Role of Excitonic Coupling and Charge-Transfer States in the

Article pubs.acs.org/JPCA

Role of Excitonic Coupling and Charge-Transfer States in the Absorption and CD Spectra of Adenine-Based Oligonucleotides Investigated through QM/MM Simulations Vincent A. Spata and Spiridoula Matsika* Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, United States S Supporting Information *

ABSTRACT: In this work, we study the photophysical properties of an adenine-based oligonucleotide using an ensemble of about 200 configurations obtained from molecular dynamics simulations. Specifically, a QM/MM approach is used to obtain the excited-state energies and properties of (dA)20(dT)20 with a dimer of π-stacked adenine bases included in the quantum region. The absorption and circular dichroism spectra are computed and analyzed using the algebraic diagrammatic construction through second order level of theory method (ADC(2)) combined with classical mechanics. We find that the experimentally observed red-shifted shoulder in the absorption spectrum is due to excitonic interactions, while charge-transfer states are present within the absorption band at the higher-energy end of the spectrum. More importantly, low-energy states with charge-transfer mixing exist, which could lead to excimers and bonded excimers. These observations suggest that mixing between charge-transfer and excitonic states plays an important role in the photophysics of oligonucleotides. They also highlight the importance of taking into account the conformational flexibility of the oligonucleotide when investigating photophysical properties.

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INTRODUCTION Understanding the processes occurring upon irradiation of DNA with ultraviolet (UV) light is important because these processes may prevent or lead to the degradation of DNA, which in turn can cause cell damage, mutation, and cancer. The photophysics and photochemistry of the DNA chromophores have been studied extensively. The photophysical properties of isolated nucleobases are fairly well understood after more than a decade of intense work.1−4 The nature of the photoinitiated processes in polynucleotides, however, is still under debate. Adenine-based oligomers are probably the most heavily studied systems, with the nature of the initial excitation and subsequent decay being explored by several groups.1,5−45 When going from a mononucleotide (an isolated chromophore) to oligonucleotides (many interacting chromophores), changes in spectra and dynamics are observed. Spectroscopic analysis of double-stranded DNA has revealed that the absorption spectrum mostly resembles the sum of the spectra of the constituent monomers46 but there are small differences. Specifically, a blue shift in the maximum of absorption and a red-shifted shoulder on the low-energy side of the band are observed. Time-resolved experimental studies have shown an even more pronounced effect in the dynamics when going from mononucleotides to oligonucleotides. Specifically, transient absorption experiments as well as time-resolved emission experiments reveal that in addition to the ultrafast components in the decay of the excited-state signal, which are similar to the © 2014 American Chemical Society

ultrafast decay in monomers, there is also a longer-lived component.1,9,11−15 The underlying reasons for both the spectroscopic and the dynamics effects have been speculated extensively. It is wellknown that multiple bases can couple and interact together to affect photophysical processes, giving rise to excitonic delocalized states or charge-transfer (CT) states. Understanding the interplay and contributions of these new features in addition to the monomeric features in the case of DNA is important. The nature of the long-lived states has been debated for many years. Early experiments showed that the long-lived states are present in both single and double strands, and they are likely to be caused by π-stacking rather than hydrogen bonding.9 These states were assigned to intrastrand excimers. More recent experimental work agrees with this assignment.11,14,17,47 Furthermore, very recently, time-resolved IR spectroscopy has been able to identify CT between bases by observing the IR signature of radical cations and ions.48−50 The importance of CT states has also been associated with recent reports that single strand (dA)20 absorbs weakly in the UVA spectral region.19 Even though the molar absorption Special Issue: David R. Yarkony Festschrift Received: July 26, 2014 Revised: September 3, 2014 Published: September 3, 2014 12021

