Implications of Intramolecular Interactions on the Fluorescence of a Highly Flexible Ethane-Bridged Porphyrin Dimer

Abstract

Understanding the role of conformational flexibility in multichromophoric systems is crucial for elucidating excited-state processes such as electronic coupling, energy transfer, and exciton–exciton annihilation, which are central to the rational design of artificial light-harvesting assemblies. In the present work, the excited-state dynamics of a highly flexible free-base porphyrin dimer has been investigated and compared with its monomer using femtosecond transient absorption spectroscopy and femtosecond optical gating. While the excited-state kinetics of the dimer closely resemble those of the monomer at low pump fluence, pump-fluence-dependent transient absorption and femtosecond optical gating measurements reveal additional ultrafast components of 1 ps and 18–28 ps. Potential energy surface scan reveals a strong dependence of electronic coupling on the dihedral angle between the two porphyrin units. Comparison of the estimated electronic coupling with the reorganization energy indicates that the dimer lies in the weak-coupling regime. Correlation of femtosecond optical gating measurements with transition dipole moments calculated at different dihedral angles suggests that conformers with more favorable transition-dipole orientations predominantly contribute to the blue side of the emission spectrum. These components are attributed to Förster-mediated singlet–singlet annihilation, arising from the significant spectral overlap between the S ₀ ← S ₁ emission and the S _n ← S ₁ excited-state absorption. Overall, these results demonstrate that conformational flexibility modulates Förster-mediated annihilation dynamics in a porphyrin dimer.

Introduction

The long-standing interest in porphyrins stems from their interesting electronic and optical properties. Their remarkably broad absorption in both the blue region (Soret-B band) and the Q-band of the visible spectrum, along with their high molar extinction coefficients, outstanding thermal and chemical stability, and customizable molecular structure, represents them as highly attractive for a variety of applications, − spanning solar energy conversion, energy storage devices, optical limiting, chemical sensing, photocatalysis, and photodynamic therapy for the targeted killing of cancer cells. Over and above porphyrin monomers, conjugated porphyrin arrays have drawn significant attention as efficient bioinspired molecular systems for light harvesting, charge separation, and photocatalytic applications. − They are examples of minimal multichromophoric systems for elucidating fundamental excited-state processes such as electronic coupling, energy transfer (ET), and exciton–exciton annihilation (EEA). − Their defined molecular connectivity provides a useful platform for investigating nonlinear relaxation pathways that emerge under high excitation densities while minimizing the structural complexity often encountered in extended arrays or supramolecular assemblies. EEA, in which two singlet excitons interact and result in the loss of one exciton and promotion of the other to a higher excited state, has been extensively studied in multichromophoric systems. − In large molecular assemblies, EEA has frequently been interpreted within a diffusion-limited framework, where excitons migrate over multiple chromophoric units prior to annihilation. In contrast, in compact architectures, where chromophores are covalently linked and held in close spatial proximity, EEA has been shown to occur intramolecularly through Coulombic coupling and resonance ET, without the requirement of long-range exciton diffusion. ,,

$$S^{*}+S^{*}\to S+S^{**}\stackrel{\mathrm{f}\mathrm{a}\mathrm{s}\mathrm{t}\mathrm{n}\mathrm{o}\mathrm{n}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{d}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{y}}{\to }S+S^{*}$$

In this context, 1,2-bis­(meso-octaethylporphyrinyl)­ethane (dimer) offers a suitable model system for investigating such intramolecular exciton–exciton interactions. The short, nonconjugated ethane linker in the dimer enforces close spatial proximity between the two porphyrin units while largely suppressing through-bond π-conjugation. As a result, the interaction between chromophores is dominated by through-space Coulombic coupling, which depends sensitively on their relative orientation. This leads to the formation of excitonic states with varying dihedral angles, reflecting the interplay between interchromophoric coupling and structural flexibility. Under sufficiently high excitation fluence, the simultaneous population of two singlet excitons within a single dimer becomes possible, creating favorable conditions for exciton–exciton interactions. In molecular systems of this size, EEA is not expected to proceed via classical exciton diffusion. Instead, annihilation can be mediated by Förster ET between interacting singlet excited states, provided that there is a significant overlap between donor emission spectra and excited-state absorption spectra of the acceptor. This mechanism has been previously invoked to describe singlet–singlet annihilation in porphyrin dendrimers, where intramolecular ET governs the annihilation kinetics rather than diffusive encounters between excitons.

In the present work, excited-state dynamics of free-base 2,3,7,8,12,13,17,18-octaethylporphyrin (H₂OEP, monomer, Figure a) and highly flexible 1,2-bis­(meso-octaethylporphyrinyl)­ethane (dimer, Figure b) are investigated using femtosecond transient absorption spectroscopy. Pronounced fluence-dependent excited-state dynamics has been observed, consistent with the onset of EEA. The strong spectral overlap between S ₀ ← S ₁ emission and S _n ← S ₁ excited-state absorption supports that the annihilation process is assigned to singlet–singlet annihilation mediated by Förster-type interactions rather than diffusion-controlled mechanisms. The results establish the ethane-bridged free-base porphyrin dimer as a minimal model system for probing conformation-dependent Förster-mediated EEA in non-metalated porphyrin assemblies.

