Left‐eigenstate completely renormalized equation‐of‐motion coupled‐cluster methods: Review of key concepts, extension to excited states of open‐shell systems, and comparison with electron‐attached and ionized approaches

The recently proposed left-eigenstate completely renormalized (CR) coupled-cluster (CC) method with singles, doubles, and noniterative triples, termed CR-CC(2,3) Piecuch and Wloch, J Chem Phys, 2005, 123, 224105; Piecuch et al. Chem Phys Lett, 2006, 418, 467 and the companion CR-EOMCC(2,3) methodology, which has been previously applied to singlet excited states of closed-shell molecular systems Wloch et al. Mol Phys, 2006, 104, 2149 and in which relatively inexpensive noniterative corrections due to triple excitations derived from the biorthogonal method of moments of CC equations (MMCC) are added to the CC singles and doubles (CCSD) or equation-of-motion (EOM) CCSD energies, have been extended to excited states of open-shell species. The resulting highly efficient computer codes for the open-shell CR-EOMCC(2,3) approach exploiting the recursively generated intermediates and fast matrix multiplication routines have been developed and interfaced with the GAMESS package, enabling CR-EOMCC(2,3) calculations for singlet as well as nonsinglet ground and excited states of closed- and open-shell systems using the restricted Hartree–Fock or restricted open-shell Hartree–Fock references. A number of important mathematical and algorithmic details related to formal aspects and computer implementation of the CR-EOMCC(2,3) method have been discussed, in addition to overviewing the key concepts behind the CR-EOMCC(2,3) and biorthogonal MMCC methodologies for ground and excited states, and the numerical results involving low-lying states of the CH, CNC, C2N, N3, and NCO species, including states dominated by two-electron transitions, have been presented. The results of the CR-EOMCC(2,3) calculations have been compared with other CC/EOMCC approaches, including the EOMCCSD and EOMCC singles, doubles, and triples methods, and their full and active-space valence counterparts based on the electron-attached and ionized EOMCC methodologies, and the predecessor of CR-EOMCC(2,3) termed CR-EOMCCSD(T) Kowalski and Piecuch, J Chem Phys, 2004, 120, 1715. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

[1]  H. Nakatsuji,et al.  Hyperfine splitting constants studied by the symmetry adapted cluster‐configuration interaction method , 1994 .

[2]  P. Piecuch,et al.  Active-space coupled-cluster study of electronic states of Be3. , 2005, The Journal of chemical physics.

[3]  Gustavo E. Scuseria,et al.  The vibrational frequencies of ozone , 1990 .

[4]  K. Kowalski.  Implementation of the locally renormalized CCSD(T) approaches for arbitrary reference function. , 2005, The Journal of chemical physics.

[5]  John F. Stanton,et al.  A simple correction to final state energies of doublet radicals described by equation-of-motion coupled cluster theory in the singles and doubles approximation , 1997 .

[6]  Marat Valiev,et al.  Noniterative corrections to equation‐of‐motion coupled‐cluster excited state energies based on the reduced method of moments of coupled cluster equations , 2008 .

[7]  G. Herzberg,et al.  Constants of diatomic molecules , 1979 .

[8]  R. Bartlett,et al.  Description of core‐excitation spectra by the open‐shell electron‐attachment equation‐of‐motion coupled cluster method , 1995 .

[9]  Anna I. Krylov,et al.  Perturbative corrections to the equation-of-motion spin–flip self-consistent field model: Application to bond-breaking and equilibrium properties of diradicals , 2002 .

[10]  H. Nakatsuji,et al.  Symmetry‐adapted cluster–configuration interaction method applied to high‐spin multiplicity , 1993 .

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

[12]  Walter Thiel,et al.  Benchmarks for Electronically Excited States: A Comparison of Noniterative and Iterative Triples Corrections in Linear Response Coupled Cluster Methods: CCSDR(3) versus CC3. , 2009, Journal of chemical theory and computation.

