The Absorption Laws - CCC/UPCMLDccc.chem.pitt.edu/wipf/Courses/1140_05_files/Spectroscopy.pdf · Chem 1140; Spectroscopy ¥ UV-VIS ¥ IR ¥ NMR The Absorption Laws I1 I0 I I2 Detector

Chem 1140; Spectroscopy

• UV-VIS

• IR

• NMR

The Absorption Laws

I1 I0 I I2Detector

transmitted light

intensity of the incident beam

I2

I1Overall transmittance: T = (what is actually measured)

I

I0Internal transmittance: T i = (of interest to the spectroscopist)

Usually T0 = Ti Such differences as might exist can be minimized by using matched cells and setting T for the reference at 100%.

UV-VIS Spectroscopy

P. Wipf 1 Chem 1140

The quantity I/I0 is independent of the intensity (I) of the source and

proportional to the number of absorbing molecules

Lambert-Beer Law: logI0

I= ! . l . c = A

l = path length of the absorbing solution in [cm]

c = concentration in moles/liter

Log I0/I = absorbance or optical density = A! = molar extinction coefficient [1000 cm2 mol-1]

! i s a characteristic of a g iven compound, or more accurately, the lightabsorbing system of the compound, the so called chromophore. ! i scorrelated to the size (Å) of the chromophore and of course wave-lengthdependent.

! = f (")! ! f (c) (Approximation! An accurate

determination of ! r equires determiningA at various concentrations)

!: 10 - 105 (scales with extended #-systems)(dyes)

P. Wipf 2 Chem 1140

UV-Vis spectra are usually plotted as A vs. ! plots:

A

!

2

1

bathochromic

hypsochromichyperchromic

hypochromic

[nm]!max

shifts

"#"$

n#"$

Though there are discrete levels of electronic excited states in a

molecule, we do not observe absorption lines but broad peaks; the

change in vibrational and rotational energy levels during absorption of

light leads to peaks containing vibrational and rotational fine

structure. Due to additional interaction with solvent molecules, this

fine structure is blurred out, and a smooth curve is observed. (vapour

phase: one can observe vibrational fine structure).

P. Wipf 3 Chem 1140

Selection Rules

The irradiation of organic compounds may or may not give rise to excitation of electrons from one orbital to another orbital. There are transitions between orbitals that are quantum mechanically forbidden.

Two selection rules:

-!Spin-rule:!! The total spin S may not change during transition (S ! S; T ! T)-!Symmetry rule:! e—transitions between orbitals of identical symmetries!!!! are not allowed.!!!! (for ex. Even/uneven with regard to inversion).

n !* even even

! In reality, these quantum mechanical rules are not rigidly observed,

however, due to molecular vibrations, the intensities (") of "forbidden"

transitions are significantly reduced (and are usually of diagnostic

importance).

n # $* band near 300 nm of ketones; " = 10-100

benzene 260 nm band with " = 100-1000.

P. Wipf 4 Chem 1140

Chromophores

Definition:! Chromophore – light absorbing electron system of a compound

Rules:! - ! or n- orbitals that do not interact lead to a spectrum that is the ! sum of the individual absorptions of the isolated chromophores. - the longer the conjugated system, the longer the wavelength of the absorption maximum and the higher its intensity. - a bathochromic and hyperchromic effect is observed, when atoms with n-orbitals are directly attached to a chromophore (-OH, -OR, NH2, SH, SR, Hal…) = auxochromic groups.

! Isolated Chromophores

Of the once listed in table, only few are of practical significance (Vacuum-UV)

C C

!"max = 190nm~

!#

$%h&

!

!#

P. Wipf 5 Chem 1140

P. Wipf 6 Chem 1140

! Conjugated Chromophores

C C

!"max = 190nm~

!#

$%h&

!

!#

!

!"A

H

HS

n

A

S

S=Auxochrome

!3"

!2

!1

P. Wipf 7 Chem 1140

! Benzene and aromatic compounds

The UV spectra of benzenes are characterized by three major bands which have

been given a variety of names.

