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Charge-Transfer Excited States in Aqueous DNA: Insights from Many-Body Green’s Function Theory 1
Huabing Yin,1 Yuchen Ma,1,* Jinglin Mu,1 Chengbu Liu,1,† and Michael Rohlfing2 School of Chemistry and Chemical Engineering, Shandong University, Jinan 250100, People’s Republic of China 2 Institut für Festkörpertheorie, Universität Münster, 48149 Münster, Germany (Received 13 December 2013; published 3 June 2014) Charge-transfer (CT) excited states play an important role in the excited-state dynamics of DNA in aqueous solution. However, there is still much controversy on their energies. By ab initio many-body Green’s function theory, together with classical molecular dynamics simulations, we confirm the existence of CT states at the lower energy side of the optical absorption maximum in aqueous DNA as observed in experiments. We find that the hydration shell can exert strong effects (∼1 eV) on both the electronic structure and CT states of DNA molecules through dipole electric fields. In this case, the solvent cannot be simply regarded as a macroscopic screening medium as usual. The influence of base stacking and base pairing on the CT states is also discussed. DOI: 10.1103/PhysRevLett.112.228301
PACS numbers: 82.37.Vb, 78.40.Dw, 78.40.Me, 87.15.-v
The absorption of solar ultraviolet (UV) light could induce a series of photophysics and photochemistry processes in DNA, resulting in radiation damages and carcinogenic mutations in the biological hereditary process [1]. Understanding the physical mechanism of excited-state dynamics in DNA is extremely important for life and is also an exciting challenge for scientific research due to the complexity in biological systems. It has been generally accepted that charge-transfer (CT) states play a vital role in the excited-state process of DNA, modulating the excitedstate decay of DNA and the probability for gene mutations [2,3]. For example, the bright ππ states [ππ ðBÞ] produced by UV absorption can rapidly decay to long-lived CT-like states, e.g., excimer and exciplex states [4,5]. Experiments suggest that CT states should be responsible for the weak UV absorption at the long wavelength region around 330 nm [6]. However, our knowledge of the CT states in DNA is still scarce; especially, there is much controversy on the energies of CT states [6]. A huge discrepancy still exists between experiment and theory. Theoretical calculations by high-level quantum chemistry approaches, such as the second-order approximate coupled-cluster method, have positioned the CT states of the single-stranded adenine dimer ðAdeÞ2 high above the ππ ðBÞ state in energy [7,8], which is contrary to the experiments. The deviation can be attributed to the difference between the calculation models [ðAdeÞ2 in the gas phase] and experimental condition [ðAdeÞ20 in aqueous solution]. Extra base-stacking interaction in ðAdeÞ20 compared to ðAdeÞ2 may lower the CT states, but its effect is not supposed to be strong enough to induce a large redshift (∼0.4 eV according to our calculations as discussed below). This raises an important question: how does the aqueous solution influence CT states? This question cannot be solved by the high-level 0031-9007=14=112(22)=228301(5)
quantum chemistry methods at present due to the necessity to include enough solvent molecules in calculations and the tremendous computational load thereafter. Instead, approximate approaches, including the combined quantum mechanics and molecular mechanics methods, and implicit solvation models, such as the polarizable continuum model (PCM), are usually applied in combination with the timedependent density functional theory [7–9]. Although much work has been done with these approaches for a variety of DNA structure models, there is still a large gap between theory and experiment. These methods predict that aqueous solution redshifts CT states by about 0.1 eV [8]. To be consistent with experiments, the effect of aqueous solution on CT states should be on the order of 1 eV. The deficiencies in these methods, such as the simplification of water molecules by points charges, the approximate exchangecorrelation functionals used in density functional theory (DFT), might be the origins for the large error. Water and CT are very important in biological systems and also in material science; it is quite necessary and also fundamental to clarify the effect of water on CT states. In this work, we reexamine this problem with a state-of-the-art ab initio method: many-body Green’s function theory, in particular the GW method and the Bethe-Salpeter equation (BSE) [10–12]. The GW method and the BSE (GW-BSE) can compute single-particle states and excitons with high accuracy, and have been successfully applied to study CT excitations between organic molecules [13–15]. Enough water molecules are explicitly included in the calculations to model the aqueous environment encompassing DNA molecules. We will show that the dipole electric field from the hydration shell can exert considerable impact on the single-particle states of DNA molecules, which causes significant redshifts of the CT states. Taking also into account the base-stacking and base-pairing effects, our