[13]  G. Herzberg.  Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules , 1939 .

[14]  K. Hirao,et al.  Cluster expansion of the wavefunction. Pseudo‐orbital theory based on the SAC expansion and its application to the spin density of open‐shell systems , 1978 .

[15]  R. Bartlett,et al.  EOMXCC: A New Coupled-Cluster Method for Electronic Excited States , 1999 .

[16]  E. C. Lim,et al.  Ab initio study of a biradical radiationless decay channel of the lowest excited electronic state of cytosine and its derivatives. , 2005, The Journal of chemical physics.

[17]  Josef Paldus,et al.  Time-dependent coupled cluster approach: Excitation energy calculation using an orthogonally spin-adapted formalism , 1986 .

[18]  Martin Schütz,et al.  Low-order scaling local electron correlation methods. III. Linear scaling local perturbative triples correction (T) , 2000 .

[19]  K Kowalski,et al.  Experimental and theoretical UV characterizations of acetylacetone and its isomers. , 2006, The journal of physical chemistry. A.

[20]  J. S. Binkley,et al.  The calculation of spin-restricted single-determinant wavefunctions , 1974 .

[21]  Josef Paldus,et al.  Correlation problems in atomic and molecular systems III. Rederivation of the coupled-pair many-electron theory using the traditional quantum chemical methodst†‡§ , 1971 .

[22]  P. Piecuch,et al.  A comparison of the renormalized and active-space coupled-cluster methods: Potential energy curves of BH and F2 , 2001 .

[23]  P. Piecuch,et al.  Automated derivation and parallel computer implementation of renormalized and active-space coupled-cluster methods , 2006 .

[24]  K. Hirao,et al.  A generalization of the Davidson's method to large nonsymmetric eigenvalue problems , 1982 .

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

[26]  Rodney J. Bartlett,et al.  Coupled-cluster methods with internal and semi-internal triply and quadruply excited clusters: CCSDt and CCSDtq approaches , 1999 .

[27]  Kimihiko Hirao,et al.  Cluster expansion of the wavefunction. Symmetry-adapted-cluster expansion, its variational determination, and extension of open-shell orbital theory , 1978 .

[28]  Mark S. Gordon,et al.  General atomic and molecular electronic structure system , 1993, J. Comput. Chem..

[29]  J. Gauss,et al.  Analytic energy derivatives for ionized states described by the equation‐of‐motion coupled cluster method , 1994 .

[30]  Rollin A King,et al.  Coupled cluster methods including triple excitations for excited states of radicals. , 2005, The Journal of chemical physics.

[31]  Krishnan Raghavachari,et al.  Highly correlated systems: Structure, binding energy and harmonic vibrational frequencies of ozone , 1989 .

[32]  Rodney J. Bartlett,et al.  The equation-of-motion coupled-cluster method: Excitation energies of Be and CO , 1989 .

[33]  Erlendur Jónsson,et al.  Two-dimensional (2+n) resonance enhanced multiphoton ionization of HCl: Photorupture channels via the F 1Delta2 Rydberg state and ab initio spectra. , 2008, The Journal of chemical physics.

[34]  Krishnan Raghavachari,et al.  An augmented coupled cluster method and its application to the first‐row homonuclear diatomics , 1985 .

[35]  Rodney J. Bartlett,et al.  Coupled-cluster theory for excited electronic states: The full equation-of-motion coupled-cluster single, double, and triple excitation method , 2001 .

[36]  Hiroshi Nakatsuji,et al.  Deepening and Extending the Quantum Principles in Chemistry , 2005 .

[37]  R. Bartlett,et al.  Recursive intermediate factorization and complete computational linearization of the coupled-cluster single, double, triple, and quadruple excitation equations , 1991 .

[38]  H. Nakatsuji,et al.  Cluster expansion of the wave function. Spin and electron correlations in doublet radicals studied by the symmetry adapted cluster and symmetry adapted cluster-configuration interaction theories , 1983 .

