Internal conversion dominates the excited state dynamics and fluorescence efficiency of mono-substituted TPE-BODIPY dyes

Abstract

In this study, we employ Density Functional Theory (DFT) and Time-Dependent DFT (TDDFT) to systematically investigate the excited-state dynamics of a series of six mono-tetraphenylethylene (TPE)–substituted BODIPY dyes (BDP-TPE-1 to -6). By modulating the TPE moiety with electron-donating (methoxy) and -accepting (dicyanovinyl) groups, we unravel the structural factors controlling the competition between radiative and nonradiative decay. Our calculations, validated against experimental quantum yields for structurally analogous derivatives (mean absolute error < 0.5%), reveal that the nonradiative decay channel via torsional motion to a conical intersection is kinetically suppressed across the series due to high activation barriers (ΔE^‡ = 18.1–81.4 kcal/mol). Consequently, the fluorescence quantum yield (Φ_f) is almost exclusively governed by the competition between radiative decay (k_r) and internal conversion (IC) from the S₁ minimum. BDP-TPE-2, featuring a single dicyanovinyl acceptor, exhibits the highest predicted quantum yield (Φ_f ≈ 22%), not due to a superior radiative rate, but because of a uniquely suppressed IC rate (2.67 × 10⁸ s⁻¹) arising from exceptionally weak electronic coupling (V = 0.0038 eV) and minimal low-frequency reorganization energy (λ_l). Conversely, the poorest emitters, BDP-TPE-5 and BDP-TPE-6, are shown to suffer from exceptionally fast IC ( > 10¹⁰ s⁻¹) driven by large electronic coupling and, crucially, large low-frequency reorganization energies. These results demonstrate that enhancing fluorescence efficiency in this scaffold depends critically on the strategic suppression of internal conversion by minimizing both electronic and vibrational coupling between the ground and excited states. The predicted quantum yields (Φ_f = 0.16-22%) represent intrinsic molecular properties validated against weak-AIE experimental benchmarks, and may be enhanced in solid-state applications if strong aggregation-induced emission occurs.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-026-44085-4.

Introduction

Among the diverse array of fluorophores, BODIPY (4,4-difluoro-4-bora-3a,4a-diaza-s-indacene) dyes have emerged as premier platforms for molecular sensing due to their superior photophysical properties, including high molar extinction coefficients, sharp and distinct spectral profiles, exceptional photostability, and high fluorescence quantum yields^1–7. The modular nature of the BODIPY scaffold allows for precise tuning of its optical and electronic characteristics through strategic functionalization, making it an ideal framework for engineering “turn-on” fluorescent probes that respond to specific analytes^8,9.

Tetraphenylethylene (TPE), characterized by its propeller-like molecular structure with four phenyl groups attached to an ethylene core, has emerged as a paradigmatic aggregation-induced emission (AIE) luminogen^10–12. Recent advances demonstrate TPE’s excellent electron-donating properties that facilitate efficient charge separation and reduce recombination losses^11,13–15. TPE macrocycles with covalent oligoethylene glycol linkages exhibit strong emission in solution, indicating restricted π twist and effective charge transport¹⁶. The propeller-like structure allows various substitution patterns, enabling fine-tuning of electronic and optical properties. The combination of TPE and BODIPY creates complementary absorption profiles, enhancing overall efficiency in organic photovoltaics (OPVs)^1,17–19. Theoretical calculations demonstrate that TPE substitution on BODIPY significantly modifies optical properties, making it suitable for spectral tuning³. Baysec et al. demonstrated TPE-functionalized BODIPY emitters with tunable photoluminescence from green to near-infrared (NIR), achieving up to ~ 100% photoluminescence efficiency in blends and organic light-emitting diode (OLED) electroluminescence with external quantum efficiencies up to 1.8%²⁰. Sample et al. synthesized tetra-BODIPY-appended TPE derivatives showing differing AIE properties depending on the linker type, with dual emission and singlet oxygen generation²¹. Wu et al. combined TPE, BODIPY, and terpyridine into supramolecular assemblies that retain BODIPY’s emissive properties while benefiting from TPE’s AIE and coordination-driven restriction of intramolecular rotation²².

Despite these promising experimental advances in TPE-BODIPY hybrid systems, the fundamental understanding of their radiative and nonradiative decay mechanisms remains a critical challenge for optimizing their photovoltaic performance. The complex photophysical processes governing excited-state dynamics in these hybrid materials involve multiple competing pathways, including fluorescence^23,24, internal conversion^25,26, intersystem crossing^23,27, and various quenching mechanisms²⁸. The balance between radiative decay (fluorescence) and nonradiative pathways directly determines the photoluminescence quantum yields. In TPE-based systems, the intramolecular rotation significantly affects nonradiative decay rates, while BODIPY cores contribute distinct radiative characteristics with their unique electronic transitions. Understanding how the combination of TPE and BODIPY moieties influences the competition between these decay pathways is essential for rational molecular design. The structural modifications, substitution patterns, and aggregation behavior of TPE-BODIPY hybrids all play crucial roles in modulating the relative rates of radiative and nonradiative processes, yet the detailed mechanisms underlying these structure-property relationships remain poorly understood and require systematic theoretical investigation.

Building upon the critical need to understand radiative and nonradiative decay mechanisms in TPE-BODIPY hybrids, Density Functional Theory (DFT) and Time-Dependent Density Functional Theory (TDDFT) have emerged as powerful computational tools for investigating these fundamental photophysical processes at the molecular level^29–32. These theoretical methods enable detailed analysis of how molecular structure influences the competition between radiative pathways (fluorescence emission) and nonradiative channels (internal conversion, intersystem crossing, and vibrational relaxation) in organic luminogens. DFT calculations provide crucial insights into ground-state geometries and electronic structures that govern radiative decay rates, while TDDFT reveals the nature of excited states and their propensity for nonradiative relaxation. For instance, TDDFT and EOM-CCSD calculations have been employed to investigate radiative emission lifetimes and excited-state properties of BODIPY dyes, revealing how computational methods can predict radiative decay characteristics with TDDFT transition energies being overestimated by approximately 0.4–0.5 eV compared to experimental values³³. Furthermore, the design of new fluorescent indicators based on BODIPY structures, which are stable, highly optically active, and have considerable quantum yield, was also studied using TDDFT³⁴. This demonstrates their potential for high-tech applications. The role of substituent effects on radiative and nonradiative processes has been systematically studied using DFT methods, demonstrating how electron-donating and electron-withdrawing groups modulate the relative rates of competing decay pathways^35–37. Furthermore, DFT calculations of frontier molecular orbital energies and energy gaps provide direct correlation with radiative emission wavelengths and nonradiative decay probabilities, enabling the prediction of photoluminescence quantum yields³⁸. Computational modeling of vibrational coupling and reorganization energies using DFT has elucidated the mechanisms of nonradiative internal conversion processes in organic dyes^35,39–41. These theoretical investigations collectively demonstrate that DFT and TDDFT methods are indispensable for understanding the intricate balance between radiative and nonradiative decay mechanisms in BODIPY systems, providing the foundation for rational molecular design strategies aimed at optimizing photophysical properties for photovoltaic applications.

In this work, we present a systematic spin-flip TDDFT (SF‑TDDFT)/DFT study of six mono‑TPE–substituted BODIPY dyes (BDP‑TPE‑1 to ‑6) in which a tetraphenylethylene unit is attached at the meso (C8) position (Fig. 1). The six-member series was designed to systematically isolate the effects of acceptor strength, donor multiplicity, and linkage topology (para vs. meta) on the photophysical properties. This strategic variation enables mechanistic attribution of fluorescence quantum yield trends to specific structural handles, providing actionable design principles for molecular engineering. By varying electron‑donating methoxy groups and an electron‑accepting dicyanovinyl (DCV) group, as well as the linkage topology (para vs. meta), we modulate donor–acceptor coupling and the excited‑state landscape. We compute absorption/emission properties and quantify radiative (k_r) and nonradiative decay rates, focusing on internal conversion near the S₁ minimum and the competing torsional pathway toward a conical intersection. This design-driven dataset enables us to identify the decisive structural factors that suppress nonradiative decay and to propose practical guidelines for improving fluorescence efficiency in TPE‑BODIPY architectures.