dx.doi.org/10.1021/jp507520c | J. Phys. Chem. A 2014, 118, 12021−12030

The Journal of Physical Chemistry A

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CT states are located at higher energies than the bright states in the Franck−Condon region. Coupling between locally excited and CT states was also predicted. Dinucleotides in the gas phase and solution were also studied by Plasser et al., and it was found that excimers exist with remarkably short intermolecular separation and with CT character.38 Recently, we published a paper on a novel nonradiative decay pathway involving a conical intersection for 9-methyladenine dimer in the gas phase.32 We found that a bonded excimer was participating in the excited- state deactivation pathways. That work suggested that mixing between CT and excitonic character on the excited state exists along the pathway. We have found similar conical intersections in other π-stacked systems,54−56 while others have found them in adenine dimers using different approaches.25,34 Furthermore, the structure and wave function of the bonded excimer resemble the ones found by Plasser et al.38 for adenine dinucleotide in solution, the main difference being that in that work, the structure corresponded to an S1 minimum while in our work it corresponds to a conical intersection. This suggests that this type of structure and wave function will be important in the photophysics of adenine and other oligomers and the environment can determine whether a minimum is stabilized or the energy continues downhill and forms a conical intersection with the ground state. For this reason, further examination of this pathway is important. The starting structure of our previous calculation was a regular BDNA structure of the dimer, and the effects of the oligomeric environment and various conformations that are accessible in reality were not included. An important question is how the environment and the structural fluctuations will affect this pathway, and this question has motivated the current work. In this work, we will focus on two π-stacked bases incorporated in an oligonucleotide and address the effect of conformations and structure on the nature of the excited states in the Franck− Condon region, paying particular attention to the contribution of CT mixing, which could facilitate the pathway to the bonded excimer previously found. In addition, we are also focusing on how the conformational flexibility affects the nature of excited states in the Franck−Condon region. In order to simulate better the biological environment of adenine in the double helix, we model a 20 base pair B-DNA • duplex, (dA)20 (dT) 20 in aqueous solution. About 200 configurations from a MD simulation are subsequently used in QM/MM calculations, where a π-stacked base is treated quantum mechanically in order to predict excited-state properties. Both the effect of interbase interactions and the effect of the local vibrations are included in our calculations because we allow the bases to vibrate and move freely as they would move in their environment. By sampling the configurational space, we will show that low-energy states with increased CT character exist, which may lead to excimers or bonded excimers. The justification for using two bases is based on experimental evidence that many of the features in the oligonucleotides that are absent in mononucleotides are also observed in dinucleotides,7,17,57,58 indicating that the basic unit of two bases that is used here should be sufficient to describe these effects.

coefficient per base in the UVA region is very small, absorption can have important consequences in DNA damage because the solar radiation reaching the earth’s atmosphere includes many more UVA photons compared to UVB or UVC. Obviously, understanding the nature and fate of the states absorbing in the UVA region is very important. One study has interpreted the nature of the states absorbing in this region to be CTdominated,14 but more work is needed before the issue is settled, as will be discussed below. Several theoretical studies have attempted to understand the excited states of π-stacked adenine bases.14,24−45 The use of accurate high-level quantum mechanical methods is limited by the size of the system and the cost of these methods. Therefore, the studies have to compromise at some level. If high-level methods are used, then only a very small number of bases can be treated, most commonly one or two. Using semiempirical methods or TDDFT, more bases can be included in the study, although in this case, the level of theory has to be carefully checked. For example, most commonly used functionals within TDDFT cannot treat CT states accurately, and this led to artificial low estimates of the energies of CT states in the past. In recent years, corrections to the functionals have been developed to treat the problems with CT states, and TDDFT approaches have been used extensively in oligonucleotides. Lange et al.30,31 included several base pairs in a model of adenine-based oligonucleotide and used TDDFT with a longranged corrected functional developed by them to calculate the excitation energies. They found that both intrastrand and interstrand CT states are present at energies close to the bright states, although they have low oscillator strength and are not expected to contribute much to the absorption. The red-shifted shoulder and the blue shift on the absorption band were attributed to excitonic interactions. Improta and co-workers have done several investigations on adenine-based oligonucleotides using TDDFT and found several decay pathways, including neutral and CT excimers.14,39−45 In a recent combined experimental and theoretical study, Banyasz et al.14 used TDDFT with long-ranged corrected functionals and concluded that the absorption on the red side of the spectrum is due to exciton coupling while the red tail in UVA observed experimentally is due to CT excited states. There have also been studies that used more sophisticated multireference approaches, specifically CASPT2, on adenine dimers and found that neutral and CT excimers can be important in the radiationless decay that includes the long-lived signal.29 Another aspect that requires consideration is the effect of the conformational space accessed when the bases are within an oligomer. This has been addressed in some studies. There are several QM/MM studies combined with molecular dynamics (MD) simulations that only treat one base quantum mechanically.24,36,37,51−53 In addition, there are limited studies where several bases are included in the quantum mechanical region treated with semiempirical methods.27,33 In one of these studies, Voituyk focused on the length of delocalization of the excited states and also predicted that absorption at energies between 5.0 and 5.3 eV can directly generate intrastrand CT excited states. The most sophisticated study to-date, to the best of our knowledge, has been performed by Plasser et al. on alternating adenine−thymine oligomers.35 They used a QM/ MM approach where the quantum region was treated with the ab initio ADC(2) method for the excited states and included up to four bases in the quantum region. They concluded that delocalization does not occur over more than two bases, while

