Chemistry Reference
In-Depth Information
found in Ref. 113, and a tutorial on linear scaling in quantum chemistry has
appeared in this topic series.
132
) Parallelization does not solve the issue. If a
parallel CCSD(T) code executed on a high-performance cluster can reduce
the time for the (H
2
O)
6
computation to 1 day, the (H
2
O)
18
calculation will
still take 6 years to finish. Even if time was not a factor, these ludicrous com-
putations would not be feasible because memory and disk requirements also
increase by the same factor of 2187.
Estimating E
int
at the CCSD(T) CBS Limit:
Another Tutorial
High-accuracy model chemistries (for all types of chemical systems, not
just weakly bound clusters) typically rely on additive schemes because of the
hefty computational demands of highly correlated electronic structure techni-
ques (see preceding section). In this section we demonstrate how to reliably
estimate the CCSD(T) CBS limit even though it is generally not feasible to
compute CCSD(T) energies for weakly bound clusters with basis sets large
enough to yield a meaningful extrapolation to the CBS limit. This feat can
be achieved because contributions from higher order (triple, quadruple, etc.)
excitations tend to converge quickly with respect to the size of the AO basis
set even though the total correlation energy converges slowly to the CBS limit
(discussed above). As a result, the general strategy is to combine the CBS limit
for a less demanding correlated method that includes only lower order excita-
tions (e.g., MP2, CCSD, CISD) with a correction for higher order correlation
effects obtained with small basis sets. The most popular combination is to use
the MP2 CBS limit with a CCSD(T) correction.
Table 5 contains the MP2, CCSD, and CCSD(T) correlation energies for
the HF monomer and trimer obtained with a series of correlation-consistent
basis sets where diffuse functions are added only to the heavy (nonhydrogen)
atoms, denoted ha
X
Z. The frozen core approximation was adopted for all of
the calculations (i.e., electrons in the 1
s
-like orbitals on F were not included in
the correlation procedure). The SCF energies converge very quickly. The
ha5Z and ha6Z data points are within 1mE
h
of the SCF CBS limit that was
obtained by fitting all five SCF energies (haDZ-ha6Z) to Eq. [41]. In contrast,
the MP2 correlation energy converges moreslowly.Theha5Zvaluesarestill
more than 9mE
h
away from the MP2 CBS limit that was obtained by simply
applying Eq. [43] to the ha5Z and ha6Z MP2 correlation energies (not the
total MP2 electronic energies). The CCSD and CCSD(T) correlation energies
are also provided for the haDZ, haTZ, and haQZ basis sets. No CCSD and
CCSD(T) CBS limits are given, however, because extrapolations with smaller
basis sets tend not to be as reliable as when larger correlation-consistent basis
sets (e.g., pentuple- or sextuple-
) are used to obtain the correlation ener-
gies.
129,130,133
Unfortunately, such computations are often prohibitively
demanding.