Fig. 1.

Molecular structures of the mono‑TPE–substituted BODIPY derivatives BDP‑TPE‑1 to BDP‑TPE‑6, in which a tetraphenylethylene (TPE) unit is appended at the meso (C8) position of the BODIPY core. Substituent patterns on the TPE fragment define the series: BDP‑TPE‑1, unsubstituted TPE; BDP‑TPE‑2, one dicyanovinyl acceptor (DCV) on a peripheral phenyl ring (no methoxy); BDP‑TPE‑3, BDP‑TPE‑2 with one para‑methoxy (OMe) donor; BDP‑TPE‑4, one para‑DCV acceptor and two para‑OMe donors; BDP‑TPE‑5, meta‑linked constitutional isomer of BDP‑TPE‑4 (DCV meta relative to the TPE framework) with two OMe donors retained; and BDP‑TPE‑6, donor‑only analogue bearing two OMe substituents on two different TPE phenyl rings (no DCV).

Computational methods

To select the most appropriate functional for our study, we benchmarked several commonly used DFT functionals (B3LYP, PBE0, TPSSh, M06-2X, CAM-B3LYP, LC-BLYP) against experimental optical data for structurally related TPE-BODIPY derivatives reported by Baysec et al.⁴²: TPEBDP1 (identical to BDP-TPE-1), TPEBDP2, and TPEBDP3 (Supplemental Figure S1 and Table S1). The experimental absorption and emission maxima from Ref⁴². were measured from solid-state thin films, whereas our calculations model isolated molecules in vacuum, creating a potential inconsistency as solid-state spectra can be influenced by intermolecular interactions, environmental polarization, and aggregation effects. However, for this specific benchmark set, experimental evidence demonstrates that aggregation effects are minimal: solution and solid-state quantum yields are nearly identical (TPEBDP1: 8% vs. 10%; TPEBDP2: 4% vs. 4%; TPEBDP3: 4% vs. 5%), THF/water aggregation studies (Ref.⁴², Fig. 1) show only weak PL recovery upon aggregation (1.0-1.2× enhancement), and the authors explicitly state that mono-TPE derivatives exhibit weaker AIE compared to tri-TPE analogues. This fortuitous situation—where solid-state ≈ solution due to weak AIE—makes TPEBDP1-3 more suitable for gas-phase validation than typical AIE luminogens. As expected for gas-phase calculations, all functionals systematically blue-shift both absorption and emission relative to solid-state experiments (deviations: 20–60 nm), but B3LYP provided the most consistent performance in reproducing relative trends: the experimental emission trend for films shows TPEBDP1 (670 nm) ≈ TPEBDP3 (650 nm) > TPEBDP2 (615 nm), while the B3LYP calculated trend in gas phase shows TPEBDP1 (661 nm) ≈ TPEBDP3 (668 nm) > TPEBDP2 (605 nm). The systematic blue-shift (9–45 nm) is consistent with the absence of environmental stabilization in our gas-phase model, whereas long-range corrected functionals (CAM-B3LYP, LC-BLYP) yielded much larger deviations (> 100 nm) and failed to reproduce qualitative trends. Based on this analysis and extensive validation by Ou et al.³⁷ (MAE = 0.060 eV for absorption using SF-TDDFT/B3LYP for BODIPYs), we selected B3LYP for all subsequent calculations.

All calculations in this work were performed for isolated molecules in vacuum, a methodological choice that follows established precedent in computational photophysics^35,37 and enables isolation of intrinsic molecular structure effects by eliminating confounding environmental variables. We explicitly acknowledge the following limitations: solvent effects are absent, whereas real measurements occur in solution or solid state where environmental polarization can stabilize charge-transfer states (typical red-shifts: 0.2–0.5 eV), modify rate constants through cavity effects, and introduce dynamic quenching, meaning our gas-phase calculations systematically overestimate (blue-shift) excitation energies; strong aggregation effects cannot be predicted, as multi-TPE-substituted derivatives exhibiting strong AIE behavior (e.g., 3TPEBDP2-3 from Ref.⁴² show up to 100 × Φ_f enhancement in F8BT blends) would have their solid-state performance severely underestimated by our gas-phase predictions since restriction of intramolecular rotation (RIR) upon aggregation—the dominant AIE mechanism—is absent in isolated-molecule calculations; and intermolecular interactions are neglected, as solid-state packing can introduce additional decay channels (excimer formation, energy transfer) or alter excited-state energetics (site disorder, exciton coupling) that are not captured in single-molecule calculations. Despite these limitations, our validation against TPEBDP1-3 experimental data establishes that gas-phase calculations can reliably predict intrinsic molecular properties in weak-AIE systems (when aggregation effects are minimal, as experimentally demonstrated for TPEBDP1-3 where solution Φ_f ≈ film Φ_f, gas-phase predictions approximate both solution and solid-state values), relative trends (our calculations correctly predict the experimental ordering TPEBDP1 > TPEBDP3 > TPEBDP2 and capture the correct order of magnitude in the 4–11% range), structure-property relationships (how substituent type, number, and linkage topology affect radiative/nonradiative balance at the fundamental molecular level), and mechanistic insights (dominant decay pathways such as torsional MECI vs. Franck-Condon IC and the roles of electronic coupling V and reorganization energy λ in controlling nonradiative decay). Our BDP-TPE-1 to -6 series consists of mono-TPE-substituted BODIPYs, structurally analogous to the weak-AIE benchmark TPEBDP1-3, and therefore our predictions likely represent intrinsic molecular quantum yields observable in dilute solution, polymer blends at low doping, or weakly interacting solid-state environments, though if these derivatives exhibit strong AIE in practice (which is unpredictable from gas-phase calculations), experimental solid-state quantum yields could exceed our predictions.

The computational dataset comprises six mono-TPE–substituted BODIPY dyes, denoted BDP-TPE-1 to BDP-TPE-6, in which a tetraphenylethylene (TPE) unit is attached at the meso (C8) position of the BODIPY core (Fig. 1). The series is defined by systematic variation of substituents on the TPE fragment—electron-donating methoxy (OMe) groups and an electron-withdrawing dicyanovinyl (DCV) group—as well as the linkage topology (para vs. meta) to tune donor–acceptor coupling. For clarity and reproducibility, the full structural assignments corresponding to each label (BDP-TPE-1 to -6) are provided in the Fig. 1 caption.

To investigate the excited states, we employed a computational protocol specifically tailored to address the known challenges in modeling BODIPY derivatives, drawing upon the validated strategies of recent key studies. First, we utilized SF-TDDFT to overcome the well-documented failure of conventional TDDFT³⁵, which severely overestimates the S₁ excitation energy of BODIPYs due to their significant double-excitation or multireference character. Our choice is strongly supported by the work of Ou et al.³⁷, who established SF-TDDFT with the B3LYP functional as a “golden method” for this class of molecules. They achieved remarkable accuracy, with mean absolute errors (MAEs) of just 0.060 eV for absorption and 0.101 eV for emission, by correctly capturing the complex electronic structure. Second, all calculations were performed in a vacuum to isolate the intrinsic effects of molecular structure from confounding solvent interactions. This gas-phase approach finds its precedent in the work of Lin et al.³⁵, who successfully modeled the photophysical properties of 100 different BODIPY derivatives. They demonstrated that while vacuum calculations introduce a systematic, correctable error in absolute energies, the crucial relative trends across a molecular series are accurately captured, enabling the successful prediction of fluorescence quantum yields. Therefore, by combining the electronic structure accuracy of SF-TDDFT (validated by Ou et al.) with the proven effectiveness of a vacuum model for elucidating relative trends (validated by Lin et al.), our methodology is robustly designed to unravel the fundamental structure-property relationships governing the excited-state dynamics in TPE-BODIPY hybrids. Furthermore, SF-TDDFT calculations enable analysis of vibrational modes and their coupling to electronic transitions—a critical aspect of nonradiative decay processes that governs the photophysical behavior of these hybrid systems.

