Computational Chemistry

HOMO localized on one atom, the error was 1.40 eV [ 117 ]. The errors from AM1 or
PM3 should be less than for these MNDO calculations.

6.3.6 Visualization......................................................

Many molecular features that have been calculated semiempirically can be visua-
lized, in a manner analogous to the case of ab initio calculations (Chapter 5,
Section5.5.6). Semiempirically calculated vibrations, electrostatic potentials, and
molecular orbitals also provide useful information when visualized, and little need
be added beyond that already discussed for the visualization of ab initio results.
AM1 and PM3 surfaces (van der Waals surfaces, electrostatic potentials, orbitals)
are usually very similar in appearance to those calculated by ab initio methods, but
exceptions occasionally occur. An example is the case of HCC", the conjugate base
of ethyne (acetylene), Fig.6.10. AM1 predicts that there is one HOMO and that it is
ofssymmetry (symmetric about the molecular axis), but an HF/3-21G()calcu-
lation predicts that there are two HOMOs of equal energy at right angles, each of
psymmetry (having a nodal plane containing the molecular axis; one of these
p-HOMOs is shown in Fig.6.10). The HF/3-21G orbital pattern persists at the
HF/6-31G and MP2/6-31G* levels. Different orbital patterns at different calcula-
tional levels is not the rule, but is understandable since near-lying MOs may have
their energetic priorities reversed on going to a different level.

eV

9.9 eV

HOMO –3.1 eV

H C C

H C C

HF / 3-21G

LUMO

14.5 eV

HOMO

–2.3 eV

LUMO

AM1

Fig. 6.10 The HOMO of the ethyne conjugate base, calculated by AM1 and by HF/3–21G().
AM1 predicts the HOMO to be unique and ofssymmetry (symmetrical about the molecular axis),
but HF/3–21G()predicts degenerate HOMO levels (the other is rotated 90about the molecular
axis) ofpsymmetry (with nodal planes containing the molecular axis) Only one of the degenerate
3–21G HOMOs is shown here. The orbitals were calculated and visualized with Spartan [ 56 ].
From your knowledge of the anion as a reagent in synthesis, which result do you think is more
likely to be the correct one?

434 6 Semiempirical Calculations