Size-extensivity molecules

It is a well-known fact that the Hartree-Fock model does not describe bond dissociation correctly. For example, the H2 molecule will dissociate to an H+ and an atom rather than two H atoms as the bond length is increased. Other methods will dissociate to the correct products however, the difference in energy between the molecule and its dissociated parts will not be correct. There are several different reasons for these problems size-consistency, size-extensivity, wave function construction, and basis set superposition error. 

Size-consistency and size-extensivity are issues that should be considered at the outset of any study involving multiple molecules or dissociated fragments. As always, the choice of a computational method is dependent on the accuracy desired and computational resource requirements. Correction formulas are so simple to use that several of them can readily be tried to see which does best for... 

The results for N2 are summarized in Table 3. The bond is streched from 2.15 a.u. up to 3.00 a.u. Opposite to the previous molecules, even at the equilibrium geometry CCSD does not perform as well as the other approaches. For the [6e/6o] active space, it differs from FCI by 12.9 mHa, while CAS-SDCI does it by 8.3 mHa, (SCf CAS-SDCI by 3.9 mHa and ec-CCSD by 2.0 mHa or 1.8 mHa, depending on the external correcting source. Again, one may observe that the minimal dressing of CAS-SDCI not only makes it size-extensive, but also improves the absolute value of the yielded energy. 

Second period diatomics are excellent representative systems for assesing the suitability of methods that are under development. A large number of vertical excitation energies are available. The size of these molecules may be small but the physical contents of the states can be very diverse. The condition required for extrapolating the mean errors to greater systems is the size-extensivity of the... 

The CC methods represent a wave function using a nonlinear (exponential) expansion, which ensures size-extensivity and, thereby, uniform high accuracy for molecules of all sizes, including solids [4]. 

It should be noted that G2 and G3 potentially fail to be size extensive because of the correction term in step 8. If one is studying a homolytic dissociation into two components, at what point along the reaction coordinate are tlie formerly paired electrons considered to be unpaired There will be a discontinuity in tlie energy at that point. In addition, G3 theory uses a different correction for atoms than for molecules, and this too fails to be size extensive. 

Second, where nondynamical correlation is unimportant (that is, mainly closed-shell molecules near their equilibrium geometries), size-extensive (or nearly size-extensive) treatments like CPF, CCSD, and CISD+Q perform well. However, as bonds are stretched, or in species where nondynamical correlation is important because of near-degeneracies or open-shell effects, the performance of these methods deteriorates fairly rapidly. As might be expected, the CCSD method generally deteriorates slowest. In general, low-order perturbation theory methods do not agree well... 

In a nutshell (electron correlated methods) Complete electronic description, straightforward interpretation Highly accurate methods that can rival experiment for small organic molecules Very time consuming Cl methods are not size-extensive CC methods are non-variational Slow convergence Strongly basis set dependent Systematic improvement straightforward. 

Table 3 summarizes for each contribution the types of model and size of molecule being studied in the mid 1990s.This summary and account are intended to give just an entry into the often large literature on each contribution and to encourage the extension of these methods to larger molecules. 

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