Stepwise photosensitized thymine dimerization mediated by an exciton intermediate
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Cyclobutane thymine dimerization is the most prominent DNA photoinduced damage. While the ultrafast mechanism that proceeds in the singlet manifold is nowadays well established, the triplet-state pathway is not completely understood. Here we report the underlying mechanism of the photosensitized dimerization process in the triplet state. Quantum chemical calculations, combined with wavefunction analysis, and nonadiabatic molecular dynamics simulations demonstrate that this is a stepwise reaction, traversing a long-lived triplet biradical intermediate, which is characterized as a Frenkel exciton with very small charge-transfer character. The low yield of the reaction is regulated by two factors: (i) a relatively large energy barrier that needs to be overcome to form the exciton intermediate, and (ii) a bifurcation of the ground-state potential-energy surface that mostly leads back to the Franck–Condon region because dimerization requires a very restricted combination of coordinates and velocities at the event of non-radiative decay to the ground state.
KeywordsDNA Thymine dimerization Quantum chemical calculations Non-adiabatic dynamics Wavefunction analysis Charge transfer
The formation of cyclobutane thymine T〈〉T dimers between two adjacent thymine bases is the most frequent DNA damage under UV radiation . This photolesion, which can take place in both the singlet and triplet manifolds, has been extensively investigated spectroscopically [2, 3, 4, 5, 6, 7] and computationally [8, 9, 10, 11, 12, 13, 14, 15]. The triplet pathway is a much slower process  and exhibits a smaller yield [6, 16] than the singlet mechanism due to inefficient intersystem crossing. As a consequence, this pathway yields very weak spectroscopic signals that preclude unambiguous statements regarding the mechanism [5, 6, 7]. In order to enhance the triplet signals, photosensitization is commonly used, increasing the T〈〉T dimerization yield [5, 17, 18, 19]. This enhancement can also play a role with photosensitizers acting as phototoxic drugs . Photosensitization involves intersystem crossing of a photosensitizer after excitation, transferring its electronic energy to a neighboring thymine, which is then promoted to the lowest triplet state.
An intriguing question in the dimerization process is the character of the 3BR state. Calculations showed that the excited electronic density of 3BR is distributed over the two thymine units  and spectroscopic measurements suggested that dimerization involves the participation of delocalized triplet states . However, electronic delocalization over the two monomers can correspond to two different electronic states: (i) a Frenkel exciton, in which two local excitations are coupled (Fig. 1d), or a charge-resonance state, in which two charge-transfer states with charge flow in opposite directions are combined (Fig. 1e) . It has been speculated that the triplet state involved in dimerization could be a charge-transfer state , as theoretically predicted for the thymine–thymine 6-4 adduct formation . However, evidence of charge-transfer states for the T〈〉T dimerization has never been reported. An additional unsolved mechanistic feature is the reason behind the very low yield of dimerization even when the triplet manifold is forced to be populated after triplet–triplet energy transfer from a photosensitizer.
In this paper, we use quantum chemical calculations, wavefunction analysis, and nonadiabatic surface-hopping molecular dynamics simulations to provide a clear-cut mechanism for the photosensitized thymine dimerization. We study the formation of the 3BR precursor electronic triplet state from the 3L state and identify the nature of these species in terms of electronic delocalization and charge-transfer character. Furthermore, we offer a rationale for the factors behind the small quantum yield of the reaction.
Results and discussion
The first step of the reaction is the population of T1 after TTET. The character of the T1 state can either be 3L or 3BR depending on its electronic configuration (see Fig. 1). For most of the geometries within the Franck–Condon region, it is expected that the T 1 electronic state corresponds to the locally excited configuration 3L as the relatively large rise distance (3.5 Å) between stacked nucleobases in DNA strands mostly precludes the direct formation of 3BR state, where the C6–C6′ bond is already preformed. The excited electronic density in 3L is completely located at one of the thymine nucleobases (Fig. 1c), while 3BR has the spin density equally distributed over the ethylenic C5 and C5′ atoms of both thymine bases (Fig. 1d, e). Since the C6–C6′ bond is already preformed in the 3BR species, it is likely that the T〈〉T dimerization is triggered by the formation of the biradical intermediate, as suggested in the literature [5, 14].
