Nonradiative Deactivation Mechanisms of Uracil, Thymine, and 5

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Nonradiative Deactivation Mechanisms of Uracil, Thymine, and 5-Fluorouracil: A Comparative ab Initio Study Shohei Yamazaki* and Tetsuya Taketsugu Division of Chemistry, Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan

bS Supporting Information ABSTRACT: The mechanisms of the ultrafast nonradiative deactivation of uracil and its substituted derivatives thymine (5-methyluracil) and 5-fluorouracil after absorption of UV light are explored and compared by means of ab initio multistate (MS) CASPT2 calculations. The MS-CASPT2 method is applied for the calculation of potential energy profiles, especially for the geometry optimization in the electronically excited state, with the aim of an accurate prediction of deactivation pathways. The resulting energy curves of each molecule exhibit that the conical intersection between the 1ππ* and ground states is accessible via small energy barriers from the minimum in the 1 ππ* state as well as from that in the 1nπ* state. The barrier of 5-fluorouracil in the 1ππ* state is calculated to be definitely higher than those of uracil and thymine, which is consistent with experiments and suggests that the elongation of the excited-state lifetime of uracil by fluorine substitution is significantly contributed from intrinsic electronic effect of the molecule. However, no evidence of the experimentally observed longer excited-state lifetime of thymine than uracil is found in the presently calculated MS-CASPT2 potential energy curves in the 1ππ* and 1nπ* states, implying nonnegligible contribution of other factors such as solvation effect and substituent mass to the photoinduced dynamics of uracil derivatives.

1. INTRODUCTION The nucleic acid bases are the primary chromophores of DNA and RNA, which strongly absorb UV light. The photophysical and photochemical behavior of the bases has therefore been extensively studied for understanding the underlying mechanism of photostability and photodamage in the nucleic acids.16 It has been well recognized that the DNA and RNA bases exhibit extremely low quantum yields of fluorescence.7,8 Recent time-resolved spectroscopic studies have confirmed that the lifetimes of electronically excited states of the natural bases are on the picosecond or subpicosecond time scale.1,2,4,5 These experimental observations suggest that the excited state of the nucleobases is efficiently quenched by particularly fast radiationless decay processes back to the electronically ground state. The ultrafast deactivation seems to prevent the nucleic acid bases from undergoing destructive photochemical reactions and thus provide DNA and RNA with a particularly high degree of photostability.1 Theoretical studies have revealed that conical intersections (CIs)9 between potential energy surfaces of the singlet ground (S0) and first excited (S1) states are responsible for the ultrafast nonradiative decay of the nucleic acid bases.1,4,6 Since in 2002 the first computational studies on the radiationless decay through CIs were reported for adenine10,11 and cytosine,12 several deactivation pathways connecting the FranckCondon (FC) region to S1S0 CIs have been proposed for each natural base on the basis of quantum chemical calculations of the potential energy profiles in the excited state. It has been shown r 2011 American Chemical Society

that the deactivation processes via CIs involve deformation of molecular structure such as ring puckering in the 1ππ* or 1nπ* state1222 and dissociation of an NH bond in the 1πσ* state.10,11,22 A large number of on-the-fly molecular dynamics simulations have also been performed to explore the nonradiative decay dynamics of the photoexcited nucleobases.20,2338 Experimentally, it is well-known that small substitution in the nucleic acid bases can significantly affect their photophysical behavior. Therefore, study of the substituent effect is expected to provide more detailed insights into the mechanisms of the ultrafast nonradiative deactivation. A most typical example that exhibits such a strong effect of substitution is the RNA base uracil (U), the DNA base thymine (T, also known as 5-methyluracil), and their substituted analogue 5-fluorouracil (5FU). See Figure 1 for the molecular structure and atom labeling of U, T, and 5FU. The only difference in the structure of these three molecules is the substituent group attached to the carbon (C) atom on the 5 position (C5 atom): hydrogen (H) atom for U, methyl (CH3) group for T, and fluorine (F) atom for 5FU. Nevertheless, the excited-state lifetimes of these bases exhibit a clear dependence on the substitution. In polar solution, the excited-state lifetime of T is longer than that of U,3942 and the lifetime of 5FU is even longer.4042 For example, the lifetime of fluorescence decay in Received: July 11, 2011 Revised: December 8, 2011 Published: December 15, 2011 491

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molecular property or partly induced by solvent effect. For the gas phase, particularly, previous theoretical studies have paid less attention to what makes the lifetime difference between U and T and rarely compared the potential energy profiles along the deactivation pathways of the three bases including 5FU at the same computational level. Second, substituent effects on the deactivation pathways from the 1nπ* minimum are less discussed, compared with those from the FC region or the 1ππ* minimum. For U and T, the decay of time-resolved electronic spectra on the picosecond time scale is often attributed to the nonradiative deactivation from the 1nπ* state.39,47 In such experiments, T still exhibits a longer excited-state lifetime than U. The purpose of the present work is to theoretically explore the nonradiative decay mechanisms of U, T, and 5FU in the gas phase at the same computational level and thus make clear the intrinsic effects of the C5 substitution on their photophysical behavior. For this purpose, excited-state potential energy profiles of the three bases are calculated with ab initio methods for the deactivation pathways from the 1ππ* state as well as from the 1nπ* state. Deactivation from the 1πσ* state is not studied since this state is much higher in energy than the 1ππ* and 1nπ* states in the case of U.58 To accurately predict the decay mechanisms, the MSCASPT2 method66 is employed for the calculation of potential energy profiles. MS-CASPT2 is an ab initio multireference perturbation method using the complete-active-space self-consistentfield (CASSCF) wave function as the reference. In this method, dynamic electron correlation is taken into account by the perturbative treatment. The MS-CASPT2 method can properly describe potential energy surfaces near CIs and avoided crossings by coupling several electronic states with an effective-Hamiltonian approach, while the single-state (SS) CASPT2 method, which does not take into account the coupling between electronic states, often gives unphysical behavior of the potential energy surfaces near crossings.67 It should be emphasized that the present work applies the MS-CASPT2 method even for the geometry optimization in the excited state, with the aim of an accurate determination of minimum-energy structures and reaction paths relevant to the decay process. In most of the previous theoretical studies on the nucleic acid bases, excited-state geometry optimizations were performed with the CASSCF method, while the SS- or MSCASPT2 method was applied only for single-point calculations at the CASSCF-optimized structures. However, the CASSCF geometry optimization may result in less accurate (and even qualitatively incorrect) structures due to the lack of dynamic correlation.68 By means of the geometry optimization at the MS-CASPT2 level, we attempt to provide a more reliable picture of the deactivation mechanisms for uracil compounds. The organization of this paper is as follows: computational methods used in the present work are given in the following section. After showing the results of vertical excitation energies in section 3.1, we examine the substituent effects on the deactivation path from the minimum of the 1ππ* state in section 3.2. In section 3.3, the validity of the present MS-CASPT2 calculation for the 1ππ* state is discussed, which is essential for the prediction of deactivation mechanism in this state. Section 3.4 compares the deactivation path from the 1nπ* minimum for the three uracil derivatives. Section 4 concludes the present work.

