20 molecular spectroscopy and...

MOLECULAR SPECTROSCOPYAND PHOTOCHEMISTRY

20.1 Introduction to Molecular Spectroscopy20.2 Experimental Methods in Molecular Spectroscopy20.3 Rotational and Vibrational Spectroscopy20.4 Nuclear Magnetic Resonance Spectroscopy20.5 Electronic Spectroscopy and Excited State

Relaxation Processes20.7 Photosynthesis

20CHAPTER

General Chemistry II

General Chemistry II 2

Fluorescence microscope image of the mouse cerebral cortex. Three different dyes were used to selectively image structural proteins called neurofilaments, a small proteincalled GFAP that is a component of intermediate filaments, and cellular nuclei.

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Stefan W. HellPrize share: 1/3

Eric BetzigPrize share: 1/3

William E. MoernerPrize share: 1/3

The Nobel Prize in Chemistry 2014

"for the development of super-resolved fluorescence microscopy"


Atomic or molecular absorption and emissionResonance condition:

Raman scattering: Inelastic collisionsEnergy conservation:

: frequencies of incident and scattered radiation, respectively Born-Oppenheimer approximation (Chapter 6)

~ Heavy nuclei move slowly, light electrons move fast~ Decoupling of electronic motion from nuclear motion

electroni nuclearl ctota ,ψψ ψ= vib rot nucelet cot l E E EE E+ += +

~ Generating a potential energy function for each electronic state(eff ) el

AB AB nn AB( ) ( ) ( )V R E R V Rα α= +

i sE h hν ν∆ = −

E hν∆ =

i s,ν ν

94220.1 INTRODUCTION TO MOLECULAR

SPECTROSCOPY


Transitions between energy levels

Fig. 20.1 (a) Absorption from the ground electronic state of HCl to an excited electronic state. (b) Vibrational levels in the ground electronic state showing pure rotation, pure vibration, and vibration-rotation transitions.

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IR spectrum of vibration-rotation spectrum of COSimultaneous excitation of vibrational and rotational motion.

Energy difference between adjacent lines→ Transition between adjacent rotational levels→ Bond length information obtained

Frequency of CO stretching vibration (⇓)→ Bond force constant and bond strength

Fig. 20.2 Vibration-rotation spectrum of CO in the gas phase,measured using IR absorptionspectroscopy. Absorbance is plotted as a function of frequencyin wave numbers.

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Two conservation laws

(1) Energy conservation: ∆E = hν ← resonance condition

(2) Angular momentum conservation: “selection rule”

P-branch: ∆J = –1, Q-branch: ∆J = 0, R-branch: ∆J = +1

Q-branch does not appear in Fig. 20.2.

Molecular properties and various spectroscopic techniques:

(1) Bond lengths, bond angles: Microwave, IR, Raman

(2) Bond force constants and effective reduced mass: Vibrational

(3) Identification of functional groups and their relative locations

in molecules: Vibrational and NMR

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Wave number, (unit: cm–1) ~ Proportional to energy,

Presentation of spectra:Microwave as a function of frequency (GHz) or energy (cm–1)IR and Raman as a function of wave numbers (cm–1)UV and Visible as a function of wavelength (nm) or energy (eV)

/ ( )(1/ )E h hc hcν λ λ= = =

944�𝜈𝜈 = 1/𝜆𝜆


Intensities of Spectral Transitions Beer-Lambert Law:

t 0 lI I e α−= dI Idl

α→ = − (1st – order ‘kinetics’)

I0: Intensity of the incident beamIt: Intensity of the transmitted beaml: Path lengthα: Absorption coefficient of the sample, α = (N/V) σ

*Intensity: Amount of energy crossing a surface per unit time, or power;

or Number of photons passing through a surface per unit time

*Absorption and scattering ~ collisions between photons and molecules, σ(=πd2): cross section

cf. , is the distance covered in unit time ↔ l

( / )t 0 e N V lI I σ−=

1 ( / )Z N V uσ≈ u

Intensity of the radiation that is absorbed or scattered:

