Excitonic Splitting, Delocalization, and Vibronic Quenching in the

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Excitonic Splitting, Delocalization, and Vibronic Quenching in the Benzonitrile Dimer Franziska A. Balmer, Philipp Ottiger, and Samuel Leutwyler* Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland ABSTRACT: The excitonic S1/S2 state splitting and the localization/ delocalization of the S1 and S2 electronic states are investigated in the benzonitrile dimer (BN)2 and its 13C and d5 isotopomers by mass-resolved twocolor resonant two-photon ionization spectroscopy in a supersonic jet, complemented by calculations. The doubly hydrogen-bonded (BN-h5)2 and (BN-d5)2 dimers are C2h symmetric with equivalent BN moieties. Only the S0 → S2 electronic origin is observed, while the S0 → S1 excitonic component is electric-dipole forbidden. A single 12C/13C or 5-fold h5/d5 isotopic substitution reduce the dimer symmetry to Cs, so that the heteroisotopic dimers (BN)2-(h5 − h513C), (BN)2-(h5 − d5), and (BN)2-(h5 − h513C) exhibit both S0 → S1 and S0 → S2 origins. Isotope-dependent contributions Δiso to the excitonic splittings arise from the changes of the BN monomer zero-point vibrational energies; these range from Δiso(12C/13C) = 3.3 cm−1 to Δiso(h5/d5) = 155.6 cm−1. The analysis of the experimental S1/S2 splittings of six different isotopomeric dimers yields the S1/S2 exciton splitting Δexc = 2.1 ± 0.1 cm−1. Since Δiso(h5/d5) ≫ Δexc and Δiso(12C/13C) > Δexc, complete and nearcomplete exciton localization occurs upon 12C/13C and h5/d5 substitutions, respectively, as diagnosed by the relative S0 → S1 and S0 → S2 origin band intensities. The S1/S2 electronic energy gap of (BN)2 calculated by the spin-component scaled approximate −1 second-order coupled-cluster (SCS-CC2) method is Δcalc el = 10 cm . This electronic splitting is reduced by the vibronic −1 quenching factor Γ. The vibronically quenched exciton splitting Δcalc ·Γ = Δcalc is in excellent agreement with the el vibron = 2.13 cm −1 observed splitting Δexc = 2.1 cm . The excitonic splittings can be converted to semiclassical exciton hopping times; the shortest hopping time is 8 ps for the homodimer (BN-h5)2, the longest is 600 ps for the (BN)2(h5 − d5) heterodimer.

1. INTRODUCTION Excitonic interactions between chromophores play an important role for electronic energy transfer in a wide range of chemical and photobiological systems such as photosynthetic light-harvesting complexes,1−5 conjugated polymers,6−8 molecular crystals, and nucleic acids.9−11 Together with the 2pyridone dimer, (2PY)2,12 the benzoic acid dimer, (BZA)2,13,14 and the anisole dimer,15−17 the benzonitrile dimer (BN)2 is one of the few inversion-symmetric self-dimers whose gas-phase rotational constants have been measured in the electronic ground (S0) and lowest excited states.18,19 The absence of solvent or solid-state lattice effects combined with the high symmetry and the well-defined and rigid geometry of these dimers allows quantitative comparisons of the calculated and experimentally observed excitonic interaction strengths.20−24 For (BZA)213,14 and for (BN)218,19 a single electronic origin band is observed by high-resolution laser-induced fluorescence (LIF) spectroscopy.13,14,18,19 This must be either the S0 → S1 or the S0 → S2 origin, thereby indicating high symmetry (C2h) of the ground and excited electronic states. However, while the nuclear geometry of both (BZA)2 and (BN)2 is planar and inversion-symmetric (C2h) in the S0 state, it is experimentally found to be asymmetric (Cs) in the excited state.13,14,18,19 This asymmetry was interpreted as a manifestation of excited state symmetry breaking, which was believed to localize the electronic excitation on one of the monomers.13,14,18,19 © XXXX American Chemical Society

Lahmani and co-workers have invoked related arguments for symmetry-breaking and localization of the lowest excited state in the excitonic self-dimers (o-cyanophenol)2 and (mcyanophenol)2.25,26 However, these interpretations raise the question why only one and not two electronic origins are observed, as would expected for self-dimers with structurally inequivalent monomers. In inversion-symmetric homodimers, the electronically excited S1 states of two equivalent monomers A and B are degenerate and are excitonically coupled.27−30 In the (BN)2 homodimer the centers of mass of the two monomers are 6.53 Å apart, see Figure 1a, and the excitonic coupling matrix element VAB is well approximated as the interaction between the two electronic transition dipoles μ⃗ A and μ⃗ B of the local S0 → S1 excitations of the A and B monomers. The size and the sign of VAB depends on the relative directions of the electronic transition dipole-moment vectors and the intermonomer distance vector R⃗ AB.27−30 Within the framework of first-order perturbation theory, the transition dipole−transition dipole coupling leads to the excitonic (Davydov) splitting of Δexc = 2VAB between the excited states.27−30 In (BN)2, the monomer S0 → S1 transition dipole vectors μ⃗A,μ⃗ B lie within the dimer Received: September 23, 2014 Revised: October 29, 2014

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dx.doi.org/10.1021/jp509626b | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

