Experimental importance of the dipole moment

The electric dipole moment lies at the heart of a widely used experimental method for probing the vibrational dynamics of a system. If a system is exposed to a monochromatic electromagnetic field from a laser, then the electric dipole moment couples to the electric field component ${\bf E}({\bf r},t)$ in such a way that the energy is

$${\cal E} = -{\bm \mu}\cdot {\bf E}({\bf r},t)$$

In general, the electric field is a function of space and time having the general wave form

$${\bf E}({\bf r},t) = {\bf E}_0\cos\left({\bf k}\cdot {\bf r}- \omega t\right)$$

where $\omega$ is the frequency of the field $\omega = 2\pi c/\lambda$, with $c$ the speed of light and $\lambda$ the wavelength, and ${\bf k}$ is called the wave vector, $\vert{\bf k}\vert = 2\pi/\lambda$, and the direction of ${\bf k}$ is the direction of wave propagation (this will be covered in more detail next semester). In most experiments, the wavelength is long enough compared to the size of the system studied that one can take the electric field to be spatially constant and consider only the time dependence. In this case,

$${\cal E} \approx -{\bm \mu}\cdot {\bf E}_0 \cos(\omega t)$$

Thus, the electric field varies as a simple cosine function at a single frequency $\omega$.

The importance of the coupling between the dipole moment and the time-dependent electric field is that the frequency of the field can be varied over a range of natural frequencies in a given chemical system. Thus, chemical bonds vibrate at a particular natural frequency, three-atom bending modes have their characteristic frequency, etc. What one seeks in this experiment is a ``report'' of the natural frequencies in the system, since from such a report, one can often tell one local chemical environment from another.

By sweeping through a range of frequencies, the coupling of the field to the dipole moment suggests that the local charge distribution will respond to the oscillations of the field at the field frequency. Thus, if the field frequency is ``tuned'' to be that of a bond stretch, the charge distribution in the bond will be stimulated and report on the frequency of the bond, etc. At each frequency, the intensity $I$ of the response can be measured, and a plot of $I$ vs. $\omega$ is produced. Such a plot is called an infrared spectrum. The figure below shows the infrared spectrum for liquid water (left) and for 13 M (blue) and 1 M (red) KOH solutions (right).

In the left panel, the solid curve is the water spectrum obtained from a computer simulation, while the dashed curve is the experimentally obtained spectrum. On the right, the red and blue curves are from computer simulations, while the inset at the upper right is the experimentally measured spectrum. The peaks in the spectra occur at particular vibrational frequencies in the system. The water spectrum shows very distinct bands, while the spectrum of the KOH solutions shows both bands and continuum regions. The latter arise from the fact that protons can be transferred from water to hydroxide. As the proton moves across a hydrogen bond between water and the hydroxide ion, the vibrations in the bond sweep through a range of frequencies as the proton is transferred, giving rise to the continuum. This feature in the infrared spectra of solutions of strong acids and bases is known as Zundel polarization. More information on how we compute these spectra and how the computer simulation are performed can be found in the following research papers:

H. S. Lee and M. E. Tuckerman, J. Chem. Phys. 126, 164501 (2007)

Z. W. Zhu and M. E. tuckerman, J. Phys. Chem. B 106, 8009 (2002).

These and any other scientific papers can be accessed through the Web of Science www.isiknowledge.com.