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6: Molecular Orbital Theory

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    553684

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    • 6.1: Overview of Colors from Transition Metal Ions
      The color for a coordination complex can be predicted using the Crystal Field Theory (CFT). Knowing the color can have a number of useful applications, such as the creation of pigments for dyes in the textile industry. The tendency for coordination complexes to display such a wide array of colors is merely coincidental; their absorption energies happen to fall within range of the visible light spectrum.
    • 6.2: Symmetry and Symmetry Operations
      This page explores the critical role of symmetry in chemistry, particularly via group theory, which aids in classifying molecular structures and predicting properties. Key concepts include symmetry elements and operations such as identity, rotation, and reflection. It elaborates on mirror planes and improper rotational symmetry through examples like BH3, H2O, PF5, and CH4, highlighting distinctions and properties of various mirror and rotation-reflection operations.
    • 6.3: Molecule Shapes (Point Groups)
      This page covers various symmetry point groups in molecular chemistry, focusing on low (C1, Cs, Ci) and high (Td, T, Oh, Ih) symmetry groups, detailing their unique symmetry elements and operations. It emphasizes operations in octahedral and icosahedral shapes, introduces cyclic (Cn) and pyramidal (Cnv) groups, and discusses classification methods for determining point groups based on symmetry elements.
    • 6.4: Point Group Assignment
      This page provides an overview of point groups, focusing on symmetry operations that maintain molecule conformations. It presents a systematic method for classifying molecules into specific point groups by identifying symmetry elements like rotation axes and mirror planes. The page differentiates between low and high symmetry point groups, discussing D, C, and S sets, along with their characteristics and examples, particularly based on perpendicular C2 axes and mirror planes.
    • 6.5: Overview of Classifying Bonding Orbitals in a Molecule
      This page details the creation of molecular orbital diagrams for polyatomic molecules through symmetry adapted linear combinations (SALCs). It outlines the steps involved, including determining the molecule's point group, identifying valence orbitals, generating reducible representations, and converting them into irreducible representations. Additionally, it covers sketching SALC shapes and drawing MO diagrams, highlighting the critical role of symmetry and nodal planes in energy levels.
    • 6.6: MO Diagram Construction of CO2
      This page explains the construction of Symmetrized Atomic Linear Combinations (SALCs) and molecular orbital diagrams for carbon dioxide (CO₂), a linear molecule with relevant symmetry properties identified through the \(D_{\infty h}\) and \(D_{2h}\) point groups. It details the process of counting valence orbitals, deriving irreducible representations, and sketching corresponding SALCs.
    • 6.7: MO Diagram Construction of H2O
      This page covers the creation of molecular orbital diagrams for carbon dioxide (CO₂) through the use of Symmetry Adapted Linear Combinations (SALCs) and atomic orbitals (AOs). It emphasizes the antisymmetric nature of certain SALCs related to orbital symmetries within the \(D_{\infty h}\) point group.
    • 6.8: MO Diagram Construction of NH3
      This page covers the construction of symmetry-adapted linear combinations (SALCs) and molecular orbital diagrams for ammonia (\(\ce{NH3}\). It details the \(C_{3v}\) point group associated with ammonia's trigonal pyramidal shape and discusses the derivation of SALCs using the projection operator method, yielding irreducible representations \(A_1\) and \(E\).
    • 6.9: MO Construction of BF3
      BF₃ is more complex than previous examples because it is the first case in which there are multiple types of valence orbitals on the pendant atoms. BF₃ possesses s and p orbitals on both the central atom and all of the pendant atoms. We can follow the same steps that we have previously to derive other molecular orbital diagrams; however, there is one important difference: we will treat each type of pendant orbital as an individual set of SALCs.
    • 6.10: Lewis Acid-Base Dative Bond and MO Diagrams
      BF₃ is more complex than previous examples because it is the first case in which there are multiple types of valence orbitals on the pendant atoms. BF₃ possesses s and p orbitals on both the central atom and all of the pendant atoms. We can follow the same steps that we have previously to derive other molecular orbital diagrams; however, there is one important difference: we will treat each type of pendant orbital as an individual set of SALCs.
    • 6.11: MO Diagram for bonding in [M(NH3)6]n+
      This page of the textbook covers Ligand Field Theory in coordination chemistry, focusing on metal d-orbital and ligand orbital interactions that lead to orbital splitting in octahedral complexes. It explains the significance of d-orbital energy levels on electron configurations, leading to high-spin and low-spin states.
    • 6.12: MO Diagram for bonding in [M(H2O)6]n+
      Ligand field theory is an extension of crystal field theory which includes orbital overlap between ligand orbitals and the metal d orbitals. It allows us to explain the differences between strong field and weak field ligands.
    • 6.13: Spectrochemical Series for Ligands
      Ligand field theory is an extension of crystal field theory which includes orbital overlap between ligand orbitals and the metal d orbitals. It allows us to explain the differences between strong field and weak field ligands.
    • 6.14: Spectrochemical Series for Metal ions
      This page explains how the magnitude of Δo in octahedral complexes affects whether they are high spin or low spin, influencing their magnetic properties and reactivity. Factors such as metal ion charge, principal quantum number, and ligand type affect Δo. Higher charges and larger orbitals lead to stronger metal-ligand bonds and greater orbital splitting, resulting in low-spin complexes, particularly in second and third row transition metals.

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