Electronic Polarization Effect of the Water Environment in Charge

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Electronic Polarization Effect of the Water Environment in Charge-Separated Donor-Acceptor Systems: An Effective Fragment Potential Model Study Kazuma Yanai, Kazuya Ishimura, Akira Nakayama, Michael W. Schmidt, Mark S. Gordon, and Jun-ya Hasegawa J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b10552 • Publication Date (Web): 30 Nov 2016 Downloaded from http://pubs.acs.org on December 9, 2016

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The Journal of Physical Chemistry

Electronic Polarization Effect of the Water Environment in Charge-Separated Donor-Acceptor Systems: An Effective Fragment Potential Model Study

Kazuma Yanai,† Kazuya Ishimura,‡ Akira Nakayama,† Michael W. Schmidt,§ Mark S. Gordon,§ Jun-ya Hasegawa†, ǁ, *

† Institute for Catalysis, Hokkaido University, Kita 21, Nishi 10, Kita-ku, Sapporo 001-0021, Japan ‡ Department of Theoretical and Computational Molecular Science, Institute for Molecular Science 38 Nishigo-Naka, Myodaiji, Okazaki 444-8585, Japan § Department of Chemistry and Ames Laboratory, Iowa State University, Ames, Iowa, 50011, U. S. A. ǁ JST-CREST, 4-1-8 Honcho, Kawaguchi, Saitama, 332-0012, Japan * Corresponding author, e-mail: [email protected]

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Abstract The electronic polarization (POL) of the surrounding environment plays a crucial role in the energetics of charge-separated systems. Here, the mechanism of POL in charge-separated systems is studied using a combined quantum mechanical and effective fragment potential (QM/EFP) method. In particular, the POL effect caused by charge separation (CS) is investigated at the atomic level by decomposition into the POL at each polarizability point. The relevance of the electric field generated by the CS is analyzed in detail. The model systems investigated are Na+–Cl- and guanine–thymine solvated in water. The dominant part of the POL arises from solvent molecules close to the donor (D) and acceptor (A) units. At short D–A distances, the electric field shows both positive and negative interferences. The former case enhances the POL energy. At longer distances, the interference is weakened, and the local electric field determines the POL energy.


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1. Introduction Charge separation (CS) is an essential process in photoelectron conversion systems, such as biological photosynthetic systems1 and solar cells2-3. Adjusting the energy of the CS state should improve the efficiency of the energy conversion.4-7 To study CS systems by computational chemistry, it is necessary to model molecular interactions with the surrounding environment because the energetics of the CS process are sensitive to the environment.8-11 In particular, polarization (POL) interactions noticeably contribute to the energetics of the CS state.12-14 For example, computational studies have been reported on the CS energetics in photosynthetic reaction centers (PSRC), and the stabilization of the CS states by POL interactions were illustrated using the dielectric continuum model.12, 15-18 Blomberg et al. performed DFT(B3LYP) with self-consistent reaction field (SCRF) calculations for bacteriochlorophylls and quinones in the PSRC. They reported that the POL effect on CS states was estimated to be approximately 50 kcal/mol.15 Zerner et al., using the ZINDO method, also reported that longer donor (D) and acceptor (A) distances in the CS state of the chromophores in the PSRC of Rhodopseudomonas viridis can increase POL interactions in SCRF calculations.12 However, little is known about the microscopic mechanism of POL interactions in CS states, in particular the D-A distance dependence, at an atomic level. In our previous studies18-21, we investigated molecular interactions in the excited states of photofunctional proteins using the three-layer ONIOM (QM/QM/MM) method22-23. Quantum mechanical interactions with the environment were found to be non-negligible in the calculated excitation energy of retinal Schiff bases.24, 19-20 Furthermore, we developed the first-order interactions space (FOIS) method, by which the effects of second-order molecular interactions on the calculated excitation energies are decomposed into polarization and dispersion interactions.21 However, the application of this method is limited to small systems. Gordon et al. have developed the effective fragment potential (EFP) method.25-28 The EFP method is based on the theory of molecular interactions and is able to reproduce ab initio calculations of molecular interactions with an accuracy that is equivalent to that of second order perturbation theory (MP2). The DFT based EFP129-30, which we used in the present study, was designed for the water molecule. The interaction energy in the QM/EFP system is written as: + + + Ψ 1 = Ψ and are one-electron operators that represent the Coulomb and polarization interactions between the QM and EFP1 (water) parts of the system. Vrem is a fitted remainder term that represents the exchange repulsion and charge transfer interactions. EFP1 has been combined with TDDFT and applied to the hydrogen atom transfer reaction of water-solvated 7-hydroxy-4-methylcoumarin in the excited state31 and to

the intramolecular CS state in water-solvated p-nitroaniline.32-33 In the EFP1 method, the POL energy due to the electric field of the QM region can be written as: "

,,-,.

