Theoretical Study of Excess Electron Attachment Dynamics to the

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Theoretical Study of Excess Electron Attachment Dynamics to the Guanine−Cytosine Base Pair: Electronic Structure Calculations and Ring−Polymer Molecular Dynamics Simulations Yuji Sugioka, Takehiro Yoshikawa, and Toshiyuki Takayanagi* Department of Chemistry, Saitama University, 255 Shimo-Okubo, Sakura-ku, Saitama City, Saitama 338-8570, Japan S Supporting Information *

ABSTRACT: Electron attachment dynamics to the guanine (G)−cytosine (C) base pair has been studied from a theoretical viewpoint. The BH&HLYP-level calculations show that the dipole-bound planar (G−C)− base pair anion can convert into the nonplanar valence-bound anion with a relatively small barrier. This nonplanar valence-bound anion can further convert into a more stable form via proton-transfer through the N−H···N hydrogen-bond from the guanine to cytosine moiety. This excess electron induced proton-transfer process has been studied using quantized ring−polymer molecular dynamics simulations (RPMD) on an interpolated potential energy surface developed on the basis of the B3LYPlevel calculations. We compare the RPMD results to the results of classical MD simulations and found that proton-transfer more effectively occurs in quantum RPMD simulations. Both vibrational quantization and corner-cutting mechanism are playing important roles in this proton-transfer process. We have also analyzed the correlation between the proton-transfer motion and other vibrational motions including ring−ring deformation motions using the reactive RPMD trajectories.

1. INTRODUCTION The discovery of the DNA damaging ability of low-energy electrons (below subionization energy of ∼20 eV) by Sanche’s group definitely stimulated further experimental and theoretical studies for understanding of the damaging mechanisms at a molecular level.1,2 Recent such studies have clearly shown that low-energy electrons can lead to breaking of chemical bonds of many biomolecules including DNA/RNA base molecules, ribose, and amino acids through dissociative electron attachment processes via temporary negative ionic states, which can also be recognized as resonance states embedded in electron scattering continuum.3−6 However, the dissociation dynamics of transient anion molecules and subsequent chemical reaction dynamics have not yet been fully understood at a microscopic level. In this article, we report results of dynamics studies on the electron attachment process to the guanine−cytosine base pair from the theoretical side. Electron attachment processes to isolated DNA/RNA base molecules have extensively been studied from both experimental and theoretical viewpoints so far.2−11 Gas-phase electron affinities of nuclear acid−base fragments have been measured using several experimental methods including photoelectron spectroscopy and have been theoretically addressed using various electronic structure calculations. All base molecules, adenine (A), cytosine (C), guanine (G), thymine (T), and uracil (U) have negative vertical electron affinities at their equilibrium planar structures, indicating that © 2013 American Chemical Society

the neutral base molecule cannot bind an electron without nuclear relaxation although C, T, and U have a large dipole moment that can weakly bind an excess electron to form a socalled dipole-bound anion state with the binding energy being 60−100 meV.9,10 It is well understood that these base molecules can have positive electron affinities (0.4−1.5 eV) when the planar neutral structure once deforms into a nonplanar structure. This is simply because the antibonding π* orbital of the isolated base molecule is playing an essential role for resonantly capturing an excess electron. In addition, previous crossed electron-molecule beam experiments reveal that these base molecules exhibit low-energy resonances in the range of 0.5−4 eV associated with the loss of a neutral hydrogen atom due to breaking of a specific N−H or C−H bond.7,9,10 This also indicates that the π*-valence anionic state nonadiabatically correlates with the σ*-anionic state of the N− H or C−H bond at its longer distances.12,13 Since most genetic material occurs in double-stranded form, it should be highly important to understand the interaction between excess electrons and hydrogen-bonded nuclear acid− base pair systems. One of the most interesting points found in the base pair systems is that electron attachment to the base pair can induce interbase proton-transfer to form a further Received: July 8, 2013 Revised: September 13, 2013 Published: October 22, 2013 11403

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Figure 1. Schematic picture of the potential energy surface for the excess electron attachment process to the (G−C) base pair. Energy values are taken from Figures 2 and 3 (see below). Also shown are singly occupied molecular orbitals (SOMOs) for the dipole-bound and valence-bound (G− C)− base pair anion.