Figure 1. Molecular structure of uracil (U), thymine (T), and 5-fluorouracil (5FU). Atom labeling is also given.

aqueous solution was measured to be 0.10, 0.39, and 1.31 ps for U, T, and 5FU, respectively.41,42 The same order of the excitedstate lifetime was reported for the DNA/RNA base cytosine and its derivatives 5-methylcytosine and 5-fluorocytosine in aqueous solution.43,44 For U and T, the order of the lifetime is unchanged in the gas phase.4547 For nucleosides, the excited-state lifetime of thymidine (nucleoside of T) was found longer than the lifetime of uridine (nucleoside of U) in aqueous solution.4850 The elongation of the excited-state lifetime of U is also induced by substitution on the C5 position with other groups such as the amino group51,52 and the hydroxyl group52 as well as by substitution on the C5 and C6 positions with the trimethylene group.53 On the theoretical side, the excited-state potential energy profiles have been extensively studied for U,14,19,24,38,41,5459 T,18,19,21,24,32,33,41,57,60 and 5FU,41,54,55,57,59,61 as well as for other 5-substituted uracils.52,53,62 For these bases, out-of-plane deformation of the six-membered ring via twisting of the C5dC6 double bond has been proposed as the dominant mechanism leading the photoexcited molecule to the S1S0 CI. Zgierski et al.54 calculated the excited-state potential energy profiles of U and 5FU in the gas phase using the configuration interaction singles (CIS) and completely renormalized equation of motion coupled-cluster singles and doubles with noniterative triples [CR-EOM-CCSD(T)] methods. On the basis of the computational results, these authors concluded that the lifetime elongation by the fluorine substitution is due to the appearance of a barrier on the reaction path of the C5dC6 twisting in the excited state, which separates the local minimum of the 1ππ* state from the S1S0 CI. The same mechanism was proposed to account for the difference between the excited-state lifetimes of cytosine and 5-fluorocytosine.63 For 5FU, Mercier and Reguero59 also reported the presence of a barrier on the deactivation pathway of the 1ππ* state in terms of potential energy profiles calculated at the multistate complete-active-space second-order perturbation theory (MS-CASPT2) level. In the case of aqueous solution, Gustavsson et al.41 attributed the lifetimes increasing in the order of U, T, and 5FU to the increasing height of the barrier in the 1 ππ* state separating the minimum and CI, on the basis of potential energy calculations using the time-dependent density functional theory (TDDFT) with inclusion of solvent effects by the polarizable continuum model (PCM). Solvent effects on the photophysical behavior in the 1ππ* and 1nπ* states of U and 5FU in the early stage of the deactivation process have been intensively studied by means of potential energy calculations as well as quantum dynamics simulations.55,56,61,64,65 Despite much theoretical effort, however, the substituent effects on the excited-state lifetime of uracil derivatives are not fully understood. First, it is still unclear whether the lifetime difference among U, T, and 5FU is completely due to an intrinsic

2. COMPUTATIONAL METHODS Ab initio calculations of U, T, and 5FU were performed with the MOLPRO 2008.1 program package,69 employing the Sapporo-DZP 492

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(double-ζ plus polarization) basis set.70 The ground-state equilibrium geometries were determined with the MøllerPlesset second-order perturbation (MP2) method. Geometry optimization in the excited state was performed with the MS-CASPT2 method, using an analytic energy gradient.71 In the MS-CASPT2 calculation, a level shift with the parameter 0.3 was applied to avoid intruder state problems.72 The 1s orbitals of C, nitrogen (N), oxygen (O), and F atoms (eight orbitals for U and nine orbitals for T and 5FU) were frozen in the calculation of perturbation energies. No symmetry constraint was imposed in the geometry optimization. For the MS-CASPT2 energy calculation of the ground- and excited-state minima and excited-state reaction paths, the CASSCF reference wave function was constructed using the (12,9) active space, where 12 electrons are distributed in nine orbitals. The nine active orbitals consist of eight π orbitals and one lone-pair orbital of the O atom on the 8 position (O8 atom, see Figure 1 for the atom labeling). The lone-pair orbital on the O7 atom was not included in the active space because the 1nπ* state for the excitation from this orbital exhibits quite high energy. The lowest five singlet states, including S0, two 1ππ*, and two 1nπ* states, were averaged with equal weights in the reference CASSCF calculations and then mixed in the MS-CASPT2 calculations using the effectiveHamiltonian approach. The computational method for the energy calculation is referred to as MS-CASPT2(12,9). Electronic energies at each geometry were also calculated with the CASSCF and SS-CASPT2 methods using the same active space, which is a prerequisite for the MS-CASPT2 calculation. For the geometry optimization in the excited state at the MSCASPT2 level, smaller active spaces were used to reduce the computational cost. In the MS-CASPT2 optimization of the 1 ππ* minimum, the CASSCF reference wave function was calculated by using the (10,8) active space with 10 electrons in eight π orbitals and averaging the lowest two singlet states (the S0 and 1ππ* states) with equal weights. The lone-pair orbitals on the O atoms were excluded from the active space in order to focus on the 1ππ* state during the optimization. In the optimization of the 1 nπ* minimum, the reference CASSCF calculation was carried out with the (8,7) active space, which consists of six π orbitals and one lone-pair orbital of the O8 atom, averaging the S0 and 1nπ* states. Two π orbitals were removed from the active space because the energy of the 1nπ* state is little affected by the inclusion of these orbitals. The lowest two electronic states were mixed in each MS-CASPT2 optimization. The computational method for the optimization of the 1ππ* and 1nπ* minima is denoted as MSCASPT2(10,8) and MS-CASPT2(8,7), respectively. To assess the effect of dynamic electron correlation on the excited-state geometry optimization, the minimum structures of the 1ππ* and 1nπ* states were also optimized with the CASSCF method. The same active spaces as used for the MS-CASPT2 optimizations were applied, and the lowest three and two states were averaged for the optimization of the 1ππ* and 1nπ* minima, respectively. The inclusion of the third state in the 1ππ* optimization is to avoid mixing of the lone-pair orbital on the O8 atom into the (10,8) active space. The reaction path connecting the minimum of the 1ππ* state and the CI between the 1ππ* and S0 states (1ππ*S0 CI) was also determined by geometry optimization at the MS-CASPT2 level. In the calculation of the CASSCF reference wave function, the (2,2) active space was employed, and all three singlet electronic states generated by this active space were averaged. The three states were mixed in the subsequent MS-CASPT2

