Most common spectroscopies that produce either a full spectrum, a tensor, or a scalar value have a specific instrument associated with them that is relatively self-contained and not custom. For example, (linear) IR spectra come from benchtop FT-IR spectrometers, NMR chemical shifts use a FT-NMR spectrometer (which is capable of many experiments), and so on. One spectroscopic property that serves as a benchmark for electronic structure theory and is important for designing optical materials is the (electric dipole) polarizability, which "is defined as the ratio of the induced dipole moment $\mathbf{p}$ of (a molecule) to the electric field $\mathbf{E}$ that produces this dipole moment":

$$ \mathbf{p} = \alpha \cdot \mathbf{E}. $$

Physically, this corresponds to how easy it is to shift a system's charge density or electron cloud around. More explicitly, it is a symmetric rank-2 tensor:

$$ \begin{bmatrix} p_{1} \\ p_{2} \\ p_{3} \end{bmatrix} = \begin{bmatrix} \alpha_{11} & \alpha_{12} & \alpha_{13} \\ \alpha_{21} & \alpha_{22} & \alpha_{23} \\ \alpha_{31} & \alpha_{32} & \alpha_{33} \end{bmatrix} \begin{bmatrix} E_{1} \\ E_{2} \\ E_{3} \end{bmatrix}, $$

as the applied electric field may have 3 independent Cartesian coordinates, and the system being measured may have some anisotropic response to this field. In some cases, calculating the tensor may be time-consuming, but formulation is well-understood and there are standardized methods for doing so. However, it is not obvious to me how it is measured experimentally. There is the Lorentz-Lorenz equation (rearranged),

$$ \alpha = \frac{n^2 - 1}{n^2 + 2} \frac{3}{4\pi N}, $$

which relates the refractive index $n$ of a system or medium to its polarizability. There is also the Clausius-Mossoti relation, which relates the dielectric constant $\epsilon$ to the polarizability, as the refractive index and (complex) dielectric constant are related:

$$ n \propto \sqrt{\epsilon}. $$

This implies to me that if you can measure the refractive index with a refractometer, then that is the preferred way of measuring the polarizability.

  • Is the refractive index the most common method of experimentally measuring the polarizability? Can it be measured directly, or must be through a relationship such as those above?
  • Does this relationship hold for oriented (anisotropic) polarizabilities, or only averaged (isotropic) ones?
  • The refractive index and the polarizability are frequency-dependent properties. How is the static (frequency-independent) polarizability measured? Or, is it even possible without extrapolation from multiple frequency-dependent data points?

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.