Even if the C6–C6′ bond is not preformed within the Franck–Condon region, we found it interesting to investigate whether any initial geometrical configuration presents 3BR character. To this aim, we analyzed the electronic transition density [21, 28, 29] of the triplet states that compose the density of states, from which the delocalization length (DL), defined as the number of nucleobases involved in the excitation process , was computed. For 3L, the excitation is localized in only one of the thymine bases (DL = 1), while in 3BR both thymine monomers are involved in the excitation (DL = 2). Figure 2b shows the calculated density of triplet states in the gas phase decomposed by delocalization length. We find that the lowest-energy triplet band is mainly composed by local excitations 3L, while the contribution of excitations delocalized over the two monomers is very small. Since the photosensitizer employed in the experiments  was initially excited at ∼ 4 eV, the calculated states composing this band (between 2.7 and 4.4 eV) are the only ones energetically accessible by triplet–triplet energy transfer. Unequivocally, most of the states populated at the Franck–Condon region are locally excited states, i.e. correspond to the 3L triplet state.
The electronic wavefunction of T 1 along the pathway between 3L and 3BR is analyzed in Fig. 3b, c. Specifically, the delocalization length (DL) and the charge-transfer fraction were computed from the electronic transition density [21, 28, 29]. The delocalization length clearly shows that the dimer is in a locally excited state (DL = 1) before the barrier and, after overcoming the barrier, it evolves towards the 3BR excited state (DL = 2). This 3BR excited state can be a Frenkel exciton state or a charge-resonance state (recall Fig. 1d, e). Due to the small separation between both thymine monomers at the 3BR minimum, the formation of charge-transfer states, favoured by orbital-overlap interactions , is possible. Therefore, the 3BR state could acquire charge-resonance character along the dimerization pathway. The solid line in Fig. 3b unambiguously shows that the charge-transfer contribution is very small along the path that connects 3L with 3BR. This demonstrates that 3BR is mainly a Frenkel exciton state. Only in the region near to the 3BR/S 0 crossing the charge-transfer contribution is around 0.15, indicating that the Frenkel state acquires a small degree of charge-transfer character. This conclusion is in contrast to the hypothesis put forward in Ref. , claiming that charge-transfer triplet states could be present in the T〈〉T dimerization. Our calculations clearly demonstrate that the precursor electronic state leading to dimerization is a Frenkel exciton state and not a charge-transfer state. Recent theoretical calculations predicted that T〈〉T dimerization in the singlet manifold is also mediated by an exciton intermediate . Figure 3d–f shows the same energy scan and wavefunction analysis computed at SA-CASSCF level. Since the energy and character of the states are very similar to the ones obtained by MS-CASPT2, as was also the case for the density of states computed at the Franck–Condon region, the subsequent gas-phase dynamics simulations are performed using SA-CASSCF for the electronic-structure calculations.
After the formation of the 3BR species, the system is trapped in the 3BR minimum (recall Fig. 3a). This minimum coincides with the crossing point with the ground state S 0. Dimerization takes place only when the appropriate region of the S 0 potential is populated after intersystem crossing from T 1. As the experimental  decay time constant is 62 ns for 3BR, the radiationless decay to the ground state is a very slow process. Once in the ground state, the system can dimerize or return to the reactant region without causing damage. The experimentally determined dimerization yield is only 4% . In order to determine the factors that govern this low yield, we have sampled the 3BR minimum of T 1 for at least 100 fs with non-adiabatic surface hopping molecular dynamics simulations in the gas phase using the SHARC code .
QM/MM calculation of density of states
The density of states associated to the lowest-energy triplet band of the thymine dimer embedded in a solvated single strand (dT)12 and in the gas phase was computed. First, a isothermal-isobaric ensemble (NPT) classical molecular dynamics simulation for solvated (dT)12 was evolved at 300 K for 20 ns using the ff14SB  and TIP3P  force fields to describe DNA and water, respectively. The classical simulation was run with the graphical processing unit (GPU) module pmemd  implemented in the Amber14 package . Then, the last snapshot of the classical simulation was taken as the starting one for running quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulations in the NPT ensemble for 10 ps. The two nucleobases in the middle of the strand were described by the B3LYP functional  with D3 dispersion correction  and the 6-31G* basis set [40, 41] using the GPU-based code TeraChem1.9 [42, 43] through the interface to external QM programs implemented in Amber14 . More computational details about the molecular dynamics simulations can be found in Ref. .
