To obtain accurate reaction barriers for gas phase chemistry the most widely used and reliable method is coupled cluster (CCSD(T)) theory. Although this method was developed more than 4 decades ago, it has been difficult to come up with alternatives that outperform it. In this talk I will present a QMC method, called auxiliary field quantum Monte Carlo, that is able to systematically improve upon CCSD(T) and deliver chemical accuracy. I will review recent developments that have enabled this, including the ability to: cheaply and systematically improve the quality of results, obtain properties (other than just energies) and scale up to large systems at a cost that is linear in the system size.

In the second part of the talk I will present our recent work on understanding magnetism, which is a ubiquitous phenomenon that is often found in systems ranging from metalloenzymes to correlated quantum materials. However, describing it theoretically with sufficient accuracy remains one of the outstanding challenges for electronic structure theory. The difficulty can be traced back to the simultaneous presence of strong electron correlation and large relativistic effects. In extended systems, the presence of an Avogadro's number of electrons further complicates the matter. I will begin by describing some of the algorithms that have been developed in my group to tackle these challenges. For example, we can now perform efficient hybrid DFT calculations in periodic systems, we can also treat relativistic effects such as spin orbit coupling on an equal footing with electron correlation. By using these techniques in concert, we will study the electronic structure of magnetic systems.