To Multireference or not to Multireference: That is the Question?

I present a personal viewpoint on multi-reference coupled-cluster theory, its pros and cons. I also suggest some criteria that should be satisfied by multi-reference CC, not the least of which is to develop a tool that will be (almost!) as easy to apply as today’s powerful array of single reference coupled-cluster methods. Some approaches like the equation of motion CC method offers a multi-reference description of some target states, while being entirely single reference in execution. Perhaps it offers a model for further generalization to a wider array of multi-reference problems.

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

[2]  J. Linderberg,et al.  State vectors and propagators in many‐electron theory. A unified approach , 1977 .

[3]  Rodney J. Bartlett,et al.  Similarity transformed equation-of-motion coupled-cluster theory: Details, examples, and comparisons , 1997 .

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

[5]  Ingvar Lindgren,et al.  Atomic Many-Body Theory , 1982 .

[6]  R. Bartlett,et al.  Connected quadruples for the frequencies of O3 , 1999 .

[7]  J. Paldus,et al.  Perturbatively selected CI as an optimal source for externally corrected CCSD , 1999 .

[8]  Anna I. Krylov,et al.  Energies and analytic gradients for a coupled-cluster doubles model using variational Brueckner orbitals: Application to symmetry breaking in O4+ , 1998 .

[9]  D. Mukherjee,et al.  Molecular applications of size-extensive quasi-Hilbert- and quasi-Fock-space coupled-cluster formalisms using incomplete model spaces , 1991 .

[10]  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 .

[11]  R. Bartlett,et al.  Coupled-cluster methods correct through sixth order , 1993 .

[12]  Rodney J. Bartlett,et al.  The expectation value coupled-cluster method and analytical energy derivatives☆ , 1988 .

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

[14]  Ivan Hubač,et al.  Size-extensivity correction for the state-specific multireference Brillouin–Wigner coupled-cluster theory , 2000 .

[15]  Isaiah Shavitt,et al.  The history and evolution of configuration interaction , 1998 .

[16]  Rodney J. Bartlett,et al.  A new method for excited states: Similarity transformed equation-of-motion coupled-cluster theory , 1997 .

[17]  P. Wormer,et al.  Relationship between configuration interaction and coupled cluster approaches , 1982 .

[18]  R. Azria,et al.  Differential cross section for dissociative attachment in HI: H- (I 2P3/2, I 2P1/2) formation , 1985 .

[19]  R. Bartlett,et al.  On the singlet–triplet separation in methylene: A critical comparison of single‐ versus two‐determinant (generalized valence bond) coupled cluster theory , 1995 .

[20]  Jeppe Olsen,et al.  Determinant based configuration interaction algorithms for complete and restricted configuration interaction spaces , 1988 .

[21]  R. Bartlett,et al.  A new approach to the problem of noniterative corrections within the coupled-cluster framework , 2001 .

[22]  Ernest R. Davidson,et al.  Configuration interaction calculations on the nitrogen molecule , 1974 .

[23]  G. Diercksen,et al.  Methods in Computational Molecular Physics , 1983 .

[24]  David H. Magers,et al.  Highly correlated single‐reference studies of the O3 potential surface. I. Effects of high order excitations on the equilibrium structure and harmonic force field of ozone , 1989 .

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

[26]  I. Lindgren,et al.  On the connectivity criteria in the open-shell coupled-cluster theory for general model spaces , 1987 .

[27]  H. Lischka,et al.  Excitation energies and transition moments by the multireference averaged quadratic coupled cluster (MR-AQCC) method , 2000 .

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

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

[30]  J. Klauder,et al.  COHERENT STATES: APPLICATIONS IN PHYSICS AND MATHEMATICAL PHYSICS , 1985 .

[31]  Jeppe Olsen,et al.  The initial implementation and applications of a general active space coupled cluster method , 2000 .

[32]  R. Bartlett,et al.  Coupled-Cluster Methods for Molecular Calculations , 1984 .

[33]  H. Lischka,et al.  Geometry optimization of excited valence states of formaldehyde using analytical multireference configuration interaction singles and doubles and multireference averaged quadratic coupled-cluster gradients, and MR-AQCC gradients and the conical intersection formed by the 1{sup 1}B{sub 1}({sigma}-{pi , 2001 .

[34]  John F. Stanton,et al.  A benchmark coupled-cluster single, double, and triple excitation (CCSDT) study of the structure and harmonic vibrational frequencies of the ozone molecule☆ , 1991 .

[35]  H. Lischka,et al.  A systematic theoretical investigation of the valence excited states of the diatomic molecules B2, C2, N2 and O2 , 2001 .

[36]  J. Gauss,et al.  Many‐body methods for excited state potential energy surfaces. II. Analytic second derivatives for excited state energies in the equation‐of‐motion coupled cluster method , 1995 .

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

[38]  R. Bartlett,et al.  COUPLED-CLUSTER CALCULATIONS OF STRUCTURE AND VIBRATIONAL FREQUENCIES OF OZONE : ARE TRIPLE EXCITATIONS ENOUGH? , 1998 .

