Quadratic coupled cluster doubles

However, there is an interesting intermediate step between standard CCD and ECCD. This is a model that includes terms quadratic in A2 in the bra function. We term this energy functional the quadratic coupled cluster doubles (QCCD) method (79) ... 

MR-AQCC multireference averaged quadratic coupled-cluster MRCI multireference configuration interaction MRD-CI multireference single and double excitation Cl... 

QCISD(T) = quadratic Cl including single, double, and triple excitations, UCCD(ST) = coupled-cluster doubles method based on the unrestricted Hartree-Fock method and corrected for single and triple replacements, MC SCF = multiconfiguration SCF, MRD Cl = multireference singles and doubles Cl, MBPT= many-body perturbation theory, SD Cl = singles and doubles Cl. 

Quadratic Cl (QCI) and coupled cluster (CC) exemplify more complex methods that are not strictly variational in character, but include physical corrections similar to those of higher-order perturbation theory. Keywords for these methods also include a specification of substitutions from the reference FIF configuration, such as QCISD or CCSD, respectively, for QCI or CC methods with all single and double substitutions. More complete descriptions of these methods are beyond the scope of this appendix. 

There is also a hierarchy of electron correlation procedures. The Hartree-Fock (HF) approximation neglects correlation of electrons with antiparallel spins. Increasing levels of accuracy of electron correlation treatment are achieved by Mpller-Plesset perturbation theory truncated at the second (MP2), third (MP3), or fourth (MP4) order. Further inclusion of electron correlation is achieved by methods such as quadratic configuration interaction with single, double, and (perturbatively calculated) triple excitations [QCISD(T)], and by the analogous coupled cluster theory [CCSD(T)] [8],... 

Instead of the very demanding CCSDT calculations one often performs CCSD (T) (note the parentheses), in which the contribution of triple excitations is represented in an approximate way (not refined iteratively) this could be called coupled cluster approximate (or perturbative) triples. The quadratic configuration method (QCI) is very similar to the CC method. The most accurate implementation of this in common use is QCISD(T) (quadratic Cl singles, doubles, triples, with triple excitations treated in an approximate, non-iterative way). The CC method, which is usually only moderately slower than QCI (Table 5.6), is apparently better [102]. CCSD(T) calculations are, generally speaking, the current benchmark for practical molecular calculations on molecules of up to moderate size. 

Two approaches to electron correlation that are widely used today for the studies of organic radical cations are Coupled Cluster (CC) calculations or the similar, but not identical, Quadratic Configuration Interaction (QCI) method with single and double excitations, often followed by CCSD(T) or QCISD(T) single point calculations with a larger basis set. These methods suffer to a much lesser extent from... 

Quadratic response theory in combination with self-consistent field (SCF), MCSCF, and coupled-cluster electronic structure methods have been used for calculation of excitation energies and transition dipole moments between excited electronic states <2000PCP5357>. The excited state polarizabilities for r-tetrazine are given by the double residues of the cubic response functions <1997CPFl(224)201>. 

---