Figure 2. Ground-state equilibrium geometries of (a) U, (b) T, and (c) 5FU, optimized at the MP2 level. Bond lengths are given in angstroms.

calculation. As the two active orbitals, the π and π* orbitals, which mainly cover the C5dC6 double bond, were selected. This selection is justified because the 1 ππ* state along the reaction path is well characterized by the excitation between these two orbitals. This computational method is referred to as MS-CASPT2(2,2). The driving coordinate representing the outof-plane deformation of the C5dC6 double bond was selected as the dihedral angle ϕ = δ(N1C6C5R), where R is the H atom, C atom of the CH3 group, and F atom on the C5 position for U, T, and 5FU, respectively (see Figure 1). The value of ϕ was fixed along the reaction path, while the other internal coordinates were optimized for the 1ππ* state at the MSCASPT2(2,2) level. Some other reaction paths, such as a path between the 1ππ* and 1nπ* minima, were also constructed using the linearly interpolated internal coordinate (LIIC). Potential energies along the reaction paths were recalculated with the MS-CASPT2(12,9) method.

3. RESULTS AND DISCUSSION 3.1. Vertical Excitation Energies. The ground-state equilibrium geometries of U, T, and 5FU determined at the MP2 level are shown in Figure 2. The Cartesian coordinates of these structures are given in the Supporting Information. For all the three bases, the optimized structures belong to the Cs point group. All atoms of each base lie in the plane of the six-membered ring, except for two H atoms of the CH3 group in T, which are placed symmetrically out of the plane. The in-plane CH bond of the CH3 group is directed to the C6H bond rather than to the C4dO8 bond. Table 1 shows the vertical excitation energies of the lowest three singlet excited states calculated with the MS-CASPT2(12,9) method. The lowest 1ππ* (21A0 ) state of U, T, and 5FU exhibits excitation energies in UV range: 4.92, 4.83, and 4.87 eV, 493



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respectively. The lowest 1nπ* (11A00 ) state of the three bases exhibits similar energy to the lowest 1ππ* state, while the energies of the second 1ππ* (31A0 ) state are higher by more than 1 eV. These results indicate that the lowest 1ππ* and 1nπ* states are the most likely to be involved in the photophysical process of U, T, and 5FU upon UV radiation. For U and T, the 1ππ* excitation energies calculated in the present study can be compared with experimental electronic spectra in the gas phase73,74 as well as with previous theoretical values at the SS- and MS-CASPT2 levels.18,19,24,32,58,75 In some other CASPT2 studies of U and T, the 1ππ* energies are higher than the present results by more than 0.5 eV.21,33,38,56 This overestimation may be because of the IPEA (ionization potentialelectron affinity) shift applied in the CASPT2 calculation. The SS-CASPT2 energies of U and T calculated by Lorentzon et al.76 are also in agreement with the present results for the 1ππ* states, while about 0.4 eV lower for the 1nπ* state. For 5FU, previous MS-CASPT2 calculations exhibited the 1ππ* energies higher than the present results by about 0.3 eV presumably because of the IPEA shift.59 For the three bases, the present MS-CASPT2 energies in the gas phase agree with the vertical excitation energies calculated at the TDDFT level, where the latter energies tend to be higher than the former energies by a few tenths of electronvolts for the 1ππ* states.41,77 Coupled-cluster methods such as CC2 (approximate second-order coupled-cluster singlesand-doubles) and EOM-CCSD as well as the multireference configuration interaction (MRCI) method yield 1ππ* excitation energies higher than the present results by about 0.3 eV or more,14,18,21,38,54,58,75,78,79 as expected for these methods. For T, the present calculation shows that the 1ππ* state is a little lower in energy than the 1nπ* state, while the reversed order was predicted in some previous theoretical studies.21,24,33,41,7578 This result suggests that the present MS-CASPT2 calculation tends to underestimate the energy of the 1ππ* state (note that some previous CASPT2 calculations18,19,32 also exhibited the

same order as this work). However, this energy order little affects the present discussion because the difference between the 1ππ* and 1nπ* energies is very small. In particular, the contribution of the 1nπ* state to the photophysics of T is not ruled out by the present results. 3.2. Decay Path from the 1ππ* Minimum. In this section, potential energy profiles in the lowest 1ππ* state of U, T, and 5FU are studied with respect to the nonradiative decay process to the S0 state. In particular, we compare the barrier height on the deactivation path from the 1ππ* minimum to the 1ππ*S0 CI, which should be an essential factor in determining the lifetime of the 1ππ* state of the uracil compounds. Figure 3 shows the minimum-energy structures of the 1ππ* state of U, T, and 5FU optimized with the MS-CASPT2(10,8) method. The Cartesian coordinates of these minima are given in the Supporting Information. For all molecules, the MS-CASPT2 optimization predicts a boat-like conformation of the six-membered ring80 where the N3 and C6 atoms exhibit a substantial out-of-plane distortion with respect to the other atoms of the ring. This boat-like deformation at the 1ππ* minimum was also reported in previous TDDFT/PCM studies for uracil derivatives in polar solution.41,55,61 The 1ππ* excitation at the MS-CASPT2optimized structure is characterized by the transition from π to π* orbital on the C5dC6 double bond, labeled as π(CdC) and π*(CdC), respectively. Owing to this excitation, the C5dC6 bond at the 1ππ* minimum of U, T, and 5FU is longer by 0.095, 0.067, and 0.052 Å, respectively, than at the S0 minimum of each base (see also Figure 2). For T, the 1ππ* minimum structure also exhibits a rotation of the CH3 group by about 60 degrees from the S0 minimum. The 1ππ* minimum lies in the S1 state for all the three molecules. Adiabatic excitation energies for the 1 ππ* state of U, T, and 5FU are calculated to be 4.53, 4.45, and 4.33 eV, Table 2. MS-CASPT2(12,9) Energies (in eV) of 1ππ* and 1nπ* Minima, 1ππ* Transition State (TS), and 1ππ*S0 Conical Intersection (CI) of U, T, and 5FU Relative to S0 Minimum Energy

Table 1. MS-CASPT2(12,9) Vertical Excitation Energies (in eV) of Low-Lying Singlet Excited States of U, T, and 5FU at S0 Minimum

structure

U

T

5FU

1

ππ* minimum

4.53

4.45

4.33

4.87

1

nπ* minimum

4.15

4.23

4.15

6.17

6.24

1

ππ* TS

4.54

4.46

4.50

4.90

4.88

1

ππ*S0 CI

4.00

3.90

3.98

state

U

T

5FU

ππ* (21A0 )

