Bridging single and multireference coupled cluster theories with universal state selective formalism.

The universal state selective (USS) multireference approach is used to construct new energy functionals which offer a possibility of bridging single and multireference coupled cluster theories (SR/MRCC). These functionals, which can be used to develop iterative and non-iterative approaches, utilize a special form of the trial wavefunctions, which assure additive separability (or size-consistency) of the USS energies in the non-interacting subsystem limit. When the USS formalism is combined with approximate SRCC theories, the resulting formalism can be viewed as a size-consistent version of the method of moments of coupled cluster equations employing a MRCC trial wavefunction. Special cases of the USS formulations, which utilize single reference state specific CC [V. V. Ivanov, D. I. Lyakh, and L. Adamowicz, Phys. Chem. Chem. Phys. 11, 2355 (2009)] and tailored CC [T. Kinoshita, O. Hino, and R. J. Bartlett, J. Chem. Phys. 123, 074106 (2005)] expansions are also discussed.

[1]  Rodney J. Bartlett,et al.  Hilbert space multireference coupled-cluster methods. II: A model study on H8 , 1992 .

[2]  H. Monkhorst,et al.  Coupled-cluster method for multideterminantal reference states , 1981 .

[3]  R. Bartlett,et al.  A general model-space coupled-cluster method using a Hilbert-space approach , 1990 .

[4]  Francesco A. Evangelista,et al.  Insights into the orbital invariance problem in state-specific multireference coupled cluster theory. , 2010, The Journal of chemical physics.

[5]  R. Bartlett,et al.  Fock space multireference coupled cluster method with full inclusion of connected triples for excitation energies. , 2004, The Journal of chemical physics.

[6]  Jean-Paul Malrieu,et al.  Intermediate Hamiltonians as a new class of effective Hamiltonians , 1985 .

[7]  Josef Paldus,et al.  Reduced multireference CCSD method: An effective approach to quasidegenerate states , 1997 .

[8]  P. Piecuch,et al.  In Search of the Relationship between Multiple Solutions Characterizing Coupled-Cluster Theories , 2000 .

[9]  Michael Hanrath,et al.  An exponential multireference wave-function Ansatz. , 2005, The Journal of chemical physics.

[10]  Francesco A Evangelista,et al.  Coupling term derivation and general implementation of state-specific multireference coupled cluster theories. , 2007, The Journal of chemical physics.

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

[12]  Rodney J. Bartlett,et al.  A Hilbert space multi-reference coupled-cluster study of the H4 model system , 1991 .

[13]  J. Paldus,et al.  Reduced multireference coupled cluster method with singles and doubles: Perturbative corrections for triples. , 2006, The Journal of chemical physics.

[14]  Josef Paldus,et al.  Orthogonally spin-adapted multi-reference Hilbert space coupled-cluster formalism: diagrammatic formulation , 1992 .

[15]  W. Kutzelnigg,et al.  Direct calculation of energy differences by a common unitary transformation of two model states, with application to ionization potentials , 1979 .

[16]  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 .

[17]  Uttam Sinha Mahapatra,et al.  Potential energy surface studies via a single root multireference coupled cluster theory. , 2010, The Journal of chemical physics.

[18]  Karol Kowalski,et al.  Universal state-selective corrections to multi-reference coupled-cluster theories with single and double excitations. , 2012, The Journal of chemical physics.

[19]  Jiří Pittner,et al.  Method of moments for the continuous transition between the Brillouin–Wigner-type and Rayleigh–Schrödinger-type multireference coupled cluster theories , 2009 .

[20]  J. Paldus,et al.  Reduced multireference coupled cluster method IV: open-shell systems , 2000 .

[21]  Debashis Mukherjee,et al.  Applications of a non-perturbative many-body formalism to general open-shell atomic and molecular problems: calculation of the ground and the lowest π-π* singlet and triplet energies and the first ionization potential of trans-butadiene , 1977 .

[22]  Michael Hanrath,et al.  An exponential multi-reference wavefunction ansatz: connectivity analysis and application to N2 , 2008 .

[23]  H. Weidenmüller,et al.  The effective interaction in nuclei and its perturbation expansion: An algebraic approach , 1972 .

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

[25]  D. Mukherjee,et al.  Application of cluster expansion techniques to open shells: Calculation of difference energies , 1984 .

[26]  Karol Kowalski,et al.  New classes of non-iterative energy corrections to multi-reference coupled-cluster energies , 2004 .

[27]  I. Hubač.  Size-Extensive Brillouin-Wigner Perturbation Theory. Size-Extensive Brillouin-Wigner Coupled Cluster Theory , 1996 .

[28]  Petr Nachtigall,et al.  Assessment of the single-root multireference Brillouin–Wigner coupled- cluster method: Test calculations on CH2, SiH2, and twisted ethylene , 1999 .

[29]  Uttam Sinha Mahapatra,et al.  State-Specific Multi-Reference Coupled Cluster Formulations: Two Paradigms , 1998 .