1.

Chemical structures of the (a) monomer and (b) dimer.

Experimental Section

Materials

Fresh batches of free-base 2,3,7,8,12,13,17,18-octaethylporphyrin (H₂OEP, monomer) and 1,2-bis­(meso-octaethylporphyrinyl)­ethane (dimer) have been synthesized using a previously reported procedure.

Sample Preparation and Steady-State Spectroscopy

All the spectroscopic measurements are carried out in spectroscopy-grade dichloromethane (CH₂Cl₂) from Spectrochem (Mumbai, India). Electronic absorption and emission spectra are recorded in a JASCO V-750 UV–vis spectrophotometer and a Horiba Jobin Yvon Fluoromax Plus fluorimeter, respectively. Maximum absorbance is kept below 0.1 at the excitation wavelength (λ_ex). Fluorescence quantum yields of the samples (ϕ_f(s)) are worked out using meso-tetraphenylporphyrin (TPP) as a standard reference (ϕ_f(R) = 0.13), using the following equation

$${\varphi }_{\mathrm{f}(\mathrm{s})}={\varphi }_{\mathrm{f}(\mathrm{R})}\times \frac{I_{\mathrm{S}}}{I_{\mathrm{R}}}\times \frac{(1-{10}^{{-A}_{\mathrm{R}}})}{(1-{10}^{{-A}_{\mathrm{S}}})}\times \frac{n_{\mathrm{S}}^2}{n_{\mathrm{R}}^2}$$ 1

where I is the integrated fluorescence intensity, determined from the area under the fluorescence spectrum. A is the absorbance at λ_ex. The equation is corrected for the solvent refractive index (n). Subscripts S and R stand for the sample and reference, respectively.

Time-Resolved Spectroscopy

Fluorescence decays are recorded on a HORIBA DeltaFlex time-correlated single-photon counting (TCSPC) spectrometer. Samples are excited with the second harmonic (λ_ex = 400 nm) of the output of a Mai-Tai Laser, operating at an 8 MHz repetition rate. Fluorescence transients are collected at a magic angle (54.7°) of polarization for vertically polarized excitation to eliminate anisotropic artifacts. The full width at half-maximum (fwhm) of the instrument response function, using a hybrid picosecond photon detector, is 66 ps. The decays are fitted to a sum of exponential functions (eq ), with iterative reconvolution by EzTime software

$$I(t)=\sum _i{a}_i\exp \left(\raisebox{1ex}{$-t$}\!\left/ \!\raisebox{-1ex}{${\tau }_i$}\right.\right)+b$$ 2

where τ _i is the lifetime of the ith species with amplitude a _i at time t = 0 and b is the background signal. The radiative rate constant (k _R) and nonradiative rate constant (k _NR) are determined following eqs and :

$$k_{\mathrm{R}}=\frac{{\varphi }_{\mathrm{f}}}{{\tau }_{\mathrm{f}}}$$ 3

$$k_{\mathrm{N}\mathrm{R}}=\frac{(1-{\varphi }_{\mathrm{f}})}{{\tau }_{\mathrm{f}}}$$ 4

Fluorescence transients in the femtosecond–picosecond domain are recorded using femtosecond optical gating (FOG) with λ_ex = 400 nm. The second harmonic, 400 nm of a modelocked 100 fs Ti:sapphire (Tsunami, Spectra Physics, USA, 1 W, 80 MHz repetition rate), is used for excitation. Details of the setup are discussed elsewhere. All of the experiments have been performed at 298 K.

Femtosecond transient absorption spectroscopy has been employed to decipher the excited-state dynamics of the monomer and dimer, revealing key differences in their photophysical behavior. Pulsed light with a wavelength of 800 nm, having an fwhm of 75 fs, an energy of 3.5 mJ, and a repetition rate of 1 kHz, has been obtained from an amplified laser (Libra, Coherent, USA). About 1.35 mJ of the output has been used to pump an optical parametric amplifier (OPA-TOPAS, Light Conversion, Lithuania) to generate tunable pump pulses of 200 fs. A pump wavelength of 400 nm is used for all the experiments reported here. A small portion of the 800 nm light is focused on a CaF₂ plate to generate white light continuum (WLC) (360–750 nm) which is used as a probe to monitor the system in the presence and absence of pump wavelength, and a delay is given to the probe pulse w.r.t the pump pulse to investigate how the excited-state processes evolve with time. The white light has been divided into probe and reference beams using a beam splitter. The reference beam is used for the correction of real-time intensity fluctuation of the WLC. The pump pulse is passed through a synchronized mechanical chopper to block every alternative pump pulse, creating a succession of “pump” and “no pump” situations. The pump (λ_pump = 400 nm) and probe pulses are spatially overlapped on the sample solution, which is placed in a rotating cell having a path length of 1 mm. To minimize any effect of rotational diffusion, polarization is set to the magic angle (54.7°). Steady-state absorbance of each sample has been recorded before and after performing the experiments to check for any degradation of the sample. All the recorded data are chirp-corrected for the removal of group velocity dispersion using Surface Minor Pro (v.4.0). Single-wavelength kinetics have been fitted with IGOR Pro (v6.0.5) software, and global analysis has been performed with the R package TIMP and its graphical user interface of Glotaran (v1.5.1).