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spectra of (BN)2, together with a structural analysis that is in agreement with that of results of Meerts and co-workers.18 Below, we present and analyze the mass-selected two-color resonant two-photon ionization spectra of the all-12C-(BN)2 homodimer, the fully deuterated (BN-d5)2 isotopomer, the (BN-h5)(BN-d5) heterodimer, and of the respective 13Cisotopomers of these three dimers. The analysis of these six spectra in the region S0 → S1/S2 origins allows to determine the S1/S2 exciton splitting of (benzonitrile)2. The question of the localization or delocalization of the excitonic excitation is analyzed as a function of the isotopic substitution and is shown to vary from completely delocalized (50:50) to completely localized (99:1). We show that the observed asymmetric excited-state geometry of (BN)218,19 does not imply that the electronic excitation is localized on one of the monomers and is not in contradiction to the observation only of the S0 → S2 origin, which indicates electronic delocalization and C2h symmetry of the electronic wave functions. We provide an explanation for the geometric asymmetry based on the properties of the adiabatic S1 and S2 state potential energy surfaces using the effective-mode approximation recently introduced by Köppel and co-workers for excitonic coupling in symmetric dimers.32 We further discuss the importance of vibronic quenching, which reduces the excitonic splitting between the S1 and S2 states Δel calculated by static ab initio calculations to produce the vibronically quenched splitting Δvibron, which corresponds to the experimentally observed excitonic splitting Δexc and is about 10 times smaller than Δel.20,23,24 Finally, we provide a detailed analysis of the extent of exciton localization by asymmetric isotopic substitution, and discuss the resulting exciton hopping times.24

Figure 1. Structures of the four experimentally observed isotopomers of (benzonitrile)2: (a) (BN-h5)2, (b) 13C-(BN-h5)2 (only one of the 7 independent 12C/13C substitutions shown), (c) (BN-h5)(BN-d5), and (d) (BN-d5)2. Further isotopomers such as (BN-h513C)(BN-d5) and 13 C-(BN-d5)2 with the 13C within either moiety are mentioned but not shown explicitly.

2. METHODS 2.1. Experimental Setup. The (BN)2 dimers are produced in a pulsed supersonic expansion of BN (Fluka, purum >98%) that is heated to 75 °C, seeded in Ne carrier gas at p0 = 1.4 bar and expanded through a pulsed thin-walled adiabatic nozzle (0.4 mm diameter). Mass-selective two-color resonant twophoton ionization (2C-R2PI) spectra were recorded by crossing the skimmed molecular beam with temporarily and spatially overlapping excitation and ionization laser beams in the source chamber of a time-of-flight mass spectrometer. For excitation, the frequency doubled output of a Nd:YAG-pumped Radiant Dyes NarrowScan dye laser (Coumarin 153) with a bandwidth of 0.038 cm−1 was used. All spectra were vacuumcorrected. For the ionization step, we used 300 μJ/pulse of 213 nm (Nd:YAG fifth harmonic) from an Innolas Spitfire 600 laser. The experimental setup and procedure for the isotopic measurements have been discussed elsewhere.20,23 The spectra of the respective 13C-isotopomers discussed were measured using the natural abundance of 13C, which is 15.4% for (benzonitrile)2. For the spectra of the half-deuterated and fully deuterated species, BN-d5 (Sigma-Aldrich, 99 atom-%) was mixed with varying amounts of BN-d0 to measure either the homodimer (BN-d5)2 or the heterodimer (BN-h5)(BN-d5). The different investigated dimer isotopic species are represented in Figure 1a−d. The fluorescence emission spectrum of the benzonitrile monomer needed for the determinations of the experimental Huang−Rhys factors (see section 4) was measured by crossing the unskimmed molecular beam with the UV excitation laser beam, fixed at the BN 000 band, about 4 mm downstream of the

plane and are tilted by 59° relative to R⃗ AB,18 see Figure 1a. With this angle and the C2h symmetry of the dimer, the higher-lying transition to the S2(Bu) state is fully allowed while the transition to the lower-lying S1(Ag) state is strictly electric dipole forbidden. This situation is closely analogous to other Hbonded self-dimers such as (2-pyridone)2,23,31,32 (2-aminopyridine)2,20,23 and (benzoic acid)2.24 The BN monomer has been extensively studied by LIF and fluorescence emission spectroscopy.33−36 The first assignment of the S0 → S1 vibronic spectrum of BN was undertaken by Sakota et al.,34 and extended by Kleinermanns and coworkers.35 Kobayashi et al. assigned the S0 → S1 electronic origin of (BN)2 to a band shifted by −95 cm−1 relative to the origin of BN.37 From the analysis of the rotational band contour, they concluded that (BN)2 has a planar structure with antiparallel alignment of the two BN molecules.37 Schmitt et al. determined the rotational constants of (BN)2 in its S0 and S1 (actually S2, see below) states by high-resolution LIF spectroscopy.18 The S0 state was determined to be C2h symmetric, in agreement with earlier MP2/6-31G(d,p) ab initio calculations.18,38 Schmitt et al. found the excited state structure to be asymmetric and proposed that the excitation is localized on one of the BN monomers, supported by CIS calculations which also predict a nonsymmetric structure.18 Pratt and co-workers19 have also reported high-resolution LIF B



