Post on 21-Jan-2016
description
Band designation in Chapter 5
Fermi Resonance(2 vib levels)
3N-63N-5 (Linear)
Normal Modes
1 ev = 1.60 X 10-12 erg
= 23 kcal/mole
= 12,000 K
= 8,000 cm-1
= 12,000 Å (1.2 μm)
= 2.4 X 1014 hz
= 12398 Å
= 1239.9 nm
100 cm-1 = 144 K
= 100 μm
= 3000 GHz
Energy Scale (order of magnitude)
Electronic transition E ~ e2/a
e = electronic charge a = Bohr radius
E ~ 10 eV ~ 105 cm-1
Vibrational transition v =
k = “spring constant” ≈ D/a2 D = dissociation energy
D ~ eV a ~ A k ~ 105 dynes cm-1
v ~ 103 cm-1
Rotational transition J = angular momentum
= mωa2 = nh K.E. = mω2a ~
E ~ 10 cm-1
• Thermal energy kT ~ mv2 (1 K ≈ 0.7 cm-1)
T = 300 K E ≈ 200 cm-1∴ Energy hierarchyElectronic > Vibrational > Thermal > Rotation
H = H1+ H2 (t)
(3.1)
(stationary states)
(3.9)
(3.10)
Rotational transitionVibrational transition
ro-vibronic transition (electronic)
SPECTROSCOPY OVERVIEW
upper state denoted by single apostrophe lower “ “ “ double “
v’ J’
v’’ J’’
ELECTRONIC SPECTROSCOPY
(visible, ultraviolet)
Born - Oppenheimer approximation
Motion of nuclei show pared to motion of electrons
∴ can separate Hamiltonian into nuclear and electronic terms
Calculate electronic potential surface as a function of internuclear coordinate
Qualitatively, different electronic states have different electron cloud geometries electric dipole allowed transitions
State designations
Linear molecules g spin multiplicity = 25 + 1
S = ∑si = 0 g=1 singlet
total electronic orbital angular momentum ½ 2 doublet
0 ∑ state 1 3 triplet
1 π
2 Δ
Nonlinear molecules
Z = species of symmetry point group to which molecule belongs
Different electron orbital configurations may behave differently with respect to symmetry operations of point group
Individual electronic states characterized by another letter
X – ground state
A, B, C, … - excited states of same spin multiplicity as ground state
a, b, c, … - excited states with different spin multiplicity
4g
Electric dipole selection rulesLinear molecules Δ = 0, ±1 (randomly oriented molecules) + - in Σ – Σ transitions (notation reflects symmetry of electronic wave functions with respect to *reflection in plane containing internuclear axis) u g (extra designation for homonuclear diatomic molecules indicating eve or odd number of odd orbitals) reflected at 0 ΔS = 0 (spin-orbit coupling weak) weaker magnetic dipole, electric quadruple transitions have different rulesNonlinear molecules symmetry of product of upper and lower states has to be of same species as transition operator ΔS = 0 (spin-orbit coupling weak )*
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phosphorescence
S = 0S = 1
S = 0 S = 1or
(1927)
Franck-Cendon factor
Hönl-London factor
Fig 3.8 anharmonicity
relative intensity of hot band no fundamental reflects population of initial states
overtone weaker than fundamental, reflects degree of anharmonicity
combination bands can be very strong if cause large change in dipole moment
Isotopic Bands: 13CO 2, C18OO, HDO
Terminology Vibrational transitions
+
2
1
0
1
0
2
Combination band
v1 v2v1 Normal modes
hot band
fundamental
Overtone (due to anharmonicity)
Rotation – Vibration bands (p. 90)
emission
absorption
J’ = J” + 1J’ = J”J’ = J” - 1
v’
v”J”
13Transition v’ , J’ – v’’ , J’’ upper lower
J’ = J’’ + 1 R – branch
J’ = J’’ Q – branch
J’ = J’’ – 1 P – branch
P RQ
Δv = ± 1 ΔJ = 0 (some cases) ±1Δv = arbitrary for different e states
I2
v1 = 213.2 cm-1
T = 300 K (= 208.7 cm-1)
vibrational population
Rotational population
N2O doubling to rotationcoupling of degenerate vibration
Spectral line shape
• Natural: arises from uncertainty principle due to finite lifetime of excited state ΔvΔT ∼ 1 ΔT = lifetimeImbuntant for resonance scattering of atomic lines
e. g. H (Lyα) 0 (1304 Å)
• Doppler: thermal motion of atoms and moleucles important in mesosphere (~100 km)
• Lorentz: collisions by other molecules. Most importan in bulk of atmosphere
• Voigt: superposition of above 2 (non-interactive)
• Dicke : superposition of Doppler + Lorentz can lead to line “narrowing”!
• Dimer and Pressure-induced by transient state brought together by collision
Oscillator with dumping
Solve for xo
2
Pure sine wave
Finite life time
(3.48)
quantum life timecollision life time
V V + W (3.52) Quantum veresion
Lorentz line width
Natural line width
Doppler Profile
Lurentz Profile
Voigt Profile
(Frequency shift)
(3.79)
(3.48)
4
(3.51)
(collision frequency)
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FWHM = 2((log2)α D2 +α L
2 )1
2
Doppler + LorentzIn dimensionless units
5
18