Chemical derivatization; Experimental evidence; Functional devices; Isolated compounds; Isolated systems; Molecular junction; Newns-anderson models; Theoretical study; Materials Science (all); Physical and Theoretical Chemistry; General Materials Science
Résumé :
[en] A central issue in molecular electronics in order to build functional devices is to assess whether changes in the electronic structure of isolated compounds by chemical derivatization are retained once the molecules are inserted into molecular junctions. Recent theoretical studies have suggested that this is not always the case due to the occurrence of pinning effects making the alignment of the transporting levels insensitive to the changes in the electronic structure of the isolated systems. We explore here this phenomenon by investigating at both the experimental and theoretical levels the I/ V characteristics of molecular junctions incorporating three different three-ring phenylene ethynylene derivatives designed to exhibit a significant variation of the HOMO level in the isolated state. At the theoretical level, our NEGF/DFT calculations performed on junctions including the three compounds show that, whereas the HOMO of the molecules varies by 0.61 eV in the isolated state, their alignment with respect to the Fermi level of the gold electrodes in the junction is very similar (within 0.1 eV). At the experimental level, the SAMs made of the three compounds have been contacted by a conducting AFM probe to measure their I/ V characteristics. The alignment of the HOMO with respect to the Fermi level of the gold electrodes has been deduced by fitting the I/ V curves, using a model based on a single-level description (Newns-Anderson model). The extracted values are found to be very similar for the three derivatives, in full consistency with the theoretical predictions, thus providing clear evidence for a HOMO level pinning effect.
Disciplines :
Chimie
Auteur, co-auteur :
Rodriguez-Gonzalez, S; Laboratory for Chemistry of Novel Materials , University of Mons , B-7000 Mons , Belgium
Xie, Z ; Department of Chemical Engineering and Materials Science , and Department of Chemistry , University of Minnesota , Minneapolis , Minnesota 55455 , United States
Galangau, O; Univ Rennes, CNRS, ISCR (Institut des Sciences Chimiques de Rennes)-UMR 6226 , Rennes F-3500 , France
Selvanathan, P; Univ Rennes, CNRS, ISCR (Institut des Sciences Chimiques de Rennes)-UMR 6226 , Rennes F-3500 , France
Norel, L; Univ Rennes, CNRS, ISCR (Institut des Sciences Chimiques de Rennes)-UMR 6226 , Rennes F-3500 , France
Van Dyck, Colin ; Université de Mons - UMONS > Faculté des Sciences > Service Chimie Physique Théorique
Costuas, K ; Univ Rennes, CNRS, ISCR (Institut des Sciences Chimiques de Rennes)-UMR 6226 , Rennes F-3500 , France
Frisbie, C D ; Department of Chemical Engineering and Materials Science , and Department of Chemistry , University of Minnesota , Minneapolis , Minnesota 55455 , United States
Rigaut, S ; Univ Rennes, CNRS, ISCR (Institut des Sciences Chimiques de Rennes)-UMR 6226 , Rennes F-3500 , France
Cornil, Jérôme ; Université de Mons - UMONS > Faculté des Sciences > Service de Chimie des matériaux nouveaux
Langue du document :
Anglais
Titre :
HOMO Level Pinning in Molecular Junctions: Joint Theoretical and Experimental Evidence.