,,-,.

'

'

1 1 = − % &'" (')*," − % &'" ('/0," 2 2

. 2

( )* and ( /0 are the electric fields originating from the density and nuclei in the QM region, respectively,

and & " are induced dipoles at the polarizability point 2, respectively. There are five polarizability points in an EFP water model, as shown in Figure 1a. In the EFP method, the polarizability is described in terms of localized molecular orbitals (LMOs), and the polarizability expansion points are taken to be the LMO centroids. For a water molecule, for example, there are four or five polarizabilty expansion points, depending on whether or not the oxygen inner ACS Paragon Plus Environment


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shell is included. In the present study, we analyzed the POL interactions between the solute and the EFP waters in CS states. In particular, the POL energy was decomposed into each polarizability point in the water molecule. The magnitude of POL was analyzed in terms of the electric field that is generated by the D and A units in the CS state. Many-body effect in CS states is also an interesting subject but beyond our scope of the present study. The article outline is as follows. The computational details are described in the next section. In Section 3, we employ a simple model to determine the physical basis of the POL interaction. For this purpose, the electric fields in the CS system are classified into three types. In subsection 3.2, a Na+ and Cl- ion pair system solvated in water was used for clarifying the mechanism of POL energy generation. In subsection 3.3, a CS state of guanine and thymine solvated in water was investigated as a more realistic CS state model. A characteristic feature of the POL energy generation was investigated at the atomic level, and the origin of the distance dependence in the POL energy was interpreted. Finally, a summary is given in Section 4. 2. Computational details To investigate the polarization energy for different guanine (D)-thymine (A) distances, we employed two models: a 7 Å model and a 13 Å model, as shown in Figures 1b and 1c, respectively. In the 7 Å and 13 Å models, the D–A distances are 7 Å and 13 Å, respectively. For the guanine-thymine models, the average of atomic coordinates among the C, N, and O atoms in each D and A unit were used to define the distance. The structures were obtained using a classical molecular dynamics (MD) simulation. To prepare the initial structure, guanine and thymine were optimized in the gas phase with a classical force field, and 1685 and 2471 TIP3P water molecules34 of the 7 Å and 13 Å models, respectively, were positioned around the guanine-thymine pair. For periodic boundary conditions of the 7 Å and 13 Å models, rectangular cells of 41 × 39 × 45 Å3 and 45 × 43 × 55 Å3 were used, respectively. Particle-mesh Ewald method35 was used to compute long-range electrostatic interactions. The MD simulations employed the general Amber force field (GAFF)36 and were performed over an NPT ensemble at a constant pressure of 1 bar. The time step was 0.5 fs, and the total simulation time was 5 ns. To equilibrate the system, the initial temperature of 500 K was reduced by an annealing method and maintained at the equilibrated temperature of 300 K with the Nosé-Hoover thermostat.37-38 To constrain the atomic coordinates of guanine and thymine in the initial structure, a harmonic potential with a force constant of 5 kcal/mol was applied. A total of 11 snapshots were taken randomly from the obtained trajectory (3-5 ns). The Amber 10 program package39, 36 was used for the classical molecular dynamics (MD) simulations. In the snapshots, the solvent box was trimmed to 10 Å from the center of each guanine and thymine unit. In regards to the QM-EFP border, guanine and thymine were calculated according to QM, and the remainder of the system was treated with the EFP method. The number of water molecules in the 7 Å and 13 Å models was 220 and 280, respectively. The number of polarizability points was 1100 and 1400, respectively. For each snapshot, the molecules treated by QM were further optimized using the CAM-B3LYP40 functional with the 6-31G(d) basis set in the presence of the fixed EFP waters. The ground and CS states energies were calculated using the PBE41 functional with the 6-31G(d) basis set. As reported in a previous study42, the electron is transferred from the HOMO of guanine to the LUMO of thymine in the CS state. The spin multiplicities of the ground and CS states was singlet and triplet, respectively. For the triplet states, the restricted open-shell DFT method was used. ACS Paragon Plus Environment

