State-universal Coupled-cluster Method Research Articles

Diagonal perturbative triple corrections to the general-model-space state-universal coupled-cluster method: are they warranted and useful?

Diagonal perturbative triple corrections to the general-model-space state-universal coupled-cluster method: are they warranted and useful?

General-Model-Space State–Universal Coupled-Cluster Method: Diagrammatic Approach

The explicit expressions for the recently formulated general-model-space (GMS) version of the multireference state-universal (SU) coupled-cluster (CC) method [X. Li and J. Paldus, J. Chem. Phys. 119 (2003) 5320], truncated at the level of single (S) and double (D) excitations, are re-derived using the spin-orbital form of the diagrammatic technique. The focus is on the so-called coupling coefficients, which represent a new type of quantity that does not appear in the single-reference CC approaches. The role of the connectivity conditions, referred to as the C-conditions, in the elimination of disconnected terms in the GMS SU CC method is analyzed in terms of the connectivity of the resulting diagrams and is illustrated on typical examples.

Size extensivity of a general‐model‐space state‐universal coupled‐cluster method

AbstractWe show that the recently formulated general‐model‐space (GMS), state‐universal (SU), coupled‐cluster (CC) method, exploiting the so‐called C‐conditions, is size extensive (in the sense that the energy of a composite system consisting of noninteracting subsystems equals the sum of the subsystem energies, while employing the appropriate method in each case). This assumes that the reference or model space employed for the composite system is size consistent, i.e., is given by a tensor product of subsystem model spaces. For pedagogical reasons, the demonstration is carried out for the single reference case before the multireference SU CC case is addressed. The importance of the C‐conditions and a relationship with earlier approaches is discussed, as well as the limiting case of a complete‐model‐space SU CC method. Finally, the size extensivity of a GMS‐based SU CCSD method is illustrated by actual numerical examples. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

The general-model-space state-universal coupled-cluster method exemplified by the LiH molecule

The salient features of the recently introduced general-model-space (GMS) state-universal (SU) coupled-cluster (CC) method are illustrated on the case of the LiH molecule. Describing the breaking of the Li–H bond by relying on an open-shell-type GMS reveals the importance of the connectivity conditions (C conditions), which represent a crucial new ingredient of the GMS SU CC theory. Only when we properly account for these C conditions can we uniquely represent the full configuration interaction (FCI) wave functions in terms of the multireference SU exponential cluster ansatz and recover the FCI energies via the GMS SU CC method, assuming that all the relevant clusters at a given level of the theory are considered. Drawing on various GMSs, we compute the potential energy curves for three Σ+1, two Σ+3, three Π,1 and three Π3 states, using the GMS SU CC method truncated at the singly- and doubly-excited level (GMS SU CCSD), as well as the externally corrected (N,M)-CCSD method that exploits the NR-CISD wave functions as the external source of higher-than-pair clusters in the MR SU CCSD method. In all cases we obtain excellent results: For Σ+ states, the maximum difference between the FCI and various SU CCSD energies is about 0.5 millihartree. These errors are further reduced when we employ the (N,M)-CCSD methods. For the Π states, the deviations of the SU CCSD energies relative to FCI amount to at most a few hundreds of a millihartree. We also report on the size-extensivity tests and the exactness of the formalism for two-electron systems.

Model study of the impact of orbital choice on the accuracy of coupled-cluster energies. III. State-universal coupled-cluster method

Model study of the impact of orbital choice on the accuracy of coupled-cluster energies. III. State-universal coupled-cluster method

Model study of the impact of orbital choice on the accuracy of coupled‐cluster energies. III. State‐universal coupled‐cluster method

Model studies of the impact of the choice of molecular orbital sets on the accuracy of the results of the state-universal coupled-cluster method involving one- and two-body excitations (SU-CCSD) were performed for the H4 model, which offers a straightforward way of representing any symmetry-adapted orbitals as well as the possibility of varying over a wide range the degree of quasi-degeneracy of a state. Energies of the three lowest 1A1 states obtained for 13 sets of standard quantum chemical orbitals as well as for a vast variety of nonstandard orbital sets defined by nodes of a two-dimensional grid are compared. It is shown that there exist nonstandard orbital sets that allow one to obtain more accurate energies than the standard orbital sets. It is also demonstrated that the recently defined [K. Jankowski et al., Int. J. Quantum Chem. 67, 221 (1998)] maximum proximity orbitals (MPO) yield more accurate results than any other of the commonly applied orbital sets. These orbitals are especially effective outside the strong-quasi-degeneracy region. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 239–250, 1998

A study of 1A 1- 3B 1 separation in CH 2 using orthogonally spin-adapted state-universal and state-specific coupled-cluster methods

The orthogonally spin-adapted (OSA) state universal coupled-cluster method involving singly and doubly excited clusters (CCSD) and the recently proposed OSA open-shell state-specific CCSD method are applied to the problem of singlet-triplet separation in methylene. Both double zeta (DZ) and DZ plus polarization bases are utilized. Comparison with other correlation treatments, including limited and full configuration and various many-body approaches based on multi-configuration self-consistent-field reference, indicates that our method represents a highly efficient theoretical tool that can lead to reliable predictions of the 1A 1- 3B 1 splitting in CH 2 when larger bases are employed.