Wilson’s renormalisation group is often regarded as the most important idea in physics from the second half of the twentieth century. It has had profound influence in fields as disparate as condensed matter physics and high-energy particle physics. One of the key ideas of the renormalisation group is that rather than study the full Hamiltonian of the system of interest, which is usually intractable, one should study an effective low energy Hamiltonian. An effective Hamiltonian is derived by ‘integrating out’ the high-energy degrees of freedom of the system.

Surprisingly the renormalisation group has made very little impact on quantum chemistry. Here the usual approach is to neglect the high-energy degrees of freedom rather than integrating them out in a controlled manner. Thus theoretical chemists work with ‘semi-empirical models’, where parameters are fitted to experiment, rather than effective low energy Hamiltonians, where parameters are derived from the Schrödinger equation.

In this project we will investigate the possibility of apply the renormalisation group to quantum chemistry by studying the simplest multi-electron molecule, H₂.  We will then begin to integrate out the high-energy degrees of freedom and derive an effective low energy Hamiltonian, which we will compare with standard semi-empirical parameterisations.