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The Journal of Physical Chemistry (a) EFP1 water

(b) 7 Å model

(c) 13 Å model

Figure 1. (a) EFP1 water was used for the solvent model. The green points denote polarizability points. Computational models for a guanine–thymine system solvated in water. In the (b) 7 Å model and (c) 13 Å model, the D-A distance is 7 Å and 13 Å, respectively.

Na+ and Cl- ions solvated in water were investigated as a model CS state. Using two models: a 2.4 Å model and a 5 Å model, as shown in Figures 2a and b, respectively. In the 2.4 Å and 5 Å models, the D and A distances were 2.4 Å and 5 Å, respectively. The structures were obtained using QM/EFP-MD simulations. The QM region contained the Na+ and Cl- ions, and the remainder was the EFP region. The number of water molecules was 160 in both models. The number of polarizability points was 800 in both models. A harmonic potential with a force constant of 100 kcal/mol was applied to constrain the EFP1 waters within a 10 Å radius from the center of the Na+ and Cl- ions.43 The QM/EFP-MD simulations were performed over a NVT ensemble. The time step was 1 fs, the total simulation time was 20 ps, and equilibration was confirmed at 10 ps. The equilibrated temperature of 300 K was maintained using the Nosé-Hoover thermostat.37-38 The QM molecules were calculated using the CAM-B3LYP40 functional with the 6-31G(d) basis set. The GAMESS program package44 was used for all QM-EFP calculations. The GaussView program package was used for the visualizations.45 To analyze the POL energy at each polarizability point, we modified the GAMESS program to show the electric fields and induced dipoles at each polarizability point.

(a) 2.4 Å model

Cl

(b) 5.0 Å model

Na

Cl

Na

Figure 2. Na+-Cl- ion pair models for a CS state solvated in water: (a) the 2.4 Å model and (b) the 5 Å model.



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3. Results and Discussion 3.1 Investigation a CS state of a simplified model system To understand the interference of the electric fields by the D and A units over short and large separations, we employed a monopole charge model, as shown in Figure 3. As shown in Figure 3a, over short separations, the electric field vectors between the D and A units strengthen relative to the electric field of isolated monopole charge, while the electric field vectors in the outer region are weakened. Hereafter, we call such enhancement and cancellation effects of the electric fields positive interference fields (PIF) and negative interference fields (NIF), respectively. Over large separations, the electric-field vectors interfere with one another less, as shown in Figure 3b. We call this electric field a local non-interference field (LNF). (a) Closely lying charge pair (short distance separation) 1. Electric field vector 2. Electrical flux line

PIF NIF

NIF

(b) Separated charge pair (long distance separation) 1. Electric field vector 2. Electrical flux line

LNF

LNF

Figure 3. Electric field and electrical flux lines in the simplified charge-separated systems: (a) a closely lying charge pair (short distance separation) and (b) a separated charge pair (long distance separation). Arrows denote electric-field vectors due to electric monopoles. The width of the arrow approximately represents the length of the electric-field vector.


