What Are the Basics and Techniques of Rotational/Vibrational Spectroscopy?

[Gokul43201]

The intent of this thread (for now) is to introduce the basic theoretic principles of rotational/vibrational spectroscopy, follow this up with a brief sketch of the expermiental techniques and finally zoom in on the experimental and theoretical aspects of a specific technique of recent interest - for which I've chosen Matrix Isolation Spectroscopy.

As of now, this is what I have in mind (and I expect to devote no more than a couple of posts to each sub-topic, barring questions or other responses) :

PART 1 : Theory of rotational/vibrational spectroscopy :

- - - classical derivation of Raman/IR/Rayleigh scattering

- - - useful intuitions for determining Raman and IR active modes of simple inorganic molecules

- - - sketch of quantum picture and comparison with derived classical results

- - - (maybe) a brief recap of the rigid rotor model for vibrational levels of simple molecules

- - - selection rules and some explanation of their origin

- - - application to identification of organic molecules/functional groups

- - - (maybe) qualitative explanation of a real spectrum based on theory developed in thread

[At this point - and, in fact at any point in the "discussion" - others are invited to correct me, add insights or ask questions about things I've posted so far.]

PART 2 : Experimental Techniques :

- - - Sample preparation : brief overview

- - - Raman Spectroscopy; Surface Enhanced Raman

- - - IR Spectroscopy; FT-IR

- - - (maybe) FT-IR, Raman microscopy

PART 3 : Matrix Isolation Spectroscopy

- - - Introduction

- - - list of references for some recent papers in MIS

- - - "free for all" discussion

Parts 2 and 3 are less well-planned in my head right now, and will likely evolve significantly from the above outline, as the thread progresses.

As a disclaimer, I should add that most of what I know and will talk about is stuff that I've read from various papers, texts or websites or have thought about over lunch. Very little of what I know comes from formal, classroom instruction, so others that are more strongly trained in the areas of discussion are urged to help, correct or supplement me.

<photon, I'll get to your question in a little bit>

It's hard to find any readable introductions to Spectroscopy, so I'll give you a simple outline. If anyone has links to any simple introductions to spectroscopy, please post them.

The idea of using spectroscopy as an analytical (qualitative) tool is based on the fact that different molecules have different electronic, vibrational and rotational energy levels which can serve as identifiers. The process simply involves irradiating the molecules under study with light and studying the spectrum of absorbed or emitted radiation. The incident photons are absorbed by the molecules/electrons causing them to be promoted to excited states. The electron/molecule then falls from this excited state to a lower state, and from there to yet another lower state and so on. Each of these lowerings is accompanied by the emission of a photon (to ensure conservation of energy).

Thus by looking at the energies of the emitted photons, one gets an idea about the energy differences between different quantum states of the molecule and from this data, can deduce what the molecule is.

 

[Gokul43201]

In the next few posts I'm going to sketch a couple of "semi-derivations" of some important and useful concepts.

The first is a simplistic argument to help you feel comfortable the idea of polarizability - and that's a key character in the Spectroscopy story. I'll run through a quick derivation to help this idea stick.

Consider an isolated atom which we shall approximate as a pointlike nucleus of positive charge 'q' at the center of a spherical cloud of negative charge '-q' and radius 'r' (fig 1).

An external electric field is applied, which separated the centers of positive and negative charge by a distance 'd'. Now, in equilibrium, the force on the positive charge from the field must equal the opposite force from the negative cloud. The force due to the negative cloud can be calculated from the electric field due the this cloud at the position of the positive nucleus.

F (external~ field) = qE
F (negative~cloud) = qE_{cloud}

The value of E_{cloud} follows directly from Gauss' Law :

E_{cloud} = \frac{q}{4\pi \epsilon_0 d^2} \cdot \frac{d^3}{r^3}
\implies ~F (negative~cloud) = \frac{q^2}{4\pi \epsilon_0} \cdot \frac{d}{r^3}

Setting these forces equal to each other gives :

qE = \frac{q^2d}{4\pi \epsilon_0 r^3}

\implies qd = (4\pi \epsilon_0 r^3) ~ E

Noticing that the quantity on the left is nothing but the dipole moment, this gives :

p = (4\pi \epsilon_0 r^3) ~ E = \alpha E~,~~say

The proportionality constant \alpha, is called the polarizability. So, we have :

\alpha = 4\pi \epsilon_0 r^3 = 3 \epsilon_0 V
where V is the volume of the atom.

The moral of this simplistic argument is that the polarizability can be thought of as a quantity that is proportional to the atomic/molecular volume.

This is a very handy Rule of Thumb to keep in mind. It will be useful later, to help identify when the polarizability changes - all you have to do is look for a change in the volume of the molecule.

