2.4 Electronic Properties
39
2.4.1 Ionization Potential and Electron Affinity
The ionization potential (I p ) and electron affinity (E A ) of a neutral molecule M are
formally defined by energy difference between the neutral species M and its cationic
species M
+ or anionic species M
− , respectively,
I p = E
M
+
−E(M)
(2.20)
and
E A = −
E
M
−
− E(M)
= E(M) − E
M
−
(2.21)
as illustrated in Fig. 2.34. It is noted that in general the molecular structures of
M, M
+ , and M
− are different as expressed in this figure. Hence E(M
+ ) and E(M
− )
should be calculated for each optimized structures R(M
+ ) and R(M
− ). Note that
E(M
+ ) and E(M) based on R(M
+ ) and R(M) ought to be examined in the same
calculation method and the same basis set for obtaining I p and vice versa for E A .
Positive I p requires energy injection to liberate an electron from M and negative
E A to add an electron to M. Hence positive E A signifies that M is apt to become
an anion in a spontaneous manner. The values I p and E A , respectively, indicate
easiness of electron-donating and accepting abilities, which is closely related to the
oxidation and reduction properties of species M. Experimental data of these quantities
can be collected by electrochemical measurement of the redox potential or electron
detachment spectroscopy. Incidentally, it is not necessary that the starting species M
should be neutral. In this case, M
+ and M
− signify the charge-deviated species by +
1 and −1 from M, respectively.
As simpler ways of estimation of these two properties, one may consider the
vertical process to obtain vertical I p and E A as also illustrated in Fig. 2.34. The vertical
process means that the molecular structure R(M) does not change during the electron
E
R (Nuclear Coordinates)
E
R (Nuclear Coordinates)
E(M)
E(M + )
E(M − )
vert I p
vert E A
E(M)
(a)
(b)
R(M + ) R(M)
R(M)R(M - )
I p
E A
Fig. 2.34 Illustrative representation of estimating a I p and b E A (see text). R(A) stands for the
coordinates of the optimized structure of species A
39
2.4.1 Ionization Potential and Electron Affinity
The ionization potential (I p ) and electron affinity (E A ) of a neutral molecule M are
formally defined by energy difference between the neutral species M and its cationic
species M
+ or anionic species M
− , respectively,
I p = E
M
+
−E(M)
(2.20)
and
E A = −
E
M
−
− E(M)
= E(M) − E
M
−
(2.21)
as illustrated in Fig. 2.34. It is noted that in general the molecular structures of
M, M
+ , and M
− are different as expressed in this figure. Hence E(M
+ ) and E(M
− )
should be calculated for each optimized structures R(M
+ ) and R(M
− ). Note that
E(M
+ ) and E(M) based on R(M
+ ) and R(M) ought to be examined in the same
calculation method and the same basis set for obtaining I p and vice versa for E A .
Positive I p requires energy injection to liberate an electron from M and negative
E A to add an electron to M. Hence positive E A signifies that M is apt to become
an anion in a spontaneous manner. The values I p and E A , respectively, indicate
easiness of electron-donating and accepting abilities, which is closely related to the
oxidation and reduction properties of species M. Experimental data of these quantities
can be collected by electrochemical measurement of the redox potential or electron
detachment spectroscopy. Incidentally, it is not necessary that the starting species M
should be neutral. In this case, M
+ and M
− signify the charge-deviated species by +
1 and −1 from M, respectively.
As simpler ways of estimation of these two properties, one may consider the
vertical process to obtain vertical I p and E A as also illustrated in Fig. 2.34. The vertical
process means that the molecular structure R(M) does not change during the electron
E
R (Nuclear Coordinates)
E
R (Nuclear Coordinates)
E(M)
E(M + )
E(M − )
vert I p
vert E A
E(M)
(a)
(b)
R(M + ) R(M)
R(M)R(M - )
I p
E A
Fig. 2.34 Illustrative representation of estimating a I p and b E A (see text). R(A) stands for the
coordinates of the optimized structure of species A