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COMPUTATIONAL METHODS In this work, we utilize hybrid QM/MM simulations of adenine and adenine dimer centered within a 20 base pair canonical BDNA duplex. Sodium counterions are used to neutralize the structure, and the whole system is solvated in a 0.1 M solution 12022



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every 5 fs, giving about 20−40 configurations per simulation. The geometrical parameters of our selected configurations are monitored so that we have distributions resembling the distributions obtained from the MD simulations that include thousands of configurations. These plots are given in Figures S1−S4 in the SI. Furthermore, collection every 5 fs ensures that we also sample the vibrational motion of intramolecular modes. The absorption and circular dichroism (CD) spectra are created using the calculated excitation energies and oscillator and rotator strengths and broadened by gaussians with full width at half-maximum values of 0.24 eV. Rotator strengths are provided in Turbomole with the ADC(2) approach using analytic second-order derivatives.67 From the same set of configurations, a smaller set is chosen (76 configurations) for further QM/MM excited-state calculations where only one base is treated quantum mechanically. These results are used to model the monomer absorption spectrum. In order to obtain a quantitative amount of CT in the excited states within the dimer system, we use the difference of the dipole moment between an excited state and the ground state (Δμ). This quantity is an observable that can be obtained by Stark spectroscopy and used to characterize CT states.68 We further translate this vector into an amount of charge transferred between the bases. For this, we define a plane within the 5′ adenine in the dimer based on the three carbon atoms in the five-membered ring. We chose these atoms because the five-membered ring should fluctuate less than the six-membered ring. From the coordinates of the atoms, we establish a vector normal to this plane (Vnorm) based on a cross product between any two vectors established from these three coordinates. In order to calculate the angle of the difference dipole to the plane, we use

of aqueous sodium chloride. Water molecules modeled with the TIP3P parameters59 are added to create a periodic solvent rectangular box with a 20 Å thick border around the solute. Ions are modeled according to the Joung/Cheatham ion parameters for TIP3P water.60 The total system size is 52 234 atoms. An image of the system and a magnification of the dimer within the DNA duplex are shown in Figure 1.

Figure 1. (Left) Overall QM/MM system. (Right) Zoom in to the QM region. The dimer is represented by balls and sticks in the center of the image.

To generate starting frames for the QM/MM simulation, we first run explicit MD with periodic boundary conditions using the ff99bsc0 force field corrections61 to the ff99 force field62 and the NAMD parallel MD code63 using a 12 Å cutoff for nonbonded interactions. Long-range electrostatic interactions are calculated using the particle mesh Ewald summation method.64 The simulation is run with a 1 fs time step. After equilibrating the system for 1.1 ns, production is run for 500 ps. An additional simulation is also run with the two adenine bases being frozen in their MP2/cc-pVDZ equilibrium geometry. This simulation was run for 1 ns with frames sampled from the last 500 ps for further analysis. The force field equilibrium geometry of adenine is not the same as the one from a quantum mechanical method, and this difference will affect the excitation energies. In order to address this difference, we run QM/MM MD simulations on the ground state for about 100−200 fs starting from six MD conformations. The hybrid MD scheme utilizes the same Amber force field, water, and ion parameters as those above from the explicit MD simulations and a 10 Å cutoff for nonbonded interactions. The QM calculations are carried out at the MP2/def2-SVP level of theory on the 28 atoms of the central adenine dimer. An electrostatic embedding scheme is used. The details of the complete protocol for this combination of explicit MD and hybrid QM/MM MD are included in the Supporting Information (SI). Several distributions of intra- and interbase parameters are also shown in Figures S1, S3, and S4 (SI). Excited-state energies and properties are obtained using QM/MM with the resolution of the identity (RI) algebraic diagrammatic construction through second order (ADC(2))65 method and the def2-SVP basis set for the QM region. A total of 209 geometries from the QM/MM MD simulations are used. These geometries are chosen so that the rise and twist distributions, as well as the bond vibrations, are sampled. Rise and twist values are used here as defined in the Calladine and Drew block scheme.66 Specifically, configurations are collected