Quantum Chemical Calculations

The electronic structure calculations for the ground and excited states are performed with Orca 6.0. The ground-state geometry optimization of the monomer and dimer is carried out using a density functional theory (DFT) method with the B3LYP/def2-SV­(P) level of theory. The final ground-state optimized geometry (Tables S1 and S2) of the compounds obtained is used to compute the absorption spectra (Tables S3 and S4) with the ωB97X-D4/def2-SVPD level of theory. Vibrational frequency analysis using DFT calculations and natural transition orbitals (NTOs) (Figure S3) using the time-dependent density functional theory (TDDFT) have been carried out with the same level of theory. A rigid potential energy surface (PES) scan along the C₂₄–C₈₁–C₈₂–C₅₁ dihedral coordinate of the dimer is computed at the same level of theory. Transition dipole moment calculations have been performed for each dihedral angle. Visualizations of the optimized geometries (Figure S4), absorption spectra, vibrational modes, and NTOs are done by IboView and Chemcraft visualization programs.

Results and Discussion

Effect of Bridging on the Steady-State Spectra

The absorption spectra of the monomer and dimer are characterized by a strong peak in the UV–visible region (300–450 nm), known as the Soret (B) band, associated with the S ₂ ← S ₀ electronic transition, and weaker red-shifted absorption bands (spanning from 500 to 700 nm, Q-bands), assigned to S ₁ ← S ₀ (Figure ). These results are the same as those reported earlier. , Both B- and Q-bands arise from π–π* transitions. A sharp Soret band centered at 398 nm and four distinct Q peaks at 496, 531, 566, and 619 nm have been observed for the monomer. Within the framework of Gouterman’s four-orbital model, , these peaks can be assigned to x-polarized Q _x (1 ← 0), Q _x (0 ← 0) and y-polarized Q _y (1 ← 0), Q _y (0 ← 0), respectively. Although two almost degenerate transition dipoles B _x and B _y create one sharp Soret band in porphyrin monomer, the porphyrin dimer exhibits a characteristic broad Soret band that is centered around 406 nm and is slightly red-shifted and four Q bands centered at 514, 549, 584, and 637 nm compared to the monomer. In a weak exciton-coupling regime, the electronic absorption spectra of interacting chromophores often retain large monomer-like spectral signatures, with only modest shifts or broadening relative to non-interacting chromophores. The structure–spectrum relationship has been further analyzed using the Kasha exciton model to describe the excitonic coupling between two weakly interacting chromophoric units in a covalently linked molecule. For side-to-side (anti) conformation (Figure ), the high-energy transition is forbidden, and in the spectrum, a red shift of the Soret band is observed relative to the Soret band of the monomer, as observed in the dimer. However, with the dipoles at an angle (syn), both the “blue” and “red” components of split B _y contribute to the Soret band (Figure ). Since the dimer is connected through a flexible ethane bridge, it can adopt several conformations with different orientations of the dipole moment vectors. Consequently, all the B _y dipole moments do not orient in the same direction during excitonic coupling, giving rise to broadening of the spectra. According to a previous report, the dimer can exist in both anti and syn conformations. With increasing solvent polarity, the anti conformation becomes more favorable. In polar solvents, such as, CH₂Cl₂, the broadened and red-shifted Soret band suggests that both anti and syn conformations may coexist in solution, although the anti conformation is expected to be more favorable, consistent with the ground-state optimized geometry having a dihedral angle of 180° (vide infra).

2.

(a) Normalized absorption spectra of the (i) monomer and (ii) dimer, (b, c) (iii, vi) Q bands (expanded from (a)), (v, viii) excitation spectra, and (iv, vii) emission spectra of the (iii–v) monomer and (vi–viii) dimer. (d) Fluorescence decays of the (ix) monomer and (x) dimer upon excitation at the Soret band.

3.

Kasha point-dipole model for the exciton coupling of electronic transitions in the dimer.

The fluorescence spectra of the monomer (Figure b) exhibit an intense Q _y (0 ← 0) emission band centered at 622 nm with a less-intense band at 688 nm, corresponding to Q _y (1 ← 0). On the contrary, the fluorescence spectra of the dimer (Figure c) broaden and red-shift to 645 and 710 nm with increasing intensity of the secondary peak, which suggests some excitonic and electronic communications between the two chromophoric units. To further probe the possible conformational heterogeneity, excitation spectra monitored at λ_em = 645 and 710 nm have been compared (Figure S1). Although both excitation spectra broadly resemble the steady-state absorption spectrum, slight differences are observed in the Soret band region. In particular, the excitation spectrum monitored at λ_em = 645 nm appears slightly broader relative to that monitored at λ_em = 710 nm, suggesting that different conformational subpopulations with varying excitonic coupling strengths contribute differently to emissive states. These observations are consistent with an inhomogeneous ensemble of structures arising from the conformational flexibility of the ethane bridge. The small Stokes shift in fluorescence (Figure c) corresponds to a lower reorganization energy (λ) of 97 cm^–1. The fluorescence quantum yield (ϕ_f) of the dimer is significantly lower than that of the monomer (0.03 and 0.14, respectively, Table ). This substantial quenching of fluorescence in the dimer cannot be explained solely by changes in radiative decay but rather by enhanced nonradiative processes. The decrease in k _R is consistent with a decrease in oscillator strength in the dimer, which suggests reduced transition dipole strength or redistribution of oscillator strength due to excitonic interaction, while the enhanced k _NR reflects additional nonradiative relaxation channels opened by the coupling between two chromophores and conformational motion.