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nozzle. The fluorescence emission was collected using a spherical mirror and quartz optics, dispersed in a SOPRA UHRS 1.5 m monochromator in second order and detected by a Peltier-cooled Hamamatsu R928 photomultiplier. 2.2. Computational Methods. The (BN)2 S0 state geometry was optimized using the SCS-MP239 and SCSCC240 methods with the aug-cc-pVDZ and aug-cc-pVTZ basis sets. Both optimizations yielded a C2h symmetric structure, in agreement with earlier MP2 calculations with smaller basis sets,38 and with the S0 state rotational constants determined by the Schmitt and Pratt groups.18,19 S0 state normal-mode vibrational calculations were performed at the SCS-MP2/augcc-pVDZ level. Vertical excitation energies to the S1 and S2 state were calculated at the C2h symmetric ground state structure using the SCS-CC2 method with the aug-cc-pVDZ and aug-cc-pVTZ basis sets. The adiabatic excitation energies were calculated at SCS-CC2/aug-cc-pVDZ level within the Cs point group, thereby allowing the S1 state to relax into an asymmetric planar geometry, cf. the discussion in section 4.2. The spin-component-scaled variant of the CC2 method was applied because it has recently been found to yield very reliable results for the valence excitations of aromatic organic molecules.41 To calculate the vibronic displacements in the S0 → S1 spectrum of BN2, the BN ground state was optimized at the SCS-CC2/cc-pVTZ level and normal-mode calculations were performed on this structure. The S1 state potentials were obtained by calculating the vertical SCS-CC2/cc-pVTZ excitation energies at geometries that were displaced by Q = ±0.5, ±1, ±2, and ±3 along the S0 state a1 normal-mode eigenvectors. All calculations were carried out using the Turbomole V6.3 program package42 with thresholds for SCF and one-electron density convergence set to 10−10 a.u. The convergence thresholds for all structure optimizations were set to 10−8 a.u. for the energy change, 6 × 10−6 a.u. for the maximum displacement element, 6 × 10−6 a.u. for the maximum gradient element, 4 × 10−6 a.u. for the RMS displacement, and 10−6 a.u. for the RMS gradient.

Figure 2. Two-color resonant two-photon ionization spectra in the region of the S0 → S1/S2 electronic origins of (a) all-12C (BN)2, measured at m/e = 206 u mass, and (b) (BN)2-13C, measured at m/e = 207 u. Note the appearance of the S0 → S1 origin in trace (b) and its absence in (a); the S0 → S1 origin (BN)2-all-12C is electric-dipole forbidden.

and comprises contributions from the excitonic splitting and from isotopic effects. The latter arise from the shifts of the 000 bands of the 12C- and 13C-BN monomers, which are shown in Figure 3a,b. These shifts arise from the change between the S0

3. RESULTS 3.1. Excitonic Splittings of the Isotopomers. All-12C- and 13C-(benzonitrile)2 Isotopomers. Figure 2a shows the two-color R2PI spectrum of (BN)2 and Figure 2b that of its 13C isotopomer, recorded in the m/e = 206 u and m/ e = 207 u mass channels. The corresponding structures are shown in Figure 1a,b, respectively. For (BN)2 the S0 → S2 (Ag → Bu) transition is allowed and gives rise to an intense band at 36420.1 cm−1, in excellent agreement with the findings of Schmitt and co-workers,18 while the S0 → S1 (Ag → Ag) transition is strictly electric-dipole forbidden. As has been shown earlier, a single 12C/13C exchange can suffice to break the C2h nuclear framework symmetry enough to weaken the g ↮ g optical selection rule.20,23,31 The massresolved two-color R2PI spectrum of 13C-(BN)2 shown in Figure 2b indeed exhibits two bands, which are separated by Δobs = 3.9 cm−1. The spectrum is recorded using the natural 13 C isotopic abundance; the integrated intensity of the two bands in Figure 2b is 13.8% of the all-12C origin in Figure 2a. The band at lower wavenumber is the S0 → S1 origin of 13C(BN)2, which is forbidden in 12C-(BN)2. It is shifted by −1.2 cm−1 relative to the S2 origin of 12C-(BN)2 in Figure 2a, while the more intense S0 → S2 origin of 13C-(BN)2 S2 origin is shifted by +2.7 cm−1. The overall splitting is Δobs = 3.9 cm−1,

Figure 3. Isotopic benzonitrile monomer spectra in the S0 → S1 origin region, measured in the all-12C mass channel (a), the 13C mass channel (b), and the mass channel of the fully deuterated benzonitrile-d5 (c).

and S1 state zero-point vibrational energy (ZPVE) upon electronic excitation, which are different for the 12C- and 13CBN monomers.24 The isotopic and excitonic contributions to the splitting are discussed in section 4.1. Partially and Fully Deuterated (BN)2 Isotopomers. The 000 band regions of four partially and fully deuterated dimer isotopomers formed in the jet expansion of a mixture of 80% C



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BN-d5 and 20% BN-h5 are shown in Figure 4c−f; for comparison purposes, Figure 4a repeats the spectrum of

Table 1. Absolute and Relative Experimental Excitation Energies of the S1 and S2 Electronic Origins of (Benzonitrile)2 Isotopomers and Corresponding S1/S2 Splittings isotopomer

state

Eabs/cm−1

Erel/cm−1

(h5 − h5)* (h5* − h5 13C)

S2 S1

36 420.1 36 418.9

0.00 −1.2

(h5 − h5 13C*) (h*5 − d5)