θ = sin−1

Vnorm ·Δμ |Vnorm||Δμ|

(1)

and convert to an absolute value of the angle between 0 and 90°. We next calculate the projection onto the normal vector as Δμproj = |Vnorm| sin θ. We are able to obtain the quantity of charge transferred in units of electronic charge based on the definition of the dipole moment and utilizing rise as a measure of the magnitude of separation according to the classical description of the dipole, Q = Δμproj/rise. We compared the results of this approach to a previously reported approach that decomposes the one-electron density69 and found comparable results. The average difference between the two approaches was, on average, about 0.05 e. The Nucleic Acid Builder70 was used to construct the BDNA strand. TLeap71 was utilized in building the 52 234 atom system through the addition of counterions and aqueous sodium chloride. The NAMD63 MM engine was utilized for explicit MD. Hybrid calculations were performed with the DlPoly MM engine (included in Chemshell) and interfaced through a locally modified version of Chemshell72 to the Turbomole software package. Ptraj71 was utilized for measurements of the adenine and interbase dimensions. 3DNA73,74 was utilized to measure the rise and twist in all trajectories. Visualization of trajectories, natural transition orbitals (NTOs), and difference dipole moments, analysis of RMSD, and the writing of starting structures and velocities for hybrid MD simulations were performed with VMD.75 Matlab76 was utilized to generate the spectra and for data analysis. 12023



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Table 1. Energies and Oscillator Strengths (in parentheses) at the ADC(2) Level of the Excited States for Monomer and Dimer Geometries in the Gas Phase (GP) and in the Oligomer using QM/MM states

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S1 S2 S3 S4 S5 S6 S7 S8 S9 S10

GP monomer 5.13 5.21 5.39 5.85 6.15 6.46

(0.005) (0.047) (0.270) (0.002) (0.001) (0.323)

n−π* π−π* π−π* n−π* n−π* π−π*

QM/MM monomer 5.15 5.32 5.56 6.19 6.53 6.58

(0.118) (0.208) (0.016) (0.017) (0.320) (0.142)

π−π* π−π* n−π* n−π* π−π* π−π*

RESULTS AND DISCUSSION Nature of the Excited States. Isolated adenine in the gas phase has three low-lying states, an n−π* and two π−π* states, with S3 having the largest oscillator strength. The ADC(2) results obtained here using the MP2-optimized structure are shown in Table 1. These energies are about 0.3−0.5 eV higher than those obtained using multiconfigurational perturbation theory calculations,77−79 as well as experimental absorption maxima in the gas phase.80,81 The ordering of the states is the same as that of other high-level methods, with the lowest being n−π* and S3 being the brightest π−π* state. When adenine is placed in the oligomer, the environment affects the excited states. The QM/MM results, taken from a single configuration where only the monomer is treated quantum mechanically and is frozen to its MP2 equilibrium geometry, are shown in Table 1. These results illustrate the destabilizing effect of the environment on the n−π* state, which raises the state’s energy by 0.4 eV and places it above the π−π* states. The energies of the π−π* states are lowered by 0.06−0.07 eV only. The purpose of this comparison is to examine closely the effect of the environment on each state. The effect of the various conformations is not included here (because this is a single random conformation) and will be examined in the next section. In the dimer gas-phase geometry, there are twice as many states as in the monomer plus additional CT states. Table 1 shows that the first two excited states are n−π* states followed by four π−π* states. In the gas-phase dimer geometry, the S6 state has the highest oscillator strength, and S3 has the second highest oscillator strength. The gas-phase and QM/MM dimer results are taken from the same conformation as those in the monomer with two adenine bases included in the QM region and being frozen to their MP2 geometries. The QM/MM results illustrate again the raising of the n−π* states to S5 and S6 and lowering of the π−π* states to S1−S4. S4 is bright in character followed by S1. The CT states for this geometry are states S9 and S10, which only appear when the environment is included, suggesting that they will have higher energies in the gas-phase dimer. NTOs showing the character of each state of the QM/MM dimer from Table 1 are shown in Figure 2. The first six states arising from the three adenine states can be either delocalized on both bases or localized on each adenine. Here, we observe both scenarios. The delocalization is observed by the fact that there are two hole−electron pairs contributing to the excitation. States S2−S4 are delocalized for this particular geometry, while states S1, S5, and S6 are more localized. The CT character of states S9 and S10 is obvious, with the hole being in one base