[39]  Josef Paldus,et al.  On the significance of quadruply excited clusters in coupled-cluster calculations for the low-lying states of BN and C2 , 2008 .

[40]  Cristina Puzzarini,et al.  Theoretical models on the Cu2O2 torture track: mechanistic implications for oxytyrosinase and small-molecule analogues. , 2006, The journal of physical chemistry. A.

[41]  R. Bartlett,et al.  Equation-of-motion coupled cluster method with full inclusion of connected triple excitations for electron-attached states: EA-EOM-CCSDT , 2003 .

[42]  P. Pulay.  Improved SCF convergence acceleration , 1982 .

[43]  G. Herzberg,et al.  Spectra of diatomic molecules , 1950 .

[44]  Rodney J. Bartlett,et al.  Equation-of-motion coupled cluster method with full inclusion of the connected triple excitations for ionized states: IP-EOM-CCSDT , 2003 .

[45]  K. Kowalski.  Completely Renormalized EOMCCSD(T) Method Employing Independent Optimization of the Cluster Product Terms , 2005 .

[46]  Ludwik Adamowicz,et al.  STATE-SELECTIVE MULTIREFERENCE COUPLED-CLUSTER THEORY EMPLOYING THE SINGLE-REFERENCE FORMALISM : IMPLEMENTATION AND APPLICATION TO THE H8 MODEL SYSTEM , 1994 .

[47]  Rodney J. Bartlett,et al.  Analytic energy derivatives in many‐body methods. I. First derivatives , 1989 .

[48]  Masahiro Ehara,et al.  Analytical energy gradients of the excited, ionized and electron-attached states calculated by the SAC-CI general-R method , 2001 .

[49]  Marat Valiev,et al.  Hybrid coupled cluster and molecular dynamics approach: application to the excitation spectrum of cytosine in the native DNA environment. , 2006, The Journal of chemical physics.

[50]  G. Herzberg,et al.  Molecular Spectra and Molecular Structure , 1992 .

[51]  Karol Kowalski,et al.  The active-space equation-of-motion coupled-cluster methods for excited electronic states: The EOMCCSDt approach , 2000 .

[52]  P. Piecuch,et al.  Efficient formulation and computer implementation of the active-space electron-attached and ionized equation-of-motion coupled-cluster methods. , 2006, The Journal of chemical physics.

[53]  Karol Kowalski,et al.  New coupled-cluster methods with singles, doubles, and noniterative triples for high accuracy calculations of excited electronic states. , 2004, The Journal of chemical physics.

[54]  Jürgen Gauss,et al.  Calculation of excited-state properties using general coupled-cluster and configuration-interaction models. , 2004, The Journal of chemical physics.

[55]  Piotr Piecuch,et al.  Computational investigation of the conrotatory and disrotatory isomerization channels of bicyclo[1.1.0]butane to buta-1,3-diene: a completely renormalized coupled-cluster study. , 2007, The journal of physical chemistry. A.

[56]  P. Piecuch,et al.  Breaking bonds of open-shell species with the restricted open-shell size extensive left eigenstate completely renormalized coupled-cluster method. , 2008, The journal of physical chemistry. A.

[57]  Anna I. Krylov,et al.  Singlet-triplet gaps in diradicals by the spin-flip approach: A benchmark study , 2002 .

[58]  Serguei Patchkovskii,et al.  On the origin of the ultrafast internal conversion of electronically excited pyrimidine bases. , 2005, The journal of physical chemistry. A.

[59]  R. Manne,et al.  A new procedure for Roothaan's symmetry-restricted open-shell SCF method , 1976 .

[60]  J. G. Snijders,et al.  Coupled cluster Green's function method: Working equations and applications , 1993 .

[61]  P. Piecuch,et al.  Application of renormalized coupled-cluster methods to potential function of water , 2008 .

[62]  Jeppe Olsen,et al.  Full configuration interaction benchmarking of coupled-cluster models for the lowest singlet energy surfaces of N2 , 2000 .

