Ligand field theory
d-orbitals and f-orbitals as they fall out of the math of the Schrödinger equation
are not in match with the real situation.
Other methods like
- crystal field theory and
- ligand field theory
are used instead.
Contents
How it works
Electron pairing energy ... from electrostatic repulsion due to double-up in an orbital
Smaller orbital => electrons closer together => higher electron pairing energy => high spin more likely
Weak field ligand and/or smaller metal orbital
Octahedral splitting energy < total electron pairing energy
– blocks fill up as one would expect from the LCOAO-energy contribution alone
– electrons do get paired up
=> high spin complex
Strong field ligand and/or bigger metal orbital
Octahedral splitting energy > total electron pairing energy
– block higher in LCOAO-energy contribution gets filled up preliminarily
– electrons don't get paired up
=> high spin complex
Influencing factors:
- oxidation state
- coordination number
- electron configuration
- coordination geometry
spectrochemical series
- For the ligands
- For the metals?
(wiki-TODO: check if there are tables for spectrochemical series)
Details
Metal orbitals:
– Get reducible representation.
– Decompose reducible representation into irreducible representations
(the ones listed in character table for the relevant pointgroup)
– Construct molecular orbital type diagram for the metal complex of given geometry
Lewis basic ligands (lone pairs facing the metal):
– Use projection operator, decompose representation
– factor separate lewis pairs of electrons into symmetries
if there are metal orbitals and ligand orbitals that have the same symmetry => interaction spossible
Linear combination of atomic orbitals (LCOAO):
– Mix in phase and out of phase (bonding and antibonding respectively).
How far to shift? The strength of an interaction is inversly proportionsal to
the seperation in energy between the fragments.
=> Farther apart less shift. Noninteracting remnants blocks stay unshifted (nonbonding orbitals)
– Fill up all the low energy bonding orbitals with the ligand electrons.
(The block in the middle energies is dominated by metal d character.)
– Fill up these mid level energy orbitals.
For d0 ions nothing changes. For d10 all is filled up.
Side-note: filling up non-bonding orbitals does not break the bonds (but influences reactivity).
Interesting it gets for the middle fillup levels d4 to d7 for octahedral coordination.
Side-note:
- Two electrons in HOMO of ligand (lewis base)
- Two holes in LUMO of the metal (lewis acid)
Because its a lewis-acid lewis-base interaction (kinda like an electron deficiency bond)
In the bonding state most of the electron density contribution comes from the ligand little from the metal
- Bonding: big contribution from ligands small contribution from metal
- Antionding: big contribution from the metal small contribution from ligands
Geometries
- octahedral: common
- tetrahedral: less direct ligand approach => less level splitting => tends to be high spin
- planar square: …
- assign symmetry to an orbital … lower case
- assign symmetry to an electronic state … upper case
Frontier atomic orbitals for octahedral coordination:
- _ _ _ _ _ 3d _ 4s _ _ _ 4p … Sc-Zn
- _ _ _ _ _ 4d _ 5s _ _ _ 5p … Y-Cd
- _ _ _ _ _ 5d _ 6s _ _ _ 6p … La-Hg
- _ _ _ _ _ nd _ (n+1)s _ _ _ (n+1)p … generally
lanthanides & actinides: bonding is dominated by electrostatic interactions
f orbitals generally don't spit, don't participate in bonding, stay at about the same energy
Comparison to crystal field theory
Crystal field theory only treats electrostatic point charges and does not take into account covalency of bonds.
Ligand field theory: Combine Crystal field theory with molecular orbital theory
Crystal field theory alone: – relative shifts: center of energy analogous to center of mass – electron pairing energy not taken under consideration?
Related
- Optical effects – see "photonic steampunk" section
- Color emulation – Passive color gemstone display – Active color gemstone display
See: Organometallic gemstone-like compound – Tuning gemstone color:
- either ultra precisely with Kaehler brackets
- or with fast programmable active pressure adjusting actuation
External links
Wikipedia:
