_P.-Powell-auth.-Principles-of-Organometallic-Chemistry-Springer-Netherlands-1988

Organometallic compounds of the transition elements
The allylligand possesses no rotation symmetry axis coincident with the z-axis.
While the description here is therefore only approximate, it gives a useful pictorial
representation.
(a) BONDING IN BIS(BENZENE)CHROMIUM. In this section, the symmetry
arguments outlined above are developed further for the complex
bis(benzene )chromium. This molecule has a sandwich structure in which the
rings adopt an eclipsed conformation. The vertical six-fold rotation z-axis (C 6 ), six
vertical planes of symmetry (aJ each of which includes a C 2 axis, and the
horizontal plane (ah) characterize the point group as D 6 h. In addition to the
symmetry elements mentioned, attention is drawn to a centre of symmetry (i),
situated at the chromium atom. The twelve C(2pz) orbitals. six on each ring,
transform according to a 1 g + a 2u + e 1 g + e 10 + e 2g + e 2u + b 2g + b 10 • Reference to
the character table ofD 6 h reveals that the metal orbitals transform as follows: a­
orbitals, d,z, s (a 1 g), Pz (a 2 u); n-orbitals, dzx, dyz (e 1 g), Px• Py (e 10 ); <5-orbitals, dxz-yz, dxy
( e 2 g). The symbols g and u refer to the parity on inversion through the metal atom.
s- and d-orbitals have even (gerade) and p-orbitals odd (ungerade) parity. The
ligand m.o.s on the two rings can be combined either to form sets of even a 1 g (a),
e 1 g (n), e 2 g (<5) and b 2 g (non-bonding) or odd a 1 u (a), e 1 u (n), e 2 u and b 1 u (nonbonding)
parities. The interactions between the metal and ligand orbitals which
are permitted on symmetry grounds are illustrated in Fig. 6.9.
The next step is to construct a qualitative molecular orbital energy level diagram
(Fig. 6.10). It must be stressed that this approach is qualitative; molecular orbital
calculations might be expected to yield a different order for the molecular orbitals,
this relative order varying depending on the assumptions made in the method of
calculation chosen. Calculations of good quality would also not neglect the
carbon s, Px and Py orbitals and the hydrogen 1s orbitals which are involved
mainly in holding together the skeletons of the benzene rings.
The metal d-orbitals are split, dzx and dyz ( e 1 g) becoming antibonding through n­
interaction with filled n 2 ligand orbitals, and dxz-yz, d,Y (e 2 g) somewhat bonding
through <5-interaction with empty n 3 ligand orbitals. dzz should be weakly
antibonding through overlap with the low-lying filled a 1 g (a) combination of n 1
ligand orbitals. There will be some mixing with the high lying metal 4s orbital.
which is also of a 1 g symmetry, however, so that the metal-centred orbital
(approximately dzz) seems to be essentially non-bonding. The 18 valence
electrons, six from chromium and six from each of the benzene rings, fill all the
bonding and non-bonding (i.e. a 1 g) orbitals. Bis(benzene)chromium is readily
oxidized in solution to an air-stable 17 -electron cation (C 6 H 6 ) 2 Cr+. The ease of
removal of one electron suggests that the highest occupied m.o. is fairly high
lying.
UV -photoelectron spectroscopy provides a means of studying the energy levels
of molecules experimentally. Simple interpretation of PE spectra relies on
Koopmans' theorem which states that the same order of molecular orbitals
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