[63]  P. Piecuch,et al.  Active-space equation-of-motion coupled-cluster methods for excited states of radicals and other open-shell systems: EA-EOMCCSDt and IP-EOMCCSDt. , 2005, The Journal of chemical physics.

[64]  Andrew G. Taube,et al.  Improving upon CCSD(T): LambdaCCSD(T). I. Potential energy surfaces. , 2008, The Journal of chemical physics.

[65]  Ernest R. Davidson,et al.  Spin-restricted open-shell self-consistent-field theory , 1973 .

[66]  J. Stanton.  Why CCSD(T) works: a different perspective , 1997 .

[67]  Lori A Burns,et al.  An exploration of electronic structure and nuclear dynamics in tropolone: II. The A (1)B2 (pi* pi) excited state. , 2009, The Journal of chemical physics.

[68]  P. Löwdin.  Studies in Perturbation Theory. IV. Solution of Eigenvalue Problem by Projection Operator Formalism , 1962 .

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

[70]  Henry F. Schaefer,et al.  A new implementation of the full CCSDT model for molecular electronic structure , 1988 .

[71]  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 .

[72]  Martin Head-Gordon,et al.  A second-order perturbative correction to the coupled-cluster singles and doubles method: CCSD(2) , 2001 .

[73]  Poul Jørgensen,et al.  Perturbative triple excitation corrections to coupled cluster singles and doubles excitation energies , 1996 .

[74]  Marcel Nooijen,et al.  Coupled cluster approach to the single-particle Green's function , 1992 .

[75]  Piotr Piecuch,et al.  Two new classes of non-iterative coupled-cluster methods derived from the method of moments of coupled-cluster equations , 2006 .

[76]  P. Piecuch,et al.  A comparison of single-reference coupled-cluster and multi-reference configuration interaction methods for representative cuts of the H2S(1A′) potential energy surface , 2008 .

[77]  P. Piecuch,et al.  Low-lying valence excited states of CNC, C2N, N3, and NCO studied using the electron-attached and ionized symmetry-adapted-cluster configuration-interaction and equation-of-motion coupled-cluster methodologies , 2009 .

[78]  Jiří Čížek,et al.  On the Use of the Cluster Expansion and the Technique of Diagrams in Calculations of Correlation Effects in Atoms and Molecules , 2007 .

[79]  John D. Watts,et al.  Coupled-cluster calculations of the excitation energies of benzene and the azabenzenes , 1997 .

[80]  P. Piecuch,et al.  Extension of the active‐space equation‐of‐motion coupled‐cluster methods to radical systems: The EA‐EOMCCSDt and IP‐EOMCCSDt approaches , 2006 .

[81]  R. Bartlett,et al.  The full CCSDT model for molecular electronic structure , 1987 .

[82]  K. Emrich,et al.  An extension of the coupled cluster formalism to excited states (I) , 1981 .

[83]  F. Coester,et al.  Bound states of a many-particle system , 1958 .

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

[85]  Donald C. Comeau,et al.  The equation-of-motion coupled-cluster method. Applications to open- and closed-shell reference states , 1993 .

[86]  Anna I Krylov,et al.  A noniterative perturbative triples correction for the spin-flipping and spin-conserving equation-of-motion coupled-cluster methods with single and double substitutions. , 2008, The Journal of chemical physics.

[87]  K. Hirao,et al.  Anharmonic vibrational state calculations in the electronic excited states studied by time-dependent density functional theory , 2007 .

[88]  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 .

[89]  Nevin Horace Oliphant,et al.  A multireference coupled-cluster method using a single-reference formalism. , 1991 .

[90]  M. Zachwieja.  New Investigations of the A2Δ-X2Π Band System in the CH Radical and a New Reduction of the Vibration-Rotation Spectrum of CH from the ATMOS Spectra , 1995 .

[91]  Hans-Joachim Werner,et al.  Local perturbative triples correction (T) with linear cost scaling , 2000 .

