vibration and rotation spectroscopy

8/3/2019 VIBRATION AND ROTATION SPECTROSCOPY

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VIBRATION AND ROTATION SPECTROSCOPY:

INFRARED, RAMAN AND MICROWAVE

Classical description of the vibrational motion of a diatomic molecule

r

k = Hookes law constant for the spring= force constant for a molecular system held together by a chemical bond

For harmonic oscillation of two masses connected by a spring, a plot of the potential energy ofthe system as a function of the distance r between the masses is a parabola which is symmetrical

about the equilibrium internuclear distance, re, as the minimum.

A B

A A

r

Energy

3

2

1

0


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Permitted energy states of a molecule which is a simple harmonic oscillator:

E = h (V + )

Where v is an integer 0, 1, 2, - the vibrational quantum number of the various states

E - the energy of the vth statehPlancks constant

- the fundamental vibration frequency (/sec)- the frequency for the transition from state, v = 0 to v = 1

ABSORPTION OF RADIATION BY MOLECULAR VIBRATIONSSELECTION

RULES

1. In order for molecules to absorb infrared radiation as vibrational excitation energy,there must be a change in the dipole moment of the molecule as it vibrates.

2. In the absorption of radiation only transitions for which v = +1 can occur.Force Constant

The difference in energy, E, between two adjacent levels, E and E + 1

E = (h/2) (k/)1/2

k = the stretching force constant

= the reduced mass for the diatomic molecule A - B, mAmB/ (mA + mB)

Stretching force constants for bonds 13 to 18 x 105

dynes/cm

= bonds 8 to 12 x 105

dynes/cm- bonds - < 8 x 105 dynes/cm

Asymmetric stretch occurs at higher frequency than the symmetric stretch while stretchingmodes occur at much higher frequencies than bending modes.

Combination bands absorption of radiation of these energies occurs with the simultaneousexcitation of both vibrational modes of the combination.

Difference bandinvolves a transition from the state in which the 2 mode is excited to that inwhich the 1 mode is excited.

Fermi resonancethe overtone and the fundamental should occur at almost the same frequency.


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RAMAN SPECTROSCOPY

Concerned with vibrational and rotational transitions A monochromatic beam of light illuminates the sample and observations are made on the

scattered light at right angles to the incident beam.

In order for a vibration to be Raman active, the change in polarizability of the molecule with

respect to vibrational motion must not be zero at the equilibrium position of the normal

vibration.

In general, for any molecule that possesses a center of symmetry, there will be no fundamental

lines in common in the infrared and Raman spectra.

Microwave Spectroscopy

Pure rotational transitions in a molecule can be induced by radiation in the far IR andmicrowave regions of the spectrum. Resolution of about 10-8 cm-1 can be obtained in the microwave region

Accurate bond distance and bond angle data can be obtained from these studies Two requirements which impose limitations on microwave studies:

o The spectrum must be obtained on the material in the gaseous state. A vaporpressure of about 10

-3mmHg is required.

o The molecule must have a permanent dipole moment in the ground state in orderto absorb microwave radiation.

Rotational energy, E for a diatomic molecule, E = hBJ(J + 1) where B = h/82I(moment of inertia)

Selection rule for microwave absorption states that J = 1. The longest wavelengthabsorption band in the spectrum will correspond to the transition J = 0 to J = 1 for which = 2B = 2h/8

2I Once the moment of inertia is determined, the equilibrium internuclear separation in the

diatomic molecule can be calculated, I = ro2

The bond distance and I will be larger for high values of J and the spacings between thepeaks will decrease slightly as J increases.

Rotational Raman Spectra The bands are detected as Stokes lines with frequencies corresponding to rotational

transitions.

In order for a molecule to exhibit a rotational Raman spectrum, the polarizabilityperpendicular to the axis of rotation must be anisotropic.

For diatomic molecules the selection rule J = 2 applies E = Bh(4J 2) and the frequency separation between the lines is 4B.

Spectra of Gases Presence of fine structure in the gaseous spectrum o and or


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Q branch

R branch P branch

Q branch corresponds to the transition in which r = 0 R branch to o + r and the P branch to o - r = o + 2hm/82I m = 0, a Q branch results; m < 0, lines in the P branch result (Jn + 1 Jn transitions) m > 0, lines in the R branch result

Selection rules for the combination of vibration and rotation transitions:

1. Diatomic molecules. Most diatomic molecules do not possess a Q branch. (L = 0, no Qbranch).

2. Linear polyatomic molecules.a. If the changing dipole moment for a given vibrational mode is parallel to the

principal rotation axis in the molecule, parallel band results which has no Q

branch. J = 1

b. If the dipole moment change for the vibration has any vector componentperpendicular to the principal axis, a perpendicular band will result with a Qbranch. J can be 0, 1.

3. Nonlinear polyatomic molecules.a. Nonlinear molecules has 3 finite I.b. In a spherical top, all three moments are equal. The selection rule for a

perpendicular band is J = 0, 1.

c. In a symmetric top, two of the three moments are equal. Any molecule with a 3or higher fold rotation axis is a symmetric top molecule.

d. In an asymmetric top, none of the three moments are equal.


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Boardwork:

1. Determine the symmetry of the normal modes of vibration of the methane molecule andassign the symmetry labels to the following observed bands for the fundamental

vibrations: 1 = 2914.2; 2 = 1526; 3 = 3020.3 and 4 = 1306.2 cm-1

.

2.

The infrared and Raman spectra of Fe(CO)5 exhibit the following bands:

Metal-carbon region Carbonyl region

IR 472, 377 cm-1

2028, 1994 cm-1

Raman 492, 414, 377 2114, 2031, 1984

By means of selection rule arguments and using these data, decide on the most probable

structure for Fe(CO)5.

3. What effect should one expect to see in the IR spectrum if one Y atom of the trigonalplanar XY3 molecule is substituted with a Z atom to give the planar XY2Z molecule?

vibration and rotation spectroscopy

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