative values of g and positive values of h (i.e., both corresponding to the ground-state geometry restoration), suggesting the high probability of an aborted photochemical reaction where the outcome is a radiationless deactivation of the excited state (i.e., internal conversion). This theoretical finding is experimentally validated

Figure 4. Top: Molecular geometry of t-PCBD in its S1/S0 conicalintersection, together with some key structural parameters. Middle: Linear approximation of the potential-energy surfaces of the S0 and S1 states in the branching space of their sloped conical intersection, computed at the SA2-CASSCF(12,11)/6-31G(d). Bottom: Nucleardisplacement vectors of the gradient-difference vector g and of the nonadiabatic-coupling vector h.

by the extremely short excited-state lifetimes of PCBD and TCBD (τ = 2.10 ps, see Figure 1) and by their high photostability in nonpolar solution, such as toluene.1 From a mere analysis of the excited-state energetics (see Figure 5), one might argue that the CI can be reached within a single vibrational oscillation form the FC region, indicating extremely short excited-state lifetime (i.e., in the femtosecond regime); however, the 1D picture of Figure 5 is oversimplified. In fact, the FC active modes involve only bond relaxations and D

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Figure 5. Energy diagrams of t-PCBD (a) and c-PCBD (b). All of the reported values are calculated at SA2-CASSCF(12,11)/6-31G(d) level of theory to allow a better consistency. The values in brackets refer to CASPT2 corrections.

torsions to lower the energy. Momentum preservation in these modes (e.g., further (CH3)2N−C shortening) would not be sufficient to reach the CI.44 In fact, the lowest CI (which is 0.22 eV above the S1 minimum) requires energy to be redistributed into the out-of-plane deformations of the benzene ring. This shifts the dynamics in the picosecond regime. Computationally expensive and time-consuming dynamic simulations would be necessary to verify this scenario. Such studies go beyond the aim of the present investigation. A substantially comparable scenario is also found in the case of c-PCBD, and a comprehensive and comparative energy diagram of both the PCBD conformers is reported in Figure 5. Case of TCBD. Because of the bigger size of TCBD, a comprehensive CASSCF study is not feasible, especially for state-averaged calculations. Therefore, we carried out only DFT and TD-DFT calculations and here we report the results obtained in vacuum using the CAM-B3LYP functional and ccpVTZ basis set. The energy-minimized S0 geometry of TCBD displays a perfect C2 symmetry, which is virtually superimposable with the pseudo-C2 structure determined by X-ray diffraction data (Figure S6, top).4 As for PCBD, the tetracyanobuta-1,3-diene moiety of TCBD is not planar, displaying a torsion angle (β) of 79.1°, to be compared with the tighter angle of the X-ray structure (β = 62.3°) probably due to packing effects in the crystal (Figure 6a and Figure S6, top).4 On the contrary, the dihedral angle between the anilino substituents and the butadiene chain (α = 23.2°) is in good agreement with the experimental ones (20 ± 4°, please note that two α angles are not precisely equivalent in the crystal).4 It is worth noting that the α angle in TCBD is virtually identical to that calculated for PCBD with the same level of theory (i.e., 26.0 and 22.4° for the cis- and trans- conformers, respectively). In Figure S6 (bottom), the energy diagram of TCBD is also reported, which displays the frontier molecular orbitals, together with the four lowest-energy vertical excitations. As in PCBD, the S0 → S1 excitation involves a charge-transfer (CT) process from the anilino-substituent (HOMO) to the strong electron withdrawing percyano-buta-1,3-diene core (LUMO); however, in TCBD, this intramolecular CT transition is estimated to occur at higher energy than in PCBD (i.e., 3.37 eV vs 2.69 ± 0.01 eV, respectively) due to the less efficient donor−acceptor−donor structure of this molecule. This finding correlates well with the experimental absorption spectra reported in Figure S1. After full geometry relaxation, the S1 state undergoes a drastic structural change and the molecule passes from the C2

Figure 6. Molecular geometry of TCBD in the ground state (a) and in its lowest excited-state minimum conformation (b), together with some key structural parameters. Data are computed at the TD-CAMB3LYP/cc-pVTZ level of theory.

symmetry (S0 minimum) to the Cs point group (Figure 6b). This structural deformation is able to strongly stabilize the S1 excited-state which is calculated 1.40 eV above S0 (vertical transition, see Figure S7). As in the case of t-PCBD, the anilino substituents and the totally planar tetracyanobutadiene moiety are now perpendicular to each other (Figures 3b and 6b), indicating that S1 is again a TICT state. Actually, the aforementioned structural changes should have led to a C2h minimum-energy geometry, but the two anilino substituents are no longer equivalent in the S1 excited state. In fact, while one unit acts as the actual donor and behaves like in PCBD, the other one essentially acts as spectator and experiences an appreciable pyramidalization compared with S0 (φ = 9.66 vs 0.52°, Figures 6b and 6a, respectively). Experimentally, fluorescence is not observed also for TCBD and its S1 TICT excited state decays to S0 within a few picoseconds.1 Because of the strong similarities between the photophysical properties of TCBD and PCBD, we suppose that the same type of CI found for PCBD also occurs in the vicinity of the TCBD S1 minimum, providing an ultrafast nonradiative deactivation channel to this excited state. To support this hypothesis, we decided to monitor the energy profiles of the ground state and the first excited state of TCBD along a linearly interpolated path between the S1 minimumenergy geometry and that of the supposed S1/S0 CI (Figure S8). The latter geometry was obtained by roughly exchanging the proper cyano substituent in the optimized S1/S0 CI geometry of PCBD with the corresponding anilino moiety of TCBD in its S1 minimum-energy conformation. Despite the fact that we are aware of the fact that, at present, TD-DFT does not properly describe CIs due to an ill-behaved topography of the PESs in the vicinity of the crossing point,45 the results reported in Figure S8 corroborate our hypothesis, at least qualitatively. In fact, the out-of-plane deformation of the E

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The Journal of Physical Chemistry A “active” aniline donor induces a stronger destabilization of the S0 PES compared with S1, leading to a narrower S1/S0 energy gap.

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CONCLUSIONS We have rationalized the peculiar photophysical properties of two representative anilino-substituted multicyanobuta-1,3-diene electron acceptors. Both DFT/TD-DFT and CASSCF/ CASPT2 methods predict the existence of a TICT excitedstate minimum with a proximate sloped CI. This easily accessible funnel is responsible for the ultrafast nonradiative deactivation processes experimentally observed. Presently, we are now seeking an effective strategy to chemically modify this class of compounds to minimize the strong geometrical distortions that occur upon relaxation of the S1 state. This can make multicyanobuta-1,3-dienes truly attractive electron acceptors in new organic materials for solar energy applications.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b09291. Computational and experimental details. (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*A.V.: E-mail: [email protected]. *F.D.: E-mail: [email protected]. *N.A.: E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by the Italian Ministry of Research (MIUR) and the National Research Council of Italy (CNR) through PRIN 2010 INFOCHEM (contract no. CX2TLM), FIRB Futuro in Ricerca SUPRACARBON (contract no. RBFR10DAK6), and Progetto Bandiera N-CHEM. We are also grateful to the CINECA for the use of the Italian SuperComputing Resource Allocation (ISCRA) through the IsC18 project SCISAS. F.M. acknowledges Stefano Ottani for his crucial technical support. F.D. acknowledges support from the Swiss National Science Foundation (SNSF). A.V. acknowledges Prof. Marco Garavelli for helpful discussions.

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DOI: 10.1021/acs.jpca.5b09291 J. Phys. Chem. A XXXX, XXX, XXX−XXX