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calculations satisfactorily confirm the existence of CT states at the long wavelength side of absorption peaks. They cannot only help us understand in depth but also give some hints to tune the excited-state dynamics and charge transfer in DNA. We use adenine-thymine complexes, which have been investigated widely in recent experiments, as the DNA structure models to conduct our research, including singlestranded polyadenine oligomers [ðAdeÞn ], single-stranded alternating adenine-thymine dimer [AdeThy], and doublestranded adenine-thymine pair oligomers [ðAde∶ThyÞn ]. Their behaviors in aqueous solution are modeled by clusters like ðAdeÞn -ðH2 OÞm , which are constructed through classical molecular dynamics simulations. GW-BSE calculations are carried out by a Gaussian-orbital based code [11,12,16]. BSE calculations are performed at two levels. For small systems, we use the full BSE, which considers the mixing between resonant and antiresonant transitions [14,17,18] and dynamical screening effects in the electron-hole interaction [18]. For larger systems, we applied the BSE within the Tamm-Dancoff approximation (TDA) and the static screening limit in the electron-hole interaction. The full BSE is more accurate but its computational cost is very high. However, for CT states which are the focus of this work, the energy difference between the full BSE and the BSE-TDA is smaller than 0.1 eV (see the Supplemental Material [19]). The BSE-TDA is a good compromise. Details on the calculation strategies and the construction of models are provided in the Supplemental Material [19]. For the gas-phase adenine (thymine) monomer, the gap between the highest occupied molecular orbital (HOMO=H) and the lowest unoccupied molecular orbital (LUMO=L) is 9.21 eV ð9.51 eVÞ from our GW calculations, which agree well with experiments and previous calculations by the GW method [20] and complete active space with second-order perturbation theory [21,22]. The absorption peaks are formed by ππ ðBÞ excitons. The full BSE predicts very well the energies of ππ ðBÞ states (see Table I). The Supplemental Material [19] gives a comprehensive comparison between our results and those by other first-principles approaches. For adenine monomer in aqueous solution, the energy of ππ ðBÞ from the full BSE is 4.69 eV on average, 0.16 eV redshifted relative to that in the gas phase. This is consistent with experiments (redshifting from 4.92 eV to 4.77 eV) [23,24]. In ðAdeÞ2 , ππ ðBÞ and the lowest CT (CT-min) are both composed by transitions H − 1=H → L=L þ 1 [see Fig. 1(a)]. However, the binding energy of the CT-min exciton is 1 eV smaller than that of the ππ ðBÞ one, making CT-min above ππ ðBÞ in energy by a large amount (see Table I). For ðAdeÞn, the position of the absorption peak changes little with n. The energy of CT-min decreases by 0.35 eV from ðAdeÞ2 to ðAdeÞ5 . For CT-min, the excited electron and hole are localized on two adjacent bases; their binding energy changes little with n. The evolution of the
TABLE I. Energies of the ππ ðBÞ and the lowest CT (CT-min) excitations for some adenine-thymine DNA models in the gas phase calculated by the full BSE.a ππ ðBÞ Model Ade Thy ðAdeÞ2 ðAdeÞ3 ðAdeÞ5 AdeThy Ade:Thy ðAde∶ThyÞ2
Ade b
4.85 4.77 4.74 4.74 4.61 4.77 4.77
CT-min
Thy
Ade → Ade
Ade → Thy
4.68c 4.56 4.55
5.75 5.52 5.40 5.61
5.16 5.72 5.50
a
Energies are in electron volts. Experimental value: 4.92 eV [23]. c Experimental value: 4.8 eV [23], 4.5–4.9 eV [25], 4.7 eV [26] b
CT-min energy with n can be estimated according to the gap between H and L, the transition between which dominates CT-min. From ðAdeÞ5 to ðAdeÞ8 , the H-L gap decreases little (see the Supplemental Material [19]). So the energy of CT-min for longer adenine oligomers will be close to that of ðAdeÞ5 . The effect of base stacking on the CT state should be ∼0.4 eV. We study eight ðAdeÞ2 -ðH2 OÞm clusters for adenine dimer in aqueous solution. Figure 2 illustrates the excited
FIG. 1 (color online). (a) Energy diagrams of the molecular orbitals for ðAdeÞ2 in the gas phase and in aqueous solution (modeled by an ðAdeÞ2 -ðH2 OÞ31 cluster at the D8 configuration) calculated by the GW method. Solid arrows illustrate the transitions that constitute the states CT-min and ππ ðBÞ. Dashed and dotted lines denote molecular orbitals that are localized on different adenine bases. (b) Real-space distribution of orbitals H=L and excitons CT-min=ππ ðBÞ [yellow (light gray): excited electron; light blue (gray): hole] for the gas-phase ðAdeÞ2 . (c) Real-space distribution of molecular orbitals for ðAdeÞ2 -ðH2 OÞ31.
