10: Bonding in Polyatomic Molecules
- Page ID
- 11787
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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 concept of a molecular orbital is readily extended to provide a description of the electronic structure of a polyatomic molecule. Indeed molecular orbital theory forms the basis for most of the quantitative theoretical investigations of the properties of large molecules. In general a molecular orbital in a polyatomic system extends over all the nuclei in a molecule and it is essential, if we are to understand and predict the spatial properties of the orbitals, that we make use of the symmetry properties possessed by the nuclear framework.
- 10.1: Hybrid Orbitals Account for Molecular Shape
- This page covers valence bond theory, focusing on hybrid orbitals and their importance in understanding molecular structure and bonding in diatomic and polyatomic molecules. It details the formation of hybrid orbitals (such as \(sp\), \(sp^2\), and \(sp^3\)) in compounds like \(H_2\), \(BeH_2\), and \(CH_4\), while highlighting limitations in predicting geometries for polyatomic molecules.
- 10.2: Hybrid Orbitals in Water
- This page explores Valence Bond Theory in relation to water's bonding and structure, specifically addressing its bond angle and lone pairs. It highlights how combining \(2s\) and \(2p\) orbitals through \(sp^3\) hybridization adjusts the bond angle from the theoretical 90° to the observed 104.45°, influenced by electron repulsion from lone pairs.
- 10.3: BeH₂ is Linear and H₂O is Bent
- This page explains the construction of molecular orbitals in water using a linear triatomic model and a multi-centered approach, focusing on LCAO from hydrogen and atom \(A\). It highlights bonding and antibonding characteristics and the need for hybridization in molecules like BeH2.
- 10.4: Photoelectron Spectroscopy
- This page covers photoelectron spectroscopy (PES) techniques, including X-ray (XPS) and Ultraviolet (UPS) spectroscopy, to analyze molecular orbitals and their kinetic energies. It discusses ionization energy concepts (adiabatic vs. vertical), binding energy, and workfunction, using examples like hydrogen and water to illustrate molecular orbital configurations.
- 10.5: The pi-Electron Approximation of Conjugation
- This page discusses Hückel's theory as a method for approximating molecular orbital theory through the independent treatment of σ and π bonding in conjugated hydrocarbons like ethylene, highlighting sp² hybridization and unhybridized 2p_z orbitals. It covers the calculation of π molecular orbital energies, focusing on Coulomb and resonance integrals to derive energy levels and molecular orbitals.
- 10.6: Butadiene is Stabilized by a Delocalization Energy
- This page explores the application of Hückel theory and molecular orbital theory to 1,3-butadiene, focusing on its molecular structure, electronic properties, and delocalization energy. The analysis shows the stability gained from resonant structures and delocalization, relating to the optimization of valence bond wavefunctions.
- 10.7: Benzene and Aromaticity
- This page explains Hückel theory's application to cyclic conjugated hydrocarbons, focusing on benzene. It covers benzene's structure, resonance, and equal bond lengths, along with Hückel's Rule for cyclic polyenes possessing (4n+2) π electrons that exhibit aromaticity. The page highlights benzene's additional stability of 15 kJ mol-1 from double bond conjugation, supported by hydrogenation heat measurements, comparing its thermodynamic stability to other hydrocarbons.
- 10.E: Bonding in Polyatomic Molecules (Exercises)
- This page covers homework exercises from McQuarrie and Simon's Physical Chemistry, focusing on \(sp^3\) hybrid orbitals' orthonormality, inner product calculations, and bond angles using vector approaches. It includes calculations for hybrid orbitals like \(sp^{3}d^{2}\) and discusses molecular orbital theory for various compounds, particularly their geometrical preferences and electron configurations.