Proton transfer-driven intersystem crossing in apigenin

Abstract

The energetics and dynamics of excited-state events that originate from the S₁ state of the apigenin molecule are studied theoretically. The dominant event is the barrierless excited-state intramolecular proton transfer process that converts the normal tautomer to the proton-transferred tautomer. The intersystem crossing is another event that can occur at the Franck–Condon region and beyond, i.e., along the proton-transfer coordinate, and can compete with proton transfer. Aided by the small energy gap and a noticeable spin–orbit coupling, the T₄ would be an energetically feasible receiver triplet state at the Franck–Condon geometry of the S₁ state compared to the other lower triplet states. The S₁–T₃ and S₁–T₂ pathways become relevant beyond the Franck–Condon point, highlighting the role of higher-lying triplets in intersystem crossing. These findings suggest that proton transfer promotes triplet formation in apigenin. Further simulations reveal an ultrafast internal conversion in the triplet manifold.

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1 Introduction

Excited-state intramolecular proton transfer (ESIPT) and triplet formation are two predominant ultrafast events in photoexcited hydroxyflavones. The intramolecular proton transfer often occurs in the range of a few tens to hundreds of femtoseconds due to there being a very low or no barrier energy along the reaction coordinate.^1–13 The triplet generation can originate from either the normal or proton-transferred tautomer, depending on the timescale of proton transfer.^14–21 The receiver triplet involved in the intersystem crossing (ISC) is often a higher-lying triplet state, and its decay depends on the energetic location of nearby triplets.^5,22–26 A longer lifetime of this state can promote photochemical transformations. The other possibility is the faster internal conversion (IC) to lower state(s), eventually reaching T₁. The efficient radiative/nonradiative T₁ to S₀ transition brings the tautomer to its S₀ state, completing a photoinduced cycle. The decay pathways of the proton-transferred tautomer ( to to to ) and its return to the reference S₀ state of the normal tautomer make tracking all events associated with the ESIPT in real time cumbersome. For instance, 5-hydroxyflavone shows a proton transfer rate of >160 fs⁻¹, and subsequently decays from to (proton-transferred tautomer) with a rate constant of 1.2 ps⁻¹.²⁷ Norikane and co-workers report a quantum yield of 0.02 for the ISC happening via the pathway. The S₁–T₁ ISC can occur; however, the barrierless potential energy profile on the T₁ state of normal tautomer would enable transformation to of the PT tautomer, similar to the S₁ to transformation.²⁸ Studying these events requires a theoretical model consisting of several singlet and triplet states of the ESIPT tautomers. Furthermore, the timescales of the involved events range from femtoseconds to nanoseconds. Including singlet–triplet energetics and long timescales in a theoretical model for simulations is a tedious task. This task can be achieved by treating the singlet and triplet manifolds separately and connecting them by evaluating ISC rates via spin–orbit coupling (SOC).

Apigenin (5,7-dihydroxy-2-(4-hydroxyphenyl)chromen-4-one) (see Fig. 1) is chosen as a prototype system to explore photoinduced events on the S₁ state. Recent findings by Chen et al. reveal a solvent-dependent ISC that can compete with ESIPT.²⁹ The ISC rates in polar aprotic solvents scale at the level of 10¹¹ s⁻¹, indicating an ultrafast ISC at the FC (Franck–Condon) geometry. Those authors propose that triplet generation via the S₁–T₃ pathway may occur through a spin–vibronic coupling mechanism. In this article, the relaxation dynamics of apigenin are evaluated by performing wavepacket simulations on the potential energy surfaces (PESs) of individual singlet and triplet manifolds. Two model vibronic Hamiltonians, a 2 × 2 matrix for S₁–S₂ and a 4 × 4 matrix for T₁–T₄ states, are employed for simulations. Relaxed scan profiles and SOC parameters of singlet–triplet states are computed at the FC point and along the proton transfer coordinate to identify the ISC pathways. Computed ISC rates in gas and solvent phases reveal the ISC via higher triplet states, with S₁–T₄ being the dominant pathway at the FC point, while the S₁–T₃ and S₁–T₂ pathways become operative away from the FC point. The ultrafast IC dynamics emerging from low-energy conical intersections suggest the efficient T₁ formation through the S₁–T_n–T₁ spin–vibronic mechanism in apigenin.

Fig. 1 Molecular structure of (a) normal and (b) proton-transferred tautomers associated with the intramolecular proton transfer process of apigenin.