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FIG. 2 (color online). Energies of the low-lying excited states for the eight ðAdeÞ2 -ðH2 OÞm clusters (D1-D8) and the gas-phase ðAdeÞ2 calculated by the BSE-TDA. ππ ðWÞ denotes the state with weak oscillator strength. The ππ ðBÞ states of D1-D8 are linked by a red dashed line.
states for them (D1–D8) computed by the BSE-TDA. ππ ðBÞ is redshifted by 0.14 eV on average compared to the gas-phase counterpart. The most amazing result is that some CT states appear below ππ ðBÞ. The energy of CT-min is lowered by 0.7–1.0 eV in aqueous solution. CT states discussed here are only related to transitions between nucleobases. CT between nucleobases and water molecules is not observed in this energy range. We take one of the ðAdeÞ2 -ðH2 OÞm clusters, D8, which contains 31 water molecules, as the example to explain the different behavior of CT states in the gas phase and aqueous solution. In the gas phase, H and H − 1, L and L þ 1, L þ 2 and L þ 3 of ðAdeÞ2 are degenerate, and they are all distributed equally on two nucleobases (see Fig. 1). In aqueous solution, the degeneracies are all lifted. The splitting between H and H − 1 reaches 1.4 eV. HðLÞ is shifted up (down) by 0.4 eV (0.8 eV), narrowing the H-L gap by 1.2 eV. Molecular orbitals, moreover, become localized on single nucleobases [Fig. 1(c)], especially with H=L þ 2=L þ 3 on a base, and H − 1=L=L þ 1 on another one. The transition H → L apparently forms the greatly redshifted CT-min. The lowest ππ ðBÞ is formed mainly by transitions H → L þ 2 and H − 1 → L with the former dominating. By doubling the number of water molecules in D8, the H-L gap changes little; i.e., the size of the ðAdeÞ2 -ðH2 OÞm clusters we construct is large enough to simulate the behavior of ðAdeÞ2 in aqueous solution. This is in accordance with previous calculations on hydroxide and hydronium showing that the influence of solvent water molecules on the electronic levels of solute molecules is mainly determined by the first hydration shell [27]. Certainly, the variation of electronic levels enlarges gradually with the increase of water molecules within the first hydration shell as shown in the Supplemental Material [19]. In the ground state there is some electron transfer between ðAdeÞ2 and nearby water molecules as can be
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seen from the occupied molecular orbitals shown in Fig. 1(c). This may break the symmetry in the gas-phase ðAdeÞ2 and lead to the reorganization of molecular orbitals as discussed above. The interaction between ðAdeÞ2 and the hydration shell is dominated by the long-range electrostatic potential. Now we model this potential in ðAdeÞ2 -ðH2 OÞ31 of D8 by replacing the oxygen and hydrogen atoms in water molecules by point charges whose magnitudes are adjusted according to the dipole moment of water in liquid [28,29]. In this model, the splitting between H and H − 1 is calculated to be 0.6 eV by DFT with the GAUSSIAN09 code [30], which reproduces that in the explicit ðAdeÞ2 -ðH2 OÞ31 model (0.7 eV by DFT). So the huge changes in the electronic structure and CT states of ðAdeÞ2 can be ascribed to the dipole electric field caused by the hydration shell. Based on this, it may be possible to modulate the excited-state dynamics of DNA molecules through external electric fields. We also performed a DFT-PCM calculation by the GAUSSIAN09 code for ðAdeÞ2, which shows that the implicit solvation model only causes respective rigid shifts of the occupied and virtual levels, modifying the H-L gap by just 0.04 eV. So aqueous solution does not just play the macroscopic screening role in DNA; its microscopic effects must be paid more attention to and implicit solvation models may have some limitations in this respect. In ðAdeÞ3 -ðH2 OÞm clusters, the gap between H and L (between H and H − 1) is also narrowed (enlarged) by more than 1.0 eV relative to those in the gas-phase ðAdeÞ3 . Compared to ðAdeÞ2 -ðH2 OÞm , CT-min is further redshifted by about 0.2 eV, while the energy of ππ ðBÞ is nearly the same. These trends are the same as those in the gas phase. From Fig. 3, we can clearly see the extension of optical
FIG. 3 (color online). (a) Optical absorption spectra of an Ade-ðH2 OÞm (black), an ðAdeÞ2 -ðH2 OÞm (red), and an ðAdeÞ3 -ðH2 OÞm (blue) cluster calculated by the BSE-TDA (solid line) and the full BSE (dash line). Vertical lines denote the positions of the states ππ ðBÞ and CT-min (the ones at 4.55 and 4.83 eV). Note that for Ade-ðH2 OÞm, there is no CT state, so there is only one black vertical line.