S2 S1

36 422.8 36 419.0

+2.7 −0.9

(h5 − d5*) (h5 13C* − d5)

S2 S1

36 574.8 36 422.5

+154.7 +2.4

(h5 − d5 13C*) (d5 − d5)* (d*5 − d5 13C)

S2 S2 S1

36 578.4 36 575.7 36 574.5

+158.0 +155.6 +154.4

(d5 − d5 13C*)

S2

36 577.4

+157.7

a

ΔS1/S2

3.9

155.6

155.6

3.9 a

Reference 18 gives 36420.10(1) cm

−1

.

and S1 states, resulting in a shift of the S0 → S1 origin of Δiso = 3.3 cm−1, as shown in Figure 3a,b. This monomer isotopic shift gives rise to a primary isotope effect. In the dimer, an additional secondary isotope effect occurs due to the changes of the frequencies of the six intermolecular vibrations between the S0 and S1 state that arise from the isotopic substitution. For 12 C/13C-substitution the secondary isotope effect is too small to be observed, but it becomes observable upon h5/d5 substitution, see below. The overall S1/S2 splitting in the spectrum of the 13 C-(BN)2 is Δobs = 3.9 cm−1, see Figure 4b. By perturbation theory, this can be written as the combination of excitonic splitting and isotopic effects:

Figure 4. Two-color resonant two-photon ionization spectra in the S1/ S2 region of (a) all-12C-(benzonitrile)2 (m/e = 206 u mass channel), (b) 13C-(benzonitrile)2 (m/e = 207 u), (c) all-12C (BN-h5)(BN-d5) measured in the m/e = 211 u mass channel, (d) 13C-(BN-h5)(BN-d5) measured in the m/e = 212 u mass channel, (e) all-12C (BN-d5)2 measured in the m/e = 216 u mass channel, and (f) 13C-(BN-d5)2 measured in the m/e = 217 u mass channel. Observed splittings are indicated in color.

all-12C-(BN)2 and Figure 4b that of 13C-(BN)2, cf. Figure 2. The structures of the semideuterated dimer (BN)2-(h5 − d5) and of the fully deuterated dimer (BN)2-(d5 − d5) are shown in Figure 1c,d, respectively; below we also discuss their respective 13 C-isotopomers. The two-color R2PI spectra were recorded simultaneously in the mass channels m/e = 211, 212, 216, and 217 u. Figure 4c (m/e = 211 u) shows the S1 and S2 origins of the (BN-h 5 )(BN-d 5 ) at 36 419.0 and 36 574.8 cm −1 , respectively; these values agree perfectly with those measured by Schmitt and co-workers.18 Thus, when fully deuterating one monomer, the splitting is Δobs = 155.6 cm−1, almost a factor of 40 larger than the 12C/13C-splitting. This significant increase of the splitting is induced by the quintuple H/D exchange, causing a larger change in the ZPVE. The m/e = 216 u spectrum in Figure 4e shows a single band at 36 575.7 cm−1 corresponding to the S0 → S2 origin of (BN-d5)2. Full deuteration of both monomers restores the C2h symmetry of the dimer, see Figure 1d, which renders the S0 → S1 transition electric-dipole forbidden. Note that the (BN-h513C)(BN-d5) and (BNd513C)(BN-d5) spectra in Figure 4d,f show nearly the same shifts and splittings as those of 13C-(BN)2 in Figure 4b. The absolute and relative transition energies of the different (BN)2 isotopomers are listed in Table 1.

Δobs =

Δexc 2 + Δiso 2

(1)

Assuming that the secondary isotope effect is negligible, the primary isotope effect Δiso = 3.3 cm−1 can be used to derive the excitonic splitting, giving Δexc = 2.1 cm−1. Note that 12C/13Csubstitution in the fully deuterated (BN-d5)2 yields the same splitting Δobs = 3.9 cm−1, see the spectrum in Figure 4f, and hence the same excitonic splitting Δexc. The scheme in Figure 5 summarizes and illustrates the energy levels used for the derivation of Δexc and Δiso: The experimentally observed energy levels are drawn in black. The excitonic splitting of Δexc = 2.1 cm−1 derived above yields the position of the 12C-(BN)2 S0 → S1 origin, which is not experimentally observable and is drawn in gray. Furthermore, the S1 energy of the BN monomer that is complexed within the symmetric dimer lies VAB = 1.0 cm−1 below the S2 energy of (BN)2 and is drawn at the far left in gray. Adding the isotopic shift Δiso = 3.3 cm−1 to the S1 energy of the BN monomer gives the S1 energy of the 13C-BN monomer, which is indicated in gray on the far right side. Interestingly, the experimental spectrum of the (BN-h5)(BNd5) dimer shown in Figure 4c,d allows to verify this determination of the S1 energies of 12C-BN and 13C-BN complexed within the dimer: The equal intensities observed for the S1 (h*5 ) and S2(D*5 ) origins of (BN-h5)(BN-d5) in Figure 4c indicate near-complete localization of the electronic excitations on the respective monomers, see also section 4.2. To a very good approximation, the S0 → S1 and S0 → S2 transitions in the

4. DISCUSSION 4.1. Excitonic S1/S2 Splitting. As mentioned above, a single 12C/13C exchange renders the S0 → S1 origin slightly allowed. The 12C/13C-substitution also alters the ZPVE of the 13 C-BN monomer. This ZPVE change differs slightly in the S0 D