4.92

4.83

ππ* (31A0 )

6.11

nπ* (11A00 )

4.85

1 1 1

Figure 3. Geometries of 1ππ* minimum optimized at the MS-CASPT2(10,8) level: (a) U, (b) T, and (c) 5FU. Bond lengths are given in angstroms. 494



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Figure 4. MS-CASPT2(12,9) potential energy profiles of low-lying electronic states of (a) U, (b) T, and (c) 5FU along the out-of-plane deformation coordinate ϕ = δ(N1C6C5R). Electronic energy of S1 state is shown as solid curve, while energies of other electronic states are shown as dashed curves. Vertical dashed line indicates the threshold value ϕ0, which is 115°, 110°, and 100° for U, T, 5FU, respectively. When ϕ e ϕ0, geometry at each value of ϕ is determined by optimization of other internal coordinates for the lowest 1ππ* state with the MS-CASPT2(2,2) method. When ϕ > ϕ0, geometry at each point is prepared by varying only ϕ and δ(C4C5C6H) from the optimized structure at ϕ = ϕ0. Potential energy is relative to the energy of ground-state equilibrium geometry of each base.

respectively, as shown in Table 2. The energy of the 1nπ* state at this minimum is higher by about 0.5 eV than the 1ππ* state. For U and T, the calculated adiabatic excitation energies are in good agreement with the peak position in the resonantly enhanced two-photon ionization (REMPI) spectrum detected by Brady et al.81 (4.58 and 4.52 eV, respectively). It is noteworthy that the present theoretical values for the 1ππ* state reproduce well the red shift of the REMPI spectrum from U to T. Figure 4 shows the MS-CASPT2(12,9) potential energy curves along the nonradiative decay path from the 1ππ* minimum to the 1ππ*S0 CI as a function of the dihedral angle ϕ = δ(N1C6C5R). This dihedral angle represents out-of-plane deformation of the C5dC6 double bond due to the distortion of the C5R bond and is defined as negative values in the figure. The solid curve represents the potential energy of the lowest 1 ππ* state, while dashed curves show the energies of other electronic states. For each point, geometry optimization for the lowest 1 ππ* state was performed at the MS-CASPT2(2,2) level with the value of ϕ fixed. The optimization with the (2,2) active space qualitatively reproduces the molecular structure optimized with the (10,8) active space, especially the boat-like structure of the sixmembered ring (see Figure 3). Electronic character of the excited state, i.e., π(CdC) f π*(CdC) excitation, is also reproduced using the (2,2) active space. If the optimization converged, the MS-CASPT2(12,9) energies of the lowest five electronic states were calculated at the resulting geometry. However, the MSCASPT2(2,2) optimization could not converge when the absolute value of ϕ is too small because the molecule encountered a CI with the S0 state by large out-of-plane distortion of the C5R bond as well as of the C6H bond. To avoid this problem, the MS-CASPT2(12,9) energies for the value of ϕ larger than a threshold ϕ0 were calculated at the geometry prepared as follows: starting with the optimized geometry at ϕ = ϕ0, the dihedral angles δ(N1C6C5R) (= ϕ) and δ(C4C5C6H) were varied by ϕ ϕ0 with all other internal coordinates kept to the values at ϕ = ϕ0. The value of ϕ0 was selected as 115°, 110°, and 100°

for U, T, and 5FU, respectively, and is indicated as the vertical dashed line in Figure 4. The MS-CASPT2-optimized potential energy curves in Figure 4 suggest that the uracil derivatives in the lowest 1ππ* state can reach the 1ππ*S0 CI passing through a single barrier from the respective minimum. The barrier for the out-of-plane deformation of the C5R group is thus confirmed to be a crucial factor determining the lifetime of the 1ππ* state. The lowest 1ππ* state is always the S1 state along the deactivation path from the 1ππ* minimum (around ϕ = 180°) to the 1ππ*S0 CI (around ϕ = 80°). It is worth noting that no crossing between the lowest 1 ππ* and 1nπ* states is observed along the path. The potential energy of the S1 state monotonically decreases from the barrier to the 1ππ*S0 CI without exhibiting any additional barrier. The MS-CASPT2 energy of the 1ππ*S0 CI (average of the 1ππ* and S0 energies) in Figure 4 is substantially lower than the vertical excitation energy of the 1ππ* state at the S0 minimum (see Tables 1 and 2), ensuring that the CI is energetically accessible after UV absorption. For more accurate comparison of the barrier height among the three molecules, structure of a transition state (TS) separating the minimum and CI was determined with geometry optimization at the MS-CASPT2(10,8) level. Starting with the geometry of the highest energy point on the 1ππ* potential energy curve in Figure 4 (ϕ = 135° for U and T and 110° for 5FU), the value of ϕ was fixed, and the other internal coordinates were optimized for the 1ππ* state. Although unconstrained geometry optimization of the saddle point (especially, calculation of Hessian) could not be completed due to a huge computational cost, the structure obtained by the above procedure can be regarded as an approximate geometry of TS. As a result of the constrained geometry optimization, the MSCASPT2(12,9) energy of the 1ππ* TS is calculated to be higher than the S0 minimum energy by 4.54, 4.46, and 4.50 eV for U, T, and 5FU, respectively; see Table 2. The barrier height in the 1ππ* state of U and T, estimated by the relative energy of the TS to the minimum in Figure 3, is less than 0.02 eV. This result suggests 495



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Figure 5. Geometries of TS in 1ππ* state of (a) U, (b) T, and (c) 5FU and CI between 1ππ* and S0 states of (d) U, (e) T, and (f) 5FU determined by MS-CASPT2 calculations. Bond lengths are given in angstroms.

that the deactivation pathways in the 1ππ* state of these bases are almost barrierless and, more importantly, that the 1ππ* decay path exhibits no evidence for the different excited-state lifetimes of U and T. The deactivation pathway of 5FU exhibits a substantial energy barrier with the height of 0.17 eV. The higher barrier suggests that 5FU is likely to exhibit longer lifetime of the 1ππ* state than U and T. These results are also consistent with recent theoretical studies of U and 5FU in the gas phase.54,59 Figure 5 shows the optimized geometries of the 1ππ* TS as well as the geometries of the 1ππ*S0 CI (see the Supporting Information for the Cartesian coordinates). The TS and CI still exhibit the boat-like structure of the six-membered ring as shown in the 1ππ* minimum (see Figure 3). The CI geometries are approximated by the structure with the smallest energy gap between the 1ππ* and S0 states on the deactivation path in Figure 4, where the value of ϕ is 80°, 85°, and 80° for U, T, and 5FU, respectively. The energy gap between the 1ππ* and S0 states at the CI structures is about 0.2 eV. The excited state at and near the CI exhibits a biradical character, which is a typical observation for 1 ππ*S0 CIs of the nucleic acid bases. The dominant configuration of the biradical state is characterized by the excitation from the p orbital on the C5 atom to the p orbital on the C6 atom.

