Ionization Energies, Electron Affinities, and Polarization Energies of Organic Molecular Crystals: Quantitative Estimations from a Polarizable Continuum Model (PCM)-Tuned Range-Separated Density Functional Approach.

We propose a new methodology for the first-principles description of the electronic properties relevant for charge transport in organic molecular crystals. This methodology, which is based on the combination of a nonempirical, optimally tuned range-separated hybrid functional with the polarizable continuum model, is applied to a series of eight representative molecular semiconductor crystals. We show that it provides ionization energies, electron affinities, and transport gaps in very good agreement with experimental values, as well as with the results of many-body perturbation theory within the GW approximation at a fraction of the computational costs. Hence, this approach represents an easily applicable and computationally efficient tool to estimate the gas-to-crystal phase shifts of the frontier-orbital quasiparticle energies in organic electronic materials.

[1]  W. Aulbur,et al.  Quasiparticle calculations in solids , 2000 .

[2]  John E. Anthony,et al.  Intermolecular Effects on the Hole States of Triisopropylsilylethynyl-Substituted Oligoacenes , 2010 .

[3]  Leeor Kronik,et al.  Quasiparticle spectra from a nonempirical optimally tuned range-separated hybrid density functional. , 2012, Physical review letters.

[4]  Lukas Gallandi,et al.  Long-Range Corrected DFT Meets GW: Vibrationally Resolved Photoelectron Spectra from First Principles. , 2015, Journal of chemical theory and computation.

[5]  A. Kahn,et al.  Physisorption-like Interaction at the Interfaces Formed by Pentacene and Samarium , 2002 .

[6]  Andreas Savin,et al.  Density functionals for the Yukawa electron-electron interaction , 1995 .

[7]  Jean-Luc Brédas,et al.  Long-range corrected hybrid functionals for π-conjugated systems: dependence of the range-separation parameter on conjugation length. , 2011, The Journal of chemical physics.

[8]  G. Scuseria,et al.  Importance of short-range versus long-range Hartree-Fock exchange for the performance of hybrid density functionals. , 2006, The Journal of chemical physics.

[9]  N. Handy,et al.  A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP) , 2004 .

[10]  Stephen R. Forrest,et al.  Introduction: Organic Electronics and Optoelectronics , 2007 .

[11]  Weitao Yang,et al.  Localization and delocalization errors in density functional theory and implications for band-gap prediction. , 2007, Physical review letters.

[12]  Matthias Scheffler,et al.  Combining GW calculations with exact-exchange density-functional theory: an analysis of valence-band photoemission for compound semiconductors , 2005, cond-mat/0502404.

[13]  A. Zunger,et al.  Self-interaction correction to density-functional approximations for many-electron systems , 1981 .

[14]  Electronic structure and surface morphology of [6,6]-phenyl-C 71-butyric acid methyl ester films , 2013 .

[15]  Claudio Attaccalite,et al.  First-principles GW calculations for fullerenes, porphyrins, phtalocyanine, and other molecules of interest for organic photovoltaic applications , 2010, 1011.3933.

[16]  F. Aryasetiawan,et al.  The GW method , 1997, cond-mat/9712013.

[17]  Haitao Sun,et al.  Influence of the delocalization error and applicability of optimal functional tuning in density functional calculations of nonlinear optical properties of organic donor-acceptor chromophores. , 2013, Chemphyschem : a European journal of chemical physics and physical chemistry.

[18]  Cathy Y. Wong,et al.  Relating the Physical Structure and Optoelectronic Function of Crystalline TIPS‐Pentacene , 2015 .

[19]  Jean-Luc Brédas,et al.  Polarization energies in oligoacene semiconductor crystals. , 2008, Journal of the American Chemical Society.

[20]  G. Galli,et al.  Large scale GW calculations. , 2015, Journal of chemical theory and computation.

[21]  K. Seki,et al.  Polarization energies of organic solids determined by ultraviolet photoelectron spectroscopy , 1981 .

[22]  Y. Saito,et al.  Threshold ionization energy of C60 in the solid state , 1992 .

[23]  Anna Köhler,et al.  Charge transport in organic semiconductors. , 2012, Topics in current chemistry.