2 Computational details

2.1 Energetics

The gas-phase computation of the equilibrium structure (C_s point group) and respective frequency calculation of the S₀ state of apigenin is performed using density functional theory (DFT). The B3LYP and M06 functionals, in combination with the 6-311++G basis set, were employed for these calculations.^30,31 Next, time-dependent density functional theory (TDDFT) is used to obtain the FC vertical transition energies and oscillator strengths of excited electronic states. Additional TDDFT computations were performed to evaluate the vibronic coupling parameters and potential energy profiles along the proton transfer reaction coordinate (i.e., the O–H distance). The vibronic coupling parameters were estimated using numerical methods, as described in ref. 32, whereas the relaxed scan approach was employed to obtain the potential energy profiles along the O–H distance. The triplet formation is analyzed based on the estimation of the ISC rate within Fermi's Golden Rule (cf., SI). The ISC rate primarily depends on the singlet–triplet energy gap and the associated SOC (cf., SI). The (TD)DFT computations were performed using the Gaussian 16 program suite,³³ whereas the SOC computations were done using the PySOC software.³⁴ The PySOC program estimates the three individual SOC components associated with three spin sub levels of the involved the S_n and T_m states, i.e., 〈S_n|[script letter H]_SO|T_m,x〉, 〈S_n|[script letter H]_SO|T_m,y〉 and 〈S_n|[script letter H]_SO|T_m,z〉. The [script letter H]_SO is the Breit–Pauli spin–orbit coupling Hamiltonian.^34,35 The total SOC magnitude of the S_n–T_m pathway is then obtained from the square root of the sum of the squares of all three components, i.e.,

The polarizable continuum model (PCM) with the integral equation formalism (IEF) variant is employed for solvent-phase calculations.^36–39

2.2 Wavepacket simulations

The IC dynamics in the singlet and triplet manifolds are evaluated by wavepacket simulation. The model Hamiltonians employed in these simulations are constructed using the linear vibronic coupling (LVC) approach. The second-order vibronic coupling parameters are small and neglected in the simulations (cf., Table SI17 and SI18). The initial wavepacket is generated using the harmonic vibrational modes of the S₀ state. This initial wavepacket is placed vertically at the FC point of S₁ and propagated on the coupled S₁–S₂ states on a 300-fs timescale. For the triplet dynamics, the initial wavepacket is started at the FC point of the T₄ state. The generation and propagation of the wavepacket are carried out within the well-established multiconfiguration time-dependent Hartree (MCTDH) method.^40–42 All these simulations are performed using the Heidelberg MCTDH code, version 8.5, Revision 11.⁴³ Details of the LVC parameters associated with the model Hamiltonians and the MCTDH wavepacket generation are provided in the SI (Tables SI3–SI18, SI21 and SI22).

3 Results and discussion

3.1 Singlet dynamics

Table 1 collects the TDDFT vertical energies of the low-lying excited electronic states of apigenin. The broad structureless absorption feature in the 300–450 nm range, with a maximum at 333 nm (3.72 eV) in methanol solvent, is attributed to the S₀ → S₁ transition.⁴⁴ The computed S₁ vertical transition (ππ*) energy within the TDDFT framework is lower than the experimental absorption maximum value. The vibronic mixing of the S₁ (ππ*) and S₂ (nπ*) states due to the closeness at the FC geometry (<0.3 eV) could be a reason for the mismatch of the absorption maximum with the computed transition energy. In this article, both the TD-B3LYP and TD-M06 methods have been utilized to analyze the energetics and dynamics associated with the low-lying electronic states of apigenin. As the findings obtained from both methods are similar, only the outcomes of the TD-B3LYP method are discussed here for brevity.

Table 1 Gas phase excited-state vertical energies (in eV) of singlet and triplet states of apigenin computed at different levels of theory. State symmetry and oscillator strengths are given in parentheses

	TD-B3LYP	TD-M06	Expt. Ref. 44 and 45
S1	3.51 (0.15, A′)	3.70 (0.23, A′)	∼3.72
S2	3.77 (0.00, A″)	3.85 (0.00, A″)
Δ S1–S2	∼0.26	∼0.15
T1	2.64 (A′)	2.68 (A′)
T2	3.17 (A′)	3.31 (A′)
T3	3.33 (A′)	3.50 (A′)
T4	3.43 (A″)	3.61 (A″)

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Fig. 2 shows the theoretical and experimental absorption bands at higher wavelengths. The experimental band is reproduced from Masahiko and coworkers.⁴⁵ The theoretical band is obtained by Fourier transforming the autocorrelation function generated during the MCTDH wavepacket propagation on S₁. A damping factor of 20 fs (equivalent to the convolution of a Lorentzian of full width at half maximum of 66 meV) is used to generate the band profile. The estimated energetics, based on the LVC model (cf.Fig. 3a), indicate that the S₂ minimum lies slightly below the FC point of S₁, enabling vibronic mixing. Hence, both the S₁ and S₂ states tend to contribute to the intensity of this low-energy band. Experimental high-resolution spectroscopy or derivative spectroscopy techniques may be helpful in identifying the absorption profiles of the S₁ and S₂ states.

