Enhancement of Carrier Mobility through Deformation Potential in

Nov 16, 2016 - Therefore, the electronic states originating from the metal–organic hybridizations, rather than the structural fluctuations, characte...
0 downloads 13 Views 1MB Size
Download PDF
Article pubs.acs.org/JPCC

Enhancement of Carrier Mobility through Deformation Potential in Metal-Containing Insulated Molecular Wires Tatsuhiko Ohto,*,† Hiroshi Masai,‡ Jun Terao,*,‡ Wakana Matsuda,‡ Shu Seki,‡ Yasushi Tsuji,‡ and Hirokazu Tada† †

Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan Graduate School of Engineering, Kyoto University, Nishikyo-ku, Kyoto 615-8510, Japan

‡

ABSTRACT: We used first-principles calculations to investigate the hole mobility of metal-containing poly(phenylene ethynylene) insulated molecular wires. The metal−organic bond effects were considered using ruthenium(II) porphyrin− pyridyl and platinum(II) acetylide as the organometallic moieties. We found that high hole mobility can be achieved even when the metal−organic dπ−pπ interaction is weak. The weak metal−organic interaction reduces the structural deformation that accompanies hole hopping and compensates the reduced conjugation inside the molecular wire. Our results suggest a new principle for the design of functionalized metallopolymers with high carrier mobilities.

1. INTRODUCTION Organometallic molecular wires (MWs) are metal complexes with π-conjugated polymers. The organometallic parts are expected to be promising components for molecular electronics1 because of their redox behaviors,2 spin properties,3 Kondo effect,4,5 and self-healing properties due to dynamic coordination bonds.6 Recently, insulated molecular wires (IMWs)7−10 have gained importance as the π-conjugated carbon backbones of organometallic MWs. The conjugated chains in IMWs are coated with nonconductive bulky side chains or macrocycles. The electronic transport and optical properties are enhanced in IMWs as a result of the steric inhibition of the molecular interactions between the chains.7−10 We recently reported the synthesis of IMWs with poly(phenylene ethynylene)s (PPEs) that were linked and covered with permethylated α-cyclodextrins (PM α-CDs).11−15 Insulated PPEs containing metals have also been synthesized.16,17 Carrier mobility is an essential quality for wiring materials. The hole-mobility value of the all-carbon insulated PPE MWs decreased dramatically when organometallic units were introduced.18 However, ruthenium(II) porphyrin-containing insulated PPE MWs exhibited a hole mobility comparable to that of the all-carbon PPE MWs.19 The reason for the different hole-mobility values remains to be clarified. Hole mobility is inversely proportional to the effective mass of the valence band, which is controlled by the strength of the metal−organic dπ− pπ interaction. It is unclear how the metal−organic bond affects the effective mass (i.e., the degree of the conjugation inside the chain) and the hole mobility. Previous first-principles studies were limited to the investigation of the carbon-backbone structural effects on hole mobility.15,20 Structural fluctuations divide the wire into hopping fragments and also modify the © XXXX American Chemical Society

interaction between the fragments. In the earlier reports, the structural fluctuations were controlled by zigzag15 or ladder20 carbon frameworks. In this study, we calculated the hole mobilities of three IMWs with density functional theory (DFT): an all-carbon moiety13 (3), a platinum(II) acetylide moiety21 (4), and a ruthenium(II) porphyrin−pyridyl moiety19 (5) (see Scheme 1). All three IMWs share a common, straight PPE backbone. Therefore, the electronic states originating from the metal−organic hybridizations, rather than the structural fluctuations, characterize their mobilities. Time-resolved microwave conductivity (TRMC22) measurements revealed that 5 and 3 display comparable intramolecular charge mobilities [0.2219 and 0.5213 cm2/(V s), respectively). In this work, the hole mobility of 4, in which the monomer-to-polymer interaction is due to a covalent bond between Pt and C, was also measured. The organization of this article is as follows: In section 2, the experimental procedure is provided, whereas section 3 describes the two theoretical models used to estimate holemobility values. In section 4, we compare the measured and calculated mobility values. Conclusions are given in section 5.