[92]  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 .

[93]  D. Chipman.  Stretching of hydrogen-bonded OH in the lowest singlet excited electronic state of water dimer. , 2006, The Journal of chemical physics.

[94]  Andrew G. Taube,et al.  Improving upon CCSD(T): LambdaCCSD(T). II. Stationary formulation and derivatives. , 2008, The Journal of chemical physics.

[95]  Rodney J. Bartlett,et al.  Equation of motion coupled cluster method for electron attachment , 1995 .

[96]  P. Piecuch,et al.  Active-space symmetry-adapted-cluster configuration-interaction and equation-of-motion coupled-cluster methods for high accuracy calculations of potential energy surfaces of radicals. , 2007, The Journal of chemical physics.

[97]  S. Hirata,et al.  Higher-order equation-of-motion coupled-cluster methods for ionization processes. , 2006, The Journal of chemical physics.

[98]  Michael C. Zerner,et al.  The linked singles and doubles model: An approximate theory of electron correlation based on the coupled‐cluster ansatz , 1982 .

[99]  John F. Stanton,et al.  Analytic energy gradients for open-shell coupled-cluster singles and doubles (CCSD) calculations using restricted open-shell Hartree—Fock (ROHF) reference functions , 1991 .

[100]  J. Cizek.  On the Correlation Problem in Atomic and Molecular Systems. Calculation of Wavefunction Components in Ursell-Type Expansion Using Quantum-Field Theoretical Methods , 1966 .

[101]  F. Coester,et al.  Short-range correlations in nuclear wave functions , 1960 .

[102]  John F. Stanton,et al.  INVESTIGATION OF AN ASYMMETRIC TRIPLE-EXCITATION CORRECTION FOR COUPLED-CLUSTER ENERGIES , 1998 .

[103]  K. Kowalski.  Excitation energies through the locally renormalized equation-of-motion formalism: singles and doubles model. , 2006, The Journal of chemical physics.

[104]  Kerstin Andersson,et al.  Second-order perturbation theory with a CASSCF reference function , 1990 .

[105]  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 .

[106]  Karol Kowalski,et al.  Efficient computer implementation of the renormalized coupled-cluster methods: The R-CCSD[T], R-CCSD(T), CR-CCSD[T], and CR-CCSD(T) approaches , 2002 .

[107]  Debashis Mukherjee,et al.  A response-function approach to the direct calculation of the transition-energy in a multiple-cluster expansion formalism , 1979 .

[108]  P. Piecuch,et al.  Biorthogonal method of moments of coupled‐cluster equations: Alternative derivation, further considerations, and application to a model magnetic system , 2008 .

[109]  Karol Kowalski,et al.  Renormalized CCSD(T) and CCSD(TQ) approaches: Dissociation of the N2 triple bond , 2000 .

[110]  Henry F. Schaefer,et al.  Accelerating the convergence of the coupled-cluster approach: The use of the DIIS method , 1986 .

[111]  John D. Watts,et al.  Iterative and non-iterative triple excitation corrections in coupled-cluster methods for excited electronic states: the EOM-CCSDT-3 and EOM-CCSD(T̃) methods , 1996 .

[112]  EOM-CCSDT study of the low-lying ionization potentials of ethylene, acetylene and formaldehyde , 2004 .

[113]  T. Dunning,et al.  Electron affinities of the first‐row atoms revisited. Systematic basis sets and wave functions , 1992 .

[114]  T. H. Dunning.  Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen , 1989 .

[115]  Marat Valiev,et al.  Asymptotic extrapolation scheme for large-scale calculations with hybrid coupled cluster and molecular dynamics simulations. , 2006, The journal of physical chemistry. A.

[116]  Anna I. Krylov,et al.  Second order perturbation corrections to singles and doubles coupled-cluster methods: General theory and application to the valence optimized doubles model , 2000 .