Fig. 2 The low-energy absorption band of apigenin. The experimental band is reproduced from ref. 45. The theoretical band is obtained from the MCTDH wavepacket simulations. The vibronic coupling parameters estimated at the TD-B3LYP/6-311++G level of theory were employed in these simulations.

The dual fluorescence emission maxima at 430 nm (2.88 eV) and 534 nm (2.32 eV) observed in methanol solvent were attributed to the ESIPT tautomers. The large Stokes-shifted emission at 534 nm, associated with the PT tautomer, has a lifetime of 0.8 ns with a very weak quantum yield (<10⁻⁴). These experimental observations lead to the conclusion that nonradiative relaxation pathways dominate the dynamics of the S₁ state.⁴⁴

The first nonradiative decay is from S₁ to S₀, which can occur on a longer timescale because the energy gap between the involved states is very high. There are no literature reports on this transition. The other decay is the IC involving higher singlet states. The S₂ (nπ*) state can affect the S₁ dynamics via vibronic mixing. The LVC estimates indicate that the minimum energy conical intersection (MECI) of the S₁–S₂ states and the equilibrium minimum of S₂ are nearly degenerate. These two stationary points lie below the FC point of S₁ (cf.Fig. 3a). A very small portion of the wavepacket transfers from S₁ to S₂ through the MECI when the wavepacket is initially started on S₁ (cf.Fig. 3b). The wavepacket tends to relax to the S₁ minimum rather than moving towards the MECI. These observations imply no role of S₂ on the S₁ decay dynamics.

Fig. 3 (a) The FC point of S₁, equilibrium minimum and MECI associated with the S₁ and S₂ PESs of apigenin obtained from the LVC model. (b) Diabatic electronic populations of S₁ and S₂ states obtained during the wavepacket propagation on the S₁ state of apigenin. The vibronic coupling parameters estimated at the TD-B3LYP/6-311++G level of theory were employed in these wavepacket simulations.

The ESIPT is another nonradiative pathway originating from the S₁ state. The relaxed scan PE profile indicates a barrierless proton transfer pathway, leading to the rapid generation of the PT tautomer upon photoexcitation to the S₁ state (cf., Fig. 4). The barrierless feature of proton transfer on the S₁ state was previously reported by Amat et al.⁴⁶ The 5-hydroxyflavone exhibits barrierless proton transfer, which tends to happen with a rate of 10¹² s⁻¹.^27,47 A similar proton transfer rate is expected for apigenin, as it also possesses the barrierless nature. Further computations in the solvent environment yield a barrierless proton transfer (cf., Fig. S5 and S6), indicating that ESIPT is a dominant deactivation pathway in apigenin.

Fig. 4 Relaxed scan profiles of S₁, T₂, T₃ and T₄ states along the O–H bond elongation of apigenin computed at the TD-B3LYP/6-311++G level of theory. Singlet–triplet crossings are shown with open circles.

The ISC is the other pathway that causes S₁ depopulation. Recent findings by Chen et al. reveal the solvent-dependent ISC, with an estimated rate of 5.0 × 10¹¹ s⁻¹ in acetonitrile.²⁹ The S₁–T₃ pathway is assigned for the observed ISC based on the computed SOC parameter (1.816 cm⁻¹) at the FC geometry. Recent reports indicate that a weak SOC can induce a considerable triplet formation in medium-sized molecules.^48–53Table 2 shows that the S₁–T₄ ISC is the dominant pathway for the triplet formation at the FC point in the gas and solvent phases. The narrow energy gap, particularly in the gas and toluene, causes a high S₁–T₄ ISC rate. The energy gap of this pathway is similar to the S₁–T₃; however, the appreciable SOC makes the S₁–T₄ ISC dominant in dichloromethane. The S₁–T₄ energy gap becomes slightly wider than the S₁–T₃ in acetonitrile, but the SOC appears as the key factor that yields a higher rate (in the order of 10⁶ s⁻¹) for the former pathway compared to S₁–T₃ (in the order of 10³ s⁻¹). The S₁–T₂ ISC would be a minor pathway, due to a weak SOC and wider energy gap, for the triplet generation at the FC point of this molecule. Overall, the S₁–T₄ pathway is responsible for the ISC at the FC point in gas and solvent phases.