P. Wipf 8 Chem 1140

Only ! is allowed. B band is forbidden (loss of symmetry due to molecular vibrations; shows vibrational fine structure).

MO Diagram of FerroceneFe FeCp2 2 Cp-

4 pa2u, e1u

4 sa1g

4 pa1g, e1g, e2g

e1u!

a1g!

e2g!

a2u!

e2ue2g, e2u

e1u

a1g

e2g

e1g, e1u

e1u

e1g

a1g

a2ua1g, a2u

-50

0

50

100

150

200

250

300

200 300 400 500 600 700 800

UV Spectrum of Ferrocene

extinction [cm

-1/M

]

lambda [nm]

Ferrocene has a molar extinction coefficient of 96 M-1cm -1 at 442 nm

P. Wipf 9 Chem 1140

Nomenclature of Electronic Transitions; Symbols of Symmetry Classes

Symbols of symmetry classes:

A: sym. (according to a Cn operation)

B: antisym. (according to a Cn operation)

E: 2-fold degenerate state

T: 3-fold degnerate state

Indices:

g: sym. (according to an inversion operation)

u: antisym. (according to an inversion operation)

1: sym. (according to a C2 axis that is orthogonal to a Cn axis)

2: antisym. (according to a C2 axis that is orthogonal to a Cn axis)

‘: sym. (according to a plane of symmetry "n that is orthogonal to a Cn axis)

‘: antisym. (according to a plane of symmetry "n that is orthogonal to a Cn axis)

Examples:

1A2 1A11B1u 1A1g1B2u 1A1g1E1u 1A1g

Calculation of spectra:

! Bonus Problem: Calculate UV and IR

Spectra of Ferrocene and Acetylferrocene,

and Compare to Experimental Data; can you

design a Ferrocene derivative that is green-

colored?

P. Wipf 10 Chem 1140

Infrared Spectroscopy

After considering ultraviolet and visible radiation (200-800 nm) which is energetic enough to affect the electronic levels in a molecule, we shall now consider radiation which has a longer wavelength: infrared radiation which extends beyond the visible into the microwave region and is capable of affecting both the vibrational and the rotational energy levels in molecules.

Range of commercial instruments:!! 2500 nm to 16’000 nm!! physical chemists:!! 25000 – 160’000 Å!! analytical chemists:!! 2.5 – 16 microns (µ)!! organic chemists:!! 4000 – 625 cm-1

!wavenumber = 1/" = !/c "normalized frequency"

Use: simple, rapid, reliable means for functional group identification.

Vibrational modes

For a molecule comprised of N atoms, there are 3N-6 normal

modes of vibration (3N-5 for linear molecules). To a good approximation, however, some of these molecular vibrations are associated with the vibrations of individual bonds or functional groups (localized vibrations) while others must be considered as vibrations of the whole molecule.

Localized vibrations are:

Stretching modes:

C H

simplecoupled:

C

H H

symmetric asymmetric

C

H H


Bending modes:

C

H H

scissoring (sym)

C

H H

rocking (asym)

in plane deformations

C

H H

wagging (sym)

C

H H

twisting (asym)

out of plane deformations

Transmission

O H C C C C other stretching

N H

C H

stretching

C N C O

X Y Z C N

stretching

bending andcombinationbands

FINGERPRINT REGION

N Ostretching

N Hbending

Absorbance

4000 3000

2500

2000

1500

1000 cm-1

wave numbers


Selection rules

1. In order to observe an absorption, the dipole moment of the

excited vibrational state must differ from that of the ground state.

Reason:!oscillating dipole interacts with oscillating electric vector of h!

