In light-harvesting complexes, how is the energy of a photon transferred from one pigment molecule to another? And in reaction-center complexes, how does the primary electron acceptor capture an electron from the chlorophyll a? It’d be best if any of you could explain this to me in terms of what’s happening at the molecular or atomic level, say with electrons.
The energy transfer is achieved by a process called "resonance energy transfer". It needs the positioning of the donor and the acceptor in very close proximity to each other - the light harvesting complexes are optimized for this. This allows the collection of small amounts of light energy and still enables photosynthesis. The figure shows how this works schematically:
The figure is from this webpage, which gives a good introduction.