1. Photophysical Parameters of the Monomer and Dimer in CH₂Cl₂ .

sample	ε(400nm)[M–1 cm–1]	τf (ns)	ϕf	k R (107 s–1)	k NR (107 s–1)
monomer	159,000	12.2	0.14	1.4	7.05
dimer	109,800	5.6	0.03	0.5	17.4

Excited-State Dynamics

No emission wavelength dependence is observed in nanosecond fluorescence dynamics (Figure d). The fluorescence decays are exponential, with a lifetime (τ_f) of 12.2 ± 0.01 ns for the monomer (similar to the previously reported value) and 5.6 ± 0.04 ns for the dimer. The shorter lifetime of the dimer can be attributed to the interchromophoric interaction between the two rings, facilitating faster nonradiative deactivation. The corresponding nonradiative rates (k _NR) are calculated using the values of ϕ_f and τ_f (Table ).

Quantum Chemical Calculation

To explore the effect of bridging in electronic states and coupling in the dimer, geometry optimization in the ground state has been performed. The two Q bands observed in the ground state for the monomer (i and ii) now split up to give four excitonic states (i, ii, iii, and iv) in the dimer (Figure S2). The oscillator strengths are calculated within the Franck–Condon approximation. The greater spectral width of the dimer compared to the monomer suggests the presence of several excitonic transitions. The Coulombic interaction between the interacting chromophore transition dipoles has been elucidated (Table ) by dipole–dipole coupling using eq

$$V^{\mathrm{d}-\mathrm{d}}=\frac{1}{4\pi {\epsilon }_0{\eta }^2}\frac{\kappa |{\mu }_{\mathrm{D}}||{\mu }_{\mathrm{A}}|}{R^3}$$ 5

2. Electronic Couplings of the Porphyrin Dimer Calculated by Dipole–Dipole Coupling at Optimized Geometry.

donor transition	acceptor transition	κ	V d–d
S 1	S 1	0.974	12.6 cm–1

Here, |μ_D| and |μ_A| represent the magnitudes of the transition dipoles. R is the center-to-center distance. Orientation factor $\kappa =\widehat{r_{\mathrm{D}}·}\widehat{r_{\mathrm{A}}·}-3(\widehat{r_{\mathrm{D}}·}\mathrm{R̂})(\widehat{r_{\mathrm{A}}·}\mathrm{R̂})$ , where R̂ is a unit vector connecting the center of the transition moments and $\widehat{r_N}$ represents unit vectors in the directions of transition dipoles. ε₀ and is the vacuum permittivity, and η is the refractive index of the solvent. NTOs of the dimer (Figure S3) show that electron density is largely localized on one chromophore for the lowest energy excitations (S ₁ ← S ₀ and S ₂ ← S ₀), whereas higher energy excitations (S ₃ ← S ₀ and S ₄ ← S ₀) are delocalized over both monomeric units. However, due to conformational heterogeneity, the dimer can exhibits a distribution of conformers with varying excitonic couplings, which can act as a perturbation and localize excitation on a given chromophore or region of the macrocycle. , The rigid PES scan along the C₂₄–C₈₁–C₈₂–C₅₁ (Figure ) dihedral coordinate reveals a minimum at 180° (Figure a), corresponding to an anti conformer of the two porphyrin units, in agreement with the optimized ground-state geometry. As the dihedral angle decreases from 90° to 180° (more planar conformations), the ground state (S ₀) is stabilized more strongly than the excited states (E _{S 1} –E _{S 0} = 2.086 eV at 90° and E _{S 1} –E _{S 0} = 2.187 eV at 180°), leading to a progressive increase in energy gaps. This indicates that enhanced planarity preferentially stabilizes the ground state relative to excited states. In addition, normal mode analysis of the ground-state optimized geometry structure reveals low-frequency vibrational modes (Figure S5) in the range of ∼288–300 cm^–1, which exhibit significant torsional motion of the ethane bridge and modulate the dihedral angle between the two porphyrin units. Such modes are expected to couple to the electronic degrees of freedom, facilitating vibronic coupling and intramolecular vibrational energy redistribution and thereby contributing to the observed nonradiative relaxation dynamics.

4.

(a) Potential energy surfaces of the dimer for singlet and triplet states by changing the C₈₁ atom coordinates in-plane and (b) transition dipole moment (TDM) as a function of C₂₄–C₈₁–C₈₂–C₅₁ dihedral angle for the dimer.