O O observed

H C C H H C C H not observed

1. frequency, shape, intensity of an absorption band have all to be considered in the interpretation

2. all characteristic absorption frequencies of a functional group have to be considered (band can be missing or is caused by another function)

3. first the obvious absorptions should be identified:!!!!!!!!!!!!!!!!X-H, C=O, C=C, out of plane C-H

4. subsequently the strong absorptions in the fingerprint region should be analyzed 5. possible structures can now be proposed and have to be checked with reference spectra (or data from other spectroscopic techniques)

Analysis of IR - Spectra of Unknown Compounds


An Introduction to NMR Spectroscopy

1H NMR

13C NMR

The types of information accessible via high resolution NMR include:

1. Functional group analysis (chemical shifts) 2. Bonding connectivity and orientation (J coupling), 3. Through space connectivity (Overhauser effect) 4. Molecular Conformations, DNA, peptide and enzyme sequence and structure. 5. Chemical dynamics (lineshapes, relaxation phenomena).

http://www.chem.ucla.edu/%7Ewebspectra/


Nuclear Spin:!The proton is a spinning charged particle and has also a magnetic moment.

m = +1/2higher energy

lowerenergy

m = -1/2

B

1H:- nuclear spin quantum number m = 1/2

- such a nucleus is is described as having a nuclear spin I of 1/2

Because nuclear charge is the opposite of electron charge, a nucleus whose magnetic moment is parallel to the magnetic field has the lower energy.

The difference in energy is given by:!!" = h# B0/2$

# = magnetogyric ratio ( a constant, typical for a nucleus, which essentially reflects

the strength of the nuclear magnet)

Bo = strength of the applied magnetic field

h = Planck’s constant (3.99 x 10-13 kJ s mol-1)


Note that as the field strength increases, the difference in energy between any two spin states increases proportionally.

O Bo

Odegenerate

!

"!

m =-1/2

m = +1/2

nuclear spin quantum #

Ei = -mh# Bo/2$

= -mµNBo

[values of = 1/ were picked for m, so that the difference in energy between two neighboring states will always be an integer multiple of Bo (!h/2")].

The number of nuclei in the low energy state (N!) and the number inthe high energy state (N") will differ by an amount determined by theBoltzmann distribution:

N"/N! = e(-#$/kT) k = 1.381 x 10-23JK-1

When a radio frequency (RF) signal is applied, this distribution is changed ifthe radio frequency matches #$.

#$ = h% = h& B0/2'

% = resonance frequency = & B0/2'

% i s therefore dependent upon both the applied field strength and thenature of the nucleus.


1H: in a 2.35 T field (earth magnetic field = 0.00006 T) = 0.999984

~ 1 in 106 (! = 100 MHz)

- The difference in population of t he two states i s exceedingly small, inthe order of few parts per million. (even smaller in 13C, because " issmaller).

- Relatively low sensitivity of NMR compared to IR or UV- Large Bo needed to increase the population difference (usually given in

MHz of 1H resonance frequency).


SUMMARY

- Nuclear spin is a property characteristic of each isotope and is a

function of Z and N.

- Each isotope with I ! 0 has a characteristic magnetogyric ratio (!) that determines the frequency of its precession in a magnetic field of strength B0

! =2"

#B0

It is this frequency that must be matched by the incident electromagnetic radiation for absorption to occur.

- When a collection of nuclei with I ! 0 is immersed in a strong magnetic field, the nuclei distribute themselves among 2I + 1 spin states, the relative population of which is determined by the Boltzmann distribution, usually being near unity

= e(-!E/kT)

N"

N#

- If two (or more) spin state populations become equal, the system is said to be saturated.


Obtaining an NMR Spectrum

MagnetSource of RF radiationDetector + amplifierPlotter, sample

The magnet:

permanent electromagnet superconducting

cheap, stable,fixed field1.4T

more expensive,stronger, variablefield

expensive, stronger, variablefield18T (24T)

Strength of magnetic field shifts: lock necessary (= substance with strong, defined NMRsignal) Older: referenceinternal, external CDCl3TMS: 0.0 ppm singlett


Once a stable field is established, the question remains as to whether

that field is completely homogeneous throughout the region between

the pole faces of the magnet.

