Sensitivity to Reference Wave Function

CCSD is similarly sensitive to multireference character, aldiough it is less obvious that this should be so based on the formalism presented above. However, inclusion of triples in the CCSD wave function is usually very effective in correcting for a single-reference treatment of a weakly to moderately multireference problem. Of course, die most common way to include die triples is by perturbation theory, i.e., CCSD(T), and as noted above, this level too can be unstable if singles amplitudes are large. In such an instance, BD(T) calculations, which eliminate die singles amplitudes, can be efficacious. 

As for basis-set convergence, triple- calculations at the MP2 and CCSD levels are provided for comparison to die double- results. For this particular property, the results for p-benzyne are not terribly sensitive to improvements in the Ilexibility of the basis set. In the pyridynium ion case, die CCSD results are also not very sensitive, but a large effect is seen at the MP2 level. This has more to do with the instability of the perturbation expansion than any intrinsic difference between the isoelectronic aryiies. 

However, the generally robust nature of MP2 in the above examples simply reflects the degree to which most minima are already fairly well described by HF wave functions. When this is not the case, e.g., in TS structures, there are no hard and fast rules that can be cited with respect to the expected quahty of any level of theory. Instead, one is thrown back on the twin responsibilities of demonstrating either (a) agreement with known experimental data of one kind or another in the same or related systems or (b) convergence with respect to treatment of electron correlation. A rough quality ordering that is often observed is 

Level of theory Equilibrium geometry Equilibrium and stretched geometries 

For single-reference correlated methods, there are several issues associated with the HF reference that can significantly affect the interpretation of the correlated calculation. First, there is the degree to which the wave function can indeed be reasonably well described by a 

As for basis-set convergence, triple- calculations at the MP2 and CCSD levels are provided for comparison to the double- results. For this particular property, the results 

However, the generally robust nature of MP2 in the above examples simply reflects the degree to which most minima are already fairly well described by HF wave functions. When 

---