Quadratic 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. 

Quadratic Cl energies, optionally including triples and quadruples terms (QCISD, QCISDOl, and QCISDfTQI) and optimizations via analytic gradients for QCISD. 

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. 

QCI methods 117 QCISD keywords 9,114 E4T option 186 quadratic Cl methods 114 quadrupole moment 21 quotation li... 

The third correction allows for inadequacies in the MP4 treatment. The QCISD(T) method is equivalent to MP4 in fourth order and also correctly incorporates parts of the fifth and higher orders. We therefore make a quadratic Cl correction using the 6-31IG basis set. This is a very expensive calculation for molecules of medium size. 

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. 

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],... 

QCISD Model. Quadratic CISD Model. A Correlated Model. 

The CCSD calculations are similar, both in methodology and in the accuracy of the results obtained, to calculations performed with Pople s quadratic Cl method. Like CCSD calculations, QCISD calculations also explicitly include single and double excitations and the effects of quadruple excitation in QCISD are obtained from quadrature of the effects of double excitations. However, CCSD does contain terms for the effects of excitations beyond quadruples, which are absent from QCISD. 

QCISD Quadratic configuration interaction including singles and doubles... 

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