5 Basics of Molecular Modeling and Molecular Simulation
205
Coupled Cluster (CC) Method
The coupled-cluster (CC) method resolves the problem of size extensibility, and is
often very accurate, but more expensive than (limited) CI. The CC method assumes
an exponential ansatz for the wave function
|Ψ CC = e
ˆ
T
|Φ 0
(5.2.17)
where
e
ˆ
T
= 1 + ˆ
T +
1
2
ˆ
T
2
+
1
6
ˆ
T
3
+ · · · =
∞
k=0
1
k!
ˆ
T
k
(5.2.18)
The approximate computational complexity of CI methods, MP methods, and CC
methods can be estimated as the chart given below.
Computational complexity
CI
MP
CC
M 5
MP2
M 6
CISD
MP3, MP4(SDQ)
CCSD
M 7
MP4
CCSD(T)
M 8
CISDT
MP5
CCSDT
M 9
MP6
M 10
CISDTQ
MP7
CCSDTQ
In practice, the user has to choose an appropriate method with a good balance
between accuracy and complexity which well fits the designated problem. For
instance, the HF method is generally used to locally optimize a configuration, the
MP2 method is widely used to obtain a rough result with acceptable accuracy and
computational cost, and the CC series are usually used to obtain very accurate results
for the purpose of calibration.
The electronic structure methods are slower than the DFT methods described
below, but have the benefit that higher level calculations guarantee to have a better
accuracy.
5.2.2 Density Functional Theory
In dealing with many-body Schrödinger Equations, DFT employs electronic density
distribution to replace electronic positions to be the variables of the wave function,
which to a large extent simplifies the computational complexity and enables this
method to be widely used in solving such equations. To use DFT methods in solving
many-body Schrödinger Equations with the form of Eq. (2.1), the key is to replace