Size consistent method

There is a variation on the coupled cluster method known as the symmetry adapted cluster (SAC) method. This is also a size consistent method. For excited states, a Cl out of this space, called a SAC-CI, is done. This improves the accuracy of electronic excited-state energies. 

The level of theory necessary for computing PES s depends on how those results are to be used. Molecular mechanics calculations are often used for examining possible conformers of a molecule. Semiempiricial calculations can give a qualitative picture of a reaction surface. Ah initio methods must often be used for quantitatively correct reaction surfaces. Note that size consistent methods must be used for the most accurate results. The specific recommendations given in Chapter 18 are equally applicable to PES calculations. 

Size Consistent. Methods for which the total error in the calculated energy is more or less proportional to the (molecular) size. Hartree-Fock and Moller-Plesset models are size consistent, while Density Functional Models, (limited) Configuration Interaction Models and Semi-Empirical Models are not size consistent. 

Other than MRCI calculations with relatively few electrons (say six or fewer), methods that do not even try to achieve correct scaling are unlikely to prove satisfactory. Even a Davidson-type correction is preferable to nothing at all. CPF/MCPF and especially CCSD/QCISD should be strongly preferred over CISD. And unless an exactly size-consistent method is being used, fragment energies should be computed using a supermolecule approach. 

The procedures described above are only valid when a size-consistent method is used to calculate the various energies. Special formulae have therefore been developed to deal with BSSE in CI(SD) calculations, since these lack size consistency. However, it seems preferable to use Eq. (20) as it stands, and to apply size-consistency corrections (cf. Section III.C) to all energies. 

For atomic structure calculations, the four-component MCSCF approach was the method of choice for a long time. The implementation of methods for treating very large CSF spaces, particularly Davidson-type diagonalization techniques, produced a tool to compete with highly precise experimental measurements. The coupled-cluster method—or MBPT approach as it is usually called in the physics community—turned out to be a valuable, alternative, size-consistent method. 

It is, however, well-known that the dissociation energies cannot be computed very accurately using the SDCI + Q level of theory as this method ignores electron-correlation effects from other reference configurations. This method is also not a size-consistent method. Dolg et al. found that relativistic effects lead to a bond expansion of 0.016 A and lowering of by 0.44 eV. Relativistic effects also increase the... 

I) Meller-Plesset second order, for closed shea systems (MP2). Second order perturbation theory calculations have been available for many years, and it is well recognised that this is the most straightforward and simple method for the indusion of dynamical correlation effects. It has also theadvantage that ft is a size-consistent method, now recognised to be a much more important crfteria than the variational crfteria of configuration interaction calculations. MP2 only needs the integrals (iai jb), where i,j are occupied orbitals and a, bare virtual orbitals, in the molecular orbital basis. 

When using a size-consistent method, the dissociation of homogeneous system such as (HF) into n identical HF monomers [(HF), HF] can be determined by computing the energy of the cluster and the energy of the monomer ... 

It was seen in Section 5.3 that to determine the QP band structures of a polymeric chain one must use a size-consistent method to determine the major part of the correlation [many-body perturbation theory (MBPT) in the Moller-Plesset partitioning, coupled-cluster theory, etc.]. Suhai, in his QP band-structure calculation on polyacetylenes and polydiace-tylenes, used second-order (MP/2) Moller-Plesset MBPT. For polydiacetylenes he obtained 5.7 eV as first ionization potential (using the generalized Koopmans theorem) for the PTS structure (see Figure 8.1), in reasonable agreement with experiment (A = 5.5 0.1 while the HF value (the simple Koopmans theorem) is 6.8 eV.< > For the TCDU diacetylene structure the theoretical value is 5.0 eV (HF value, 6.2 eV). Unfortunately, there is no reliable experimental ionization-potential value available for the TCDU structure of polydiacetylene. 

Regardless of whether a single- or multireference wavefunction is used for a CISD calculation, the effects of higher excitations (e.g., triples and quadruples) are obviously not included. Quadruple excitations are particularly important because it is their absence from CISD wavefunctions for closed-shell molecules that results in these wavefunctions not being size consistent. Methods for estimating the effect of quadruple excitations have been developed, both by Davidson and by Pople. The Davidson corrections for quadruples can easily be computed by hand, but they are also automatically calculated as part of the CISD modules in the MOLPRO and MOLCAS programs. 

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