Because of this localized excitation, the determination of the CI structure based on the optimization with the (2,2) active space is expected to qualitatively reproduce the result of optimization with larger active space. The most important finding in this section is that U and T exhibit no significant difference of barrier height on the 1ππ* deactivation path in the gas phase, while 5FU shows a substantially higher barrier than the other two molecules. Note that the former and latter points have been simultaneously exhibited for the first time in the present work. The latter result is supported by the experimental observation that 5FU exhibits the longest excited-state lifetime of the three bases in polar solution. The intrinsic electronic effect induced by the fluorine substitution on the C5 position is likely to have significant contribution to the higher barrier of 5FU than U and T. However, the very similar barriers of U and T imply that the intrinsic electronic effect induced by the methyl substitution is very weak. In the case of polar solution, the experimentally observed longer excited-state lifetime of T than U may be because of solvation effects such as solutesolvent electrostatic interaction and solvent friction. Previous TDDFT/PCM calculations for the 1ππ* state exhibited that the barrier of T is higher than that of U in aqueous solution,41 496



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Figure 7. Potential energy curves of low-lying electronic states of U along LIIC path connecting MS-CASPT2- and CASSCF-optimized structures of 1ππ* minimum, calculated at the (a) CASSCF(12,9) (solid curves) and (b) SS- and MS-CASPT2(12,9) (dashed and solid curves, respectively) levels. Square and diamond indicate the energy of the lowest 1ππ* state calculated at the MS-CASPT2- and CASSCFoptimized minima, respectively. Potential energy is relative to the energy of ground-state equilibrium geometry at each computational level.

Figure 6. Molecular orbitals involved in 1ππ* excitation of U at the corresponding minimum optimized with the (a) MS-CASPT2 and (b) CASSCF methods. The orbitals at each geometry are natural orbitals calculated with the CASSCF(10,8) method, where the lowest two electronic states are averaged with equal weights.

minimum is longer by only a few hundredths of angstroms than that of the S0 minimum; see Figure 3. For the MS-CASPT2optimized minimum, the excitation from the π(CdO) orbital is unlikely to contribute to the 1ππ* transition. The CASSCF geometry optimization of the 1ππ* minimum also predicts considerably different bond lengths and less extent of out-of-plane deformation of the six-membered ring compared with the MSCASPT2-optimized structures presumably because of the different character of the 1ππ* state. For a more detailed understanding of the effect of dynamic electron correlation on the excited-state geometry optimization, potential energy curves along the LIIC path connecting the MSCASPT2- and CASSCF-optimized structures of the 1ππ* minimum were calculated. Figure 7 shows the resulting curves of U, calculated at the CASSCF and SS- and MS-CASPT2 levels using the (12,9) active space (potential energy curves of T and 5FU are shown in the Supporting Information). For the 1ππ* states, the CASSCF and CASPT2 potential energy profiles (Figure 7a and b, respectively) are quite different from each other. The CASSCF energy curves exhibit an avoided crossing between the two 1ππ* (S2 and S3) states characterized by the excitation from the π(CdC) and π(CdO) orbitals to the π*(CdC) orbital. On the LIIC path in the lower 1ππ* state, the CASSCF-optimized structure shows a minimum of the π(CdO) f π*(CdC) state (diamond in Figure 7a), whose energy is much lower than the energy of the π(CdC) f π*(CdC) state at the same structure. However, the MS-CASPT2-optimized structure shows a shoulder in the lower 1ππ* state (square in Figure 7a), where the excitation is dominated by the π(CdC) f π*(CdC) transition. The 1ππ* energy at the shoulder is much higher than at the minimum (by 0.66 eV for U). In the MS-CASPT2 potential energy curves (solid lines in Figure 7b), the 1ππ* states are considerably stabilized by dynamic electron correlation, while the 1 nπ* states are less affected. In particular, the energy lowering of the π(CdC) f π*(CdC) state is significantly larger than that of the π(CdO) f π*(CdC) state. As a result, the energy of the

which is consistent with the longer lifetime of T. As another possibility, dynamical effects due to the heavier mass of the CH3 group of T than the H atom of U on the C5 position may be a reason for the different lifetimes of these bases. This conjecture is supported by the fact that the out-of-plane distortion of the C5R group is an essential motion in the deactivation of the 1 ππ* state. 3.3. Effect of Dynamic Electron Correlation. Before showing the results about the decay from the 1nπ* minimum, let us discuss the validity of the present MS-CASPT2 calculations for the 1ππ* state in section 3.2. As an important result of the present work, it should be emphasized that the MS-CASPT2-optimized geometries of the 1ππ* minimum are quite different from CASSCFoptimized geometries. This finding suggests that the neglect of dynamic electron correlation effects may lead to a serious error in geometry optimization of the 1ππ* state. The CASSCFoptimized structures and their Cartesian coordinates are shown in the Supporting Information. These geometries exhibit the C4dO8 double bond longer by about 0.1 Å than the MP2optimized geometries of the S 0 minimum: 1.329, 1.314, and 1.322 Å for U, T, and 5FU, respectively. The substantial bond elongation is attributed to the fact that the 1ππ* excitation at these minima is significantly contributed by the transition from the π orbital on the C4dO8 bond, referred to as the π(CdO) orbital, to the π*(CdC) orbital on the C5dC6 bond. Figure 6 shows the π and π* orbitals of U at the MS-CASPT2- and CASSCF-optimized minimum structures (orbitals of T and 5FU are shown in the Supporting Information). The π(CdO) f π*(CdC) excited state (also called as 1πOπ* state) at the CASSCF-optimized minimum was also reported in previous theoretical studies of U and T.33,38 When the MS-CASPT2 method is used for the geometry optimization, however, the C4dO8 bond at the 1ππ* 497



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Figure 8. Geometries of 1nπ* minimum optimized at the MS-CASPT2(8,7) level: (a) U, (b) T, and (c) 5FU. Bond lengths are given in angstroms.