2. EXPERIMENTAL DETAILS We examined the intramolecular charge mobility characteristics of IMW 4 in the solid state by flash-photolysis TRMC (FPTRMC) and transient absorption spectroscopy (TAS) measurements. Compound 4 was overcoated onto a quartz plate, giving uniform thin films with transmittance values at 355 Received: August 24, 2016 Revised: October 7, 2016

A

DOI: 10.1021/acs.jpcc.6b08557 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C Scheme 1. Molecular Wires 3−5 and Synthetic Procedures from 1 and 2

⎛1⎞ 2Δω Δ⎜ ⎟ − i = F(Δσr + iΔσi) ω0 ⎝Q ⎠

nm of less than 5%. Photoexcitation of the film was carried out by third harmonic generation (THG, 355 nm) of nanosecond laser pulses from an INDI-HG Nd:YAG laser (SpectraPhysics). The excitation photon density was set to 1.8 × 1015 photons/cm2. For TRMC measurements, the microwave frequency and power were approximately 9.1 GHz and 3 mW, respectively. The TRMC signal was evolved in a diode (rise time of 5′ > 4′, which is in qualitative agreement with the experiments. The deformation potential describes the coupling between the frontier molecular orbital and the acoustic phonon. Therefore, the deformation potential of the hole increases as the stretching of the molecular chain changes the shape of the HOMO.26 As shown in Figure 1c, the wave function has a large amplitude around the Pt atom of 4′; therefore, the ε values are similar for 3′ and 4′. In contrast, the amplitude of the wave function around the Ru atom is very small for 5′ (upper panel in Figure 2), resulting in a significant reduction of ε. The weak hybridization between the PE units and the porphyrin (reflected by a larger m* value) is indicated by the energy separation between the frontier molecular orbitals (Figure 2). Here, we discuss the origin of the different values of C, which is related to the mechanical stiffness of the chemical bonds. The C−C, Pt−C, and Ru−N bond lengths were found to be 1.43, 2.02, and 2.12 Å, respectively. The vibrational frequencies of these bonds were found to be 2194, 421, and 177 cm−1, respectively. This explains the metal−organic bond dependence of C (Table 1): C becomes slightly smaller for weaker metal− polymer bonds. However, the change in C is too small to affect the hole-mobility values. In conclusion, the charge mobility is governed by the molecular orbital wave function distribution of the metal-containing units, not by the local metal−organic bonding. The calculated hole-mobility values are approximately 2 orders of magnitude larger than the experimental values. We attribute this overestimation to the defect-free structure used in the calculations. Similar overestimations were reported previously.20,26 We also assume a defect- and bending-free chain; therefore, the calculated values can be regarded as the upper limit for an ideal one-dimensional wire. Nevertheless, the deformation potential model can describe qualitative differences in the mobilities of carbon and organic systems.26

3′ (3) 3′ (4) 3′ (5) 4′ 5′ 3′ (3) 3′ (4) 3′ (5) 4′ 5′ 3′ (3) 3′ (4) 3′ (5) 4′ 5′ 3′ (3) 3′ (4) 3′ (5) 4′ 5′

V (eV)

λ (eV)

B3LYP 0.16 0.18 0.10 0.15 0.07 0.13 0.11 0.29 0.03 0.04 Constrained DFT B3LYP 0.16 0.17 0.10 0.13 0.07 0.11 0.11 0.24 0.03 −b PBE 0.15 0.11 0.10 0.09 0.07 0.07 0.10 0.21 0.03 0.03 CAM-B3LYP 0.17 0.31 0.11 0.29 0.07 0.27 0.12 0.44 0.02 0.03

μ [cm2/(V s)] 155.2 158.8 161.9 30.4 105.3 163.8 210.4 222.2 53.1 −b 299.5 313.5 303.0 62.7 201.2 38.6 32.7 30.7 6.3 43.5

a Numbers of PE units included in the “monomer” used for calculating 3′ given in parentheses. bWe could not obtain converged results for 5′ using constrained DFT.

monomer, we performed calculations with various monomer sizes (three, four, and five PE units) in the case of IMW 3′. The B3LYP results indicated that the hole mobility does not vary significantly with the monomer size, whereas it increases slightly with the monomer length. This tendency agrees with previous measurement results.15 At the standard B3LYP level of theory, the calculated hole mobility decreases in the order 3′ > 5′ > 4′, which is in qualitative agreement with the experimental results. The trend of the parameters is similar to that obtained using the deformation potential model; the transfer integral is the lowest for 5′, but the low λ value compensates for the reduction of the hole mobility. E

DOI: 10.1021/acs.jpcc.6b08557 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

estimate of the actual contributions from these two mechanisms.