GP dimer 5.09 5.09 5.21 5.25 5.32 5.44 5.76 5.76 6.15 6.15

(0.0023) (0.0038) (0.0334) (0.0045) (0.0268) (0.4251) (0.0027) (0.0016) (0.0008) (0.0009)

n−π* n−π* π−π* π−π* π−π* π−π* n−π* n−π* n−π* n−π*

QM/MM dimer 5.07 5.20 5.24 5.34 5.48 5.53 6.09 6.15 6.26 6.29

(0.085) (0.035) (0.020) (0.351) (0.022) (0.012) (0.003) (0.013) (0.009) (0.000)

π−π* π−π* π−π* π−π* n−π* n−π* n−π* n−π* CT CT

Figure 2. NTOs of the excited states for the hybrid QM/MM dimer geometry shown in Table 1. The contribution of the given pair of NTOs to the overall transition is given above the arrows.

while the electron is in the other. There are two CT states very close energetically where the localization of the hole−electron densities is switched between bases. Another way to numerically access the CT character of a state is by the magnitude and direction of the vector Δμn0, which is defined as the difference of the dipole moment of state Sn and the dipole moment of the ground state. This has already been explained in the Computational Methods section. These vectors for the same states described above are shown in Figure 3. The difference dipole for excitonic states is parallel to the plane of the bases, while that of CT states is almost perpendicular to them. This difference will be used later to access the character of states in the large number of conformations that we have. Absorption Spectrum. In order to gain insight into the initial characteristics of the photoprocesses of adenine, we have reproduced theoretically the absorption spectrum using the excited states of the adenine dimer in the QM/MM environment. Figure 4 illustrates the absorption spectrum calculated as a sum of gaussians plotted based on the energies and oscillator strengths taken from ADC(2) calculations on all of the 209 geometries that we have selected. The figure compares the absorption of the dimer within a DNA duplex to the absorption of the monomer within the duplex. A subset of the conformations used for the dimer (76 geometries) was used for the monomer absorption spectrum. In the experimental spectrum for poly(dA)(dT), the maximum of absorption is 4.78 eV and is shifted by 0.051 eV compared to the sum of the monomer spectra (dA + dT).27 A 12024



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we are only treating two bases quantum mechanically; therefore, only their oscillator strengths affect the spectrum. Hypochromism strongly depends on the length of the oligomer for oligomers containing between 2 and 10 bases.83 CD Spectrum. When studying interacting chromophores, the CD spectrum is much more useful than the absorption spectrum in determining the magnitude of excitonic coupling because the coupling leads to minor effects in the absorption band but major effects in a CD spectrum. The CD spectrum for our system is shown in Figure 5. In an ideal case when each

Figure 3. Difference dipole moments Δμn0 between S0 and excited state Sn for the hybrid QM/MM dimer geometry shown in Table 1

Figure 5. CD spectrum with sticks showing the contribution from each state S1−S4.

