What is crystal field theory?
1 Answer
Crystal field theory (CFT) describes the nature of the metal orbital splitting in the presence of surrounding ligands that form a certain molecular geometry.
The basic facets of CFT are:
- Ligands come in, and their important orbitals interact with the metal
#d# orbitals. - Electrons repel electrons to destabilize certain metal
#d# orbitals. In an octahedral field, these are known as the#e_g^"*"# orbitals. - Electrons are attracted to the electropositive metal center to stabilize certain metal
#d# orbitals. In an octahedral field, these are known as the#t_(2g)# orbitals.
For undergraduate inorganic chemistry courses, it is easiest to focus on octahedral and tetrahedral complexes involving
More specifically...
We have a crystal field splitting energy
#uarrE" "color(white)({(" "" "color(black)(ul(color(white)(uarr darr))" "ul(color(white)(uarr darr))" "e_g^"*")),(" "),(color(black)(Delta_o)),(" "),(" "color(black)(ul(color(white)(uarr darr))" "ul(color(white)(uarr darr))" "ul(color(white)(uarr darr))" "t_(2g))):})#
We have a crystal field splitting energy
#uarrE" "color(white)({(" "color(black)(ul(color(white)(uarr darr))" "ul(color(white)(uarr darr))" "ul(color(white)(uarr darr))" "t_2)),(color(black)(Delta_t = 4/9Delta_o)),(" "" "color(black)(ul(color(white)(uarr darr))" "ul(color(white)(uarr darr))" "e)):})#
And the filling of these orbitals depends on whether the ligands are strong-field ligands, weak-field ligands, or in between.
That is given by the spectrochemical series:
#"O"_2^(2-) < "I"^(-)< "Br"^(-) < "S"^(2-) < "SCN"^(-) "(S–bonded)"# #< "Cl"^(-)# #< "N"^(3-)# #< "F"^(-)# #< "NCO"^(-)# #< "OH"^(-)# #< "C"_2"O"_4^(2-)# #~~# #"H"_2"O"# #< "NCS"^(-) "(N-bonded)"# #< "CH"_3"CN"# #< "py" ("pyridine")# #< "NH"_3# #< "en" ("ethylenediamine")# #< "bipy" ("2,2'-bipyridine")# #< "phen" ("1,10-phenanthroline")# #< "NO"_2^(-)# #< "PPh"_3# #< "CN"^(-)# #< "CO"#
Stronger-field ligands promote low-spin complexes, and vice versa (tetrahedral complexes are usually high-spin). See here for more info.