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3.2 Electronic polarization of water solvent in a simple system Initially, we used a Na+ Cl- ion pair solvated in water as a model CS state. This simple system is useful for illustrating the polarization mechanism and its dependence on the electric field. To analyze the effects of the D-A distance, two Na+-Cl- distances, 2.4 Å and 5.0 Å, were investigated (hereafter, these models are called the 2.4 Å and 5 Å models, respectively). In the 2.4 Å and 5 Å models, the EFP water molecules stabilize the total energy by 8.55 eV and 10.07 eV, respectively, relative to the total energy without EFP. In the EFP contribution, the electrostatic (ES) interactions of the 2.4 Å and 5 Å models are 9.03 eV and 9.63 eV, respectively. The electronic polarization (POL) interaction contributes 1.14 eV and 1.59 eV, respectively. Longer distance CS generates larger POL contributions, as indicated in a previous study using the SCRF model.12 The polarizability points that effectively stabilized the system are visualized in Figure 4-1. The number of polarizability points with stabilizations larger than |0.03| eV is 12 and 10 in the 2.4 Å and 5 Å models, respectively, as shown in the lower half of Figure 4-1. In the 2.4 Å model, the POL contribution from these points is -0.73 eV, which accounts for 64% of the total POL energy. In the 5 Å model, the POL contribution is -0.93 eV, which accounts for 58% of the total POL energy. One striking difference between the 2.4 Å and 5 Å models is in the polarizability points that stabilize the polarization energy by more than 0.1 eV. As shown in the upper half of Figure 4-1a, there are no polarizability points with significant stabilization in the 2.4 Å model. However, three such polarizability points are found in the 5 Å model (see Figure 4-1b). These three points alone contribute -0.54 eV to the POL energy, which accounts for 34% of the entire POL energy. The polarizability points with enhanced POL interactions were located between the Na+ and Cl- ions and are highlighted by a purple circle in Figure 4-1b. At the -0.03 eV threshold, 6 of the 10 points were located between the Na+ and Cl- ions. Because the POL energy is defined as the inner product of the electric fields arising from the QM region and the induced dipole at the polarizability point (see Eq. 2), the electric fields arising from the QM region are visualized for the 2.4 Å and 5 Å models, as shown in Figure 4-2a and 4-2b, respectively. We found a PIF at the polarizability points between Na+ and Cl- in the 5 Å model. The results show that the electric field is enhanced in the space between the D and A units and that the polarizability points in this space contribute to the enhanced POL interaction energy. However, an enhanced POL interaction energy is not observed in the 2.4 Å model, because there is no space for solvent molecules between the Na+ and Cl- ions.



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(1) Polarizability points with large energetic contributions (a) 2.4 Å model (b) 5.0 Å model 34 34 " 5 −0.1 eV " 5 −0.1 eV

Cl

Na

Cl

34 " 5 −0.03 eV

Na

34 " 5 −0.03 eV

Cl Na Cl

Na

(2) Electric field at polarizability points (b) 5.0 Å model (a) 2.4 Å model

34 Figure 4. (1) Polarizability points that contribute polarization energy " 5 -0.1 eV (upper figures) and

34 " 5 -0.03 eV (lower figures) are shown as yellow balls with black circles. (2) Electric fields at the O

atoms due to the Na+ Cl- pair. The results of the (a) 2.4 Å model and (b) 5.0 Å model are illustrated. The

purple and green balls represent Na+ and Cl-, respectively.


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3.3 Guanine–thymine system in aqueous solution Table 1 shows the EFP contributions decomposed into electrostatic (ES), POL, and exchange-repulsion plus charge-transfer (EX+CT) interactions in the ground and charge-separation (CS) states of the 7 and 13 Å models. The electronic structures of guanine and thymine of the 7 and 13 Å models are similar to each other in the ground and CS states. In the CS state, one electron is transferred from guanine to thymine42. The ∆ value in Table 1 denotes the difference between the CS and ground states, which is the contribution to the excitation energy. For the ES interaction, the ∆ values in the 7 Å and 13 Å models are 0.85 eV and 0.69 eV, respectively, which were the largest contributions among the components. The ES interaction increases the excitation energies in both the 7 Å and 13 Å models in the present study, focusing on the vertical excitation from the ground state. The structures used were taken from the ground state MD trajectory. For the POL interaction, the ∆ values in the 7 Å and 13 Å models are -0.55 eV and -0.78 eV, respectively. The POL interaction lowers the excitation energies in both the 7 Å and 13 Å models. In contrast to the ES interaction, the POL contribution in the CS state is larger than that in the ground state, because the electric field around guanine and thymine in the CS state is more intense than that in the ground state. Furthermore, the POL contribution to the excitation energy in the 13 Å model is 0.23 eV larger than that in the 7 Å model. The results indicate that the POL interaction becomes the dominant contributor at longer D-A distances, which is the same trend as observed in the Na+-Cl- model (1.14 eV and 1.59 eV in the 2.4 Å and 5 Å models, respectively). The results also show the same behavior as for the CS state in a photosynthetic reaction center studied with the SCRF model.12

