Coupled-cluster method multireference

Figure 1. The shape of the potential curve for nitrogen in a correlation-consistent polarized double-zeta basis set is presented for the variational 2-RDM method as well as (a) single-reference coupled cluster, (b) multireference second-order perturbation theory (MRPT) and single-double configuration interaction (MRCl), and full configuration interaction (FCl) wavefunction methods. The symbol 2-RDM indicates that the potential curve was shifted by the difference between the 2-RDM and CCSD(T) energies at equilibrium.

Modular FORTRAN programs for performing general ab initio multireference single- and double-excitation configuration interaction, averaged coupled-pair functional and linearized couple-cluster method calculations. Cray and other versions. 

Finally, Pittner and coworkers " examined the PESs of singlet and triplet TMEs using two multireference coupled cluster methods (two-determinant CCSD and multireference Brillouin-Wigner CCSD) with the cc-pVDZ basis set. With both methods, the singlet is always below the triplet for all values of t. The smallest singlet-triplet gap, 1.3 kcal moE, occurs at an angle r = 45° and Ihis is reduced when a near-cc-pVTZ basis set is used. 

Demel, O. Pittner, J. Multireference Brillouin-Wigner coupled cluster method with singles, doubles, and triples efficient implementation and comparison with approximate approaches, 7. Chem. Phys. 2008,128,104108-104111. 

L. Meissner and R. J. Bartlett, J. Chem. Phys., 94, 6670 (1991). Transformation of the Hamiltonian in Excitation Energy Calculations Comparison Between Fock-Space Multireference Coupled-Cluster and Equation-of-Motion Coupled-Cluster Methods. 

P. Piecuch and L. Adamowicz, /. Chem. Phys., 102, 898 (1995). Breaking Bonds with the State-Selective Multireference Coupled-Cluster Methods Employing the Single-Reference Formalism. 

Keywords many-electron correlation problem, post-Hartree-Fock methods, coupled cluster approaches, configuration interaction, externally corrected coupled cluster methods, reduced multireference coupled cluster method... 

Multireference coupled cluster methods, which started development more recently, are generally divided into two types. Hilbert space CC methods use multiple reference functions to obtain a description of a few states, including the reference state (for a review see (4)). Fock space methods (for a review see (5)), on the other hand, provide direct state-to-state energy differences, relative to some common reference state. The Fock space approach is particularly well-suited to the calculation of ionization potentials (IPs), electron affinities (EAs), and excitation energies (EEs). For principal IPs and EAs, FSCC is equivalent (6, 7) to the EOM-IP and EOM-EA CC methods (1, 2, 7, 8). In this paper, we will focus primarily on the IP problem. 

In the Fock space coupled cluster method, the Hartree-Fock solution for an iV-electron state, 0), is used as the vacuum. The Fock space is divided into sectors, (m,n), according to how many electrons are added to and removed from 0). Thus, the vacuum is in the (0,0) sector, single ionizations are in the (0,1) sector, one-electron attached states are in (1,0), and (1,1) are single excitations relative to 0). The orbitals are also divided into active, which can change occupation, and inactive, for which the occupation is fixed. All possible occupations of the active orbitals in all possible sectors constitute the multireference space for the system. 

M. Schreiber, M.R. Silva-Junior, S.P.A Sauer, W. Thiel, Benchmarks for electronically excited states CASPT2, CC2, CCSD, and CCS, J. Chem. Phys. 128 (2008) 134110 M.R. Sflva-Junior, M. Schreiber, S.P.A. Sauer, W. Thiel, Benchmarks for electronically excited states Time-dependent density functional theory and density functional theory based multireference configuration interaction, J. Chem. Phys. 129 (2008) 104103 S.P.A. Sauer, M. Schreiber, M.R. Silva-Junior, W. Thiel, Benchmarks for Electronically Excited States A Comparison of Noniterative and Iterative Triples Corrections in Linear Response Coupled Cluster Methods CCSDR(3) versus CCS, J. Chem. Theory Comput. 5 (2009) 555 M.R. Silva-Junior, S.P.A. Sauer, M. Schreiber, W. Thiel, Basis set effects on coupled cluster benchmarks of electronically excited states CCS, CCSDR(3) and CC2, Mol. Phys. 108 (2010) 453 M.R. Silva-Junior, M. Schreiber, S.P.A. Sauer, W. Thiel, Benchmarks of electronically excited states basis set effects on CASPT2 results, J. Chem. Phys. 133 (2010) 174318. 

Molecular Applications of Multireference Coupled-Cluster Methods Using an Incomplete Model Space. Direa Calculation of Excitation Energies. (FS-MRCCSD.)... 

A Fock space multireference coupled cluster method was described by Rittby and Bartlett <91TCA469>, applied to the calculation of ionization potentials and excitation energies of 1,2,4,5-tetrazines, and compared with conventional ab initio calculations and experimental results. 

U. Kaldor, Atomic and molecular applications of the multireference coupled-cluster method, in U. Kaldor (Ed.), Many-body methods in quantum chemistry, lecture notes in chemistry, Vol. 52, Springer, Berlin, 1989, pp. 199-213, J. Chem. Phys., 87 (1987) 467. 

Multireference coupled cluster method based on the Brillouin-Wigner perturbation theory... 

MULTIREFERENCE BRILLOUIN-WIGNER COUPLED CLUSTER METHOD... 

P.G. Szalay, Towards state-specihc formulation of multireference coupled-cluster theory Coupled electron pair approximations (CEPA) leading to multireference configuration interaction (MR-CI) type equations, in R.J. Bartlett (Ed.), Modem ideas in coupled-cluster methods, World Scientific, Singapore, 1997, pp. 81-123. 

Chapter 18 - Multireference coupled cluster method based on the Brillouin-Wigner perturbation theory. Pages 465-481, Petr Carsky, Jin Pittner and Ivan Hubac... 

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