Computational Chemistry

1. Theshapeof a molecular species can provide clues to the existence of theoreti-
   cal principles (why is it that benzene has six equal-length CC bonds, but
   cyclobutadiene has two “short” and two “long” bonds [ 246 ]?), or act as a
   guide to designing useful molecules (docking a candidate drug snugly into the
   active site of an enzyme requires a knowledge of the shapes of the drug and of
   the active site [ 109 ]). Although shape is one of the fundamental characteristics
   of a molecule, it is amusing and yet thought-provoking that the question has
   been asked whether this is really a necessary property [ 247 ]! The basic problem
   here seems to be that according to quantum mechanics, for any observable
   property of a system there is a corresponding operator, which in principle allows
   the property (its expectation value, actually) to be calculated using the wave-
   function (Section 5.2.3.3); however, there is no shape operator. Trindle has
   worked on reconciling this quantum mechanical conundrum with reality [ 248 ].
   Molecular shape has been treated at book length by Mezey [ 249 ].

80

60

40

20

0

IR_INTENS

0

37

73

1.1e+002

4000

4000

3000

3500 3000

2000

FREQ_VAL

2500 2000

1000

1500 1000 500

3091

Benzene

Experimental

3050

HF / 6-31G* 3376

1653

766

1143

1040

674

1480

IR_INTENS

0

37

73

1.1e+002

4000 3500 3000

FREQ_VAL

(^2500200015001000500)
3239
MP2 / 6-31G
1540
1083
689
Fig. 5.34 Experimental (gas phase), HF/6–31G and MP2(fc)/6–31G* calculated IR spectra of
benzene
338 5 Ab initio Calculations