lecture 3 - chapter 2-9-07-05
DESCRIPTION
curs IR spectroscopyTRANSCRIPT
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CHMBD 449 Organic Spectral AnalysisFall 2005Chapter 2: IR SpectroscopySpectroscopic ProcessIR Absorption ProcessUses of IRCovalent bonds Vibrational Modes Absorption Trends
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IR Spectroscopy
IntroductionSpectroscopy is the study of the interaction of matter with the electromagnetic spectrum
Electromagnetic radiation displays the properties of both particles and waves
The particle component is called a photon
The energy (E) component of a photon is proportional to the frequency . Where h is Plancks constant and n is the frequency in Hertz (cycles per second)
E = hn
The term photon is implied to mean a small, massless particle that contains a small wave-packet of EM radiation/light we will use this terminology in the course
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IR Spectroscopy
IntroductionBecause the speed of light, c, is constant, the frequency, n, (number of cycles of the wave per second) can complete in the same time, must be inversely proportional to how long the oscillation is, or wavelength:
Amplitude, A, describes the wave height, or strength of the oscillation
Because the atomic particles in matter also exhibit wave and particle properties (though opposite in how much) EM radiation can interact with matter in two ways:Collision particle-to-particle energy is lost as heat and movementCoupling the wave property of the radiation matches the wave property of the particle and couple to the next higher quantum mechanical energy level
n = c = 3 x 1010 cm/s___lc E = hn = ___lhc
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IR Spectroscopy
IntroductionThe entire electromagnetic spectrum is used by chemists:
UVX-raysIRg-raysRadioMicrowaveEnergy (kcal/mol)300-30300-30~10-4> 300~10-6
VisibleFrequency, n in Hz~1015~1013~1010~105~1017~1019Wavelength, l10 nm1000 nm0.01 cm100 m~0.01 nm~.0001 nm
nuclear excitation (PET)core electron excitation (X-ray cryst.)electronic excitation (p to p*)molecular vibrationmolecular rotationNuclear Magnetic Resonance NMR (MRI)
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Irradiation: Molecule is bombarded with photons of various frequencies over the range desiredhnhnhnDetection: Photons that are reemitted and detected by the spectrometer correspond to quantum mechanical energy levels of the moleculeEnergyAbsorption: Molecule takes on the quantum energy of a photon that matches the energy of a transition and becomes excited hnRelaxation
rest staterest stateexcited stateExcitationIR Spectroscopy
IntroductionEvery spectroscopic method works using the same principle
Each method uses a method of irradiation, absorption-excitation, re-emission-relaxation, and detection.
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IR Spectroscopy
IntroductionThe IR Spectroscopic ProcessThe quantum mechanical energy levels observed in IR spectroscopy are those of molecular vibration
We perceive this vibration as heat
When we say a covalent bond between two atoms is of a certain length, we are citing an average because the bond behaves as if it were a vibrating spring connecting the two atoms
For a simple diatomic molecule, this model is easy to visualize:
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IR Spectroscopy
IntroductionThe IR Spectroscopic ProcessThere are two types of bond vibration:Stretch Vibration or oscillation along the line of the bond
Bend Vibration or oscillation not along the line of the bond
scissorasymmetricsymmetricrocktwistwagin planeout of plane
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IR Spectroscopy
IntroductionThe IR Spectroscopic ProcessEach stretching and bending vibration occurs with a characteristic frequencyTypically, this frequency is on the order of 1.2 x 1014 Hz
(120 trillion oscillations per sec. for the H2 vibration at ~4100 cm-1)
The corresponding wavelengths are on the order of 2500-15,000 nm or 2.5 15 microns (mm)
When a molecule is bombarded with electromagnetic radiation (photons) that matches the frequency of one of these vibrations (IR radiation), it is absorbed and the bonds begin to stretch and bend more strongly (emission and absorption)
When this photon is absorbed the amplitude of the vibration is increased but NOT the frequency
The molecule will slowly decay to its resting state by emission of a photon of this particular frequency, which is detected by the spectrometer (detection)
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IR SpectroscopyIR Spectroscopy
IntroductionThe IR Spectroscopic ProcessThe result of the spectroscopic process is a spectrum of the various stretches and bends of the covalent bonds in an organic molecule
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IR Spectroscopy
IntroductionThe IR SpectrumThe x-axis of the IR spectrum is in units of wavenumbers, n, which is the number of waves per centimeter in units of cm-1 (Remember E = hn or E = hc/l)
This unit is used rather than wavelength (microns) because wavenumbers are directly proportional to the energy of transition being observed chemists like this, physicists hate it
High frequencies and high wavenumbers equate higher energyis quicker to understand thanShort wavelengths equate higher energy
This unit is used rather than frequency as the numbers are more real than the exponential units of frequency
IR spectra are observed for what is called the mid-infrared: 400-4000 cm-1
The peaks are Gaussian distributions of the average energy of a transition
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IR Spectroscopy
IntroductionThe IR Spectrum bond differences
So how does the IR detect different bonds?