process. In fact, as shown in Figure 1, zero-point harmonic vibrational energy correction significantly reduces the protontransfer barrier due to quantized vibrational modes. In order to understand the role of nuclear quantum effects in this reaction, we here perform ring−polymer molecular dynamics (RPMD) simulations23−26 on the full-dimensional potential energy surface of the (G−C)− anionic pair system, developed on the basis of density-functional theory calculations. The RPMD model is an approximate quantum mechanical simulation technique based on path-integral formalism that enables inclusion of nuclear quantization effects such as the zero-point energy and tunneling. The RPMD model allows for the simulation of real-time dynamical trajectories and provides a consistent framework for simulating both quantum mechanical and classical mechanical degrees of freedom. This method has been recently applied to obtain various dynamical quantities including chemical reaction rate coefficients27−29 as well as diffusion coefficients.30−32 Very recently, Kretchmer and Miller33 applied the RPMD method to direct simulation of proton-coupled electron transfer within a system-bath model. In this study, instead of calculating physical quantities obtained from time-correlation functions, the RPMD simulation method is used to understand the real-time reaction dynamics of the proton-transfer process in the (G−C)− anion pair. It should also be interesting to compare the RPMD results to classical molecular dynamics simulation results on the same potential energy surface.

deformed anion structure compared to the original structure in the neutral state.14−22 In fact, recent photoelectron spectroscopy experiments suggest that, for the methyl-substituted A−T base pair as well as G−C base pair, the proton-transferred base pair anions are produced in electron attachment to these pairs from the detailed analyses of the measured vertical electron detachment energies.22 Similarly, previous electronic structure studies based on density-functional theory show that the proton-transferred pair anions are more stable than the protonnontransferred forms for specific base pair systems.14−21 In addition, the energy barrier of the proton-transfer process is calculated to be relatively small although the calculated barrier height should be strongly dependent on the electronic structure level employed. The knowledge of the detailed molecular mechanisms of the electron attachment processes to base pairs is very important in order to understand the DNA/RNA damage mechanisms by low-energy electrons. In this article, we report computational studies of the electron attachment process to the G−C base pair in the gas phase. Figure 1 displays a schematic picture of the overall electron attachment process to the G−C pair obtained from the previous and present electronic structure calculations. Since the neutral planar G−C pair has a relatively large dipole-moment (∼6 D), this pair should have the dipolebound anion state, which can easily convert into the more stable nonplanar valence-bound anion state presumably because of the relatively small activation energy. Thus, it is probable that low-energy electrons can produce vibrationally excited dipolebound G−C anions or valence-bound G−C anions directly. The initially formed valence-bound G−C anion can further convert into a more stable form via proton-transfer from G to C. Previous theoretical studies show that the corresponding classical barrier height measured from the valence-bound G−C anion minimum is calculated to be 3.54 kcal/mol at the B3LYP/6-31+G(d) density-functional level.9,10,14 Here, we mainly focus on the dynamical aspect of this proton-transfer process. In particular, it is expected that nuclear quantum effects are playing an essential role in this proton-transfer

2. RESULTS AND DISCUSSION 2.1. Potential Energy Profile of Excess Electron Attachment to the G−C Pair. We have first studied the anionic conversion process from the dipole-bound G−C anion into the valence-bound G−C anion using the BH&HLYP density-functional level34−36 with the Gaussian03 package program.37 This functional was chosen since we have previously found, in our study on U and hydrated U anions,38,39 that it can reasonably describe both the dipole-bound and valence-bound 11404

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Figure 2. Potential energy profiles of neutral and anionic (G−C)− base pair along the linear scaling factor s calculated at the BH&HLYP level of theory. Singly occupied orbitals (SOMOs) at some selected points are shown, where the total excess electron density inside of the isosurface is also indicated.

Figure 3. B3LYP/6-31+G(d)-level potential energy profile of the (G−C)− anion pair from the valence-bound state to proton-transferred valencebound state as a function of the N−H distance. Singly occupied orbitals (SOMOs) at initial, transition-state, and final structures are also shown. q(C) or q(G) means the total effective negative charge summed over the cytosine moiety or guanine moiety, respectively. Hydrogen-bond distances are shown in Å.