Sample

lines of magnetic flux not uniform

sample has to be placed near the center of the pole gap

N S

!For 2.35 T, to achieve a precision of +/- 1 Hz (10 ppb at 100 MHz) the field must be homogeneous to the extent of +/- 2.35 x 10-8 T! Such a phenomenal uniformity, even at the center of the field , can be achieved only by means of two additional techniques:

Spinning of the sample ("averages" out small inhomogeneities)

Variation of the contour of the field by passing extremely small currents through shim coils wound around the magnet itself: Shimming (manually, automatically)

Paradox: Large sample in order to have as many nuclei as possible, small sample to increase uniformity of the field.

! narrow bore tubes


The Pulsed Fourier Transform Technique

Further advances in S/N ratio improvement had to await the development of faster

computer microprocessors: ~1970’s.

- RF radiation is supplied by a brief but powerful pulse of RF current through the

transmitter coil. The spectral width of the pulse is chosen to cover absorption of all

nuclei of interest.

Optimum tp are obtained by trial and error and are usually in the order of 10 µs for ! = 90° for best S/N ratio.

RF

2SW

intensity

!o

The duration of the pulse (tp) determinesthe frequency range covered (Heisenberg's uncertainty principle: "# "t h)>_

Frequency

SW ~ tp-1 ; tp

>_(4SW)-1

The next step in the PFT process is to monitor the induced AC

receiver signal. Digital data collection gives us the modulated free

induction decay (function of Mxy). FID because the current intensity

decreases with time. This decay is the result of T2 (spin-spin)

relaxation.

M


Time

Voltage

t0

t0

td

the microprocessor samples thevoltage in the receiver coil at a regularinterval, called dwell time, td.

td > (2SW)-1

In a set of nuclei with different ! precession and T1/T2, the digital FID curve becomes very complex:

f( x) = ao + an cos2!nso x + bn sin 2!nsox{ }n=1

"

#

CH3

$%1

frequency

$%2 $%3

where:a0 = constant; an = amplitude; x = period; so = fundamental frequency; xo = 1/so; andn = order of harmonic

The parent function is constructedby summing together a series of sine waves.

line width: uncertainty principle: $%$t > 1

%1/2 > 1T2*

Nuclei that are slow to relax give sharp signals,nuclei that relax rapidly give broad signals (solids).

paramagnetic residues line broadening

At this point it becomes necessary for the computer torecognize the patterns mathematically and extract thesignal frequencies and relative intensities for each set of nuclei. This analysis is performed by a Fourier transfor-

mation of the FID date.

0


- Wink, D. J. J. Chem. Ed., 1989, 66, 810. Spin-Lattice Relaxation Times in 1H NMR Spectroscopy.

- Glasser, L. J. Chem. Ed., 1987, 64, A228. Fourier Transforms for Chemists.

- King, R. W.; Williams, K. R. J. Chem. Ed., 1989, 66, A213, A243. The Fourier Transform in

Chemistry.

Summary:

A typical example of the generation of a PFT spectrum:


!tp:! pulse time (µsec)

!tacq: the length of the time a given FID signal is actually monitored

! !(resolution, the ability to distinguish two nearby signals, is inversely

!! prop. to tacq. R = (tacq)-1 3 sec ! 0.3 Hz

tw: delay time, to allow for equilibrium distribution

tw = 3T1 - tacq.

+ dead time ( phasing necessary)

(for 1H no waiting time)

phase correction

adding up, FT, spectrum


Taking an NMR – Practical Consideration

- Use 5 mm tube filled with ~ 0.5 mL of solution containing 1-5 mg of sample (1H

NMR).

- common deuterated solvents:

CCl4, CDCl3, C6D6, DMSO-d6, D2O, CD3CN, CD2Cl2, d6-acetone, CD3OD

(because of HCl formation, do not leave sample in CDCl3!)

- peak listings in ppm and/or Hz.

- paramagnetic metal ion ! broad peaks

Chemical shift

!H depends on Bo " therefore relative frequencies are reported:

1.39 ppm = ! = downfield from TMS.

