Correlation energy quadruple excitations

Usually, SD-CI wavefiinctions recover about 90-95% of the correlation energy, inclusion of triply and quadruply substituted configurations is adequate for many purposes, and inclusion of quintuply and sextuply excited configurations is sufficient for describing most chemical reactions. Since the explosion of the number of configurations typically starts with the quadruple excitations, our first priority is the predictive deletion of deadwood from this group. 

The delocalization is, of course, not a problem for MOCI calculations, but the electron correlation is. The numbers show that the double excitations produce acon-siderable portion of the correlation energy possible with this basis, while including excitations up through quadruple produces essentially all. 

RJ. Bartlett et al., Non-iterative fifth-order triple and quadruple excitation energy corrections in correlated methods. Chem. Phys. Lett. 165, 513-522 (1990)... 

Cl SD calculations are currently almost routine (ref. 13 and references therein), and in many cases (particularly systems with few electrons) they have been used to obtain a large fraction of the correlation energy. However, in very accurate calculations it is necessary to include triple and quadruple excitations, in which case the most common ab initio technique to tackle this problem consists in building up single and double excitations from a multiple... 

Table VI CPU times on the CRAY-1 computer required to evaluate the double-excitation/ tD/ triple-excitation/ and quadruple-excitation/ t / components of the correlation energy.

Table VII Fourth-order linked-diagram triple-excitation and quadruple excitation components of the electron correlation energy in a number of atoms and small molecules...

Triple-excitations and Quadruple-excitations.—Only double excitations contribute to the correlation energy and other properties through third-order triple-, quadruple and higher-order excitations are usually neglected. Triple- and quadruple-excitations first arise in the fourth-order of the perturbation series. 

Table 5 Contribution of triple-excitations and quadruple-excitations to the correlation energy of the water molecule at its equilibrium nuclear geometry...

In ref. 36 Song et al. introduced an analogue of Davidson s correction for VBCISD wavefunctions, which provides an estimate of the contribution of quadruple excitations that are products of double excitations to the correlation energy. This has been shown to alleviate, just as in the MO case, the size-consistency problem in calculations on small molecules. 

R. J. Bartlett,. D. Watts, S. A. Kucharski, and. Noga, Chem. Phys. Lett., 165,513 (1990) Erratum 167, 609 (1990). Non-iterative Fifth-Order Triple and Quadruple Excitation Energy Corrections in Correlated Methods. 

Much of the above discussion points to the importance of properly balancing various correlation effects and the need to account for the triple as well as quadruple excitations in the high quality calculations of molecular potential energy surfaces. The properly constructed theory should provide an accurate description of... 

---