However, the above calculations significantly overestimate the mobility. One possible origin of the overestimation is the interaction between the hopping sites. It has been reported that the intermolecular interaction between a donor and an acceptor increases the value of λ by up to 0.25 eV.45 To estimate this contribution, we performed constrained DFT calculations43,44 using dimers of IMWs. The results in Table 2, however, indicate that the interaction between monomers slightly reduces λ instead. This is because the two monomers interact with each other only through a single bond. One of the monomer units even acts as a weak geometrical constraint on the other charged monomer and reduces the conformational change of the latter due to the charging. Thus, the interaction among hopping sites cannot be the origin of our overestimated IMW mobility. Another possible origin is the underestimation of reorganization energies due to the DFT method. To investigate this possibility, we compared the results of calculations with the PBE and CAM-B3LYP functionals. CAM-B3LYP includes a long-range correction, which improves the excessively delocalized electronic states described by conventional DFT methods such as B3LYP and PBE.48 Table 2 shows that λ strongly depends on the choice of the functional, while V is insensitive to it. PBE gives smaller λ and larger μ values than B3LYP, because of its more delocalized electronic distribution.49 In contrast, CAM-B3LYP gives significantly larger λ values, although there are some aspects that should be improved. (For example, the calculated μ value of 5′ is higher than that of 3′, and μ becomes smaller for the longer monomer.) Consequently, the hole-mobility values are almost 20% smaller than those calculated with B3LYP. This result indicates that the underestimation of λ in conventional DFT is a principal origin of the overestimated μ values. The structural fluctuations at ambient temperature such as rotations of the wire reduce V20 and induce the wave function localization.15 This localization produces fragments with various hopping localization lengths, resulting in energy disorder between hopping sites. These effects, which we did not include, contribute to the overestimation as well.15,20 Note that the nuclear quantum tunneling, which is also not included in our calculations, increases mobility.50 Additional work is needed to estimate the mobility more accurately by including the siteenergy disorder with molecular dynamics simulations and the nuclear quantum tunneling. Finally, we comment on the ratios of the calculated holemobility values between the IMWs. The ratio between 5′ and 4′ (7.3) is better reproduced with Marcus theory (3.5 with B3LYP and 6.9 with CAM-B3LYP) than with the deformation potential model (1.3). The deviation of the ratios mainly comes from the variations in λ and ε. Specifically, λ changes by a factor of close to 10 between 4′ and 5′, whereas this factor is only 3 in ε. These behaviors of λ and ε are related to the extent of +1 charge delocalization, namely, whether a monomer part is totally ionized or the hole is delocalized over the chain. The better agreement of the mobility ratio with Marcus theory indicates that the conduction mechanism is more likely to be hopping than band-like transport. The hopping transport mechanism is also indicated by the fact that the experimentally measured mobility values are below 1 cm2/(V s).30 Nevertheless, this comparison does not completely exclude the presence of the band-like transport mechanism. Measuring the temperature-dependent mobility51 could provide a quantitative

5. CONCLUDING REMARKS In summary, we have estimated the hole mobilities of several IMWs both experimentally and theoretically. Both the deformation potential model and Marcus theory reproduced the experimentally measured mobilities qualitatively. The holemobility value of the ruthenium(II) porphyrin−pyridyl moiety is higher than that of the platinum(II) acetylide moiety, because of the weaker metal−organic interaction in the former. The weaker interaction causes a larger hole effective mass, which is compensated, however, by the small structural change due to the hole hopping. The deformation potential model analysis clearly illustrated that the metal−organic interaction strength is determined by the molecular orbital wave function distribution of the metal-containing units, not by the local metal−organic bond strength. Our results suggest that a strong hybridization between the carbon backbones and the organometallic units is not always necessary for obtaining high mobilities in IMWs, a conclusion that leads to more freedom in the design of functionalized MWs. Although the exchange-correlation functional and the model should be improved to reduce the overestimation of carrier mobilities, gas-phase DFT calculations at the standard level were shown to be useful for predicting charge mobilities and screening candidate materials.

