Quadratic configuration interaction method QCISD

Among the most widely used ab initio methods are those referred to as Gl" and 02." These methods incorporate large basis sets including d and / orbitals, called 6-311. The calculations also have extensive configuration interaction terms at the Moller-Plesset fourth order (MP4) and fiirther terms referred to as quadratic configuration interaction (QCISD). ° Finally, there are systematically applied correction terms calibrated by exact energies from small molecules. 

A disadvantage of all these limited Cl variants is that they are not size-consistent.The Quadratic Configuration Interaction (QCI) method was developed to correct this deficiency. The QCISD method adds terms to CISD to restore size consistency. QCISD also accounts for some correlation effects to infinite order. QCISD(T) adds triple substitutions to QCISD, providing even greater accuracy. Similarly, QCISD(TQ) adds both triples and quadruples from the full Cl expansion to QCISD. 

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],... 

In the 1980s, Pople and co-workers developed the non-variational quadratic configuration interaction (QCI) method, which is intermediate between CC and Cl methods. Similar to the CC methods, QCI also has the corresponding QCISD and QCISD(T) options. Both the CCSD(T) and QCISD(T) have been rated as the most reliable among the currently computationally affordable methods. 

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... 

There are a few minor variations on the CC methods. The quadratic configuration interaction including singles and doubles (QCISD)" ° method is nearly equivalent to CCSD. Another variation on CCSD is to use the Brueckner orbitals. Brueckner orbitals are a set of MOs produced as a linear combination of the HF MOs such that all of the amplitudes of the singles configurations ( f) are zero. This method is called BD and differs from CCSD method only in fifth order." Inclusion of triples configurations in a perturbative way, BD(T), is frequently more stable (convergence of the wavefunction is often smoother) than in the CCSD(T) treatment. 

C. Hampel, K. A. Peterson, and H.-J. Werner, Chem. Phys. Lett., 190, 1 (1992). A Comparison of the Efficiency and Accuracy of the Quadratic Configuration Interaction (QCISD), Coupled-Cluster (CCSD), and Brueckner Coupled-Cluster (BCCD) Methods. 

Quadratic configuration interaction (QCISD) is an approximation to CCSD methods (it is also the same up to fifth-order terms) and will give similar results. Generally (QCISD) < (CCSD) because the higher order nonlinear terms in CCSD tend to be positive. For the purposes of the present discussion, we do not need to consider it separately. The details and numerical results compared to full Cl are presented in the Appendix. 

Pople and co-workers developed the nonvariational quadratic configuration-interaction (QCI) method, which is intermediate between the CC and Cl methods. The QCI method exists in the size-consistent forms QCISD, which is an approximation to CCSD, and QCISD(T), which is similar to CCSD + T(CCSD). QCISD(T) has given excellent results for correlation energies in many calculations and is available as an option in Gaussian [J. A. Pople, M. Head-Gordon, and K. Raghavachari, J. Chem. Phys., 87, 5968 (1987) 90, 4635 (1989) K. Raghavachari and G. W. Trucks, /. Chem. Phys., 91, 1062, 2457 (1989) J. Paldus et al., J. Chem. Phys., 90, 4356 (1989)]. 

This mechanistic question is one of the examples of the success of density functional theory (DFT) methods for metal-organic chemistry. Earher work on the reaction mechanism could not discriminate between the two alternatives. Analysis of the different orbitals based on Extended Hueckel theory (EHT) calculations led to the conclusion that the (3+2) pathway is more likely, but the authors could not exclude the possibility of a (2+2) pathway [4] similar to the results of HE calculations in combination with Quadratic configuration interaction (QCISD(T)) single points [32]. 

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