132C GUH

Beers Law

T = 100%-Abs

I/I₀= T

A=E[c]l

Highest possible degeneracy

Highest number in E column

Point Groups that are chiral

Chiral = asymmetric

If a molecule does NOT have Sn it is chiral

Point Groups that are polar

If a molecule has a Cn, Cnv, Cs = sigma it is polar

Transition Dipole

⟨ 𝜓𝑓 ∣ 𝜇̂ ∣ 𝜓𝑖 ⟩ = 0 ?

If integrand contains A1 symmetry, ≠ 0

If integrand does NOT contain A1 symmetry, = 0

Electric-dipole selection rule

An electronic transition is electric-dipole allowed if the transition moment integral is nonzero:

⟨ 𝜓𝑓 ∣ ∣ 𝜇̂ ∣ ∣ 𝜓𝑖 ⟩ ≠ 0

Stimulated Absorption

B_fi

Spontaneous Emission

A_if

Stimulated Emission

B_if

Energy of a photon

E = hv

Effect of temp on distribution of population level between initial and final state

at lower T, population will be higher in initial state

Homogeneous broadening

Lorenzian cruve

5.3 cm-1 equation

Natural line width

Spontaneous emission

A_if= 1/𝜏spon

Inhomogeneous broadening

Doppler Broadening —> Gaussian

𝛿𝜈obs equation

Collisional deactivation

Use: 𝜏 = N/z

N = # of collisions to be effective

• ex) every collsion effective, N=1

• every 1/100 collisions effectibe, N=100

z is collision frequency

Then use: 𝛿𝜈≈ 5.3cm-1/(𝜏/ps)

More pressure, less 𝜏, more 𝛿Ecollision where 𝛿Ecollision= hbar/𝜏

Rigid rotor

Bond lengths dont change

Linear rotor

linear molecule

Spherical Rotor

Td or Oh

Symmetric Rotor

n≥3 —> C3, C4, C5, etc

Asymmetric rotor

Not another rotor

Prolate

For symmetric rotor

When hevay atoms are on principle axis

Oblate

For symmetric rotor

When hevay atoms are NOT on principle axis

Reduction Formula

#irrep = 1/hΣX_redX_irrN

Moment of inertia

sum of mass*r² for each mass along axis