Johnston Flashcards
Spectroscopy involves interaction of ________________
Light with matter
Explain absorption in terms of electron transitions
Light with an energy hv excites the electron from the ground state (ψ’’) to a quantised energy level known as the excited state (ψ’)
What is the fine structure of an electronic structure?
Electronic is broken down into Vibrational
Vibrational is broken down into Rotational
What is the energy change of the electronic fine structure?
2x10^4 - 10^5 cm^-1
wavelength is approximately 500-100nm
UV - Vis
What is the energy change of the vibrational fine structure?
10^2 - 5x10^3 cm^-1
Wavelength is approximately 100μm -2μm
Infrared region
What is the energy change of the rotational fine structure?
3-300 GHz
Wavelength is approximately 10-1mm
Microwave region
Equation linking velocity of light in vacuum (c) with wavelength and frequency
c = νλ
Equation of wavenumber
ν ˜=ν/c = 1 / λ
What is the mass of an electron?
0.910953x10-30 kg
What is planks constant?
6.626x10-34 J s
What is the Boltzmann constant?
1.390x20-23J K-1
What does the hat mean above a letter “^”?
Operator
What is the basic format of the Schoringer equation?
Ĥψ(x)=Eψ(x)
Explain the Born Oppenheimer approximation and when would this approximation be used?
Electrons are much lighter than the nucleus and therefore move much faster. This leads to the assumption that the nucleus is stationary and the electrons move around the nucleus in electronic spectroscopy. This does not stand true for vibrational spectroscopy
Why is the fine structure for translational symmetry not observed?
They are so close in energy the levels turn into a continuum therefore there’s no distinct transitions
What is the name of the simplest MO theory
Linear Combination of Atomic Orbitals
Explain the outcome when you produce two molecular orbitals from atomic orbitals
A bonding and an anti bonding molecular orbital is formed. The bonding orbital will be lower in energy than the anti bonding orbital with the descriptor ψ+ where ψ+= CAφA + CBφB (where A and B are subscripts).
The anti bonding orbital will be higher in energy than the bonding orbital and the atomic orbitals with a descriptor ψ-= CAφA - CBφB (where A and B are subscripts).
How do you label MO’s?
g = symmetrical u = anti-symmetrical
σ = 0 Nodes (analogous of s) π = 1 Node (analogous of p) δ = 2 Nodes (analogous of d)
What is the difference between the bonding and anti-bonding orbitals?
Bonding orbitals:
If R is large there is a large nuclear separation leaving the 2 independent AO’s. Smaller R leads to constructive interference between one another. σg
ψ+ = N+(φA + φB)
Anti-bonding orbitals:
If R is large there is a large nuclear separation leaving the 2 independent AO’s. Smaller R leads to destructive interference between one another. σu*
ψ- = N-(φA - φB)
What is observed on a MO diagram when there is a small 2s-2p energy gap?
E(3θg) > E (1πu)
What are the 4 required symbols to find when calculating the term symbols of a diatomic molecule?
Orbital angular momentum Λ
Spin angular momentum (S) and thus Spin multiplicity = 2S+1
Total Electronic Angular Momentum Ω
Overall symmetry (gg=uu=g vs gu=ug=u)
What are Hunds rules when calculating the ground state term symbol?
1) Maximum multiplicity
2) Max S, Min Λ
3) >1/2 filled = max Ω
<1/2 filled = min Ω
What happens to the energy of molecular orbitals when there is small 2s-2p mixing?
mixing and E(5θ) > E (1π)
What happens to the energy of molecular orbitals when there is large 2s-2p mixing?
mixing and E (1π) > E(5θ)
What is the Pauli Exclusion Principle?
No 2 electrons can have the same 4 quantum numbers
For heteronuclear diatomics of A2 symmetry, what point group is applied? What affect does this have on the term symbol?
C∞v
The two π electrons will have π symmetry as such:
πxπ = ∑+ + [∑-] + Δ where [] shows the triplet term
For homonuclear diatomics of A2 symmetry, what point group is applied? What affect does this have on the term symbol?