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substitution fully localizes the excitation.24 According to degenerate perturbation theory24,27,29 the two excitonic wave functions are given in terms of the ground- and excited state monomer wave functions ϕi0, ϕiexc (i = A, B) by the relations: A B B Ψ+ = Ψ(S2) = cos α ·φexc φ0 + sin α ·φ0A φexc

(3)

A B B Ψ− = Ψ(S1) = sin α ·φexc φ0 − cos α ·φ0A φexc

(4)

where α is tan(2α) = |Δexc|/(|EA*B − EAB*|). Using the monomer S0 → S1 oscillator strength, denoted f mon, the ± corresponding oscillator strengths of the dimer fdim are24

(BN-h5)(BN-d5) correspond to the local S0 → S1 electronic excitations of BN-h5 and BN-d5 within the dimer. As Figure 5 shows, the observed S0 → S1 transition energy of the h5* − d5 dimer in Figure 4(c) and of the 13Ch*5 − d5 dimer in Figure 4d are identical to the S1 energies of 12C-BN (left) and the 13CBN, which were not observed but follow from the analysis above. This near coincidence of inferred and experimental values is also illustrated in Figure 5 by gray and red lines and confirms the above analysis. Comparison of the observed Δobs = 155.6 cm−1 splitting in the (BN-h5)(BN-d5), Figure 4c, with the isotopic shift Δmon iso = 157.2 cm−1 of the BN-d5 monomer, see Figure 3c, reveals that the isotopic shift of the monomer is larger than that in the heterodimer. Inserting these two values in eq 1 results in a negative excitonic splitting, which is not possible. The implication is that a small, but significant secondary isotope effect is observed in the (BN-h5)(BN-d5) heterodimer. This is not unexpected, given the cumulative effect of five H/D exchanges. The existence of a secondary isotope effect is also suggested by the −0.9 cm−1 shift of the S2 origin of (BN-h5)(BN-d5) relative to that of (BN-d5)2. We extend eq 1 to include a secondary isotope shift as Δexc 2 + (Δiso,prim + Δiso,sec)2

(5)

− f dim = fdim (S1) = (1 − 2cos α sin α)fmon

(6)

For the C2h-symmetric homodimers (BN)2 and (BN-d5)2, the localized excitation energies are degenerate, giving α = π/4, fdim(S2) = 2f mon, and fdim(S1) = 0. Using the experimental values for 13C-BN2, Δexc = 2.1 cm−1 and |EA*B − EAB*| = |Δiso(13C))| = 3.3 cm−1 results in α = 16.1°. The wave function Ψ+ = 0.96ϕAexcϕB0 + 0.28ϕA0 ϕBexc is 92.2% localized on the 13C monomer, and its oscillator strength is f±dim = 1.53f mon. The transition to the lower (S1) state Ψ− is 92.2% localized on the 12C-BN monomer, and its oscillator strength is f−dim = 0.47 f mon. The predicted relative band intensity is f−dim:f+dim = 0.31:1. This is in excellent agreement with the integrated intensities of the S1 and S2 origin bands, which are I(S1):I(S2) = 0.38:1. The band intensities are very sensitive to the mixing angle α, which is dependent on the ratio of Δexc and Δiso.24 Thus, the agreement between the calculated and observed intensity ratio further supports the attributed splittings. For the h5−/d5-substituted heterodimer, the isotopic splitting taken as |Δiso(d5)| = 155.6 cm−1. Combination with the excitonic splitting Δexc = 2.1 cm−1 gives an angle α = 0.38°. The lower transition is described by the wave function Ψ− = 0.999ϕAexcϕB0 + 0.007ϕA0 ϕBexc, which is 99.9% localized on the BN-h5 moiety with an oscillator strength of f−dim = 0.99 f mon. The S2 transition is 99.9% localized on the BN-d5 moiety and has an oscillator strength of f+dim = 1.01f mon. The calculated relative band intensities are f−dim:f+dim = 0.97:1, which is again in excellent agreement with the observed intensity ratio of I(S1):I(S2) = 0.99:1. 4.3. Excitation Transfer Rates. In asymmetric dimers such as 13C-(BN)2 and (BN-h 5)(BN-d5) the monomers are distinguishable. Upon optical excitation with a bandwidth that is wide enough to cover both electronic origins, the exciton oscillates back and forth between the two monomers. The resonance transfer rate kAB between monomers A and B is given as27

Figure 5. Schematic exciton splitting diagram illustrating the observed and calculated splittings of (benzonitrile)2 on the left, and of the 13C(BN)2 isotopomer on the right. Experimental transition energies are drawn in black, and calculated values in gray. The red lines indicate the localized 12C-BN and 13C-BN S0 → S1 excitations are observed in the spectra of (BN-h5)(BN-d5) and 13C-(BN-h5)(BN-d5); see the text.

