Chemistry   Consider a molecule of ammonia NH3. (a) Choose a suitable principal axis system and plot it with the molecule. (b) What is the approximate symmetry of the molecule? Is there any approximation that must be made to consider this symmetry? (c) What is the Hamiltonian for the rigid rotor of this molecule? Include structural parameters of the molecule.

r=−4sinθ+4cosθ+4θ Which of the following types of symmetry is demonstrated in the equation above based on the three symmetry tests for polar equations?

(A)Write the Hückel Hamiltonian matrix for benzene. (B)The pictures below represent a top view of the molecular orbitals for benzene. They are labeled from A to F, in no order. Place the labels A, B, C, etc., in the boxes according to their energy. SHOW THE NODES. (B)

Identify the irreducible representations to which all five d orbitals of the central Xe atom in XeF4 (D4h) belong. Give reasons to support your answer  ( please answer in detail )

6) Given below are the molecule BH3, its character table, and its molecular orbital diagram. By convention, the z-axis lies along the principal rotation axis: (a) What Mulliken symbol represents the symmetry of the MOs I-V? (b) Which of the given atomic orbitals on boron would match the MOS I-V? (c) Depict the in-phase (bonding) and out-of-phase (anti-bonding) of these MOS. B 2p orbitals B 2s orbitals II H 2s orbitals D₂ A, A₂' A," E" 1 1 2 1 1 2 2C, 3C₂ 0₂ 25, 1 1 1 1 1 -1 1 -1 1 -1 0 1 2 -1 -1 30, 1 1 -1 R₂ -1 0 -1 -1 -1 1 1 0 (x, y) (R., R.) x+y²,2² (x²-y, xy) (xz, yz)

Im confused with this C3 C P C32 Point Group: σh S3

PCl3 belong to C3V point group ? (b)  Write down the totally symmetric representation of the point group of PCl3. (c)  What is a symmetry-adapted linear combination of atomic orbitals? (d)  Construct a linear-combination of 3s(Cl) atomic orbitals, ?1, such that ?1 belongs to the totally symmetric representation of the point group of PCl3.  (e)  Construct a linear-combination of 3p(Cl) atomic orbitals, ?2, such that ?2 belongs to the totally symmetric representation of the point group of PCl3.

The point group for IF5 is

(1) (a) Draw an energy level diagram showing the ground state electronic struc- ture of each of the following diatomics: H₂, N2, O2, F2, and Ne₂. (b) Use the above diagram to predict the bond order of each of these diatomics. (c) Use the same procedure to predict the bond order of C and O

Use as a basis the 2pz orbitals on each atom in BF3 to find the representative of the operation σh. Take z as perpendicular to the molecular plane.