New tools for the systematic analysis and visualization of electronic excitations. I. Formalism.

A variety of density matrix based methods for the analysis and visualization of electronic excitations are discussed and their implementation within the framework of the algebraic diagrammatic construction of the polarization propagator is reported. Their mathematical expressions are given and an extensive phenomenological discussion is provided to aid the interpretation of the results. Starting from several standard procedures, e.g., population analysis, natural orbital decomposition, and density plotting, we proceed to more advanced concepts of natural transition orbitals and attachment/detachment densities. In addition, special focus is laid on information coded in the transition density matrix and its phenomenological analysis in terms of an electron-hole picture. Taking advantage of both the orbital and real space representations of the density matrices, the physical information in these analysis methods is outlined, and similarities and differences between the approaches are highlighted. Moreover, new analysis tools for excited states are introduced including state averaged natural transition orbitals, which give a compact description of a number of states simultaneously, and natural difference orbitals (defined as the eigenvectors of the difference density matrix), which reveal details about orbital relaxation effects.

[1]  Andreas Dreuw,et al.  New tools for the systematic analysis and visualization of electronic excitations. II. Applications. , 2014, The Journal of chemical physics.

[2]  A. Voityuk,et al.  Exciton delocalization, charge transfer, and electronic coupling for singlet excitation energy transfer between stacked nucleobases in DNA: an MS-CASPT2 study. , 2014, The Journal of chemical physics.

[3]  A. Dreuw,et al.  Investigating excited electronic states using the algebraic diagrammatic construction (ADC) approach of the polarisation propagator , 2014 .

[4]  P. Salvador,et al.  Characterization and Quantification of Polyradical Character. , 2014, Journal of chemical theory and computation.

[5]  F. Plasser,et al.  Study of the diradicaloid character in a prototypical pancake-bonded dimer: the stacked tetracyanoethylene (TCNE) anion dimer and the neutral K(2)TCNE(2) complex. , 2014, Chemphyschem : a European journal of chemical physics and physical chemistry.

[6]  A. Krylov,et al.  Fission of Entangled Spins: An Electronic Structure Perspective , 2013 .

[7]  H. Lischka,et al.  Multiscale simulation of the ground and photo-induced charge-separated states of a molecular triad in polar organic solvent: exploring the conformations, fluctuations, and free energy landscapes. , 2013, The journal of physical chemistry. B.

[8]  D. Mazziotti,et al.  Cumulant reduced density matrices as measures of statistical dependence and entanglement between electronic quantum domains with application to photosynthetic light harvesting , 2013 .

[9]  F. Plasser,et al.  Electronic excitation and structural relaxation of the adenine dinucleotide in gas phase and solution , 2013, Photochemical & photobiological sciences : Official journal of the European Photochemistry Association and the European Society for Photobiology.

[10]  A. Voityuk.  Effects of dynamic disorder on exciton delocalization and photoinduced charge separation in DNA , 2013, Photochemical & photobiological sciences : Official journal of the European Photochemistry Association and the European Society for Photobiology.

[11]  J. Wahl,et al.  Coherent exciton transport driven by torsional dynamics: a quantum dynamical study of phenylene-vinylene type conjugated systems. , 2013, Faraday discussions.

[12]  Anna I. Krylov,et al.  Q‐Chem: an engine for innovation , 2013 .

[13]  F. Plasser,et al.  Synthesis, Spectroscopy, and Computational Analysis of Photoluminescent Bis(aminophenyl)-Substituted Thiophene Derivatives , 2013, Chemphyschem : a European journal of chemical physics and physical chemistry.

[14]  Hans Lischka,et al.  Electronically Excited States in Poly(p-phenylenevinylene): Vertical Excitations and Torsional Potentials from High-Level Ab Initio Calculations , 2013, The journal of physical chemistry. A.

[15]  Thomas Müller,et al.  The Multiradical Character of One- and Two-Dimensional Graphene Nanoribbons , 2013, Angewandte Chemie.

[16]  Hans Lischka,et al.  UV absorption spectrum of alternating DNA duplexes. Analysis of excitonic and charge transfer interactions. , 2012, The journal of physical chemistry. A.

[17]  Hans Lischka,et al.  Analysis of Excitonic and Charge Transfer Interactions from Quantum Chemical Calculations. , 2012, Journal of chemical theory and computation.

[18]  Daniel Escudero,et al.  Progress and challenges in the calculation of electronic excited states. , 2012, Chemphyschem : a European journal of chemical physics and physical chemistry.

[19]  Hans Lischka,et al.  Electronically excited states and photodynamics: a continuing challenge , 2012, Theoretical Chemistry Accounts.

[20]  R. Baer,et al.  Charge-Transfer-Like π→π* Excitations in Time-Dependent Density Functional Theory: A Conundrum and Its Solution. , 2011, Journal of chemical theory and computation.

[21]  Ryan M. Richard,et al.  Time-Dependent Density-Functional Description of the (1)La State in Polycyclic Aromatic Hydrocarbons: Charge-Transfer Character in Disguise? , 2011, Journal of chemical theory and computation.

[22]  A. Dutoi,et al.  Tracing molecular electronic excitation dynamics in real time and space. , 2010, The Journal of chemical physics.

[23]  Tracey M. Clarke,et al.  Charge photogeneration in organic solar cells. , 2010, Chemical reviews.

[24]  D. Trembath,et al.  Exciton localization in polymers with static disorder , 2009 .

[25]  A. V. Luzanov,et al.  Electron invariants and excited state structural analysis for electronic transitions within CIS, RPA, and TDDFT models , 2009 .

