and nucleic acids, which a few years ago were limited to molecular mechanics, can
now be done routinely [ 89 ] with semiempirical methods on inexpensive personal
computers with the program MOZYME [ 90 ], which uses localized orbitals to solve
the SCF equations [ 91 ]. Localized orbitals speed up the Roothaan-Hall SCF process
(Section5.2.3.6.2) because with these more compact orbitals (compared to the
dispersed canonical orbitals; Section5.2.3.1) fewer long-range basis function
interactions need be considered. Clearly, this saving in “outreach” is especially
important in a very big molecule.
Let’s compare AM1, PM3, and MP2(fc)/6-31G (Section 5.4.2) and experimen-
tal geometries; the MP2(fc)/6-31G method is a reasonably high-level ab initio
method that is routinely used. Figure6.2gives bond lengths and angles calculated
by these three methods and experimental bond lengths and angles, for the same 20
molecules as in Fig.5.23. The geometries shown in Fig.6.2are analyzed in
Table6.1, and Table6.2provides information on dihedral angles for the same
eight molecules as in Table5.8. Figure6.2corresponds exactly to Fig. 5.23,
Table6.1to Table 5.7, and Table6.2to Table 5.8.
This survey suggests that: AM1 and PM3 give quite good geometries (although
dihedral angles, below, show quite significant errors): bond lengths are mostly
within 0.02 A ̊ of experimental (although the AM1 C–S bonds are about 0.06 A ̊
too short), and angles are usually within 3of experimental (the worst case is the
AM1 HOF angle, which is 7.1too big).
Of AM1 and PM3, neither has a clear advantage over the other in predicting
geometry, although PM3 C–H and C–X (X¼O, N, F, Cl, S) bond lengths appear to
be more accurate than AM1. MP2 geometries are considerably better than AM1
and PM3, but HF/3-21G()and HF/6-31G (basis sets: Section5.3.3) geometries
(Fig.5.23and Table5.7) are only moderately better.
AM1 and PM3 C–H bond lengths are almost always (AM1) or tend to be (PM3)
longer than experimental, by ca. 0.004–0.025 (AM1) or ca. 0.002 A ̊(PM3). AM1
O–H bonds tend to be slightly longer (up to 0.016 A ̊) and PM3 O–H bonds to be
somewhat shorter (up to 0.028 A ̊) than experimental.
Both AM1 and PM3 consistently underestimate C–C bond lengths (by about
0.02 A ̊).
C–X (X¼O, N, F, Cl, S) bond lengths appear to be consistently neither over- nor
underestimated by AM1, while PM3 tends to underestimate them; as stated above,
the PM3 lengths seem to be the more accurate (mean errors 0.013 versus 0.028 A ̊
for AM1). Both AM1 and PM3 give quite good bond angles (largest error ca. 4,
except for HOF for which the AM1 error is 7.1).
AM1 tends to overestimate dihedrals (10þ,0"), while PM3 may do so to a
lesser extent (7þ,3"). PM3 breaks down for HOOH (calculated 180, experimen-
tal 119.1, and does poorly for FCH 2 CH 2 F (calculated 57, experimental 73).
Omitting the case of HOOH, the mean dihedral angle errors for AM1 and PM3
are 5and 4.5; however, the variation here is from 1to 11for AM1 and from" 1
to" 16 for PM3 (although not wildly out of line with the AM1, PM3 or MP2
calculations, the reported experimental ClCH 2 CH 2 OH HOCC dihedral of 58.4is
suspect; see Section5.5.1).
6.3 Applications of Semiempirical Methods 413