1 Introduction

The efficient formation of long-lived triplet excited states is essential for several applications such as photoredox catalysis [1,2,3], photodynamic therapy (PDT) [4,5,6] and triplet–triplet annihilation up-conversion [7,8,9].

Although boron dipyrromethene (BODIPY) derivatives display efficient fluorescence, in recent years, judicious modifications of the BODIPY skeleton have been proposed to obtain efficient triplet state populations by enhancing the non-radiative decay to the triplet state [10]. This result can be obtained by introducing heavy atoms [11, 12], by coupling BODIPY to electron donating chromophores in donor–acceptor (DA) dyads [13,14,15], by linking BODIPY to radical species (e.g., 2,2,6,6-tetramethylpiperidine 1-oxyl, TEMPO) [16] or by exploiting covalently-linked BODIPY dimers [17, 18]. In the last two cases, the population of the T1 excited state is mediated by a photoinduced electron transfer (PeT) process [19] leading to a charge transfer (CT) state. The long-lived triplet excited state may then be involved in bimolecular sensitization processes, e.g. production of singlet oxygen used in photocatalysis and photodynamic therapy [5, 13, 20].

CT-mediated triplet state generation has been observed not only in donor–acceptor (DA) dyads based on BODIPYs [21,22,23,24,25,26,27,28], but also for several other organic chromophores [29,30,31,32,33]. According to this process, the photo-generated CT state can undergo two further processes: a non-radiative charge recombination (CR) into the ground state (CRGR) or into the lowest triplet excited state (CRT) via spin–orbit charge transfer intersystem crossing (SOCT-ISC). Recent investigations on a library of BODIPY dyads have shown that high yields of triplet state formation are observed when the CT state lies close in energy to the lowest singlet excited state (S1). In this case, the CRGR process falls within the Marcus inverted region [34] and is relatively slow due to a large negative value of the free energy change associated to the process. Under such conditions, the CRT process can become considerably faster due to a smaller energy gap between the CT state and the lowest triplet excited state (T1) [24].

The rate constants associated with the PeT and CR steps can be modulated by varying the number of alkyl substituents in BODIPY dyads, thereby tuning the reduction potentials of the BODIPY core [35]. Since the energy of the CT state is strongly affected by the polarity of the environment, the efficiency of triplet state formation by SOCT-ISC is also expected to be solvent dependent.

With the above concepts in mind, this work focuses on two BODIPY dyads, o-BND and o-BNDet (Fig. 1), featuring an orthogonally-oriented electron donating moiety, 2-methoxynaphthalene, covalently linked in the meso position. The design is such that (Fig. 2), upon excitation of the BODIPY core a PeT from the donor to the BODIPY unit takes place, leading to the population of a CT singlet excited state (1CT). This decays by CR to form the T1 state localized on the BODIPY unit. Very recently o-BND was used for the first time in metallaphotoredox catalysis [13]. Here we expand the study by exploring how the ethyl substituted BODIPY core and solvent effects impact the population of the lowest triplet excited state. These effects are investigated by combining photophysical, electrochemical and computational studies. The relative order of the low-lying excited states plays a crucial role in both the PeT and the CR processes, and is strongly influenced by substitution, as well as solvent effects. For this reason, we determined excited state optimized geometries with time-dependent density functional theory (TD-DFT) calculations and explore solvent effects in the framework of the polarizable continuum model (PCM) [36] using different available correction schemes: the standard linear response (LR), the corrected linear response (cLR) [37, 38] and the recently proposed cLR2 schemes [39]. Finally, spin–orbit couplings (SOCs), which crucially influence the efficiency of the CRT and CRGR processes, are computed to rationalize the observed differences.

