Quantum chemistry and electronic structure calculations are primarily concerned with establishing the behaviour of electrons in molecules and solids. Modern techniques rely heavily on the qualities of electronic wavefunctions to solve the Schrodinger equation in a computationally tractable way. However, electrons are not the only quantum mechanical particles in the world around us.
In this seminar, I will discuss the quantum treatment of two other sub-atomic particles: the proton and the positron. Understanding the quantum mechanical behaviour of these two particles in molecules and solids is a subject of immense theoretical and practical interest. The quantum nature of protons has important consequences for the zero-temperature phase diagram of solid hydrogen, embrittles metals due to diffusive tunnelling, and plays a key role in charge-transfer reactions in chemistry. The enhanced annihilation rate of positrons in materio is a sensitive probe in the characterisation of material defects, medical imaging by positron emission tomography, and understanding the interstellar medium of our galaxy.
Here I will show how recently developed neural network anstäze for ground-state wavefunctions can be used to treat the quantum mechanical nature of protons and positrons on equal footing with the electron. We find that this approach yields state-of-the-art results for the positron binding energy of molecules and can describe a broad range of qualitatively distinct modes of positron binding with no fine-tuning. Finally, I will present some early results concerning a fully quantum mechanical treatment of solid hydrogen and discuss future perspectives