 

[Gokul43201]

In the next post (sometime tomorrow), I shall skim go over a classical derivation of scattering from a vibrating dipole and show how this gives rise to IR and Raman spectra. This will be followed up by a couple of examples where we'll apply the above results to determining the IR/Raman activity of a few simple compounds. The argument and the math will be kept simple to allow it to be accessible to a wide audience.

I shall follow this up with a simplistic sketch of the quantum picture, and use this to sort out one important inaccuracy of the classical result. At this point, I'll also introduce the effect of rotational eigenmodes to the spectra.

With that, I shall assume the theoretical groundwork (more or less complete) complete and move on to a discussion of techniques and applications.

Also, I intend to restrict this discussion to IR and Raman spectroscopy (if UV/Vis comes up along the way, so be it; but for the most part, I'd like to not get into XRD, NMR and other stuff in this thread).

 

[photon79]

Thank you Gokul,,but I have exam on 7th so if possible please reply to my specrtoscopic threads (also those regarding P,Q,R branches in solidstate forum, if you want I'll post them again here) as soon as possible.
Just give small and adequate replies and then we can continue on the regular discussion.And make this thread Sticky if possible!
Thanks!

 

[Gokul43201]

Okay, then I'll start by sketching the quantum picture - which I think might help clarify your doubt.

Consider a molecule sitting in one of its vibrational eigenstates. If the spacing between states is large or comparable to thermal energies (kT), the likelihood of this being a highly excited vibrational state will be low in the absense of incident radiation. In fact, the probability of occupation is given by the Bose occupation factor (since normal modes are bosons).

An incident photon in the visible range can excite [1] this molecule to some high state (often referred to as a "virtual state"). The molecule then falls back to one of the low-lying vibrational states. If it falls back to the original state, the emitted frequency is the same as the exciting frequency, and you have what is known as Rayleigh Scattering (the reason why the sky is blue). If the molecule falls back into one of the neighboring vibrational states, the emitted frequency will differ from the exciting frequency by \omega_n, the spacing between the vibrational states. This emission makes up the Stokes [3] and Antistokes [2] lines of the Raman Scattering spectra. If it falls by to an excited vibrational state, the molecule can subsequently fall further to lower lying vibrational states by IR emission [4],[5].

 

[Gokul43201]

The next step in laying the foundations is a simple, classical "semi-derivation" of inelastic scattering from a vibrating dipole.

In this derivation we treat scattering as the radiation from an oscillating dipole - the oscillations induced by the incident radiation and by existing vibrations in the molecule.

Let's start with a molecule that has intrinsic dipole moment \mathbf{p_0} in the absense of an applied electric field (from the incident light). Now, if we turn on the light, there is an applied field \mathbf{E} = \mathbf{E_0}cos(\omega_0t), and an induced dipole moment due to it. Recalling the expression for the induced moment from the earlier post, we have :

\mathbf{p}(t) = \mathbf{p_0} + \mathbf{p_{ind}} = \mathbf{p_0} + \alpha \mathbf{E} = \mathbf{p_0} + \alpha \mathbf{E_0}cos(\omega_0t) ~~~--(1)

Now consider that the molecule is set into vibrations, either by the external field or due to collisions with other molecules (ie : "thermally"). Without going into the details of the nature of these vibrations let's assume that there exists a set of natural frequencies (also known as normal modes) that the molecule will choose to vibrate in, that are a characteristic of the molecule. Assume it is in one of these vibrational modes, with frequency \omega_n.

As a result of this vibration, we would expect the intrinsic dipole moment \mathbf{p_0}, and the polarizability \alpha, of the molecule to also oscillate at the same frequency about some mean value. After all, both these properties depend on the geometry of the molecule, which is changing at a frequency \omega_n.

So, we replace :

\mathbf{p_0} \longrightarrow \mathbf{p_0} + \mathbf{p_1}cos(\omega_nt)~~~--(2)<br />
\alpha \longrightarrow \alpha_0 + \alpha_1cos(\omega_nt)~~~--(3)<br />

Now, it is possible, depending on the symmetry of the molecule and the nature of the vibrational mode involved, that either the dipole moment or the polarizability not change with the oscillations of the molecule. In such cases, we would have \mathbf{p_1}=0 or \alpha_1=0. This is an important aspect that we shall utilize later.

Plugging (2) and (3) into (1) gives :

\mathbf{p}(t) = \mathbf{p_0} + \mathbf{p_1}cos(\omega_nt) + [\alpha + \alpha_1cos (\omega_nt)][\mathbf{E_0}cos(\omega_0t)]

(and using the sum rule for cosines 2cosAcosB = cos(A+B) + cos(A-B) from kindergarten trigonometry )
=\mathbf{p_0} + \mathbf{p_1}cos(\omega_nt) + \alpha \mathbf{E_0}cos(\omega_0t) +\frac{1}{2}\alpha_1 \mathbf{E_0}cos(\omega_0 - \omega_n)t + \frac{1}{2}\alpha_1 \mathbf{E_0}cos(\omega_0 + \omega_n)t ~~~--(4)

This last line above delivers a wealth of information (which I summarize below) !