[ ]{ }a,s 0 t 0 1 exp ( / )I I I I N V lσ= − = − −

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Thermal Occupation of Molecular Energy Levels Boltzmann distribution Intensity of a spectral line depends on…

(1) Strength of the transition (2) Population ratio of the initial and final states

Probability that the energy level is occupied ← Boltzmann distribution

kB = 1.38×10–23 J K–1 : Boltzmann constant ( kBNA = R )gi : degeneracy of level iAt thermal equilibrium, very few molecules have energy

i i i i B ( ) / exp( / ) P N N g k Tε ε= ≈ −

i Bk Tε >

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Thermal energy, kBTkBT = 2.5 kJ mol–1 at room temperature

Larger than the spacing between rotational energy levels→ Many rotational levels are occupied

Smaller than the spacing between vibrational energy levels→ Most molecules are in their ground vibrational state


Difference in the population between two energy levels εi and εf

Assume that . Then

Comparison of the magnitudes of ∆ε and kBT:

Electronic energy levels, ∆ε >> kBT → Only ground level is populated

Vibrational energy levels, ∆ε > kBT → Only 3% in the 1st excited state

Rotational energy levels, ∆ε << kBT

→ Many rotational levels are populated at room temperature

[ ]i f i i B f f Bexp( / ) exp( / )N N N g k T g k Tε ε− = − − −

( ) [ ]i f i f i f i f i B/ ( ) / 1 / 1 ( / ) exp[ ( ) / )N N N N N N N g g k Tε ε∆ ≈ − = − = − − −

[ ]f i B1 ( / ) exp[ / )g g k Tε= − −∆

iN N≈

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Molecular Spectroscopy consists of…

1) A source of EM radiation (gas discharge lamp, white light, laser)

2) An element that either disperses the different wavelengths

or modulates the frequencies (prism, diffraction grating)

3) A detector (photographic film, charge-coupled device (CCD) detector

FTIR or FT-NMR

~ Irradiation over a range of frequencies simultaneously.

~ Spectra are extracted from the raw data by a mathematical

algorithm, Fourier transform.

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20.2 EXPERIMENTAL METHODS IN MOLECULAR SPECTROSCOPY


Fig. 20.3 Schematic of dual-beam absorption spectrometer for UV and visible lights.

Fig. 20.4 Schematic of an emissionor Raman scattering experiment.

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UV-VISSpectrophotometer


Diatomic Molecules

Rigid rotor model Moment of inertia,

Reduced mass,

Center of mass at

,

e2I Rµ=

1 2 1 2/( )m m m mµ = +

11 e

1 2

mr Rm m

= +

22 e

1 2

mr Rm m

= +

Fig. 20.5 A diatomic moleculerotates about its center of mass.

948

20.3 ROTATIONAL AND VIBRATIONAL SPECTROSCOPY


2 2( 1)( / 2 ) , 0,1, 2,3...J J J h Jπ= + =

Projection of J along the z-axis

( / 2 ), , 1,...0,... 1,z J JJ M h M J J J Jπ= = − − + −

with degeneracy, 2 1Jg J= +

Energy levels for the linear rigid rotor:

𝑜𝑜𝑜𝑜 𝐸𝐸𝐽𝐽 = ℎ𝑐𝑐 �𝐵𝐵𝐽𝐽 𝐽𝐽 + 1 , �𝐵𝐵 = (ℎ/8𝜋𝜋2𝑐𝑐𝑐𝑐) rotational constant in cm-1

𝐸𝐸𝐽𝐽 = ℎ𝐵𝐵𝐽𝐽 𝐽𝐽 + 1 , 𝐵𝐵 = (ℎ/8𝜋𝜋2𝑐𝑐) rotational constant in Hz

Square of angular momentum, J

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Microwave absorption spectroscopy~ Heteronuclear diatomic molecules: Permanent dipole moment

