Rather than just throwing a selection rule out there, I find it is helpful to show what the selection rule means and where it comes from. This can help students understand the nature of spectroscopic transitions. Take what you want from this.
First, a word about light:
Light can be described as an oscillating electronmagnetic field. Ignore the magnetic component for now. For the purpose of basic spectroscopy, light is an oscillating electric field and the electric field vector can be described by a sinusoidal function. The magnitude of the electric field gets large in one direction, reaches a maximum, gets smaller, passes through zero, then gets large in the opposite direction, reaches a maximum, gets smaller, passes through zero, and so on. The direction of propogation of a photon is perpindicular to the direction of the electric field oscillation. So, if the photon is moving in the z-direction, the electric field is getting larger/smaller in either the y-direction, the x-direction, or some intermediate between the y- and x-direction. Polarized light is light in which the electric field oscillations of all the individual photons in a "beam" are oriented in the same direction. So - y-polarized light is light in which every photon is travelling in the z-direction and the electric fields are oscillating in the y (and -y) direction.
Here are a few crude but very simple figures illustrating this concept:
http://www.cfht.hawaii.edu/~manset/PolarIntro_eng.htmlNow a word about how a charge behaves in an electric field:
Simply put, a stationary point charge experiences a force when in the presence of an electric field. In the presence of an oscillating field, the point charge will experience an oscillating force - it will want to move back/forth in a direction parallel to the direction of the electric field vector.
With that brief background, can we understand why vibrational transitions require a change in molecular dipole moment?
In the quantum mechanical model, the energy states of molecules and atoms are quantized, which is a fancy way of saying that molecular/atomic systems can only take on certain energy values. We might define these as "states" of the system. Each various allowed state is thus defined by an energy value and is characterized by some spatial arrangement of the system's particles (electrons and nuclei) in space. Since these particles are charged, each state is characterized by a specific charge distribution. The dipole moment is a reflection of any (average) asymetry in the charges in space for a particular state - i.e., if at a certain energy state there are more negative charges one side of the molecule than the other, we'd say the state has a non-zero dipole moment.
The basic mechanism with which light can interact with matter is by moving charged particles around, a process which takes energy. This is essentially what it means for a molecule to "absorb" a photon. The fundamental question we're asking is: under what circumstances can an incident photon transfer a molecule/atom from one of these states to the other?
In a first approximation, there are two basic criteria that must be met for light to induce a molecular change of state:
1. The energy of the photon must be the same (or nearly so) as the difference in energy between the two states. In a classical system, this is the same as saying that in order to throw a ball to the top of a hill, you must provide at least enough energy to get it up there - otherwise it will fall short. The difference between the classical and quantum world is that while in a classical world you can throw the ball halfway up the hill by providing half the energy needed to get to the top, in the quantum world the ball either has to go to the top of the hill, or it goes nowhere. There are no half-measures allowed in the quantum world.
2. The photon has to be able to drive the spatial rearrangement of the particles (electrons/nuclei) between the initial and final state. This is probably best demonstrated by an rough analogy. Supposing a molecule is a sailboat and the initial state of the sailboat is New York and the final state of the sailboat is London. The light in this analogy is wind. Even if the wind is blowing with sufficient energy to get your boat from New York to London, you won't get there unless the wind is blowing east. The only change in state an east-bound wind can produce is a change in state from New York to, say, Boston. Likewise, using wind alone it is not possible to induce a change in state from New York to a cloud directly above New York, because there is no directional change that wind can induce in order to drive this change of state (ignoring the possibility that the wind can blow straight up).
Let's think about how that works in a vibrating molecule. For the moment, let's pretend the molecular and laboratory frames are both fixed. And let's assume that light is propogating in the z-direction and it is x-polarized, so that means the electric field is only oscillating in the +x and -x direction. Now let it be incident on a single molecule fixed in space but allowed to vibrate. It's hard to depict this graphically, but let the direction of propagation be indicated by the arrow and we'll have a diatomic molecule X-Y oriented along the same axis (call it z-axis - left to right on your screen) as follows:
X-Y
The electric field, note, is "up" and "down" in the plane of your computer screen.