chromophore has one bright state, the CD spectrum will show two bands of opposite sign, and the separation of them is a measure of the coupling. In adenine, however, there are two π−π* states in each monomer at low energies (and even more at higher energies) so the dimer has at least four states that can be coupled. Therefore, it is quite interesting to see the contribution of each state to the spectrum. Figure 5 shows the contributions of states S1−S4. S1 and S4 clearly contribute the most to the positive and negative bands, respectively. Most of the contributions from the S2 and S3 states are canceled because they show positive and negative features in the same energetic range. Because of this cancelation, the CD spectrum measures roughly the overall coupling between S1 and S4. The corresponding figure showing the S1−S4 contributions on the absorption spectrum is shown in Figure S5 (SI). That figure also shows that the red-shifted shoulder and the blue shift of the spectrum compared to the monomer originate mostly from the same states that lead to the CD characteristics, namely, S1 and S4. The CD spectrum in dinucleotides or other structures that allow for efficient π-stacking of two adenines has been reported recently by Kohler and co-workers.58 These spectra are very similar to the one calculated here. The positions of the maxima and minima corresponding to the first peak in the experimental spectrum are about 4.63 and 4.96 eV, respectively. Our reproduced spectrum overestimates these values with a positive maximum at 4.82 eV and a negative minimum at 5.21 eV, in accordance with the expected errors in excitation energies. The value of the excitonic coupling is calculated as the distance between the maximum and minimum peaks divided by 2.84 In the experimental spectrum, this value is 0.16 eV. We calculate the excitonic coupling in the dimer system as 0.195 eV, which is in reasonable agreement with experiment. Deviations from the experimental value are likely caused by the fact that we have not accounted for all of the states in adenine. Higher bright states

Figure 4. Absorption spectrum for monomer adenine and for the dimer using the energies and oscillator strengths obtained from QM/ MM and sums of gaussians.

shoulder appears at the longer wavelengths of the spectrum compared to the monomer spectrum. In the calculated spectrum, the red-shifted shoulder is present, but the maximum is slightly blue-shifted in the dimer compared to that in the monomer (0.0015 eV compared to the experimental 0.051 eV). The peak maximum for the spectrum is 5.15 eV, and this is in agreement with the expected overestimation of the locations of the band maxima by the ADC(2) calculations by about 0.4 eV, as also seen in the energies reported in Table 1. We believe that our initial calculation underestimates the coupling because it uses only a dimer in the quantum region. If more bases are present, then as the distance of the middle adenine to the neighboring base on one side increases, the distance between the middle adenine and the other neighboring base will decrease, ensuring increased interactions between neighboring bases. Finally, the calculated spectrum reproduces the effect of hypochromism observed experimentally. The hypochromism for poly(dA)poly(dT) has been measured by Markovitsi and co-workers to be about 50%.22,82 In our calculations, the dimer spectrum has an area that is 24% less in comparison to the monomer spectrum. The difference is likely due to the fact that 12025



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been addressed with ADC(2) for the alternating system (dAdT)6(dAdT)6.35 Here, we examine the appearance of states with CT character in the Franck−Condon region for all of the conformations that we have selected. The degree of CT mixing is also addressed. As discussed earlier, a good way to look at CT states is by using the difference of the dipole moments of each state from the dipole moment of the ground state. To measure quantitatively the amount of CT, we project the difference dipole moment on a vector normal to the plane of the 5′ adenine and then divide by the magnitude of the distance according to the definition of a dipole, as discussed in the Computational Methods section. As an example, the Δμ vectors shown in Figure 3 produce CT of 0.000−0.018 e for the first eight states and 0.72−0.73 e for states S9 and S10. Figure 7

cause additional signal at higher energies, but they may also affect the lower band. The experimental CD spectrum of duplex poly(dA)poly(dT) is also available in the literature.85 Even though we are including a duplex in our QM/MM calculations, there are only two bases coupled; therefore, our spectrum should be, and is, closer to that of the dinucleotide. The CD spectrum of poly(dA)poly(dT) is much more asymmetric than that of the dinucleotide, and the coupling extracted from it is smaller. Coupling with the other adenines and the effect of the thymine bases can naturally affect the CD spectrum. More information about which geometries contribute more to the coupling could be useful. We assess the nature of the excitonic coupling in relation to the dimensions of rise and twist in the system. We focus on the S4 minus S1 difference as a measure of the coupling because this is the part that contributes mostly to the CD spectrum, as already discussed. Figure 6

Figure 6. Contour plot of the difference in energy (ΔE) between states S4 and S1 related to the coupling as a function of rise and twist.