Fig. 1
figure 1

Structure of the studied dyads: (left) o-BND and (right) o-BNDet

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Fig. 2
figure 2

Jablonski diagram illustrating the main energy levels and deactivation pathways for CT-mediated triplet state generation in BODIPY derivatives. The local excitation nature of the excited states schematically depicted in the diagram is indicated in parenthesis (D for the donor, B for BODIPY). ET energy transfer, PeT photoinduced electron transfer, ISC intersystem crossing, ABS absorption, FLUO fluorescence, PHOS phosphorescence. The production of singlet oxygen by sensitization is also indicated in the diagram

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2 Experimental and computational details

2.1 Photophysical and electrochemical characterization

Photophysical measurements were carried out in acetonitrile at room temperature. UV–vis absorption spectra were recorded with a PerkinElmer λ40 spectrophotometer using quartz cells with path length of 1.0 cm. Emission spectra were acquired with either a Perkin Elmer LS55 spectrofluorometer, equipped with a Hamamatsu R928 phototube, or an Edinburgh FLS920 spectrofluorometer. Excitation spectra in the visible range were acquired with the fluorimeter Perkin-Elmer LS55. Emission quantum yields were measured following the method of Demas and Crosby [40]. Standard used: fluoresceine in NaOH 0.1 M (ΦFLUO = 95%) [41]. Singlet oxygen emission was measured using Edinburgh FLS920 spectrofluorometer equipped with a liquid nitrogen cooled ultrapure germanium crystal as a detector. The quantum yield of population of the luminescent singlet excited state of dioxygen (ΦΔ) was evaluated by comparison of luminescence intensity of 1O2 at 1270 nm of the sample of interest and of [Ru(bpy)3]2+ standard (ΦΔ = 57%)[42], recorded for isoabsorbing acetonitrile solutions at the excitation wavelength [43]. Emission intensity decays were measured by the above-mentioned Edinburgh FLS920 spectrofluorometer equipped with a TCC900 card for data acquisition in time-correlated single-photon counting experiments (0.5 ns time resolution) with a 405 nm laser. The estimated experimental errors are: 2 nm on the absorption and emission band maximum, 5% on the molar absorption coefficient and luminescence lifetime, and 10% on the luminescence and photoisomerization quantum yields.

Electrochemical experiments were carried out in argon-purged acetonitrile at room temperature with an EcoChemie Autolab 30 multipurpose instrument interfaced to a personal computer. The working electrode was a glassy carbon electrode (0.08 cm2, Amel); the counter electrode was a Pt spiral and a silver wire was employed as a quasi-reference electrode (QRE). The potentials reported are referred to SCE by measuring the potential with respect to ferrocene (+ 0.39 V vs. SCE in acetonitrile). The substrate concentrations were in the mM range and the supporting electrolyte (TEAPF6) was 0.1 M. The errors on the redox potential values are estimated to be ± 10 mV for reversible processes and ± 20 mV for irreversible processes.

2.2 Computational details

Ground state equilibrium structures of the two dyads shown in Fig. 1 were determined with DFT calculations using the M06-2X functional with the 6-311G* basis set (Figures S1–S2). Solvent effects (MeCN and, for selected computations, n-Hexane) were included with the PCM [36]. All the reported optimized geometries correspond to minima as verified by vibrational frequency calculations.

Excited state wavefunctions and excitation energies were calculated with TD-DFT, using the M06-2X functional and the 6-311G* basis set. Generally, ten triplet and ten singlet excited states were included in the calculations. Due to the constrained cyanine nature of BODIPY and the generally insufficient electron correlation at TD-DFT level, excitation energies are systematically overestimated by ca. 0.4–0.5 eV [44,45,46,47] at this level of theory. Nevertheless, several benchmark works have demonstrated that the M06-2X functional is suitable to describe the variations induced by side groups, modifications of the skeleton, stiffening or extension of the conjugated path on excitation energies of BODIPY derivatives [47,48,49,50].

Solvent polarization effects on excitation energies in solution were determined with the use of the standard linear response (LR), with the state specific (SS) corrected linear response (cLR) [37, 38] and with the cLR2 approach [39] (see the supporting information for additional details). The LR and SS approaches can be used to compute corrected excitation energies, either equilibrating the fast or the complete solvent degrees of freedom on the ground and excited states, such as to include the effect of solvent reorganization energy on absorption or emission processes. Only the fast solvent component was equilibrated (hereafter indicated as NEQ) in calculations of excited state energies used to model absorption spectra, while a fully equilibrated solvent was assumed (hereafter labelled EQ) for excited state energies employed in the discussion of photo-deactivation processes. Accordingly, the solvent correction included in excited state calculations is indicated by the label LRNEQ, LREQ, cLRNEQ, cLREQ, cLRNEQ2, cLREQ2.