The potential energy stretching or bending vibrations of covalent bonds follow the model of the classic harmonic oscillator (Hookes Law)
Potential Energy (E)Interatomic Distance (y)Remember: E = ky2
where: y is spring displacementk is spring constant
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IR Spectroscopy
IntroductionThe IR Spectrum bond differences
Aside: Physically here are the movements we are discussing:Stretching vibration: a typical C-C bond with a bond length of 154 pm, the displacement is averages 10 pm:
Bending vibration: For C-C-C bond angle a change of 4 is typical, which corresponds to an average displacement of 10 pm.
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IR Spectroscopy
IntroductionThe IR Spectrum bond differences
The energy levels for these vibrations are quantized as we are considering quantum mechanical particles
Only discrete vibrational energy levels exist:
Note there is no energy level below n = 0, at any temperature above absolute zero there is always the first vibrational energy levelPotential Energy (E)Interatomic Distance (r)rotational transitions (in microwave region)Vibrational transitions, n
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IR Spectroscopy
IntroductionThe IR Spectrum bond differences
However, the application of the classical vibrational model fails apart for two reasons:As two nuclei approach one another through bond vibration, potential energy increases to infinity, as two positive centers begin to repel one another
At higher vibrational energy levels, the amplitude of displacement becomes so great, that the overlapping orbitals of the two atoms involved in the bond, no longer interact and the bond dissociates
We say that the model is really one of an aharmonic oscillator, for which the simple harmonic oscillator model works well for low energy levels
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IR Spectroscopy
IntroductionThe IR Spectrum bond differences
Here is the derivation of Hookes Law we will apply for IR theory:
Vibrational frequency given by:
n = 1 K 2pc m
where:
n : frequencyc : speed of lightK: force constant bond strengthm: reduced mass = m1m2/(m1+m2)
Reduced mass is used, as eachatom in the covalent bond oscillatesabout the center of the two masses
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IR Spectroscopy
IntroductionThe IR spectrum bond differences
Vibrational frequency given by: n = 1 K 2pc mWhat does this mean for the different covalent bonds in an organic molecule?
Lets consider reduced mass, m, first:
The C-H and C-C single bonds differ by only 16 kcal/mole:99 kcal mol-1 vs. 83 kcal mol-1 (similar K)
Due to the reduced mass term, these two bonds of similar strenght show up in very different regions of the IR spectrum:CC 1200 cm-1 m = (12 x 12)/(12 + 12) = 6(.408)CH 3000 cm-1m = (1 x 12)/(1 + 12) = 0.92(.95)A smaller atom therefore gives rise to a higher wavenumber (and n and E)
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IR Spectroscopy
IntroductionThe IR spectrum bond differences
Vibrational frequency given by: n = 1 K 2pc m
When greater masses are added, the trend is similar (Ks here are different)CI 500 cm-1CBr 600 cm-1CCl 750 cm-1CO 1100 cm-1CC 1200 cm-1CH 3000 cm-1 A smaller atom therefore gives rise to a higher wavenumber (and n and E)and a larger atom gives rise to lower wavenumbers (and n and E)
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IR Spectroscopy
IntroductionThe IR spectrum bond differences
Lets consider reduced bond strength (force constant, K):
A CC bond is stronger than a C=C bond is stronger than a C-C bond
Therefore higher wavenumbers result from stronger bonds K wavenumber, cm-1 From IR spectroscopy we find: CC ~2100 C=C ~1650 CC ~1200
Which is in good accord with the heats of formation (Hf) for each bond: kcal mol-1CC 200 C=C 146 CC 83
Stronger bonds give higher wavenumbers (and higher n and E)