Division of Chemistry Agence Nationale de la Recherche Centre National de la Recherche Scientifique Fonds De La Recherche Scientifique - FNRS Universit? de Rennes 1 National Institute for Nanotechnology, University of Alberta
Subventionnement (détails) :
The work of S.R.G. is supported by the Belgian National Fund for Scientific Research (F.R.S.-FNRS). We also acknowledge the Consortium des Equipements de Calcul Intensif (CECI) funded by the Belgian National Fund for Scientific Research (F.R.S.-FNRS) for providing the computational resources. J.C. is an FNRS research director. C.V.D. thanks the support of the National Institute for Nanotechnology (NINT), which is operated as a partnership between the National Research Council, Canada, the University of Alberta and the Government of Alberta. C.D.F. acknowledges financial support from the U.S. National Science Foundation (CHE-1708173). XPS and UPS were carried out in the Characterization Facility, University of Minnesota. This work was also supported by the Universite de Rennes 1 the CNRS, and the Agence Nationale de la Recherche (RuOxLux - ANR-12-BS07-0010-01)).The work of S.R.G. is supported by the Belgian National Fund for Scientific Research (F.R.S.-FNRS). We also acknowledge the Consortium des Équipements de Calcul Intensif (CÉCI) funded by the Belgian National Fund for Scientific Research (F.R.S.-FNRS) for providing the computational resources. J.C. is an FNRS research director. C.V.D. thanks the support of the National Institute for Nanotechnology (NINT), which is operated as a partnership between the National Research Council, Canada, the University of Alberta, and the Government of Alberta. C.D.F. acknowledges financial support from the U.S. National Science Foundation (CHE-1708173). XPS and UPS were carried out in the Characterization Facility, University of Minnesota. This work was also supported by the Université de Rennes 1, the CNRS, and the Agence Nationale de la Recherche (RuOxLux - ANR-12-BS07-0010-01)).
Krzeminski, C.; Delerue, C.; Allan, G.; Vuillaume, D.; Metzger, R. M. Theory of electrical rectification in a molecular monolayer. Phys. Rev. B: Condens. Matter Mater. Phys. 2001, 64, 854051-854056, 10.1103/PhysRevB.64.085405
Van Dyck, C.; Ratner, M. A. Molecular rectifiers: A new design based on asymmetric anchoring moieties. Nano Lett. 2015, 15, 1577-1584, 10.1021/nl504091v
Van Dyck, C.; Geskin, V.; Kronemeijer, A. J.; De Leeuw, D. M.; Cornil, J. Impact of derivatization on electron transmission through dithienylethene-based photoswitches in molecular junctions. Phys. Chem. Chem. Phys. 2013, 15, 4392-4404, 10.1039/c3cp44132f
Osella, S.; Samorì, P.; Cornil, J. Photoswitching azobenzene derivatives in single molecule junctions: A theoretical insight into the I/V characteristics. J. Phys. Chem. C 2014, 118, 18721-18729, 10.1021/jp504582a
Dulić, D.; Van Der Molen, S. J.; Kudernac, T.; Jonkman, H. T.; De Jong, J. J. D.; Bowden, T. N.; Van Esch, J.; Feringa, B. L.; Van Wees, B. J. One-way optoelectronic switching of photochromic molecules on gold. Phys. Rev. Lett. 2003, 91, 207402, 10.1103/PhysRevLett.91.207402
