Discussion  Fr 13.01.2006 at 12:15,  HR30.1

Exercise 1:   

a)   To which irreducible representations belong  s,  p_x, p_y, and p_z oxygen atomic orbitals in H₂O molecule?  Are these representations degenerate, or non-degenerate?

b)  Consider the above problem for the  s,  p_x, p_y, and p_z nitrogen atomic orbitals in NH₃ molecule.

Exercise 2:

           a)  Consider the ammonia molecule. Prove that the combination of  hydrogen atomic orbitals:

                s₁ = Y_a(1s) + Y_b(1s)  + Y_c(1s) 

               belongs  to the totally symmetric A₁ representation. 

            b)  For the same molecule prove that the combinations of  atomic orbitals

                 s₂ = -Y_a(1s) + ¹/₂ [ Y_b(1s)  + Y_c(1s)]     and      s₃ = Y_b(1s)  - Y_c(1s)

                 belong to the doubly degenerate E representation.

Hint:  Show that under operations of the ammonia molecule symmetry group the wavefunctions s₂ and s₃ are transformed as linear combinations of each other.

Exercise 3:

            a)  Consider the wavefunction obtained from two hydrogen atom orbitals in water molecule: 

                   h_s = h_a(1s) + h_b(1s).

                Which representation this wavefunction belongs to? Which oxygen atom atomic orbitals can be used in combination  with  the wavefunction h_s  for building binding and anti-binding molecular orbitals?  

Auf diesem Webangebot gilt die Datenschutzerklärung der TU Braunschweig mit Ausnahme der Abschnitte VI, VII und VIII.