Femtosecond Optical Gating

Ultrafast components of excited-state relaxation have been probed by FOG, with 10 mW of λ_ex = 400 nm and λ_em = 584–680 nm. Interestingly, both the monomer and the dimer exhibit λ_em dependence in the ultrafast time regime (Figure ). No rise time is discernible following excitation at the Soret band, which suggests that the S ₁ state is populated instantaneously (i.e., within the instrument time scale of 300 fs). An ultrafast decay component appears on the blue side of the spectrum and, toward the fluorescence maximum, vanishes, indicating ultrafast processes occurring prior to the formation of the relaxed S ₁ state in the monomer. Three different time constants of 1 ps, 6–21 ps, and a long component have been obtained for the monomer (Table S5). The origin of the two ultrafast components is elucidated in the femtosecond transient absorption (fs-TA) experiments (vide infra). The contribution of the ultrafast component is more for the dimer compared to the monomer. The initial decay components of 0.25–1 ps and 4–31 ps (Table S5) in the fluorescence temporal profiles of the porphyrin dimer exhibit an excitation fluence dependence (Figure S7). Thus, these components arise from EEA processes contributed by the high density of excitons produced under high excitation fluences, and the long-lived tail is due to the fluorescence emission of the porphyrin dimer as obtained from TCSPC. ,

5.

Ultrafast fluorescence decays of the (a) monomer and (b) dimer following Soret band excitation (λ_ex = 400 nm) with a laser power of 10 mW in CH₂Cl₂ solvent. The emission wavelengths are written alongside each decay.

Wavelength-dependent ultrafast fluorescence dynamics observed in the FOG measurements can be rationalized in terms of conformational heterogeneity within the ethane-bridged porphyrin dimer. As evidenced by the dihedral angle-dependent PES scan (Figure a), a distribution of dimer geometries exists in solution, giving rise to varying degrees of interchromophore electronic coupling. The electronic couplings between porphyrin units can be correlated to the dihedral angle between porphyrin units. Conformers with smaller dihedral angles bring the two porphyrin units into closer proximity and more favorable mutual orientation, resulting in enhanced dipole–dipole coupling and larger excitonic splitting (Figure b). ,, These higher-energy conformers with relatively enhanced coupling contribute predominantly to the blue side of the emission spectrum and exhibit significantly faster singlet–singlet exciton annihilation mediated by Förster-type ET. Consequently, an ultrafast annihilation component is most pronounced at shorter emission wavelengths. In contrast, emission toward the red side of the spectrum is dominated by more stable conformers with larger dihedral angles, increased interchromophore separation, and reduced dipole–dipole coupling strength. Förster-mediated singlet–singlet annihilation remains operative in these geometries but proceeds on a slower time scale, giving rise to the longer annihilation component observed in the fluorescence temporal profiles. The opposite trend in the wavelength dependence of the two amplitudes associated with the fast and slow annihilation components thus reflects the spectral weighting of distinct conformational sub-ensembles rather than sequential annihilation dynamics. Near the fluorescence maximum, where emission is governed by the lowest-energy conformers with minimal interchromophore coupling, the contribution from annihilation becomes negligible, and the decay is dominated by the intrinsic radiative lifetime of the dimer.

Femtosecond Transient Absorption Spectroscopy

Transient absorption spectroscopy of the monomer and dimer has been performed on degassed solutions of CH₂Cl₂, λ_pump = 400 nm, i.e., in the spectral region of the Soret band. A low pump fluence (i.e., 0.2 μJ) is maintained to avoid the effect of EEA. A broad photoinduced absorption (PIA) arises throughout the visible region with several dips at 495, 525, 558, and 622 nm, which represents ground-state bleach (GSB) corresponding to S ₁ ← S ₀ transition, taking place within 1 ps (Figure a). Post excitation at 400 nm, ultrafast S ₁ ← S ₂ internal conversion takes place within a sub 100 fs time scale. ,, Hence, the photophysics that has been observed is mainly from the S ₁ state, as evident by the rapid formation of the GSB. The PIA feature narrows down toward 455 nm, accompanied by the shift and rise in GSB at 556, 595, and 664 nm, which denotes vibrational relaxation occurring within the S ₁ state. The PIA spectral feature, however, changes at a longer wavelength, giving rise to an absorption peak at around 690 nm. At longer time scales, the intensity of the PIA feature decreases with a change in shape (peak broadening at 450 nm). Single-wavelength kinetics at λ_probe = 460 nm for the monomer yields 3 components, i.e., two rise components of 1 and 34 ps and a non-decaying long component (Table S6). It is difficult to trace such complicated dynamics by single-wavelength kinetics. Global analysis has been performed to address this issue. Five principal components have been obtained (Figure b and Table ). The ultrafast component of 0.9 ps exhibit growth in absorbance from 430 to 535 nm and loss in absorption at longer wavelengths, which can be attributed to intramolecular vibrational relaxation within the Q bands. The observed temporal and spectral features are consistent with an intramolecular vibrational energy redistribution (IVR) process, wherein energy initially localized in a specific subset of vibrational modes is rapidly redistributed across a broader manifold of vibrational states. This redistribution occurs at constant total energy and is driven by the coupling between intramolecular vibrational modes. Next, a decay component of 14 ps is observed. The HOMO–LUMO energy gap renormalization in the porphyrin macrocycle can occur as a result of photoexcitation-induced thermal expansion, followed by the gradual structural recovery of the macrocycle, which is facilitated through vibrational relaxation mediated by coupling with the surrounding solvent. , Next, another rise component of 60 ps has been observed, which has a similar contribution as the previous component. At this similar time scale, a small spectral shift of the Q bands has been monitored. The 60 ps component has a significant contribution toward GSB and SE. Hence, this rise component may be related to vibrational cooling (VC) in the Q _y state. Next, another 315 ps component which has a different PIA shape and contribution to GSB denotes relaxation of Q _y (0) prior to fluorescence emission. This time scale is too slow to be ascribed to solvent relaxation; rather, this component is ascribed to conformational changes, i.e., inter-porphyrin torsional relaxation in the excited-state geometry. , Now, the population dynamics for equilibrated Q _y and T ₁ are combined in a non-decaying fourth component which is much longer than our instrument time scale.