[30]  J. Paldus,et al.  Valence universal exponential ansatz and the cluster structure of multireference configuration interaction wave function , 1989 .

[31]  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 .

[32]  Kiran Bhaskaran-Nair,et al.  Multireference state-specific Mukherjee's coupled cluster method with noniterative triexcitations using uncoupled approximation. , 2011, The Journal of chemical physics.

[33]  J. Paldus,et al.  Spin-Adapted Multi-Reference Coupled Cluster Formalism Including Non-Linear Terms and its Application to the H4 Model System , 1989 .

[34]  Rodney J. Bartlett,et al.  A multireference coupled‐cluster study of the ground state and lowest excited states of cyclobutadiene , 1994 .

[35]  Michael Hanrath,et al.  Initial applications of an exponential multi-reference wavefunction ansatz , 2006 .

[36]  D. Mukherjee,et al.  Formulation and implementation of a unitary group adapted state universal multi-reference coupled cluster (UGA-SUMRCC) theory: excited and ionized state energies. , 2012, The Journal of chemical physics.

[37]  Rodney J. Bartlett,et al.  The multi-reference Hilbert space coupled-cluster study of the Li2 molecule. Application in a complete model space , 1991 .

[38]  J. Pittner,et al.  Towards the multireference Brillouin-Wigner coupled-clusters method with iterative connected triples: MR BWCCSDT-alpha approximation. , 2005, The Journal of chemical physics.

[39]  Ivan Hubač,et al.  Multireference Brillouin-Wigner Coupled-Cluster Theory. Single-root approach. , 1998 .

[40]  Wenjian Liu,et al.  A spin-adapted size-extensive state-specific multi-reference perturbation theory. I. Formal developments. , 2012, The Journal of chemical physics.

[41]  Rodney J. Bartlett,et al.  Hilbert space multireference coupled-cluster methods. I: The single and double excitation model , 1991 .

[42]  John F. Stanton,et al.  Fock space multireference coupled-cluster theory for general single determinant reference functions , 1992 .

[43]  Karol Kowalski,et al.  A universal state-selective approach to multireference coupled-cluster non-iterative corrections. , 2011, The Journal of chemical physics.

[44]  J. Pittner,et al.  Multireference Brillouin-Wigner coupled clusters method with noniterative perturbative connected triples. , 2006, The Journal of chemical physics.

[45]  L. Meissner.  Fock-space coupled-cluster method in the intermediate Hamiltonian formulation: Model with singles and doubles , 1998 .

[46]  Jiří Pittner,et al.  Continuous transition between Brillouin-Wigner and Rayleigh-Schrödinger perturbation theory, generalized Bloch equation, and Hilbert space multireference coupled cluster , 2003 .

[47]  A non-perturbative open-shell theory for ionisation potential and excitation energies using HF ground state as the vacuum , 1979 .

[48]  Josef Paldus,et al.  General-model-space state-universal coupled-cluster theory: Connectivity conditions and explicit equations , 2003 .

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

[50]  Jiří Pittner,et al.  Uncoupled multireference state-specific Mukherjee's coupled cluster method with triexcitations. , 2010, The Journal of chemical physics.

[51]  Kiran Bhaskaran-Nair,et al.  Multireference state-specific Mukherjee's coupled cluster method with noniterative triexcitations. , 2008, The Journal of chemical physics.

[52]  Piotr Piecuch,et al.  Active-space coupled-cluster methods , 2010 .

[53]  U. Kaldor,et al.  Open-shell coupled-cluster theory applied to atomic and molecular systems , 1985 .

[54]  Rodney J Bartlett,et al.  Coupled-cluster method tailored by configuration interaction. , 2005, The Journal of chemical physics.

[55]  Josef Paldus,et al.  Spin‐adapted multireference coupled‐cluster approach: Linear approximation for two closed‐shell‐type reference configurations , 1988 .

[56]  Ludwik Adamowicz,et al.  Multireference state-specific coupled-cluster methods. State-of-the-art and perspectives. , 2009, Physical chemistry chemical physics : PCCP.

[57]  U. Kaldor,et al.  Degeneracy breaking in the Hilbert‐space coupled cluster method , 1993 .

[58]  R. Bartlett,et al.  The general model space effective Hamiltonian in order‐for‐order expansion , 1989 .

[59]  U. Kaldor,et al.  Hilbert space coupled-cluster method in an incomplete model space , 1992 .

[60]  Karol Kowalski,et al.  Extension of the method of moments of coupled-cluster equations to a multireference wave operator formalism ☆ , 2001 .

[61]  Uttam Sinha Mahapatra,et al.  A size-consistent state-specific multireference coupled cluster theory: Formal developments and molecular applications , 1999 .

[62]  Uttam Sinha Mahapatra,et al.  A state-specific multi-reference coupled cluster formalism with molecular applications , 1998 .