Quek, S. Y.; Kamenetska, M.; Steigerwald, M. L.; Choi, H. J.; Louie, S. G.; Hybertsen, M. S.; Neaton, J. B.; Venkataraman, L. Mechanically controlled binary conductance switching of a single-molecule junction. Nat. Nanotechnol. 2009, 4, 230-234, 10.1038/nnano.2009.10
Van Dyck, C.; Geskin, V.; Cornil, J. Fermi level pinning and orbital polarization effects in molecular junctions: The role of metal induced gap states. Adv. Funct. Mater. 2014, 24, 6154-6165, 10.1002/adfm.201400809
Crispin, X.; Geskin, V.; Crispin, A.; Cornil, J.; Lazzaroni, R.; Salaneck, W. R.; Brédas, J. L. Characterization of the interface dipole at organic/metal interfaces. J. Am. Chem. Soc. 2002, 124, 8131-8141, 10.1021/ja025673r
Lenfant, S.; Guerin, D.; Tran Van, F.; Chevrot, C.; Palacin, S.; Bourgoin, J. P.; Bouloussa, O.; Rondelez, F.; Vuillaume, D. Electron transport through rectifying self-assembled monolayer diodes on silicon: Fermi-level pinning at the molecule-metal interface. J. Phys. Chem. B 2006, 110, 13947-13958, 10.1021/jp053510u
Bâldea, I.; Xie, Z.; Frisbie, C. D. Uncovering a law of corresponding states for electron tunneling in molecular junctions. Nanoscale 2015, 7, 10465-10471, 10.1039/C5NR02225H
Yoon, H. J.; Bowers, C. M.; Baghbanzadeh, M.; Whitesides, G. M. The rate of charge tunneling is insensitive to polar terminal groups in self-assembled monolayers in AgTSS(CH2) nM(CH2)mT//Ga2O3/EGaIn junctions. J. Am. Chem. Soc. 2014, 136, 16-19, 10.1021/ja409771u
Baghbanzadeh, M.; Simeone, F. C.; Bowers, C. M.; Liao, K. C.; Thuo, M.; Miller, M. S.; Carmichael, T. B.; Whitesides, G. M.; Baghbanzadeh, M. Odd-even effects in charge transport across n-alkanethiolate-based SAMs. J. Am. Chem. Soc. 2014, 136, 16919-16925, 10.1021/ja509436k
Sayed, S. Y.; Fereiro, J. A.; Yan, H.; McCreery, R. L.; Bergren, A. J. Charge transport in molecular electronic junctions: Compression of the molecular tunnel barrier in the strong coupling regime. Proc. Natl. Acad. Sci. U. S. A. 2012, 109, 11498-11503, 10.1073/pnas.1201557109
Heimel, G.; Romaner, L.; Brédas, J. L.; Zojer, E. Interface energetics and level alignment at covalent metal-molecule junctions: -conjugated thiols on gold. Phys. Rev. Lett. 2006, 96, 196806, 10.1103/PhysRevLett.96.196806
Lasser, L.; Ronca, E.; Pastore, M.; De Angelis, F.; Cornil, J.; Lazzaroni, R.; Beljonne, D. Energy level alignment at titanium oxide-dye interfaces: Implications for electron injection and light harvesting. J. Phys. Chem. C 2015, 119, 9899-9909, 10.1021/acs.jpcc.5b01267
Van Dyck, C.; Ratner, M. A. Molecular Junctions: Control of the Energy Gap Achieved by a Pinning Effect. J. Phys. Chem. C 2017, 121, 3013-3024, 10.1021/acs.jpcc.6b07855
Kim, B.; Choi, S. H.; Zhu, X. Y.; Frisbie, C. D. Molecular tunnel junctions based on -conjugated oligoacene thiols and dithiols between Ag, Au, and Pt contacts: Effect of surface linking group and metal work function. J. Am. Chem. Soc. 2011, 133, 19864-19877, 10.1021/ja207751w