■

APPENDIX: ORIGIN OF THE CALIBRATION FACTOR F The factor F plays a crucial role in the quantitative determination of mobility values from microwave-based dielectric loss spectroscopy. To assess the origin of F, we consider the dielectric loss (dissipation loss) of a small dielectric specimen in an alternating-current electric field E. The electric conductive specimen (dimensions of S × d, conductivity of σ, and dielectric constant of εs) interacting with E in the cavity has an electrical capacitance of Cs, given by Cs = εs

S d

(A1)

Thus, the loss tangent, tan δ, can be defined as tan δ =

1 σ = ωCsR ωεs

(A2)

where R is the resistance and ω is the angular frequency. As in eq 2 in the main text, the assumption of a complex dielectric constant (εc) of the specimen means that the relationship between the conductivity and the dielectric constant is given by ε σ tan δ = = i ωεs εr (A3) where εc = εs −

iσ = εr + iεi ω

(A4)

On the other hand, the quality factor Q of the resonant system is given by Q=

ω0L 1 = R ω0CsR

(A5)

where L is the inductance. One can then write F

DOI: 10.1021/acs.jpcc.6b08557 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C 1 P 1 σ = = ≈ tan δ = Q ω0W ω0CsR ωεs

(13) Terao, J.; Tanaka, Y.; Tsuda, S.; Kambe, N.; Taniguchi, M.; Kawai, T.; Saeki, A.; Seki, S. Insulated Molecular Wire with Highly Conductive π-Conjugated Polymer Core. J. Am. Chem. Soc. 2009, 131, 18046−18047. (14) Terao, J.; Tsuda, S.; Tanaka, Y.; Okoshi, K.; Fujihara, T.; Tsuji, Y.; Kambe, N. Synthesis of Organic-Soluble Conjugated Polyrotaxanes by Polymerization of Linked Rotaxanes. J. Am. Chem. Soc. 2009, 131, 16004−16005. (15) Terao, J.; Wadahama, A.; Matono, A.; Tada, T.; Watanabe, S.; Seki, S.; Fujihara, T.; Tsuji, Y. Design Principle for Increasing Charge Mobility of π-Conjugated Polymers Using Regularly Localized Molecular Orbitals. Nat. Commun. 2013, 4, 1691. (16) Terao, J.; Homma, K.; Konoshima, Y.; Taniguchi, M.; Kiguchi, M.; Komoto, Y.; Horikawa, M.; Naito, Y.; Fujihara, T.; Tsuji, Y. Molecular Wiring Method Based on Polymerization or Copolymerization of an Insulated π-Conjugated Monomer. Bull. Chem. Soc. Jpn. 2014, 87, 871−873. (17) Masai, H.; Terao, J.; Tsuji, Y. Insulated π-Conjugated Metallopolymers. Tetrahedron Lett. 2014, 55, 4035−4043. (18) Terao, J.; Homma, K.; Konoshima, Y.; Imoto, R.; Masai, H.; Matsuda, W.; Seki, S.; Fujihara, T.; Tsuji, Y. Synthesis of Functionalized Insulated Molecular Wires by Polymerization of an Insulated πConjugated Monomer. Chem. Commun. 