Table 2 ISC pathway associated with the S₁ and corresponding triplet states of apigenin. The energy gap of the involved electronic states (ΔE_ST in cm⁻¹), SOC parameter (in cm⁻¹) and the ISC rate (K_ISC in s⁻¹) of those pathways estimated at the TD-B3LYP/6-311++G level of theory

ISC pathway	ΔEST	SOC	K ISC
Gas phase
S1–T2	2742	0.02	0.02 × 10^1
S1–T3	1452	0.07	2.62 × 10^3
S1–T4	645	8.07	8.46 × 10^8
Toluene
S1–T2	2420	0	0
S1–T3	1290	0.07	5.36 × 10^3
S1–T4	403	4.94	6.84 × 10^8
Dichloromethane
S1–T2	2420	0.02	0.13 × 10^1
S1–T3	1210	0.06	5.55 × 10^3
S1–T4	1129	3.73	2.99 × 10^7
Acetonitrile
S1–T2	2420	0.02	0.13 × 10^1
S1–T3	1210	0.06	5.55 × 10^3
S1–T4	1452	3.55	6.73 × 10^6

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Fig. 4 shows the crossing of the S₁ state with triplet states along the proton transfer coordinate. The S₁ energy decreases gradually upon the elongation of the O–H distance, making the proton transfer a barrierless process. This phenomenon enables the S₁ crossing at the O–H distances of 1.03, 1.10 and 1.28 Å with T₄, T₃ and T₂ states, respectively. As these crossings happen near the FC geometry (O–H = 1.00 Å), particularly the S₁–T₄ and S₁–T₃, the molecule can display ISC before transforming to the PT tautomer.

A slightly different scenario arises when the solvent is introduced. Fig. 5 shows only the S₁–T₃ and S₁–T₂ crossings. The T₄ lies slightly above the S₁ at the FC point, and diverges upon O–H elongation. Even though its energy decreases after the O–H distance of 1.25 Å, the gap remains large (>0.7 eV), making the S₁–T₄ pathway unfavorable for ISC away from the FC point. The S₁–T₃ crossing occurs at the O–H distance of 1.10 Å, similar to the gas phase (cf.Fig. 4). On the other hand, the S₁–T₂ crossing occurs at a larger O–H distance (∼1.50 Å) than the gas phase (1.28 Å, Fig. 4). The relaxed scan profiles (Fig. 4 and 5) suggest that the S₁–T₃ and S₁–T₂ pathways can contribute to the ISC away from the FC point.

Fig. 5 Relaxed scan profiles of S₁, T₂, T₃ and T₄ states along the O–H bond elongation of apigenin in acetonitrile solvent computed at the TD-B3LYP/6-311++G level of theory. Singlet–triplet crossings are shown with open circles.

To further understand the ISC away from the FC point, the O–H distance-dependent ISC rate is analyzed (cf., Tables SI25–SI36). Fig. 6 shows the gas phase ISC rates of different pathways along the proton transfer coordinate (solid lines). The S₁–T₄ ISC rate is at the FC point (O–H = 1.00 Å) 8.93 × 10⁸ s⁻¹ and increases to 4.0 × 10⁹ s⁻¹ upon the O–H elongation to 1.04 Å. Further O–H elongation brings the rate in the order of 10⁶ s⁻¹, and remains constant thereafter. The S₁–T₃ ISC rate increases gradually from 10³ s⁻¹ from the FC point to 3.95 × 10⁵ s⁻¹ and then decreases thereafter. The rate of the S₁–T₂ ISC is below 10³ s⁻¹ till an O–H distance of 1.15 Å and increases thereafter reaching a maximum of 4 × 10⁵ s⁻¹ at O–H length of 1.28 Å. This rate decreases gradually as the O–H distance is further elongated.

Fig. 6 ISC rate associated with different pathways along the proton transfer coordinate of apigenin computed at the TD-B3LYP/6-311++G level of theory. Solid and dashed lines represent the gas and acetonitrile phase, respectively. The O–H distance is 1.00 Å at the FC geometry (arrow symbol) of apigenin.