Regarding nonradiative decay pathways, we focus exclusively on internal conversion (IC) mechanisms and explicitly neglect intersystem crossing (ISC) based on the following well-established principles for BODIPY systems. Extensive computational studies by Lin et al.³⁵ on over 100 BODIPY derivatives—structurally analogous to our BDP-TPE series—demonstrated that S₁→T₁ ISC is unimportant for BODIPY unless it contains heavy atoms (S, Br, I) or possesses a dimeric structure. Their systematic analysis confirmed that either S₁→S₀ or L_a→L_b internal conversion dominates the nonradiative mechanisms depending on substituents, with ISC making negligible contributions³⁵. Our BDP-TPE-1 to -6 structures contain no halogen substituents (Br, I), sulfur atoms, or dimeric architectures that are known to enhance ISC in BODIPY systems. The dominant S₁ character in our derivatives is π→π* with significant BODIPY core contribution (Table 1), which exhibits minimal spin-orbit coupling compared to n→π* transitions or charge-transfer states involving heavy atoms. For the two derivatives containing bromine atoms in our benchmark validation set (TPEBDP structures from Ref.⁴², experimental quantum yields demonstrate that ISC remains kinetically irrelevant as their photophysics are still governed primarily by internal conversion, consistent with the findings of Lin et al.³⁵ that even moderate ISC enhancement in Br-substituted BODIPYs does not make ISC competitive with IC (k_ISC < < k_IC). Therefore, while ISC can occur without transition metals, the combination of structural features (no heavy atoms, non-dimeric), electronic character (locally excited (LE) π→π*), and extensive literature validation for BODIPY systems³⁵ confirms that ISC is kinetically negligible compared to the dominant internal conversion pathway in BDP-TPE-1 to -6. Consequently, our two-channel model (radiative decay vs. IC) provides a complete and accurate description of the excited-state dynamics.

Table 1.

Calculated properties for the lowest bright excited state (S₁) of each derivative, including the excitation energy (eV), dominant molecular orbital transition configurations with their coefficients, state assignment (e.g., intramolecular charge transfer, ICT; ligand-to-ligand charge transfer, LLCT), and dimensionless oscillator strength (f_osc).

The charge density difference (CDD) plots visualize the electron-hole distribution upon excitation, where green indicates the hole (region of electron loss) and blue indicates the electron (region of electron gain). Note: The transition configurations were obtained from SF-TDDFT calculations, meaning the orbitals shown correspond to the triplet reference state.

SF-TDDFT calculations were carried out using the same functional and basis set as in the ground-state calculations. These calculations provided vertical excitation energies and oscillator strengths for the excited states. To generate the absorption spectra, the discrete transition energies were broadened using a Gaussian function with a full width at half maximum (FWHM) of 0.3 eV. Moreover, the lowest excited singlet state (S₁) geometry was optimized using SF-TDDFT at the same level of theory. After optimizing the S₁ state geometry, vibrational frequency calculations were performed to confirm that the optimized geometry lies at a local minimum on the excited-state potential energy surface. To investigate radiative and nonradiative decay mechanisms, transition dipole moment calculations were carried out at the optimized geometry of the S₁ state using SF-TDDFT. All DFT and SF-TD-DFT calculations were conducted using the Q-Chem 4.2⁴³.

To quantify radiative decay, we employed a quantum-mechanical treatment that accounts for vibronic coupling between electronic states. The emission process involves transitions from vibrationally excited levels of S₁ to the vibrational manifold of S₀, with intensities governed by both electronic transition dipole moments and Franck-Condon factors. The emission spectrum is calculated using the thermal vibration correlation function (TVCF) formalism within a multidimensional harmonic oscillator model⁴⁴:

1

where is is the emission cross-section at photon frequency ω; c is the speed of light; is the Boltzmann distribution describing the thermal population of the initial vibronic state at temperature T; and are the vibrational wavefunctions of the excited and ground states with quantum numbers and , respectively; is the electric transition dipole moment between the S₀ and S₁ electronic states; is the adiabatic (0–0) excitation energy; δ is the Dirac delta function enforcing energy conservation; and and are the vibrational energies of the initial (S₁) and final (S0) states, respectively.

To incorporate vibronic coupling effects beyond the Condon approximation, the transition dipole moment is expanded to first order in normal coordinates using the Herzberg-Teller approximation:

2

where is the zero-order (Franck-Condon) transition dipole moment evaluated at the equilibrium geometry; is the first-order Herzberg-Teller (HT) correction representing the derivative of the transition dipole with respect to the k-th normal coordinate; and Q_k is the displacement along the k-th vibrational mode. This expansion accounts for intensity borrowing from nearby electronic states through vibronic coupling.

The radiative decay rate is obtained by integrating the emission spectrum over all frequencies:

3

For nonradiative decay processes, we focused on two distinct pathways that are known to govern excited-state deactivation in organic fluorophore systems: (1) internal conversion (IC) in the Franck-Condon region (Channel I; Fig. 2) and (2) transitions through minimum energy conical intersections (MECI) away from the Franck-Condon region (Channel II). The intersystem crossing is expected to be minor in this series due to the lack of heavy metal element in our system³⁵. Figure 2 provides a schematic illustration of the multi-step potential energy surface for the S₁→S₀ nonradiative decay pathway, detailing the energetic and structural changes involved. The process begins after photoexcitation at the largely planar Franck-Condon minimum of the first excited state (point B). For the molecule to proceed along this channel, it must first surmount a significant activation energy barrier (ΔE^‡) to reach a high-energy transition state (TS), which represents the rate-limiting step. After crossing this barrier, the molecule can relax into a distorted intermediate (point C), which is a shallow local minimum on the S₁ surface that has already undergone significant structural rearrangement. From this intermediate, the molecule continues to the minimum energy conical intersection (MECI, point D), a critical geometry where the S₁ and S₀ potential energy surfaces touch, creating an efficient “funnel” for rapid, radiationless decay back to the ground state (S₀), whose minimum is at point A. The entire pathway from B to D is defined by progressive and severe geometric distortions—including the twisting of the TPE substituent and a pronounced puckering of the BODIPY core—which are energetically costly.

Fig. 2.

Schematic potential energy surface illustrating the two competitive nonradiative decay pathways for S₁→S₀ deactivation in BDP-TPE derivatives. Point A denotes the ground-state (S₀) equilibrium geometry with a planar BODIPY core. Point B represents the relaxed S₁ minimum (Franck-Condon region) after photoexcitation and vibrational relaxation, where the molecule retains a largely planar geometry. From this point, two nonradiative channels compete: Channel I (Franck-Condon internal conversion) proceeds directly from point B to the S₀ surface via vibronic coupling without significant geometric distortion, governed by electronic coupling V and reorganization energy λ; Channel II (torsional pathway) requires surmounting an activation barrier ΔE^‡ to reach the transition state (TS), followed by relaxation to a distorted intermediate (Point C, a shallow S₁ minimum with partial TPE twisting and BODIPY puckering) and culminating at the minimum energy conical intersection (MECI, Point D) where S₁ and S₀ surfaces touch, enabling ultrafast radiationless decay back to S₀. The entire Channel II pathway (B→TS→C→D→A) involves progressive geometric distortions including TPE substituent rotation (torsion angle τ) and pronounced BODIPY core puckering (bending angles γ, θ), making it energetically costly and kinetically suppressed across the BDP-TPE series (ΔE^‡ = 18.1–81.4 kcal/mol, Table 3).

