  The effect of smooth shape changes of metallic nanoparticles on localized
surface plasmon resonances is assessed with a boundary integral equation
method. The boundary integral equation method allows compact expressions of
nanoparticle polarizability which is expressed as an eigenmode sum of terms
that depends on the eigenvalues and eigenfunctions of the integral operator
associated to the boundary integral equation method. Shape variations change
not only the eigenvalues but also their coupling weights to the electromagnetic
field. Thus, rather small changes in the shape may induce large variations of
the coupling weights. It has been found that shape changes that bring volume
variations >12% induce structural changes in the extinction spectrum of
metallic nanoparticles. Also, the largest variations in eigenvalues and their
coupling weights are encountered by shape changes along the smallest
cross-sections of nanoparticles. These results are useful as guiding rules in
the process of designing plasmonic nanostrucrures.
