Multireference state-specific Mukherjee's coupled cluster method with noniterative triexcitations using uncoupled approximation.

A new version of the multireference Mukherjee's coupled cluster method with perturbative triexcitations has been formulated, which is based on the uncoupled approximation applied to the triples equation. In contrast to the method developed by Evangelista et al. [J. Chem. Phys. 132, 074107 (2010)], the proposed approach does not require to solve the equation for T(3) amplitudes iteratively, yet yields results of essentially the same quality. The method, abbreviated as MR MkCCSD(Tu), has been implemented in the ACES II program package and its assessment has been performed on the BeH(2) model and on the tetramethyleneethane molecule.

[1]  Sanghamitra Das,et al.  Development and pilot molecular applications of the uncoupled state-specific MRCC (UC-SS-MRCC) theory , 2008 .

[2]  J. Pittner,et al.  The performance of the multireference Brillouin–Wigner coupled cluster singles and doubles method on the insertion of Be into H2 , 2004 .

[3]  Ron Shepard,et al.  C2V Insertion pathway for BeH2: A test problem for the coupled‐cluster single and double excitation model , 1983 .

[4]  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.

[5]  J. Pittner,et al.  State-specific Brillouin–Wigner multireference coupled cluster study of the F2 molecule: assessment of the a posteriori size-extensivity correction , 2001 .

[6]  Ioannis S. K. Kerkines,et al.  On the ground states of CaC and ZnC: A multireference Brillouin–Wigner coupled cluster study , 2002 .

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

[8]  R. Mcweeny,et al.  Quantum Systems in Chemistry and Physics. Trends in Methods and Applications , 1997 .

[9]  Josef Paldus,et al.  Orthogonally spin‐adapted state‐universal coupled‐cluster formalism: Implementation of the complete two‐reference theory including cubic and quartic coupling terms , 1994 .

[10]  J. Pittner,et al.  Analytic gradient for the multireference Brillouin-Wigner coupled cluster method and for the state-universal multireference coupled cluster method. , 2007, The Journal of chemical physics.

[11]  J. Pittner,et al.  Coupled Cluster Study of Polycyclopentanes: Structure and Properties of C5H2n, n = 0-4 , 2008 .

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

[13]  Ernest R. Davidson,et al.  Effects of electron repulsion in conjugated hydrocarbon diradicals , 1977 .

[14]  Trygve Helgaker,et al.  Mo/ller–Plesset energy derivatives , 1988 .

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

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

[17]  J. Pittner,et al.  Multireference Brillouin-Wigner coupled cluster singles and doubles (MRBWCCSD) and multireference doubles configuration interaction (MRD-CI) calculations for the Bergman cyclization reaction , 2003 .

[18]  J. Pittner,et al.  State-Specific Brillouin−Wigner Multireference Coupled Cluster Study of the Singlet−Triplet Separation in the Tetramethyleneethane Diradical , 2001 .

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

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

[21]  S. Shaik,et al.  Tetramethyleneethane (TME) Diradical: Experiment and Density Functional Theory Reach an Agreement , 1999 .

[22]  U. Kaldor The Fock space coupled cluster method: theory and application , 1991 .

[23]  R. Caballol,et al.  The Controversial Ground State of Tetramethyleneethane. An ab Initio CI Study , 2000 .

[24]  J. Pittner,et al.  Four-Reference State-Specific Brillouin-Wigner Coupled-Cluster Method: Study of the IBr Molecule , 2001 .

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

[26]  J. Pittner,et al.  The singlet-triplet gap in trimethylenmethane and the ring-opening of methylenecyclopropane: a multireference Brillouin-Wigner coupled cluster study. , 2006, The journal of physical chemistry. A.

[27]  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.

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

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

[30]  Josef Paldus,et al.  Multireference Coupled-Cluster Methods: Recent Developments , 2010 .

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

[32]  D. Herschbach,et al.  New methods in quantum theory , 1996 .

[33]  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.

[34]  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.

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

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

[37]  Rodney J. Bartlett,et al.  The multireference coupled‐cluster method in Hilbert space: An incomplete model space application to the LiH molecule , 1991 .

[38]  J. Noga,et al.  Multireference R12 Coupled Cluster Theory , 2010 .

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

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

[41]  M. Hanrath On the concepts of connectivity, separability, and consistency: An illustration by partitioned diagrams and numerical probing , 2009 .

[42]  Josef Paldus,et al.  Model space incompleteness in multireference state-universal and state-selective coupled-cluster theories , 2010 .

[43]  I. Hubač,et al.  Multireference Brillouin—Wigner Coupled-Cluster Theory: Hilbert Space Approach , 1997 .