2014, 50, 658−660. (19) Masai, H.; Terao, J.; Seki, S.; Nakashima, S.; Kiguchi, M.; Okoshi, K.; Fujihara, T.; Tsuji, Y. Synthesis of One-Dimensional Metal-Containing Insulated Molecular Wire with Versatile Properties Directed toward Molecular Electronics Materials. J. Am. Chem. Soc. 2014, 136, 1742−1745. (20) Kocherzhenko, A. A.; Patwardhan, S.; Grozema, F. C.; Anderson, H. L.; Siebbeles, L. D. A. Mechanism of Charge Transport Along Zinc Porphyrin-Based Molecular Wires. J. Am. Chem. Soc. 2009, 131, 5522−5529. (21) Masai, H.; Terao, J.; Makuta, S.; Tachibana, Y.; Fujihara, T.; Tsuji, Y. Enhancement of Phosphorescence and Unimolecular Behavior in the Solid State by Perfect Insulation of Platinum-Acetylide Polymers. J. Am. Chem. Soc. 2014, 136, 14714−14717. (22) Seki, S.; Saeki, A.; Sakurai, T.; Sakamaki, D. Charge Carrier Mobility in Organic Molecular Materials Probed by Electromagnetic Waves. Phys. Chem. Chem. Phys. 2014, 16, 11093−11113. (23) Saeki, A.; Seki, S.; Sunagawa, T.; Ushida, K.; Tagawa, S. ChargeCarrier Dynamics in Polythiophene Films Studied by in-Situ Measurement of Flash-Photolysis Time-Resolved Microwave Conductivity (FP-TRMC) and Transient Optical Spectroscopy (TOS). Philos. Mag. 2006, 86, 1261−1276. (24) Acharya, A.; Seki, S.; Saeki, A.; Koizumi, Y.; Tagawa, S. Study of Transport Properties in Fullerene-Doped Polysilane Films Using Flash Photolysis Time-Resolved Microwave Technique. Chem. Phys. Lett. 2005, 404, 356−360. (25) Seki, S.; Koizumi, Y.; Kawaguchi, T.; Habara, H.; Tagawa, S. Dynamics of Positive Charge Carriers on Si Chains of Polysilanes. J. Am. Chem. Soc. 2004, 126, 3521−3528. (26) Xi, J.; Long, M.; Tang, L.; Wang, D.; Shuai, Z. First-Principles Prediction of Charge Mobility in Carbon and Organic Nanomaterials. Nanoscale 2012, 4, 4348−4369. (27) Berlin, Y. A.; Hutchison, G. R.; Rempala, P.; Ratner, M. A.; Michl, J. Charge Hopping in Molecular Wires as a Sequence of Electron-Transfer Reactions. J. Phys. Chem. A 2003, 107, 3970−3980. (28) Deng, W. Q.; Goddard, W. A. Predictions of Hole Mobilities in Oligoacene Organic Semiconductors from Quantum Mechanical Calculations. J. Phys. Chem. B 2004, 108, 8614−8621. (29) Wen, S.-H.; Li, A.; Song, J.; Deng, W.-Q.; Han, K.-L.; Goddard, W. A., III. First-Principles Investigation of Anistropic Hole Mobilities in Organic Semiconductors. J. Phys. Chem. B 2009, 113, 8813−8819. (30) Saeki, A.; Koizumi, Y.; Aida, T.; Seki, S. Comprehensive Approach to Intrinsic Charge Carrier Mobility in Conjugated Organic Molecules, Macromolecules, and Supramolecular Architectures. Acc. Chem. Res. 2012, 45, 1193−1202.

(A6)

where P is the loss of energy and W is the energy stored in the cavity. Eventually, the first-order perturbation of Q and σ leads to ⎛1⎞ Δω0 Δ⎜ ⎟ − i = F(Δσr + iΔσi) ω0 ⎝Q ⎠

(A7)

Here, the factor F has been introduced because of the imperfect spatial overlap of E and the specimen. Thus, in principal, F depends only on the geometrical setup of the specimen in the cavity (E in the cavity). This parameter is often referred to as the “filling factor”.52−54

■

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. Phone: +81-6-6850-6433. *E-mail: [email protected]. Phone: +81-75-383-2516. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by JSPS KAKENHI Grants JP16H00835, JP16K17855, JP16H00834, JP16H00965, and JP25110012. H.M. thanks the JSPS Research Fellowship.

