Quadratic configuration interaction triples

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],... 

Quadratic Configuration Interaction with Singles and Doubles Quadratic Configuration Interaction with Singles, Doubles, and Noniterative Approximation of Triples Symmetry Adapted Cluster-Configuration Interaction Split-Valence basis set plus Polarisation functions Zero-Order Regular Approximation Zero-Point Energy... 

QCISD(T) quadratic configuration interaction calculation, including single and double-substitutions and non-iteratively triple excitations R2 correlation coefficient... 

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. 

T. J. Lee, A. P. Rendell, and P. R. Taylor, /. Phys. Chem., 94,5463 (1990). Comparison of the Quadratic Configuration Interaction and Coupled-Cluster Approaches to Electron Correlation Including the Effect of Triple Excitations. 

QCISD(T) Quadratic configuration interaction with single double and perturbative triple excitations... 

Z. He and D. Cremer, Int. J. Quantum Chem., Quant. Chem. Symp., 25,43 (1991). Analysis of Coupled Cluster and Quadratic Configuration Interaction Theory in Terms of Sixth-Order Perturbation Theory. Z. He and D. Cremer, Theor. Chim. Acta, 85, 305 (1993). Analysis of Coupled Cluster Methods. 11. What Is the Best Way to Account for Triple Excitation in Coupled Cluster Theory. ... 

A major achievement in the noniterative treatment of triples correction was the introduction of the so-called (T) correction, first defined for the quadratic configuration interaction (QCISD) model and later for the CCSD approach. Here, the energy correction from CCSD + T(CCSD) is augmented by an additional fifth-order term which couples single and triple excitations ... 

B3LYP = hybrid Hartree-Fock and density functional theory using Becke s three-parameter formula and the Lee-Yang-Parr correlation functional QCISD(T) = quadratic configuration interaction singles, doubles, and triples. 

B3LYP = Becke s 3-parameter exchange functional with the Lee, Yang, and Parr correlation functional MERP = minimum energy reaction path QCISD(T) = quadratic configuration interaction for single and double substitutions and a contribution from triple substitutions. 

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