Table 1. The EFP contribution to the total energy decomposed into ES, POL, and exchange-repulsion plus charge-transfer (Ex+CT) interactions. The analysis was performed for the ground and CS states of the 7 Å model and 13 Å model of the guanine-thymine pair. These values are averaged over 11 snapshots. Units are eV. Term

Ground state

CS state

∆a

7 Å model Electrostatic

-7.21

-6.36

0.85

Polarization

-0.71

-1.10

-0.55

0.25

0.24

-0.01

-7.81

-7.52

0.29

Ex+CT Total

13 Å model Electrostatic

-8.03

-7.34

0.69

Polarization

-1.04

-1.82

-0.78



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Ex+CT Total a

0.35

0.34

-0.00

-8.82

-8.72

-0.10

The ∆ value denotes (CS state) – (Ground state).


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The contribution of the POL energy to the excitation energy was also investigated. We selected one of the snapshots (∆ = -0.38 eV and -0.69 eV in the 7 Å and 13 Å models, respectively) and classified the polarizability points in terms of the absolute value of the POL energy as follows: (i) 0.000 eV 6 POL 2 5 POL 34 0.005 eV, (ii) 0.005 eV 6 POL 2 5 0.010 eV, (iii) 0.010 eV 6 2 5 0.022 eV, and (iv) " :

0.022 eV. The thresholds were determined on the basis of the POL energy distribution (see Figure S1 in supporting information). The results of the 7 Å and 13 Å models are shown in Figures 5a and 5b, respectively. For each class, the number of polarizability points and the POL energy are represented by both the percentage and actual value (shown in parentheses). The results indicate that a small number of polarizability points generate the majority of the POL energy. This trend is observed in both the 7 Å and 13 Å models. In the energy range of 0.005 eV 6 POL 2 5 0.022 eV, even though there are only 42 (10%) and 185 (13%) polarizability points in the 7 Å and 13 Å models, respectively, the contribution to the POL energy reaches 78% (-0.3 eV) and 87% (-0.6 eV) in the 7 Å and 13 Å models, respectively. We also note that these polarizability points greatly influence the dependence of the POL energy on the D-A distance. 34 On the other hand, the upper class that is defined as " ; 0.022 eV has only 9 polarizability points (1%) and contributes 10–15% (-0.06 eV and -0.07 eV in the 7 Å and 13 Å models, respectively) of the POL energy. Most of the polarizability points fall into the energy range of 0.000 eV 6 POL 2 5 0.005 eV: 977 polarizability points (89%) and 1206 polarizability points (86%) in the 7 Å and 13 Å models, respectively. These polarizability points, however, contribute only 8% (-0.03 eV) and 3% (-0.02 eV) of the POL energy in the 7 Å and 13 Å models, respectively.

(a) 7 Å model

(b) 13 Å model

Figure 5. Contributions to the polarization energy that are classified into several energy ranges for the (a) 7 Å and (b) 13 Å models. The absolute value of the polarization energy was used for the classification. For each class, the number of polarizability points and their energy contributions are given in percentages with actual values in parenthesis. ACS Paragon Plus Environment


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The spatial distribution of the polarizability points that effectively stabilize the CS state are visualized in Figure 6. The snapshots of the CS states given in Figure 5 were used. In the 7 Å and 13 Å models, the EFP water molecules stabilize the total POL energy by -1.10 eV and -1.59 eV, respectively. The polarizability points with stabilizations larger than 0.01 eV are colored yellow in the upper half of Figures 6a and 6b. The number of polarizability points in the 7 Å and 13 Å models are 27 and 40, respectively. In the 7 Å model, the contribution to the POL interaction energy from these points is -0.98 eV, which accounts for 89% of the total POL interaction energy. In the 13 Å model, the contribution to the POL interaction energy is -1.40 eV, which accounts for 89% of the total POL interaction energy. In the 7 Å model, 20 of the 27 points (74%) are located in the space between guanine and thymine. In the 13 Å model, 27 of the 40 points (68%) are located between guanine and thymine. It is notable that, in the 13 Å model, more yellow points are found in the area surrounding guanine and thymine. The polarizability points with stabilizations larger than 0.03 eV are shown in the lower half of Figure 6. The number of the polarizability points in the 7 Å and 13 Å models are similar (3 and 2, respectively). These points located are on the EFP waters that have hydrogen bonds to the carbonyl O atom in thymine. As we discuss later, the charge of this O atom changes significantly upon charge separation.