~ Rotation of oscillating dipole moment of a heteronuclear diatomics

~ Conservation of energy,

~ Conservation of angular momentum for microwave absorption

and emission ← Selection rule

~ Frequencies of the allowed transitions for microwave absorption

E hν∆ =

( 1)J∆ = + ( 1)J∆ = −

→ Microwave spectrum of a heteronuclear diatomic molecule

consists of a series of equally spaced lines separated by .2B

950

Δ�̌�𝜈 = �𝐵𝐵 𝐽𝐽𝑓𝑓 𝐽𝐽𝑓𝑓 + 1 − 𝐽𝐽𝑖𝑖(𝐽𝐽𝑖𝑖 + 1)

= �𝐵𝐵 𝐽𝐽𝑖𝑖 + 1 𝐽𝐽𝑖𝑖 + 2 − 𝐽𝐽𝑖𝑖(𝐽𝐽𝑖𝑖 + 1)

= 2 �𝐵𝐵 𝐽𝐽 + 1


Fig. 20.6 The dipole moment of a Fig. 20.7 The angular momentumrotating heteronuclear diatomic of a photon (blue circular arrow) ismolecule oscillates at its rotational transferred to a molecule (redfrequency. circular arrows) upon absorption.

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Fig. 20.8 Rotational energy levels and allowed transitions for a heteronucleardiatomic molecule predicted by the rigid rotor model. The energy levels are givenby 𝐸𝐸𝐽𝐽 = �𝐵𝐵𝐽𝐽 𝐽𝐽 + 1 and the selection rule Δ𝐽𝐽 = +1 for the absorption predicts a seriesof lines equally spaced by 2 �𝐵𝐵, where �𝐵𝐵 is the rotational constant in cm–1.

951


Fig. 20.9 Microwave absorption spectrum of gas-phase CO.

Spacing between adjacent line → Rotational constant → Bond length

e2I Rµ=

951

�𝐵𝐵 = (ℎ/8𝜋𝜋2𝑐𝑐𝑐𝑐)


Raman scattering

~ Absorption of radiation from rotational levels of the ground

electronic state to a set of “virtual” electronic states followed

by emission to different rotational (or vibrational) levels of the

ground electronic state.

~ Selection rule for rotational Raman spectroscopy: Δ𝐽𝐽 = 0, ±2anti-Stokes (Δ𝐽𝐽 = −2), Rayleigh (Δ𝐽𝐽 = 0), Stokes lines (Δ𝐽𝐽 = +2)

higher frequency same frequency lower frequency

~ Microwave spectroscopy cannot be used to measure

bond lengths of homonuclear diatomic molecules because

they have no dipole moments. → Raman can for both!

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Fig. 20.11 QM picture of Raman scattering arising from absorption and emission by virtual electronic states.

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Fig. 20.13 The pure rotationalRaman spectrum of N2.Alternating intensity pattern dueto effects of nuclear spin on theeffective symmetry of the molecule.

Fig. 20.12 First published rotational Ramanspectra of O2 and N2. The spectrum of N2provided the first measurement of the bond length of that molecule.

953


Sir C. V. Raman(India, 1888-1970)

Nobel Prize in Physics (1930)"for his work on the scattering of light and for the discovery of the effect named after him".

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Polarizability~ A measure of the extent to which electrons in atoms or moleculesare displaced by electric fields, most often the electric fields of electro-magnetic radiation, leading to induced dipole moments.

Polarizability is larger for molecules aligned with the electric field

Fig. 20.10 Schematic of the polarization induced in a diatomic molecule by the electric field component of EM radiation.

Polarizability of a homonuclear diatomic molecule oscillates at twice the rotational frequency, producing an oscillating dipole moment that emits radiation at a frequency shifted from that of the incidentradiation by that amount.

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Vibrational spectroscopy

Hookean force:

e( )F k R R= − −21

e e2( ) ( )V R R k R R− = −

~ harmonic potential

Oscillation frequency:

12

kνπ µ

=Fig. 20.14 Potential energy curves for a diatomicmolecule (black) and a harmonic oscillator (red)that have the same equilibrium bond length Re, bond dissociation energy De, and similar curvature near the minimum.

