Computational Chemistry

HF/3–21G(*)basis often gives good geometries (Section 5.3.3). Where necessary,
the truncation problem can be minimized by using a large (provided the size of the
molecule makes this practical), appropriate basis set.

Table 5.4 (cf. Fig.5.18). Dependence of the calculated energy of H 2 on basis set and on corre-
lation level
Correlated energy
Basis No. basis
functions

HF energy Method Energy

3-21G() 4 #1.12292 – –
6-31G 10 #1.13127 MP2 #1.15761
6-311þþG** 14 #1.13248 MP2 #1.16029
6-311þþG(3df,3pd) 36 #1.13303 MP2 #1.16493
6-311þþG(3df,3p2d) 46 #1.13307 MP2 #1.16543
6-311þþG(3df,3p2d) 46 #1.13307 MP4 #1.17226
6-311þþG(3df,3p2d) 46 #1.13307 full CI #1.17288
All calculations are single-point, without ZPE correction, on H 2 at the experimental bond length of
0.742 A ̊, using G94W [ 198 ]; energies are in hartrees. The accepted Hartree–Fock (EtotalHF;
Eq. (5.149¼5.93)) and correlated limiting energies are about#1.1336 and#1.1744 h, respec-
tively [ 78 ], cf.#1.13307 and#1.17288 h here)

–1.13

–1.18

energy (hartrees)

0

10 20 30 40 50

number of basis functions

–1.122

–1.124

–1.126

–1.128

–1.130

–1.132

–1.134

–1.13307 h, Hartree-Fock limit

according to these calculations

–1.17288 h, "exact" energy (full CI

with the 6-311++G(3df, 3p2d) basis set

correlation energy = –1.17288 – (–1.13307) h

= – 0.03981 h

–1.13307 h, Hartree-Fock limit

Fig. 5.18 (Based on Table5.4). The Hartree–Fock limit and correlation energy for H 2. From the
values calculated here, the HF limit, the exact energy (see text) and the correlation energy are
#1.13307,#1.17288 and#0.03981 h (see inset); the accepted values [ 78 ] are about#1.1336,
#1.17439 and#0.04079

5.4 Post-Hartree–Fock Calculations: Electron Correlation 257