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Lecture 38: Selection Rules The material in this lecture covers the following in Atkins.

Lecture 38: Selection Rules The material in this lecture covers the following in Atkins. 15 Molecular Symmetry 15.5 Vanishing integrals and orbital overlaps (a) The criteria for vanishing integrals

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Lecture 38: Selection Rules The material in this lecture covers the following in Atkins.

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  1. Lecture 38: Selection Rules The material in this lecture covers the following in Atkins. 15 Molecular Symmetry 15.5 Vanishing integrals and orbital overlaps (a) The criteria for vanishing integrals (b) Orbitals with nonzero overlaps (c) Symmetry-adapted linear combinations 15.6 Vanishing integrals and selection rules Lecture on-line Selection Rules (PowerPoint) Selection Rules (PDF) Handouts for this lecture

  2. Symmetry operations in the same class are related to one another by the symmetry operations of the group. Thus, the three mirror planes shown here are related by threefold rotations : C3sv=sv’ and the two rotations shown here are related by reflection in sv. svC3=C3-1

  3. Typical symmetry -adapted linear combinations of orbitals in a C 3v molecule.

  4. Construct a table showing the effect of each operation on each orbital of the original basis To generate the combination of a Specific symmetry species, take Each column in turn and (I) Multiply each member of the Column by the character of the Corresponding operator

  5. (I) Multiply each member of the Column by the character of the Corresponding operator (2) Add and divide by group order

  6. (I) Multiply each member of the Column by the character of the Corresponding operator (2) Add and divide by group order

  7. (I) Multiply each member of the Column by the character of the Corresponding operator (2) Add and divide by group order

  8. Orbitals of the same symmetry species may have non-vanishing overlap. This diagram illustrates the three bonding orbitals that may be constructed from (N2s, H1s) and (N2p, H1s) overlap in a C3v molecule. (a) a1; (b) and (c) the two components of the doubly degenerate e orbitals. (There are also three antibonding orbitals of the same species.)

  9. Construct a table showing the effect of each operation on each orbital of the original basis To generate the combination of a Specific symmetry species, take Each column in turn and (I) Multiply each member of the Column by the character of the Corresponding operator

  10. (I) Multiply each member of the Column by the character of the Corresponding operator (2) Add and divide by group order

  11. (I) Multiply each member of the Column by the character of the Corresponding operator (2) Add and divide by group order

  12. (I) Multiply each member of the Column by the character of the Corresponding operator (2) Add and divide by group order

  13. For Ci x,y,and z do not belong to totally symmetric rep For C1 x,y, and z all belong to totally symmetric rep For Cs x,y, belong to totally symmetric rep

  14. For Cn and Cnv the z components belongs to totally symmetric rep For cnh all components different from totally symmetric rep

  15. For higher symmetries :

  16. The polarizations of the allowed transitions in a C2v molecule. The shading indicates the structure of the orbitals of the specified symmetry species. The perspective view of the molecule makes it look rather like a door-stop; however, from the side, each `door-stop' is in fact an isosceles triangle.

  17. What you should learn from this lecture

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