Excited state geometry optimizations were carried out at TD-M06-2X/6-311G* level of theory including solvent corrections with the LR approach. The optimization of the S1 state localized on the BODIPY moiety was readily obtained for both dyads (Figure S3). Hereafter, such state as well as the state T1 bearing the same BODIPY localized excitation nature, will be labelled as S1(B) and T1(B), as done in Fig. 2. We also carried out geometry optimization for the CT states, conscious that for such states the LR approach may be inaccurate for large electron–hole separations [51]. The LR method is indeed well suited for electronic excitations characterized by small changes of electron density as is the case for the BODIPY localized S1(B) state. One of the major limits of the LR approach is that solvent stabilization is proportional to the transition dipole moment. Thus, because of its smaller transition dipole moment, the stabilization of the 1CT state is always underestimated. Such over stabilization of the S1(B) state prevented the optimization of the 1CT state for o-BND because during its geometry optimization, whenever it became closer to the BODIPY localized S1(B) state, a larger erroneous stabilization of the latter led to an inversion of states. In contrast, for o-BNDet the 1CT optimized geometry was determined (Figure S4), owing to its higher energy compared to the BODIPY localized S1(B) state. Nevertheless, for both dyads we were able to obtain the equilibrium geometry of the 3CT state (Figure S5), which shares a similar wavefunction with 1CT. The geometries of the 3CT and 1CT states of o-BNDet display modest differences (Figure S6) and therefore the former can be assumed as representative of the 1CT equilibrium structure of o-BND. Hereafter, both 3CT and 1CT structures will be considered for the SOC calculations (see below).

The intra-molecular reorganization energies \({\lambda }_{i}\) associated with the S1(B) → 1CT, 1CT → S0 (CRGR) and 1CT → T1(B) (CRT) photo-induced processes, were determined for o-BNDet with the four points adiabatic potential approach [52], using in vacuo optimized geometries (see Figure S7). For highly polar solvents, equilibrium and non-equilibrium regimes represent very different solvent configurations and their energy difference is generally known as solvent reorganization energy \({\lambda }_{{\text{s}}}\) [37]. To separate the solvent reorganization energy from the total reorganization energy, and to gain insight on the magnitude of the solvent reorganization at different geometries, we performed the complete absorption (non-equilibrium regime) / emission (equilibrium regime) cycle by keeping the molecular geometry frozen at each optimized molecular structure (ground and excited states) and extracted the values of solvent reorganization with the four points adiabatic potential approach (Figure S8). All calculations were performed with the Gaussian 16 package [53].

SOC calculations were carried out at the ground state and CT state geometries optimized in MeCN. The SOC integrals were calculated with the spin–orbit mean-field (SOMF) method, with one-center approximation applied to the exchange term, (SOMF(1X)) [54, 55]. Relativistic corrections were included with the zeroth order regular approximation (ZORA) [56] using the basis sets specifically designed for these all-electrons calculations ZORA-def2-TZVP. The calculations were carried out with ORCA 5.0.1 package [57] with the Tamm-Dancoff approximation (TDA) [58].

3 Results and discussion

3.1 Electrochemical characterization

Electrochemical characterization was performed by cyclic voltammetry in degassed MeCN solution (Table 1 and Figure S9). The observed electron transfer processes are chemically and electrochemically reversible for both compounds. The processes reported in Table 1 are likely located on the BODIPY core, as suggested by the more positive and chemically-irreversible electron transfer process observed for the oxidation of 2-methoxynaphthalene[41] and by the similarity of redox potentials with literature values for BODIPY dyes [35]. This result indicates that the BODIPY and naphthalene units are electronically decoupled.