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absorption tails to the long-wavelength region from adenine monomer to trimer, which is due to the contribution from CT states. Taking into account the effects of both aqueous solution and base-stacking interaction, we can estimate that CT states can emerge ∼0.3 eV below the absorption peak of ðAdeÞ20 in aqueous solution. This is in good agreement with recent experiments, supporting their speculations [6]. CT states are sensitive to the local configuration of the hydration shell at room temperature as can be seen from Fig. 2, which makes them spread over a wide spectral range. In the single-stranded AdeThy dimer, molecular orbitals are nondegenerate. H and L are localized on adenine and thymine monomers, respectively, the transition between which constitutes CT-min. Surrounding AdeThy by a hydration shell reduces its H-L gap by about 0.6 eV, redshifting CT-min to the same extent accordingly (see the Supplemental Material [19]). These effects are much weaker than those in ðAdeÞ2 . However, due to the lower energy (by 0.6 eV) of CT-min in AdeThy than that in ðAdeÞ2 in the gas phase (Table I), in aqueous solution the energy of CT-min in AdeThy is close to that in ðAdeÞ2 . We also study the influence of base pairing on CT states (Table I). From ðAdeÞn to ðAde∶ThyÞn (n ¼ 2; 3), the lowest intrastrand CT state among the adenine bases redshifts by about 0.15 eV. The lowest interstrand CT transition is 0.10 eV lower than the lowest intrastrand one. Due to the large dimension of ðAde∶ThyÞn , it is hard to study its excited states in aqueous solution by the GW-BSE at present. But we can undoubtedly come to the conclusion that base pairing can further enhance the UV absorption in terms of both intensity and spectral range in the longwavelength region through CT transitions, as has been observed in recent experiments [6]. In summary, using high-level first-principles calculations, we have found that aqueous solution can significantly modify the electronic structure of DNA molecules through dipole electric fields, stabilizing CT states at long wavelengths. We give a comprehensive picture of the effects of base stacking, base pairing, and aqueous environment on the excited states of DNA molecules. Our results fill the gap between theory and experiment on the excited-state energy levels of DNA in aqueous solution. We think that it is crucial that approximate solvent models reproduce the electronic structure of solute molecules in solvent when using them in excited state calculations. Although our studies are focused on adenine-thymine complexes, the conclusions should be also applicable to guanine-cytosine complexes. We believe that the influence of aqueous solution on the CT excitations in other stacked systems, e.g., RNA, might also be of great importance. This work was supported by the National Natural Science Foundation of China (Grants No. 21173130 and No. 91127014) and the Natural Science Foundation of
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Shandong Province (Grant No. BS2012CL022). Computational resources have been provided by the National Supercomputing Centers in Jinan and Tianjin (TH-1A system).
*
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[25] M. K. Shukla and J. Leszczynski, J. Comput. Chem. 25, 768 (2004). [26] M. K. Shukla and P. C. Mishra, Chem. Phys. 240, 319 (1999). [27] C. W. Swartz and X. F. Wu, Phys. Rev. Lett. 111, 087801 (2013).