2

10

ppm (!)

downfield

deshielded

upfield

shielded

! =!act."!

TMS

!o

=83.4Hz

60x106= 1.39x10

"6=1.39 ppm


Integration

! Area under absorption peak ~ # of nuclei resonating at that !

But:!nuclei must relax to equilibrium between pulses, not generally true of 13C NMR!


First-Order Spin-Spin-Coupling

From previous discussions one could have gotten the impression that

a typical 1H NMR spectrum exhibits just one signal for each set of

equivalent 1H-nuclei and that the same thing is true for 13C spectra,

as well as for spectra of any other isotope. However, there are many

more lines in a spectrum, and while these extra lines do make a

spectrum more complex, they also offer valuable structural

information that complements the chemical shift data.

1H -

1H


CH3CH2OH:!!The spin states of two hydrogens (methylene group):

! For methyl hydrogens the net experienced field will depend on the magnetization of the neighboring methylene group!

! The methyl signal will be split into three lines with intensity ratio 1 : 2 : 1 (= spin-spin-coupling, homonuclear coupling because the coupling is between nuclei of the same isotope). ! Triplet.

B0

Total MagnetizationM=-1 0 0 1

Three spin states with population ratio of 1:2:1

Accordingly, for the methylene signal, the possible spin states of the

methyl group determine its multiplicity (number of lines in the

signal).

The spin states of three hydrogens:

M=3/2

M=1/2 M=-1/2

M=-3/2

4 spin states with populationratio of 1 : 3 : 3 : 1

Quartet


Accordingly, a doublet is observed for hydrogens that are coupled to

a methine (CH) proton.

The multiplicity of a given resonance = n+1 (n=# of neighboring

equivalent nuclei). The relative intensities of the multiplet follow

Pascal’s triangle.


J = spacing between lines.

The slight difference in energy between the resonances is the

coupling constant J [Hz]. J’s are independent of instrumental

parameters!

J J

Consider a 3-spin system with/without equivalent nuclei:

Ha will be a doublet with

3J

ab

Hb will be a “doublet of doublets” with 3Jab and

3Jbc

Hc will be a doublet with

3J

bc

C

Ha

C

Hb

C

Hc


Jab

Ha Hb Hc

Jbc

Jbc

Jab


13C NMR

• 12C (98%) has I = 0 ! no NMR

• 13C (1.1.%) has I = 1/2 ! NMR

•

• Observe typically 0 – 230 ppm (rel. to TMS)

(! = h" = #hBo/2$ % gyromagnetic ratio such that "obs & 1/4 that of 1H (300 MHz ' 75 !MHz)

Typically decouple the protons by saturating them with a second

broadband RF puls (double resonance technique, second

transmitter coil; “white noise” ! if the irradiating field is strong

enough, not only will the 1H nuclei approach saturation, but virtually

all the 1H magnetization will be tipped into the x1y plane. Since the 1H

nuclei are no longer aligned with (or against) the applied field (which

is along the z axis) they can no longer augment or diminish the

magnetic field experienced by the carbons. As a result, the coupling

interaction disappears, and each 13C multiplet collapses to a singlet!

(D coupling not effected!)

! causes all 13C resonances to be singlets

! affords Nuclear Overhauser Effect

! makes integration of 13C spectra unreliable


Aromatics: not effected by ring current

substituted C’s are typically of lower intensity

128.5 ppm

176.8 176.8

++

209.0 102.1

- -

85.3


Carbonyls:

O O

H

O

OH

O

OEt

O

ClRO OR

O

NH

CH3

O

I

205.1 199.6 177.3 169.5

168.6

~ 100 - 110

Heavy atom effect.

174.9 158.9


Documents

The Absorption Laws - CCC/UPCMLDccc.chem.pitt.edu/wipf/Courses/1140_05_files/Spectroscopy.pdf · Chem 1140; Spectroscopy ¥ UV-VIS ¥ IR ¥ NMR The Absorption Laws I1 I0 I I2 Detector