Xie, Z.; Bâldea, I.; Smith, C. E.; Wu, Y.; Frisbie, C. D. Experimental and Theoretical Analysis of Nanotransport in Oligophenylene Dithiol Junctions as a Function of Molecular Length and Contact Work Function. ACS Nano 2015, 9, 8022-8036, 10.1021/acsnano.5b01629
Taylor, J.; Brandbyge, M.; Stokbro, K. Theory of rectification in tour wires: The role of electrode coupling. Phys. Rev. Lett. 2002, 89, 1383011-1383014, 10.1103/PhysRevLett.89.138301
Taylor, J.; Brandbyge, M.; Stokbro, K. Conductance switching in a molecular device: The role of side groups and intermolecular interactions. Phys. Rev. B: Condens. Matter Mater. Phys. 2003, 68, 1211011-1211014, 10.1103/PhysRevB.68.121101
Zangmeister, C. D.; Robey, S. W.; Van Zee, R. D.; Yao, Y.; Tour, J. M. Fermi level alignment and electronic levels in ″molecular wire″ self-assembled monolayers on Au. J. Phys. Chem. B 2004, 108, 16187-16193, 10.1021/jp048134c
Malen, J. A.; Doak, P.; Baheti, K.; Tilley, T. D.; Segalman, R. A.; Majumdar, A. Identifying the length dependence of orbital alignment and contact coupling in molecular heterojunctions. Nano Lett. 2009, 9, 1164-1169, 10.1021/nl803814f
Heimel, G.; Romaner, L.; Brédas, J. L.; Zojer, E. Organic/metal interfaces in self-assembled monolayers of conjugated thiols: A first-principles benchmark study. Surf. Sci. 2006, 600, 4548-4562, 10.1016/j.susc.2006.07.023
Heimel, G.; Romaner, L.; Zojer, E.; Bredas, J. L. The interface energetics of self-assembled monolayers on metals. Acc. Chem. Res. 2008, 41, 721-729, 10.1021/ar700284q
Tour, J. M.; Rawlett, A. M.; Kozaki, M.; Yao, Y.; Jagessar, R. C.; Dirk, S. M.; Price, D. W.; Reed, M. A.; Zhou, C. W.; Chen, J.; Wang, W.; Campbell, I. Synthesis and preliminary testing of molecular wires and devices. Chem.-Eur. J. 2001, 7, 5118-5134, 10.1002/1521-3765(20011203)7:23<5118::AID-CHEM5118>3.0.CO;2-1
Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77, 3865-3868, 10.1103/PhysRevLett.77.3865
Perdew, J. P.; Burke, K.; Ernzerhof, M. Erratum: Generalized gradient approximation made simple (Phys. Rev. Lett. 77, 3865(1996)). Phys. Rev. Lett. 1997, 78, 1396, 10.1103/PhysRevLett.78.1396
Zhang, Y. et al. Comment on ″Generalized Gradient Approximation Made Simple″. Phys. Rev. Lett. 1998, 80, 890, 10.1103/PhysRevLett.80.890
Artacho, E.; Anglada, E.; Diéguez, O.; Gale, J. D.; García, A.; Junquera, J.; Martin, R. M.; Ordejón, P.; Pruneda, J. M.; Sánchez-Portal, D.; Soler, J. M. The SIESTA method; Developments and applicability. J. Phys.: Condens. Matter 2008, 20, 064208, 10.1088/0953-8984/20/6/064208
Soler, J. M.; Artacho, E.; Gale, J. D.; García, A.; Junquera, J.; Ordejón, P.; Sánchez-Portal, D. The SIESTA method for ab initio order-N materials simulation. J. Phys.: Condens. Matter 2002, 14, 2745-2779, 10.1088/0953-8984/14/11/302
Sánchez-Portal, D.; Ordejón, P.; Artacho, E.; Soler, J. M. Density-functional method for very large systems with LCAO basis sets. Int. J. Quantum Chem. 1997, 65, 453-461, 10.1002/(SICI)1097-461X(1997)65:5<453::AID-QUA9>3.0.CO;2-V
Lide, D. R. CRC Handbook of Chemistry and Physics: A Ready-reference Book of Chemical and Physical Data, 89 th ed.; CRC Press, 2008.
