Network dynamics

A Lagrangian formalism is set up within which the vibrational spectrum of any covalently bonded network with nearest-neighbor central forces can be discussed. The covalent bonds are used as directions that define coordinate axes at each site. The nonorthogonality and in some cases overcompleteness of the displacements is taken care of in a simple way within the Lagrangian formulation. It is shown that the vibrational eigenvalues can be obtained from the corresponding quantities for the connectivity matrix of the network. This allows the spectral limits delineating the allowed spectral regions to be found, and their dependence on the masses and bond angles is simply exposed.