Single-reference methods substitutions method

In this research, the coupled-cluster single and double substitutions method with a perturbative treatment of triple excitations CCSD(T) [16-18] was adopted based on unrestricted Hartree-Fock reference wave functions. For the CCSD(T) computations, the cc-pVDZ, cc-pVTZ, and cc-pVQZ quality basis sets were used, where cc-pVnZ is an abbreviation for the correlation-consistent polarized valence basis sets of Dunning et al. [19-22]. With the coupled-cluster methods used in this research, the core orbitals are frozen. That is, the Is-like molecular orbital is frozen for O, while the Is2s2p3s3p3d-like molecular orbitals are frozen for Br. 

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. 

Rather than record a single spectrum that contains both sample and reference, the frequency of the reference compound can be measured in a separate experiment. This technique, the substitution method, depends on the high stability of modern NMR spectrometers when a deuterated solvent is used to provide a field/fre-quency lock, as described in Section 3.3. This method requires two measurements but is quite versatile. If the sample and the reference compound are each dissolved... 

Hence there is a need to make SOCI more computationally efficient so that it can be used for larger chemical systems, and to develop related methods which scale better with the system size. Although the Cl space can be reduced by individual selection of references or A-electron functions, for the reasons stated above it is beneficial to select the Cl space in an a priori manner, once a minimal set of parameters, such as the active space, has been specified. For example, we have advocated a method we call CISD[TQ],16-18 which is a SOCI in which higher-than-quadruple substitutions have been excluded. For systems dominated by a single reference, CISD[TQ] performs nearly as well as SOCI.16,17... 

If a CISD procedure includes all the important JV-electron functions from the zeroth-order wavefunction (the references ) and also the single and double substitutions for each of these references, then the resulting method is referred to as multireference (MR) CISD. The MR-CISD wavefunction may be written... 

Most studies limit the Cl space to single and double substitutions from a single reference (CISD). Occasionally, when one reference does not provide a sufficient zeroth-order wavefunction, the multi-reference CISD method will be employed. The applications of such methods are too numerous to discuss here their general performance has already been described in section 2. We consider studies which go beyond CISD for one or a few references such highly correlated wavefunctions are useful when very accurate results are desired or when several electron configurations are needed for a qualitatively correct reference wavefunction (such as when multiple bonds are broken). We will limit our attention to methods which select the Cl space in an a priori fashion based on the distribution of electrons among various orbital subspaces. 

An alternative method, named internally contracted Cl, was suggested by Meyer and was applied by Werner and Reinsch in the MCSCF self-consistent electron-pair (SCEP) approach. Here only one reference state is used, the entire MCSCF wavefunction. The Cl expansion is then in principle independent of the number of configurations used to build the MCSCF wavefunction. In practice, however, the complexity of the calculation also strongly depends on the size of the MCSCF expansion. A general configuration-interaction scheme which uses, for example, a CASSCF reference state, therefore still awaits development. Such a Cl wavefunction could preferably be used on the first-order interacting space, which for a CASSCF wavefunction can be obtained from single and double substitutions of the form ... 

In this context one should also mention the rather old MRD-CI-method of Buenker and Peyerimhoff [160]. There one starts from a multideterminant reference function and improves it by Cl with single and double substitution. This method has not been designed for single states, but rather for the computation of various states simultaneously. 

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