Simple Harmonic Oscillator Model

955


1D-Schrödinger equation with the harmonic oscillator potential 2 2

22 2

( ) 1 ( ) ( )8 2

h d x kx x E xm dx

ψ ψ ψπ

− + =

Energy levels of a simple harmonic oscillator

: vibrational quantum number

state allowed (no violation of uncertainty principle)

: zero-point energy

( )1vib, 2 , ( 0, 1, 2,...) E hν= + =v v v

10 2E hν=

v0=v

→ Independent of the vibrational quantum number→ Vibrational energy levels are equally spaced!

956

∆𝐸𝐸 = 𝑣𝑣𝑓𝑓 +12 ℎ𝜈𝜈 − 𝑣𝑣𝑖𝑖 +

12 ℎ𝜈𝜈 = 𝑣𝑣𝑖𝑖 + 1 +

12 ℎ𝜈𝜈 − 𝑣𝑣𝑖𝑖 +

12 ℎ𝜈𝜈 = ℎ𝜈𝜈


Fig. 20.15 Energy levels and wavefunctions for the lower energy statesof the harmonic oscillator.

Absorption of Vibrational energy

Dipole moment change (IR)

Polarizability change (Raman)

Selection rule (IR & Raman)

Anharmonicity: Morse potential1∆ = ±v

First two SHO wavefunctions:

where

957


Fourier Transform Infrared spectroscopy (FTIR) Very rapid acquiring of IR spectra

All wavelengths are measured simultaneously, instead of sequentially as done by scanning the prism or grating in amonochromator.

FTIR spectrometer consists of…IR source, Sample compartment, Interferometer, Detector

Fourier Transform ~ mathematical algorithm

Fig. 20.16 Schematic of a Michelsoninterferometer. The movable mirror isscanned back and forth, which causesa periodic modulation in the detectedsignal due to interference between thetwo beams.

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Two beams are recombined at thebeam splitter and sent to a detectorwhere an interference pattern (aninterferogram) is recorded and sub-sequently transformed into a spectrumby a Fourier transform.

Fig. 20.17 (a) FTIR interferogram and(b) its Fourier transform. �̃�𝜈 is the frequency in wave numbers and p is the difference in path length.

958


Badger’s rule: ~ An empirical relationship between the stretching forceconstant for a molecular bond and the bond length

A : a constant that is the same for all bondsB : b constant that depends on the period of the bonded atoms

3e/( )k A R B= −

1 2

kνπ µ

=

Molecular properties obtained from vibrational spectra

e3/( )Rk A B= −

959


Mores potential:

~ Anharmonicity included~ Investigate dissociation process (at higher vibrational levels)~ Schrödinger equation solvable analytically~ Energy levels are not uniformly spaced

( ) ( )( )e2

e e 1 e a R RV R R D − −− = −

2

e2 4ea vm D

xµω

= =

Anharmonicity:

For 1∆ = +v

Fig. 20.18 Morse potential and associated vibrational energy levels.

960

�𝐺𝐺 𝑣𝑣 = 𝑣𝑣 +12 �̃�𝜈 − (𝑣𝑣 +

12)2𝑥𝑥𝑒𝑒�̃�𝜈

𝑥𝑥𝑒𝑒 =𝑎𝑎2ℏ2𝑚𝑚𝜇𝜇𝜇𝜇 =

�̌�𝜈4�𝐷𝐷𝑒𝑒

Δ �𝐺𝐺𝑣𝑣+12

= �𝐺𝐺 𝑣𝑣 + 1 − �𝐺𝐺 𝑣𝑣

= 𝜈𝜈 − 2 𝑣𝑣 + 1 𝑥𝑥𝑒𝑒 �𝑣𝑣 + ⋅⋅⋅


Fig. 20.19 Birge-Sponer plot used to determine the bond dissociation energy of H2+.