D∞h
Electron in πg/πu* has πg/πu symmetry as such πxπ = ∑+ + [∑-] + Δ
all combinations of S and Λ are allowed
When writing the electronic configuration of a diatomic molecule, how does the makeup of the molecule affect the numbers within the configuration? eg 1,1,2,2,3,3 vs 1,2,3,4,5,6
staggered if the diatomic is the same atom eg O2 eg 11,22,33,44
continuous if diatomic is different eg CO
Energy of orbitals for a large atomic gap (hormo and hetero)
HOMONUCLEAR 1θ <1π. EG O2, F2
HETERNUCLEAR 5θ >1π. EG CO
Energy of orbitals for a small atomic gap (homo and hetero)
HOMONUCLEAR 1π < 1θ. EG C2, B2
HETERNUCLEAR 1π > 5θ. EG NF
How do you calculate intermolecular separation from ωe and Be?
Be = h/8π^2 I*c I = μRe^2
Describe Valence excited states
The excitation of an electron within the degenerate set of MO’s
When a molecule is excited, how is Re (eqbm bond length) and ωe (vib wavenumber) effected?
Stays pretty constant constant
What is the Rydberg excited state?
An atom/molecule that is electronically excited with energy following the Rydbergg
What is the Rydberg formula?
E(n) = -R/(n-d1)2
Where R = Rydberg constant
n = Principle quantum number
d1 = quantum defect
What are the selection rules for molecular excitation?
1) Orbital Angular Momentum ΔΛ = 0 or +/- 1
2) Spin: ΔS = 0
3) Total angular momentum: ΔΩ = 0, +/- 1
4) Laporte (g/u symmetry): u g
5) symmetry -> ∑+ –> ∑+ and ∑- –> ∑-
Intensity of an electronic transition moment:
Proportional to the Rel^2
Why must ΔS = 0 ?
A photon does not contain any spin and therefore results in no change in the total spin
What is the Beer-Lambert law?
Absorbance = ε.C.L where ε is the molar absorption coefficient, C is concentration and L = length of sample
Why are forbidden transitions seen?
spin orbit coupling
What is the term symbol for a closed shell?
1∑g where S=0 ALWAYS
What is the rules for applying +/- with the term symbols for ∑ values
Completely filled orbital = +
Partially filled θ orbital = +
Partially filled π orbital = -
What is the potential energy of a harmonic oscillator?
V(x) = 1/2 k x^2 where x = R-Re
How do you calculate the harmonic wavenumber?
ωe = (1/2πc)*(sqrt(k/μ)
How do you calculate the harmonic frequency?
v = 1/2π*(sqrt(k/μ)
What is the Franck Condon Principle?
The relative absorption and emission intensities of v’ and v’’ peaks are partially dependant on the degree of overlap of the wave function.
Where I(v’,v’’) = [integral Ψ’v(v’)*Ψ’‘(v”) dt]^2
When v’max = large, band width is broad
when v’ max = small, band width is narrow
Describe a band head and determine the two types?
an abrupt edge of a rotational spectroscopic band in a molecular electronic spectrum. A band head is observed when dṽ/dJ = 0
1) Red-degraded band head
2) Blue-degraded band head
Explain red-degraded band heads
Arise from Re’>Re’’ and thus B’<b>λBH = no rotational structure
λ< λBH = intensity of the rotational lines decay</b>
Causes BOND WEAKENING
J head = (3B’ - B’’)/2(B” - B’) </b>
Explain blue-degraded band heads
Arise from Re’>Re’’ and thus B’>B” (ΔB > 0)
P BRANCH
λ λBH = intensity of the rotational lines decay
Causes BOND STRENGTHENING
Jhead = (B’ + B”)/2(B’-B”)
Explain bond weakening transitioning
R Branch: J head = (3B’ - B’’)/2(B” - B’)
P Branch: ṽ[P(J)] = ṽ(v’v”) - J(B’ + B”) + J^2 (B’ - B”)
(no change in direction)
Q Branch: Overlaps its P branch
Explain bond strengthening transitioning
Blue degraded
P branch: Jhead = (B’ + B”)/2(B’-B”)
R Branch: ṽ[R(J)] = ṽ(v’v” + 2B’) - J(3B’ + B”) + J^2 (B’ - B”)
Q Branch: Overlaps its P branch