Table 1 Redox potentials of the studied compounds in degassed MeCN, in V vs. SCE
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It is worth noting that o-BNDet displays oxidation and reduction processes cathodically shifted (ca. 100 mV) compared to those observed for o-BND. The cathodic shift is correlated to the ethyl substitution that increases the electron density on the core, as previously reported [35].

3.2 Photophysical characterization

o-BND and o-BNDet’s photophysical properties in MeCN were compared in order to understand the effect of alkylation of the BODIPY core (Table 2). o-BND’s absorption spectrum is characterized by a slightly vibrationally-structured band at 502 nm, which is typical of the S0 → S1(B) electronic transition in BODIPY derivatives. Moreover, its fluorescence spectrum is specular to the lowest absorption band and the small Stokes shift (13 nm) suggests a small geometrical distortion of the S1(B) and S0 states. Similar remarks can be drawn by observing o-BNDet’s absorption and emission spectra, although a bathochromic shift is present in the latter (Fig. 3), as explained by computational results (vide infra). Besides, we observed a slightly longer lifetime for o-BNDet compared to o-BND (Table 2) and a significantly higher fluorescence quantum yield of o-BNDet compared to o-BND (60%). Based on these values, we calculated the fluorescence decay constants (kFLUO) and the non-radiative decay constants (knr), i.e. the sum of the rate constants of non-radiative processes deactivating the S1(B) state of the BODIPY core, namely internal conversion S1(B) → S0, inter system crossing S1(B) → T1(B) and photoinduced electron transfer S1(B) → 1CT (Table 2). kFLUO is very similar for the two dyes, while a sixfold reduction of knr is observed for o-BNDet compared to o-BND. Indeed, as previously discussed the addition of ethyl groups on the BODIPY skeleton cathodically shifts the reduction potential of the BODIPY core. As a result, the photoinduced electron transfer from 2-methoxynaphthalene to the BODIPY core is less favoured and fluorescence becomes the predominant deactivation pathway of the S1(B) excited state. In a parallel manner, the quantum yield for the generation of singlet oxygen is 27% in the case of o-BND (Figure S10) and negligible for o-BNDet. Population of the luminescent singlet excited state of dioxygen dissolved in solution occurs via energy transfer by the lowest T1(B) state of o-BND, therefore indicating that the CT-state-mediated mechanism that leads to the population of T1(B) is viable in this derivative (see introduction and Fig. 2), but not in the case of o-BNDet.

Table 2 Photophysical properties of the studied compounds in air-equilibrated MeCN
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Fig. 3
figure 3

Normalised absorption (A) and emission (B) spectra of o-BND (black; λEXC: 480 nm) and o-BNDet (green; λEXC: 450 nm) in air-equilibrated MeCN at room temperature

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3.3 Modeling photophysical properties of BODIPY dyads

To assist the interpretation of experimental data and, specifically, to assess the effect of solvent and ethyl substitution on the sequence of photoinduced events, we investigated the two BODIPY dyads in their ground and excited states.

3.3.1 Electronic structure effects of BODIPY core alkylation

The effect of substitution on the BODIPY core was investigated in previous studies on BODIPY-anthracene dyads bearing different numbers of alkyl substituents [15]. Upon substitution, the HOMO energy increases gradually, while the HOMO–LUMO gap steadily decreases because the destabilization of the LUMO is more limited. Our results reveal a similar trend: in Fig. 4 we compare the computed orbital energies of o-BND, o-BNDet, with those of the simple BODIPY and its alkylated derivatives. The orbital energy trends change as expected, and as a result o-BNDet is characterized by a lower HOMO–LUMO gap compared to o-BND. Such reduced energy gap is expected to be reflected in a red-shifted maximum in the absorption spectrum of o-BNDet since the main band in the absorption spectrum is due to the excited state dominated by the HOMO–LUMO excitation (Table S2).