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[28] A. Hermann, W. G. Schmidt, and P. Schwerdtfeger, Phys. Rev. Lett. 100, 207403 (2008). [29] P. L. Silvestrelli and M. Parrinello, Phys. Rev. Lett. 82, 3308 (1999). [30] M. J. Frisch et al., GAUSSIAN 09, Revision B.01 (Gaussian, Inc., Wallingford, CT, 2010).
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Charge-Transfer Excited States in Aqueous DNA: Insights from Many-Body Green’s Function Theory 1
Huabing Yin,1 Yuchen Ma,1,* Jinglin Mu,1 Chengbu Liu,1,† and Michael Rohlfing2 School of Chemistry and Chemical Engineering, Shandong University, Jinan 250100, People’s Republic of China 2 Institut für Festkörpertheorie, Universität Münster, 48149 Münster, Germany (Received 13 December 2013; published 3 June 2014) Charge-transfer (CT) excited states play an important role in the excited-state dynamics of DNA in aqueous solution. However, there is still much controversy on their energies. By ab initio many-body Green’s function theory, together with classical molecular dynamics simulations, we confirm the existence of CT states at the lower energy side of the optical absorption maximum in aqueous DNA as observed in experiments. We find that the hydration shell can exert strong effects (∼1 eV) on both the electronic structure and CT states of DNA molecules through dipole electric fields. In this case, the solvent cannot be simply regarded as a macroscopic screening medium as usual. The influence of base stacking and base pairing on the CT states is also discussed. DOI: 10.1103/PhysRevLett.112.228301
PACS numbers: 82.37.Vb, 78.40.Dw, 78.40.Me, 87.15.-v
The absorption of solar ultraviolet (UV) light could induce a series of photophysics and photochemistry processes in DNA, resulting in radiation damages and carcinogenic mutations in the biological hereditary process [1]. Understanding the physical mechanism of excited-state dynamics in DNA is extremely important for life and is also an exciting challenge for scientific research due to the complexity in biological systems. It has been generally accepted that charge-transfer (CT) states play a vital role in the excited-state process of DNA, modulating the excitedstate decay of DNA and the probability for gene mutations [2,3]. For example, the bright ππ states [ππ ðBÞ] produced by UV absorption can rapidly decay to long-lived CT-like states, e.g., excimer and exciplex states [4,5]. Experiments suggest that CT states should be responsible for the weak UV absorption at the long wavelength region around 330 nm [6]. However, our knowledge of the CT states in DNA is still scarce; especially, there is much controversy on the energies of CT states [6]. A huge discrepancy still exists between experiment and theory. Theoretical calculations by high-level quantum chemistry approaches, such as the second-order approximate coupled-cluster method, have positioned the CT states of the single-stranded adenine dimer ðAdeÞ2 high above the ππ ðBÞ state in energy [7,8], which is contrary to the experiments. The deviation can be attributed to the difference between the calculation models [ðAdeÞ2 in the gas phase] and experimental condition [ðAdeÞ20 in aqueous solution]. Extra base-stacking interaction in ðAdeÞ20 compared to ðAdeÞ2 may lower the CT states, but its effect is not supposed to be strong enough to induce a large redshift (∼0.4 eV according to our calculations as discussed below). This raises an important question: how does the aqueous solution influence CT states? This question cannot be solved by the high-level 0031-9007=14=112(22)=228301(5)
quantum chemistry methods at present due to the necessity to include enough solvent molecules in calculations and the tremendous computational load thereafter. Instead, approximate approaches, including the combined quantum mechanics and molecular mechanics methods, and implicit solvation models, such as the polarizable continuum model (PCM), are usually applied in combination with the timedependent density functional theory [7–9]. Although much work has been done with these approaches for a variety of DNA structure models, there is still a large gap between theory and experiment. These methods predict that aqueous solution redshifts CT states by about 0.1 eV [8]. To be consistent with experiments, the effect of aqueous solution on CT states should be on the order of 1 eV. The deficiencies in these methods, such as the simplification of water molecules by points charges, the approximate exchangecorrelation functionals used in density functional theory (DFT), might be the origins for the large error. Water and CT are very important in biological systems and also in material science; it is quite necessary and also fundamental to clarify the effect of water on CT states. In this work, we reexamine this problem with a state-of-the-art ab initio method: many-body Green’s function theory, in particular the GW method and the Bethe-Salpeter equation (BSE) [10–12]. The GW method and the BSE (GW-BSE) can compute single-particle states and excitons with high accuracy, and have been successfully applied to study CT excitations between organic molecules [13–15]. Enough water molecules are explicitly included in the calculations to model the aqueous environment encompassing DNA molecules. We will show that the dipole electric field from the hydration shell can exert considerable impact on the single-particle states of DNA molecules, which causes significant redshifts of the CT states. Taking also into account the base-stacking and base-pairing effects, our
