Chemistry Reference
In-Depth Information
For a molecule or atom of N
electrons, the electronic chemical potential μ is
defined as follows (Parr et al. 1978):
µ=
∂
∂
E
N
(3.13)
v(r)
where E is the ground-state energy and v(r) is the composite nuclear potential at the
point r.
Chemical potential is correlated with ionization energy and electron affinity, and
as a result, also with Mulliken electronegativity (Equation [3.7]).
Molecular electronegativity (Iczowski and Margrave 1961; Parr et al. 1978) is
defined as follows:
∂
∂
E
N
µ=
∂
∂
E
N
=−χ
χ=−
=−µ
or
(3.14)
V(r)
V(r)
where μ is the electronic chemical potential.
In DFT, the most important descriptors are hardness and softness indices (Parr
and Yang 1989, Geerlings et al. 1996a, Geerlings et al. 1996b).
3.2.1.1 Hardness Indices
The second derivative of energy with respect to the number of electrons is called
absolute hardness
(η) or
chemical hardness
(Parr and Pearson 1983). For a molecule
with N electrons, the absolute hardness is defined by
2
∂µ
∂
1
2
∂
∂
E
N
1
2N
1
2S
η=
=
=
h(r)dr
=
(3.15)
∫
2
V(r)
V(r)
where μ is the electronic chemical potential, h(r) is called
local hardness
(or
hard-
ness density
), and S is the total softness (defined below). Absolute hardness is the
resistance of the chemical potential to change the number of electrons. The harder a
chemical species, the more difficult it will be to change its oxidation state.
3.2.1.2 Softness Indices
The total softness is defined by
1
2
∂
∂µ
N
1
2
(3.16)
S
=
=
s(r) dr
=
∫
η
V(r)
where η represents the absolute hardness, μ is the electronic chemical potential, and
s(r) is the local softness (or softness density).
Based on molecular orbital energies, especially the frontier orbital energies (Clare
1994; Huang et al. 1996), some main descriptors can be defined and information can
be obtained about reactivity/stability of specific regions of the molecule.