illustrates the energy difference between the S4 and S1 excited states in order to see which geometries are responsible for most of the coupling. As one would expect, low rise and twist values are characterized by increased excitonic coupling. The more intense coupling values appear at values between 27 and 30° of twist and rise values less than 3.3 Å. CT Contributions. The role of CT states on the photophysical properties of poly(dA)(dT) has been discussed in the literature extensively. It has been argued that the observed long-lived state in this system arises from excimers, which often are expected to have CT character.1,9,11,20,29,86 Theoretical studies have examined the presence of CT states in absorption as well as in photophysical pathways. There is some disagreement about the accessibility of CT states in the Franck−Condon region, with some calculations using TDDFT predicting that they are responsible for UVA absorption either because of their low energy or because of inhomogeneous broadening,14,39 while other calculations predict that they are higher than the first bright absorption state.31,32 The calculations of one configuration with a regular B-DNA conformation shown in Table 1 show that CT states are more than 1 eV above the first excited state, making them inaccessible at initial absorption. The question however of how the different conformations accessed by the system can affect these states has not been addressed before with high-level ab initio methodology for poly(dA)(dT). This question has been addressed with semiempirical methods before,33 and it has also

Figure 7. (Top) Contour plots of the CT amount for states Sn for n = 1−9 for all dimer geometries versus rise and twist. (Bottom) Same contour plots focusing on the lower four states S1−S4 and lower values of CT for more information on weaker CT mixing.

shows a contour plot of the amount of CT versus rise and twist for the first nine states. It is clear from these plots that CT states dominate state S7, and they are also prominent in states above S7. This is in agreement with what one would expect from Table 1. A closer look (see the bottom of Figure 7) however shows that in some cases, a small amount of CT mixing exists for the lower states as well. Because the presence of CT states at lower energies is very important, we examine these states more carefully. Figure 8 shows a plot of CT amount as a function of energy for the S1−S4 states superimposed on the absorption spectrum. This figure reveals the significant fact that there are several CT mixed states at the lower-energy end of the absorption spectrum (with energies of 4.6 eV in some cases) as a result of the configurational fluctuations! The fact that these CT 12026



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characteristic of the wave function, that is, the increased density between the two carbons on the neighboring bases, is not present in all of the states that have CT mixing, but it is present in many of them. The energy of the state characterized in Figure 9 is 4.6 eV, and the oscillator strength is 0.04; therefore, it can be populated either directly radiatively or radiationlessly from other brighter states. There are other states that show the CT mixing and have even higher oscillator strengths. An example and the distribution of such a state is shown in Figure S10 (SI). It should be noted that the present work does not provide proof that the CT mixed states will lead to bonded or regular excimers, but it provides information that these states are precursors to the excimers, and it is very likely that the population of them will lead to excimers. Future work will attempt to prove this idea with geometry optimizations. The last issue that deserves some discussion is whether these states can be populated directly through absorption of light or indirectly through radiationless decay. We already discussed isolated cases where both CT mixing and some oscillator strength are present, but how prominent is this and will it affect the absorption spectrum? Related to this question is previous claims that the red-shifted shoulder on the low-energy side of the band is caused by low-lying CT states.14 In that work, the actual CT states were found at higher energies, but a large inhomogeneous broadening was assumed, which will extend the bands to the UVA region. In order to address this question, we examine the oscillator strength and the CT character of states simultaneously. Using the degree of CT as the cutoff for identifying states with mixed CT character, we show their contribution to the overall absorption spectrum in Figure 10.

Figure 8. Plots of the CT amount for states Sn for n = 1−4 for all dimer geometries superimposed on the absorption spectrum.

mixed states are so low in energy indicates that they can be accessed easily either radiatively or radiationlessly from the bright states, and thus, they will have an important role in photophysics. One should be careful with misinterpreting this figure. This figure demonstrates the energetic position of the mixed states, but it contains no information about their brightness and thus their ability to absorb photons. This point will be discussed below. On the basis of our previous work and work by others,32,38 these mixed states could lead to excimers and even bonded excimers and conical intersections. To illustrate how the character of these states resembles the previously found bonded excimer on the adenine dimer, we show NTOs of one CT mixed state with low energy. Figure 9 shows NTOs from an S1

Figure 9. (a) NTOs describing the S1 state for one selected configuration in this work. (b) NTOs for the bonded excimer found in ref 32. The percentage contribution of the given pair of NTOs is given on top of the arrows.