The S₁–T₄ and S₁–T₂ ISC rates vary upon inclusion of the solvent. The ISC rate of the former pathway is much lower at and near the FC point in acetonitrile (dashed line in Fig. 6a) compared to the gas phase. The rate of this pathway becomes negligible slightly away from the FC point, both in the gas and solvent phases. The increasing trend of the latter pathway's rate away from the FC point in the solvent is similar to that of the gas phase; however, the rates tend to be higher in the solvent phase (cf., Fig. 6c). The rate of the S₁–T₃ pathway remains the same in both the gas and solvent phases, except at the crossing point. The rate of this pathway at the S₁–T₃ crossing point is lower in the solvent phase (cf., Fig. 6b). The observed rates (cf., Fig. 6) are consistent with the energy gap trends (cf., Fig. 4 and 5) along the proton transfer coordinate, demonstrating the contribution of T₄, T₃ and T₂ states in the ISC process of apigenin.

3.2 Triplet decay

Table 2 indicates that the ISC happens efficiently via S₁–T₄ at the FC point of S₁. Upon successful formation of T₄via the latter pathway, the depopulation of this state can happen in two ways: (1) the reverse ISC (rISC), i.e., T₄ to S₁ and (ii) the IC to lower triplet states. Considering that the possible rISC can be at the same rate as ISC (10⁸ s⁻¹), a faster T₄ decay via IC can hamper the rISC process. To unravel the T₄ decay, MCTDH wavepacket simulations are performed by starting the wavepacket at the FC point of the T₄ state. A 4 × 4 vibronic Hamiltonian matrix is used to investigate the evolution of this wavepacket on vibronically coupled T₁–T₄ PESs (cf., Table SI6).

Fig. 7 shows the triplet population obtained from those simulations. The wavepacket initiated on T₄ decays to lower triplet states extremely rapidly, i.e., about 80% of T₄ depopulation occurs within the first 50 fs of the simulation time. The instantaneous population accumulation in the lower triplet states is facilitated by the low-energy conical intersections (cf., Table SI20). Separate simulations show a slower decay of T₃ and T₂ states, compared to T₄, with T₂ decay as the slowest among these states (cf., Fig. S8 and S9). Those decay profiles suggest a few hundred femtoseconds to a few picoseconds timescale for the T₁ formation. This process may occur on a somewhat longer timescale in the solvent phase as the T₄–T₁ gap becomes relatively wider upon introducing the solvent. The ISC involving higher triplet states, i.e., S₁–T₄/T₃/T₂ ISC, and the vibronic coupling in the triplet manifold, manifests the spin–vibronic coupling in apigenin. Experimental real-time monitoring of the formation and decay of the ISC receiver triplet state(s) can provide valuable insights into the extent of spin–vibronic coupling (S₁–T₄–T₁) and the role of ESIPT in triplet formation.

Fig. 7 The MCTDH diabatic population of triplet states obtained by propagating the initial wavepacket on the T₄ state. The vibronic coupling parameters estimated at the TD-B3LYP/6-311++G level of theory were employed in these simulations.

4 Conclusions

Gas phase computations show that the photoexcited apigenin exhibits a barrierless intramolecular proton transfer via the S₁ state. The ISC can occur in the FC region and along the proton-transfer coordinate. The T₄, T₃, and T₂ states would act as receiver triplet states for ISC via the S₁ state. The estimated rates indicate that the dominant ISC via the S₁–T₄ pathway occurs at the FC geometry, driven by the narrow energy gap and appreciable SOC. The S₁ state crossing with the T₃ and T₂ states along the proton transfer coordinate makes the S₁–T₃ and S₁–T₂ pathways more relevant beyond the FC point. The S₁–T₄ ISC rate decreases upon increasing the solvent polarity; whereas the rate of S₁–T₃ remains unchanged, except at the S₁–T₃ crossing point, upon varying the solvent polarity. The S₁–T₂ ISC, which is active away from the FC region, has a higher rate constant in the solvent environment than in the gas phase. Experimental investigation using high-resolution transient absorption spectroscopy can reveal the involvement of higher triplet states in the intramolecular proton-transfer-driven ISC in apigenin.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data supporting this article have been included as part of the supplementary information (SI). Supplementary information is available. See DOI: https://doi.org/10.1039/d5cp04655f.

Acknowledgements

SB and AB acknowledge the Indian Institute of Science Education and Research Thiruvananthapuram (IISER TVM) for the doctoral fellowship. We thank IISER TVM for the computational facilities.

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