The document discusses the calculation of pyramidality indices for the β-lactam ring in β-lactam antibiotic derivatives using various computational methods. It finds that semiempirical quantum mechanical methods like MNDO perform best, while molecular mechanics methods like MM2 can be used with caution. Ab initio methods at HF 3-21G or BLYP 6-21G* levels provide the most precise results and agree with experimental X-ray structures.

1. The preparation of 2-substituted cephalosporin sulfoxides via LDA-generated
anionic intermediates give rise to a mixture of C-2 and C-4 substituted products
owing to the delocalised nature of the negative charge.
N
SO
R
H
O
CH3
O O
CH3
H
H
-.82
.21
-.27-.52
.51
-.50
-.41
-.33
.29
.98
The C-2 carbon next to the sulphur
possesses the highest value of negative
charge. C-4 exhibits also a high value of
electron density, owing to the charge-
delocalization over the unsaturated
system.
The HOMO is concentrated mainly on
atoms C-2 and C-4 (and in lesser extent
on the ß-lactam ring), both atoms
sharing practically the same level of
electron density on the HOMO orbital.
This is in full agreement with the
experimental findings.
Mullikan point
charges

2. On the calculation of the N-pyramidality of ß-lactam ring – The pyramidality
indices of about 40 randomly selected ß-lactam antibiotic derivatives have been
calculated by several force field, semiempirical and ab initio QM methods and
O N
O
H
HHH
P = 0.0 P = 0.77 POAV
N
Bending of N-Me vs. energy
0.00
2.00
4.00
6.00
8.00
10.00
12.00
110120130140150160170180
Out-of-plane bending (deg)
E (kcal/mol)
AM1
MNDO
MINDO3
PM3
STO-3G
3-21G
Bending of N-Me vs. energy
0.000
0.100
0.200
0.300
0.400
0.500
150155160165170175180
Out-of-plane bending (deg)
E (kcal/mol)
AM1
MNDO
MINDO3
3-21G
O
N
NH2
Me
12
3
Of the MM methods, only the
old MM2 can be used with
cautions and the MMFF94 in
the case strained systems.
Of the semiempricial QM
methods the MNDO proved to
be the best one, AM1 and PM3
produced clearly bad results.
The most precise ones are
undoubtly the ab initio
methods on the HF 3-21G or
BLYP 6-21G* or better levels.
compared with those of
the original X-ray-
determined structures. Of
the possible pyramidality
measures index P of
Radhakrisnan was used for
the comparison.

3. The cis-/-ratio of the -
lactam products of the chiral
Staudinger reaction is highly
influnced by the chirality of the
N-substituent of the starting
diene. Only cis -lactams were
formed, this is in accordance
with the generally accepted
two-step mechanism of the
ketene addition, i.e. zwitter-
ionic intermedier via the attack
of the LUMO of the ketene
carbonyl group by the imine,
followed by conrotatory ring
closure as depicted here:
By using bulky protective
groups as R, the ratio of the
/cis isomers were ~8:1.
Stereoselective construction of optically pure -lactam intermediates

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