The algebraic diagrammatic construction scheme for the polarization propagator for the calculation of excited states

The algebraic diagrammatic construction (ADC) scheme for the polarization propagator provides a series of ab initio methods for the calculation of excited states based on perturbation theory. In recent years, the second‐order ADC(2) scheme has attracted attention in the computational chemistry community because of its reliable accuracy and reasonable computational effort in the calculation of predominantly singly excited states. Owing to their size‐consistency, ADC methods are suited for the investigation of large molecules. In addition, their Hermitian structure and the availability of the intermediate state representation (ISR) allow for straightforward computation of excited‐state properties. Recently, an efficient implementation of ADC(3) has been reported, and its high accuracy for typical valence excited states of organic chromophores has been demonstrated. In this review, the origin of ADC‐based excited‐state methods in propagator theory is described, and an intuitive route for the derivation of algebraic expressions via the ISR is outlined and comparison to other excited‐state methods is made. Existing computer codes and implemented ADC variants are reviewed, but most importantly the accuracy and limits of different ADC schemes are critically examined. WIREs Comput Mol Sci 2015, 5:82–95. doi: 10.1002/wcms.1206

[1]  S. Rettrup,et al.  Benchmarking second order methods for the calculation of vertical electronic excitation energies: valence and Rydberg states in polycyclic aromatic hydrocarbons. , 2009, The journal of physical chemistry. A.

[2]  Walter Thiel,et al.  Benchmarks for electronically excited states: time-dependent density functional theory and density functional theory based multireference configuration interaction. , 2008, The Journal of chemical physics.

[3]  Andreas Dreuw,et al.  Calculating core‐level excitations and x‐ray absorption spectra of medium‐sized closed‐shell molecules with the algebraic‐diagrammatic construction scheme for the polarization propagator , 2014, J. Comput. Chem..

[4]  W. A. Bingel,et al.  Propagators in Quantum Chemistry , 1975 .

[5]  S. Peyerimhoff,et al.  Excited‐State Potentials , 2007 .

[6]  Lorenz S. Cederbaum,et al.  Many-body theory of core holes , 1980 .

[7]  Schirmer,et al.  Algebraic propagator approaches and intermediate-state representations. I. The biorthogonal and unitary coupled-cluster methods. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[8]  J. Schirmer,et al.  Review of biorthogonal coupled cluster representations for electronic excitation , 2009, 0906.5513.

[9]  L. Adamowicz,et al.  Conformational topology of ribose: A computational study , 2006 .

[10]  A. Trofimov,et al.  Electron excitation energies using a consistent third-order propagator approach: Comparison with full configuration interaction and coupled cluster results , 2002 .

[11]  L. Cederbaum.  Green's Functions and Propagators for Chemistry , 2002 .

[12]  Schirmer,et al.  Algebraic propagator approaches and intermediate-state representations. II. The equation-of-motion methods for N, N+/-1, and N+/-2 electrons. , 1996, Physical Review A. Atomic, Molecular, and Optical Physics.

[13]  John F. Stanton,et al.  The equation of motion coupled‐cluster method. A systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited state properties , 1993 .

[14]  Roland Lindh,et al.  Multiconfiguration second‐order perturbation theory approach to strong electron correlation in chemistry and photochemistry , 2012 .

[15]  L. Cederbaum,et al.  Many-Body Theory of Core-Valence Excitations , 1981 .

[16]  Poul Jørgensen,et al.  Response functions from Fourier component variational perturbation theory applied to a time-averaged quasienergy , 1998 .

[17]  R. Bartlett.  The coupled-cluster revolution , 2010 .

[18]  Jens Oddershede,et al.  Polarization Propagator Calculations , 1978 .

[19]  Lorenz S. Cederbaum,et al.  New approach to the one-particle Green's function for finite Fermi systems , 1983 .

[20]  Vincenzo Barone,et al.  Computational strategies for spectroscopy : from small molecules to nano systems , 2011 .

[21]  Hideo Sekino,et al.  A linear response, coupled‐cluster theory for excitation energy , 1984 .

[22]  Michael C. Zerner,et al.  An intermediate neglect of differential overlap technique for spectroscopy: Pyrrole and the azines , 1973 .

[23]  Christof Hättig,et al.  Implementation of RI-CC2 triplet excitation energies with an application to trans-azobenzene , 2002 .

[24]  C. Hättig,et al.  A pair natural orbital implementation of the coupled cluster model CC2 for excitation energies. , 2013, The Journal of chemical physics.

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

[26]  J. Schirmer,et al.  Size consistency of an algebraic propagator approach , 1998 .

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

[28]  Matthew L. Leininger,et al.  Psi4: an open‐source ab initio electronic structure program , 2012 .

[29]  Evgeny Epifanovsky,et al.  New implementation of high‐level correlated methods using a general block tensor library for high‐performance electronic structure calculations , 2013, J. Comput. Chem..

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

[31]  A. Dreuw,et al.  The Art of Choosing the Right Quantum Chemical Excited‐State Method for Large Molecular Systems , 2011 .

