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- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Symmetry_(Vallance)Group Theory is a branch of the mathematical field of algebra. One important application, the theory of symmetry groups, is a powerful tool for the prediction of physical properties of molecules and c...Group Theory is a branch of the mathematical field of algebra. One important application, 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)/13%3A_Molecular_Spectroscopy/13.14%3A_Group_Theory_Determines_Infrared_ActivityThis page explains how to determine if molecular normal modes are infrared (IR) or Raman active, requiring changes in dipole moment for IR activity and changes in polarizability for Raman activity. It...This page explains how to determine if molecular normal modes are infrared (IR) or Raman active, requiring changes in dipole moment for IR activity and changes in polarizability for Raman activity. It uses water (H2O) as an example to show the application of group theory in identifying active modes. The analysis confirms the vibrational transitions related to different symmetry representations, detailing the IR and Raman active modes along with their energy levels.
- 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_Symmetry/12.06%3A_Character_Tables_Summarize_the_Properties_of_a_Point_GroupThis page discusses matrix representations of point groups and their role in molecular symmetry, including similarity transforms and the formation of character tables. It highlights the invariance of ...This page discusses matrix representations of point groups and their role in molecular symmetry, including similarity transforms and the formation of character tables. It highlights the invariance of characters and includes the character table for the C_{3v} group.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/12%3A_Group_Theory_-_The_Exploitation_of_Symmetry/12.E%3A_Group_Theory_-_The_Exploitation_of_Symmetry_(Exercises)This page covers homework exercises from McQuarrie and Simon's "Physical Chemistry," focusing on symmetry and molecular orbital theory. It addresses wave function normalization, Huckel determinant cal...This page covers homework exercises from McQuarrie and Simon's "Physical Chemistry," focusing on symmetry and molecular orbital theory. It addresses wave function normalization, Huckel determinant calculations, and eigenvalues related to molecular symmetry in groups like C_{2v} and C_{3v}. Character tables for symmetry point groups C_i, T_d, and O_h are discussed, alongside the derivation of symmetry orbitals and irreducible representations.
- 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/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)/12%3A_Group_Theory_-_The_Exploitation_of_Symmetry/12.10%3A_Molecular_Motions_of_a_Molecule_can_be_Represented_by_a_Reducible_ReperesentationThis page explains how to determine the normal vibrational modes of polyatomic molecules, specifically using group theory with H_2O as an example. It covers the 3N Cartesian basis for molecula...This page explains how to determine the normal vibrational modes of polyatomic molecules, specifically using group theory with H_2O as an example. It covers the 3N Cartesian basis for molecular motions, focusing on the 9 elements of H_2O.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/12%3A_Group_Theory_-_The_Exploitation_of_Symmetry/12.04%3A_Symmetry_Operations_as_MatricesThis page discusses how transformation matrices represent symmetry operations within groups, focusing on the C_{2v} point group and its key operations like identity, reflection, and n-fold rotatio...This page discusses how transformation matrices represent symmetry operations within groups, focusing on the C_{2v} point group and its key operations like identity, reflection, and n-fold rotation. It emphasizes that combining two elements must result in another group element, satisfying properties such as associativity and the existence of inverses.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/12%3A_Group_Theory_-_The_Exploitation_of_Symmetry/12.03%3A_Symmetry_Operations_Define_GroupsThis page defines a mathematical group in relation to symmetry operations in chemistry, outlining criteria such as identity, closure, associativity, and reciprocality. It contrasts non-Abelian groups ...This page defines a mathematical group in relation to symmetry operations in chemistry, outlining criteria such as identity, closure, associativity, and reciprocality. It contrasts non-Abelian groups (non-commuting elements) with Abelian groups (commuting elements) and highlights the representation of symmetry operations by matrices for easier calculations.