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calculations satisfactorily confirm the existence of CT states at the long wavelength side of absorption peaks. They cannot only help us understand in depth but also give some hints to tune the excited-state dynamics and charge transfer in DNA. We use adenine-thymine complexes, which have been investigated widely in recent experiments, as the DNA structure models to conduct our research, including singlestranded polyadenine oligomers [ðAdeÞn ], single-stranded alternating adenine-thymine dimer [AdeThy], and doublestranded adenine-thymine pair oligomers [ðAde∶ThyÞn ]. Their behaviors in aqueous solution are modeled by clusters like ðAdeÞn -ðH2 OÞm , which are constructed through classical molecular dynamics simulations. GW-BSE calculations are carried out by a Gaussian-orbital based code [11,12,16]. BSE calculations are performed at two levels. For small systems, we use the full BSE, which considers the mixing between resonant and antiresonant transitions [14,17,18] and dynamical screening effects in the electron-hole interaction [18]. For larger systems, we applied the BSE within the Tamm-Dancoff approximation (TDA) and the static screening limit in the electron-hole interaction. The full BSE is more accurate but its computational cost is very high. However, for CT states which are the focus of this work, the energy difference between the full BSE and the BSE-TDA is smaller than 0.1 eV (see the Supplemental Material [19]). The BSE-TDA is a good compromise. Details on the calculation strategies and the construction of models are provided in the Supplemental Material [19]. For the gas-phase adenine (thymine) monomer, the gap between the highest occupied molecular orbital (HOMO=H) and the lowest unoccupied molecular orbital (LUMO=L) is 9.21 eV ð9.51 eVÞ from our GW calculations, which agree well with experiments and previous calculations by the GW method [20] and complete active space with second-order perturbation theory [21,22]. The absorption peaks are formed by ππ ðBÞ excitons. The full BSE predicts very well the energies of ππ ðBÞ states (see Table I). The Supplemental Material [19] gives a comprehensive comparison between our results and those by other first-principles approaches. For adenine monomer in aqueous solution, the energy of ππ ðBÞ from the full BSE is 4.69 eV on average, 0.16 eV redshifted relative to that in the gas phase. This is consistent with experiments (redshifting from 4.92 eV to 4.77 eV) [23,24]. In ðAdeÞ2 , ππ ðBÞ and the lowest CT (CT-min) are both composed by transitions H − 1=H → L=L þ 1 [see Fig. 1(a)]. However, the binding energy of the CT-min exciton is 1 eV smaller than that of the ππ ðBÞ one, making CT-min above ππ ðBÞ in energy by a large amount (see Table I). For ðAdeÞn, the position of the absorption peak changes little with n. The energy of CT-min decreases by 0.35 eV from ðAdeÞ2 to ðAdeÞ5 . For CT-min, the excited electron and hole are localized on two adjacent bases; their binding energy changes little with n. The evolution of the
TABLE I. Energies of the ππ ðBÞ and the lowest CT (CT-min) excitations for some adenine-thymine DNA models in the gas phase calculated by the full BSE.a ππ ðBÞ Model Ade Thy ðAdeÞ2 ðAdeÞ3 ðAdeÞ5 AdeThy Ade:Thy ðAde∶ThyÞ2
Ade b
4.85 4.77 4.74 4.74 4.61 4.77 4.77
CT-min
Thy
Ade → Ade
Ade → Thy
4.68c 4.56 4.55
5.75 5.52 5.40 5.61
5.16 5.72 5.50
a
Energies are in electron volts. Experimental value: 4.92 eV [23]. c Experimental value: 4.8 eV [23], 4.5–4.9 eV [25], 4.7 eV [26] b
CT-min energy with n can be estimated according to the gap between H and L, the transition between which dominates CT-min. From ðAdeÞ5 to ðAdeÞ8 , the H-L gap decreases little (see the Supplemental Material [19]). So the energy of CT-min for longer adenine oligomers will be close to that of ðAdeÞ5 . The effect of base stacking on the CT state should be ∼0.4 eV. We study eight ðAdeÞ2 -ðH2 OÞm clusters for adenine dimer in aqueous solution. Figure 2 illustrates the excited
FIG. 1 (color online). (a) Energy diagrams of the molecular orbitals for ðAdeÞ2 in the gas phase and in aqueous solution (modeled by an ðAdeÞ2 -ðH2 OÞ31 cluster at the D8 configuration) calculated by the GW method. Solid arrows illustrate the transitions that constitute the states CT-min and ππ ðBÞ. Dashed and dotted lines denote molecular orbitals that are localized on different adenine bases. (b) Real-space distribution of orbitals H=L and excitons CT-min=ππ ðBÞ [yellow (light gray): excited electron; light blue (gray): hole] for the gas-phase ðAdeÞ2 . (c) Real-space distribution of molecular orbitals for ðAdeÞ2 -ðH2 OÞ31.
