Within the theoretical chemistry community, we usually worry more about molecules/materials than about photon fields. For the most part, we consider classical (as opposed to quantum) electromagnetic fields, and we use perturbation theory to express electromagnetic signals as a function of correlation functions of molecular. And yet this perspective is limiting for two reasons. First, if one cannot visualize EM fields, one cannot build intuition for coupling the Schrodinger equation to the Maxwell equations.
Second, in the context of modern plasmonics, because nanostructures are so much larger than molecules with such stronger absorption cross-sections, light-matter interactions are no longer perturbative always. Thus, there is a need to go beyond traditional dynamics approaches.
Furthermore, there is reason to think that we can make progress here: there has been a ton of work done in the area of coupled nuclear-electronic dynamics over the years, but far less has been done in the arena of coupled electron-photon dynamics. Modeling EM fields has historically been the perview of the quantum optics community, where little attention has focused on the matter side of things. One interesting result that has already arisen: when you mix quantum electrons and classical light, you cannot recover electron-electron correlations while also obeying causality. The world of semiclassical theory has many surprises in store for us when we turn to light-matter interactions.
With this background in mind, one of the main questions that we are asking nowadays in the context of light-matter interactions is this: What is the most natural semiclassical approach for modeling electronic transitions and electromagnetic (EM) fields explicitly at the same time? A naive, Ehrenfest merger of the Liouville equation with Maxwell's equations does not recapitulate spontaneous emission: can we do better? To that end, we are now structuring a new dynamics approach (``Ehrenfest+R'') to do just that: to improve upon Ehrenfest dynamics by incorporating vacuum fluctuations and putting in spontaneous emission. The preliminary results are looking very good so far.
89. T. E. Li, H-T Chen, A. Nitzan, M. Sukharev and J. E. Subotnik
“A Necessary Trade-off for Semiclassical Electrodynamics: Accurate Short-Range Coulomb Interactions versus the Enforcement of Causality?”
J. Phys. Chem. Lett. 9, 5955-5961 (2018) [PDF]           link
86. T. E. Li, A. Nitzan, M. Sukharev, T. Martinez, H. T. Chen, and J. E. Subotnik
"Mixed Quantum Classical Electrodynamics: Understanding Spontaneous Decay and Zero Point Energy"
Phys. Rev. A 97, 032105 (2018) [PDF]           link