6.

Femtosecond transient absorption spectra of the (a) monomer and (c) dimer following Soret band excitation (λ_pump = 400 nm) in CH₂Cl₂ solvent. Decay-associated spectra obtained from global analysis of the (b) monomer and (d) dimer.

3. Time Constants for the Dimer from the Global Analysis of TA Data.

	τ (ps)
	monomer	dimer
energy redistribution in the singlet excited state manifold	0.9
	14	13
	60	68
	315
fluorescence decay and triplet relaxation	>1000

Soret-band excitation of the dimer at low pump fluence (0.2 μJ) leads to a broad PIA across the visible region within the instrument response (<0.2 ps), arising from rapid internal conversion from higher-lying singlet states to the S ₁ manifold (Figure c). The early time PIA, peaking at 465 nm, is assigned to S _n ← S ₁ transitions and reshapes within 1 ps, during which weak GSB features emerges at 508 and 575 nm, corresponding to the Q-band transitions of the dimer. On the 1–10 ps time scale, the PIA decreases in intensity and red-shifts to 475 nm, accompanied by a slight blue shift of the GSB, indicative of VC and conformational relaxation within the S ₁ excitonic state. SE centered at 623 nm develops on a sub-picosecond time scale, reflecting formation of a fully relaxed emissive S ₁ state. At longer delay times (>1 ns), the PIA feature decreases in intensity, and a broad, long-lived PIA persists.

Three components have been obtained from the global analysis of the TA data of the dimer (Figure d and Table ). The longest component corresponds to the long-lived excited-state population, accounting for incomplete GSB recovery and SE decay. Two components of 13 and 68 ps have contributions to the PIA and formation of GSB. The 68 ps component has negative contribution around 460 nm and positive contribution around 570 nm, indicating an increase of transient absorption spectra amplitude and some spectral red shift in the region from 460 to 570 nm. This can clearly be seen (Figure ), where at early time scales, the positive band at 460 nm and the negative band at 570 nm increase in amplitude and then red-shift. Therefore, these two components account for the energy redistribution in the singlet excited-state manifold. A number of physical processes, i.e., intramolecular vibrational energy redistribution, VC, and electronic ET, within the excited-state manifold may contribute, which are difficult to distinguish. Finally, the long component has a contribution to the broad and positive PIA and negative GSB signals throughout the visible wavelength side of the transient spectra. The incomplete recovery of the GSB at the longest measured pump–probe delays suggests the presence of a long-lived excited-state population, indicating that a fraction of the excited-state population may have undergone triplet formation.

Excitation Intensity Dependence

At higher pump fluence (2.8 μJ), the kinetics of the PIA of the fs-TA spectra of the dimer change significantly, while no intensity dependence is observed for the monomer, which excludes excimer formation and aggregation. The probability of two excitations per dimer within the pump–probe overlap volume increases with increasing pump fluence.

The average number of excitons ⟨n*⟩ per dimer generated by different pump fluence is calculated using eq (Table )­

$${⟨n^{*}⟩}_{\mathrm{v}\mathrm{o}\mathrm{l}}=\frac{N_{\mathrm{p}\mathrm{u}\mathrm{m}\mathrm{p}}}{\pi d{r}_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{b}\mathrm{e}}^2}[1-{10}^{-\mathrm{O}\mathrm{D}({\lambda }_{\mathrm{p}\mathrm{u}\mathrm{m}\mathrm{p}})}]$$ 6

where N _pump denotes the number of photons in the sample region in which the pump and probe pulse are overlapping, d is the sample thickness (1 mm), and OD (at λ_pump = 400 nm) is kept as 1.

$$N_{\mathrm{p}\mathrm{u}\mathrm{m}\mathrm{p}}=\frac{{\int }_0^{r_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{b}\mathrm{e}}}r{e}^{-2r^2/r_{\mathrm{p}\mathrm{u}\mathrm{m}\mathrm{p}}^2}dr}{{\int }_0^{\infty }r{e}^{-2r^2/r_{\mathrm{p}\mathrm{u}\mathrm{m}\mathrm{p}}^2}dr}\times \frac{E_{\mathrm{p}\mathrm{u}\mathrm{m}\mathrm{p}}{\lambda }_{\mathrm{p}\mathrm{u}\mathrm{m}\mathrm{p}}}{hc}$$ 7

where

$$2r_{\mathrm{p}\mathrm{u}\mathrm{m}\mathrm{p}}=500\mu \mathrm{m}$$

$${2r}_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{b}\mathrm{e}}=205\mu \mathrm{m}$$

$${⟨n^{*}⟩}_{\mathrm{m}\mathrm{o}\mathrm{l}}=\frac{{⟨n^{*}⟩}_{\mathrm{v}\mathrm{o}\mathrm{l}}}{c_{\mathrm{d}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{r}}}$$ 8

where c _dimer is the molar concentration of the dimer, obtained from the Beer–Lambert relation.