Δobs =

+ f dim = fdim (S2) = (1 + 2cos α sin α)fmon

(2) −1

Inserting the observed S1/S2 splitting Δobs = 155.6 cm of (BN-h5)(BN-d5), the excitonic splitting Δexc = 2.1 cm−1 and the primary isotope effect Δiso,prim = 157.2 cm−1 from the BN-d5 spectrum in Figure 3c, gives a value of Δiso,sec = −1.6 cm−1 for the secondary isotope shift. One sees that Δiso,sec is about 100 times smaller than Δiso,prim; this justifies the assumption made above for the 13C-isotopomer where we had neglected the secondary isotope shift. 4.2. Localization or Delocalization of the S1/S2 States of (Benzonitrile)2? Given that only the S2 origin is observed for the (BN-h5)2 and (BN-d5)2 homodimers, one concludes that the electronic excitation is completely delocalized in these strictly C2h symmetric complexes. Here we show that the 12 C/13C substitution suffices to partially localize the excitation on either the BN-h5 or the BN-d5 monomer, and that the h5/d5

kAB =

4|sin(2α)||VAB| h

(7)

For the homodimers (BN)2 and (BN-d5)2, the angle is α = π/4 and the transfer rate is kAB = 4|VAB|/h.27 Given that VAB = 1/ 2Δexc = 1.0 cm−1, one obtains a transfer rate of kAB = 1.25 × 1011 s−1 for the homodimers and a hopping time texc = (kAB)−1 = 8.02 ps. This about twice the hopping rate previously observed for the benzoic acid dimer.24 In the asymmetric dimers with partial localization the hopping rates decrease quite strongly: For the case of 13CBN2 with a Δiso(13C) = 3.3 cm−1, the excitation transfer rate drops by a factor of ∼2 to kAB = 6.65 × 1010 s−1, equivalent to a E



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hopping time of texc = 15.0 ps. Note that the exciton hopping picture is especially relevant here, since the electronic excitations are 92.2% localized on BN or BN−13C. Compared to the benzoic acid dimer, the hopping rate of the 13Cisotopomer is a factor 8 faster, which goes along with the smaller localization. In the strongly localized h5/d5 heterodimer, eq 7 predicts that the exciton hopping rate drops to kAB = 1.67 × 109 s−1, or increases to a hopping time of texc = 600 ps. This hopping rate is 40 times smaller compared to 13C-BN2, reflecting the large effect of the 5-fold deuteration on the localization. 4.4. Ab Initio Calculated S1/S2 Energy Gaps and Vibronic Quenching. In Table 2, we list the SCS-CC2

eigenvectors and calculated the corresponding S1 state potentials via vertical excitation energies. From the groundand excited-state potentials along the a1 modes, the Huang− Rhys factors Si were determined as the first derivative of the excited state potentials at Q = 0. By multiplying the calculated −1 splitting Δcalc with the calculated quenching factor el = 10 cm Γcalc = 0.228, we obtain a vibronic excitonic splitting of Δcalc vibron = 2.3 cm−1. The quenching factor Γ can also be experimentally derived from the FC-factors (FCF) of the a1 vibrations observed in the dispersed fluorescence spectrum of the BN monomer,23 as shown in Figure 6. The band frequencies are in very good

Table 2. S0 → S1 and S0 → S2 Excitation Energies (in cm−1), Excited-State Symmetries and Oscillator Strengths fel of (Benzonitrile)2, Calculated at the SCS-CC2 level at the S0 State C2h Geometrya Cs aug-cc-pVDZ S1 S2 Δcalc adiab aug-cc-pVTZ S1 S2 a

C2h

irrep

adiabatic energy

irrep

vertical energy

fel

A′ A′

37 207 37 903 696

Ag Bu Δcalc vert

38 573 38 583 10

0.000 0.010

Ag Bu Δcalc vert

39 227 39 237 10

0.000 0.011

Figure 6. Dispersed fluorescence spectrum of the benzonitrile monomer with vibronic band assignments from ref 35. Bands without assignments are combination bands.

Adiabatic excitation energies calculated in Cs symmetry.

calculated vertical and adiabatic electronic excitation energies for (BN)2. Note that these were calculated with the SCS-CC2 method and differ slightly from the previously reported CC2 energies.23 The calculated vertical S1/S2 energy gap is Δcalc el = 10 cm−1, which is about five times larger than the experimentally determined excitonic splitting Δexc. This difference is due to the quenching of the purely electronic excitation by the vibronic displacement along the Franck−Condon (FC) active totally symmetric (a1) intramolecular vibrations of benzonitrile monomer that couple to its S0 → S1 transition.20,23,32 The calculation of the vibronic quenching factor Γ = ∏i (e−si) = exp(−∑iSi) is calculated from the Huang− Rhys factors Si of the seven a1 vibrations given in Table 3. Details have been discussed previously.20,23 We distorted the SCS-CC2/cc-pVTZ optimized ground state geometry of the BN monomer stepwise along its a1 vibrational normal-mode

agreement with those reported by Kleinermanns and coworkers, and are given in Table 3.35 The intensity of the 0 → 1 vibronic band of the ith normal mode to the 000 band intensity yields the experimental Huang−Rhys factors as Si,exp = FCF(i10)/FCF(000); these are also given in Table 3. The vibronic quenching factor is then determined as Γexp = exp(−∑iSi,exp) = 0.213.23 Multiplying this with the ab initio calculated S1/S2 splitting Δel yields a vibronic splitting of Δexp vibron = 2.13 cm−1. This is in excellent agreement with the fully calc computational result Δvibron = 2.28 cm−1 and with the experimental splitting Δexc = 2.1 cm−1. The model used for the calculation of the quenching factor is an approximation, inasmuch as it takes only the intramolecular normal modes into account. For (BN)2 dimer the intermolecular vibrations are excited only weakly in the S1/S2 transitions. As can be seen in the 2C-R2PI spectrum shown in Figure 7, hardly any intermolecular normal modes are observed and thus, the intermolecular normal modes do not contribute markedly to the quenching factor. This is in contrast to the vibronic spectrum of (2-aminopyridine)2,20 which is dominated by intermolecular vibronic bands. 4.5. Asymmetric Structure of (Benzonitrile)2 in Its S1/ S2 States. As outlined in the Introduction, the experimentally observed geometric asymmetries of excited-state (benzoic acid)2 and (benzonitrile)2 led several groups to postulate the localization of the excitonic excitation on one of the monomers.13,14,18,19,25,26 In section 4.1 we showed that a single 000 band is observed in inversion-symmetric (Ci or C2h) homodimers and that two electronic origins are only observed upon symmetry breaking such as isotopic substitution. In sections 4.2 and 4.3 we have discussed the topic of excitonic