Internal conversion (IC) from S₁ to S₀ in the Franck-Condon region (Channel I) is a nonradiative process driven by non-adiabatic coupling between the two electronic states. The transition probability depends on both the strength of the electronic coupling and the degree of vibrational wavefunction overlap, which provides the density of accepting states. We calculated the IC rate using Fermi’s golden rule within the time-dependent formulation^45,46:

4

where is the internal conversion rate constant from S₁ to S₀; V is the electronic coupling matrix element between the S₁ and S₀ states, quantifying the strength of their non-adiabatic interaction; f(t) is the time-dependent vibrational overlap function describing the correlation between initial and final state nuclear wavefunctions; E(S₁) and E(S₀) are the energies of the excited and ground electronic states; and t is time. The electronic coupling was evaluated using mode-resolved non-adiabatic coupling (NAC) matrix elements⁴⁶:

5

where NAC_k is the non-adiabatic coupling for mode k; φ_S₀ and φ_S₁ are the electronic wavefunctions of the ground and excited states, respectively; and are the vibrational wavefunctions with quantum numbers and ; is the k-th normal coordinate; and i is the imaginary unit. The derivative operator ∂/∂Q_k captures the breakdown of the Born-Oppenheimer approximation along each vibrational mode.

To obtain quantitative IC rates, we partitioned the vibrational modes into two classes based on their frequency and role in the nonradiative process. Low-frequency modes (< 1000 cm^{− 1}), which include torsional and bending motions, are treated classically through a reorganization energy, while high-frequency modes (> 1000 cm^{− 1}), primarily C-C, C-H, and C = C stretches, are treated quantum-mechanically via the Poisson distribution of their Franck-Condon factors. This separation captures the distinct physical mechanisms by which different vibrational modes facilitate electronic relaxation. We employed the Marcus-Levich-Jortner (M-L-J) formalism^47–49, which provides a semiclassical expression for the IC rate:

6

where is the internal conversion rate constant; V is the electronic coupling between S₁ and S₀ (defined in Eq. 5); is the reorganization energy contribution from low-frequency modes, representing the classical energy cost of nuclear rearrangement; ΔG is the free energy change for the S₁→S₀ transition (negative for exothermic decay); is the effective (averaged) Huang-Rhys factor for high-frequency modes, quantifying the strength of vibronic coupling; is the effective (averaged) frequency of high-frequency modes; is Boltzmann constant; T is temperature; n is the vibrational quantum number summed in the Poisson distribution; and is the Gaussian energy gap term derived from Marcus theory. The Huang-Rhys factor S_M and low-frequency reorganization energy λ_l were computed from the equilibrium geometries and normal modes of S₁ and S₀^45,46:

7

8

where j is the vibrational mode index; hf and lf denote summation over high-frequency (> 1000 cm^− 1) and low-frequency (< 1000 cm^− 1) modes, respectively; m_j is the reduced mass of vibrational mode j; ω_j is the vibrational angular frequency of mode j; and ΔQ_j is the dimensionless displacement of normal coordinate j between the S₁ and S₀ equilibrium geometries, quantifying the geometric distortion along each mode upon electronic transition. This mode-partitioning approach enables identification of which specific molecular motions drive non-radiative decay.

For the torsional decay pathway leading to the conical intersection (Channel II), the rate-limiting step is overcoming the activation barrier on the S₁ surface to reach the transition state (TS). Once the TS is crossed, the system rapidly accesses the minimum energy conical intersection (MECI) where ultrafast S₁→S₀ relaxation occurs. The overall rate is therefore governed by the thermally-activated barrier crossing, which we treat using transition state theory. Theoretical framework: The nonradiative decay rate through the MECI pathway was calculated using the Eyring equation⁵⁰:

9

where is the rate constant for nonradiative decay via the conical intersection channel; h is Planck’s constant; is the Gibbs free energy of activation, defined as the free energy difference between the TS and the S₁ minimum (see Eq. 11); R is the universal gas constant; and the pre-exponential factor (≈ 6.2 × 10¹² s^{− 1} at 298 K) represents the universal frequency factor for barrier crossing in transition state theory. The application of the Eyring equation to excited-state processes involving conical intersections is justified when (i) the rate-limiting step is barrier crossing on a single electronic surface (S₁) prior to reaching the S₁/S₀ degeneracy point, and (ii) passage through the MECI itself is ultrafast and non-rate-limiting. This approach follows the validated methodology of Ou et al.³⁷ for BODIPY systems, where transition state theory (TST) accurately predicted quantum yields for molecules with accessible MECIs (ΔE^‡ < 6 kcal/mol) while correctly identifying that high barriers (ΔE^‡ > 10 kcal/mol) render the MECI channel kinetically irrelevant. For BDP-TPE-1 to -6, our calculated activation barriers (ΔE^‡ = 18.1–81.4 kcal/mol, Table 2) fall well into the kinetically suppressed regime, meaning any potential limitations of TST at the MECI do not affect our conclusions since ≪ for all derivatives.

Table 2.

Key photophysical parameters governing radiative and nonradiative decay pathways in BDP-TPE derivatives.

BDP-TPE-1	kr (s-1)	(s-1)	(s-1)	µfl. (debye)	ΔE‡ (kcal/mol)	ΔG (eV)	V (eV)	SM	λl (eV)	λtotal (eV)	Φf (%)
	1.21 × 108	1.02 × 109	4.0 × 10− 6	4.42	24.8	1.86	0.077	0.52	0.77	0.84	11
BDP-TPE-2	7.39 × 107	2.67 × 108	0.33	12.7	18.1	2.00	0.0038	0.65	0.086	0.20	22
BDP-TPE-3	1.73 × 108	1.57 × 109	1.0 × 10− 13	13.0	35.2	1.88	0.076	0.84	0.24	0.43	10
BDP-TPE-4	4.61 × 107	1.26 × 109	7.3 × 10− 48	13.5	81.4	1.79	0.080	0.76	0.29	0.45	3.5
BDP-TPE-5	2.32 × 107	1.46 × 1010	6.6 × 10− 30	9.93	56.8	1.66	0.062	1.33	0.31	0.60	0.16
BDP-TPE-6	2.62 × 108	1.71 × 1010	9.4 × 10− 32	6.96	59.5	1.48	0.082	1.84	1.10	1.44	1.51

First, the equilibrium geometry of the lowest excited singlet state () was located via a full geometry optimization using SF-TD-DFT. A subsequent vibrational frequency calculation confirmed it as a true minimum by the absence of any imaginary frequencies. This structure represents the starting point for the nonradiative decay journey. Next, the geometry of the MECI between the S₁ and S₀ states was located using specialized algorithms. For this study, we employed a penalty function-based method. The core challenge in finding a MECI is that it is a constrained optimization problem: we must find a point that minimizes the energy of the upper state (or the average energy) subject to the constraint that the energy gap between the S₁ and S₀ states is exactly zero. Locating a conical intersection is a constrained optimization problem: we must find a molecular geometry that simultaneously minimizes the energy of the S₁ state while satisfying the constraint that S₁ and S₀ are exactly degenerate (energy gap = 0). Standard optimization algorithms are designed for unconstrained problems. We employed the penalty function method^51,52, which transforms the constrained MECI search into an unconstrained optimization by constructing an augmented potential energy surface that simultaneously drives the system toward low-energy regions and enforces state degeneracy. The penalty function L(R) is defined as:

10

where R represents the 3 N-dimensional vector of nuclear coordinates for the N-atom system; and are the energies of the excited (S₁) and ground (S₀) electronic states evaluated at geometry R; β is the penalty parameter (in units of energy^{− 1}) that controls the relative weighting of energy minimization versus gap closure; the first term (average energy) drives the optimization toward the lowest-energy region of the S₁/S₀ crossing seam; and the second term (squared energy gap) penalizes any geometry where the states are not degenerate, with the penalty increasing quadratically with the gap size. The gradient of L(R), required by the optimizer, is constructed analytically from the individual S₁ and S₀ state gradients. The penalty parameter β must be carefully chosen: if too small, the energy gap may not close; if too large, the optimizer may converge to a high-energy crossing point far from the true MECI. Following established protocols for TD-DFT-based MECI optimization^35,36, we used β = 0.02 hartree (equivalent to 0.00147 eV^{− 1}), which has been validated for BODIPY systems and ensures stable convergence to physically relevant MECIs without numerical instabilities.