[117]  Jürgen Gauss,et al.  Coupled‐cluster methods with noniterative triple excitations for restricted open‐shell Hartree–Fock and other general single determinant reference functions. Energies and analytical gradients , 1993 .

[118]  Rodney J. Bartlett,et al.  Noniterative energy corrections through fifth-order to the coupled cluster singles and doubles method , 1998 .

[119]  P. Piecuch,et al.  Extrapolating potential energy surfaces by scaling electron correlation: isomerization of bicyclobutane to butadiene. , 2008, The Journal of chemical physics.

[120]  Anna I. Krylov,et al.  Size-consistent wave functions for bond-breaking: the equation-of-motion spin-flip model , 2001 .

[121]  K. Raghavachari,et al.  Electron Correlation Techniques in Quantum Chemistry: Recent Advances , 1991 .

[122]  P. Pulay.  Convergence acceleration of iterative sequences. the case of scf iteration , 1980 .

[123]  N. Nakatsuji,et al.  Cluster expansion of the wavefunction. Excited states , 1978 .

[124]  Ludwik Adamowicz,et al.  A state-selective multireference coupled-cluster theory employing the single-reference formalism , 1993 .

[125]  So Hirata,et al.  Combined coupled-cluster and many-body perturbation theories. , 2004, The Journal of chemical physics.

[126]  S. J. Cole,et al.  Towards a full CCSDT model for electron correlation , 1985 .

[127]  V. R. Saunders,et al.  On methods for converging open-shell Hartree-Fock wave-functions , 1974 .

[128]  Serguei Patchkovskii,et al.  Biradical radiationless decay channel in adenine and its derivatives , 2007 .

[129]  Karol Kowalski,et al.  Excited-state potential energy curves of CH+: a comparison of the EOMCCSDt and full EOMCCSDT results , 2001 .

[130]  Julia E. Rice,et al.  The closed‐shell coupled cluster single and double excitation (CCSD) model for the description of electron correlation. A comparison with configuration interaction (CISD) results , 1987 .

[131]  J. Hammond,et al.  Coupled-cluster dynamic polarizabilities including triple excitations. , 2008, The Journal of chemical physics.

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

[133]  M. Head‐Gordon,et al.  A fifth-order perturbation comparison of electron correlation theories , 1989 .

[134]  So Hirata,et al.  Perturbative corrections to coupled-cluster and equation-of-motion coupled-cluster energies: A determinantal analysis , 2001 .

[135]  A. Metropoulos,et al.  An accurate description of the ground and excited states of SiH , 1999 .

[136]  Clemens C. J. Roothaan,et al.  New Developments in Molecular Orbital Theory , 1951 .

[137]  J. Hammond,et al.  Linear response coupled cluster singles and doubles approach with modified spectral resolution of the similarity transformed Hamiltonian. , 2007, The Journal of chemical physics.

[138]  Martin Head-Gordon,et al.  A second-order correction to singles and doubles coupled-cluster methods based on a perturbative expansion of a similarity-transformed Hamiltonian , 2000 .

[139]  Hiroshi Nakatsuji,et al.  Description of two- and many-electron processes by the SAC-CI method , 1991 .

[140]  Piotr Piecuch,et al.  Extension of the renormalized coupled-cluster methods exploiting left eigenstates of the similarity-transformed hamiltonian to open-shell systems: a benchmark study. , 2007, The journal of physical chemistry. A.

[141]  P. Piecuch,et al.  Breaking bonds with the left eigenstate completely renormalized coupled-cluster method. , 2007, The Journal of chemical physics.

[142]  So Hirata,et al.  Second- and third-order triples and quadruples corrections to coupled-cluster singles and doubles in the ground and excited states. , 2007, The Journal of chemical physics.

[143]  Josef Paldus,et al.  Coupled cluster approaches with an approximate account of triexcitations and the optimized inner projection technique , 1990, Physical review. B, Condensed matter.

[144]  M. Musiał,et al.  Method of moments of coupled-cluster equations: a new formalism for designing accurate electronic structure methods for ground and excited states , 2004 .

