Density matrix renormalization group pair-density functional theory (DMRG-PDFT): singlet–triplet gaps in polyacenes and polyacetylenes† †Electronic supplementary information (ESI) available: Absolute energies in hartrees, timings, geometry comparison, and Cartesian coordinates. See DOI: 10.1039/c8sc

The density matrix renormalization group (DMRG) is a powerful method to treat static correlation.

[1]  A. Kuppermann,et al.  Triplet states in 1,3-butadiene , 1973 .

[2]  R. Weinkauf,et al.  Photodetachment photoelectron spectroscopy of mass selected anions: anthracene and the anthracene-H2O cluster , 1997 .

[3]  White,et al.  Density matrix formulation for quantum renormalization groups. , 1992, Physical review letters.

[4]  Sebastian Wouters,et al.  DMRG-CASPT2 study of the longitudinal static second hyperpolarizability of all-trans polyenes. , 2016, The Journal of chemical physics.

[5]  Roland Lindh,et al.  Parallelization of a multiconfigurational perturbation theory , 2013, J. Comput. Chem..

[6]  Takeshi Yanai,et al.  Multistate Complete-Active-Space Second-Order Perturbation Theory Based on Density Matrix Renormalization Group Reference States. , 2017, Journal of chemical theory and computation.

[7]  A. Becke Density-functional thermochemistry. III. The role of exact exchange , 1993 .

[8]  A. Kuppermann,et al.  Singlet → triplet transitions in methyl-substituted ethylenes , 1975 .

[9]  A. Heeger,et al.  Synthesis of electrically conducting organic polymers: halogen derivatives of polyacetylene, (CH)x , 1977 .

[10]  A. Heeger Nobel Lecture: Semiconducting and metallic polymers: The fourth generation of polymeric materials* , 2001 .

[11]  Rebecca K. Carlson,et al.  Multiconfiguration Pair-Density Functional Theory. , 2014, Journal of chemical theory and computation.

[12]  H. Werner,et al.  New ab initio potential energy surfaces for the F+ H2 reaction. , 2007, The Journal of chemical physics.

[13]  F. Verstraete,et al.  Tensor product methods and entanglement optimization for ab initio quantum chemistry , 2014, 1412.5829.

[14]  Michele Muccini,et al.  Morphology and Field‐Effect‐Transistor Mobility in Tetracene Thin Films , 2005 .

[15]  Markus Reiher,et al.  The Density Matrix Renormalization Group Algorithm in Quantum Chemistry , 2010 .

[16]  B. Batlogg,et al.  Field-induced charge transport at the surface of pentacene single crystals: A method to study charge dynamics of two-dimensional electron systems in organic crystals , 2003 .

[17]  Paul M Zimmerman,et al.  Singlet fission in pentacene through multi-exciton quantum states. , 2010, Nature chemistry.

[18]  Dimitri Van Neck,et al.  The density matrix renormalization group for ab initio quantum chemistry , 2014, The European Physical Journal D.

[19]  Fred Wudl,et al.  Tetrathiafulvalenes, oligoacenenes, and their buckminsterfullerene derivatives: the brick and mortar of organic electronics. , 2004, Chemical reviews.

[20]  T. Jackson,et al.  Stacked pentacene layer organic thin-film transistors with improved characteristics , 1997, IEEE Electron Device Letters.

[21]  Markus Reiher,et al.  Second-Order Self-Consistent-Field Density-Matrix Renormalization Group. , 2016, Journal of chemical theory and computation.

[22]  Giovanni Li Manni,et al.  The generalized active space concept in multiconfigurational self-consistent field methods. , 2011, The Journal of chemical physics.

[23]  Markus Reiher,et al.  New Approaches for ab initio Calculations of Molecules with Strong Electron Correlation. , 2015, Chimia.

[24]  Takeshi Yanai,et al.  Multireference configuration interaction theory using cumulant reconstruction with internal contraction of density matrix renormalization group wave function. , 2013, The Journal of chemical physics.

[25]  Sandeep Sharma,et al.  The density matrix renormalization group in quantum chemistry. , 2011, Annual review of physical chemistry.

