typical covalent bond. Molecules often don’t have a “real” electron affinity, fre-
quently ejecting an added electron spontaneously (the EA is negative), but for those
with a positive EA a reasonable value might be ca. 2 eV (1,4-benzoquinone,
1.9 eV). The term IE when applied to a molecule normally means theminimum
energy needed to remove an electron to infinity, i.e. to form the radical (for an
originally closed-shell molecule) cation, and the term electron affinity normally
means themaximumenergy released when the molecule accepts an electron to form
the radical anion (for an originally closed-shell molecule). The IE of a “stable”
species, i.e. any molecule or atom that can exist (a relative minimum on the
potential energy surface), is always positive. The EA of a molecule is positive if
the accepted electron is bound, i.e. if it is not spontaneously ejected; if the new
electron is ejected in microseconds or less (is unbound), the molecule has a negative
EA (is a “resonance state” – this has nothing to do with the term resonance as in a
resonance hybrid).
IEs and EAs may beverticaloradiabatic: the energy difference between the
precursor molecule M 1 and the species M 2 formed by removing or adding an
electron gives the vertical value if M 2 is at the same geometry as M 1 , while the
adiabatic value is obtained if M 2 has its own actual, equilibrium geometry. Since
the equilibrium geometry of M 2 is clearly of lower energy than the unrelaxed
geometry corresponding to M 1 , vertical IEs are larger than adiabatic IEs, and
vertical EAs are smaller than adiabatic EAs.ExperimentalIEs and EAs may be
vertical or adiabatic, depending on how fast the ionization process is; see the
discussion by Gross [ 311 ]. Compilations of IEs and EAs sometimes do not state
explicitly whether their listed values are adiabatic or vertical; a welcome exception
is the book by Levin and Lias [ 312 ]. Many IEs and EAs are available on the
worldwide web, e.g. [ 205 a], and a good brief discussion of these, including various
measurement techniques, is to be found in the compilation by Lias et al. [ 205 b]. The
vertical values of IE ought to be of more interest to chemists, since these represent a
more inherent property of the molecule (see Koopmans’ theorem below) than the
adiabatic, the latter being the energy difference between a neutral and a cationafter
its geometric reorganization. In fact, the initial cation may even rearrange to a
species with quite a different structure.
Ionization energies and electron affinities can be calculated simply as the energy
difference between the neutral and the ion. Approximate IEs can be obtained by
applying Koopmans’ (not Koopman’s) theorem [ 313 ], which says that the energy
required to remove an electron from an orbital is the negative of the orbital energy.
Thus the IE of a molecule is approximately the negative of the energy of its HOMO
(the principle does not work as well for ionization of electrons more tightly bound
than those in the HOMO). This makes it simple to obtain approximate IEs for
comparison with photoelectron spectroscopy [ 314 ] results. Unfortunately, the prin-
ciple does not work well for EAs: the EA of a molecule is not reasonably well
approximated as the negative of the LUMO energy. In fact, ab initio calculations
normally give virtual MOs (vacant MOs) positive energies, implying that molecules
will not accept electrons to form anions (i.e. that they have negative EAs), which is
often false. Koopmans’ theorem works because of a cancellation of errors in the IE
5.5 Applications of the Ab initio Method 363