Energy scan in the T 1 potential energy surface
The static calculations for the potential energy scan (Fig. 3), which goes from the Franck–Condon region to dimer formation, were carried out using MS-CASPT2 (Fig. 3a) and SA-CASSCF (Fig. 3d) with the previously described (4,4) active space and the cc-pVDZ basis set. The 3L geometry of the Franck–Condon region was taken from the ground state QM/MM molecular dynamics simulation explained above. Specifically, for every of the 30 snapshots whose vertical energy for T 1 is below 3.5 eV, which corresponds to the maxima of lowest-energy band of the density of states, the static scan was performed. Only the scan with the lowest energy barrier in the T 1 state, which tries to mimic a minimum-energy path calculation, is shown in Fig. 3. The geometry at the crossing point between S 0 and T 1 was taken from Ref. . The energies of the two lowest triplet states were computed along a linearly interpolated pathway between both geometries. From the crossing point a second linearly interpolated pathway was connected to the dimer structure, which was taken from our previous work . Moreover, the charge-transfer contribution and delocalization length were also computed along the interpolated pathway using both MS-CASPT2 (Fig. 3b, c) and SA-CASSCF (Fig. 3e, f) [21, 29].
Non-adiabatic molecular dynamics simulations
Non-adiabatic molecular dynamics simulations were run to sample the T 1/S 0 degeneracy region, in which the T 1 state presents biradical character. Therefore, an arbitrary initial geometry was built with interatomic C5–C5′ and C6–C6′ distances of 3.13 and 2.45 Å, respectively. From this geometry 1000 initial conditions (coordinates and velocities) were generated from a zero-Kelvin Wigner distribution  based on ground-state frequencies calculated at second-order Møller-Plesset (MP2) perturbation theory  using the cc-pVTZ basis set  implemented in MOLPRO . From these 1000 initial conditions, 25 were randomly selected to run dynamics on. All trajectories were initially excited to the T 1 state and ran for at least 100 fs or until they left the T 1/S 0 degeneracy region. As the dynamics starts at a close thymine–thymine distance, it was assumed that the reaction is already in progress at the start of the dynamics. Therefore, the initial velocities of all trajectories were modified so that the center of mass of each monomer moves towards each other at a velocity corresponding to the thermal energy (k B T) at a temperature of 298 K.
From the trajectories running in the degeneracy region, 32 geometries were chosen based on a combination of random selection as well as an 3BR/S 0 energy gap smaller than 0.15 eV and continued to run on the ground state potential energy surface. This approach was necessary as none of the trajectories that ran in T 1 hopped to the ground state during their simulation time. The geometries and velocities for the new trajectories running in S 0 were taken from the point where they manually hopped from the parent trajectory, and the electronic coefficients were adapted to put the population on the ground state.
The dynamics simulations were carried out using the ab initio molecular dynamics program SHARC (surface hopping including arbitrary couplings) [32, 51], which uses a modification of the Tully surface hopping method  allowing for treating both singlet and triplet states on the same footing. The time step used for the nuclear motion was 0.5 fs, and the time step for the integration of the time-dependent electronic Schrödinger equation was 0.02 fs. All electronic structure properties (energies, gradients, and couplings) were calculated at the SA-CASSCF level of theory using the above described (4,4) active space and the cc-pVDZ basis set. For both the singlet and the triplet state calculations, 3 states were averaged with equal weights each. The non-adiabatic couplings were calculated from the wavefunction overlaps by using a local-diabatization scheme . Additionally, this procedure monitors the wavefunction phase and makes sure that it is maintained throughout the dynamics . Moreover, the Persico decoherence correction , with a decoherence parameter of 0.1 a.u. was employed. To save computational time, the gradients of not-populated states were only calculated when their energy was within 0.5 eV of the currently populated state. This procedure is in accordance with previous studies showing that higher lying states only have a minimal effect on the potential of the populated states .
Open access funding provided by University of Vienna. CR gratefully acknowledges the University of Vienna within the uni:docs programme for financial support. CR also thanks Chemical Monthly, Springer, the Austrian Academy of Sciences, and the Austrian Chemical Society (GÖCH) for a mobility fellowship. The authors thank Felix Plasser for fruitful discussions. The computational results have been achieved in part using the Vienna Scientific Cluster (VSC).
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