Vibrational Normal Modes of Polymer Nanoparticle Dimers Using the Time-Averaged Normal Coordinate Analysis Method

Abstract

The recently developed time-averaged normal coordinate analysis method is employed to investigate the normal modes of polymer nanoparticle dimers. In addition to providing the first accurate calculation of vibrational frequencies and vibrational displacements in dimerized nanoparticles, the normal mode corresponding to the particle dimer vibration is observed for the first time. It is observed that the nanoparticle dimer vibration is only minimally coupled to the other internal motions of the particle, showing a true correspondence to the vibrational motion in diatomic species. Several other characteristic vibrations of the dimerized species are observed, which correspond to coupled indifferent modes of the monomer particles.

Conformational Sub-states and Populations in Enzyme Catalysis

“…This method is similar to NMA in the sense that the vibrational modes of a protein (or protein vibrational modes) are obtained by diagonalization of the Hessian matrix (Hathorn, Sumpter, Noid, Tuzun, & Yang, 2002; Tuzun, Noid, Sumpter, & Yang, 2002). However, NMA suffers from some limitation when considering a highly flexible molecular system such as a protein.…”

Normal mode analysis and applications in biological physics

“…Polymer science is one area that made many novel developments and advances. For example, normal mode eigenvectors and eigenvalues can be averaged over trajectories in molecular dynamics to obtain a time average Hessian [15,16]. Preconditioning iterative solutions of the normal mode problem have been advanced [18].…”

“…Preconditioning iterative solutions of the normal mode problem have been advanced [18]. Spares matrix techniques based on a variant of the Arnoldi process in the software package ARPACK [17] which extend the popular Lanczos algorithm are often used [16].…”

“…Here (η ν ) α is the αth component of the displacement vector | η ν and Q ν Q ν = 0 for ν = ν . Recalling that the squared deviations Q 2 ν in thermal equilibrium are k b T /ω 2 ν (see equation (16)), the correlation matrix can be written in a compact notation as…”

“…We take as a toy model to illustrate the connection between the covariance and dynamical matrices two equal masses m connected by a spring k which are allowed to move in one dimension. There is one non-zero frequency mode, ω (see equation (16)…”