anionic states at reasonable computational costs. We have employed the standard 6-311++G(2d,p) basis set. In order to accurately describe the dipole-bound anion state, the basis set centered on the one hydrogen atom at the excess electron binding site in the cytosine side was further supplemented with a set of 2s4p diffuse functions. The exponents used were 0.012 and 0.004 for the s-functions while those of the p-functions were 0.25, 0.0833, 0.0278, and 0.00926. These exponent values were determined from the outermost sp functions of the 6311++G(2d,p) basis set with a scaling factor of 3. The potential energy profile of the transformation is displayed in Figure 2, where the calculations were done along

the straight line vector connecting the planar dipole-bound minimum (s = 0) and nonplanar valence-bound anion minimum (s = 1). Also shown in this figure are singly occupied molecular orbitals of the (G−C)− anion at some selected points. It is found that an excess electron is smoothly transferred from the diffuse dipole-bound type orbital to the π* antibonding orbital with an increase of s. The vertical detachment energy (VDE) value for the dipole-bound state and valence anion state were calculated to be 108 and 1073 meV, respectively. The former value is slightly larger than the previous result (95 meV) at the MP2 level with the 6-31++G** augmented with very diffuse basis functions.40 The latter VDE 11405

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Figure 4. Time dependence of the N−H and N−N distances (in Å) for a typical RPMD trajectory. Snapshots of selected configurations are also shown. Notice that all atomic bead positions in the (G−C)− anion pair are shown for understanding the quantum nature of nuclei.

2.00 Å. However, the distance between H in cytosine amino group and O of guanine is changed from 2.03 into 1.77 Å. These alternative changes in hydrogen-bonding strength should significantly affect a change in the G−C ring−ring configuration. Thus, it may be interesting to understand the correlation between the proton-transfer motion and this ringstructure deformation motion in real-time RPMD simulations. Also shown in Figure 3 are changes in base effective charge. For the initial (G−C)− valence anion, the negative charge is mainly localized on the cytosine moiety, while in the protontransferred form, the negative charge is localized on the guanine moiety. This means that a transferring particle is indeed a proton in this process and that the transfer reaction finally leads to the separation of charge and spin in the base pair complex. Thus, the proton-transferred product can be formally written as a pair of (G−H)− and (C+H)•. This behavior has already been discussed in ref 14 in detail. 2.2. Construction of the Potential Energy Function for the Proton-Transfer Process in the (G−C) Base Pair Anion. Along the proton-transfer reaction pathway presented in Figure 3, we have calculated the first and second derivatives of the potential energy at the same B3LYP/6-31+G(d) level of theory. A total of 82 points were sampled in the N−H distance range of 1.06−1.87 Å. In order to construct the fulldimensional potential energy surface V(Q), we have employed the following interpolation-type equation as

value for the valence-bound anion can also be compared to the recent result (1210 meV) at the B3LYP/DZP++ level of theory.21 From Figure 2, the transition state behavior is seen at s = 0.4−0.5. Using the geometry around these points as an initial geometry, we have carried out transition-state geometry optimization at the BH&HLYP/6-311++G(2d,p) + diffuse[2s4p] level of theory. The transition-state structure thus obtained is presented in Figure 1 together with atomic displacement vectors for the imaginary-frequency vibrational mode. The barrier height measured from the dipole-bound minimum was calculated to be only 1.22 kcal/mol without zeropoint vibrational energy correction. It was found that zero-point correction further reduces the barrier into −2.0 kcal/mol, indicating that the change into the valence-bound (G−C)− anion is a barrierless process. The VDE value at the transitionstate was also calculated to be 173 meV at the BH&HLYP level, which is somewhat larger than the VDE value of the dipolebound anion. These results suggest that, once the excess electron attaches to G−C pair, the subsequent dynamics can be described with an electronically adiabatic picture although the full electron attachment dynamics should be described using electron scattering theory.7 Next, we have carried out reaction path calculations for the proton-transfer process from the valence-bound G−C anion minimum. Figure 3 displays the potential energy profile for this process along the N−H distance, which has been obtained by minimizing the total energy with respect to all other internal coordinates. These calculations were performed at the B3LYP/ 6-31+G(d) level of theory since previous calculations by Sevilla’s group using exactly the same level had already been available.10,14 In this proton-transfer process, the initial N−H distance (1.06 Å) finally changes to 1.87 Å via the intermediate distance (1.28 Å) at the transition state. As was already found in the previous study, the N−N distance is compressed to 2.62 Å around the transition state from the initial (2.87 Å) or final (2.92 Å) structure. Another important structural change can be seen in the other hydrogen-bond lengths, which have also been discussed in the previous work.14 The distance between H in guanine amino group and O of cytosine is changed from 1.70 to

n

V (Q ) =

∑ wi(R , R i)[V0(Q i) + V1(Q i)(Q − Q i) i=1

+

1 V2(Q i)(Q − Q i)2 ] 2

(1)

where Q is the molecular coordinate, Qi is the coordinate at a sample point i, and w is the weight function. R is chosen to be the N−H distance corresponding to the most important reaction coordinate. V0(Qi), V1(Qi), and V2(Qi) are the potential energy, its first derivatives, and second derivatives at a sample point i, respectively. We have used a simple normalized Gaussian form as the weight function: 11406