[24]  H. Yoshida Low-Energy Inverse Photoemission Study on the Electron Affinities of Fullerene Derivatives for Organic Photovoltaic Cells , 2014 .

[25]  J. Brédas,et al.  Electronic Polarization Effects upon Charge Injection in Oligoacene Molecular Crystals: Description via a Polarizable Force Field , 2013 .

[26]  A. Heeger,et al.  Semiconducting and Metallic Polymers: The Fourth Generation of Polymeric Materials , 2001, Angewandte Chemie.

[27]  Bryan M. Wong,et al.  Nonempirically Tuned Range-Separated DFT Accurately Predicts Both Fundamental and Excitation Gaps in DNA and RNA Nucleobases , 2012, Journal of chemical theory and computation.

[28]  R. Baer,et al.  Reliable prediction of charge transfer excitations in molecular complexes using time-dependent density functional theory. , 2009, Journal of the American Chemical Society.

[29]  Donald G Truhlar,et al.  Perspectives on Basis Sets Beautiful: Seasonal Plantings of Diffuse Basis Functions. , 2011, Journal of chemical theory and computation.

[30]  Cherno Jaye,et al.  Direct determination of the electronic structure of the poly(3-hexylthiophene):phenyl-[6,6]-C61 butyric acid methyl ester blend , 2010 .

[31]  David J. Tozer,et al.  Relationship between long-range charge-transfer excitation energy error and integer discontinuity in Kohn–Sham theory , 2003 .

[32]  N. Armstrong,et al.  Energy Level Alignment in PCDTBT:PC70BM Solar Cells: Solution Processed NiOx for Improved Hole Collection and Efficiency , 2012 .

[33]  F. Lipparini,et al.  Embedding effects on charge-transport parameters in molecular organic materials. , 2007, The Journal of chemical physics.

[34]  T. Nishi,et al.  Ultraviolet photoelectron spectroscopy and inverse photoemission spectroscopy of [6,6]-phenyl-C61-butyric acid methyl ester in gas and solid phases , 2008 .

[35]  G. Scuseria,et al.  Assessment of a long-range corrected hybrid functional. , 2006, The Journal of chemical physics.

[36]  Erich Runge,et al.  First-principles GW calculations for DNA and RNA nucleobases , 2011, 1101.3738.

[37]  M. Head‐Gordon,et al.  Systematic optimization of long-range corrected hybrid density functionals. , 2008, The Journal of chemical physics.

[38]  Michael Bendikov,et al.  From oligomers to polymer: convergence in the HOMO-LUMO gaps of conjugated oligomers. , 2006, Organic letters.

[39]  Xiaofeng Qian,et al.  First-principles investigation of organic photovoltaic materials C-60, C-70, [C-60]PCBM, and bis-[C-60]PCBM using a many-body G(0)W(0)-Lanczos approach , 2014, 1411.2149.

[40]  Noa Marom,et al.  Strategy for finding a reliable starting point for G 0 W 0 demonstrated for molecules , 2012 .

[41]  Antoine Kahn,et al.  Fermi level, work function and vacuum level , 2016 .

[42]  James R. Chelikowsky,et al.  Optical spectra and exchange-correlation effects in molecular crystals , 2008, 0802.3168.

[43]  Antoine Kahn,et al.  Charge-separation energy in films of π-conjugated organic molecules , 2000 .

[44]  Seth Pettie,et al.  Mind the gap , 2006, Nature Reviews Drug Discovery.

[45]  Haitao Sun,et al.  Electronic Energy Gaps for π-Conjugated Oligomers and Polymers Calculated with Density Functional Theory. , 2014, Journal of chemical theory and computation.

[46]  A. Kahn,et al.  N-doping of pentacene by decamethylcobaltocene , 2009 .

[47]  Haitao Sun,et al.  Reliable Prediction with Tuned Range-Separated Functionals of the Singlet-Triplet Gap in Organic Emitters for Thermally Activated Delayed Fluorescence. , 2015, Journal of chemical theory and computation.