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FIG. 2 (color online). Energies of the low-lying excited states for the eight ðAdeÞ2 -ðH2 OÞm clusters (D1-D8) and the gas-phase ðAdeÞ2 calculated by the BSE-TDA. ππ ðWÞ denotes the state with weak oscillator strength. The ππ ðBÞ states of D1-D8 are linked by a red dashed line.
states for them (D1–D8) computed by the BSE-TDA. ππ ðBÞ is redshifted by 0.14 eV on average compared to the gas-phase counterpart. The most amazing result is that some CT states appear below ππ ðBÞ. The energy of CT-min is lowered by 0.7–1.0 eV in aqueous solution. CT states discussed here are only related to transitions between nucleobases. CT between nucleobases and water molecules is not observed in this energy range. We take one of the ðAdeÞ2 -ðH2 OÞm clusters, D8, which contains 31 water molecules, as the example to explain the different behavior of CT states in the gas phase and aqueous solution. In the gas phase, H and H − 1, L and L þ 1, L þ 2 and L þ 3 of ðAdeÞ2 are degenerate, and they are all distributed equally on two nucleobases (see Fig. 1). In aqueous solution, the degeneracies are all lifted. The splitting between H and H − 1 reaches 1.4 eV. HðLÞ is shifted up (down) by 0.4 eV (0.8 eV), narrowing the H-L gap by 1.2 eV. Molecular orbitals, moreover, become localized on single nucleobases [Fig. 1(c)], especially with H=L þ 2=L þ 3 on a base, and H − 1=L=L þ 1 on another one. The transition H → L apparently forms the greatly redshifted CT-min. The lowest ππ ðBÞ is formed mainly by transitions H → L þ 2 and H − 1 → L with the former dominating. By doubling the number of water molecules in D8, the H-L gap changes little; i.e., the size of the ðAdeÞ2 -ðH2 OÞm clusters we construct is large enough to simulate the behavior of ðAdeÞ2 in aqueous solution. This is in accordance with previous calculations on hydroxide and hydronium showing that the influence of solvent water molecules on the electronic levels of solute molecules is mainly determined by the first hydration shell [27]. Certainly, the variation of electronic levels enlarges gradually with the increase of water molecules within the first hydration shell as shown in the Supplemental Material [19]. In the ground state there is some electron transfer between ðAdeÞ2 and nearby water molecules as can be
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seen from the occupied molecular orbitals shown in Fig. 1(c). This may break the symmetry in the gas-phase ðAdeÞ2 and lead to the reorganization of molecular orbitals as discussed above. The interaction between ðAdeÞ2 and the hydration shell is dominated by the long-range electrostatic potential. Now we model this potential in ðAdeÞ2 -ðH2 OÞ31 of D8 by replacing the oxygen and hydrogen atoms in water molecules by point charges whose magnitudes are adjusted according to the dipole moment of water in liquid [28,29]. In this model, the splitting between H and H − 1 is calculated to be 0.6 eV by DFT with the GAUSSIAN09 code [30], which reproduces that in the explicit ðAdeÞ2 -ðH2 OÞ31 model (0.7 eV by DFT). So the huge changes in the electronic structure and CT states of ðAdeÞ2 can be ascribed to the dipole electric field caused by the hydration shell. Based on this, it may be possible to modulate the excited-state dynamics of DNA molecules through external electric fields. We also performed a DFT-PCM calculation by the GAUSSIAN09 code for ðAdeÞ2, which shows that the implicit solvation model only causes respective rigid shifts of the occupied and virtual levels, modifying the H-L gap by just 0.04 eV. So aqueous solution does not just play the macroscopic screening role in DNA; its microscopic effects must be paid more attention to and implicit solvation models may have some limitations in this respect. In ðAdeÞ3 -ðH2 OÞm clusters, the gap between H and L (between H and H − 1) is also narrowed (enlarged) by more than 1.0 eV relative to those in the gas-phase ðAdeÞ3 . Compared to ðAdeÞ2 -ðH2 OÞm , CT-min is further redshifted by about 0.2 eV, while the energy of ππ ðBÞ is nearly the same. These trends are the same as those in the gas phase. From Fig. 3, we can clearly see the extension of optical