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wi(R , R i) = exp[−a(R − R i)2 ]/∑ exp[−a(R − R i)2 ]

quantized zero-point vibrational energy correction within harmonic approximation significantly reduces the barrier height into 1.13 kcal/mol from the corresponding classical barrier height of 3.54 kcal/mol. In addition, we found that, in all the RPMD trajectories, the N−H stretch fluctuation in the reactant (G−C) valence-bound potential minimum (before protontransfer) is much larger than that for the classical MD results. This difference is, of course, coming from the difference in the stretching amplitude between quantum and classical simulations. In addition, after proton-transfer, it is seen that the N− H stretch vibration is somewhat excited due to the reaction exothermicity (see Figure 3), as is expected. In order to further understand the proton-transfer mechanism, Figure 5 displays the RPMD probability density

i

(2)

where a is an appropriate range parameter so as to give a smooth potential energy surface and was chosen to be 5000 a0−2 in this work. Strictly speaking, it should be emphasized that the above interpolation-type potential energy surface is not fully global and can describe only a limited region of the potential energy surface around the proton-transfer reaction pathway; however, we believe that this is a good starting point for the short-time reaction dynamics investigation presented below. The accuracy of our one-dimensional interpolation scheme has been further checked, and the details are reported in the Supporting Information. 2.3. RPMD Simulations of the Proton-Transfer Reaction in the (G−C) Base Pair Anion. Using the developed potential energy surface function, we have carried out RPMD simulations. In order to apply the RPMD simulations, we have first performed the standard imaginarytime path-integral molecular dynamics (PIMD) simulation with a constant temperature of T = 300 K to obtain an initial structure and momenta under the thermal equilibrium condition. The massive Nóse−Hoover chain technique in velocity Verlet algorithm was used to control the system temperature.41−43 We have randomly sampled a total of 70 initial configurations and momenta from the PIMD results. In this PIMD simulation, we have added an artificial exponetial potential, exp[β(RNH − RNH0)], to avoid proton-transfer events such as that of the PIMD trajectory samples in only the reactant potential well. The RPMD trajectory was subsequently propagated with a time step being δt = 0.1 fs. Each RPMD trajectory was calculated up to t = 10 ps. All the PIMD and RPMD calculations presented in this article were carried out with 32 polymer beads, which were determined from numerical convergence tests. We have also carried out classical MD simulations (also up to t = 10 ps) using the same potential energy surface for comparison purposes. Snapshots of a typical RPMD trajectory are displayed in Figure 4 along with the time dependence of the N−H and N− N distances, where it is seen that proton-transfer occurs at t ≈ 2.1 ps in this RPMD trajectory. Notice that snapshots of all the 32 beads are presented in this figure, qualitatively showing the quantum nature of nuclei. In particular, it is interesting to note that the bead fluctuation of the transferring proton becomes somewhat larger at t = 2.13 ps than that at a different time. At this time, the centroid N−H distance can be calculated to be 1.29 Å (close to the transition-state value), where it is suggested that proton-transfer may be dominantly occurring via quantum tunneling. Out of the sampled 70 PRMD trajectories (calculated up to t = 10 ps), 11 trajectories were found to be nonreactive. However, in the case of classical-mechanics simulations, protontransfer occurred in only ten trajectories out of 70 classical trajectories sampled. This suggests that the quantum rate constants are much larger than the classical rates at least for T = 300 K although calculations of thermal rate constants are beyond the present scope since the reaction dynamics presented in this work includes an electron attachment process. It should be mentioned that the observed difference in reactivity between the PRMD and classical MD results can be simply explained from the energy difference in the protontransfer barrier height. As is already shown in Figure 1,

Figure 5. Probability density distribution obtained from all the reactive RPMD trajectories plotted as a function of the N−H and N−N distances. Bold gray line shows the minimum energy profile of the proton-transfer reaction on the present potential energy surface. The distributions are extracted where the proton-transfer event is occurring for each RPMD trajectory (see text for details).