From Atkins & Paula, “Physical Chemistry,” 9th ed (2010). p.467

2H+

Bond dissociation energy:

Area under the plot of Δ �𝐺𝐺𝑣𝑣+12against 𝜈𝜈 + 1

2is equal to the sum, �𝐷𝐷0

961�𝐷𝐷0 = Δ �𝐺𝐺1

2+ Δ �𝐺𝐺3

2+ ⋅⋅⋅ = �

𝑣𝑣

Δ �𝐺𝐺𝑣𝑣+12


Polyatomic Molecules

Rotational Spectroscopy Moment of inertia,

~ Mass property of a rigid body that determines the torque needed

for a desired angular acceleration about an axis of rotation

~ Corresponds to mass in translational motion

Linear triatomic rotors (CO2) ~ single moment of inertia, Ix

Spherical rotors (CH4) ~ 3 moments of inertia,

Symmetric rotors (NH3) ~ 3 moments of inertia,

Asymmetric rotors (H2O) ~ 3 moments of inertia,

2I rµ=

x y zI I I= =

x y zI I I≠ ≠

x y zI I I= ≠

962


“Normal” modes of vibration for polyatomic molecules

~ Transformation of complex correlated vibrations into

unique and independent vibrational modes

3N – 5 vibrational degrees of freedom (linear molecule)

3N – 6 vibrational degrees of freedom (nonlinear molecule)

Vibrational Spectroscopy

Ex. CO2, linear → 3 x 3 – 5 = 4 different “normal” modes of vibration

962


Change in dipole moment:Bending and antisymmetric stretching → IR active

Change in polarizability:Polarizability increases during stretching…

…decreases during compression

Symmetric stretching → Raman active

962


963

Mutual exclusion rule for all centrosymmetric molecules:

~ IR active modes are not Raman active ← Inversion symmetry

IR: Vibrations involving polar bonds

Raman: Motions of highly polarizable covalent bonds (π bonds,

conjugated bonds) for heavy elements


Cystine:Dimer of cysteineDisulfide bond (S–S) stretch

dominates in Ramanbarely visible in IR

Characteristic frequencies of functional groups:

– COOH – NH2

of “normal” or “local” modes C–H bond stretch in –CH3 groupO–H bond stretch in alcohol

Fig. 20.20 Infrared and Raman spectrumof the amino acid L-cystine, showing thecomplementary nature of the techniques.

IR

Raman

965


965


Analysis of an IR spectrum of an organic molecule.

966

EXAMPLE 20.8


Analysis with imagination:From the combined spectral information… N-H, C=O, C-N absorption bands

→ The molecule is an amide, wth the R(CO)N– functional group C-H and C-C bands → The molecule is alkyl amide

The molecule is H3CCH2(CO)NHCH3.

966


Transitions between electronic states (UV or visible range)

Electronic emission spectroscopy (fluorescence)

~ Study of dynamics of energy and electron transfer processes

(femtosecond processes, 1 fs = 10–15 s)

Relaxation of excited electronic states by…

~ Emission of fluorescence or phosphorescence

~ Dissipation of energy as heat by nonradiative processes

973

20.5 ELECTRONIC SPECTOSCOPY AND EXCITED STATE RELAXATION PROCESSES

Electronic spectroscopy


Organic chromophores

Molecules with closed-shells (no unpaired electrons)

Excited states with paired electron spins (singlet states)

Combined LCAO (σ framework) and VB method (π bonds)

σ, σ*, π, π*, n (nonbonding)

~ Nonbonding orbitals occupied by lone pairs of electrons

on heteroatoms (O, S, N, S)

973


Fig. 20.28 Radiative and nonradiative photophysical processes, and energy and electron transfer from electronically excited states to nearby molecules.