Fig. 4
figure 4

Shapes and energies of HOMO (blue) and LUMO (green) of BODIPY and its derivatives calculated at M06-2X/6-311G* level at the ground state optimized geometry

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Accurate computational predictions of redox potentials require comparison of energies for both the starting molecule and its reduced/oxidized forms. However, we can qualitatively use Koopmans’ theorem [59] to correlate the redox potentials of BODIPY dyads with HOMO/LUMO computed energies (Table S1). Compared to o-BND, the higher HOMO energy of o-BNDet implies an easier oxidation, in agreement with its lower oxidation potential. Similarly, the additional alkyl groups in the BODIPY core determine a higher LUMO energy which implies a lower tendency to be reduced in very good agreement with the experimental observation. Since the LUMO is localized on the BODIPY core, its increased energy in o-BNDet implies a reduced efficiency as electron acceptor which is expected to be reflected in higher lying charge transfer excited states in the ethylated dyad.

3.3.2 Low-lying excited states of BODIPY dyads

To discuss the efficiency of deactivation pathways for the two BODIPY derivatives, we determined the most relevant excitation energies and excited state wavefunctions in vacuo and including solvent effects, at the optimized ground state geometries (Table S2). As expected, among lowest-lying excited states we find the T1(B) and S1(B) states, dominated by the HOMO → LUMO excitation, localized on the BODIPY core. In addition, the two CT states 1CT, 3CT, almost degenerate are easily identified from computed results, due the localized nature of the frontier molecular orbitals (Figure S11) at the optimized ground state geometry of the two dyads, characterized by an almost perfect orthogonality of the donor with respect to the BODIPY core (Figure S1 and S2).

The quality of predicted excited states can be assessed by comparing the computed excitation energies in MeCN of o-BND to o-BNDet, with the experimental absorption spectra. To this end, we can consider three levels of solvent corrections, LRNEQ, cLRNEQ and cLR2NEQ on predicted excitation energies of the BODIPY localized lowest singlet excited state S1(B), characterized by a large oscillator strength (Table S2), the state responsible for the main absorption band. The observed red shift of the main absorption band in o-BNDet compared to o-BND, is directly related with the reduced HOMO/LUMO gap of the former and is nicely reproduced by the calculations (Figure S12) at all levels of solvent correction. Disregarding the well-known overestimate of computed excitation energies at TD-DFT level [45,46,47] described in Sect. 2.2, we note that the red shift from o-BND to o-BNDet is predicted to be 0.11, 0.13 and 0.11 eV from LRNEQ, cLRNEQ and cLR2NEQ calculations, respectively, in excellent agreement with experimental results in MeCN, showing a bathochromic shift of 0.12 eV.

The stabilization of the 1CT singlet state, with respect to the BODIPY centered S1(B) state, depends on alkyl substitution and on the environment, as expected given the large, computed, dipole moment of the charge separated state (Table S3). Both effects are crucial for the efficiency of the photoinduced processes, but solvent stabilization is also influenced by the timescale of the photoinduced process, which may or may not allow full solvent equilibration. To get some insight on the magnitude of solvent stabilization associated with different timescales, in addition to the already discussed calculations of solvent effects with the fast solvent component equilibrated (LRNEQ and cLRNEQ) we also determined the relevant low-lying excited states including fully equilibrated solvent effects (LREQ and cLREQ schemes). These calculations show remarkably different results for o-BND and o-BNDet (Figs. 5 and S13). Specifically, the 1CT state is predicted above S1(B) in vacuo for both dyads, while in MeCN a remarkable stabilization occurs. With only the fast solvent component equilibrated, (cLRNEQ calculations) the 1CT gets closer to S1(B) for o-BNDet and becomes the lowest singlet for o-BND. Finally, with solvent fully equilibrated in the excited state (cLREQ predictions) the 1CT state drops below the S1(B) state for both dyads, although it remains closer to the S1(B) state for o-BNDet (0.17 eV), compared to o-BND (0.37 eV). The lower stabilization of the 1CT state for o-BNDet can be traced back to the alkyl substituent effect.