Table 3. Benzonitrile Monomer Vibrational Frequencies (in cm−1) from the Dispersed Fluorescence Spectrum, with Experimental Huang−Rhys Factors Si and Vibronic Quenching Factor Γexp mode

frequency

Si

exp(−Si)

6a δC−CN 1 12 18 9a νC−CN

456 542 761 1001 1029 1176 1190

0.331 0.131 0.038 0.639 0.079 0.085 0.254 Γexp =

0.718 0.877 0.963 0.528 0.924 0.919 0.783 0.213 F



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maximum probabilities of both the symmetric (+) and antisymmetric (−) nuclear wave functions are close to the ±Q−min minima of the S1 potential. Thus, the average nuclear geometries of both the “dark” v = 0 level of the S1 state and the “bright” v = 0 level of the S2 electronic state are asymmetric. The S1 state optimization indeed results in a planar but asymmetrically distorted geometry of Cs symmetry, corresponding to either of the ±Q−min minima of the S1 adiabatic potential. Table 4 summarizes the changes of selected geometrical parameters between the S 0 and S 1 states, as derived experimentally by Schmitt et al.,18 Borst et al.,19 and as calculated with the SCS-CC2/aug-cc-pVDZ method. The calculated geometry changes are in good agreement with experiment. The only exception is that the SCS-CC2 calculation predicts a decrease of the center-of-mass intermolecular distance RAB,COM of −0.3 pm, significantly smaller than the −2.8 and −2 pm analyzed by Schmitt and coworkers.18,19 The small change of intermolecular distance is in agreement with the fact that the intermolecular vibronic excitations in the (BN)2 spectrum are very weak. Table 4 predicts that the structure change between the S0 and S1 state (BN)2 are almost entirely restricted to one of the BN monomers, while the other retains the structure of the ground state. However, this structure represents only one of the two equivalent minima over which the dimer S1 and S2 states are delocalized, and does not imply excitonic localization. Within the picture of exciton hopping the excitation as well as the geometric distortion oscillates between the monomers with the hopping time of texc = 8.02 ps, determined above (cf. section 4.3). Thus, on the nanosecond time scale of the end-over-end rotation, the excited state geometry of both the S1 and S2 states corresponds to a linear combination of the two equivalent asymmetrically distorted minimum geometries.

Figure 7. Two-color R2PI spectrum of the benzonitrile dimer with vibronic band assignments. The wavenumber scale is relative to the 000 band at 36513.5 cm−1.

wave function localization vs delocalization. Here we show how a C2h symmetric excitonic homodimer whose electronic wave function is completely delocalized over both monomers can have an asymmetric excited-state geometry. Figure 8 shows an artists’ view of the adiabatic S1 and S2 excited state potentials of (BN)2, plotted along the “effective”

5. CONCLUSIONS The excitonic splittings of (BN)2 and (BN-d5)2 are not directly measurable, because the S0 → S1 transition is Ag → Ag in the C2h point group of the dimer and is electronic dipole-forbidden; only the S0 → S2 transition can be observed spectroscopically. We have measured the mass- and isotope-selected resonant two-color resonant two-photon ionization spectra of the S1 and S2 vibronic band origins of 12C/13C- and h5/d5-substituted benzonitrile dimers, namely 13C-BN2, (BN-h5)(BN-d5), 13C(BN-h5)(BN-d5), and 13C-(BN-d5)2. In these asymmetric (Cs) dimers, the S1 origin is observed due to the symmetry breaking by isotopic substitution. The combined spectroscopic information allows to determine the gas-phase excitonic splitting of the BN dimer as Δexc = 2.1 cm−1. This is about twice the splitting observed for (benzoic acid)224 but is still one of the smallest gas-phase excitonic splittings observed until now. Isotopic shifts arise for the electronic origins of the 13C- and d5-substituted dimers because of changes in ZPVE between the electronic ground and excited states. In case of 13C-BN2, the isotopic shift of the origin is Δiso(13C) = 3.3 cm−1, which corresponds to that of the S0 → S1 origin of the 13C-BN monomer relative to 12C-BN. Secondary isotope effects are negligibly small. For the h5 − d5 heterodimer, the isotopic shift Δiso(d5) = 155.6 cm−1 is large, because of the substantial relative mass change by 5-fold deuteration. As the S2 origin was red-shifted relative to the (BN-d5)2 S2 origin and the heterodimer S1/S2 splitting was 1.6 cm−1 smaller than the shift of BN-d5 relative to BN-h5, a secondary isotopic shift had to be taken into account.