[63]  Francesco A Evangelista,et al.  Perturbative triples corrections in state-specific multireference coupled cluster theory. , 2010, The Journal of chemical physics.

[64]  Karol Kowalski,et al.  Complete set of solutions of multireference coupled-cluster equations: The state-universal formalism , 2000 .

[65]  Piotr Piecuch,et al.  Biorthogonal moment expansions in coupled-cluster theory: Review of key concepts and merging the renormalized and active-space coupled-cluster methods , 2012 .

[66]  Edoardo Aprà,et al.  Implementation of the multireference Brillouin-Wigner and Mukherjee's coupled cluster methods with non-iterative triple excitations utilizing reference-level parallelism. , 2012, The Journal of chemical physics.

[67]  Josef Paldus,et al.  The general-model-space state-universal coupled-cluster method exemplified by the LiH molecule , 2003 .

[68]  H. Weidenmüller,et al.  Perturbation theory for the effective interaction in nuclei , 1973 .

[69]  Leszek Meissner,et al.  A coupled‐cluster method for quasidegenerate states , 1988 .

[70]  Josef Paldus,et al.  N-reference, M-state coupled-cluster method: Merging the state-universal and reduced multireference coupled-cluster theories , 2003 .

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

[72]  L. Meissner.  Various formulations of the Fock-space coupled-cluster method: Advantages and disadvantages in their practical implementations , 2012 .

[73]  D. Mukherjee,et al.  Size-extensive effective Hamiltonian formalisms using quasi-Hilbert and quasi-Fock space strategies with incomplete model spaces , 1989 .

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

[75]  P. Piecuch,et al.  Non-iterative coupled-cluster methods employing multi-reference perturbation theory wave functions , 2006 .

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

[77]  Sanghamitra Das,et al.  Full implementation and benchmark studies of Mukherjee's state-specific multireference coupled-cluster ansatz. , 2010, The Journal of chemical physics.

[78]  J. Pittner,et al.  Multireference Brillouin-Wigner coupled cluster method with singles, doubles, and triples: efficient implementation and comparison with approximate approaches. , 2008, The Journal of chemical physics.

[79]  R. Bartlett,et al.  Coupled‐cluster method for an incomplete model space , 1992 .

[80]  Piecuch,et al.  Application of Hilbert-space coupled-cluster theory to simple (H2)2 model systems: Planar models. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[81]  J. Paldus,et al.  Reduced multireference couple cluster method. II. Application to potential energy surfaces of HF, F2, and H2O , 1998 .

[82]  Kiran Bhaskaran-Nair,et al.  Multireference Mukherjee's coupled cluster method with triexcitations in the linked formulation: Efficient implementation and applications. , 2010, The Journal of chemical physics.

[83]  Emily A Carter,et al.  Approximately size extensive local Multireference Singles and Doubles Configuration Interaction. , 2012, Physical chemistry chemical physics : PCCP.

[84]  Dmitry I. Lyakh,et al.  State-specific multireference complete-active-space coupled-cluster approach versus other quantum chemical methods: dissociation of the N2 molecule , 2007 .

[85]  J. Paldus,et al.  Force field of para- and metabenzyne diradicals: a multireference coupled-cluster study. , 2010, The Journal of chemical physics.

[86]  Jun Shen,et al.  Merging Active-Space and Renormalized Coupled-Cluster Methods via the CC(P;Q) Formalism, with Benchmark Calculations for Singlet-Triplet Gaps in Biradical Systems. , 2012, Journal of chemical theory and computation.

[87]  Daniel Maynau,et al.  Multi-scale multireference configuration interaction calculations for large systems using localized orbitals: partition in zones. , 2012, The Journal of chemical physics.

[88]  Garnet Kin-Lic Chan,et al.  Tailored coupled cluster singles and doubles method applied to calculations on molecular structure and harmonic vibrational frequencies of ozone. , 2006, The Journal of chemical physics.

[89]  R. Bartlett,et al.  A multireference coupled‐cluster method for special classes of incomplete model spaces , 1989 .

[90]  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.

[91]  Dmitry I. Lyakh,et al.  Multireference State-specific Coupled Cluster Approach with the CAS Reference: Inserting Be into H2 , 2006 .

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

[93]  Sanghamitra Das,et al.  Inclusion of selected higher excitations involving active orbitals in the state-specific multireference coupled-cluster theory. , 2010, The Journal of chemical physics.

[94]  M. Nooijen,et al.  Effective and intermediate Hamiltonians obtained by similarity transformations , 1995 .

[95]  Jürgen Gauss,et al.  Triple excitations in state-specific multireference coupled cluster theory: application of Mk-MRCCSDT and Mk-MRCCSDT-n methods to model systems. , 2008, The Journal of chemical physics.

[96]  Mihály Kállay,et al.  Superior performance of Mukherjee’s state-specific multi-reference coupled-cluster theory at the singles and doubles truncation scheme with localized active orbitals , 2012 .