■

REFERENCES

(1) Nitzan, A.; Ratner, M. A. Electron Transport in Molecular Wire Junctions. Science 2003, 300, 1384−1389. (2) Tam, A. Y.-Y.; Yam, V. W.-W. Recent Advances in Metallogels. Chem. Soc. Rev. 2013, 42, 1540−1567. (3) Dul, M.-C.; Pardo, E.; Lescouezec, R.; Journaux, Y.; FerrandoSoria, J.; Ruiz-Garcia, R.; Cano, J.; Julve, M.; Lloret, F.; Cangussu, D.; et al. Supramolecular Coordination Chemistry of Aromatic Polyoxalamide Ligands: A Metallosupramolecular Approach toward Functional Magnetic Materials. Coord. Chem. Rev. 2010, 254, 2281− 2296. (4) Ciszek, J. W.; Keane, Z. K.; Cheng, L.; Stewart, M. P.; Yu, L. H.; Natelson, D.; Tour, J. M. Neutral Complexes of First Row Transition Metals Bearing Unbound Thiocyanates and Their Assembly on Metallic Surfaces. J. Am. Chem. Soc. 2006, 128, 3179−3189. (5) Liang, W. J.; Shores, M. P.; Bockrath, M.; Long, J. R.; Park, H. Kondo Resonance in a Single-Molecule Transistor. Nature 2002, 417, 725−729. (6) Holten-Andersen, N.; Harrington, M. J.; Birkedal, H.; Lee, B. P.; Messersmith, P. B.; Lee, K. Y. C.; Waite, J. H. PH-Induced MetalLigand Cross-Links Inspired by Mussel Yield Self-Healing Polymer Networks with near-Covalent Elastic Moduli. Proc. Natl. Acad. Sci. U. S. A. 2011, 108, 2651−2655. (7) Frampton, M. J.; Anderson, H. L. Insulated Molecular Wires. Angew. Chem., Int. Ed. 2007, 46, 1028−1064. (8) Taniguchi, M.; Nojima, Y.; Yokota, K.; Terao, J.; Sato, K.; Kambe, N.; Kawai, T. Self-Organized Interconnect Method for Molecular Devices. J. Am. Chem. Soc. 2006, 128, 15062−15063. (9) Yamada, R.; Kumazawa, H.; Noutoshi, T.; Tanaka, S.; Tada, H. Electrical Conductance of Oligothiophene Molecular Wires. Nano Lett. 2008, 8, 1237−1240. (10) Yamada, R.; Kumazawa, H.; Tanaka, S.; Tada, H. Electrical Resistance of Long Oligothiophene Molecules. Appl. Phys. Express 2009, 2, 025002. (11) Terao, J. Permethylated Cyclodextrin-Based Insulated Molecular Wires. Polym. Chem. 2011, 2, 2444−2452. (12) Terao, J. π -Conjugated Molecules Covered by Permethylated Cyclodextrins. Chem. Rec. 2011, 11, 269−283. G

DOI: 10.1021/acs.jpcc.6b08557 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

Rings and C20 Bowl, Cage, and Ring Isomers. J. Chem. Phys. 2010, 132, 234113. (49) Zheng, X.; Liu, M.; Johnson, E. R.; Contreras-García, J.; Yang, W. Delocalization Error of Density-Functional Approximations: A Distinct Manifestation in Hydrogen Molecular Chains. J. Chem. Phys. 2012, 137, 214106. (50) Nan, G.; Yang, X.; Wang, L.; Shuai, Z.; Zhao, Y. Nuclear Tunneling Effects of Charge Transport in Rubrene, Tetracene, and Pentacene. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 79, 115203. (51) Karakus, M.; Jensen, S. A.; D’Angelo, F.; Turchinovich, D.; Bonn, M.; Cánovas, E. Phonon−Electron Scattering Limits Free Charge Mobility in Methylammonium Lead Iodide Perovskites. J. Phys. Chem. Lett. 2015, 6, 4991−4996. (52) Slater, J. C. Microwave Electronics. Rev. Mod. Phys. 1946, 18, 441−512. (53) Tomonaga, S. A General Theory of Ultra-Short-Wave Circuits II. J. Phys. Soc. Jpn. 1948, 3, 93−105. (54) Honsho, Y.; Miyakai, T.; Sakurai, T.; Saeki, A.; Seki, S. Evaluation of Intrinsic Charge Carrier Transport at InsulatorSemiconductor Interfaces Probed by a Non-Contact MicrowaveBased Technique. Sci. Rep. 2013, 3, 3182.