Figure 8. Schematic representation of the adiabatic S1 and S2-state potentials along the effective antisymmetric mode Q as defined in ref 32 with the respective v = 0 levels and nuclear wave functions indicated in black and red, respectively.

mode introduced by Kopec et al.32 This antisymmetric Q− coordinate reproduces the energy gain and amount of distortion that occurs in the multidimensional normal coordinate space of the excitonic dimer, and the diagram applies generally to excitonic dimers in the weak-coupling limit.32 Figure 8 additionally emphasizes the v = 0 nuclear wave functions of the S1 and S2 states (in black and red, respectively) that characterize the geometry; note that both of these are located within the S1 state double-minimum potential. Within the adiabatic description of the vibronic quenching of excitonic splittings in molecular dimers given in ref 32, the level separation Δvibron can be interpreted as a nonadiabatic tunneling splitting on the lower adiabatic double minimum potential. The G



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Table 4. Structure Parameters of (Benzonitrile)2 in the S0 and First Excited State Calculated at the SCS-CC2/aug-cc-pVDZ Levela parameterb

S0

S1

Δ(S1 − S0)

ref 18c

d(N8H10a) d(N16H2a) α(N8H10aC10) α(C7N8H10a) d(C1C2) d(C2C3) d(C3C4) d(C2H2a) d(C3H3a) d(C4H4a) d(C1C7) d(C7N8) d(C9C10) d(C10C11) d(C11C12) d(C10H10a) d(C11H11a) d(C12H12a) d(C9C15) d(C15N16) RAB,COM Ae/MHz Be/MHz Ce/MHz

235.81 235.81 160.21° 139.99° 141.55 140.78 141.04 109.41 109.45 109.51 145.09 119.01 141.55 140.78 141.04 109.41 109.45 109.51 145.08 119.01 653.78 1607.8 184.7 165.6

233.97 233.56 160.97° 139.16° 145.41 144.35 144.01 109.39 109.40 109.31 142.71 119.64 141.55 140.78 141.04 109.41 109.45 109.51 145.08 119.01 653.51 1579.8 184.3 165.1

−1.84 −2.25 0.76° −0.83° 3.87 3.57 2.96 −0.02 −0.06 −0.20 −2.38 0.62 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 −0.27 −28.0 −0.4 −0.5

−5.36 0.25 0.13 4.0 3.2 3.1 −0.9 −1.1 −0.9 −2.4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 −2.81 −28.08d −0.01d −0.31d

ref 19

−2 −28c +1c −2c

a

Comparison to the experimental results of refs 18 and 19. Bond lengths in pm, and angles in degrees. bAtom numbering as in Figure 1 of ref 18. From column 5 of Table 5 in ref 18. dExperimental values are differences of vibrationally averaged rotational constants (A0′ − A0″, B0′ − B0″, C0′ − C0″). c

−1 The calculated S1/S2 splitting is Δcalc and is a el = 10 cm factor of 5 larger than the observed splitting. The ab initio calculated excitonic splittings cannot be directly compared to the experimental ones, because the effect of vibronic quenching must be considered.20,23,24 The vibronic quenching factor Γ was determined theoretically and experimentally, the values are very close, Γexp = 0.213 and Γcalc = 0.228. The calculated vibronic excitonic splitting between the v = 0 levels of the S1/S2 states is −1 thereby reduced to Δcalc vibron = 2.28 cm , which is in very good agreement with the experimental splitting of 2.1 cm−1. As no S0 → S1 transition is observed for the homodimers (BN)2 and (BN-d5)2, the mixing angle in eq 3 is α = 90°, leading to a complete delocalization of the excitation over the entire dimer. In contrast, for 13C-BN2 the excitation is 92.2% localized on monomers A* and B*, respectively. For the (BNh5)(BN-d5) heterodimer, the excitations are 99.9% localized on either monomer. Our interpretation of the S0 → S1/S2 excitations as being delocalized in (benzonitrile)2 disagrees with the interpretation of Schmitt et al.18 but not with their experimental observations. The fact that the excited state rotational constants for (BN)2 indicate an asymmetric (Cs) symmetric structure18,19 does not contradict the delocalization of the electronic excitation, but is actually expected within the adiabatic description of the vibronic quenching of excitonic splittings in molecular dimers given by ref 32. In the effective-mode description, the lower (S1 state) adiabatic surface of the excitonic dimer exhibits a doubleminimum along the effective antisymmetric coordinate Q−, with the two minima displaced to ±Q−min, away from the symmetric structure at ±Q− = 0. While the excitonically coupled monomers A and B are not symmetry-equivalent at

either of these minima, the S1/S2 coupled vibronic wave functions are delocalized over both wells of the doubleminimum effective-mode potential. Thus, the geometric asymmetry and the electronic symmetry of the delocalized electronic wave functions are not mutually contradictory but arise as a consequence of the vibronic (nuclear-electronic) coupling between the closely spaced S1 and S2 states in the excitonic weak-coupling limit27−29,32 as one of the manifestations of the breakdown of the Born−Oppenheimer approximation in the treatment of excitonic dimers.23,24,32

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected],Tel.++41316314479. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support by the Schweiz. Nationalfonds (Projects 200020-152816 and 200021-132540) is gratefully acknowledged.

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REFERENCES

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Excitonic Splitting, Delocalization, and Vibronic Quenching in the

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