[44]  Andrew C Simmonett,et al.  A companion perturbation theory for state-specific multireference coupled cluster methods. , 2009, Physical chemistry chemical physics : PCCP.

[45]  Ioannis S. K. Kerkines,et al.  Ground states of BeC and MgC: A comparative multireference Brillouin–Wigner coupled cluster and configuration interaction study† , 2005 .

[46]  Eileen P. Clifford,et al.  Properties of tetramethyleneethane (TME) as revealed by ion chemistry and ion photoelectron spectroscopy , 1998 .

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

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

[49]  G. I. Gellene,et al.  σ Bond Activation by Cooperative Interaction with n s 2 Atoms: Be + n H 2 , n = 1−3 , 2000 .

[50]  Ioannis S. K. Kerkines,et al.  A multireference coupled-cluster potential energy surface of diazomethane, CH(2)N(2). , 2005, The journal of physical chemistry. A.

[51]  J. Pittner,et al.  Multireference Brillouin−Wigner Coupled Cluster Singles and Doubles Study of the Singlet−Triplet Separation in Alkylcarbenes† , 2004 .

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

[53]  J. Pittner,et al.  Multireference configuration interaction and coupled-cluster calculations on the X3Σ−, a1Δ, and b1Σ+ states of the NF molecule , 2005 .

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

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

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

[57]  K. Jordan,et al.  Theoretical study of the low-lying triplet and singlet states of tetramethyleneethane: prediction of a triplet below singlet state at the triplet equilibrium geometry , 1993 .

[58]  Uttam Sinha Mahapatra,et al.  Development of a size-consistent state-specific multireference perturbation theory with relaxed model-space coefficients , 1999 .

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

[60]  J. Pittner,et al.  Multireference coupled-cluster calculations on the energy of activation in the automerization of cyclobutadiene: Assessment of the state-specific multireference Brillouin–Wigner theory , 2000 .

[61]  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.

[62]  K. Jankowski,et al.  A valence-universal coupled-duster single- and double-excitations method for atoms. II. Application to Be , 1994 .

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

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

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

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

[67]  Josef Paldus,et al.  Recent Progress in Coupled Cluster Methods , 2010 .

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

[69]  P. Mach,et al.  Multireference Brillouin–Wigner Coupled-Cluster Theory , 1999 .

[70]  W. T. Borden,et al.  Ab initio calculations predict a singlet ground state for tetramethyleneethane , 1987 .

[71]  K. Kowalski,et al.  Applicability of valence-universal multireference coupled-cluster theories to quasidegenerate electronic states. I. Models involving at most two-body amplitudes , 1992 .

[72]  Ivan Hubač,et al.  Four- and 8-reference state-specific Brillouin-Wigner coupled-cluster method: Study of the singlet oxygen , 2002 .

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

[74]  Mihály Kállay,et al.  A general state-selective multireference coupled-cluster algorithm , 2002 .

[75]  Francesco A Evangelista,et al.  High-order excitations in state-universal and state-specific multireference coupled cluster theories: model systems. , 2006, The Journal of chemical physics.

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

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

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

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

[80]  T. Dunning The Cl + Bk extrapolation method. Application to hydrogen fluoride , 1979 .

[81]  Michael Hanrath,et al.  Dissociating N2: a multi-reference coupled cluster study on the potential energy surfaces of ground and excited states , 2009 .

[82]  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 .

[83]  Debashis Mukherjee,et al.  Reflections on size-extensivity, size-consistency and generalized extensivity in many-body theory , 2005 .

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

[85]  Sanghamitra Das,et al.  An externally-corrected size-extensive single-root MRCC formalism: its kinship with the rigorously size-extensive state-specific MRCC theory , 2006 .

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

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

[88]  J. H. van Lenthe,et al.  Multireference coupled electron-pair approximations to the multireference coupled cluster method. The MR-CEPA1 method , 2005 .

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

[90]  Jae Shin Lee,et al.  Critical comparison of single-reference and multireference coupled-cluster methods: Geometry, harmonic frequencies, and excitation energies of N2O2 , 2003 .

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

[92]  Josef Paldus,et al.  Multireference general-model-space state-universal and state-specific coupled-cluster approaches to excited states. , 2010, The Journal of chemical physics.

[93]  Y. Paik,et al.  Tetramethyleneethane, a ground-state triplet , 1986 .

[94]  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.

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

[96]  J. Urban,et al.  Brillouin-Wigner Perturbation Theory as a Possible more Effective Alternative to Many-Body Rayleigh-Schrodinger Perturbation Theory and Coupled Cluster Theory , 1995 .

[97]  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 .

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

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