Abstract <p> A numerical method for solving the boundary value problem of diffraction on a system ofpaired nanoparticles with a subnanometer gap is developed and implemented. The diffractionboundary value problem includes the system of Maxwell equations and mesoscopic boundaryconditions with Feibelman parameters. The solution of the problem is constructed using thediscrete source method with the location of sources for the internal field in the complex plane.A complete mathematical justification of the method is provided. For a pair of gold nanoparticles,numerical analysis of the influence of quantum effects on the field intensity in the subnanometergap is carried out. It is found that taking into account quantum effects has a significant influenceon the field characteristics. In particular, the decrease in the plasmon resonance amplitude canreach 65 %, and the shift of its position to the long-wave region can be as large as 25 nm.</p>