Chemistry Reference
In-Depth Information
Table 6
SCS-CCSD and Other Correlated Methods in Comparison to Estimated
CCSD(T) Results
a
Sandwich
Benzene Dimer
b
Methane Dimer
c
E
R
e
E
R
e
MP2
3.25
3.7
0.50
3.7
SCS-MP2
1.76
3.9
0.32
3.8
SCSN-MP2
1.83
3.9
0.36
3.8
CCSD
0.89
4.1
0.41
3.7
SCS-CCSD
1.63
3.9
0.57
3.6
CCSD(T)
1.64
3.9
0.54
3.6
a
Energies in kcal mol
1
and distances in angstroms. Data from Ref. 103.
b
Evaluated with the aug-cc-pVTZ basis set. Coupled-cluster methods estimated via an addition
of the difference between MP2 and coupled-cluster correlation energies with the aug-cc-pVDZ
basis set to the MP2/aug-cc-pVTZ energies.
c
Extrapolated to the CBS limit.
Explicitly Correlated R12 and F12 Methods
One way to accelerate convergence to the complete-basis-set limit is to
employ
explicitly correlated
methods, which make the electronic wave func-
tion depend explicitly on the distances between electrons. These methods
have been motivated by the observation that the shape and size of the Cou-
lomb hole around an electron (i.e., the effect that the electron has on decreas-
ing the probability of finding another electron in the same vicinity) is slowly
convergent with respect to the size of the basis set. However, convergence is
improved greatly by introducing interelectronic distances into the expression
of the wave function, as first noted by Hylleraas in 1929 in his work on the
helium atom.
104
Interest in such methods has been limited because they are
more mathematically complex than conventional approaches, and they can
lead to a large number of integrals that are difficult to evaluate. However, a
number of strategies have been developed to avoid these formal difficulties,
one of the most successful of which is the ''linear R12'' approach of Kutzelnigg
and Klopper,
105,106
which introduces terms linear in the interelectronic dis-
tance and prescribes
standard approximations
for the elimination of some
integrals and the estimation of others using a resolution of the identity. Our
group used such an approach in conjunction with the MP2 method, known
as MP2-R12/A,
105,106
to estimate the CBS MP2 results with a custom basis
set smaller than the explicit aug-cc-pVQZ basis.
38
These linear R12 approaches, while helpful for very careful benchmark-
ing studies, have had the drawback that they are rather expensive to use. One
of the main reasons for this is that the particular resolution of the identity
approximation they have typically employed is valid only when a large basis
set is used. However, a number of recent developments indicate that in the