(31) Beleznay, F. B.; Bogár, F.; Ladik, J. Charge Carrier Mobility in Quasi-One-Dimensional Systems: Application to a Guanine Stack. J. Chem. Phys. 2003, 119, 5690. (32) Bruzzone, S.; Fiori, G. Ab-Initio Simulations of Deformation Potentials and Electron Mobility in Chemically Modified Graphene and Two-Dimensional Hexagonal Boron-Nitride. Appl. Phys. Lett. 2011, 99, 222108. (33) Fishman, G. Mobility in a Quasi-One-Dimensional Semiconductor: An Analytical Approach. Phys. Rev. B: Condens. Matter Mater. Phys. 1986, 34, 2394−2401. (34) Fishman, G. Phonon-Limited Mobility in a Quasi-OneDimensional Semiconductor. Phys. Rev. B: Condens. Matter Mater. Phys. 1987, 36, 7448−7456. (35) Northrup, J. E. Two-Dimensional Deformation Potential Model of Mobility in Small Molecule Organic Semiconductors. Appl. Phys. Lett. 2011, 99, 062111. (36) Walukiewicz, W.; Ruda, H. E.; Lagowski, J.; Gatos, H. C. Electron Mobility in Modulation-Doped Heterostructures. Phys. Rev. B: Condens. Matter Mater. Phys. 1984, 30, 4571−4582. (37) Soler, J. M.; Artacho, E.; Gale, J. D.; Garcia, A.; Junquera, J.; Ordejon, P.; Sanchez-Portal, D. The Siesta Method for Ab Initio Order-N Materials Simulation. J. Phys.: Condens. Matter 2002, 14, 2745−2779. (38) Troullier, N.; Martins, J. L. Efficient Pseudopotentials for PlaneWave Calculations. Phys. Rev. B: Condens. Matter Mater. Phys. 1991, 43, 1993−2006. (39) Kleinman, L.; Bylander, D. M. Efficacious Form for Model Pseudopotentials. Phys. Rev. Lett. 1982, 48, 1425−1428. (40) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (41) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A., Jr.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Keith, T.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, Ö .; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian C.01; Gaussian, Inc.: Wallingford, CT, 2009. (42) Yanai, T.; Tew, D. P.; Handy, N. C. A New Hybrid Exchange− Correlation Functional Using the Coulomb-Attenuating Method (CAM-B3LYP). Chem. Phys. Lett. 2004, 393, 51−57. (43) Wu, Q.; Van Voorhis, T. Direct Optimization Method to Study Constrained Systems within Density-Functional Theory. Phys. Rev. A: At., Mol., Opt. Phys. 2005, 72, 024502. (44) Valiev, M.; Bylaska, E. J.; Govind, N.; Kowalski, K.; Straatsma, T. P.; Van Dam, H. J. J.; Wang, D.; Nieplocha, J.; Apra, E.; Windus, T. L.; et al. Nwchem: A Comprehensive and Scalable Open-Source Solution for Large Scale Molecular Simulations. Comput. Phys. Commun. 2010, 181, 1477−1489. (45) Vaissier, V.; Frost, J. M.; Barnes, P. R. F.; Nelson, J. Influence of Intermolecular Interactions on the Reorganization Energy of Charge Transfer between Surface-Attached Dye Molecules. J. Phys. Chem. C 2015, 119, 24337−24341. (46) Terao, J.; Masai, H.; Fujihara, T.; Tsuji, Y. Synthesis of Insulated Pt-Alkynyl Complex Polymer. Chem. Lett. 2012, 41, 652−653. (47) Kocherzhenko, A. A.; Whaley, K. B.; Sforazzini, G.; Anderson, H. L.; Wykes, M.; Beljonne, D.; Grozema, F. C.; Siebbeles, L. D. A. Effects of the Environment on Charge Transport in Molecular Wires. J. Phys. Chem. C 2012, 116, 25213−25225. (48) Heaton-Burgess, T.; Yang, W. Structural Manifestation of the Delocalization Error of Density Functional Approximations: C4n+2 H

DOI: 10.1021/acs.jpcc.6b08557 J. Phys. Chem. C XXXX, XXX, XXX−XXX