[26]  V. Chernyak,et al.  Exciton scattering approach for branched conjugated molecules and complexes. I. Formalism. , 2008, The Journal of chemical physics.

[27]  W. Barford,et al.  Excitons in conjugated polymers: wavefunctions, symmetries, and quantum numbers. , 2008, The Journal of chemical physics.

[28]  N. Kirova.  Understanding excitons in optically active polymers , 2008 .

[29]  István Mayer,et al.  Identifying a pair of interacting chromophores by using SVD transformed CIS wave functions , 2007 .

[30]  H. Lischka,et al.  Dependence of optical properties of oligo-para-phenylenes on torsional modes and chain length. , 2007, The journal of physical chemistry. B.

[31]  Vidmantas Gulbinas,et al.  Excited state and charge photogeneration dynamics in conjugated polymers. , 2007, The journal of physical chemistry. B.

[32]  Péter R. Surján,et al.  Natural orbitals in CIS and singular-value decomposition , 2007 .

[33]  István Mayer,et al.  Using singular value decomposition for a compact presentation and improved interpretation of the CIS wave functions , 2007 .

[34]  R. Bartlett,et al.  Coupled-cluster theory in quantum chemistry , 2007 .

[35]  Mengtao Sun,et al.  Comparison of the electronic structure of PPV and its derivative DIOXA-PPV , 2006 .

[36]  Andreas Dreuw,et al.  Single-reference ab initio methods for the calculation of excited states of large molecules. , 2005, Chemical reviews.

[37]  V. Chernyak,et al.  Exciton sizes of conducting polymers predicted by time-dependent density functional theory , 2005 .

[38]  A. Trofimov,et al.  Intermediate state representation approach to physical properties of electronically excited molecules. , 2004, The Journal of chemical physics.

[39]  M. Head‐Gordon,et al.  Failure of time-dependent density functional theory for long-range charge-transfer excited states: the zincbacteriochlorin-bacteriochlorin and bacteriochlorophyll-spheroidene complexes. , 2004, Journal of the American Chemical Society.

[40]  Martin Head-Gordon,et al.  Characterizing unpaired electrons from the one-particle density matrix , 2003 .

[41]  T. Pedersen,et al.  Ab initio tight-binding study of exciton optical and electro-optic properties of conjugated polymers , 2003 .

[42]  Richard L. Martin,et al.  NATURAL TRANSITION ORBITALS , 2003 .

[43]  Karina Sendt,et al.  Failure of density-functional theory and time-dependent density-functional theory for large extended π systems , 2002 .

[44]  Sergei Tretiak,et al.  Density matrix analysis and simulation of electronic excitations in conjugated and aggregated molecules. , 2002, Chemical reviews.

[45]  P. Schwerdtfeger,et al.  Excited states of ladder-type poly- p -phenylene oligomers , 2001, cond-mat/0103320.

[46]  Allan L. L. East,et al.  Naphthalene dimer: Electronic states, excimers, and triplet decay , 2000 .

[47]  S. Louie,et al.  Electron-hole excitations and optical spectra from first principles , 2000 .

[48]  H. C. Pedersen,et al.  Particle-in-a-box model of one-dimensional excitons in conjugated polymers , 2000 .

[49]  Jochen Schirmer,et al.  A consistent third-order propagator method for electronic excitation , 1999 .

[50]  Dept. of Physics,et al.  Ab initio calculation of the electronic and optical excitations in polythiophene: Effects of intra- and interchain screening , 1999, cond-mat/9909412.

[51]  Steven G. Louie,et al.  Optical Excitations in Conjugated Polymers , 1999 .

[52]  David Beljonne,et al.  Excited-State Electronic Structure of Conjugated Oligomers and Polymers: A Quantum-Chemical Approach to Optical Phenomena , 1999 .

[53]  Martin Head-Gordon,et al.  ANALYSIS OF ELECTRONIC TRANSITIONS AS THE DIFFERENCE OF ELECTRON ATTACHMENT AND DETACHMENT DENSITIES , 1995 .

[54]  Gregory D. Scholes,et al.  Electronic Interactions and Interchromophore Excitation Transfer , 1994 .

[55]  Schirmer,et al.  Closed-form intermediate representations of many-body propagators and resolvent matrices. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[56]  G. Strinati.  Effects of dynamical screening on resonances at inner-shell thresholds in semiconductors , 1984 .

[57]  István Mayer,et al.  Charge, bond order and valence in the AB initio SCF theory , 1983 .

[58]  Jochen Schirmer,et al.  Beyond the random-phase approximation: A new approximation scheme for the polarization propagator , 1982 .

[59]  Kazuo Takatsuka,et al.  Distribution of odd electrons in ground-state molecules , 1978 .

[60]  A. V. Luzanov,et al.  Application of transition density matrix for analysis of excited states , 1976 .

[61]  R. S. Mulliken.  Electronic Population Analysis on LCAO–MO Molecular Wave Functions. I , 1955 .

[62]  P. Löwdin.  Quantum Theory of Many-Particle Systems. I. Physical Interpretations by Means of Density Matrices, Natural Spin-Orbitals, and Convergence Problems in the Method of Configurational Interaction , 1955 .

[63]  F. Plasser.  Quantum Mechanical Simulations of Defect Dynamics in DNA and Model Systems , 2012 .

[64]  A. V. Luzanov,et al.  Excited State Structural Analysis: TDDFT and Related Models , 2011 .

[65]  Oleg V. Prezhdo,et al.  Irreducible charge density matrices for analysis of many‐electron wave functions , 2005 .

[66]  Shawn T. Brown,et al.  Advances in methods and algorithms in a modern quantum chemistry program package. , 2006, Physical chemistry chemical physics : PCCP.