Quadratic CISD

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. 

QCISD Model. Quadratic CISD Model. A Correlated Model. 

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. 

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

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. 

Laidig and Bartlett/li8(a)/ have implemented the theory in its linearized form. They applied it to the symmetric dissociating potential curve for the ground state of water and the symmetric abstraction from BeH2. Each T is truncated at the two-body level. The results were compared to the corresponding MR-CISD values. To our knowledge, a quadratic extension of the formalism has not been applied computationally. A spin-adapted version of the linearized model has also been recently formu1 ated/118[Pg.332]

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. 

The QCISD projection equations differ from the equivalent CISD equations only in the addition of the quadratic terms CiC2 and C%, which lead to size-extensive energies. Alternatively, the QCISD equations may be considered an approximation to CCSD in which certain terms have been neglected. Pople and co-workers show how to extend this approach to include triples fully (QCISDT) or perturbatively [QCISD(T)].118... 

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. 

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