[32]  A. Fetter,et al.  Quantum Theory of Many-Particle Systems , 1971 .

[33]  Andreas Dreuw,et al.  Nature of the lowest excited states of neutral polyenyl radicals and polyene radical cations. , 2009, The Journal of chemical physics.

[34]  J. Olsen,et al.  Excitation energies of H2O, N2 and C2 in full configuration interaction and coupled cluster theory , 1996 .

[35]  M. Sierka,et al.  Turbomole , 2014 .

[36]  J Schirmer,et al.  Intermediate state representation approach to physical properties of electronically excited molecules. , 2004, The Journal of chemical physics.

[37]  J. Grunenberg.  Computational Spectroscopy: Methods, Experiments and Applications , 2010 .

[38]  R. Mcweeny,et al.  Methods Of Molecular Quantum Mechanics , 1969 .

[39]  Anna I Krylov,et al.  Equation-of-motion coupled-cluster methods for open-shell and electronically excited species: the Hitchhiker's guide to Fock space. , 2008, Annual review of physical chemistry.

[40]  Michael C. Zerner,et al.  An intermediate neglect of differential overlap technique for spectroscopy of transition-metal complexes. Ferrocene , 1980 .

[41]  Trygve Helgaker,et al.  The CC3 model: An iterative coupled cluster approach including connected triples , 1997 .

[42]  A. Szabó,et al.  Modern quantum chemistry : introduction to advanced electronic structure theory , 1982 .

[43]  Poul Jørgensen,et al.  The second-order approximate coupled cluster singles and doubles model CC2 , 1995 .

[44]  C. Hättig,et al.  Scaled opposite-spin CC2 for ground and excited states with fourth order scaling computational costs. , 2011, The Journal of chemical physics.

[45]  Walter Thiel,et al.  Orthogonalization corrections for semiempirical methods , 2000 .

[46]  A. Barth,et al.  Theoretical core-level excitation spectra of N2 and CO by a new polarisation propagator method , 1985 .

[47]  Hiroshi Nakatsuji,et al.  Cluster expansion of the wavefunction. Calculation of electron correlations in ground and excited states by SAC and SAC CI theories , 1979 .

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

[49]  Walter Thiel,et al.  Implementation of a general multireference configuration interaction procedure with analytic gradients in a semiempirical context using the graphical unitary group approach , 2003, J. Comput. Chem..

[50]  H. Koch,et al.  Calculation of size‐intensive transition moments from the coupled cluster singles and doubles linear response function , 1994 .

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

[52]  Manuela Merchán,et al.  Quantum chemistry of the excited state: 2005 overview , 2005 .

[53]  M. E. Casida.  Time-Dependent Density Functional Response Theory for Molecules , 1995 .

[54]  Walter Thiel,et al.  Semiempirical quantum–chemical methods , 2014 .

[55]  Ş. Selçuk Bayin,et al.  Mathematical Methods in Science and Engineering: Bayin/Mathematical , 2006 .

[56]  M. Ratner.  Molecular electronic-structure theory , 2000 .

[57]  Peter Comba,et al.  Modeling of molecular properties , 2011 .

[58]  J. Weller,et al.  Algebraic-diagrammatic construction propagator approach to molecular response properties , 2006 .

[59]  Hiroshi Nakatsuji,et al.  Cluster expansion of the wavefunction. Electron correlations in ground and excited states by SAC (symmetry-adapted-cluster) and SAC CI theories , 1979 .

[60]  Andreas Dreuw,et al.  Unrestricted algebraic diagrammatic construction scheme of second order for the calculation of excited states of medium-sized and large molecules. , 2009, The Journal of chemical physics.

[61]  Stefan Grimme,et al.  Density functional calculations of the vibronic structure of electronic absorption spectra. , 2004, The Journal of chemical physics.

[62]  Trygve Helgaker,et al.  Excitation energies from the coupled cluster singles and doubles linear response function (CCSDLR). Applications to Be, CH+, CO, and H2O , 1990 .

[63]  M. E. Casida,et al.  Progress in time-dependent density-functional theory. , 2011, Annual review of physical chemistry.

[64]  Andreas Dreuw,et al.  Quantum chemical methods for the investigation of photoinitiated processes in biological systems: theory and applications. , 2006, Chemphyschem : a European journal of chemical physics and physical chemistry.

[65]  A B Trofimov,et al.  Algebraic-diagrammatic construction polarization propagator approach to indirect nuclear spin-spin coupling constants. , 2012, The Journal of chemical physics.

[66]  Jochen Schirmer,et al.  An efficient polarization propagator approach to valence electron excitation spectra , 1995 .

[67]  Trygve Helgaker,et al.  Molecular Electronic-Structure Theory: Helgaker/Molecular Electronic-Structure Theory , 2000 .

[68]  Stefan Grimme,et al.  Density functional calculations with configuration interaction for the excited states of molecules , 1996 .