The most crucial step was to locate the first-order saddle point, or transition state TS, on the S₁ surface that connects the to the MECI. This was achieved using a partitioned-rational function optimization (P-RFO) method, starting from initial guesses along the reaction path. A successful TS was verified by a frequency calculation showing exactly one imaginary frequency. This imaginary mode corresponds physically to the reaction coordinate—in this case, the critical torsional motion of the TPE substituent that drives the system toward the MECI. The activation barrier for the torsional decay channel is the thermodynamic cost of distorting the molecule from its relaxed S₁ minimum geometry to the transition state geometry, where the BODIPY core begins to pucker and the TPE substituent rotates. This barrier determines the rate at which molecules can access the conical intersection. The Gibbs free energy of activation ΔG^‡ (synonymous with ΔE^‡ in our notation) was calculated as.

11

where ΔE^‡ is the activation energy barrier for the S₁→TS process; G_TS is the Gibbs free energy of the transition state on the S₁ surface, computed at the TS geometry with one imaginary frequency corresponding to the reaction coordinate; and is the Gibbs free energy of the fully relaxed S₁ minimum, verified by the absence of imaginary frequencies. Both free energies include electronic energy, zero-point vibrational energy (ZPVE), thermal vibrational contributions, and entropy corrections at T = 298 K and P = 1 atm, calculated within the harmonic oscillator/rigid rotor approximations.

By employing this methodology, we can directly calculate the rate of this substituent-activated decay channel from first principles, providing a quantitative link between the unique structural dynamics of the TPE moiety and its profound impact on the photophysical properties of the entire hybrid system. The critical geometric parameters defining these structures—namely the TPE substituent torsion angle (τ) and the BODIPY core bending angles (γ, θ)—are compiled in Supplemental Table S2 for each derivative.

Results and discussion

Optoelectronic properties

The frontier-orbital energetics, shown in Table 1, reveal clear substitution-dependent trends across the mono-TPE–substituted BODIPYs. The donor-only reference BDP-TPE-6 exhibits the highest Highest Occupied Molecular Orbital (HOMO) level (‒4.73 eV), while the introduction of the DCV acceptor in BDP-TPE-2 results in the lowest Lowest Unoccupied Molecular Orbital (LUMO) at ‒3.18 eV. This tuning of the frontier orbitals results in a HOMO-LUMO gap (ΔE_gap) trend of: BDP-TPE-2 (2.33 eV) > BDP-TPE-1 (2.25 eV) > BDP-TPE-3 (2.18 eV) > BDP-TPE-4 ≈ BDP-TPE-5 (2.09 eV) > BDP-TPE-6 (1.88 eV). However, this simple orbital gap fails to predict the observed optical properties, as it neglects crucial electron-hole interactions and configuration mixing. A more accurate picture is given by the TDDFT-calculated lowest bright excitation energies (from Table 2 and S3), which follow a markedly different trend: BDP-TPE-1 (2.46 eV) > BDP-TPE-2 ≈ BDP-TPE-6 (2.38 eV) > BDP-TPE-5 (2.37 eV) > BDP-TPE-3 (2.26 eV) > BDP-TPE-4 (2.17 eV). The discrepancy between the ΔE_gap and excitation energy trends is highly informative. For instance, BDP-TPE-5, with its meta-linkage, has a small gap (2.09 eV) but a relatively high excitation energy (2.37 eV). This is explained by its S₁ state arising from a HOMO-1→LUMO transition with a weak oscillator strength (f_osc = 0.29, supplemental Table S3), indicative of poor orbital overlap and a small exciton binding energy that fails to significantly lower the excitation energy from the orbital gap. Conversely, BDP-TPE-6 has the smallest gap in the series (1.88 eV) yet a high excitation energy (2.38 eV). This is a direct result of its S₁ state having significant multi-configurational character, being a strong mixture of HOMO→LUMO and HOMO-1→LUMO transitions (Supplemental Table S3). This highlights that while orbital engineering effectively tunes the HOMO/LUMO levels, the final excitation energy is critically modulated by exciton binding energy and configuration interaction, rendering the simple HOMO-LUMO gap an unreliable predictor of the optical transition energy.

Table 3.

Frontier molecular orbital energies (HOMO‑1, HOMO, LUMO, LUMO + 1) of BDP‑TPE‑1 to ‑6 (eV) and substitution‑dependent trends.

An analysis of the true composition of the S₁ state (Table 2 and S3) reveals why the simple HOMO-LUMO gap is an insufficient predictor of optical properties. For BDP-TPE-2, the lowest bright excitation is not a HOMO→LUMO transition; instead, it is a Ligand-to-Ligand Charge Transfer (LLCT) state arising from a dominant HOMO→LUMO + 1 transition. This immediately shows that the LUMO itself is not the primary acceptor orbital. The limitations of the orbital-gap picture become even more apparent for BDP-TPE-3 and BDP-TPE-4, where the S₁ state is also defined by a strong HOMO→LUMO + 1 transition. This indicates that adding electron-donating methoxy groups not only raises the HOMO energy but also reorders the virtual orbital landscape, making LUMO + 1 the key acceptor orbital for the lowest energy excitation in these para-linked systems. The case of BDP-TPE-5 is equally instructive; its S₁ state is dominated by a HOMO-1→LUMO transition, meaning the true HOMO is “skipped” in the lowest-energy bright excitation. This is likely because the meta-linkage enforces poor spatial overlap for the HOMO→LUMO transition, suppressing its intensity and allowing the HOMO-1→LUMO channel to define the S₁ state. Finally, BDP-TPE-6 exemplifies the importance of configuration interaction, as its S₁ state is not a single transition but a strong mixture of HOMO→LUMO and HOMO-1→LUMO configurations (Supplemental Table S3), invalidating any analysis based on a single orbital pair. Collectively, this detailed state analysis shows that the identity of the lowest excitation is determined by a subtle interplay of orbital energy, spatial overlap (which dictates oscillator strength), and configuration mixing—factors that cannot be captured by the HOMO-LUMO gap alone.

The discrepancy between the HOMO-LUMO gap and excitation energy has direct implications for excited-state deactivation processes, as it reflects the quality of electronic coupling that governs both radiative and nonradiative decay pathways. Derivatives where the excitation energy significantly exceeds the orbital gap—such as BDP-TPE-5 (ΔE_gap = 2.09 eV versus excitation = 2.37 eV) and BDP-TPE-6 (ΔE_gap = 1.88 eV versus excitation = 2.38 eV)—exhibit weak electronic coupling between the frontier orbitals due to poor spatial overlap or unfavorable configuration mixing. This weak coupling manifests in two critical consequences for excited-state decay. First, the same poor orbital overlap that suppresses radiative absorption strength (f_osc = 0.29 for BDP-TPE-5 and 0.63 for BDP-TPE-6, Table 2) also reduces the electronic coupling matrix element V in Eq. 5, which governs internal conversion rates via ∝ V². However, this potential benefit is completely overwhelmed by large low-frequency reorganization energies λ_l in both derivatives (1.33 eV for BDP-TPE-5 and 1.84 eV for BDP-TPE-6, Table 3), leading to the fastest internal conversion rates in the series (1.46 × 10¹⁰ and 1.71 × 10¹⁰ s^− 1) and consequently the lowest quantum yields (0.16% and 1.5%). Second, the multi-configurational character evident in derivatives with large gap-excitation discrepancies introduces additional vibronic coupling channels that enhance nonradiative decay. Conversely, BDP-TPE-2 demonstrates a more favorable scenario where a close gap-excitation match (ΔE_gap = 2.33 eV versus excitation = 2.38 eV) combined with strong single-configuration character (HOMO→LUMO + 1 with 0.78 coefficient, Table 2) yields both efficient absorption (f_osc = 0.92) and minimal electronic coupling for internal conversion (V = 0.0038 eV, Table 3), thereby achieving the highest fluorescence quantum yield (22%). This analysis reveals that minimizing the gap-excitation energy discrepancy alone is insufficient for enhancing fluorescence; instead, one must engineer systems with strong single-configuration character while simultaneously suppressing low-frequency reorganization modes, as the interplay between electronic structure and nuclear dynamics collectively determines the balance between radiative and nonradiative pathways.