Fig. 5
figure 5

Relevant excited states pattern of o-BND and o-BNDet calculated at the ground state geometry in vacuo and in MeCN (solvent effects described with the cLR scheme). The energy of S0 is destabilized or stabilized accordingly. Note that in the cLREQ scheme, the S0 energy is also state dependent and the color codes of S0 cLREQ reflect the excited state on which the solvent is equilibrated

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The optimized S1(B) geometry (Figure S3) clearly reflects the localized character of the BODIPY centered excitation as can be seen in Fig. 6, showing modest bond length changes localized only on the BODIPY core. Interestingly, the donor is not perfectly perpendicular to the BODIPY core and the S1(B) equilibrium structure is characterized by a deviation from orthogonality of the naphthyl substituent, with a change of the dihedral angle from ca. 91° in the ground state to ca. 72° (Table S4). Notably, the relative energy order of low-lying excited states (Figure S14) is very similar to what has been discussed for the ground state geometry: the 1CT state of both dyads becomes the lowest singlet excited state for fully equilibrated solvent but its stabilization is larger (0.24 eV below S1(B)) for o-BND compared to o-BNDet (0.03 eV below S1(B)).

Fig. 6
figure 6

Comparison between the bond lengths of o-BND in its ground and S1(B) electronic states. From M06-2X/6-311G* calculations in MeCN

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As discussed in Sect. 2.2, due to the limits of the LR method, the 1CT equilibrium geometry was determined only for o-BNDet. Its comparison with the ground state geometry shows clear traces of the electron transfer character since both the donor and the acceptor moieties are subject to substantial bond length changes (Fig. 7). Similar bond length changes are determined for the 3CT equilibrium structure (Figure S15) which, therefore can be taken as an acceptable representation of the 1CT state for o-BND.

Fig. 7
figure 7

Comparison between the bond lengths of o-BNDet in its ground S0 and excited 1CT electronic states. From M06-2X/6-311G* calculations in MeCN

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3.3.3 Efficiency of S1(B) → 1CT, 1CT → S0 and SOCT-ISC deactivations

According to the excited state stabilizations investigated in the previous section, we can discuss the deactivation processes following excited state population. Based on the present and previous experimental investigations on similar BODIPY dyads [24], the internal conversion taking place in S1(B) to generate the 1CT state, is expected to be fast but the timescales of solvent reorganization [60] (picosecond, sub-picosecond [60]) are faster, such that we can discuss this process (schematically depicted in Fig. 8) assuming solvent equilibrated excited state energies (from cLREQ calculations) at the equilibrium S1(B) geometry (Figure S14, Table S5). For both molecules, the 1CT state is more stable than the S1(B) state: ∆E(1CT/S1(B)) is − 0.24 eV for o-BND and − 0.03 eV for o-BNDet. Our computed ∆E(1CT/S1(B)) energy differences compare qualitatively well with the ∆G0 values of this deactivation process, previously reported for similar dyads [24]. We note that the energy difference predicted for o-BNDet is less than one kcal/mol which, on one hand implies a non-negligible population of the S1(B) fluorescent state and on the other hand is probably smaller that the error of the method. Thus, we cannot rule out that the 1CT state is indeed above S1(B) for o-BNDet. Accordingly, we can conclude that the rate constant associated with PeT is expected to be considerably larger for o-BND compared to o-BNDet, owing to the larger stability of the 1CT state. The predicted inefficient formation of the 1CT state for o-BNDet is in agreement with its predominant fluorescence deactivation.

Fig. 8
figure 8

Schematic representation of the three deactivation processes: PeT, CRGR and CRT in a o-BND and b o-BNDet, from computed excited state energies (TD-M06-2X/6-311G* level, including cLREQ solvent corrections)

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The two major deactivation pathways of the 1CT state are 1CT → S0 and 1CT → T1(B). The CRGR is expected to be slow because of the large ∆E(1CT/S0) energy difference, falling in the Marcus inverted region. Thus, solvent equilibrated energies (cLREQ) computed at the CT state geometry (Table S5) are considered for this process (also shown schematically in Fig. 8). Because the ∆E(1CT/S0) is slightly larger for o-BNDet compared to o-BND, the CRGR processes is expected to be slightly less efficient for the former. Thus, the PeT is more favored for o-BND, while CRGR is expected to be inefficient for both dyads although slightly more efficient for o-BND.

