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- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/18%3A_Partition_Functions_and_Ideal_Gases/18.10%3A_Ortho_and_Para_HydrogenThis page explores hydrogen's ortho and para forms, highlighting their impact on rotational states and thermodynamics, and detailing the temperature-dependent ortho-para ratio and its behavior during ...This page explores hydrogen's ortho and para forms, highlighting their impact on rotational states and thermodynamics, and detailing the temperature-dependent ortho-para ratio and its behavior during cooling. It notes the slow interconversion rates without catalysts and examines oxygen molecules' contribution to the rotational partition function, emphasizing statistical thermodynamics principles.
- https://chem.libretexts.org/Courses/East_Tennessee_State_University/CHEM_3110%3A_Descriptive_Inorganic_Chemistry/04%3A_Molecular_Symmetry_and_Point_Groups/4.02%3A_Point_GroupsIn group theory, molecules or other objects can be organized into point groups based on the type and number of symmetry operations they possess. Every molecule in a point group will have all of the sa...In group theory, molecules or other objects can be organized into point groups based on the type and number of symmetry operations they possess. Every molecule in a point group will have all of the same symmetry operations as any other molecule in that same point group.
- https://chem.libretexts.org/Courses/East_Tennessee_State_University/CHEM_4110%3A_Advanced_Inorganic_Chemistry/14%3A_Appendix/14.01%3A_Advanced_Group_TheoryThe theory of symmetry groups is a powerful tool for the prediction of physical properties of molecules and crystals. It is, for example, possible to determine whether a molecule can have a dipole mom...The theory of symmetry groups is a powerful tool for the prediction of physical properties of molecules and crystals. It is, for example, possible to determine whether a molecule can have a dipole moment. Many important predictions of spectroscopic experiments (optical, IR or Raman) can be made purely by group theoretical considerations.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/12%3A_Group_Theory_-_The_Exploitation_of_SymmetryThis page highlights the importance of symmetry in chemistry, emphasizing its role in simplifying molecular analysis using group theory. It explains how understanding symmetry operations aids in predi...This page highlights the importance of symmetry in chemistry, emphasizing its role in simplifying molecular analysis using group theory. It explains how understanding symmetry operations aids in predicting molecular behavior and spectral transitions, while group theory facilitates numerical simplifications and vibrational analyses.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/12%3A_Group_Theory_-_The_Exploitation_of_Symmetry/12.T%3A_Character_TablesThis page discusses classification groups in symmetry, including Nonaxial Groups (e.g., \(C_1\), \(C_s\), \(C_i\)) and Cyclic \(C_n\) Groups (e.g., \(C_2\) to \(C_7\)). It outlines molecular point gro...This page discusses classification groups in symmetry, including Nonaxial Groups (e.g., \(C_1\), \(C_s\), \(C_i\)) and Cyclic \(C_n\) Groups (e.g., \(C_2\) to \(C_7\)). It outlines molecular point groups \(C_{2h}\), \(C_{3h}\), \(D_{nh}\), and antiprismatic \(D_{nd}\) groups, detailing symmetry operations, character tables, and irreducible representations (e.g., \(A_g\), \(B_g\)).
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/32%3A_Math_Chapters/32.04%3A_Spherical_CoordinatesThis page explores various coordinate systems like Cartesian, polar, and spherical, focusing on their applications in mathematics and physics, as well as their significance for different problems. It ...This page explores various coordinate systems like Cartesian, polar, and spherical, focusing on their applications in mathematics and physics, as well as their significance for different problems. It highlights the necessity of adapting integration methods, particularly in quantum mechanics for normalizing wave functions using double and triple integrals.
- https://chem.libretexts.org/Bookshelves/Inorganic_Chemistry/Supplemental_Modules_and_Websites_(Inorganic_Chemistry)/Coordination_Chemistry/Structure_and_Nomenclature_of_Coordination_Compounds/Isomers/Optical_Isomers_in_Inorganic_Complexes/Identifying_Planes_of_Symmetry_in_Octahedral_ComplexesThe symmetry of a molecule is determined by the existence of symmetry operations performed with respect to symmetry elements. A symmetry element is a line, a plane or a point in or through an object, ...The symmetry of a molecule is determined by the existence of symmetry operations performed with respect to symmetry elements. A symmetry element is a line, a plane or a point in or through an object, about which a rotation or reflection leaves the object in an orientation indistinguishable from the original. A plane of symmetry and the reflection operation is the coincidence of atoms on one side of the plane with corresponding atoms on the other side, as though reflected in a mirror.
- https://chem.libretexts.org/Courses/CSU_Fullerton/Chem_325%3A_Inorganic_Chemistry_(Cooley)/05%3A_d-Block_Metal_Chemistry-_General_Considerations/5.12%3A_Optical_Isomers_in_Inorganic_Complexes/5.12.02%3A_Identifying_Planes_of_Symmetry_in_Octahedral_ComplexesThe next six planes are harder to identify and can be viewed as rotations of those in Figure 2 by 45°. These planes bisect one angles between ligands, but still have two ligands on the plane (instead ...The next six planes are harder to identify and can be viewed as rotations of those in Figure 2 by 45°. These planes bisect one angles between ligands, but still have two ligands on the plane (instead of four in the planes of Figure 2). The perspective makes it difficulty to resolve, but the atoms behind the plane are lighter colored and the slope of the plane can be identified by the projection through the central \(Cr\) atom.
- https://chem.libretexts.org/Courses/Centre_College/CHE_332%3A_Inorganic_Chemistry/03%3A_Molecular_Symmetry_and_Point_Groups/3.02%3A_Point_GroupsIn group theory, molecules or other objects can be organized into point groups based on the type and number of symmetry operations they possess. Every molecule in a point group will have all of the sa...In group theory, molecules or other objects can be organized into point groups based on the type and number of symmetry operations they possess. Every molecule in a point group will have all of the same symmetry operations as any other molecule in that same point group.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/09%3A_Chemical_Bonding_in_Diatomic_Molecules/9.14%3A_Molecular_Term_Symbols_Describe_Electronic_States_of_MoleculesThis page explains molecular term symbols for diatomic molecules within the Russell-Saunders coupling framework. It details the four components of these symbols—spin multiplicity, azimuthal angular mo...This page explains molecular term symbols for diatomic molecules within the Russell-Saunders coupling framework. It details the four components of these symbols—spin multiplicity, azimuthal angular momentum, total angular momentum, and symmetry—while highlighting differences between homonuclear and heteronuclear diatomics.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/12%3A_Group_Theory_-_The_Exploitation_of_Symmetry/12.08%3A_Using_Symmetry_to_Solve_Secular_DeterminantsThis page explores the conditions for zero integrals using group theory to assess symmetry, establishing that integrals remain invariant under symmetry operations. It examines secular equations relate...This page explores the conditions for zero integrals using group theory to assess symmetry, establishing that integrals remain invariant under symmetry operations. It examines secular equations related to molecular orbital energies and coefficients. Additionally, the text details the construction of molecular orbitals from atomic orbitals, emphasizing the use of symmetry-adapted linear combinations (SALCs) for bonding and antibonding orbitals, specifically in the context of \(NH_3\).