4. Average Number of Excitons per Dimer for Different Pump Pulse Energies.

εdimer [M–1 cm–1]	E pump [μJ]	$${⟨n^{*}⟩}_{\mathrm{m}\mathrm{o}\mathrm{l}}$$
109,800	0.2	0.056
	0.7	0.192
	1.2	0.332
	1.9	0.524
	2.8	0.772

From these data, it is evident that, for higher fluences, exciton density increases (Table S7) and the probability of more than one exciton generation increases in the dimer (Table ). This increases the probability of EEA, thereby opening an additional excited-state relaxation pathway. Experimentally, this manifests as the emergence of a faster decay component at early time scales, evident from the steeper initial slope of the transient absorption traces in the 440–500 nm excited-state absorption region for the dimer.

Assignment of the Annihilation Time Constants

The dimer is highly flexible, and therefore, there are distributions of different distances and dipole-moment orientations. The annihilation rate is strongly dependent on the distance between the chromophores and the orientation of the dipole moments. The significant overlap between the S ₀ ← S ₁ emission and S _n ← S ₁ PIA strongly supports the assignment of the observed annihilation to a singlet–singlet annihilation process. However, the poor spectral overlap between the T ₁ absorption and the S ₁ emission renders singlet–triplet annihilation inefficient. Since the transition dipole coupling for the lowest excited-state transition (Table ) is smaller than the reorganization energy (λ), the dimer can be reasonably treated within the weak-coupling regime. Therefore, the excitation intensity-dependent decay is assigned to Förster-mediated singlet–singlet annihilation, in which one excited monomeric unit transfers energy to a neighboring excited monomeric unit through Coulombic coupling, generating a higher excited state that rapidly relaxes back to the lowest singlet state. To quantitatively assess this assignment, the Förster radius has been estimated from the spectral overlap of the normalized emission spectrum of the donor, F _D(λ) and the excited-state spectrum of the acceptor (Note S1), yielding R ₀ ≃ 2.5 nm, and the corresponding Förster energy transfer time (t ^ET) is estimated to vary from 10 ps to 65 ps (Note S1), providing a quantitative basis for the assignment of the annihilation time constants discussed below.

Assuming that the annihilation can be divided into fast (f) and slow (s) processes, the change in the number of exciton pairs responsible for each process is given by

$$\frac{{\mathrm{d}E}_{\mathrm{M}}}{\mathrm{d}t}=-k_{\mathrm{M}}{E}_{\mathrm{M}}$$ 9

where E _M is the number of the exciton pairs related to either the fast (M = f) or the slow (M = s) annihilation process with E _M (t = 0) = E _M0. The corresponding annihilation rate constants k _M include the Förster ET, which can doubly excite one chromophore and deexcite the other, and the following fast internal conversion process within the first chromophore. Internal conversion, ISC, and radiative decay to the ground state are not accounted in eq , as it only describes the exciton pairs that annihilate. The decay of the singlet state (S) and the rise of the triplet state (T) are given by

$$\frac{\mathrm{d}S}{\mathrm{d}t}=-kS(t)+k_{\mathrm{f}}{E}_{\mathrm{f}}(t)+k_{\mathrm{s}}{E}_{\mathrm{s}}(t)$$ 10

where k _f E _f(t) and k _s E _s(t) represent the formation of a surviving S ₁ exciton following annihilation of exciton pairs.

$$\frac{\mathrm{d}T}{\mathrm{d}t}=k_{\mathrm{I}\mathrm{S}\mathrm{C}}S(t)-k_{\mathrm{T}}T(t)$$ 11

where k is the sum of the radiative decay rate (k _r), the internal conversion rate (k _IC), and the intersystem crossing (ISC) rate to triplet states (k _ISC), S(t = 0) = S ₀, and T(t = 0) = 0. The decay of the triplet state k _T ≪ k _ISC and is therefore set to zero.