former state at the MS-CASPT2-optimized structure (square in Figure 7b) is lower than the energy of the latter state at the CASSCF-optimized structure (diamond in Figure 7b). In the case of U, the energy difference is estimated to be 0.27 eV. This finding also suggests that adiabatic excitation energy of the 1 ππ* state is considerably overestimated when the minimumenergy geometry is determined at the CASSCF level, even if the SS- or MS-CASPT2 method is applied for the single-point energy calculation at the CASSCF-optimized structure. Such overestimation was also reported in previous theoretical studies of uracil derivatives.18,32,33,38 At the CASSCF-optimized structure of U, the MS-CASPT2 energy curve exhibits a shoulder in the S2 state; see Figure 7b. An avoided crossing between the lowest 1ππ* and 1nπ* states is also observed. For T and 5FU, the 1ππ* and 1nπ* states are considerably mixed at the CASSCF-optimized geometry. In the SS-CASPT2 potential energy curves (dashed lines in Figure 7b), the two 1ππ* states exhibit almost the same energies in the intermediate region between the MS-CASPT2- and CASSCF-optimized minima. However, this degeneracy is likely to be an artificial one, which is the result of the lack of the coupling between electronic states, because the two 1ππ* curves are largely separated at the MS-CASPT2 level.67 For the 1nπ* states, the SS- and MS-CASPT2 curves are very similar to each other. The qualitative differences between the CASPT2 and CASSCF potential energy curves in Figure 7 strongly indicate that the inclusion of dynamic correlation is critical for determining the minimum-energy geometry in the 1ππ* state of uracil derivatives. This conclusion has also been pointed out in recent CC2 calculations of T18 as well as of xanthine,82 another analogue of uracil, which has the same structure of six-membered ring. The MS-CASPT2 geometry optimization of the 1ππ* minimum was performed also in recent theoretical studies on U and T24 as well as on 5FU.59 However, the resulting structures are located in the S2 state rather than the S1 state, and more similar to the CASSCF-optimized geometries than the MS-CASPT2-optimized geometries in the present work. In particular, the previous studies reported the C4dO8 bond length of more than 1.3 Å, suggesting a considerable contribution from the π(CdO) f π*(CdC) excitation. This discrepancy may be attributed to a different amount of dynamic electron correlation taken into account by the present and previous MS-CASPT2 methods, which are different from one another in details. To support this

conclusion, we calculated potential energy curves of U, T, and 5FU corresponding to Figure 7b with the MS-CASPT2 method using the larger number of frozen orbitals, which leads to less electron correlation. The resulting curves (shown in the Supporting Information) exhibit the 1ππ* minimum for the CASSCFoptimized structure, which corresponds to the previous MSCASPT2-optimized geometry,24,59 as well as the 1ππ* minimum for the present MS-CASPT2-optimized structure. This finding suggests that the disappearance of the CASSCF-optimized minimum in the present work is a result of further inclusion of dynamic electron correlation compared to the previous MS-CASPT2 calculations. The less amount of electron correlation in the previous studies may be assigned to smaller active space for the reference CASSCF wave function or the inclusion of the IPEA shift. For the latter, the IPEA shift tends to overestimate the energy of the 1ππ* state of uracil derivatives, as mentioned in section 3.1. The doubleminimum feature of the potential energy curves also suggests that the presently calculated 1ππ* minimum in the S1 state might be found also in the previous MS-CASPT2 studies. Note that the previous studies focused on the potential energy surface in the S2 state. The potential energy profiles of the deactivation path in Figure 4 based on the MS-CASPT2 geometry optimization are quite different from the previously calculated ones based on the CASSCF geometry optimization, which exhibit the 1ππ* minimum in the S2 state and a 1ππ*1nπ* crossing on the path between the minimum and the 1ππ*S0 CI.32,33,38 In addition, even for single-point energy calculations along the deactivation path in Figure 4, the MS-CASPT2 method gives qualitatively different results from the CASSCF and SS-CASPT2 methods. The potential energy curves calculated with the latter methods are shown in the Supporting Information. At the CASSCF level, the 1 nπ* state is the S1 state around ϕ = 180° and switched to the S2 state via an avoided crossing with the 1ππ* state when the molecular structure is deformed. The SS-CASPT2 curves also exhibit a crossing between the lowest 1ππ* and 1nπ* states, but it is an unphysical one due to the lack of coupling between electronic states.67 As shown in Figure 4, the 1ππ* and 1nπ* potential energy curves are largely separated when the electronic energies are calculated at the MS-CASPT2 level. Thus, it is critical to use the MS-CASPT2 method rather than the CASSCF or SS-CASPT2 method also for a reliable calculation of potential energy curves along the decay pathways of uracil derivatives. 498



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Figure 9. MS-CASPT2(12,9) potential energy profiles of low-lying electronic states along LIIC path connecting 1ππ* and 1nπ* minima of (a) U, (b) T, and (c) 5FU. Electronic energy of S1 state is shown as solid curve, while energies of other electronic states are shown as dashed curves. Potential energy is relative to the energy of ground-state equilibrium geometry of each base.

The CI structure determined by the MS-CASPT2 calculation shown in Figure 5df is also considerably different from the CI structure optimized at the CASSCF level. The latter structure of each base is shown in the Supporting Information, whose optimization was performed using the (10,8) active space with averaging the lowest two singlet states. The CASSCF-optimized CIs exhibit an envelope-like structure of the six-membered ring where the C5 atom is distorted from the molecular plane. They also show larger out-of-plane deformation of the C5R bond compared with the CIs in Figure 5df. 3.4. Decay Path from the 1nπ* Minimum. In this section, the nonradiative decay path starting at the minimum of the lowest 1 nπ* state is compared for the three uracil derivatives for the first time. The minimum-energy structures of the 1nπ* state determined at the MS-CASPT2(8,7) level are shown in Figure 8. The optimized structures are nearly planar, with the exception of a slight pyramidalization at the N3 atom in the three bases as well as rotation of the CH3 group in T by about 30 degrees from the S0 minimum. In the case of the 1nπ* state, geometry optimization at the CASSCF level gives very similar minimum structures as the MS-CASPT2 optimization (see the Supporting Information). The 1nπ* excitation corresponds to the transition from the lonepair orbital on the O8 atom to the π*(CdC) orbital on the C5dC6 bond. For the minimum of each base, this excitation makes the C4dO8 bond longer by more than 0.1 Å than the S0 minimum. Elongation of the C5dC6 bond and shortening of the C4C5 bond are also observed, reflecting the increase of the antibonding and bonding characters for the former and latter bonds, respectively, by the excitation to the π*(CdC) orbital (see Figure 6). Figure 9 shows the MS-CASPT2(12,9) potential energy curves along the LIIC path connecting the 1ππ* and 1nπ* minima whose structures are shown in Figures 3 and 8, respectively. One can see that both minima are located on the potential energy curve of the S1 state (solid line). For the 1nπ* minima, adiabatic excitation energies of U, T, and 5FU are calculated to be 4.15, 4.23, and 4.15 eV, respectively (see also Table 2). For U and T, these values are slightly lower than the onset of the REMPI spectrum (4.54 and 4.50 eV, respectively).81