[48]  R. Baer,et al.  Prediction of charge-transfer excitations in coumarin-based dyes using a range-separated functional tuned from first principles. , 2009, The Journal of chemical physics.

[49]  P. Kebarle,et al.  Electron Affinities of Some Polycyclic Aromatic Hydrocarbons, Obtained from Electron‐Transfer Equilibria , 1993 .

[50]  Michel B. Johnson,et al.  Origins of ultralow thermal conductivity in bulk [6,6]-phenyl-C61-butyric acid methyl ester (PCBM). , 2016, Physical chemistry chemical physics : PCCP.

[51]  Haitao Sun,et al.  Applicability of optimal functional tuning in density functional calculations of ionization potentials and electron affinities of adenine-thymine nucleobase pairs and clusters. , 2015, Physical chemistry chemical physics : PCCP.

[52]  J. Tomasi,et al.  Quantum mechanical continuum solvation models. , 2005, Chemical reviews.

[53]  G. Galli,et al.  Self-consistent hybrid functional for condensed systems , 2014, 1501.03184.

[54]  Jean-Luc Brédas,et al.  Charge transport in organic semiconductors. , 2007, Chemical reviews.

[55]  P R C Kent,et al.  Neutral and charged excitations in carbon fullerenes from first-principles many-body theories. , 2008, The Journal of chemical physics.

[56]  Massimo Malagoli,et al.  The vibrational reorganization energy in pentacene: molecular influences on charge transport. , 2002, Journal of the American Chemical Society.

[57]  Leeor Kronik,et al.  Valence electronic structure of gas-phase 3,4,9,10-perylene tetracarboxylic acid dianhydride: Experiment and theory , 2006 .

[58]  Ariel Biller,et al.  Quasiparticle and optical spectroscopy of the organic semiconductors pentacene and PTCDA from first principles , 2012 .

[59]  Jeffrey B. Neaton,et al.  Solid-state optical absorption from optimally tuned time-dependent range-separated hybrid density functional theory , 2015, 1505.01602.

[60]  Jean-Luc Brédas,et al.  Organic electronic materials: recent advances in the DFT description of the ground and excited states using tuned range-separated hybrid functionals. , 2014, Accounts of chemical research.

[61]  Fabien Bruneval,et al.  Benchmarking the Starting Points of the GW Approximation for Molecules. , 2013, Journal of chemical theory and computation.

[62]  Jeffrey B. Neaton,et al.  Gap renormalization of molecular crystals from density-functional theory , 2013 .

[63]  Jochen Autschbach,et al.  Charge-transfer excitations and time-dependent density functional theory: problems and some proposed solutions. , 2009, Chemphyschem : a European journal of chemical physics and physical chemistry.

[64]  S. Krause,et al.  Determination of transport levels of organic semiconductors by UPS and IPS , 2008 .

[65]  Patrick Rinke,et al.  Accurate Ionization Potentials and Electron Affinities of Acceptor Molecules III: A Benchmark of GW Methods. , 2016, Journal of chemical theory and computation.

[66]  J. D. Talman Linked-cluster expansion for Jastrow-type wave functions and its application to the electron-gas problem , 1974 .

[67]  Suzuki,et al.  Pseudo-gap at the Fermi level in K3C60 observed by photoemission and inverse photoemission. , 1992, Physical review letters.

[68]  Isaac Tamblyn,et al.  Simultaneous Determination of Structures, Vibrations, and Frontier Orbital Energies from a Self-Consistent Range-Separated Hybrid Functional. , 2014, The journal of physical chemistry letters.

[69]  T. B. de Queiroz,et al.  Charge-transfer excitations in low-gap systems under the influence of solvation and conformational disorder: exploring range-separation tuning. , 2014, The Journal of chemical physics.

[70]  R. Baer,et al.  Density functional theory with correct long-range asymptotic behavior. , 2004, Physical review letters.

[71]  Paul L. Burn,et al.  Calculation of solid state molecular ionisation energies and electron affinities for organic semiconductors , 2011 .

[72]  L. Reining,et al.  Efficient GW calculations for SnO 2 , ZnO, and rubrene: The effective-energy technique , 2012 .

