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Alkali metal atoms in the gas phase can form small clusters of atoms, such as M8. One possible shape of an M8 cluster is square anti-prismatic, which is shown below. Use a symmetry analysis to determine the symmetries of the molecular orbitals derived from the symmetry adapted linear combinations of the eight metal ns orbitals (e.g., Lithium with n = 2). (Hint: This is done in exactly the same way as for determining the symmetries of the outer atom s-orbitals of any molecule. You first need to determine the point group, then prepare the reducible representation by moving the s-orbitals through the operations of the group, then reduce it to obtain an answer below, which describes the symmetries of the MOs.)

Alkali metal atoms in the gas phase can form small clusters of atoms, such as M8. One possible shape of an M8 cluster is square anti-prismatic, which is shown below. Use a symmetry analysis to determine the symmetries of the molecular orbitals derived from the symmetry adapted linear combinations of the eight metal ns orbitals (e.g., Lithium with n = 2). (Hint: This is done in exactly the same way as for determining the symmetries of the outer atom s-orbitals of any molecule. You first need to determine the point group, then prepare the reducible representation by moving the s-orbitals through the operations of the group, then reduce it to obtain an answer below, which describes the symmetries of the MOs.)

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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Alkali metal atoms in the gas phase can form small clusters of atoms, such as M8. One possible shape of an M8 cluster is square anti-prismatic, which is shown below. Use a symmetry analysis to determine the symmetries of the molecular orbitals derived from the symmetry adapted linear combinations of the eight metal ns orbitals (e.g., Lithium with n = 2). (Hint: This is done in exactly the same way as for determining the symmetries of the outer atom s-orbitals of any molecule. You first need to determine the point group, then prepare the reducible representation by moving the s-orbitals through the operations of the group, then reduce it to obtain an answer below, which describes the symmetries of the MOs.)
Transcribed Image Text:Alkali metal atoms in the gas phase can form small clusters of atoms, such as M8. One possible shape of an M8 cluster is square anti-prismatic, which is shown below. Use a symmetry analysis to determine the symmetries of the molecular orbitals derived from the symmetry adapted linear combinations of the eight metal ns orbitals (e.g., Lithium with n = 2). (Hint: This is done in exactly the same way as for determining the symmetries of the outer atom s-orbitals of any molecule. You first need to determine the point group, then prepare the reducible representation by moving the s-orbitals through the operations of the group, then reduce it to obtain an answer below, which describes the symmetries of the MOs.)
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