From the Kołos–Wolniewicz calculations to the quantum-electrodynamic treatment of the hydrogen molecule: Competition between theory and experiment

Abstract

The hydrogen molecule—two and a half centuries after Cavendish’s discovery, a dozen decades after Lyman’s first spectroscopic observations and almost a centennial after Heitler and London’s quantum-mechanical explanation of its stability—is still the subject of intense research, both theoretical and experimental. Being the simplest neutral molecule, it serves as a benchmark for testing quantum-mechanical theories and methods; being the most ubiquitous molecule in the Universe, plays an essential role in astronomy and the fundamentals of physics. Over decades, advances in increasing experimental precision have stimulated ever more accurate calculations. In this review, we summarize the progress made in the field of the quantum-mechanical description of the electronic structure of the hydrogen molecule, starting from the pioneering calculations of Kołos and Wolniewicz in the early 1960s and ending with the current state of knowledge, including applications of quantum electrodynamics. Bearing in mind the topic of this special issue, we will focus on the achievements of Polish scientists in this matter.