Section 8.3.6: Tetrahedral Complexes
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Transitions in tetrahedral complexes are Laporte-allowed
Tetrahedral metal complexes often have more intense electronic transitions than their octahedral counterparts. This is due to the fact that the \(d-d\) transitions in a tetrahedron are allowed by the Laporte selection rule, while \(d-d\) transitions in an octahedral complex are Laporte-forbidden. Recall that the Laporte selection rule applies to centrosymmetric complexes only. The Laporte rule applies to octahedral complexes but not to tetrahedral complexes because a tetrahedron does not have a center of inversion. Notice that the terms (and orbital labels) in a tetrahedron do not include the \(g\) subscripts that are present under octahedral symmetry (Figure \(\PageIndex{1}\)). The splitting pattern of a tetrahedral complex is exactly opposite to the octahedral case. In the case of a tetrahedron, however, the "\(g\)" subscripts are inappropriate because of the tetrahedron's lack of a center of inversion, and transitions between the terms in a tetrahedron do not violate the Laporte Rule.
Another way to explain this in terms of electron transitions between orbitals is through the orbital mixing required to form a tetrahedral complex. Orbital types (i.e., \(s,p,d\)) must mix to form the moleculare orbitals of a tetrahedral transition metal complex. The mixing of \(s\) and \(p\) orbitals with the \(d\) orbitals allows transitions that are forbidden in the case of pure d-orbitals.
It is also worth noting that \(\Delta_t = \frac{4}{9} \Delta_o\). The smaller \(\Delta\) for transition metals means that the tetrahedral complexes can absorb at a lower energy and longer wavelength relative to an analogous octahedron.
Tanabe-Sugano diagrams for tetrahedral complexes
Due to the opposite splitting pattern, the transitions for a \(d^n\) tetrahedral complex are sufficiently represented by the \(d^{10-n}\) Tanabe-Sugano diagram (just drop the \(g\) subscripts from the diagrams). For example, the electronic spectrum of a \(d^8\) tetrahedral complex (e.g., \(\ce{[Ni(H2O)6]^2+}\)) can be interpreted using the \(d^2\) Tanabe-Sugano diagram.