974


Ethylene Lewis model: 12 valence electrons

8 electrons with 4 localized C-H σ orbitals

4 with the C=C bond:

σ, σ*, π, π*, n (nonbonding)

Nonbonding orbitals occupied by lone pairs

of electrons on heteroatoms (O, S, N, S)

The lowest configuration: (σ)2(π)2

Frontier orbitals:

HOMO (highest occupied molecular orbirtal): π

LUMO (lowest unoccupied molecular orbital): π*

Fig. 20.29 π molecular orbitals and energy level diagram for ethylene.

974


The lowest energy electronic transition

between the singlet states:

An electron in HOMO → LUMO

(σ)2(π)2 → (σ)2(π)1(π*)1

Excited states configurations are labeled

using only partially filled orbitals:

The lowest-energy excited state of

ethylene is called a π,π* state.

The lowest energy transition:

π → π* transition

Very high energy transition:

σ → σ* transition

974


Beer-Lambert law

t 0 lI I e α−= [ ]t 0 exp ( / )I I N V lσ= − 0. ( ) ktcf c t c e−=

α: absorption coefficient, σ : cross section

Beer’s law

0 10 clI I ε−= → 0 log IA clI

ε = =

A: absorbance, c: concentration (molarity)ε : molar extinction coefficient (or molar absorption coefficient)

0

log log IA TI

= − = −

0/T I I= : transmittance

975


Calculating absorption cross section (σ) (~size of a molecule)from the measured molar absorption coefficient (ε):

( A / )0 A / 10 ( )(ln10) ( / )cl N V lI I e cl N Vε σ ε σ− −= = → − = −

3 20A A( / ) / 2.303 /(2.303)(10 ) 2.6 10N V c Nε σ σσ= = = ×

Strong π → π* transition of ethylene

ε = 1.5 ×104 M–1 cm–1 at

For l = 1 cm, at 0.001 atm and 300 K of ethylene gas, A = 0.61.

→ Transmits only 25 % of the incident radiation

Ex. ε = 105 M–1 cm–1 → σ = 10 A2 (benzene)

max 163 nmλ =

975


Transition between singlet states of conjugate polymers

~ Electronic configuration:

(π1)2(π2)2

~ The lowest absorption band from

π2 → π3* transition at 217 nm

~ The higher energy transition,

π2 → π4*, is possible.

trans-1,3-butadiene

Fig. 20.30 π molecular orbitals and energy level diagram for 1,3-butadiene.

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(1) Length of the box, L, is equal to the number of C atoms in the chain

times the average of the C-C single and C=C double bond length, d.

(2) n for the HOMO is equal to N/2 where N is the number of π electrons.

(3) Energy of the HOMO-LUMO transition is given approximately by

(4) Explains the increase in the wavelength of longest absorption.

Orbitals of linear conjugated polymers↔ Particle-in-a-box wave functions

2 2/(8 )h md Nε∆ ≈

977


Perception of colors

Perceived color:

~ Light transmitted through or reflected from the material

Perceived colour ← complementary → Absorbed colour

Three primary colors: Red, Green, Blue (RGB)

~ RGB system used in computer displays and TV

Complementary colors: Cyan, Magenta, Yellow (CMY)

~ CMYK system (K is black) used in color printing

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Fig. 20.31 (a) Color wheel showing the three primary colors and their correspondingcomplementary colors. (b) Schematic of absorption of visible light by a solution of carotene. (c) Schematic of the absorption of visible light by a solution of indigo.

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β-Carotene

Indigo dye

Fig. 20.32 Absorption spectra for the dyes indigo and carotene. The familiarmnemonic for remembering colors is written on the top of the spectra.

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Aromatic hydrocarbons Benzene

Fig. 20.33 π molecular orbitals and energy level diagram for benzene.

Electronic configuration of the ground state: (π1)2(π2)2(π3)2

The strongest UV absorption band from π → π* transition (λmax = 180 nm, εmax = 6 ×104)

2D-Particle-in-a-box model “Particle-on-a-ring”

979


Transition involving “nonbonding” electrons Formaldehyde, HCHO

Fig. 20.34 Approximate frontier molecular orbitalsand energy level diagram for formaldehyde.