distribution, extracted around the proton-transfer event for each RPMD trajectory, plotted as a function of the N−H and N−N distances. More specifically, the structural distribution was extracted from the structural configurations in the range of treac = ±0.5 ps, where treac is the time at which the centroid of the N−H distance becomes 1.28 Å (the distance at the transition-state). Also shown is the minimum energy path of the proton-transfer reaction on the present B3LYP-level potential energy surface. From the result presented in Figure 5, a corner-cutting behavior is seen. The proton-transfer processes mostly occur at shorter N−N distances (∼2.67 Å) presumably due to corner-cutting tunneling although the obtained distribution shows a somewhat broad feature. As mentioned before, the importance of tunneling is also seen in the large bead fluctuation of ring-polymer at the time when the proton-transfer is occurring in a typical trajectory presented in Figure 4. This is a typical behavior frequently seen in many proton-transfer reactions as well as light atom transfer reactions. It is generally known that quantum tunneling is dominated at low temperatures; however, the present RPMD results at T = 300 K suggests that tunneling is also important even around room temperature although the contribution of 11407

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Figure 6. RPMD trajectory distributions as a function of the N−H distance and other three coordinates: (a) N−H−N angle, (b) ring−ring buckletype deformation angle, and (c) ring−ring propeller-twist deformation angle. The distributions are extracted where the proton-transfer event is occurring for each RPMD trajectory (see text for details). Bold gray lines show the minimum energy profiles of the proton-transfer reaction.

simulations are very useful for understanding real-time reaction dynamics beyond classical mechanics simulations.

tunneling should be carefully checked using a more quantitative scheme such as calculations of temperature dependence of thermal rate constants. Finally we have examined the correlation of the N−H stretch coordinate motion (proton-transfer reaction coordinate motion) with other motions obtained from the RPMD trajectories. Figure 6a shows the RPMD trajectory distribution around the proton-transfer events projected on the twodimensional surface consisting of the N−H distance and N− H−N angle. The minimum energy profile shows that protontransfer should occur via nearly linear N−H−N configurations; however, it is seen that the obtained distribution shows a very broad feature distributed in a wide range of 165−180 degrees. Figure 6b shows the correlation between the proton-transfer mode and G−C buckle-type ring−ring deformation mode. Similarly, Figure 6c displays the correlation to the G−C ring− ring propeller-twist mode. These two modes were chosen because the previous DFT study shows that these two modes have very low vibrational frequencies and can be useful to roughly characterize the G−C structural changes.20 In the present case, the vibrational frequencies for the buckle-type ring−ring deformation mode and ring−ring propeller-twist mode are calculated to be 31.4 and 56.7 cm−1, respectively, at the proton-transfer transition state. The obtained distributions clearly show that the proton-transfer events can occur in wide ranges of these coordinates. Thus, the calculated RPMD trajectories show a character of non-IRC dynamics. Of course, we cannot conclude that these broad features purely come from nuclear quantum effects since we cannot compare the RPMD results to the classical MD results (due to a very small number of proton-transfer events in the classical MD simulations). Nevertheless, it should be mentioned that the RPMD

3. CONCLUSIONS We have used the quantized RPMD molecular dynamics simulation method to characterize the role of nuclear quantum effects in the electron attachment-induced proton-transfer dynamics in the G−C base pair anion. The RPMD approach is a powerful tool to understand real-time reaction dynamics mechanisms including both vibrational quantization effect and quantum tunneling effect. In this article, it has been demonstrated that nuclear quantum effects are playing a very important role in the proton-transfer dynamics through the N− H···N hydrogen-bond in the (G−C)− base pair anion. In particular, the corner-cutting mechanism that avoids the classical transition-state region is important even at room temperature presumably quantum tunneling although the total number of the RPMD trajectories is not still large enough for a fully statistical discussion. However, it is suggested that a quantum dynamics picture is indeed necessary to understand the DNA/RNA damage mechanisms by low-energy electrons at a molecular level.

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ASSOCIATED CONTENT

S Supporting Information *

The accuracy of the present simple potential energy surface has been checked, and the details are described. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*(T.T.) E-mail: [email protected]. Tel: +81-48-8589113. 11408

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Notes

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Grant-in-Aid for Scientific Research of the Ministry of Education, Culture, Sports, Science, and Technology of Japan (Grant No. 21550005).

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