The demarcation of the chemical elements into metals and non-metals dates back to the dawn of Dmitri Mendeleev's construction of the periodic table; it still represents the cornerstone of our view of modern chemistry. In this contribution, a particular emphasis will be attached to the question 'Why do the chemical elements of the periodic table exist either as metals or non-metals under ambient conditions?' This is perhaps most apparent in the p-block of the periodic table where one sees an almost-diagonal line separating metals and non-metals. The first searching, quantum-mechanical considerations of this question were put forward by Hund in 1934. Interestingly, the very first discussion of the problem-in fact, a pre-quantum-mechanical approach-was made earlier, by Goldhammer in 1913 and Herzfeld in 1927. Their simple rationalization, in terms of atomic properties which confer metallic or non-metallic status to elements across the periodic table, leads to what is commonly called the Goldhammer-Herzfeld criterion for metallization. For a variety of undoubtedly complex reasons, the Goldhammer-Herzfeld theory lay dormant for close to half a century. However, since that time the criterion has been repeatedly applied, with great success, to many systems and materials exhibiting non-metal to metal transitions in order to predict, and understand, the precise conditions for metallization. Here, we review the application of Goldhammer-Herzfeld theory to the question of the metallic versus non-metallic status of chemical elements within the periodic system. A link between that theory and the work of Sir Nevill Mott on the metal-non-metal transition is also highlighted. The application of the 'simple', but highly effective Goldhammer-Herzfeld and Mott criteria, reveal when a chemical element of the periodic table will behave as a metal, and when it will behave as a non-metal. The success of these different, but converging approaches, lends weight to the idea of a simple, universal criterion for rationalizing the instantly-recognizable structure of the periodic table where …the metals are here, the non-metals are there … The challenge of the metallic and non-metallic states of oxides is also briefly introduced. This article is part of the theme issue 'Mendeleev and the periodic table'.
Keywords: Goldhammer–Herzfeld criterion; Mott criterion; metal; metal-non-metal transition; non-metal; periodic table.