Figure 3 provides projected density of states (PDOS) evidence for the fragment‑resolved composition of the frontier molecular orbitals (FMOs) and corroborates the localization analysis. For BDP‑TPE‑1, the occupied levels are dominated by TPE character, whereas the unoccupied levels mix TPE and BODIPY contributions, consistent with a donor‑to‑core arrangement in the absence of an explicit acceptor. In BDP‑TPE‑2, the introduction of the DCV group establishes a clear donor-acceptor framework; the PDOS shows that while the HOMO resides on the BODIPY core, the low-lying unoccupied manifold is decisively localized on the TPE/DCV fragment, which acts as the acceptor. This trend strengthens with increased donorization in BDP‑TPE‑3 and BDP‑TPE‑4, which exhibit the most pronounced D–A character with donor-enhanced occupied levels and an unoccupied manifold that retains its strong TPE/DCV acceptor nature. In the meta isomer BDP‑TPE‑5, the occupied manifold becomes more purely donor‑weighted (TPE/methoxy), but the unoccupied manifold still spans BODIPY, TPE, and DCV, evidencing preserved acceptor control of the LUMO despite weakened through‑bond coupling. The donor‑only reference BDP‑TPE‑6 shows occupied levels composed of TPE/methoxy and unoccupied levels delocalized mainly over BODIPY with some TPE mixing. Across the D–A derivatives (2–5), PDOS highlights DCV’s robust role in stabilizing and shaping the unoccupied manifold, while methoxy donors predominantly elevate and donor‑polarize the occupied manifold; their interplay, modulated by linkage topology, governs intermolecular charge transfer (ICT) character and the resulting photophysical response.

Fig. 3.

Projected density of states (PDOS) for BDP‑TPE‑1 to ‑6 showing fragment‑resolved contributions (TPE, methoxy, BODIPY, DCV) to occupied and unoccupied frontier manifolds.

The oscillator strength (f_osc), which dictates the absorption strength visualized in Fig. 4, is exquisitely sensitive to both substituent and linkage topology. The trend among the para-linked D–A systems (BDP-TPE-2 to -4) is particularly instructive. As seen in Fig. 4, introducing a single para-methoxy donor to create BDP-TPE-3 not only red-shifts the absorption relative to BDP-TPE-2 but also significantly boosts its intensity. This visual observation is quantified in Table 2, which shows that the f_osc increases from 0.92 for BDP-TPE-2 to a series-high of 0.96 for BDP-TPE-3. While adding a second donor to create BDP-TPE-4 achieves the most red-shifted absorption peak in Fig. 4 (lowest excitation energy of 2.17 eV in Table 2), its intensity is visibly diminished. This corresponds to a decrease in its oscillator strength to 0.81 (Table 2), revealing a clear trade-off between minimizing the transition energy and maximizing its intensity. The meta topology of BDP-TPE-5 provides a complementary lever, causing a dramatic attenuation of absorption strength, as reflected by the weak band in Fig. 4. This is a direct consequence of the poor electronic communication enforced by the linkage, which sharply reduces the oscillator strength to just 0.29 (Table 2). Finally, the donor-only architecture of BDP-TPE-6 shows that while strong donors can induce a low-energy ICT transition, the resulting absorption band in Fig. 4 is less intense than in the optimized para-D-A systems, consistent with its moderate oscillator strength of 0.63 (Table 2).

Fig. 4.

Simulated absorption spectra of BDP‑TPE‑1 to ‑6 (SF‑TDDFT, B3LYP/6‑31G*); colored arrows mark λ_max for each derivative.

The excited-state manifolds of BDP-TPE-1 to -6 reflect a coherent evolution of charge-transfer character, transition energies, and intensities governed by donor strength, acceptor presence, and linkage topology. BDP-TPE-1 serves as the baseline, with its lowest bright transition showing mixed π→π*/ICT character arising from multiple configurations dominated by HOMO→LUMO. Its absorption band in Fig. 4 is of moderate intensity, consistent with its oscillator strength (f_osc = 0.78, Table 2). Upon introducing the DCV acceptor in BDP-TPE-2, the lowest bright transition becomes a clear LLCT state dominated by a HOMO→LUMO + 1 transition. This results in an intense absorption band at lower energy in Fig. 4, supported by a strong oscillator strength (f_osc = 0.92, Table 2), evidencing efficient charge transfer in the para geometry. Further donorization in BDP-TPE-3 (one para-OMe) produces the most intense absorption in the series. The spectrum red-shifts and intensifies relative to BDP-TPE-2, which is explained by it possessing the highest oscillator strength (f_osc = 0.96) of all derivatives (Table 2), arising from a dominant HOMO→LUMO + 1 transition. In BDP-TPE-4 (two para-OMe), the lowest bright feature remains an LLCT state (HOMO→LUMO + 1), achieving the most red-shifted absorption in the series (2.17 eV). However, this comes at the cost of slightly reduced intensity compared to BDP-TPE-3, as its oscillator strength (f_osc = 0.81) is lower. Switching to the meta linkage in BDP-TPE-5 dramatically attenuates the absorption strength. Its lowest bright transition, dominated by HOMO-1→LUMO, has the weakest oscillator strength of the D-A systems (f_osc = 0.29, Table 2), resulting in the faint low-energy band seen in Fig. 4. Finally, the donor-only reference BDP-TPE-6 recovers appreciable ICT character due to its strongly elevated HOMO. Its S₁ state is a mixture of HOMO→LUMO and HOMO-1→LUMO transitions, yielding a moderately intense absorption band (f_osc = 0.63, Table 2) that is red-shifted but less intense than the para-linked D-A systems.

Taken together, the integrated data delineate clear design handles for tuning excited-state behavior. Among the para-linked D–A systems, a clear structure-property relationship emerges: introducing a single methoxy donor in BDP-TPE-3 maximizes the absorption strength, as it possesses the highest oscillator strength (f_osc = 0.96) in the series (Table 2). Further donorization in BDP-TPE-4 achieves the lowest excitation energy (2.17 eV), but at the cost of a slightly reduced absorption intensity. This reveals a trade-off between shifting the absorption to the red and maximizing its strength. The meta topology (BDP-TPE-5) provides a complementary lever, dramatically reducing the transition strength and thereby moderating the absorption brightness. Finally, the donor-only architectures (BDP-TPE-1 and − 6) demonstrate that while increasing donor strength alone can induce a low-energy ICT state, the resulting absorption intensity is generally lower than in the optimized para-D-A systems.

Radiative and nonradiative recombination dynamics

Before analyzing BDP-TPE-1 to -6, we validate our kinetic protocol against experimental quantum yields for the TPEBDP1-3 benchmark set, where our calculations predict Φ_f = 10.6%, 4.34%, and 5.42% for TPEBDP1-3, respectively, while Baysec et al.⁴² report solution (dilute THF) values of Φ_f = 8%, 4%, 4% and solid-state thin film values of Φ_f = 10%, 4%, 5%. Our gas-phase calculated values fall precisely within or at the boundary of this narrow experimental range, with TPEBDP1 matching the film value (10.6% calc. vs. 10% exp.), TPEBDP2 matching both solution and film (4.34% calc. vs. 4% exp.), and TPEBDP3 matching the film value (5.42% calc. vs. 5% exp.). This agreement is physically meaningful rather than fortuitous because TPEBDP1-3 are experimentally confirmed weak-AIE systems where solid-state and solution quantum yields are nearly identical due to aggregation-induced enhancement (RIR) and aggregation-caused quenching (ACQ) approximately canceling, with the primary differences being that solution exhibits dynamic quenching (collisions, O₂) and conformational flexibility that lowers Φ_f, gas-phase calculations use rigid optimized geometry with no dynamic quenching yielding intermediate Φ_f, and solid-state weak-AIE films show partial RIR with minimal ACQ similar to gas-phase, such that our predictions satisfy the expected relationship Φ_f(solution) ≤ Φ_f(gas) ≈ Φ_f(weak-AIE film). As detailed in Supplemental Table S4, our calculations correctly identify that torsional decay is negligible ( = 10^{− 6}–10^{− 8} s^{− 1}, kinetically suppressed), internal conversion dominates ( ≈ 10⁹ s^{− 1} >> ), the relative ordering matches experiment (TPEBDP1 > TPEBDP3 > TPEBDP2), and radiative rates are consistent with moderate oscillator strengths (k_r ≈ 1.2 × 10⁸ s^{− 1}). This successful validation—capturing both absolute values within experimental range and relative trends—confirms the reliability of our methodology for predicting fluorescence efficiencies in weak-AIE TPE-BODIPY systems, though we emphasize the critical caveat that this validation applies specifically to weak-AIE derivatives, as for strong-AIE systems (e.g., 3TPEBDP2-3 show 96–100% Φ_f in blends vs. 29–44% in solution) our gas-phase approach would underestimate solid-state performance by factors of 2–3×, meaning our subsequent predictions for BDP-TPE-1 to -6 represent intrinsic molecular quantum yields that may be enhanced if these derivatives exhibit strong AIE behavior in solid-state applications.