On the LIIC path in Figure 9, the two minima in the S1 state are separated by a small energy barrier resulting from a crossing between the 1ππ* and 1nπ* states. For U, T, and 5FU, the barrier from the 1ππ* minimum (from the 1nπ* minimum) is estimated to be 0.03, 0.08, and 0.12 eV (0.32, 0.18, and 0.30 eV), respectively. This small barrier suggests that both the 1ππ* and 1 nπ* states can be populated in an early stage of the excited-state processes via the transition between the two S1 minima and thus that nonradiative deactivation from the 1nπ* minimum as well as from the 1ππ* minimum is likely to considerably contribute to the photophysical process of the three bases. The significant population of the 1nπ* state as well as of the 1ππ* state in U, T, and 5FU has also been predicted by recent quantum dynamics calculations based on the potential energy surfaces at the TDDFT level.65,83 The 1ππ*1nπ* crossing in Figure 9 is expected to be a CI when other internal coordinates of the molecule are taken into account. The 1ππ* and 1nπ* states are expected to be strongly coupled with each other via this 1ππ*1nπ* crossing, which may support the broad and structureless band in the REMPI spectra of U and T.81 For the nonradiative decay from the 1nπ* minimum, one can assume a reaction path leading to the 1ππ*S0 CI, which involves the transition from the 1nπ* to 1ππ* state. This mechanism was also proposed in some recent studies.21,52,56 Figure 10 shows the potential energy curves of U, T, and 5FU along the LIIC path connecting the 1nπ* minimum and 1ππ*S0 CI. The solid line shows the potential energy curve of the S1 state, while dashed lines show the energies of other electronic states. For all the three bases, the potential energy curves along the LIIC path exhibit a crossing between the lowest 1nπ* and 1ππ* states. This crossing shows an energy barrier separating the 1nπ* minimum from 1ππ*S0 CI with the height of 0.56, 0.52, and 0.72 eV for U, T, and 5FU, respectively, at the MS-CASPT2(12,9) level. However, the barrier height may be significantly overestimated because the geometry of TS on this pathway is not optimized. As another deactivation route from the 1nπ* minimum to the 1 ππ*S0 CI, which is energetically more likely than calculated in Figure 10, a two-step pathway through the minimum of the 1ππ* state can be considered. The first step is the transition from the 499



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Figure 10. MS-CASPT2(12,9) potential energy profiles of low-lying electronic states along LIIC path connecting 1nπ* minimum and 1ππ*S0 CI of (a) U, (b) T, and (c) 5FU. Electronic energy of S1 state is shown as a solid curve, while energies of other electronic states are shown as dashed curves. Potential energy is relative to the energy of ground-state equilibrium geometry of each base.

nπ* to 1ππ* minimum along the S1 potential energy curve in Figure 9, while the second step is the decay from the 1ππ* minimum to the 1ππ*S0 CI along the S1 potential energy curve in Figure 4. At the MS-CASPT2(12,9) level, the barrier for the first step (the highest energy point in the S1 curve connecting the 1ππ* and 1nπ* minima in Figure 9) lies in lower energy than the barrier for the second step (the 1ππ* TS whose geometry is shown in Figure 5). Therefore, the barrier height on this two-step pathway can be estimated as the energy difference between the 1nπ* minimum in Figure 8 and the 1ππ* TS in Figure 5ac. The energies of these structures are given in Table 2. The calculated value of the barrier height at the MS-CASPT2 level is 0.39, 0.23, and 0.35 eV for U, T, and 5FU, respectively, which is considerably smaller than the barrier height estimated from Figure 10. For uracil derivatives in the gas phase, the present results suggest that the deactivation from the 1nπ* minimum is likely to occur as well as from the 1ππ* minimum because the energy of the barrier along the decay path is much lower than the vertical excitation energy of the 1ππ* state at the equilibrium geometry of the S0 state. The deactivation from two minima in the S1 state is consistent with experimentally studied time-resolved spectroscopy of isolated uracil derivatives, which often exhibits the biexponential decay of the excited-state signal.46,47 In the case of polar solution, the deactivation from the 1ππ* state is expected to be more dominant because this state should be more stabilized than the 1nπ* state by the electrostatic interaction with the solvent. Such stabilization of the 1ππ* state has been pointed out in recent theoretical studies of uracil derivatives.41,56,8486 It is interesting that the calculated potential energy profiles from the 1nπ* minimum exhibit no evidence of the longer lifetime of T than that of U. For the deactivation from the 1nπ* minimum to the 1ππ*S0 CI through the 1ππ* TS, T exhibits a lower barrier than U as well as than 5FU; see Table 2. However, the time-resolved electronic spectra of U and T, which are assigned to the decay of the 1nπ* state, exhibit a longer lifetime of T than that of U in the gas phase47 as well as in solution.39 This discrepancy implies that the lifetime of the 1nπ* state may be determined by other factors, which were not considered in the present calculations. First, the mass of the substituent on the C5 1

position may affect the lifetime of the 1nπ* state as well as that of the 1ππ* state. Second, there may be a more efficient decay path connecting the 1nπ* minimum and 1ππ*S0 CI without passing through the 1ππ* minimum or TS. Finally, but not least, intersystem crossing to a triplet state may play a significant role in the deactivation of the 1nπ* state. In experiments of methylated compounds of U and T, the existence of a dark electronic state with a lifetime of tens to hundreds of nanoseconds was reported.8790 This dark state can be assigned to a triplet state populated by the intersystem crossing with the 1nπ* state. Recent theoretical studies have discussed the possibility of the transition from the 1 nπ* to 3ππ* state in U and T.9193 Interestingly, the rate constant for the 1nπ*-to-3ππ* intersystem crossing has been calculated to be larger for U than for T,92 which may lead to shorter 1nπ* lifetime of U.

4. CONCLUSIONS A comparative theoretical study of the nonradiative decay mechanisms of U, T, and 5FU has been performed by means of MS-CASPT2 calculations of the potential energy profiles in lowlying excited states. In particular, the MS-CASPT2 method has been employed even for the geometry optimization in the excited state, aiming to accurately determine minimum-energy structures and reaction paths relevant to the deactivation process. Two decay mechanisms of uracil derivatives leading to the CI between the 1ππ* and S0 states have been exhibited in the present MS-CASPT2 calculation. One mechanism is the deactivation from the 1ππ* minimum. The other is the deactivation from the 1 nπ* minimum, which involves the transition to the 1ππ* state. For each base, the minima of the 1ππ* and 1nπ* states are located on the potential energy surface of the S1 state and separated by a small energy barrier. The double-minimum feature suggests that both the 1ππ* and 1nπ* minima can be populated after UV absorption. The 1ππ*S0 CI is shown to be energetically accessible from the 1ππ* minimum as well as from the 1nπ* minimum via the reaction path through a TS in the 1ππ* state. It is therefore likely that both the excited states significantly contribute to the nonradiative decay via the 1ππ*S0 CI. 500


