Quantum mechanics in Earth sciences: a one-century-old story

Nowadays, it is possible to calculate, at the ab initio level, large classes of properties of condensed matter, from the crystal structure and mechanical properties, to the thermodynamics, and therefore the stability in a given environment and in a range of temperature and pressure conditions. Predictions from calculations of this type can be used to estimate geophysical properties such as densities of mantle rocks as they change along geotherms, the geotherms themselves, phase transitions and their features, seismic velocity profiles to be compared with models derived from other paradigms and techniques. Moreover, known facts and observations concerning structure, behaviour, properties of materials and properties of whole complex systems of materials can be explained or at least rationalized within a common and very general frame that is at the basis of all the currently known physics and chemistry. However, the development of ideas, paradigms and related techniques did not come out all of a sudden, but steadily proceeded from the early days till now, without a real solution of continuity. During the time, quantum mechanics heavily contributed to create a language, a set of basic ideas and a frame of mind that is extensively used by chemists and crystallographers to interpret the relevant facts. What we know today, and how we currently apply quantum mechanics to systems of our interest, is largely dependent upon the path followed during the years to implement the theory in practical and efficient algorithms to make calculations for real systems. This paper will present a brief review of the paths followed, along with their motivations, since those early and heroic days of physics at the beginning of the last past century. The aim is to provide the reader with a general view of the subject that could possibly drive her/him toward the choice of more specific papers from the huge literature, concerning more restricted and specialized topics.