This repo is a demonstration of material classification based on the Goldhammer-Herzfeld criterion, and its comparison with machine learning. Herzfeld’s theory is based on the classical (Lorentz) oscillator model of an atom. Herzfeld pointed out that electrons localized around atomic nuclei constitute polarizable objects and that their internal dynamics in the dense assembly of the element leads to local corrections to the polarizing tendency of any external field impressed on the system. He proposed that the corresponding element (viewed obviously as a collection of atoms) becomes metallic when the frequency of the oscillator placed in this dense, dielectric medium approaches zero; i.e. the valence electron is set free and the element—under those critical conditions—acquires metallic status. Assuming long range interactions are isotropic, the relevant equation from the Lorenz–Lorentz or Claussius–Mosotti relation is then:

Where n is the index of refraction, epsilon is the dielectric constant, alpha is the atomic electronic polarizability, V is the molar volume, and R is the molar refractivity. When R/V = 1, n or epsilon diverge, which can only occur if the electrons are no longer bound to individual atoms (i.e. the system becomes metallic).

Below, we reproduce one of the figures from the 2015 work of Friedrich Hensel, Daniel R. Slocombe and Peter P. Edwards link where they show this criterion's ability to separate metallic and non-metallic elements under ambient conditions on Earth. Our data's R/V values differ slightly from theirs probably due to a different source for the atomic polarizabilities or molar volumes.

Using 21 chemical descriptors from the Magpie feature set, we train a machine learning model to also perform this classification. Here is a comparison from one cross-validation run.

• molar_refractivity.ipynb: Jupyter notebook containing data processing and plots
• Elemental_conductivities.xlsx: Ambient conductivity values for elements
• molar_refractivities.csv: Molar refractivities computed from Clausius–Mosotti relation, molar volumes, and R/V ratios.

Atomic polarizability values are taken from the CRC Handbook of Chemistry and Physics 85th edition Chapter 10 page 168. Molar volumes are taken from Mathematica's ElementData function via periodictable.com. Elemental conductivity values are available from Mathematica and Angstrom Sciences.