[73]  R. Baer,et al.  Deviations from piecewise linearity in the solid-state limit with approximate density functionals. , 2014, The Journal of chemical physics.

[74]  T. B. de Queiroz,et al.  Tuned range separated hybrid functionals for solvated low bandgap oligomers. , 2015, The Journal of chemical physics.

[75]  Haitao Sun,et al.  Theoretical study of excited states of DNA base dimers and tetramers using optimally tuned range‐separated density functional theory , 2016, J. Comput. Chem..

[76]  Benedetta Mennucci,et al.  Polarizable continuum model , 2012 .

[77]  J. Autschbach,et al.  Does a Molecule-Specific Density Functional Give an Accurate Electron Density? The Challenging Case of the CuCl Electric Field Gradient. , 2012, The journal of physical chemistry letters.

[78]  Monika Srebro,et al.  Delocalization error and "functional tuning" in Kohn-Sham calculations of molecular properties. , 2014, Accounts of chemical research.

[79]  Angel Rubio,et al.  Unified description of ground and excited states of finite systems: The self-consistent GW approach , 2012, 1202.3547.

[80]  Leeor Kronik,et al.  Excitation Gaps of Finite-Sized Systems from Optimally Tuned Range-Separated Hybrid Functionals. , 2012, Journal of chemical theory and computation.

[81]  Haitao Sun,et al.  Charge-Transfer Versus Charge-Transfer-Like Excitations Revisited. , 2015, Journal of chemical theory and computation.

[82]  L. Hedin NEW METHOD FOR CALCULATING THE ONE-PARTICLE GREEN'S FUNCTION WITH APPLICATION TO THE ELECTRON-GAS PROBLEM , 1965 .

[83]  Louie,et al.  Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies. , 1986, Physical review. B, Condensed matter.

[84]  Norbert Koch,et al.  Design of Organic Semiconductors from Molecular Electrostatics , 2011 .

[85]  Curvature and Frontier Orbital Energies in Density Functional Theory. , 2012, The journal of physical chemistry letters.

[86]  J. Brédas,et al.  Theoretical Study of the Local and Charge-Transfer Excitations in Model Complexes of Pentacene-C60 Using Tuned Range-Separated Hybrid Functionals. , 2014, Journal of chemical theory and computation.

[87]  A. De Vita,et al.  Supramolecular self-assembly driven by electrostatic repulsion: The 1D aggregation of rubrene pentagons on Au111. , 2010, ACS nano.

[88]  Patrick Rinke,et al.  Accurate Ionization Potentials and Electron Affinities of Acceptor Molecules II: Non-Empirically Tuned Long-Range Corrected Hybrid Functionals. , 2016, Journal of chemical theory and computation.

[89]  Angel Rubio,et al.  Benchmark of GW methods for azabenzenes , 2012 .

[90]  Bryon W. Larson,et al.  Electron Affinity of Phenyl–C61–Butyric Acid Methyl Ester (PCBM) , 2013 .

[91]  B. Dunietz,et al.  Orbital gap predictions for rational design of organic photovoltaic materials , 2014 .

[92]  Y. Qi,et al.  Solution doping of organic semiconductors using air-stable n-dopants , 2012 .

[93]  J. Brédas,et al.  Impact of molecular packing on electronic polarization in organic crystals: the case of pentacene vs TIPS-pentacene. , 2014, Journal of the American Chemical Society.

[94]  Weitao Yang,et al.  Many-electron self-interaction error in approximate density functionals. , 2006, The Journal of chemical physics.

[95]  Adrienn Ruzsinszky,et al.  Spurious fractional charge on dissociated atoms: pervasive and resilient self-interaction error of common density functionals. , 2006, The Journal of chemical physics.

[96]  J. P. Calbert,et al.  Organic semiconductors: A theoretical characterization of the basic parameters governing charge transport , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[97]  Burke,et al.  Generalized Gradient Approximation Made Simple. , 1996, Physical review letters.

[98]  D. Lichtenberger,et al.  Electronic properties of pentacene versus triisopropylsilylethynyl-substituted pentacene: environment-dependent effects of the silyl substituent. , 2010, Journal of the American Chemical Society.