3.3: Valence Bond Theory - Hybridization of Atomic Orbitals
- Page ID
- 444001
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The geometrical shape and the inherent physical/chemical properties seen in molecules can be attributed to atomic and molecular orbitals. Features of molecular structure can be explained by taking into consideration (1) how orbitals interact within a single atom to form hybrid atomic orbitals and (2) how atomic orbitals between different atoms interact, giving rise to molecular orbitals. This module will serve as a reminder of the fundamental concepts of bonding as they relate to molecular structure, as well as an investigation into the complexities of hybridized atomic orbitals.
Orbitals and Hybridization
Valence Bond theory describes the formation of a chemical bond in terms of overlapping between atomic orbitals. Atomic orbitals within the same atom are considered to interact and give rise to hybrid atomic orbitals. Linear combinations of atomic orbitals yield an equal number of hybrid orbitals in the correct orientations to account for observed bond angles. Molecular orbital theory dictates that the number of hybrid orbitals produced must equal the sum of the orbitals that underwent hybridization.
The degree of orbital hybridization is governed by the number of attachments (ligands) found on a central atom, includign lone pairs. Table \(\PageIndex{1}\) provides a summary of orbital hybridization wherein the number of ligands attached to a central molecule corresponds to the electron geometry.
Table \(\PageIndex{1}\): Summary of hybridization
| Steric Number | Hybridization | Electron Geometry | Bond Angles(s) |
|---|---|---|---|
| 2 | sp | linear | 180° |
| 3 | sp2 | trigonal planar | 120° |
| 4 | sp3 | tetrahedral | 109.5° |
| 5 | sp3d | trigonal bipyramidal | 120°, 90° |
| 6 | sp3d2 | octahedral | 90° |
sp Hybridization
Combining an s orbital and a p orbital yields two sp hybrid orbitals pointed in opposite directions. These two sp hybrid orbitals generate a bond angle of 180˚, yielding linear electron geometry.
sp2 Hybridization
The sp2 hybridization is the mixing of one s and two p atomic orbitals. The combination of these atomic orbitals creates three sp2 hybrid orbitals that are equal in energy. The hybrid orbitals are higher in energy than the s orbital but lower in energy than the p orbitals and are closer in energy to the p orbitals because they contain more p orbital charcter. The sp2 hybrid orbitals generates a bond angle of 120˚, yielding trigonal planar electron geometry.
Figure \(\PageIndex{2}\): Three sp2 hybrid orbitals oriented at 120˚ angles. (CC-BY-NC-SA; Wikipedia)sp3 Hybridization
The sp3 hybridization is the mixing of one s orbital and three p orbitals to yield four hybrid sp3 orbitals that are equal in energy. The hybrid orbitals are higher in energy than the s orbital but are lower in energy than the p orbitals and are closer in energy to the p orbitals due to having more p orbital character. The sp3 hybrid orbitals generate a bond angle of 109.5˚, yielding tetrahedral electron geometry.
Figure \(\PageIndex{3}\): Four sp3 hybrid orbitals oriented at 109.5˚ angles. (CC-BY-NC-SA; Wikipedia)Other Hybrid Orbitals
Additional hybrid orbitals can conceptualized by including d orbitals into the mix of orbitals. Incorporation of d orbitals can be used to explain hypervalency and molecular geometries for steric numbers 5 and greater.
Problems
References
- Brown W H, Foote C S, Iverson B L, Anslyn E V. Organic Chemistry, 5th Ed. Brooks/Cole Cengage Learning 2009, 2005.
- Wade, L.G. Organic Chemistry 5th Edition. Pearson Education, INC. New Jersey 2003
- Barrett, Jack Structure and Bonding. Published by The Royal Society of Chemistry Cambridge, UK 2001
- Preparing for Your ACS Examination in Organic Chemistry10 Printing; American Chemical Society Division of Chemical Education Examinations Institute. Washington D.C. 2009
- Zumdahl, Steven S., Zumdahl, Susan A. Chemistry 7th Edition. Houghton Mifflin Company, Boston 2007
- Interactive Molecular Structure & Bonding at www2.chemistry.msu.edu:80/fac...Jml/intro3.htm
Contributors and Attributions
- Carter, James C., B.S. Environmental Toxicology
- Abel Silva, Michael Dai (Yicong)
- Quynh Nhu Nguyen