Troullier, N.; Martins, J. L. Efficient pseudopotentials for plane-wave calculations. Phys. Rev. B: Condens. Matter Mater. Phys. 1991, 43, 1993-2006, 10.1103/PhysRevB.43.1993
Troullier, N.; Martins, J. A straightforward method for generating soft transferable pseudopotentials. Solid State Commun. 1990, 74, 613-616, 10.1016/0038-1098(90)90686-6
Kleinman, L.; Bylander, D. M. Efficacious form for model pseudopotentials. Phys. Rev. Lett. 1982, 48, 1425-1428, 10.1103/PhysRevLett.48.1425
Monkhorst, H. J.; Pack, J. D. Special points for Brillouin-zone integrations. Phys. Rev. B 1976, 13, 5188-5192, 10.1103/PhysRevB.13.5188
Cornil, J.; Dos Santos, D. A.; Beljonne, D.; Brédas, J. L. Electronic structure of phenylene vinylene oligomers: Influence of donor/acceptor substitutions. J. Phys. Chem. 1995, 99, 5604-5611, 10.1021/j100015a051
Gierschner, J.; Cornil, J.; Egelhaaf, H. J. Optical bandgaps of -conjugated organic materials at the polymer limit: Experiment and theory. Adv. Mater. 2007, 19, 173-191, 10.1002/adma.200600277
Milian Medina, B.; Beljonne, D.; Egelhaaf, H. J.; Gierschner, J. Effect of fluorination on the electronic structure and optical excitations of -conjugated molecules. J. Chem. Phys. 2007, 126, 111101, 10.1063/1.2713096
Bengtsson, L. Dipole correction for surface supercell calculations. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59, 12301-12304, 10.1103/PhysRevB.59.12301
Cornil, D.; Van Regemorter, T.; Beljonne, D.; Cornil, J. Work function shifts of a zinc oxide surface upon deposition of self-assembled monolayers: A theoretical insight. Phys. Chem. Chem. Phys. 2014, 16, 20887-20899, 10.1039/C4CP02811B
Neugebauer, J.; Scheffler, M. Adsorbate-substrate and adsorbate-adsorbate interactions of Na and K adlayers on Al(111). Phys. Rev. B: Condens. Matter Mater. Phys. 1992, 46, 16067-16080, 10.1103/PhysRevB.46.16067
Xie, Z.; Bâldea, I.; Demissie, A. T.; Smith, C. E.; Wu, Y.; Haugstad, G.; Frisbie, C. D. Exceptionally Small Statistical Variations in the Transport Properties of Metal-Molecule-Metal Junctions Composed of 80 Oligophenylene Dithiol Molecules. J. Am. Chem. Soc. 2017, 139, 5696-5699, 10.1021/jacs.7b01918
Haynes, W. M. L., D. R Bruno, T. J. CRC handbook of Chemistry and Physics: A Ready reference Book of Chemical and Physical Data, 97 th ed.; 2017.
Crivillers, N.; Liscio, A.; Di Stasio, F.; Van Dyck, C.; Osella, S.; Cornil, D.; Mian, S.; Lazzerini, G. M.; Fenwick, O.; Orgiu, E.; Reinders, F.; Braun, S.; Fahlman, M.; Mayor, M.; Cornil, J.; Palermo, V.; Cacialli, F.; Samorì, P. Photoinduced work function changes by isomerization of a densely packed azobenzene-based SAM on Au: A joint experimental and theoretical study. Phys. Chem. Chem. Phys. 2011, 13, 14302-14310, 10.1039/c1cp20851a
Hong, W.; Manrique, D. Z.; Moreno-García, P.; Gulcur, M.; Mishchenko, A.; Lambert, C. J.; Bryce, M. R.; Wandlowski, T. Single molecular conductance of tolanes: Experimental and theoretical study on the junction evolution dependent on the anchoring group. J. Am. Chem. Soc. 2012, 134, 2292-2304, 10.1021/ja209844r
Cornil, D.; Cornil, J. Work-function modification of the (111) gold surface upon deposition of self-assembled monolayers based on alkanethiol derivatives. J. Electron Spectrosc. Relat. Phenom. 2013, 189, 32-38, 10.1016/j.elspec.2013.06.004
Dhirani, A. A.; Zehner, R. W.; Hsung, R. P.; Guyot-Sionnest, P.; Sita, L. R. Self-assembly of conjugated molecular rods: A high-resolution STM study. J. Am. Chem. Soc. 1996, 118, 3319-3320, 10.1021/ja953782i
Yang, G.; Qian, Y.; Engtrakul, C.; Sita, L. R.; Liu, G. Y. Arenethiols form ordered and incommensurate self-assembled monolayers on Au(111) surfaces. J. Phys. Chem. B 2000, 104, 9059-9062, 10.1021/jp001611g
Press, W. H.; et al., Numerical Recipes. The Art of Scientific Computing; Cambridge University Press: Cambridge, U.K., 1986.
