Bond breaking multireference methods

Recent years have witnessed a considerable activity towards extending the standard single-reference coupled-cluster (CC) methods (1-9) to potential energy surfaces (PESs) involving bond breaking without invoking a multireference description (see, e.g., refs 9-31). Undoubtedly, it would be very useful if we could routinely calculate large portions of molecular PESs with the ease-... 

Due to the inherent multireference nature of bond-breaking problems, it seems rather unlikely that single-determinant CC methods of any sort will ever provide a satisfactory solution to these problems. It seems much more sensible to use MR approaches to study problems of this sort when they are relevant for a particular chemical application. For small molecules, MRCI offers a suitable option, while CASSCF calculations corrected by perturbation theory are more generally useful for larger systems. 

Abstract The block correlated coupled cluster method, with the complete active-space self-consistent-field reference function (CAS-BCCC), has been applied to investigate the bond-breaking potential energy surfaces (PESs) for a C—C bond in two alkanes (ethane and 2,3-dimethyl-butane) and a C=C bond in two alkenes (ethylene and 2,3-dimethyl-2-butene). The results are compared with those from other multireference methods (CASPT2, MR-CISD, and MR-CISD+Q). It is demonstrated that the CAS-BCCC method can provide more accurate PESs for C—C bond-breaking PESs than CASPT2 and MR-CISD. The overall performance of CAS-BCCC is shown to be comparable to that of MR-CISD-pQ for systems under study. 

To overcome the failures of the CCSD(T) method in dealing with bond-breaking and open-shell species, several multireference (MR) CC methods have been developed, but none of these methods is fully satisfactory. Reviews of MR CC methods noted that even now the situation in the MRCC field is not satisfactory, since none of the MRCC methods is in a wide use [D. 1. Lyakh et al., Chem. Rev., 112,182 (2012)] and a generally accepted multireference CC theory is still lacking (A. Kohn et al., WIREs Comput. Mol. Sci. 2012, doi 10.1002/wcms.ll20). 

The main restriction of the methods discussed in the main part of this chapter is the assumption of a single dominant configuration. This requirement is not met for systems with strong non-dynamical correlation effects such as biradicals (e.g. in bond-breaking situations) or transition metal compounds. In this case the reference function must be a multireference expansion. The fixed-amplitude approximation lends itself very well to a multireference extension of the formalism, as demonstrated first by Ten-no who devised an F12-based internally contracted geminal correction to the multireference MP2 (MRMP2) method. A closely related approach was considered by Torheyden and Valeev, who proposed a generalized perturbative correction to arbitrary wavefunctions and which they applied to a MRCI wavefunction. A spin-free formulation was reported recently.The approach was also used by Booth et al. to get a basis set limit estimate for their full Cl quantum Monte Carlo method, which can also be seen as an approach to tackle systems with multireference character. 

As a prototype multireference application, we performed calculations of potential curves for the symmetric breaking of the water molecule H2O in which the two O-H bonds are stretched simultaneously. We used both the 6-3IG [54] and cc-pVDZ [55] basis sets. The results of L-CTD and L-CTSD calculations, together with a number of conventional methods— Hartree-Fock (HF), full... 

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. 

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