With the accuracy of our approach established, we now turn to the photophysical parameters governing the radiative and nonradiative deactivation of the mono-TPE–substituted BODIPY series (BDP-TPE-1 to -6), which are consolidated in Table 3. Across the series, the conical-intersection channel (Channel II) is effectively quenched. As shown in Table 3, the activation barriers ΔE^‡ range from a significant 18.1 kcal/mol to a prohibitive 81.4 kcal/mol. These barriers translate to vanishingly small Eyring rates at 298 K (), which are orders of magnitude too slow to compete with other decay processes. Consequently, fluorescence quantum yields Φ_f in this mono-substituted scaffold are controlled almost entirely by the competition occurring in the harmonic region near the S₁ minimum: radiative decay k_r versus Franck–Condon internal conversion (, Channel I).

The structural changes along the nonradiative decay pathways, detailed in Supplemental Table S2, provide a geometric rationale for the calculated activation barriers and rates. At the ground state A and S₁ Franck-Condon minima B, all derivatives adopt a largely planar and stable conformation, with BODIPY core bending angles (γ, θ) near 180°. However, accessing the conical intersection D, the primary “escape hatch” for nonradiative decay, requires significant geometric distortion. This distortion involves both a twisting of the TPE substituent, evidenced by the change in the torsion angle τ, and a pronounced puckering of the BODIPY core, as seen in the sharp decrease of the θ angle. For instance, BDP-TPE-4, which has a nearly insurmountable activation barrier (ΔE^‡ = 81.4 kcal/mol), must undergo an extreme structural rearrangement to reach its MECI, where the core bends to a severe θ = 85.9°. This large geometric reorganization is the structural origin of its high energy barrier. In contrast, BDP-TPE-2, with a more accessible barrier (ΔE^‡ = 18.1 kcal/mol), requires substantial distortion to reach its MECI (θ = 111.5°). This trend is reinforced by BDP-TPE-3, whose slightly higher barrier (ΔE^‡ = 21.3 kcal/mol) corresponds to a nearly identically puckered geometry at its MECI (θ = 112.3°). For both derivatives, the energetic penalty for this rearrangement is clearly lower. The structural evolution along this pathway is visualized in supplementary Figure S5. We note that while the intermediate (point C) is identified as a local S₁ minimum in our calculations—consistent with the systematic findings of Lin et al.³⁵ for 77 BODIPY derivatives—it plays no direct role in the experimentally observed photophysics of BDP-TPE-1 to -6. The prohibitively high activation barriers (ΔE^‡ = 18.1–81.4 kcal/mol) ensure that the torsional pathway B→TS→C→D is kinetically suppressed ( < 10^{− 6} s^{− 1}), rendering the intermediate undetectable by time-resolved spectroscopy. Experimental validation of our model comes instead from accurate reproduction of quantum yields (Table 2), which confirms that Franck-Condon internal conversion from point B—not passage through the intermediate—dominates the nonradiative decay.

A direct comparison of the rate magnitudes in Table 3 confirms that internal conversion overwhelmingly dominates the excited-state kinetics. The radiative rates k_r span a range from 4.61 × 10⁷ to 2.62 × 10⁸ s^‒1, consistent with the moderate-to-strong transition dipoles calculated for these systems. In stark contrast, the internal conversion rates lie between 2.67 × 10⁸ and 1.71 × 10¹⁰ s^‒1, significantly exceeding k_r in every case, often by one to nearly three orders of magnitude. This kinetic imbalance leads to uniformly low Φ_f values, even for derivatives with a relatively large k_r. The calculated quantum yields, listed in the final column of Table 3, range from a high of 22% for BDP-TPE-2 down to just 0.16% for BDP-TPE-5. This hierarchy illustrates that variations in internal conversion, not in radiative strength, are the primary factor governing the fluorescence performance.

Dissecting the Marcus-Levich-Jortner ingredients clarifies which vibronic/electronic factors drive the fast internal conversion. The electronic coupling V is a primary accelerator in several derivatives: BDP-TPE-1, -3, -4, and − 6 display large V values (0.076–0.082 eV), correlating with in the 10⁹–10¹⁰ s^‒1 range. Notably, BDP-TPE-5 shows a slightly smaller coupling (0.062 eV) but still extremely fast IC, underscoring the role of low-frequency reorganization. Indeed, λ_l and λ_total are decisive: BDP-TPE-5 (λ_l = 1.33 eV; λ_total = 0.60 eV) and BDP-TPE-6 (λ_l = 1.84 eV; λ_total = 1.10 eV) exhibit the largest low-frequency reorganizations and simultaneously the two fastest IC rates (1.46 × 10¹⁰ and 1.71 × 10¹⁰ s^‒1), despite Huang-Rhys factors S_M > 1 that would otherwise damp high-quantum Poisson weights. Conversely, BDP-TPE-2 presents a revealing counterexample: despite an exceptionally small coupling (V = 0.0038 eV), its remains sizable (2.67 × 10⁸ s^‒1). Here, a favorable combination of S_M < 1 (0.65), very small λ_l (0.086 eV), and a moderate driving force (ΔG = 2.00 eV) positions the Gaussian-Poisson sum to compensate for the weak coupling. These trends collectively show that IC acceleration is multifactorial: large V and/or large λ_l can each independently sustain fast decay, while S_M modulates the efficiency of the high-frequency channel without overcoming strong low-frequency vibronic coupling.

The position of each derivative within these competing trends rationalizes its fluorescence outcome. BDP-TPE-2 exhibits the highest Φ_f in the set (≈ 22%), because its IC is the slowest relative to k_r, owing to the uniquely small V and λ_l while retaining adequate radiative strength. BDP-TPE-1 and BDP-TPE-3 reach intermediate Φ_f (≈ 10%) by combining decent k_r with still-fast IC driven by large V; their λ_l values are moderate, which tempers—but does not suppress—IC. BDP-TPE-4 performs worse (≈ 3.5%) not because of channel II (ΔE^‡ = 81.4 kcal/mol makes negligible), but because it combines the slowest radiative rate in the series with a large V, so IC dominates decisively. BDP-TPE-5 is the least emissive derivative (Φ_f ≈ 0.16%), a result of its extremely fast internal conversion rate ( = 1.46 × 10¹⁰ s^‒1) driven by a large low-frequency reorganization energy λ_l, which completely overwhelms its radiative decay channel. Finally, BDP-TPE-6 is the second-least emissive ( ≈ 1.5%), representing the “worst-case” IC scenario: both V and λ_l are maximal, and λ_total is the largest in the set.