Figure 10. Absorption spectrum showing separately the contribution of CT mixed states by separating them based on their amount of CT.

low-lying state with mixed CT character (0.248 e) and compares them to the NTOs describing the bonded excimer in our previous work.32 The excitation in both cases shows CT character, although the degree of CT is much more in the bonded excimer. Another very important characteristic that is signature in the bonded excimer is the fact that there is increased density between the two bases, especially connecting C6 of each base. This increased density is seen in the S1 state of our chosen configuration already in the Franck−Condon region. Population of this state will be rapid, and the wave function of the bonded excimer is already prepared immediately or shortly after absorption. Depending on the restrictions imposed by the environment, population of this state can lead to a minimum or a conical intersection.32,38 This second

This figure shows that the contribution of CT states on the spectrum is very low, and it is entirely concentrated on the higher energies of the band. The contribution to the spectrum rapidly decreases when we increase the cutoff and look only at more “pure” CT states. Therefore, the claim that the red-shifted absorption shoulder and UVA absorption originate from CT states is not supported by our calculations. Because the geometries that we use are taken from MD simulations, the inhomogeneous broadening should already be included in our calculations; therefore, our work also does not support the idea that inhomogeneous broadening will place the CT states in the UVA region. This is in agreement with several previous studies that use ab initio methods or carefully calibrated func12027



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tionals.31,35 We should note however that we have used a limited number of conformations, and it is possible that we do not have a converged value for the broadening. The contribution of CT mixed states on the absorption spectrum for several configurations of oligomers has been discussed before, but their relation to excimers and bonded excimers has not been addressed. QM/MM studies using semiempirical methods on (dA)6(dT)6 found that chargeseparated states can be directly populated by UV absorption at energies of 5.0−5.3 eV. On the other hand, QM/MM studies using ADC(2) on (dAdT)6(dAdT)6 found that CT states are located in the higher-energy range of the absorption spectrum somewhat above the major portion of the energy distribution of the bright states. This conclusion agrees with ours. Both of the previous studies have also concluded that the intrabase vibrations are important for the accurate representation of the absorption spectrum. These vibrations are included in our work, although we have not examined how the results would change if we had not included them.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Support by the National Science Foundation under Grant CHE-1213614 is acknowledged. We would also like to thank Dr. Sudipto Mukherjee and Prof. Vincent Voelz for helpful discussions, as well as Mr. Chris Clement for helping us with various software issues. S.M. acknowledges support from the Alexander von Humboldt foundation. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant Number ACI-1053575.

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REFERENCES

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CONCLUSION In this work, we have studied the excited states of the (dA)20(dT)20 oligomer using an ensemble of about 200 configurations obtained from MD simulations and a QM/ MM approach with two π-stacked adenine bases included in the quantum region. Using the ADC(2) method, we were able to reproduce the absorption and CD spectra and compare them to spectra produced by a single base. From our findings, we conclude that the exciton coupling in polyadenine oligomers contributes to the red-shifted shoulder and blue-shifted maximum in the absorption spectrum of the oligomers compared to the monomer. Even though treating a dimer quantum mechanically reproduces the experimental features qualitatively, a more quantitative agreement with experimental poly(dA)(dT) spectra could probably be reached if the excited states of more adenine and thymine bases were included. We have focused on the involvement of CT states in the initial absorption as well as in the production of excimers, which may be responsible for the experimentally observed longlived component in the decay of the excited-state population of adenine-based oligonucleotides. We have found that states with a large degree of CT are located at high energies, while there are states with mixed CT character having low excitation energies. The contribution of CT states to the absorption spectrum is very small and concentrated on the high-energy end of the band. The low-energy mixed CT states however should be easily accessed after UV absorption of the oligomer indirectly through radiationless decay from the higher bright states. The wave function of the mixed states resembles the wave function of excimers and bonded excimers found previously, indicating that after they are populated, they could easily reach these final states. Their involvement arises from the flexibility of the oligomer and its ability to access a variety of conformations. Although these states can be present at low energies, our results indicate that they do not contribute to the red-shifted absorption shoulder or the UVA absorption.

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ASSOCIATED CONTENT

* Supporting Information S

More specifics of the methodology and its validation are presented. Additional figures describing the excited states are also shown. This material is available free of charge via the Internet at http://pubs.acs.org. 12028



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Role of Excitonic Coupling and Charge-Transfer States in the

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