FIG. 3 (color online). (a) Optical absorption spectra of an Ade-ðH2 OÞm (black), an ðAdeÞ2 -ðH2 OÞm (red), and an ðAdeÞ3 -ðH2 OÞm (blue) cluster calculated by the BSE-TDA (solid line) and the full BSE (dash line). Vertical lines denote the positions of the states ππ ðBÞ and CT-min (the ones at 4.55 and 4.83 eV). Note that for Ade-ðH2 OÞm, there is no CT state, so there is only one black vertical line.
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absorption tails to the long-wavelength region from adenine monomer to trimer, which is due to the contribution from CT states. Taking into account the effects of both aqueous solution and base-stacking interaction, we can estimate that CT states can emerge ∼0.3 eV below the absorption peak of ðAdeÞ20 in aqueous solution. This is in good agreement with recent experiments, supporting their speculations [6]. CT states are sensitive to the local configuration of the hydration shell at room temperature as can be seen from Fig. 2, which makes them spread over a wide spectral range. In the single-stranded AdeThy dimer, molecular orbitals are nondegenerate. H and L are localized on adenine and thymine monomers, respectively, the transition between which constitutes CT-min. Surrounding AdeThy by a hydration shell reduces its H-L gap by about 0.6 eV, redshifting CT-min to the same extent accordingly (see the Supplemental Material [19]). These effects are much weaker than those in ðAdeÞ2 . However, due to the lower energy (by 0.6 eV) of CT-min in AdeThy than that in ðAdeÞ2 in the gas phase (Table I), in aqueous solution the energy of CT-min in AdeThy is close to that in ðAdeÞ2 . We also study the influence of base pairing on CT states (Table I). From ðAdeÞn to ðAde∶ThyÞn (n ¼ 2; 3), the lowest intrastrand CT state among the adenine bases redshifts by about 0.15 eV. The lowest interstrand CT transition is 0.10 eV lower than the lowest intrastrand one. Due to the large dimension of ðAde∶ThyÞn , it is hard to study its excited states in aqueous solution by the GW-BSE at present. But we can undoubtedly come to the conclusion that base pairing can further enhance the UV absorption in terms of both intensity and spectral range in the longwavelength region through CT transitions, as has been observed in recent experiments [6]. In summary, using high-level first-principles calculations, we have found that aqueous solution can significantly modify the electronic structure of DNA molecules through dipole electric fields, stabilizing CT states at long wavelengths. We give a comprehensive picture of the effects of base stacking, base pairing, and aqueous environment on the excited states of DNA molecules. Our results fill the gap between theory and experiment on the excited-state energy levels of DNA in aqueous solution. We think that it is crucial that approximate solvent models reproduce the electronic structure of solute molecules in solvent when using them in excited state calculations. Although our studies are focused on adenine-thymine complexes, the conclusions should be also applicable to guanine-cytosine complexes. We believe that the influence of aqueous solution on the CT excitations in other stacked systems, e.g., RNA, might also be of great importance. This work was supported by the National Natural Science Foundation of China (Grants No. 21173130 and No. 91127014) and the Natural Science Foundation of
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Shandong Province (Grant No. BS2012CL022). Computational resources have been provided by the National Supercomputing Centers in Jinan and Tianjin (TH-1A system).
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