The observed transient absorption signal at a given probe wavelength, where ground-state bleaching and stimulated emission are not present, i.e., from 425 to 500 nm, can be described by

$$\mathrm{\Delta }A(t)=S(t)+pT(t)+2E_{\mathrm{f}}(t)+2E_{\mathrm{s}}(t)$$ 12

The annihilation amplitudes contribute twice since they each denote a pair of excitons. p is the ratio between the extinction coefficient of the singlet excited transition and the triplet transition at the selected probe wavelength. The solutions to eqs – inserted in eq yield

$$\mathrm{\Delta }A(t)=A_0+A_1\exp (-kt)+A_2\exp (-k_{\mathrm{s}}t)+A_3\exp (-k_{\mathrm{f}}t)$$ 13

where

$$A_0=\frac{{pk}_{\mathrm{I}\mathrm{S}\mathrm{C}}}{k}[S_0+E_{\mathrm{S}0}+E_{\mathrm{f}0}]$$ 14

$$A_1=(1-\frac{{pk}_{\mathrm{I}\mathrm{S}\mathrm{C}}}{k})[S_0+\frac{k_{\mathrm{f}}}{k_{\mathrm{f}}-k}{E}_{\mathrm{f}0}+\frac{k_{\mathrm{s}}}{k_{\mathrm{s}}-k}{E}_{\mathrm{S}0}]$$ 15

$$A_2=[1+\frac{k-{pk}_{\mathrm{I}\mathrm{S}\mathrm{C}}}{k-k_{\mathrm{s}}}]E_{\mathrm{S}0}$$ 16

$$A_3=[1+\frac{k-{pk}_{\mathrm{I}\mathrm{S}\mathrm{C}}}{k-k_{\mathrm{f}}}]E_{\mathrm{f}0}$$ 17

The singlet–singlet annihilation kinetics (Figure ) have been reproduced using eq . For the monomer, no annihilation can occur (Figure S6), and eq reduces to exponential (ignoring τ_rise as the origin is different and has been discussed earlier). The transient kinetics measured at the lowest excitation intensity is exponential with a long non-decaying component. With increasing excitation intensity, multiexponential kinetics are observed in the dimer. The need for at least three components to fit the decays (Figure ) suggests two annihilation time constants observed in the dimer. The two ultrafast time constants, 1 ps and 18–28 ps, and a slow (>1 ns) non-decaying PIA component associated with a triplet state absorption are obtained by fitting the single-wavelength kinetics at high pump fluences (Table ). Since neither of the two ultrafast components is observed in the monomer, they are assigned to the singlet–singlet annihilation processes. The calculated Förster energy transfer times (t ^ET) of 10–65 ps are in reasonable agreement with the experimentally extracted annihilation components and corroborate the assignment of the excitation intensity-dependent decay to Förster-mediated singlet–singlet annihilation. Hence, it is reasonable to expect that the two different structural conformer distributions, i.e., anti conformers and syn conformers, may give rise to the two annihilation time constants.

7.

Single-wavelength kinetics of the dimer at different pump fluences. λ_probe = 460 nm.

5. Time Constants Obtained from Single-Wavelength Kinetics Fitting of the Dimer at Different Pump Fluences .

pump fluence (μJ)	τ1 (ps)	A 1	τ2 (ps)	A 2	τ3 (ns)	A 3
0.2	-	-	-	-	>1	1.00
0.7	0.90 ± 0.04	0.19	28.00 ± 1.54	0.50	>1	0.3
1.2	1.03 ± 0.06	0.42	25.00 ± 1.72	0.48	>1	0.09
1.9	1.18 ± 0.05	0.50	18.01 ± 0.44	0.46	>1	0.04
2.8	1.32 ± 0.03	0.67	23.26 ± 0.72	0.30	>1	0.03

^aλ_probe = 460 nm.

Conclusion

The present work elucidates the effect of conformational flexibility introduced by an ethane bridge in the electronic structure and excited-state dynamics of a porphyrin dimer. Compared with the monomer, the dimer exhibits broadened and slightly red-shifted Soret absorption and structured Q bands, consistent with excitonic interactions and conformational heterogeneity. The reduced fluorescence quantum yield and shortened lifetime indicate efficient nonradiative decay, suggesting significant interactions between the two chromophores. Global analysis of the transient absorption data at low pump fluence reveals three components of 13 ps, 68 ps, and a non-decaying component governed by internal conversion, intramolecular vibrational energy redistribution, VC, and conformational relaxation closely resembling monomeric behavior. At higher pump fluences, however, the dimer displays clear pump fluence-dependent dynamics, manifested as additional ultrafast decay components of 1 ps and 18–28 ps that are absent in the monomer. These features are conclusively assigned to singlet–singlet exciton annihilation, enabled by the increased probability of multiple excitations within a single dimer and facilitated by favorable chromophore orientations in specific conformers. PES scan and transition dipole moment calculations show that the electronic coupling varies with the dihedral angle between the two porphyrin units. The estimated Coulombic interaction between the interacting chromophores is smaller than the reorganization energy, placing the dimer in a weak coupling regime. Within this regime, conformational variations in interchromophore distance and transition-dipole orientation modulate the efficiency of Förster-mediated singlet–singlet annihilation. Higher-energy conformations with more favorable dipole orientations are proposed to contribute predominantly to the blue side of the emission spectrum, where faster annihilation is observed. These findings provide important insights into structure–dynamics relationships in multichromophoric systems and are directly relevant for the rational design of artificial light-harvesting assemblies and excitonic materials where controlled energy flow and annihilation processes are critical.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsphyschemau.6c00042.

• Optimized geometries, coordinates, TD-DFT plots, torsional mode and additional experimental details such as estimation of exciton density, single-wavelength kinetics and fitting of TA and FOG data, estimation of Förster radius, Förster-type annihilation rate, and spectral overlap plot (PDF)

The authors declare no competing financial interest.