Chapters
- Page ID
- 281952
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 1.1: Symmetry Elements
- Symmetry elements of the molecule are geometric entities: an imaginary point, axis or plane in space, which symmetry operations: rotation, reflection or inversion, are performed. Their recognition leads to the application of symmetry to molecular properties and can also be used to predict or explain many of a molecule’s chemical properties. Symmetry elements and symmetry operations are two fundamental concepts in group theory.
- 1.4: Representations
- A representation is a set of matrices, each of which corresponds to a symmetry operation and combine in the same way that the symmetry operators in the group combine. Symmetry operators can be presented in matrices, this allows us to understand the relationship between symmetry operators through calculation from matrices. In order to understand representations, knowing matrix notions for symmetry operations is essential.
- 1.6: SALCs and the projection operator technique
- SALCs refers to Symmetry Adapted Linear Combinations, which are generated via use of the projection operator technique. This technique is a mathematical method which outputs a function called a SALC that models the orbitals of the atoms of interest. These SALCs are mathematical representations and therefore bare no physical meaning. They are commonly used in the generation of molecular orbitals.
- 1.12: Normal Modes of Vibration
- Molecular vibrations are one of three kinds of motion, occurs when atoms in a molecule are in periodic motion. Molecular vibrations include constant translational and rotational motion. Translational motion occurs when the whole molecule goes in the same direction while the rotational motion occurs when the molecule spins like a top. Molecule vibrations fall into two main categories of stretching and bending.
- 1.15: Vibrational Spectroscopy of Linear Molecules
- Groups with axial symmetry are also known as continuous groups due to the infinite amount of rotations and reflections that leave the molecule invariant. Due to the sheer number of symmetry operations, determining irreducible representations is not feasible. There is one aspect of group theory that can be taken advantage of and these are the group, subgroup relationships.
- 1.17: Jahn-Teller Distortions
- The Jahn–Teller effect occurs because the unequal occupation of orbitals with identical energies is unfavorable. To avoid these unfavorable electronic configurations, molecules distort (lowering their symmetry) to render these orbitals no longer degenerate. The Jahn–Teller distortion, describes the geometrical distortion of molecules and ions that result from certain electron configurations.
- 1.19: Electron Counting and the 18 Electron Rule
- The 18 Electron Rule is a useful tool to predict the structure and reactivity of organometallic complexes. It describes the tendency of the central metal to achieve the noble gas configuration in its valence shell, and is somewhat analogous to the octet rule in a simplified rationale. Exceptions to this rule exist, depending on the energy and character of atomic and molecular orbitals.
- 1.20: Dative ligands - CO and phosphines
- Dative ligands represent a class of compounds that form dative covalent bonds, otherwise known as coordinate bonds, in which both electrons come from the same atom. In the case of transition metals, a dative ligand can form a coordinate bond with a transition metal. The dative ligand can form a sigma bond (σ) with the metal center and can donate both of its electrons to the metal, contributing to a transition metal complex.
- 1.23: Dissociative Mechanism
- Dissociative substitution mechanism describes one of the common pathways through which a ligand substitution reaction takes place. Found often in octahedral complexes, dissociative mechanisms are distinguished by having an ion X- dissociate from a metal complex, resulting in an intermediate compound with a lower coordination number.