Abstract: We use the discrete dipole approximation to investigate the electromagnetic fields induced by optical excitation of localized surface plasmon resonances of silver nanoparticles, including monomers and dimers, with emphasis on what size, shape, and arrangement leads to the largest local electric field (E-field) enhancement near the particle surfaces. The results are used to determine what conditions are most favorable for producing enhancements large enough to observe single molecule surface enhanced Raman spectroscopy. Most of the calculations refer to triangular prisms, which exhibit distinct dipole and quadrupole resonances that can easily be controlled by varying particle size. In addition, for the dimer calculations we study the influence of dimer separation and orientation, especially for dimers that are separated by a few nanometers. We find that the largest /E/2 values for dimers are about a factor of 10 larger than those for all the monomers examined. For all particles and particle orientations, the plasmon resonances which lead to the largest E-fields are those with the longest wavelength dipolar excitation. The spacing of the particles in the dimer plays a crucial role, and we find that the spacing needed to achieve a given /E/2 is proportional to nanoparticle size for particles below 100 nm in size. Particle shape and curvature are of lesser importance, with a head to tail configuration of two triangles giving enhanced fields comparable to head to head, or rounded head to tail. The largest /E/2 values we have calculated for spacings of 2 nm or more is approximately 10(5).