(a) 7 Å model 34 " 5 −0.01 eV

(b) 13 Å model 34 " 5 −0.01 eV

34 " 5 −0.03 eV

34 " 5 −0.03

34 34 Figure 6. Polarizability points with POL energies " 5 -0.01 eV and " 5 -0.03 eV are shown as

yellow balls with black circles in the upper and lower figures, respectively. The results of the (a) 7 Å model and (b) 13 Å model are illustrated.


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The electric fields arising from the QM region are visualized for the 7 Å and 13 Å models, as shown in Figures 7-1a and 7-1b, respectively, for the reason that the POL energy is defined as the inner product of the electric field arising from the QM region and the induced dipole at the polarizability point (see Eq. 2). In the 7 Å model, the results show that the electric field is enhanced in the space between the D and A units relative to that in the 13 Å model. The polarizability points in this space contribute to the enhanced POL energy. However, electric fields are weakened outside the D-A unit, which would represent the cancelation of the electric field from guanine and thymine. That is, we found a PIF at the polarizability points between guanine and thymine and an NIF at the polarizability points in the outer area. Essentially, the mechanism is the same as the 5 Å Na+-Cl- model. Now, consider hydration structure and its relevance to the electric field. In a previous study, Choi, Sugita, and co-workers calculated Na+-Cl- in a water (EFP) system.46 They analyzed the interionic hydration structure and found ring and bridge structures. The snapshots in the present analysis also involve a so-called “full-bridge” structure (See Figure S3 in SI). However, the snapshots were taken from molecular dynamics trajectory with a classical non-polarizable force field. Therefore, the formation of the bridged structure would be ascribed not to the electric field but to the electrostatic effect. In the 13 Å model, the electric field surrounds guanine and thymine in an almost radial manner. This could be classified as an LNF. The results indicate that guanine and thymine are separated enough for the electric fields not to intensify or cancel. In the LNF, the POL interaction energy follows the monopole electric field close to the polarizability point. The electric fields on the O atoms that stabilize the energy by more than 0.03 eV are specified in Figures 7-2a and 7-2b. The electric fields in both of the CS models were similar. Due to charge-transfer effects, the electric field in the CS state increases significantly compared with that in the ground state.



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(1) Electric field on the O atoms in the CS state (a) 7 Å model (b) 13 Å model

(2) Electric field on the O atoms close to (a) 7 Å model (ii) CS state (i) Ground state

(b) 13 Å model (i) Ground state

(ii) CS state

Figure 7. (1) Electric fields on the O atoms due to the QM atoms in the CS state. (2) Electric fields on the O atoms close to thymine in the (i) ground and (ii) CS states. The atoms highlighted by purple circles are the O atoms that stabilize the energy by more than 0.03 eV.


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To understand the origin of the change in electric fields from the ground state to the CS state, we analyzed the difference in the atomic charges (∆q) of guanine and thymine. The result of the 7 Å and 13 Å models is shown in Figures 8-1a and 8-1b, respectively (see Figures 8-2a and 8-2b for the atomic labels). In both models, the 22nd C atom and 31st O atom show a large change in ∆q due to electron transfer to thymine in the CS state (see Figure S2 in supporting information). In the excited state, the amplitudes on the 22nd C atom and 31st O are significant. As shown in Figure 7-2, the EFP waters, which are highlighted by purple circles, hydrogen bond with the 31st atom (carbonyl oxygen). These EFP waters contribute large POL energies (larger than 0.03 eV). Alternatively, the 22nd atom (a carbon atom in the ring skeleton; see Figure 8-2 does not hydrogen bond with any EFP waters. As a result, the EFP waters closest to the 22nd C atom were not above the threshold of 0.03 eV. This result indicates that the carbonyl O atom remains close to the water molecule through a hydrogen bond and exerts an electric field in the CS state.

