Errors in Relative Heats of Formation of Water Dimers (kcal/mol)

As a result of a careful examination (1) of 10 stationary points on the water dimer surface, an accurate determination of the relative energies of the different conformers was made.

An estimate of the accuracy of prediction of the energies and structures involved in hydrogen bonding in water for the various semiempirical methods can be obtained by seeing how well they reproduce the various relative energies of the water dimers.  In the table below are the errors in the relative energies.  In the first table are the energies of the lowest-energy dimer relative to two separated water molecules.

Errors in Heat of Reaction of two water molecules forming a water dimer

Water Dimer

  Ref.

PM6

PM5

PM3

AM1

Non-planar open Cs

-5.00

1.04

4.76

2.21

2.19

From Ref. 1, the heat of reaction is -5 kcal/mol.  That is, if two water molecules combine to form a water dimer, 5.00 kcal/mol of heat is released.  PM6 under-estimates this by 1.04 kcal/mol.

Errors in Heat of Reaction of Water Dimer going to various Stationary Points on the H4O2 Potential Energy Surface

Stationary Point

  Ref.

PM6

PM5

PM3

AM1

Planar Bifurcated C2v

2.71

-1.29

-4.48

-1.43

-2.76

Open Ci

0.52

0.31

-0.02

0.39

0.12

Planar Open Cs

0.57

0.09

-0.32

0.36

-0.11

Cyclic Ci

0.70

-0.41

-0.59

1.40

-1.64

Cyclic C2

0.95

-0.18

-0.56

1.68

-1.46

Cyclic C2h

0.99

-0.40

-0.78

1.72

-1.66

Triply Hydrogen Bonded

1.81

-0.88

-3.66

-0.65

-2.76

Non-planar Bifurcated

3.57

-0.90

-4.40

-1.86

-2.31

Non-planar Bifurcated

1.79

-1.06

-3.74

-0.64

-2.66

Average Unsigned Error 0.61 2.061.121.72

From Ref. 1, the energies of the various stationary points on the water dimer PES above the lowest water dimer energy are given in the column "Ref.", thus the heat of formation of the planar bifurcated C2v structure was calculated to be 2.71 kcal/mol above that of the non-planar open Cs conformer.  The errors in the various semiempirical methods are given in the other columns.  Thus PM6 underestimates the height of the planar bifurcated C2v structure above the lowest energy dimer conformer by 1.29 kcal/mol

 

1. G. S. Tschumper, M. L. Leininger, B. C. Hoffman, E. F. Valeev, H. F. Schaefer III, M. Quack, J. Chem. Phys. 116, 690 (2002)