[26]  Josef Michl,et al.  Singlet fission. , 2010, Chemical reviews.

[27]  J. Stephen Binkley,et al.  Theoretical models incorporating electron correlation , 2009 .

[28]  Daoben Zhu,et al.  Recent progress of high performance organic thin film field-effect transistors , 2011 .

[29]  Takeshi Yanai,et al.  Complete active space second-order perturbation theory with cumulant approximation for extended active-space wavefunction from density matrix renormalization group. , 2014, The Journal of chemical physics.

[30]  Michael W. Schmidt,et al.  Are atoms intrinsic to molecular electronic wavefunctions? I. The FORS model , 1982 .

[31]  Rebecca K. Carlson,et al.  Molcas 8: New capabilities for multiconfigurational quantum chemical calculations across the periodic table , 2016, J. Comput. Chem..

[32]  Donald G Truhlar,et al.  Multiconfiguration Pair-Density Functional Theory: A Fully Translated Gradient Approximation and Its Performance for Transition Metal Dimers and the Spectroscopy of Re2Cl8(2-). , 2015, Journal of chemical theory and computation.

[33]  T. Yanai,et al.  Theoretical Study of the π → π* Excited States of Oligoacenes: A Full π-Valence DMRG-CASPT2 Study , 2014 .

[34]  G. Chan,et al.  Chapter 7 The Density Matrix Renormalization Group in Quantum Chemistry , 2009 .

[35]  A. Heeger,et al.  Focus Article: Twenty-five years of conducting polymers , 2003 .

[36]  Peter M W Gill,et al.  The two faces of static correlation. , 2011, The Journal of chemical physics.

[37]  N. Handy,et al.  Left-right correlation energy , 2001 .

[38]  Paul M Zimmerman,et al.  Mechanism for singlet fission in pentacene and tetracene: from single exciton to two triplets. , 2011, Journal of the American Chemical Society.

[39]  John E Anthony,et al.  Functionalized acenes and heteroacenes for organic electronics. , 2006, Chemical reviews.

[40]  A. Heeger,et al.  Organic Metals and Semiconductors: The Chemistry of Polyacetylene, (CH)x, and Its Derivatives. , 1980 .

[41]  O. Sǐnanoğlu,et al.  Many‐Electron Theory of Nonclosed‐Shell Atoms and Molecules. I. Orbital Wavefunction and Perturbation Theory , 1966 .

[42]  Eric M. Woerly,et al.  Synthesis of most polyene natural product motifs using just twelve building blocks and one coupling reaction , 2014, Nature chemistry.

[43]  Markus Reiher,et al.  Spin-adapted matrix product states and operators. , 2016, The Journal of chemical physics.

[44]  Wataru Mizukami,et al.  Density matrix renormalization group for ab initio calculations and associated dynamic correlation methods: A review of theory and applications , 2015 .

[45]  Murad J Y Tayebjee,et al.  Beyond Shockley-Queisser: Molecular Approaches to High-Efficiency Photovoltaics. , 2015, The journal of physical chemistry letters.

[46]  Debashree Ghosh,et al.  Orbital optimization in the density matrix renormalization group, with applications to polyenes and beta-carotene. , 2007, The Journal of chemical physics.

[47]  Garnet Kin-Lic Chan,et al.  Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms. , 2016, The Journal of chemical physics.

[48]  B. Roos,et al.  A complete active space SCF method (CASSCF) using a density matrix formulated super-CI approach , 1980 .

[49]  Oana D. Jurchescu,et al.  Effect of impurities on the mobility of single crystal pentacene , 2004, cond-mat/0404130.

[50]  N. Handy,et al.  Dynamical and Nondynamical Correlation , 1996 .

[51]  E. Davidson,et al.  Nature of ground and electronic excited states of higher acenes , 2016, Proceedings of the National Academy of Sciences.

[52]  U. Schollwoeck The density-matrix renormalization group in the age of matrix product states , 2010, 1008.3477.

