Chemistry Reference
In-Depth Information
1.130
FCI
CI
CC
MBPT
1.125
1.120
1.115
1.110
1.105
1.100
SD
2
SDT
3
SDTQ
4
SDTQP
5
SDTQPH
6
CI and CC Excitation Level
MBPT Order
Figure 5
Convergence of correlated methods to the FCI bond length of N
2
. All results
were obtained with the cc-pVDZ basis set. The CCSDTQ bond length was computed for
this work while all other data points were taken from Ref. 116.
Consequently, the most popular progression toward the FCI limit is MBPT2
ð
MP4. The
CCSD(T) method, which includes a perturbative estimate of triple substitu-
tions, is often referred to as the ''gold standard'' of quantum chemistry
because (i) it generally provides results that are close to the FCI limit, espe-
cially for the systems that are the focus of this chapter, and (ii) it can be
applied feasibly to moderately sized systems (a few dozen atoms). [Estimates
of higher order correlation effects (e.g., quadruple substitutions) suggest that
the CCSD(T) method provides converged results for the entire spectrum of
noncovalent interactions.
118-120
]TheCCSD
or MP2
Þ!
CCSD(T) rather than MBPT2
ð
or MP2
Þ!
MP3
!
CCSD(T) sequence is also
useful but is less commonly used because the CCSD method has more signifi-
cant computational demands than MP2. These computational demands (or
computational overhead) are the topic of the discussion below on the scaling
problem.
!
Primer on Atomic Orbital Basis Sets
To introduce the concepts of a basis set and basis functions, we begin with
a simple (unknown) function of a single variable,
f
. A variety of procedures
can be used to ''fit'' (or estimate) this function. For example, a simple power
series could be used to approximate this simple function of the variable
x
:
ð
Þ
x
c
2
x
2
c
3
x
3
f
ð
x
Þ
c
0
þ
c
1
x
þ
þ
½
38
