Supplementary Information
Dissecting molecular descriptors into atomic contributions
in density functional reactivity theory
Chunying Rong,1 Tian Lu,2 and Shubin Liu 1,3*
1
Key Laboratory of Chemical Biology and Traditional Chinese Medicine Research
(Ministry of Education of China) and Key Laboratory of Resource Fine-Processing and Advanced Materials of
Hunan Province, College of Chemistry and Chemical Engineering,
Hunan Normal University, Changsha Hunan 410081, China
2
School of Chemical and Biological Engineering, University of Science and Technology Beijing, Beijing, China
3
Research Computing Center, University of North Carolina,
Chapel Hill, North Carolina 27599-3420, U.S.A.
1. Local distributions of a few quantities for ethylene
Figure S1. Local distributions of (a) Shannon entropy, (b) Fisher information, (c) Laplacian of electron
density, and (d) the alternative Fisher information (from Eq. (4)) for the ethylene molecule.
2. Figures S2 and S3 (see SI) are results for the H-O-H bending of the water molecule, where we
displayed profiles of the molecular and atomic values for Fisher information and Shannon entropy
(Fig. S2), plus the strong linear correlations for these quantities (Fig. S3). As the angle is bended from
50 to 180, molecular and atomic values of Fisher information keep decreasing (Fig. S2a), with the
hydrogen values fall off in a rather slow pace. For the Shannon entropy, the same pattern is seen for
the molecular value and for the hydrogen atomic value, but for oxygen, its atomic Shannon entropy
keeps increasing as the bond angles increases from 50 to 180. Again, we can understand this result
from the viewpoint of what Shannon entropy measures, i.e., the spatial delocalization. As the angle
enlarges, there is more space for oxygen atom to delocalize its electron distribution, leading to the
increase of the entropy. In Fig. S3, strong linear correlations from atomic values of these two
quantities with the correlation coefficient larger than 0.90 are displayed. They are atomic values
between H and O atoms of Shannon entropy (Fig. S3a) and Fisher information (Fig. S3d), atomic
values of Shannon entropy and Fisher information between hydrogen and oxygen atoms (Figs. S3b
and S3c). No strong linear correlation was found at the molecular level nevertheless.
Figure S2. Molecular and atomic profiles of (a) Fisher information and (b) Shannon entropy for the water
molecule (black), oxygen atom (red) and hydrogen atom (green) in water molecule as a function of the
H-O-H angle changed from 50 to 180.
3. Strong linear correlations among atomic contributions of Shannon entropy and Fisher information
obtained from water molecule
Figure S3. Strong linear correlations among atomic contributions of Shannon entropy and Fisher
information obtained from water molecule when the H-O-H angle is rotated from 50 to 180.
4. Strong linear correlations among molecular and atomic values of Shannon entropy and Fisher
information obtained from the ethane molecule
Figure S4. Strong linear correlations among molecular and atomic values of Shannon entropy and Fisher
information obtained from the ethane molecule as the H-C-C-H dihedral angle is rotated from 0 to
360.