Symmetry and Bonding

what normal modes are

vibrational normal modes (not translations and rotations)

section which shows raman active (VRS) irreducible representations

where xy, yz, xz, etc.are

section which shows what irreducible representations are IR active

where x, y, z are

reduction formula:

• sum all the symmetry elements at the top (including any integers they have) to fine the 1/n

• multiply the value in the table w/ the reducible value and the coefficient of the symmetry element

• sum all of these

• should only be integers, 1 or 0, otherwise mistake somewhere

Fundamental transition

transition from everything in the ground state to a state where ONE normal mode is excited to the next level (v=0 to v=1)

symmetry element for everything

E, identity

SOs for atoms that can be interconverted

θ = 1/√n (φ₁ ± φ₂)

SOs for orbitals that cant be interconverted with another

θ = φ1 (probably transforms as A1 too)

how to find coefficiens for Huckel approx.

sub x into the matrix, get SEs, set c1 to 1 and solve for ψ and normalisation factor

whats lower in E, α + β or α - β

α+β (because they are both -ve)

which d orbitals map onto each other

z², x²-y² (Eg)
xy, yz, xz (T2g)

shape of HAOs

sp - 2 lobes (like 8)

sp2 - 3 lobes

sp3 - 4 lobes

if a NM is 2E + 2A1, both IR active, how many peaks are there?

4, 1 for each coefficient (2×2)