The molecule X-Y has a permanent dipole moment. And when it vibrates, the dipole moment increases and decreases in an oscillatory fashion (when the bond length is long, the dipole moment increases and when the bond length is short, the dipole moment decreases; dipole moment is the difference in charge magnitude times separation distance). When the molecule absorbs energy, the vibration becomes...er... more vigrorous and the average separation between the nuclei increases. This has the effect that the average dipole moment increases between the lower state and the upper state. Dipole moment is a vector (it's oriented in a direction) and in our X-Y molecule, the dipole moment is oriented also along the z-axis. So, to induce a change in a vibrational state - that is, for the molecule to absorb the energy of a photon and have that energy go into increasing the energy of the molecular vibration - the electric field of the photon has to be in the same direction as the dipole moment change. If it is isn't, the "force" of the electric field can't move the "charges" in the molecule associated with the change in vibrational state. The wind isn't blowing in the right direction. In the orientation shown above, the electric field direction is perpendicular to the dipole moment vectors, so no transition is allowed. Light travelling in the z-direction cannot induce a change on the X-Y molecule when the bond axis is also the z-direction.
Compare that scenario to this one:
X-Y
Now, the direction of propogation is in the y-direction (say) and the electric field is oriented in the z-direction. The electric field can interact with the molecular vibration and the transition is allowed - provided the energy of the photon is equal to the energy difference between the lower and upper vibrational states.
Some additional but very important notes:
1. so far we've only looked at situations where the light vectors are either parallel or perpendicular to the dipole moment vector. Obviously, this doesn't have to be the case. The probability of a transition occurring is actually related to the square cosine between the two vectors.
2. In a real laboratory frame, the molecular axes are not fixed in space. Molecules are oriented in random directions. What this means in practice is that unless molecules are frozen in an aligned way, the directionality of the dipole moment vector doesn't really matter. As long as there is some dipole moment change between the states, there will be some molecules at any point in time which can interact with the light's electric field.
This second bit is the origin of the common wisdom that a vibrational transition has to involve a change in dipole moment to be allowed. Molecules with more than two nuclei have multiple possible vibrations. Only those changes in vibration state that involve a change in dipole moment are able to be induced by the oscillating electric field of the incident light. Higher vibrations of a symmetric molecule like nitrogen (N2) certainly exist, but they cannot be produced (to a first order approximation) with light, because there's no way for an electric field to "push" the nuclei in dinitrogen further apart - there's no charge asymmetry to interact properly with the electric force. As the previous poster noted, though, a permanent dipole moment is not required - carbon dioxide is symmetric and has no permament dipole moment, but some vibrations involve an asymmetric motion of the nuclei, such that higher vibration states DO have a non-zero dipole moment. There is a dipole moment change, so the "transition dipole" can couple with the light electric field in this case.
As a final note, this discussion has been completely qualitative. A quantitative assessment of "allowedness" results from solution of the transition dipole moment integral, which uses the initial and final state wavefunctions and the dipole moment operator. Solving this expression will tell you what properties of the initial and final states lead to allowed transitions (and, in principle, can quantify the probability of a transition). In the case of vibrational transitions, for example, not only is a dipole moment change required, but only transitions between adjacent states are allowed, at least in a first, harmonic oscillator approximation. In essence, though, the meaning of this integral is essentially what has been presented above: what is the ability of the light electric field to induce a change between the initial state and the final state, and this ability relates to the efficiency of coupling between the change in dipole moment between the two states and the electric field of the incident photon. Note also that these considerations also apply to other kinds of transitions, such as rotational and electronic. But the vibrational selection rules are especially easy to understand because "vibration" is a very pseudoclassical phenomenon.
http://en.wikipedia.org/wiki/Transition_dipole_momentRegarding your follow up question:
With the exception of symmetric diatomic molecules, virtually every molecule has IR-active modes, because there are always asymmetric vibrations (stretches and bends/wags/whatever). Therefore the question isn't what molecules are IR-active, but which vibrational modes are, where they appear, and how strong they are. Predicting all the modes of molecules requires some fairly sophisticated symmetry and/or quantum mechanical treatments that are beyond the scope of this thread. Also note that in big molecules, usually it is vibrations of functional groups that are the focus of practical study rather than vibrations that span the entire molecule, because vibrations in very large molecules aren't necessarily "globally coordinated". So we usually speak of C=O stretches and so forth rather than, "the stretching mode of trypsin".
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Topic: IR Radiation (Read 11924 times)