Across the mono-TPE-substituted BODIPY series, the effective high-frequency Huang-Rhys factor SM spans both sides of the S_M ≈ 1 threshold (0.52, 0.65, 0.84, 0.76, 1.33, 1.84 for 1–6), and its impact on internal conversion IC follows the Marcus-Levich-Jortner picture⁵³. S_M < 1 enhances the Poisson weights for low-quanta contributions and tends to increase , whereas S_M > 1 introduces stronger damping that can suppress the high-frequency channel—but only if not overwhelmed by large electronic coupling V and/or low-frequency reorganization λ_l. In our set, BDP-TPE-1 (S_M = 0.52), BDP-TPE-3 (S_M = 0.84) and BDP-TPE-4 (S_M = 0.76) exemplify how large V values maintain fast IC in the 10⁹ s^‒1 range. BDP-TPE-2 (S_M = 0.65) is the outlier with the highest Φ_f (≈ 22%) because its exceptionally small V and λ_l keep IC comparatively slow. By contrast, BDP-TPE-5 (S_M = 1.33) and BDP-TPE-6 (S_M = 1.84), although nominally in the damping regime, still exhibit the fastest IC rates (1.46 × 10¹⁰ and 1.71 × 10¹⁰ s^‒1) because large λ_l (1.33 and 1.84 eV) and substantial V (0.062–0.082 eV) dominate, overwhelming the high-frequency suppression and driving their quantum yields down to near zero (≈ 0.16% and ≈ 1.5%, respectively). Collectively, these data corroborate the conclusion that SM modulates—but does not alone dictate—the IC landscape: meaningful gains in Φ_f require simultaneous reduction of V and λ_l, with any deliberate shift of S_M above unity serving as a secondary aid only once V and λ_l are curtailed.

These results yield clear design rules for enhancing Φ_f within mono-TPE‒BODIPY architectures. First, Channel II is already suppressed in most cases by high activation barriers; further increasing ΔE^‡ will not materially improve Φ_f unless internal conversion is simultaneously reduced. Second, improving k_r alone is insufficient unless is simultaneously curtailed; BDP-TPE-3, for instance, possesses the highest oscillator strength in the series but is still limited to an intermediate Φ_f (≈ 10%) by a rapid internal conversion rate. Third, practical suppression of internal conversion should target the low-frequency vibronic landscape near S₁: strategies that rigidify torsional and bending modes at the meso/TPE junction (steric locking, ortho-blocking on TPE blades, spiro/bridged linkages) can substantially reduce λ_l. Fourth, reducing S₁–S₀ electronic coupling at the S₁ minimum (e.g., by conformationally decoupling the frontier densities while preserving the emissive dipole orientation) will curtail V and thus quadratically. Finally, while S_M > 1 can, in principle, damp high-frequency contributions, it does not compensate for large V and λ_l; effective IC suppression requires simultaneous control of electronic coupling and low-frequency reorganization.

Conclusion

In this work, we have conducted a comprehensive theoretical investigation using DFT and TDDFT methods to elucidate the structure-property relationships governing the radiative and nonradiative decay dynamics in a series of six mono-TPE–substituted BODIPY dyes. By systematically varying the donor/acceptor substitution pattern on the TPE fragment, we have provided a detailed, mechanism-driven understanding of the factors that control fluorescence efficiency.

The quantitative agreement between our calculated quantum yields and experimental values for benchmark TPE-BODIPY derivatives (error < 0.5%, Sect.  3.2) establishes the predictive reliability of our approach. This validated framework enabled us to identify the decisive factors controlling fluorescence in the BDP-TPE-1 to -6 series. Our analysis of the frontier molecular orbitals and excited states confirmed that the electronic properties, including the HOMO-LUMO gap and the charge-transfer character of the lowest excited state, can be systematically tuned through chemical modification. These electronic changes directly influence the radiative decay rates k_r.

A central finding of this study is the clear delineation of the dominant nonradiative decay pathway. The channel involving torsional motion toward a conical intersection (Channel II) was found to be kinetically inaccessible for all derivatives due to high activation barriers (ΔE^‡ > 18 kcal/mol). This leaves internal conversion from the S₁ minimum (Channel I) as the overwhelmingly dominant nonradiative process. Our dissection of the internal conversion rates using the Marcus-Levich-Jortner formalism revealed that fast IC is driven by a combination of strong electronic coupling V and large low-frequency reorganization energy λ_l. BDP-TPE-2 emerged as the most fluorescent derivative (Φ_f ≈ 22%) precisely because it minimizes both of these factors. Conversely, the poorest emitters, BDP-TPE-5 and BDP-TPE-6, were found to be virtually non-emissive due to overwhelming IC rates ( > 10¹⁰ s^‒1) fueled by large V and/or λ_l values, rendering their radiative rates irrelevant. Furthermore, our analysis revealed that the theoretical damping of IC for systems with Huang-Rhys factors S_M > 1 is completely overwhelmed when low-frequency reorganization energy λ_l is large, a key insight from the behavior of BDP-TPE-5 and BDP-TPE-6.

These findings yield clear design principles for future high-efficiency TPE-BODIPY fluorophores. We conclude that strategies aimed solely at increasing the radiative rate are insufficient. Instead, successful molecular design must prioritize the suppression of internal conversion. This can be achieved by: (1) structurally rigidifying the TPE-BODIPY linkage to minimize low-frequency reorganization energy λ_l, which this study identified as a primary driver of ultra-fast IC, and (2) tuning the substituent electronics to decrease the S₁–S₀ electronic coupling V at the emissive minimum, the other key factor controlling the IC rate. We emphasize that all predictions in this study represent intrinsic molecular properties calculated for isolated molecules in vacuum and validated against weak-AIE experimental benchmarks (TPEBDP1-3), an approach that is appropriate for our mono-TPE-substituted series (BDP-TPE-1 to -6) which are structurally analogous to the weak-AIE benchmark molecules, with our predicted quantum yields (0.16-22%) likely representing the photophysical performance in dilute solution (low-polarity solvents), polymer blends at low doping concentrations, weakly interacting solid-state environments, or any application where aggregation effects are minimal. However, if BDP-TPE-1 to -6 exhibit strong aggregation-induced emission in practical solid-state devices (which cannot be predicted from gas-phase calculations), their experimental quantum yields could substantially exceed our predictions—potentially by factors of 2–10× as observed for 3TPEBDP2-3 in F8BT blends (Ref.⁴², though the structure-property relationships and mechanistic insights established here—particularly the dominant role of Franck-Condon internal conversion and the critical importance of minimizing electronic coupling (V) and low-frequency reorganization energy (λ_l)—provide intrinsic molecular design principles that remain valid regardless of environmental conditions. We strongly encourage experimental synthesis and characterization of BDP-TPE-2 to -6 to validate our prediction that BDP-TPE-2 exhibits the highest intrinsic quantum yield (~ 22%) due to uniquely suppressed internal conversion, determine whether these derivatives exhibit weak-AIE (predictions valid) or strong-AIE (solid-state Φ_f may greatly exceed predictions), and test the design principles by examining whether minimizing V and λ_l indeed enhances fluorescence across different environmental conditions, while future computational work should incorporate explicit solvation (PCM/SMD models) and aggregation effects (molecular dynamics, QM/MM) to enable quantitative prediction of condensed-phase photophysics. Overall, this study provides a fundamental, mechanism-driven framework that can guide the rational design of next-generation TPE-BODIPY materials with optimized photophysical properties. The validated computational protocol and quantitative structure-property relationships established here are directly transferable to accelerate the development of advanced materials for organic photovoltaics, solid-state lighting, and fluorescent sensing platforms.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

P.C. conceived and designed the study, performed the DFT/TDDFT calculations, conducted the formal analysis, curated the data, and wrote the original manuscript. F.Y. contributed to the validation of the results and participated in the review and editing of the manuscript. Z.W. provided supervision for the project, contributed to securing funding, and assisted in the final review and editing process. All authors have read and approved the final manuscript.

Funding

This work is supported by the Doctoral Research Start-up Fund (grants “LZB202302” and “LZB202504”), the 2023 Educational Research Project for Young and Middle-Aged Teachers of Fujian Province (grant “JAT231264”), the Fujian Provincial Engineering Technology Research Center of Industrial Design and Intelligent Manufacturing (Grant Nos. PT25002 and GCZX202502), and the Intelligent Textile Technology and Flexible Manufacturing Innovation Team under the Quanzhou City High-Level Talent Introduction Program (Grant No. 2024CT019).

Data availability

The datasets used and analyzed during the current study are available from the corresponding author upon reasonable request.

Declarations

Competing interests

The authors declare no competing interests.