[53]  Sheng Guo,et al.  A projected approximation to strongly contracted N-electron valence perturbation theory for DMRG wavefunctions. , 2016, The Journal of chemical physics.

[54]  C. K. Chiang,et al.  Polyacetylene, (CH)x: n‐type and p‐type doping and compensation , 1978 .

[55]  C. Dimitrakopoulos,et al.  Organic Thin Film Transistors for Large Area Electronics , 2002 .

[56]  P. Zimmerman Singlet-Triplet Gaps through Incremental Full Configuration Interaction. , 2017, The journal of physical chemistry. A.

[57]  A. Nozik,et al.  Solar conversion efficiency of photovoltaic and photoelectrolysis cells with carrier multiplication absorbers , 2006 .

[58]  Matthias Troyer,et al.  An efficient matrix product operator representation of the quantum chemical Hamiltonian. , 2015, The Journal of chemical physics.

[59]  Garnet Kin-Lic Chan,et al.  The radical character of the acenes: a density matrix renormalization group study. , 2007, The Journal of chemical physics.

[60]  Kimihiko Hirao,et al.  Theoretical study of the π→π* excited states of linear polyenes: The energy gap between 11Bu+ and 21Ag− states and their character , 1998 .

[61]  M. Frisch,et al.  Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields , 1994 .

[62]  Donald G Truhlar,et al.  Multiconfiguration Pair-Density Functional Theory: A New Way To Treat Strongly Correlated Systems. , 2017, Accounts of chemical research.

[63]  Yukio Kawashima,et al.  Theoretical study of the valence π → π* excited states of polyacenes: anthracene and naphthacene , 1999 .

[64]  H. Angliker,et al.  Electronic spectra of hexacene in solution (ground state. Triplet state. Dication and dianion) , 1982 .

[65]  Young-Geun Ha,et al.  Studies of tetracene- and pentacene-based organic thin-film transistors fabricated by the neutral cluster beam deposition method. , 2005, The journal of physical chemistry. B.

[66]  B. Batlogg,et al.  Hole mobility in organic single crystals measured by a flip-crystal field-effect technique , 2004 .

[67]  U. Schollwoeck The density-matrix renormalization group , 2004, cond-mat/0409292.

[68]  M. Head‐Gordon,et al.  Highly correlated calculations with a polynomial cost algorithm: A study of the density matrix renormalization group , 2002 .

[69]  A Eugene DePrince,et al.  Large-Scale Variational Two-Electron Reduced-Density-Matrix-Driven Complete Active Space Self-Consistent Field Methods. , 2016, Journal of chemical theory and computation.

[70]  Michael W. Schmidt,et al.  Hybrid Correlation Energy (HyCE): An Approach Based on Separate Evaluations of Internal and External Components. , 2018, The journal of physical chemistry. A.

[71]  Enhua Xu,et al.  Multireference second order perturbation theory with a simplified treatment of dynamical correlation. , 2015, Journal of chemical theory and computation.

[72]  White,et al.  Density-matrix algorithms for quantum renormalization groups. , 1993, Physical review. B, Condensed matter.

[73]  Takeshi Yanai,et al.  Second-order perturbation theory with a density matrix renormalization group self-consistent field reference function: theory and application to the study of chromium dimer. , 2011, The Journal of chemical physics.

[74]  A. J. Merer,et al.  Ultraviolet spectra and excited states of ethylene and its alkyl derivatives , 1969 .

[75]  Josef Michl,et al.  Recent advances in singlet fission. , 2013, Annual review of physical chemistry.

[76]  W. Siebrand Radiationless Transitions in Polyatomic Molecules. II. Triplet‐Ground‐State Transitions in Aromatic Hydrocarbons , 1967 .

[77]  Ali Alavi,et al.  Combining Internally Contracted States and Matrix Product States To Perform Multireference Perturbation Theory. , 2016, Journal of chemical theory and computation.

[78]  J. Moore Investigation of the low energy singlet-triplet and singlet-singlet transitions in ethylene derivatives by ion impact , 1972 .

[79]  Celestino Angeli,et al.  Multireference Perturbation Theory with Cholesky Decomposition for the Density Matrix Renormalization Group , 2016, Journal of chemical theory and computation.

