40
2 Actual Potentials of Theoretical Chemistry: What Can Be Obtained
liberation or attachment in an instantaneous interval. The structural relaxation leading
to R(M
+ ) or R(M
− ) ought to successively occur as a matter of course. Nonetheless,
vertical I p and E A could provide reasonable measures to estimate their actual values
as described in the below. Vertical I p and E A values are further approximated as
vert I p −ε HO
(2.22)
vert E A −ε LU
(2.23)
with using negatives of the HOMO and the LUMO energies. Within the framework of
the ordinary MO method such as HF and DFT, equality in Eq. (2.22) holds (Koopmans
1934; Janak 1978; Perdew et al. 1982). On the other hand, Eq. (2.23) is nothing but
an approximation for both the HF and the DFT methods. In general, one should
include polarization and diffuse functions in the basis set (see Sect. 3.6) especially
for better description of the anionic species since the excessive electron is likely
to be captured in the unoccupied MO (mostly the LUMO) with spatial extension.
Table 2.9 gives the DFT calculation (DFT/B3LYP/6-31+G*) data of I p and E A for
several molecules with the available experimental values (Zhan et al. 2003). Note
that the degree of approximation by Eqs. (2.22) and (2.23) is moderate in the DFT
Table 2.9 Calculated data of ionization potential (I p ), electron affinity (E A ), electronegativity (χ),
and hardness (η), and negatives of the HOMO and the LUMO energies (−ε HO and −ε LU ) in eV
obtained by DFT/B3LYP/6-31+G* with the available experimental data a
Molecule
I p
E A
χ
η b
−ε HO
−ε LU
LiH
8.283
(7.9)
0.408
(0.342)
4.346
(4.121)
3.938
(3.779)
5.322
1.318
LiCl
10.050
(10.01)
0.717
(0.59)
5.383
(5.30)
4.667
(4.71)
6.887
1.690
NaCl
9.320
(9.20)
0.873
(0.73)
5.096
(4.97)
4.224
(4.24)
6.270
2.103
CO 2
13.838
(13.773)
−0.922
(−)
6.458
(−)
7.380
(−)
10.471
0.561
H 2 O
12.700
(12.621)
−2.938
(−)
4.881
(−)
7.819
(−)
8.688
−0.678
Methane
14.176
(14.40)
−1.906
(−)
6.135
(−)
8.041
(−)
10.739
−0.463
Ethylene
10.487
(10.514)
−1.772
(−)
4.357
(−)
6.130
(−)
7.546
0.218
Acetylene
11.276
(11.400)
−1.435
(−)
4.920
(−)
6.356
(−)
8.069
−0.401
Stylene
8.224
(8.43)
−0.433
(−)
3.895
(−)
4.329
(−)
6.316
1.286
a In parentheses are shown the experimental data from Zhang et al. (2003) and the references therein
b Note that in the above reference, values of 2η are actually given
2 Actual Potentials of Theoretical Chemistry: What Can Be Obtained
liberation or attachment in an instantaneous interval. The structural relaxation leading
to R(M
+ ) or R(M
− ) ought to successively occur as a matter of course. Nonetheless,
vertical I p and E A could provide reasonable measures to estimate their actual values
as described in the below. Vertical I p and E A values are further approximated as
vert I p −ε HO
(2.22)
vert E A −ε LU
(2.23)
with using negatives of the HOMO and the LUMO energies. Within the framework of
the ordinary MO method such as HF and DFT, equality in Eq. (2.22) holds (Koopmans
1934; Janak 1978; Perdew et al. 1982). On the other hand, Eq. (2.23) is nothing but
an approximation for both the HF and the DFT methods. In general, one should
include polarization and diffuse functions in the basis set (see Sect. 3.6) especially
for better description of the anionic species since the excessive electron is likely
to be captured in the unoccupied MO (mostly the LUMO) with spatial extension.
Table 2.9 gives the DFT calculation (DFT/B3LYP/6-31+G*) data of I p and E A for
several molecules with the available experimental values (Zhan et al. 2003). Note
that the degree of approximation by Eqs. (2.22) and (2.23) is moderate in the DFT
Table 2.9 Calculated data of ionization potential (I p ), electron affinity (E A ), electronegativity (χ),
and hardness (η), and negatives of the HOMO and the LUMO energies (−ε HO and −ε LU ) in eV
obtained by DFT/B3LYP/6-31+G* with the available experimental data a
Molecule
I p
E A
χ
η b
−ε HO
−ε LU
LiH
8.283
(7.9)
0.408
(0.342)
4.346
(4.121)
3.938
(3.779)
5.322
1.318
LiCl
10.050
(10.01)
0.717
(0.59)
5.383
(5.30)
4.667
(4.71)
6.887
1.690
NaCl
9.320
(9.20)
0.873
(0.73)
5.096
(4.97)
4.224
(4.24)
6.270
2.103
CO 2
13.838
(13.773)
−0.922
(−)
6.458
(−)
7.380
(−)
10.471
0.561
H 2 O
12.700
(12.621)
−2.938
(−)
4.881
(−)
7.819
(−)
8.688
−0.678
Methane
14.176
(14.40)
−1.906
(−)
6.135
(−)
8.041
(−)
10.739
−0.463
Ethylene
10.487
(10.514)
−1.772
(−)
4.357
(−)
6.130
(−)
7.546
0.218
Acetylene
11.276
(11.400)
−1.435
(−)
4.920
(−)
6.356
(−)
8.069
−0.401
Stylene
8.224
(8.43)
−0.433
(−)
3.895
(−)
4.329
(−)
6.316
1.286
a In parentheses are shown the experimental data from Zhang et al. (2003) and the references therein
b Note that in the above reference, values of 2η are actually given