[69]  Christof Hättig,et al.  CC2 excitation energy calculations on large molecules using the resolution of the identity approximation , 2000 .

[70]  D. Danovich.  Green's function methods for calculating ionization potentials, electron affinities, and excitation energies , 2011 .

[71]  Walter Thiel,et al.  Benchmarks for electronically excited states: CASPT2, CC2, CCSD, and CC3. , 2008, The Journal of chemical physics.

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

[73]  Manabu Oumi,et al.  Quasidegenerate second-order perturbation corrections to single-excitation configuration interaction , 1999 .

[74]  A. Dreuw,et al.  Calculations of nonlinear response properties using the intermediate state representation and the algebraic-diagrammatic construction polarization propagator approach: two-photon absorption spectra. , 2012, The Journal of chemical physics.

[75]  Andreas Dreuw,et al.  The third-order algebraic diagrammatic construction method (ADC(3)) for the polarization propagator for closed-shell molecules: efficient implementation and benchmarking. , 2014, The Journal of chemical physics.

[76]  S. Grimme.  Calculation of the Electronic Spectra of Large Molecules , 2004 .

[77]  V. Barone,et al.  Recent advances in density functional methods , 1995 .

[78]  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.

[79]  Adèle D. Laurent,et al.  TD-DFT benchmarks: A review , 2013 .

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

[81]  M. Head‐Gordon,et al.  Long-range charge-transfer excited states in time-dependent density functional theory require non-local exchange , 2003 .

[82]  S. Grimme,et al.  A COMBINATION OF KOHN-SHAM DENSITY FUNCTIONAL THEORY AND MULTI-REFERENCE CONFIGURATION INTERACTION METHODS , 1999 .

[83]  Hiroshi Nakatsuji,et al.  Cluster expansion of the wavefunction. Pseduo-orbital theory applied to spin correlation , 1977 .

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

[85]  C. Marian,et al.  Performance of the Density Functional Theory/Multireference Configuration Interaction Method on Electronic Excitation of Extended π-Systems. , 2008, Journal of chemical theory and computation.

[86]  Björn O. Roos,et al.  Second-order perturbation theory with a complete active space self-consistent field reference function , 1992 .

[87]  John Heading,et al.  Mathematical methods in science and engineering , 1970 .

[88]  Christof Hättig,et al.  Structure Optimizations for Excited States with Correlated Second-Order Methods: CC2 and ADC(2) , 2005 .

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

[90]  Ove Christiansen,et al.  Atomic integral driven second order polarization propagator calculations of the excitation spectra of naphthalene and anthracene , 2000 .

[91]  Rodney J. Bartlett,et al.  Coupled‐cluster theory and its equation‐of‐motion extensions , 2012 .

[92]  Jeppe Olsen,et al.  Excitation energies of BH, CH2 and Ne in full configuration interaction and the hierarchy CCS, CC2, CCSD and CC3 of coupled cluster models , 1995 .

[93]  H. Monkhorst,et al.  Some aspects of the time-dependent coupled-cluster approach to dynamic response functions , 1983 .

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

[95]  E. Davidson.  The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices , 1975 .

[96]  Keli Han,et al.  Hydrogen bonding and transfer in the excited state , 2010 .

[97]  Andreas Dreuw,et al.  Simulation of photoelectron spectra using the reflection principle in combination with unrestricted excitation ADC2 to assess the accuracy of excited-state calculations. , 2011, Chemphyschem : a European journal of chemical physics and physical chemistry.

[98]  Martin Head-Gordon,et al.  Scaled opposite-spin second order Møller-Plesset correlation energy: an economical electronic structure method. , 2004, The Journal of chemical physics.

[99]  Ove Christiansen,et al.  Excited state coupled cluster methods , 2012 .

[100]  A. Köhn,et al.  Solvent Effects on Electronically Excited States Using the Conductor-Like Screening Model and the Second-Order Correlated Method ADC(2). , 2013, Journal of chemical theory and computation.

[101]  H. Koch,et al.  Integral-direct coupled cluster calculations of frequency-dependent polarizabilities, transition probabilities and excited-state properties , 1998 .

[102]  Henrik Koch,et al.  Coupled cluster response functions , 1990 .

[103]  Ghosh,et al.  Density-functional theory for time-dependent systems. , 1987, Physical review. A, General physics.

[104]  D. Neck,et al.  Many-Body Theory Exposed!: Propagator Description of Quantum Mechanics in Many-Body Systems , 2005 .

[105]  A. Dreuw,et al.  Application of the scaled-opposite-spin approximation to algebraic diagrammatic construction schemes of second order. , 2013, The Journal of chemical physics.

[106]  M. Head‐Gordon,et al.  Quasidegenerate scaled opposite spin second order perturbation corrections to single excitation configuration interaction. , 2008, The Journal of chemical physics.

[107]  Lorenz S. Cederbaum,et al.  Computational methods for the one-particle green's function , 1984 .

[108]  Andreas Dreuw,et al.  How much double excitation character do the lowest excited states of linear polyenes have , 2006 .