Essentials of Computational Chemistry

7.6 PRACTICAL ISSUES IN APPLICATION 227
Thus, there do not exist any ‘higher’ levels of QCISD, although such levels could be defined
to include additional excitations by analogy to CCSD.
Finally, Levchenko and Krylov (2004) have defined spin-flip versions of coupled cluster
theories along lines similar to those previously described for SF-CISD. Applications to date
have primarily been concerned with the accurate computation of electronically excited states,
but the models are equally applicable to computing correlation energies for ground states.
7.6 Practical Issues in Application
The goal of most calculations is to obtain as high a level of accuracy as possible within the
constraints of the available computational resources. As including electron correlation in a
calculation can be critical to enhancing accuracy, but can also be excruciatingly expensive
in large systems, it is important to appreciate the strengths and weaknesses of different
correlation techniques with respect to various system characteristics. This section provides
some discussion of factors affecting all correlation treatments, and compares and contrasts
certain specific issues associated with individual treatments.
7.6.1 Basis Set Convergence
As noted in Chapter 6, basis-set flexibility is key to accurately describing the molecular
wave function. When methods for including electron correlation are included, this only
becomes more true (see, for instance, He and Cremer 2000b). One can appreciate this in an
intuitive fashion from thinking of the correlated wave function as a linear combination of
determinants, as expressed in Eq. (7.1). Since the excited determinants necessarily include
occupation of orbitals that are virtual in the HF determinant, and since the HF determinant in
some sense ‘uses up’ the best combinations of basis functions for the occupied orbitals (from
the requirement that the excited states be orthogonal to the ground state), the excited states
are more dependent on basis-set completeness (this generalizes to the MCSCF case as well,
although the discussion in this section is primarily focused on single-reference theories).
This differential sensitivity is illustrated in Table 7.1, which compares the convergence of
the HF energy for CO with the convergence of the full-CI energy for just the O atom. In this
case, the convergence is with respect to adding higher angular momentum basis functions
into a set that is saturated with functions of lower angular momentum. Note that even though
Table 7.1 Basis set convergence for HF and full CI energies of
CO and O, respectively
Saturated basis functions EHF(CO) (a.u.) ECI(O) (a.u.)
s, p −112.717 −74.935
s, p, d −112.785 −75.032
s, p, d, f −112.790 −75.053
s, p, d, f, g −75.061
Infinite limit −112.791 −75.069