Computational Chemistry

TPSS was given precedence over PBE because it lies on a higher rung, which does
not mean that for every task it will be more accurate; however “TPSS usually
provides better accuracy than PBE for a very modest increase of computational
cost....TPSS is close to being the best nonempirical functional so far...”.^3 A choice
could not be made between M06 and TPSS and for geometries (and energies)
calculated here both were used, because M06, as suggested above, may become
the general purpose functional of choice, while TPSS is nonempirical, giving it an
esthetic virtue as well as (one hopes) shielding it against “catastrophic failure” (see
the end of Section7.2.3.4g). Thus in Fig.7.1and Table7.1we compare geometries
from B3LYP, M06, TPSS, and MP2(fc)/6-31G (the highest-level ab initio method
in routine use) with experiment.
Table7.1presents for examination 43 bond lengths and 19 bond angles, taken
from 20 molecules. For each of these parameters the deviation from experiment
(calculated – experimental value) is shown for B3LYP, M06, TPSS, and MP2 (with
the 6-31G basis in each case). The mean absolute deviations from experiment
(arithmetic mean of the unsigned errors), MAD, are:

B3LYP M06 TPSS MP2

Bond lengths 0.008 0.008 0.013 0.008

Bond angles 0.75 0.8 0.95 0.7

For bond lengths the biggest error was 0.053 A ̊ (TPSS, for the C–S bond of
Me 2 SO). For bond angles, the biggest error was 2(M06, for an HCN angle
of CH 3 NH 2 ). For the bonds, the number of parameters for which the direction of
deviation was zero (bond or angle the same as experiment), positive (bond bigger
than experiment), and negative are:

B3LYP M06 TPSS MP2

Zero deviation 2 1 0 3

Positive 30 25 38 27

Negative 11 17 5 13

For bond angles the corresponding deviations are:

B3LYP M06 TPSS MP2

Zero deviation 0 1 0 1

Positive 11 10 11 11

Negative 8 8 8 7

Qualitative conclusions from all this are: reasonably good bond lengths (to
within ca. 0.01 A ̊) are given with the 6-31G* basis by B3LYP, M06, and MP2;
TPSS values (0.013 MAD error) are satisfactory for most purposes. All four

(^3) Personal communication from Professor J.P. Perdew, 2009 November 7.
7.3 Applications of Density Functional Theory 473