The other competing deactivation pathway, the formation of the T1(B) state via SOCT-ISC, due to the typical magnitude of the SOC integrals (ca. 1 cm−1), is also a slow process [24] (of the order of 107–108 s−1) compared to typical timescales of solvent reorganization [60]. Thus, solvent-equilibrated excited state energy differences (cLREQ values, see Table S5) and computed SOC integrals are employed to discuss the efficiency of this process. The SOC integrals between the 1CT and T1(B) states, computed at two different geometries (ground state and CT, see Table 3) are in line with the typical values above, and also agree with those deduced for other BODIPY dyads [24]. Notably, although the two geometries (optimized ground and CT states) display different degrees of orthogonality between the naphthyl substituent and the BODIPY core, both consistently suggest a similar decay pattern, with the computed SOCs larger for o-BND compared to o-BNDet. For radiationless transitions slower than vibrational relaxation [61], and for relatively large \({\Delta E}_{S-T}\) energy gaps, the ISC process can be discussed in terms of a simplified relation (Eq. 1), where the rate constant (\({k}_{{\text{ISC}}})\) is proportional to the SOC matrix element, \(\langle {{\text{T}}}_{1}({\text{B}})|\widehat{{H}_{{\text{SO}}}}|{}^{1}{\text{CT}}\rangle\) in this case, and inversely proportional to the square of the energy gap \({\Delta E}_{S-T}\), namely the ∆E(1CT/T1(B)) values [61,62,63,64]:

Table 3 Computed SOC magnitudes between 1CT and T1(B) for o-BND and o-BNDet
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$${k}_{{\text{ISC}}}\propto \frac{{\left|\langle {{\text{T}}}_{1}({\text{B}})|\widehat{{H}_{{\text{SO}}}}|{}^{1}{\text{CT}}\rangle \right|}^{2}}{{({\Delta E}_{S-T})}^{2}}$$
(1)

Since ∆E(1CT/T1(B)) is smaller for o-BND (0.92 eV) with respect to o-BNDet (1.18 eV) at the CT state geometry (Fig. 8, Table S5), and the SOC is larger, both factors favor the ISC of o-BND. Notably, such predicted ∆E(1CT/T1(B)) energy differences are in very good agreement with those reported for other similarly efficient dyads [24] (∆E(1CT/T1(B)) in the range 0.81–1.01 eV). Thus, calculations also predict a less efficient triplet generation for o-BNDet compared to o-BND.

In summary, the computed relative stabilization of the 1CT state in MeCN for the two dyads, crucially determines the efficiency of the two sequential processes S1(B) → 1CT and SOCT-ISC, leading to the T1(B) state population. These are both predicted to be more efficient for o-BND, fully supporting the experimental evidence of preferential triplet state population for o-BND.

3.3.4 Intra-molecular and solvent reorganization energies.

The intramolecular reorganization energies \({\lambda }_{i}\) associated with the three photoinduced events discussed above were computed for o-BNDet. Not surprisingly, for S1(B) → 1CT PeT and CRGR process, the computed values are similar (0.60 and 0.66 eV, respectively) since the two deactivation pathways involve very similar geometry changes. Indeed, the two processes share a common state (1CT), but the S0 and S1(B) states involved as the initial or final states, have already been shown to display very similar geometries (see Fig. 6). These computed values are in reasonable agreement with the \({\lambda }_{i}\) of 0.37 eV deduced from the fitting of PeT and CRGR experimental data, recently determined for a library of BODIPY dyads [24]. Such previously investigated set of BODIPY dyads included rather different donors and the smaller 0.37 eV value (compared to our predicted \({\lambda }_{i}\)) may result from the average over rather different donor substituents. The reorganization energy computed for the CRT process amounts to 0.87 eV, in good agreement with the 0.70 eV deduced from the same set of BODIPY dyads [24].

