Combining experiment and theory, evidence from surface-enhanced Raman scattering (SERS) were obtained for p,p'-dimercaptoazobenzene (DMAB) produced from p-aminothiophenol (PATP) by selective catalytic coupling reaction on silver nanoparticles. The time-dependent SERS spectra of PATP are consistent with the calculated SERS spectra of DMAB, which is the direct evidence for the production of DMAB from PATP by selective catalytic coupling reaction on silver nanoparticles. The so-called "b(2) modes" of PATP is the -N=N- related vibrational modes of DMAB. The silver nanoparticles could be assembled together to form different size of aggregates with different concentration of PATP solution. When the concentration of Ag nanoparticle (the radius 40 nm) in colloid is 35 pM, the time-dependent SERS of DMAB reveals that the better experimental conditions for observing SERS signals of DMAB are (1) concentration of PATP is around 5 x 10(-6) M in which condition the aggregates consist with about 3-5 silver nanoparticles, which are not too big and suitable for SERS measurement, and (2) the Raman signal will be strongest at the time delay about 27 min for this concentration. By analyzing the symmetry of strong enhanced vibrational modes, it is derived that all of six strong vibrational modes are mostly enhanced by surface plasmons (electromagnetic field). The SERS enhancement calculated with finite-difference time-domain method is on the order of |M|(4) = 9.0 x 10(8) in junctions of AgNPs at 632.8 nm, where |M| = E(loc)/E(in), and E(loc) and E(in) are local and incident electric fields, respectively. The total chemical enhancements, including static chemical and resonant enhancements, are on the order of 10(3).