Homework Problems Section 2 Exercise 1 Determine all symmetry elements and all unique symmetry operations of the following molecules: a) b) c) d) e) bromine tetrafluoride f) Boric acid g) Dinitrogen tetroxide h) i) j) k) l) m) Answer a) b) c) d) e) f) g) h) i) j) k) l) m) Exercise 2 When is a molecule chiral? a) It has no mirror planes b) It is has no inversion center c) It has no principal axis d) It has no rotation reflections (improper rotations) Answer d) It has no rotation reflections (improper rotations) Exercise 3 If a molecule has a principal axis C n , and n additional C 2 axes standing perpendicular to C n then it belongs to a) A dihedral point group b) A rotational point group c) A low symmetry point group d) A high symmetry point group Answer a) A dihedral point group Exercise 4 Which of the following molecules are chiral: a) CH 4 b) CHCl 3 c) HCFClBr d) HOF e) BHFCl Answer c) HCFClBr Exercise 5 Determine the point groups of the molecules at symmetry.otterbein.edu/challenge/index.html until you feel that you can determine point groups effortlessly Section 3 Exercise 1 Can the following matrices be multiplied and if so what is the product matrix? a) b) c) d) Answer a) b) c) d) Exercise 2 Determine the irreducible representations for the following orbitals in the point group D 2h . The z axis is defined as the axis of the principal C 2 axis. C 2 ’ is defined as the axis rotating around y. σ v is defined as the xz plane. Answer Exercise 3 Determine the matrix representations of the symmetry elements of the following point groups: a) D 2 Define principal C 2 axis as the axis running along z. C 2 ’ runs along x. b) C 3 If we define the principal C 3 axis running along the z axis: Answer a) b) Dr. Kai Landskron ( Lehigh University ). If you like this textbook, please consider to make a donation to support the author's research at Lehigh University: Click Here to Donate .