Lewis dot model for HCHO: 12 valence electrons

~ 4 for two C-H bonds, 4 for C=O bond, 4 for two lone pairs on O

~ One of the O lone pairs resides in the low energy O 2s orbital

~ The second lone pair on O resides in an O 2py orbital

~ Nonbonding n orbital is localized on O atom~ Ground state electronic configuration:

(σ)2(π)2(n)2

980


~ Lowest energy transition: n(HOMO) → π*(LUMO)

→ Excited state configuration: (σ)2(π)2(n)1(π*)1 (n, π* configuration)

~ Higher energy transition: π → π*

→ (σ)2(π)1(n)2(π*)1 (π, π* configuration)

Possible transitions:

Photoelectron spectrum of formaldehyde

980


Fig. 20.35 (a) Photoelectron spectrum of formaldehyde. The lines labeled Arand Xe are due to photoemission from residual rare gases in the sample chamber. (b) Formaldehyde vibrational modes and frequencies in the ground electronic state.

981


1st peaks at 10.88 eV ~ Electrons with the lowest binding energy

→ Assigned to the HOMO, nonbonding (n) orbital~ Very little vibrational fine structure, only 3 vibrational modes

→ C-H and C=O stretching and H-C-H bending vibrations 2nd peaks between 14 and 15 eV

→ Assigned to C=O stretchingAlmost no effect on deuteration (from comparison of spectra)

→ Lower vib. freq. due to reduction in the CO bond orderRemoval of electron from the bonding orbital

→ Identify the orbital as the C-O π-bonding orbital 3rd peaks around 16 eV

→ Vib. freq. measured is lower than that in the ground state→ Vib. freq. further reduced on deuteration→ Assigned to C-H σ-bonding orbitals

981


Representative chromophores

Aromatics:

Conjugated alkenes:

982


Carbonyls:

Aza-aromatics:

982


~ Molar absorption coefficient (εmax) for the most intense peak(λmax) in the range of 103 –105 M–1 cm–1

~ Colors of dyes~ Electric field is oriented parallel to the molecular plane~ Induced by the linear force of the electric field of the radiation

→ Strong

transition

~ Molar absorption coefficient (εmax) for the most intense peak(λmax) in the range of 10 –103 M–1 cm–1

~ Nonbonding orbital, n, is perpendicular to the antibonding π* orbital~ Induced by the torque of the electric field of the radiation → Weak~ Molecules with heteroatoms (O, N, S)

transition

*π π→

*n π→

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983


Excited State Relaxation Processes Multiplicity Singlet state with

Spins are paired,0S =

1 12 2(1) (2) 0, 0,0 ( ) / 2z z zS s s= + = ↑↓ − ↓= ↑= + −

Sz: z-component of the total spin angular moment sz(i): z-component of the ith electron’s spin angular momentum

Degeneracy of the level for this state: ( ) 2 1 1g S S= + =

Triplet state with , 1S = ( ) 2 1 3g S S= + =

1 12 2

1 12 2

1 12 2

(1) (2) 1,

0,

1,

1,1

1,0 ( ) / 2

1, 1

z z zS s s= + = + + = + =

= + − =

= −

↑↑

= ↑↓ +

− −

↓↑

− == ↓↓

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(1) There is no triplet state with the same electronic configuration

as the ground electronic state because of the Pauli principle.

(2) and

(3)

(Overlap: between π and π* > between n and π*)

, * , *S Tπ π π πε ε> , * , *

S Tn nπ πε ε>

, * , *ST ST nπ π πε ε∆ > ∆

Singlet and triplet energy levels of formaldehyde

984


Fig. 20.37 Energy level diagram for formaldehyde. The singlet energy levels areshown on the left and the triplet energy levels are shown on the right. The singlet-

triplet splitting energy ∆εST is greater for π, π* states than for n, π* states.