Otálvaro, D.; Veening, T.; Brocks, G. Self-assembled monolayer induced Au(111) and Ag(111) reconstructions: Work functions and interface dipole formation. J. Phys. Chem. C 2012, 116, 7826-7837, 10.1021/jp300512k
Diez-Cabanes, V.; Rodriguez Gonzalez, S.; Osella, S.; Cornil, D.; van Dyck, C.; Cornil, J. Energy Level Alignment at Interfaces between Au(111) and Thiolated Oligophenylenes of Increasing Chain Size: Theoretical Evidence of Pinning Effects. Adv. Theory. Simul. 2018, 1, 1700020, 10.1002/adts.201700020
Masillamani, A. M.; Osella, S.; Liscio, A.; Fenwick, O.; Reinders, F.; Mayor, M.; Palermo, V.; Cornil, J.; Samorì, P. Light-induced reversible modification of the work function of a new perfluorinated biphenyl azobenzene chemisorbed on Au (111). Nanoscale 2014, 6, 8969-8977, 10.1039/C4NR01880J
Crivillers, N.; Osella, S.; Van Dyck, C.; Lazzerini, G. M.; Cornil, D.; Liscio, A.; Di Stasio, F.; Mian, S.; Fenwick, O.; Reinders, F.; Neuburger, M.; Treossi, E.; Mayor, M.; Palermo, V.; Cacialli, F.; Cornil, J.; Samorì, P. Large Work Function Shift of Gold Induced by a Novel Perfluorinated Azobenzene-Based Self-Assembled Monolayer. Adv. Mater. 2013, 25, 432-436, 10.1002/adma.201201737
Osella, S.; Cornil, D.; Cornil, J. Work function modification of the (111) gold surface covered by long alkanethiol-based self-assembled monolayers. Phys. Chem. Chem. Phys. 2014, 16, 2866-2873, 10.1039/c3cp54217c
Wang, L.; Rangger, G. M.; Ma, Z.; Li, Q.; Shuai, Z.; Zojer, E.; Heimel, G. Is there a Au-S bond dipole in self-assembled monolayers on gold?. Phys. Chem. Chem. Phys. 2010, 12, 4287-4290, 10.1039/b924306m
Taylor, J.; Guo, H.; Wang, J. Ab initio modeling of quantum transport properties of molecular electronic devices. Phys. Rev. B: Condens. Matter Mater. Phys. 2001, 63, 2454071-24540713, 10.1103/PhysRevB.63.245407
Brandbyge, M.; Mozos, J. L.; Ordejón, P.; Taylor, J.; Stokbro, K. Density-functional method for nonequilibrium electron transport. Phys. Rev. B: Condens. Matter Mater. Phys. 2002, 65, 1654011-16540117, 10.1103/PhysRevB.65.165401
Imry, Y.; Landauer, R. Conductance viewed as transmission. Rev. Mod. Phys. 1999, 71, S306-S312, 10.1103/RevModPhys.71.S306
Buttiker, M.; Imry, Y.; Landauer, R.; Pinhas, S. Generalized many-channel conductance formula with application to small rings. Phys. Rev. B: Condens. Matter Mater. Phys. 1985, 31, 6207-6215, 10.1103/PhysRevB.31.6207
Jin, C.; Strange, M.; Markussen, T.; Solomon, G. C.; Thygesen, K. S. Energy level alignment and quantum conductance of functionalized metal-molecule junctions: Density functional theory versus GW calculations. J. Chem. Phys. 2013, 139, 184307, 10.1063/1.4829520
Evans, S. D.; Urankar, E.; Ulman, A.; Ferris, N. Self-Assembled Monolayers of Alkanethiols Containing a Polar Aromatic Group: Effects of the Dipole Position on Molecular Packing, Orientation, and Surface Wetting Properties. J. Am. Chem. Soc. 1991, 113, 4121-4131, 10.1021/ja00011a010