0. What I've done so far is simply separate out the different contributions to the dipole moment by their frequencies.

1. The first term is a constant, non-oscillating term, and will produce no radiation - so we ignore it.

2. The second term represents an oscillation at the frequency \omega_n - one of the natural vibrational frequencies of the molecule. This will give rise to radiation that oscillates at this same frequency, \omega_n. On the spectrometer, we see a peak at \omega_n, which is nothing but the contribution to IR scattering.

3. The third term represents an oscillation at the frequency \omega_0 - the frequency of the incident light. This is nothing but Rayleigh Scattering, and will produce a peak at \omega_0 on the spectrometer.

4. The fourth and fifth terms are contributions to Raman Scattering. They give rise to peaks at frequencies \omega_0- \omega_n and \omega_0 + \omega_n - equally spaced on either side of the Rayleigh peak, and separated from it by the natural frequency \omega_n. These two satellite peaks are called the Stokes and Anti-Stokes lines of the Raman spectrum.

We have thus extracted the essential features of vibrational spectroscopy from a simple classical calculation involving radiation from an oscillating dipole.

http://www.fbi.gov/hq/lab/fsc/backissu/oct2001/images/eknrf2cs.jpg

 

[Gokul43201]

Notice from eq(4) above, that the IR term will be absent if \mathbf{p_1} =0 and the Raman peaks will disappear if \alpha_1 = 0. And going back a few lines, we recall that these terms are zero if the dipole moment or polarizability does not change as the molecule oscillates in a certain mode.

Now while it's easy to guess whether or not the dipole moment changes, it would appear to be harder to guess when the polarizability changes. Fortunately, for this purpose, we've developed the intuition (in post#3) to associate polarizability with molecular volume. So, to tell if the polarizability changes we would only have to look for a change in the volume.

When the IR term is present (ie : the dipole moment does change during oscillations), we say the molecule is "IR active" in that vibrational mode. When the Raman terms are present (ie:when the polarizability changes) we say that the mode is "Raman active".

In the next post I'll illustrate how we determine IR and Raman activity in a couple of simple molecules (say CO2 and H2O) with different symmetries.

 

[GCT]

I'll be sure to read up on this when I have the time, I was hoping to get more familiar with spectroscopic concepts.

 

[Gokul43201]

I'll post a couple more posts going over the basic theory before we can talk about methods and techniques. For that part, I'd like to invite others, like GCT, inha, Claude or anyone else that has direct knowledge of the field. If no one takes on the offer, I'll summarize those over a couple of posts and then introduce the topic that I started this thread for : Matrix Isolation Spectroscopy.

In the next post, we'll figure out the IR and Raman activity of some of the modes of CO2 and H2O, based on the theory developed above. After that, I'll probably say a little something about rotational modes (not deriving anything more than just the simple rigid rotor results) and describe how they typically affect the spectrum.

 

[inha]

I'll post a couple more posts going over the basic theory before we can talk about methods and techniques. For that part, I'd like to invite others, like GCT, inha, Claude or anyone else that has direct knowledge of the field. If no one takes on the offer, I'll summarize those over a couple of posts and then introduce the topic that I started this thread for : Matrix Isolation Spectroscopy.

I don't think I can contribute here as I only have experience on x-ray spectroscopy and I don't even know what MIS is. But I'm looking forward to finding out about it.

 

[Moonbear]

Note for those following this thread: the Original Post, as best I can tell, was eaten by PF Gremlins. Gokul has recreated the content, and I've edited it into the first post that's actually appearing in the thread now. I've split a couple of posts off into a new discussion, because they had no way to know what the topic really was without the OP appearing, thus drifted off topic. Hopefully everything is remedied here.

 

[inha]

It's hard to find any readable introductions to Spectroscopy, so I'll give you a simple outline.

Are there any? I doubt it. I think the best (non old professor dude who knows everything) sources are review articles on the particular spectroscopic method one is interested about.

Anyways, I might have some input on the QM-picture but I'd rather wait until I've seen what and at what level you had in mind.

 

[Gokul43201]

Anyways, I might have some input on the QM-picture but I'd rather wait until I've seen what and at what level you had in mind.

I don't intend to go into much depth there...just throw in a couple of illustrative arguments.

First, I plan to explain the different intensities of the stokes and anti-stokes lines (based on Bose occupation numbers) - a result that conflicts with the classical calculation above (which predicts equal intensities). After that, I was thinking I'd do a quick derivation of the rotational levels of a rigid rotor (maybe throw in a paragraph about the classical limit, \hbar \omega &lt;&lt; k_BT), and use this to hand-wave an argument on how rotational eigenstates show up in the IR spectrum.

That's all I have in mind for that, so feel free to add your inputs whenever you think they'll be useful.