The Journal of Physical Chemistry A The most important suggestion having been made in the present work is that the different excited-state lifetimes of U and T may not be because of the difference in potential energy profiles, while the longer lifetime of 5FU can be attributed to it. With respect to the decay path in the 1ππ* state, this work is the first theoretical study that has exhibited the similarity between U and T and the difference between 5FU and the other two bases at the same time. The present work has also given the first comparison of the decay path from the 1nπ* minimum among the three uracil derivatives. For the deactivation from the 1ππ* minimum, our theoretical results support the longer lifetime of 5FU than those of U and T, which is experimentally observed in polar solution. The barrier on the 1ππ* deactivation path is considerably enhanced by the fluorine substitution on the C5 position, suggesting that the lifetime elongation of 5FU is significantly contributed from intrinsic electronic effects of the molecule. However, no computational evidence supporting the longer lifetime of the 1 ππ* state of T than that of U was found in the calculated potential energy curves. In the present calculation, the barrier in the 1 ππ* state is little affected by the methyl substitution. This result implies that the difference between the 1ππ* lifetimes of U and T in solution may be the result of solvent effect. The mass of the substituent on the C5 position or the transition to the 1nπ* state may also affect the 1ππ* lifetime. In addition, for the deactivation path from the 1nπ* minimum to the 1ππ*S0 CI, the order of the barrier height among the three bases is different from the experimentally observed order of the excited-state lifetime. The 1 nπ* lifetime of uracil derivatives may be determined by other factors that were not considered in the present study, such as the competition with intersystem crossing to a triplet state. Another point of this work is that the inclusion of dynamic electron correlation in electronic-structure calculations can be critical for a reliable theoretical prediction of the deactivation mechanisms in the nucleic acid bases. This conclusion is certainly true for the study of uracil derivatives, especially for the determination of nonradiative decay paths with geometry optimization in the excited state. In the present calculations, MS-CASPT2 and CASSCF optimizations have led to drastically different structures of the 1ππ* minimum. This discrepancy is attributed to the qualitative alteration of potential energy surfaces in the lowest two 1 ππ* states, whose dynamic correlation energies are quite different from each other. Such a considerable effect of dynamic correlation on the excited-state potential energy surface may be observed also in other nucleic acid bases because low-lying excited states of the bases are found in a small energy range. As mentioned in the Introduction, the excited-state lifetimes of cytosine derivatives are in the order of cytosine < 5-methylcytosine < 5-fluorocytosine, as are those of uracil derivatives U, T, and 5FU. In the previous theoretical study, the longer lifetime of 5-fluorocytosine than cytosine was accounted for by the difference of the barrier height on the excited-state potential energy surface.63 However, to the best of our knowledge, the longer lifetime of 5-methylcytosine than cytosine has not been supported by any computational studies. Rationalization of the effect of methyl substitution may provide further insights into the photophysical behavior of cytosine as well as of uracil. The role of polar solvation as well as of intersystem crossing to triplet states would be interesting for the full understanding of substituent effects on the photoinduced dynamics, especially for the rationalization of the lifetime difference between U and T. We would like to emphasize that in such studies the accuracy of the potential energy profiles should be verified very carefully,

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which would be essential for a qualitatively correct prediction of the deactivation mechanisms.

’ ASSOCIATED CONTENT

bS

Supporting Information. Cartesian coordinates of minima, transition states, and conical intersections and additional figures of optimized structures, molecular orbitals, and potential energy curves. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT This work has been supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT), Japan. S.Y. thanks the Japan Society for the Promotion of Science (JSPS) for the Research Fellowships for Young Scientists. We acknowledge substantial allocation of computing time by the Research Center for Computational Science (RCCS), Okazaki, Japan. We are also grateful to Professor Akira Nakayama for his careful reading of the manuscript. ’ REFERENCES (1) Crespo-Hernandez, C. E.; Cohen, B.; Hare, P. M.; Kohler, B. Chem. Rev. 2004, 104, 1977–2019. (2) Saigusa, H. J. Photochem. Photobiol., C 2006, 7, 197–210. (3) de Vries, M. S.; Hobza, P. Annu. Rev. Phys. Chem. 2007, 58, 585–612. (4) Radiation Induced Molecular Phenomena in Nucleic Acids: A Comprehensive Theoretical and Experimental Analysis; Shukla, M., Leszczynski, J., Eds.; Springer: Berlin, Germany, 2008. (5) Middleton, C. T.; de La Harpe, K.; Su, C.; Law, Y. K.; CrespoHernandez, C. E.; Kohler, B. Annu. Rev. Phys. Chem. 2009, 60, 217–239. (6) Barbatti, M.; Aquino, A. J. A.; Szymczak, J. J.; Nachtigallova, D.; Hobza, P.; Lischka, H. Proc. Natl. Acad. Sci. U.S.A. 2010, 107, 21453–21458. (7) Daniels, M.; Hauswirth, W. Science 1971, 171, 675–677. (8) Callis, P. R. Annu. Rev. Phys. Chem. 1983, 34, 329–357. (9) Conical Intersections: Electronic Structure, Dynamics and Spectroscopy; Domcke, W., Yarkony, D. R., K€oppel, H., Eds.; World Scientific: Singapore, 2004. (10) Sobolewski, A. L.; Domcke, W.; Dedonder-Lardeux, C.; Jouvet, C. Phys. Chem. Chem. Phys. 2002, 4, 1093–1100. (11) Sobolewski, A. L.; Domcke, W. Eur. Phys. J. D 2002, 20, 369–374. (12) Ismail, N.; Blancafort, L.; Olivucci, M.; Kohler, B.; Robb, M. A. J. Am. Chem. Soc. 2002, 124, 6818–6819. (13) Merchan, M.; Serrano-Andres, L. J. Am. Chem. Soc. 2003, 125, 8108–8109. (14) Matsika, S. J. Phys. Chem. A 2004, 108, 7584–7590. (15) Marian, C. M. J. Chem. Phys. 2005, 122, 104314. (16) Perun, S.; Sobolewski, A. L.; Domcke, W. J. Am. Chem. Soc. 2005, 127, 6257–6265. (17) Chen, H.; Li, S. J. Chem. Phys. 2006, 124, 154315. (18) Perun, S.; Sobolewski, A. L.; Domcke, W. J. Phys. Chem. A 2006, 110, 13238–13244. (19) Merchan, M.; Gonzalez-Luque, R.; Climent, T.; SerranoAndres, L.; Rodríguez, E.; Reguero, M.; Pelaez, D. J. Phys. Chem. B 2006, 110, 26471–26476. 501



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