Zehner, R. W.; Parsons, B. F.; Hsung, R. P.; Sita, L. R. Tuning the Work Function of Gold with Self-Assembled Monolayers Derived from X-[C6H4-C«C]nC6H4-SH (n = 0, 1, 2; X = H, F, CH3, CF3, and OCH3. Langmuir 1999, 15, 1121-1127, 10.1021/la981114f
Wu, K. Y.; Yu, S. Y.; Tao, Y. T. Continuous modulation of electrode work function with mixed self-assembled monolayers and its effect in charge injection. Langmuir 2009, 25, 6232-6238, 10.1021/la900046b
Chen, C. Y.; Wu, K. Y.; Chao, Y. C.; Zan, H. W.; Meng, H. F.; Tao, Y. T. Concomitant tuning of metal work function and wetting property with mixed self-assembled monolayers. Org. Electron. 2011, 12, 148-153, 10.1016/j.orgel.2010.10.013
Heimel, G.; Romaner, L.; Zojer, E.; Bredas, J. L. Toward control of the metal-organic interfacial electronic structure in molecular electronics: A first-principles study on self-assembled monolayers of -conjugated molecules on noble metals. Nano Lett. 2007, 7, 932-940, 10.1021/nl0629106
Romaner, L.; Heimel, G.; Zojer, E. Electronic structure of thiol-bonded self-assembled monolayers: Impact of coverage. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 77, 045113, 10.1103/PhysRevB.77.045113
Obersteiner, V.; Egger, D. A.; Heimel, G.; Zojer, E. Impact of collective electrostatic effects on charge transport through molecular monolayers. J. Phys. Chem. C 2014, 118, 22395-22401, 10.1021/jp5084955
Obersteiner, V.; Egger, D. A.; Zojer, E. Impact of Anchoring Groups on Ballistic Transport: Single Molecule vs Monolayer Junctions. J. Phys. Chem. C 2015, 119, 21198-21208, 10.1021/acs.jpcc.5b06110
Bâldea, I. Ambipolar transition voltage spectroscopy: Analytical results and experimental agreement. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 85, 035442, 10.1103/PhysRevB.85.035442
Liu, Z. F.; Neaton, J. B. Voltage dependence of molecule-electrode coupling in biased molecular junctions. J. Phys. Chem. C 2017, 121, 21136-21144, 10.1021/acs.jpcc.7b05567
Garcia-Lastra, J. M.; Rostgaard, C.; Rubio, A.; Thygesen, K. S. Polarization-induced renormalization of molecular levels at metallic and semiconducting surfaces. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 80, 245427, 10.1103/PhysRevB.80.245427
Garcia-Lastra, J. M.; Rostgaard, C.; Rubio, A.; Thygesen, K. S. Erratum: Polarization-induced renormalization of molecular levels at metallic and semiconducting surfaces (Phys. Rev. B. Condens. Matter. Mater. Phys. 80, 245427 (2009)). Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 81, 049901, 10.1103/PhysRevB.81.049901
Neaton, J. B.; Hybertsen, M. S.; Louie, S. G. Renormalization of molecular electronic levels at metal-molecule interfaces. Phys. Rev. Lett. 2006, 97, 216405, 10.1103/PhysRevLett.97.216405
Garcia-Lastra, J. M.; Thygesen, K. S. Renormalization of optical excitations in molecules near a metal surface. Phys. Rev. Lett. 2011, 106, 187402, 10.1103/PhysRevLett.106.187402
Wu, Q.; Van Voorhis, T. Extracting electron transfer coupling elements from constrained density functional theory. J. Chem. Phys. 2006, 125, 164105, 10.1063/1.2360263