[145]  Karol Kowalski,et al.  Extensive generalization of renormalized coupled-cluster methods. , 2005, The Journal of chemical physics.

[146]  K. Evenson,et al.  The rotational spectrum of the CH radical in its a 4Σ− state, studied by far‐infrared laser magnetic resonance , 1990 .

[147]  Piotr Piecuch,et al.  Renormalized coupled-cluster methods exploiting left eigenstates of the similarity-transformed Hamiltonian. , 2005, The Journal of chemical physics.

[148]  Ludwik Adamowicz,et al.  Multireference coupled cluster method for electronic structure of molecules , 1993 .

[149]  K. Kowalski,et al.  On the electronically excited states of uracil. , 2008, Journal of Physical Chemistry A.

[150]  R. Bartlett,et al.  Ammonia: the prototypical lone pair molecule , 1997 .

[151]  Geerd H. F. Diercksen,et al.  Self‐Consistent Perturbation Theory. II. Extension to Open Shells , 1968 .

[152]  K. Hirao,et al.  Cluster expansion of the wave function. Electron correlations in the ground state, valence and Rydberg excited states, ionized states, and electron attached states of formaldehyde by SAC and SAC–CI theories , 1981 .

[153]  Jerzy Leszczynski,et al.  COMPUTATIONAL CHEMISTRY: Reviews of Current Trends , 2006 .

[154]  R. Bartlett,et al.  Coupled‐cluster calculations of the excitation energies of ethylene, butadiene, and cyclopentadiene , 1996 .

[155]  Donald G Truhlar,et al.  Can a single-reference approach provide a balanced description of ground and excited states? A comparison of the completely renormalized equation-of-motion coupled-cluster method with multireference quasidegenerate perturbation theory near a conical intersection and along a photodissociation coordin , 2005, The journal of physical chemistry. A.

[156]  Masahiro Ehara,et al.  Analytical energy gradient of the symmetry-adapted-cluster configuration-interaction general-R method for singlet to septet ground and excited states. , 2004, The Journal of chemical physics.

[157]  K. Hirao,et al.  Cluster expansion of the wave function. Electron correlations in singlet and triplet excited states, ionized states, and electron attached states by SAC and SAC–CI theories† , 1981 .

[158]  So Hirata,et al.  Higher-order equation-of-motion coupled-cluster methods. , 2004, The Journal of chemical physics.

[159]  John D. Watts,et al.  Economical triple excitation equation-of-motion coupled-cluster methods for excitation energies , 1995 .

[160]  John F. Stanton,et al.  Perturbative treatment of the similarity transformed Hamiltonian in equation‐of‐motion coupled‐cluster approximations , 1995 .

[161]  Marat Valiev,et al.  Large-scale parallel calculations with combined coupled cluster and molecular mechanics formalism: Excitation energies of zinc–porphyrin in aqueous solution , 2008 .

[162]  B. A. Brown,et al.  Coupled-cluster and configuration-interaction calculations for heavy nuclei. , 2007, Physical review letters.

[163]  P. Surján,et al.  Comparison of low-order multireference many-body perturbation theories. , 2005, The Journal of chemical physics.

[164]  P. Pulay,et al.  Direct inversion in the iterative subspace (DIIS) optimization of open‐shell, excited‐state, and small multiconfiguration SCF wave functions , 1986 .

[165]  P. Piecuch,et al.  New type of noniterative energy corrections for excited electronic states: Extension of the method of moments of coupled-cluster equations to the equation-of-motion coupled-cluster formalism , 2001 .

[166]  R. L. Roy,et al.  Orbital invariant single-reference coupled electron pair approximation with extensive renormalized triples correction , 2006 .

[167]  Josef Paldus,et al.  Orthogonally spin-adapted coupled-cluster equations involving singly and doubly excited clusters. Comparison of different procedures for spin-adaptation , 1989 .

