Chemistry Reference
In-Depth Information
0.25
0.2
0.15
0.1
0.05
0
0
0.2
0.4
0.8
1
0.6
fraction of trans H-bonds
Figure 18.
Relative DFT energy of H-bond isomers of a 16-water (
•
) and 32-water (
◦
) unit
cell of ice VII plotted against fraction of trans bonds for each isomer. The lowest and highest energy
isomers for both unit cells contain no H-bonds in the trans configuration thus indicating that features
of the H-bond topologies other than cis-trans H-bonds are important if physical properties are to be
correctly described.
shown in Fig. 17b. However, there is a small systematic discrepancy in which the
invariant prediction overestimates the energy differences in the 32-water cell. This
discrepancy is actually not a consequence of requiring more invariant parameters
for the larger cell, but instead arises because of the lack of
k
-point sampling in the
electronic structure calculations for the smaller cell.
A fit of the DFT energies incorporating invariants whose generating bond pairs
were farther apart than possible in the smaller 16-water unit cell (Fig. 17c) yielded
a fit just as good in quality as that obtained from only using invariants whose
generating bond pairs existed in the smaller cell (Fig. 17d). We conclude that
the energy of the H-bond isomers is accurately described by invariants whose
generating bond pair contain vertices that are nearest neighbors. Energy plotted as
a function of the percent of trans H-bonds is shown in Fig. 18. For both unit cells,
the ground-state and highest energy configurations contain no bonds that are trans.
If the relative number of trans bonds was the only feature of the H-bond topology
used to describe the energetics, those configurations would then be degenerate.
Clearly, it is evident that additional features of the H-bond topology, exhibited by
the graph invariants, are necessary to accurately describe the relative energetics of
H-bond isomers of ice.
Using the improved invariant parameters and Eq. (11), we have a Hamiltonian
describing the energy differences due to fluctuating H-bonds in a large simulation
