Quadratic CISD method

QCISD Quadratic (—>) CISD. Method to include an estimate of the contribution of quadruple excitations to the energy of a CISD wavefunction. 

Another commonly used method is Quadratic CISD (QCISD). It was originally derived from CISD by including enough higher-order terms to make it size extensive. 

Anntbpr curnmnnlv used method is Quadratic CISD fOClSD). It was originally than MP methods. Since the singly excited determinants allow the MOs to relax in order... 

CISD was also extended to quadratic CISD (QCISD) by the inclusion of some higher-order terms to yield a size-extensive method. 

The CISD method produces typical errors of 0.4-0.7 eV for the ground states of elements from manganese to copper even after the inclusion of relativistic effects. The Coupled Cluster method called CPF produces an error of 0.4 eV for the d s to d s splitting in nickel. The basis set cited in the main text comes from a study in which an elaborate quadratic Cl method was used in which the already large basis set was augmented with numerous diffuse orbitals (Raghavachari and Trucks, 1989). The use of M-P perturbation theory produced what the authors of this article describe as wild oscillations for the same excitation energy. 

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. 

In 1970, Bender and Schaefer " reported afc initio computations of triplet methylene. Employing the CISD/DZ method, they computed the energy of triplet methylene at 48 different geometries, varying the C-H distance and H-C-H angle. Fitting this surface to a quadratic function, they predicted that the H-C-H angle is 135.1°, and emphatically concluded that the molecule is not linear. 

Instead, that step was left to Pople, Head-Gordon, and Raghavachari [69,70] who, by virtue of looking at the problem from the viewpoint of what they called quadratic CT, meant to be a simplified CC method (but see [71,72]) considered that like in CISD, if the doubles were there, the singles should be too. This added the numerically small, but... 

The Pople corrections for higher excitations in CISD calculations result in a method called quadratic (Q) CISD, which can be regarded as an approximation to the coupled-cluster methods discussed in a separate section below. QCISD is available in the Gaussian series of programs, along with analytical derivatives and a method for the estimation of triple excitations called QCISD(T). Note that in Gaussian, CISD on open-shell molecules is performed with UHF MOs. Therefore, for such molecules, the methods just named should really be called UQCISD or UQCISD(T), respectively. 

For correlated methods such as truncated configuration interaction (CID or CISD), coupled cluster (CCD or CCSD), quadratic configuration interaction (QCISD) and Brueckner doubles (BD) (see Configuration Interaction and Coupled-cbister Theory), the energy and wavefunction can be written as... 

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