The effect of solvent can be assessed also by estimating solvent reorganization energy \({\lambda }_{{\text{s}}}\), associated with S0 → X processes (where X = S1(B), 1CT and T1(B) excited states). Larger values are expected for excited states featuring a dipole moment substantially different from the ground state, but computed values also depend on the scheme adopted to introduce solvent effects (Table S6). Solvent corrections described with the LR approach are strongly dependent on the transition dipole moment, which explains the large reorganization energy predicted for the S1(B) state (0.24 eV) and the almost negligible values computed for the 1CT and T1(B) states. In contrast, the SS cLR scheme predicts the largest reorganization energy for the CT state (0.56 eV at the S0 geometry), as expected due to its large dipole moment compared to the ground state (Table S3). The most remarkable difference between predicted cLR and cLR2 contributions is found for the S1(B) state (0.01 and 0.25 eV, respectively), and can be traced back to the influence of the LR term (namely the solvent response through the transition density) to the cLR2 correction [39, 65]. When moving from the ground state geometry to the S1(B) geometry, the computed solvent reorganization energies undergo modest changes (Table S6) in agreement with the modest S0–S1(B) geometry change. In contrast, the computed equilibrium structures of the CT state imply rather remarkable geometry changes and are accompanied by a mixing of the S1(B) and CT character. This is reflected in remarkably different computed \({\lambda }_{{\text{s}}}\) values for the S0 → S1(B) and S0 → 1CT processes, with the latter generally reduced and the former increased. The computed reorganization energy of the S0 → 1CT process can be directly compared with the solvent reorganization deduced for the CRGR process by fitting experimental data on a series of BODIPY dyads [24], which is reported to be 0.17 eV. Such value is considerably smaller compared to our computed values of 0.56 eV (o-BND) and 0.54 eV (o-BNDet) at the ground state geometry or 0.49 eV (o-BND) and 0.45 eV (o-BNDet) at the optimized S1 geometry. Interestingly, however, the \({\lambda }_{{\text{s}}}\) computed at the equilibrium structure of the 1CT state, the most appropriate geometry to discuss the CRGR process, range between 0.13 and 0.17 eV with the latter (obtained with the cLR2 scheme) perfectly matching the experimentally deduced value. These results further support the reliability of solvent corrections introduced in our calculations to describe the photo-induced processes in these BODIPY dyads.

4 Conclusion

In this work, we rationalized the efficiency of CT-mediated triplet state generation in two BODIPY dyads featuring a methoxy-naphthalene donor covalently linked in the meso-position of the BODIPY core with different alkyl substituents, by combining an experimental photophysical and electrochemical investigation with computational studies of the relevant photo-induced processes.

The photophysical measurements indicated that the CT-state-mediated mechanism that leads to the population of T1(B) is viable in o-BND, but not in the case of o-BNDet, the latter showing a significantly higher fluorescence quantum yield.

To assess the effects of solvent and ethyl substitution on the sequence of photoinduced events, DFT and TD-DFT calculations were carried out including different solvent correction schemes. We found that LRNEQ, cLRNEQ and cLR2NEQ approaches predict, in MeCN, a red shift of the most intense absorption band of o-BNDet compared to o-BND, in excellent agreement with experimental data. To further assess the accuracy of the computed results, intramolecular and solvent reorganization energies associated with photo-induced processes were determined and showed to agree with values deduced by fitting photophysical data from a large set of BODIPY dyads.

Quantum-chemical calculations demonstrated that solvent equilibration in the excited states (cLREQ predictions) stabilizes the 1CT state below the S1(B) state to a different extent for the two dyads, with o-BNDet displaying a reduced stabilization compared to o-BND that can be traced back to the alkyl substituent effect. As a result, the S1(B) → 1CT PeT in MeCN is predicted to be more efficient for o-BND compared to o-BNDet which supports the higher fluorescence of o-BNDet. The rate constant of the CRGR process is expected to be small for both dyads due to the large energy gap between the S0 and the 1CT states falling in the inverted Marcus region. In contrast, a more efficient triplet state generation via SOCT-ISC is expected for o-BND thanks to a larger SOC and reduced T1(B)/1CT energy gap. The predictions of more efficient PeT and CRT processes for o-BND in MeCN fully support the experimental observation and demonstrate how alkyl substitution and solvent stabilization can crucially determine the outcome of photoinduced events.