Question

What is the structure of pentavalent coordination compounds using crystal field theory specifically, $Fe{\left( {CO} \right)_5}$ .

Answer 1

The Crystal Field Theory is a paradigm for the bonding relationship between transition metals and ligands. Hans Bethe and VanVleck introduced the crystal field theory. The attraction between the metal cation’s positive charge and the negative charge of the ligand's non-bonding electrons is explained by the Crystal Field Theory.

Complete answer:
Crystal field theory discusses the destruction of degeneracies of electron orbital states, generally $d$ or $f$ orbitals, caused by a static electric field created by a surrounding charge distribution.
The arrangements of pentavalent coordination compounds are trigonal bipyramidal. The $CO$ group is a neutrally charged, heavy field ligand and it forces electron pairing. This produces a $dsp3$ hybrid orbital by the hybridisation of one pair of d electrons from the $3d$ orbital, one pair of $s$ electrons from the $4s$ orbital, and three pairs of $p$ electrons from the $4p$ orbital. This explains the molecule's trigonal bipyramidal structure.
$Fe{\left( {CO} \right)_5}$ has a trigonal bipyramidal configuration with the $Fe$ atom being enclosed by five $CO$ ligands, three of which are equatorial and two of which are axially bound. Each of the $Fe-C-O$ linkages are linear. The Berry mechanism results in a comparatively low rate of interchange between the axial $CO$ and equatorial groups in $Fe{\left( {CO} \right)_5}$ .

Note:
It must be noted that the Crystal Field theory excludes the existence of $p$ bonding. Which is a significant disadvantage since it is present in many complexes. The orbits of the ligands have little significance in the theory. As a result, it cannot justify any properties of ligand orbitals or their interactions with metal orbitals.