(1) Difference in atomic charges (a) 7 Å model

(2) Atomic labels (a) Guanine

(b) 13 Å model

(b) Thymine

Figure 8. (1) The difference in the atomic charges (∆q) of guanine and thymine. Löwdin population analysis was performed. The blue, sky blue, and red diamonds denote N, H-N, and O atoms, respectively, that have hydrogen bonds to water molecules. (2) Atomic labels of (a) guanine and (b) thymine.



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Finally, the spatial distribution of the polarizability points in the energy range of 0.005 eV 0.022 eV were visualized, as shown Figures 9a and 9b. These polarizability points are

6 POL 2 5

distributed rather close to guanine and thymine. In particular, as shown by the points highlighted in yellow, 63% and 64% of the polarizability points are located between guanine and thymine in the 7 Å and 13 Å models, respectively. The results indicate that one must include electronic polarization effects of the solvent molecules located between D and A units in order to model the energetics of CS states.

(a) 7 Å model

(b) 13 Å model

Guanine Guanine

Thymine Thymine

34 Figure 9. Polarizability points with contributions in the range of 0.005 eV 5 " 5 0.022.

Polarizability points located between guanine and thymine are displayed as yellow balls with black circles.


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4. Conclusion The energetics of charge separation (CS) is relevant to the efficiency of photoelectric conversion and is important in many areas of chemistry and materials science. The CS state is significantly polarized; therefore, the effect of electronic polarization (POL) of the surrounding environment has been discussed for many years. In this study, we employed the effective fragment potential (EFP) method to elucidate the POL mechanism at the atomic level. We also investigated the POL mechanism at different donor (D)-acceptor (A) distances. To characterize the mechanism, the electric field generated by the D and A units were analyzed, and the interference of the two fields were classified in terms of positive interference fields (PIF), negative interference fields (NIF), and local non-interference fields (LNF). An extremely simple Na+-Clsystem and a more realistic guanine-thymine system were investigated. In both models, longer distance CS generated larger POL energies, in accordance with a previous study using the self-consistent reaction field (SCRF) model.12 This study showed that a small number of the polarizability points close to the D and A units contribute the majority of the POL energy. In the Na+-Cl- system, 12 and 10 polarization points produce 64% and 58% of the POL energy in the 2.4 Å and 5 Å models, respectively. The guanine-thymine system showed the same trend. In the 5 Å model of the Na+-Cl- system and the 7 Å model of the guanine-thymine system, the POL effect in the space between the D and A units is important. In the former case, two polarizability points in that space contribute 0.54 eV to the POL stabilization, which accounts for 34% of the entire POL energy. In the 7 Å model of the guanine-thymine system, 27 polarizability points contribute 0.98 eV, which accounts for 89% of the total POL energy. We also found that 20 of the 27 points were located between the guanine and thymine molecules. Based on our analysis of the electric field, a PIF is formed at the polarizability points between the donor and acceptor molecules in the 5 Å model of the Na+-Cl- system and the 7 Å model of the guanine-thymine system. Enhancement of the electric field occurs in the space between the donor and acceptor molecules, and the polarizability points located in this space enhance the POL energy. In the 13 Å model of the guanine-thymine system, 40 polarizability points have stabilization energies larger than 0.01 eV. In contrast to the 7 Å model, these polarizability points surround the guanine and thymine units in an almost spherical manner. Their POL contribution is -1.40 eV, which accounts for 89% of the total POL energy. We found an LNF at the polarizability points located near guanine and thymine in the 13 Å model. The results show that the electric field interference has little influence on the POL energy and that the polarizability points near the D and A units independently contribute the POL energy.



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Acknowledgements This work was financially supported by JST-CREST, JSPS KAKENHI (Grant Number 15H05805, 16H00952, 15K06563, and 16K00175) and the FLAGSHIP2020 (priority study 5) program from MEXT. Part of the computations were carried out at RCCS (Okazaki, Japan), ACCMS (Kyoto University), and RIIT (Kyushu University). MSG and MWS acknowledge the support of the US Air Force Office of Scientific Research, Award No. FA9550-14-1-0306. Supporting Information Available: Classification of the absolute values of polarization energies. HOMO and LUMO distributions of the guanine–thymine system. This material is available free of charge via the Internet at http://pubs.acs.org.


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Electronic Polarization Effect of the Water Environment in Charge

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