Bond alternation (PM6 only)

A sensitive test of the ability of computational chemistry methods to reproduce the electronic structure of molecular systems is provided by comparing the the degree of bond alternation predicted by a method with that observed experimentally. Bond alternation is the difference in bond-lengths of two adjacent bonds that, except for electronic effects, would be expected to have equal lengths. For example, in the hypothetical poly-acetylene, all C-C bonds would be expected to be equal, because they are in the same chemical environment, but electronic effects (double - single bonds alternating) might cause bond-length alternation.

For this test, a set of known species is used, this set covers the range from no bond alternation to large bond alternation. All reference systems are based on X-ray structures, with most of these coming from the Cambridge Structural Database.

RHF PM6 severely over-estimates bond-alternation, and therefore was not used here, instead UHF PM6 was used. With the exception of spin-free systems, such as benzene, UHF methods do not give spin-quantized states, instead the states are mixtures of states. This, however, does not appear to affect the results: the degree of bond-alternation predicted by UHF PM6 appears to be similar to that observed.

Species	X-ray structure			UHF PM6 structure
	Short	Long	Diff	Short	Long	Diff
GAYTAB	1.361	1.463	0.102	1.347	1.486	0.139
EDIMEJ	1.334	1.500	0.166	1.337	1.483	0.146
FLCBOC	1.358	1.434	0.076	1.331	1.469	0.138
SELQIK	1.400	1.418	0.018	1.376	1.447	0.071
SENQEI	1.365	1.460	0.095	1.393	1.434	0.041
Nonaphyrin (WALJEZ)	1.381	1.400	0.019	1.411	1.424	0.013
[18]-Annulene	1.401	1.410	0.009	1.410	1.410	0.000
[22]-Annulene	-	-	-	1.405	1.405	0.000
[26]-Annulene	-	-	-	1.405	1.405	0.000
[30]-Annulene	-	-	-	1.405	1.405	0.000
Polyacene	-	-	-	1.416	1.417	0.001
Polyacetylene	-	-	-	1.405	1.406	0.001
Pentacene (PENCEN02)	1.406	1.407	0.001	1.403	1.405	0.002
Azulene	-	-	-	1.398	1.398	0.000
Azulene	-	-	-	1.414	1.414	0.000
Naphthalene	1.368	1.406	0.038	1.372	1.423	0.051
Triphenylene	1.421	1.460	0.039	1.421	1.460	0.039
Triangular-4-phenylene	1.344	1.492	0.148	1.340	1.524	0.184
Perfluoro Benzotricyclobutane (PFTEBZ11)	1.386	1.393	0.007	1.468	1.342	-0.126
SAJSOL02	1.386	1.400	0.014	1.380	1.429	0.049

The table given here shows the degree of bond-alternation found in the X-ray structure and that predicted by UHF PM6. Specific bonds used in determining bond alternation are:

   GAYTAB: the bond connecting two rings and the adjacent annulene bond.
    SELQIK, SENQEI, and WALJEZ: the bonds at the meso position
    [18]-Annulene: outer rim bonds.
    [22]-Annulene, [26]-Annulene, and [30]-Annulene: the two bonds at the middle of the straight polyacetylene section.
   Polyacene and polyacetylene: any pair of adjacent C-C bonds in the backbone.
   Pentacene: the middle bonds in the direction of the long axis.
   Azulene: the two pairs of bonds that would be symmetry related if azulene had C2v symmetry.
   Naphthalene: the C1-C2 and C2-C3 distances.
   Triphenylene, triangular-4-phenylene, perfluoro benzotricyclebutane, and SAJSOL02: adjacent bonds in the central benzene ring.

When spin quantization is important, RHF-CI methods can be used. Here is a guide to the size of the active space to be used in the C.I.: If the system is small, such as benzene, use a C.I. equal to the number of double-bonds. For larger systems, try using a C.I. of 5 (C.I.=5) then a larger C.I., e.g., C.I.=6. If there is no significant change in the results, then stop. Otherwise increase the size of the C.I. and repeat until geometric changes are negligible.

A useful keyword here is MECI, this allows the low-lying electronic excited states to be printed.

There is no obvious reason for the large error in bond-alternation in perfluoro benzotricyclebutane.