[80]  D. V. Lang,et al.  Field-effect transistor on pentacene single crystal , 2003 .

[81]  Quan Manh Phung,et al.  Cumulant Approximated Second-Order Perturbation Theory Based on the Density Matrix Renormalization Group for Transition Metal Complexes: A Benchmark Study. , 2016, Journal of chemical theory and computation.

[82]  Markus Reiher,et al.  Density matrix renormalization group with efficient dynamical electron correlation through range separation. , 2015, The Journal of chemical physics.

[83]  Takeshi Yanai,et al.  Fully Internally Contracted Multireference Configuration Interaction Theory Using Density Matrix Renormalization Group: A Reduced-Scaling Implementation Derived by Computer-Aided Tensor Factorization. , 2015, Journal of chemical theory and computation.

[84]  Markus Reiher,et al.  New electron correlation theories for transition metal chemistry. , 2011, Physical chemistry chemical physics : PCCP.

[85]  A. Kuppermann,et al.  Low energy, variable angle electron-impact excitation of 1,3,5-hexatriene☆ , 1977 .

[86]  M. Zander Polycyclic Hydrocarbons. Band I, Von E. Clar. Academic Press, London‐New York und Springer‐Verlag, Berlin‐Göttingen‐Heidelberg 1964. 1. Aufl., XXVIII, 488 S., 80 Abb., 8 Tab., Ln. DM 70.–. , 1965 .

[87]  Garnet Kin-Lic Chan,et al.  The ab-initio density matrix renormalization group in practice. , 2015, The Journal of chemical physics.

[88]  Dawei Zhang,et al.  Excitation energy calculation of conjugated hydrocarbons: a new Pariser-Parr-Pople model parameterization approaching CASPT2 accuracy. , 2011, The Journal of chemical physics.

[89]  M. Deleuze,et al.  Focal point analysis of the singlet-triplet energy gap of octacene and larger acenes. , 2011, The journal of physical chemistry. A.

[90]  Krishnan Raghavachari,et al.  Electron Correlation Effects in Molecules , 1996 .

[91]  W. G. Schneider,et al.  Laser Generation of Excitons and Fluorescence in Anthracene Crystals , 1965 .

[92]  S. Godtfredsen,et al.  Ullmann ' s Encyclopedia of Industrial Chemistry , 2017 .

[93]  J. B. Birks,et al.  Quenching of excited singlet and triplet states of aromatic hydrocarbons by oxygen and nitric oxide , 1970 .

[94]  E. Veen Low-energy electron-impact spectroscopy on ethylene , 1976 .

[95]  Hai-bo Ma,et al.  Full Quantum Dynamics Simulation of a Realistic Molecular System Using the Adaptive Time-Dependent Density Matrix Renormalization Group Method. , 2018, The journal of physical chemistry letters.

[96]  Thomas N. Jackson,et al.  Thin-film transistors based on well-ordered thermally evaporated naphthacene films , 2002 .

[97]  Qiming Sun,et al.  N-Electron Valence State Perturbation Theory Based on a Density Matrix Renormalization Group Reference Function, with Applications to the Chromium Dimer and a Trimer Model of Poly(p-Phenylenevinylene). , 2015, Journal of chemical theory and computation.

[98]  Timothy C. Berkelbach,et al.  The quantum coherent mechanism for singlet fission: experiment and theory. , 2013, Accounts of chemical research.

[99]  J. Olsen,et al.  Pushing configuration-interaction to the limit: Towards massively parallel MCSCF calculations. , 2017, The Journal of chemical physics.

[100]  Naoki Nakatani,et al.  Density matrix renormalization group (DMRG) method as a common tool for large active-space CASSCF/CASPT2 calculations , 2017 .

[101]  P. Löwdin Quantum Theory of Many-Particle Systems. III. Extension of the Hartree-Fock Scheme to Include Degenerate Systems and Correlation Effects , 1955 .

[102]  R. R. Alfano,et al.  Heterofission in pentacene-doped tetracene single crystals , 1977 .