What are the applications of quantum field theory to chemistry?
Have a look at this article: "The Physics behind Chemistry and the Periodic Table"
Pekka Pyykkö Chem. Rev. 2012 112 (1), 371-384
(http://pubs.acs.org/doi/abs/10.1021/cr200042e)
I think it answers your question and has most of the references to work done in that particular field. For most questions in chemistry the non-relativistic Schrödinger Equation is good enough. Even for systems with an appreciable amount of relativistic effects, the Dirac Equation is often not solved directly. So, the number of applications where Quantum Electrodynamics is used is really limited.