Biomedical Engineering Reference
In-Depth Information
Table 19.2
Geometry optimization for ethene
HF/STO-3G
HF/6-311G**
MP2/6-311G**
MP2/cc-pVTZ
ε
HF
/
E
h
−
77.0789547
−
78.0547244
−
78.0539661
−
78.0638977
ε
MP2
/
E
h
−
78.3442916
−
78.3993063
ε
corr
/
E
h
0.2903255
0.3354086
R
CC
/pm
130.6
131.7
133.7
133.2
R
CH
/pm
108.2
107.6
108.5
108.0
HCH/
◦
115.7
116.7
117.2
117.3
Cpu time/s
28
41
70
881
There are two sources of error in the calculations: the choice of a finite basis set, and
truncation of the MP
n
series at MP2. According to the literature, the basis set error is the
larger of the two. One has to be careful to compare like with like and the results of the
calculations should be compared with geometric parameters at the bottom of the potential
energy well. Experimental values very often refer to the lowest vibrational energy level. The
estimate of the correlation energy depends markedly on the quality of the basis set. Electron
correlation studies demand basis sets that are capable of high accuracy, and a number of
suitable basis sets are available in the literature. One popular family is the
correlation
consistent
basis sets of Dunning, which go by acronyms such as cc-pV6Z. This contains
seven s-type, six p-type, four d-type, two g-type and one h-type primitives.
We usually find that MP2 calculations give a small but significant correction to the
corresponding HF-LCAO geometries. It is probably more worthwhile using MP
n
models
to investigate effects that depend crucially on electron correlation; bond breaking and bond
making phenomena spring to mind. Figure 19.1 shows representative potential energy
curves for dihydrogen, following the discussion of Chapter 15.
-0.75
-0.8
-0.85
-0.9
-0.95
-1
-1.05
-1.1
-1.15
-1.2
0.5
1
1.5
2
Distance/bohr
2.5
3
3.5
4
Figure 19.1
Dihydrogen electron correlation
