Page 419 - Academic Press Encyclopedia of Physical Science and Technology 3rd Analytical Chemistry

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Encyclopedia of Physical Science and Technology EN012C-568 July 26, 2001 15:32

Photoelectron Spectroscopy 69

should be equal to the number of occupied orbitals. There- ally less than 10% (see Table III). Therefore, KT is a close
fore, all the prominent bands in the valence region of free approximation.
molecules and all main lines in the inner shell region of However, one point always must be kept in mind if KT is
free molecules and solids are usually assignable in the applied: orbital energies are quantities solely related to the
single-particle picture. Basically, this type of interpreta- initial state of the photoemission process. The application
tion also holds for photoemission from solids. However, in of KT is equivalent to neglecting any influence of the final
this case some special aspects must be considered, which state on the binding energies. Obviously, this cannot be
will be discussed in Section IV.B. true. To take final state effects into account, we must go
Additional structures in PE spectra can result from mul- beyond the FOA. We return to this point in the following
tiplet splitting (Fig. 10b shows an example), which is dis- section.
cussed in more detail in Section II.H, plasmon losses, and In the application of PES to the study of molecular
even the X-ray source itself. Plasmon losses, which are electronic structure, KT is seldom used in the form of
of little analytical use, are observed in the PE and Auger Eq. (7). In most cases, a direct comparison of calculated
spectra of clean metal surfaces, as shown in Fig. 10c for ε i and measured E B (i) is not the main objective. Often it is
a clean aluminum surface. They result from collective os- more interesting to investigate how a certain ε and corre-
cillations in the conduction band excited by the outgoing spondingly a certain E B vary with alterations in chemical
electron which thereby suffers a discrete energy loss. The constitution. In this case we use a “weaker” form of KT:
plasmon frequency and multiples thereof are observed as
a characteristic series of peaks on the high binding energy E B (i) = ε i (8)
side of the main core line. where we connect binding energy shifts ( E B ) with or-
The radiation source also gives rise to weak additional bital energy shifts. In considering these chemical shifts,
photoelectron signals, as, for example, both the AlK α and we do not completely neglect final state effects. We only
the MgK α lines have satellites some 10 eV below the assume that they are approximately constant within a cer-
main line with around 10% of its intensity. In addition to tain class of compounds. The chemically appealing fea-
these satellites, an oxidized or damaged anode (CuK α )as ture of this approach lies in the great variety of models
well as cross-talk from the complementary side of a badly available to estimate orbital energy shifts. For example,
aligned twin anode can lead to the appearance of unwanted all the models that have been developed to describe the
radiation. influence of different substituents on physical properties
and chemical reactivities of molecules can be applied, and
D. Koopmans’ Theorem frequently a more direct proof of a given model is possi-
ble with PES. Examples of this type of application are
The correspondence between orbital picture and PE spec- discussed in Sections IV.A and IV.C.
trum goes even further than the one-to-one correspon- Of special importance is a model which connects core
dence between main lines and occupied orbitals. In the electron binding energy shifts to atomic charges. Chemists
FOA, the binding energies relative to the vacuum level are usuallyattributepartialchargesq A tothedifferentatomsof
directly connected with the orbital energy of the occupied a molecule, even though this concept is problematic from
orbitals a strictly theoretical point of view. In the “point charge
approximation,” the energy ε i (A) of a core orbital at atom
E B (i) =−ε i (7)
A can be expressed in terms of partial charges by
This relation was derived by T. Koopmans in 1932 and is
now known as Koopmans’ theorem (KT). It is the ba- ε i (A) = k(i, A)q A + V (q B ) + k 0 (i, A) (9)
sis of most applications of PES in electronic structure
where q A is the charge at the considered atom, V (q B )
elucidation. If KT were strictly valid, we could experi-
the “off-atom potential” created by the charges at all other
mentally observe orbital or single-particle energies, which
atoms, and k 0 and k are parameters specific for atom A and
in reality exist only in the theoretical framework of the
orbital i. Within the limits of applicability of Eq. (8), the
independent-particle model. It must be clearly understood
model allows one to estimate changes in atomic charges
that orbital energies are not observable in the sense of
from measured shifts of core electron binding energies.
quantum mechanics. However, they can be calculated by
a variety of different methods, and these calculations can
be performed with a high degree of accuracy for small
E. Final State Effects
and medium size molecules. A comparison of orbital ener-
gies from such calculations with experimentally observed In the preceding section we saw that the most prominent
binding energies shows that the deviation from KT is usu- structures in PE spectra can be explained adequately in the