[168]  Active-Space Equation-of-Motion Coupled-Cluster Methods through Quadruples for Excited, Ionized, and Electron-Attached States. , 2007, Journal of chemical theory and computation.

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

[170]  P. Piecuch,et al.  Stereoelectronic effects on molecular geometries and state-energy splittings of ligated monocopper dioxygen complexes. , 2008, The journal of physical chemistry. A.

[171]  Karol Kowalski,et al.  The active-space equation-of-motion coupled-cluster methods for excited electronic states: Full EOMCCSDt , 2001 .

[172]  Peter Pulay,et al.  Localizability of dynamic electron correlation , 1983 .

[173]  Ove Christiansen,et al.  Response functions in the CC3 iterative triple excitation model , 1995 .

[174]  Karol Kowalski,et al.  Extension of renormalized coupled-cluster methods including triple excitations to excited electronic states of open-shell molecules. , 2005, The Journal of chemical physics.

[175]  Piotr Piecuch,et al.  Single-reference, size-extensive, non-iterative coupled-cluster approaches to bond breaking and biradicals , 2006 .

[176]  Dmitry I. Lyakh,et al.  A generalization of the state-specific complete-active-space coupled-cluster method for calculating electronic excited states. , 2008, The Journal of chemical physics.

[177]  Piotr Piecuch,et al.  Theoretical characterization of end-on and side-on peroxide coordination in ligated Cu2O2 models. , 2006, The journal of physical chemistry. A.

[178]  Karol Kowalski,et al.  The method of moments of coupled-cluster equations and the renormalized CCSD[T], CCSD(T), CCSD(TQ), and CCSDT(Q) approaches , 2000 .

[179]  Mihály Kállay,et al.  Equation-of-motion coupled-cluster methods for ionized states with an approximate treatment of triple excitations. , 2005, The Journal of chemical physics.

[180]  Karol Kowalski,et al.  Extension of the method of moments of coupled-cluster equations to excited states: The triples and quadruples corrections to the equation-of-motion coupled-cluster singles and doubles energies , 2002 .

[181]  Michael J. McGuire,et al.  Recent advances in electronic structure theory: Method of moments of coupled-cluster equations and renormalized coupled-cluster approaches , 2002 .

[182]  R. Bartlett,et al.  A dressing for the matrix elements of the singles and doubles equation‐of‐motion coupled‐cluster method that recovers additive separability of excitation energies , 1995 .

[183]  C. David Sherrill,et al.  The XΣg+1, BΔg1, and B′Σg+1 states of C2: A comparison of renormalized coupled-cluster and multireference methods with full configuration interaction benchmarks , 2005 .

[184]  P Pulay,et al.  Local Treatment of Electron Correlation , 1993 .

[185]  S. I. Bokarev,et al.  Molecular parameters of tetraatomic carbonyls X2CO and XYCO (X, Y = H, F, Cl) in the ground and lowest excited electronic states, part 1: A test of ab initio methods , 2009 .

[186]  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 .

[187]  W. C. Lineberger,et al.  Laser photoelectron spectrometry of CH , 1975 .

[188]  Martin Head-Gordon,et al.  A perturbative correction to the quadratic coupled-cluster doubles method for higher excitations , 2002 .

[189]  A. Para,et al.  New Spectroscopic Analysis of theB2Σ−–X2Π Band System of the CH Molecule , 1996 .

[190]  R. Bartlett,et al.  A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples , 1982 .

[191]  M. Dupuis,et al.  Reaction pathways and excited states in H(2)O(2)+OH-->HO(2)+H(2)O: a new ab initio investigation. , 2007, The Journal of chemical physics.

[192]  T. Crawford,et al.  A comparison of two approaches to perturbation triple excitation corrections to the coupled‐cluster singles and doubles method for high‐spin open‐shell systems , 1996 .

[193]  T. H. Dunning.  Gaussian Basis Functions for Use in Molecular Calculations. III. Contraction of (10s6p) Atomic Basis Sets for the First‐Row Atoms , 1970 .