984


985


Fluorescence~ Emission from transitions between states of the same spin

Si → Sf or Ti → Tf fluorescence

Phosphorescence(very slow with lower intensity than fluorescence)

~ Emission from transitions between states of different spinTi → S0 phosphorescence

Radiative transitions

Internal conversion ~ transition between states of the same spin

Intersystem crossing ~ transition between states of different spin

Nonradiative transitions

985


Vibrational relaxation~ Excited vibrational levels return to lower vibrational levels

by dissipating the energy as heat

Intensities of Spectral Transitions

~ “Allowed” transition between states of the same spin

~ “Forbidden” transition between states of different spins

Intensity of spin-forbidden transition depends on the

degree of spin-orbit coupling → large for heavy atoms

986

General Chemistry IIFig. 20.38 Absorption, emission, and nonradiative relaxation processes.

986


~ Lower values of εmax for singlet-triplet transitions~ Splitting between the singlet and triplet π, π* states is

greater than for the n, π* states~ Range of εmax for each class of transition due to symmetry

Ex. Singlet-singlet transition

→ Symmetry requirement for a fully allowed transition:(Initial & final states) x (electric vector) → totally symmetric

*π π→

987


1. (Total 12 pts)

(a) Draw the molecular orbital and energy level diagram of the ethylene.

(Draw two lowest unoccupied MOs and two highest occupied MOs. Put them

in the order of energy and draw the shape of the molecular orbitals as in the

textbook.)

(b) Indicate the electron configuration of

the ground electronic state and the first

excited electronic state of ethylene.

2015 Final


2. (Total 5 pts)

(a) When you heat up a glass of milk using a microwave oven, what molecule is

actually absorbing the microwave energy?

(b) What kind of physical property the molecule above should have in order to

absorb the microwave energy?

2015 Final


3. (Total 11 pts) How many lines appear in the proton NMR spectrum?

Include signals arising from both the chemical shift and J couplings.

2015 Final

(a) C2H4 (b)

(c) CH3CH2COCH2CH3 (e)

1 4

7 7


2016 Mid8. (total 10 points)

(a) The line positions of the fourth, fifth, and sixth lines of the pure rotational

microwave spectrum of HCI are 𝑣𝑣4 = 83.03𝑐𝑐𝑚𝑚−1 , 𝑣𝑣5 = 103.8 cm−1, and 𝑣𝑣6 =

124.3 𝑐𝑐𝑚𝑚−1.

Calculate the equilibrium bond length of the HCI molecule.

e2I Rµ=�𝐵𝐵 = (ℎ/8𝜋𝜋2𝑐𝑐𝑐𝑐)

2 �𝐵𝐵∆ν =


(b) The C-H bonds in 𝐶𝐶𝐶𝐶3 and 𝐶𝐶𝐶𝐶2 groups stretch at frequencies near

2900 𝑐𝑐𝑚𝑚−1 in the infrared (IR) spectrum. Calculate the vibration

frequency if hydrogen atoms were replaced by deuterium.

2016 Mid

ν =

= 1.714 atomic mass unit

= 0.923 atomic mass unit

(2900 ) = 2130

= =

= =

= x =


2016 Mid

(b) Selection rule for rotational spectroscopy is ∆J = ±1, and that for Raman

spectroscopy is ∆J = ±2.

(c) In a quantized harmonic oscillator, the energy of the ground state is zero.

(d) If an electron in the π orbital of C2H4 is excited by a photon to the π* orbital,

the vibrational frequency in the excited state will be higher than in the ground

state.

10. (Total 14 points) Determine whether the following statements are True or

False.

F

F

F


(e) Absorption of ultraviolet lights in 1,3-butadiene occurs at longer

wavelength than in ethylene.

(f) A strong absorption observed in the ultraviolet region of the spectrum

of formaldehyde is attributed to an n to π* transition.

(g) Phosphorescence generally occurs more slowly than fluorescence.

2016 Mid

T

F

T

20 molecular spectroscopy and...

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