What is crystal field theory?

1 Answer
Truong-Son N.
Dec 14, 2017

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:

  1. Ligands come in, and their important orbitals interact with the metal #d# orbitals.
  2. Electrons repel electrons to destabilize certain metal #d# orbitals. In an octahedral field, these are known as the #e_g^"*"# orbitals.
  3. 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 #d#-block metals.

More specifically...

We have a crystal field splitting energy #Delta_o# for the splitting of #t_(2g)# and #e_g^"*"# metal orbitals in an octahedral field:

Inorganic Chemistry, Miessler et al., pg. 365

#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 #Delta_t = 4/9Delta_o# for the splitting of #e# and #t_2# metal orbitals in a tetrahedral field:

Inorganic Chemistry, Miessler et al., pg. 381

#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.

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