Coupled-cluster method extension

The use of Cl methods has been declining in recent years, to the profit of MP and especially CC methods. It is now recognized that size extensivity is important for obtaining accurate results. Excited states, however, are somewhat difficult to treat by perturbation or coupled cluster methods, and Cl or MCSCF based methods have been the prefen ed methods here. More recently propagator or equation of motion (Section 10.9) methods have been developed for coupled cluster wave functions, which allows calculation of exited state properties. 

M. Wloch, J.R. Gour, K. Kowalski, P. Piecuch, Extension of renormalized coupled-cluster methods including triple excitations to excited electronic states of open-shell molecules, J. Chem. Phys. 122 (2005) 214107. 

The CASSCF method itself is not very useful for anything else than systems with few electrons unless an effective method to treat dynamical correlation effects could be developed. The Multi-Reference Cl (MRCI) method was available but was limited due to the steep increase of the size of the Cl expansion as a function of the number of correlated electrons, the basis set, and the number of active orbitals in the reference function. The direct MRCI formulation by P. Siegbahn helped but the limits still prevented applications to larger systems with many valence electrons [20], The method is still used with some success due to recent technological developments [21], Another drawback with the MRCI approach is the lack of size-extensivity, even if methods are available that can approximately correct the energies. Multi-reference coupled-cluster methods are studied but have not yet reached a state where real applications are possible. 

Szalay, P. G. Bartlett, R. J. Multi-reference averaged quadratic coupled-cluster method a size-extensive modification of multi-reference Cl, Chem. Phys. Lett. 1993, 214, 481-488. 

Paldus, elsewhere in this book, discusses that there is as yet no generally applicable, open-shell, size-extensive, coupled cluster method, and the same holds for open-shell S APT methods. Therefore, for the computation of potentials of open-shell van der Waals molecules one has the choice between CASSCF followed by a Davidson-corrected MRCl calculation of the interaction energy, or the single reference, high spin, method RCCSD(T). When the ground state of the open-shell monomer is indeed a high spin state, then RCCSD(T) is the method of choice. With regard to the latter method we recall that a major difficulty in open-shell systems is the adaptation of the wave function to the total spin operator S for the CCSD method a partial spin adaptation was published by Knowles et al. [219,220] who refer to their method as partially spin restricted . When non-iterative triple corrections [221] are included, the spin restricted CCSD(T) method, RCCSD(T), is obtained. 

Linear Scaling Local Correlation Extensions of the Standard and Renormalized Coupled-Cluster Methods... 

Keywords Block correlated coupled cluster method energy surface Size-extensivity error... 

Approaches which consider one state at a time are often referred to as one-state or state-selective or single-root . They were first proposed in the late 1970s. A paper published by Harris [113] in 1977, entitled Coupled cluster methods for excited states, first introduced the state-selective approach. Four papers which were published in 1978 and 1979 advancing the state-selective approach parts 6 and 7 of a series of papers entitled Correlation problems in atomic and molecular systems part 6 entitled Coupled cluster approach to open-shell systems by Paldus et al. [114] and part 7 with the title Application of the open-shell coupled cluster approach to simple TT-electron model systems by Saute, Paldus and Cfzek [115], and two papers by Nakatsuji and Hirao on the Cluster expansion of wavefunction, the first paper [116] having the subtitle Symmetry-adapted-cluster expansion, its variational determination, and extension of open-shell theory and the second paper [117] having the subtitle Pseudo-orbital theory based on sac expansion and its application to spin-density of open-shell systems. 

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