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

[40]  Thomas Müller,et al.  High-level multireference methods in the quantum-chemistry program system COLUMBUS: Analytic MR-CISD and MR-AQCC gradients and MR-AQCC-LRT for excited states, GUGA spin–orbit CI and parallel CI density , 2001 .

[41]  J. Linderberg,et al.  Characteristics of the consistent ground state of the random phase approximation , 1979 .

[42]  R. Bartlett.  Analytical Evaluation of Gradients in Coupled-Cluster and Many-Body Perturbation Theory , 1986 .

[43]  Marcel Nooijen,et al.  Extended similarity transformed equation-of-motion coupled cluster theory (extended-STEOM-CC): Applications to doubly excited states and transition metal compounds , 2000 .

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

[45]  Charles W. Bauschlicher,et al.  Theoretical calculation of ozone vibrational infrared intensities , 1985 .

[46]  R. Bartlett,et al.  The description of N2 and F2 potential energy surfaces using multireference coupled cluster theory , 1987 .

[47]  R. Bartlett.  Many-Body Perturbation Theory and Coupled Cluster Theory for Electron Correlation in Molecules , 1981 .

[48]  Martin Head-Gordon,et al.  Connections between coupled cluster and generalized valence bond theories , 2001 .

[49]  Rodney J. Bartlett,et al.  Approximately extensive modifications of the multireference configuration interaction method: A theoretical and practical analysis , 1995 .

[50]  R. Bartlett,et al.  Multireference coupled-cluster methods using an incomplete model space: Application to ionization potentials and excitation energies of formaldehyde , 1987 .

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

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

[53]  R. Bartlett,et al.  Analytical gradients for the coupled-cluster method† , 1984 .

[54]  Ludwik Adamowicz,et al.  The implementation of the multireference coupled‐cluster method based on the single‐reference formalism , 1992 .

[55]  N. S. Barnett,et al.  Private communication , 1969 .

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

[57]  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 .

[58]  Mihály Kállay,et al.  Higher excitations in coupled-cluster theory , 2001 .

[59]  B. Roos,et al.  A direct CI method with a multiconfigurational reference state , 1980 .

[60]  Rodney J. Bartlett,et al.  COUPLED-CLUSTER THEORY: AN OVERVIEW OF RECENT DEVELOPMENTS , 1995 .

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

[62]  U. Kaldor,et al.  Many-Body Methods in Quantum Chemistry , 1989 .

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

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

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

[66]  R. Bartlett,et al.  Fifth‐order many‐body perturbation theory for molecular correlation energies , 1989 .

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

[68]  D. Mukherjee,et al.  Molecular applications of coupled-cluster-based linear response theory: Inner and outer valence ionization potentials of nitrogen and water , 1985 .

[69]  Rodney J. Bartlett,et al.  Multi-reference averaged quadratic coupled-cluster method: a size-extensive modification of multi-reference CI , 1993 .

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

[71]  S. Pal,et al.  Use of Cluster Expansion Methods in the Open-Shell Correlation Problem , 1989 .

[72]  Rodney J. Bartlett,et al.  Alternative coupled-cluster ansätze II. The unitary coupled-cluster method , 1989 .

[73]  Michael W. Schmidt,et al.  Concerted dihydrogen exchange between ethane and ethylene. SCF and FORS calculations of the barrier , 1982 .

[74]  Robert J. Gdanitz,et al.  The averaged coupled-pair functional (ACPF): A size-extensive modification of MR CI(SD) , 1988 .

[75]  C. E. Dykstra.  Exploiting the link between CI and the coupled cluster model. estimates for cluster energies and wavefunctions and a means for the rapid determination of CCD wavefunctions , 1982 .

[76]  J. Cullen,et al.  Generalized valence bond solutions from a constrained coupled cluster method , 1996 .

[77]  R. Bartlett,et al.  An efficient way to include connected quadruple contributions into the coupled cluster method , 1998 .

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

[79]  So Hirata,et al.  High-order determinantal equation-of-motion coupled-cluster calculations for electronic excited states , 2000 .

[80]  W. D. Allen,et al.  The analytic evaluation of energy first derivatives for two‐configuration self‐consistent‐field configuration interaction (TCSCF‐CI) wave functions. Application to ozone and ethylene , 1987 .

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

[82]  R. Bartlett.  Coupled-cluster approach to molecular structure and spectra: a step toward predictive quantum chemistry , 1989 .

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

[84]  Anna I. Krylov,et al.  Excited states theory for optimized orbitals and valence optimized orbitals coupled-cluster doubles models , 2000 .

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

[86]  R. Bartlett,et al.  Coupled-cluster method for open-shell singlet states , 1992 .

[87]  T. Sorensen,et al.  Valence States of BeO Feynman's Way , 2000 .

[88]  Josef Paldus,et al.  Simultaneous handling of dynamical and nondynamical correlation via reduced multireference coupled cluster method: Geometry and harmonic force field of ozone , 1999 .

[89]  R. Chaudhuri,et al.  A comparative study of core-extensive and core-valence-extensive coupled-cluster theories for energy differences: excitation energies , 1990 .