Local electric field and scattering cross section on Ag nanoparticles were evaluated by the FDTD (finite difference time domain) method with respect to single-molecule sensitivity (SMS) in SERS (surface-enhanced Raman scattering). As a result, (1) vast enhancement of >300-fold (in amplitude enhancement) in the SMS level was obtained at a junction between two connecting Ag particles with various shapes and sizes in addition to an edge of isolated triangular cylinders. Other sites of the connecting particles and of isolated circular and ellipsoidal cylinders gave only modest enhancement of ca. 20-30-fold. (2) The enormously large electric field at the junction rapidly decays with increasing gap sizes <1 nm, irrespective of particle size or shape. In contrast, the LSP (localized surface plasmon) extinction spectra from connecting particles gradually shift toward those from isolated particles with the gap. Thus, in addition to the dipole LSP excitation, nanostructures such as sharp edges, which yield higher order surface modes, are crucial for the vast enhancement. Two-dimensional ordered structures do not yield any additional enhancement concerning SMS-SERS. (3) A red shift of the LSP extinction peak with decreasing height of Ag particles was reproduced only by use of three-dimensional simulation, while broadening and larger extinction at longer wavelength are given by two-dimensional calculation. (4) Blinking of SERS signal observed for dye and DNA base is most probably due to thermal diffusion of adsorbates between the junction with vast enhancement and ordinary sites with modest enhancement, which was supported by the numerical simulation and also experimentally evidenced by suppression of the phenomena at low temperature.