5_04_f08_ps1 - representation (Hint: The eigenvectors are...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
MIT OpenCourseWare http://ocw.mit.edu 5.04 Principles of Inorganic Chemistry II Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Chemistry5 .04(F08) Problem Set 1 Due Friday, 19 September 1. Determine the general matrix rep for a ± v at angle ² from the xz plane on a point (x 1 ,y 1 ,z 1 )at angle ³ from the xz plane. Provide matrix reps for the v in C 3v . 2. Consider the generators C 5 and ± h . a. What group is generated from these two operations? b. Construct a multiplication table. c. Determine the classes in the group. d. Do C 5 and ± h commute? Show both by matrix algebra and by operating on a vector (x 1 ,y 1 ,z 1 ). rd 3. Do the following problems in Cotton (3 edition): A3.2, A3.4, 4.4 and 4.7. 4. Consider the trigonal planar molecule, BF 3 . Use the three fluorine atoms as an arbitrary basis set to describe the matrix representation for each of the operations in the point group (relying on the methods employed above, solve the appropriate eigenvalue problem). v ,C 2 F(1) B F(3) F(2) v ´´,C 2 ´´ v ´,C 2 ´ a. Construct the matrix representations for the operations in the D 3h point group. b. Find the three eigenvalues i and normalize the eigenvectors for the C 3
Background image of page 2
Background image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: representation (Hint: The eigenvectors are orthogonal to each other. For complex eigenvectors, remember that the normalization is defined as A*A where A* is the complex conjugate). 1 c. Construct the similarity transformation matrix from the eigenvectors and determine . For the case where the eigenvectors are complex, take linear combinations to yield 1 eigenvectors in real space. is the adjoint of divided by the determinant. See pg 424 in Cotton for the definition of an adjoint. d. Using and 1 block-diagonalize the matrices in Part (a) and calculate the characters of the irreducible representations for the given basis. e. To what irreducible representations do the F atom basis functions belong? f. Complete the D 3h character table using the algebraic rules governing irreducible representations. Show work....
View Full Document

Page1 / 3

5_04_f08_ps1 - representation (Hint: The eigenvectors are...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online