Normal coordinate analysis for polymer systems: Capabilities and new opportunities

Normal coordinate analysis is an important tool in studying the structure, dynamics, and physical properties of polymer systems. In this article the capabilities of normal coordinate analysis (NCA) are explored in some detail. The use of the eigenvalues and eigenvectors from NCA is catalogued for a wide variety of purposes: for assigning or interpreting polymer spectra, for structural determination, for constructing force fields, for computing heat capacity and other thermodynamic properties, and for computing other physical properties. Examples are given for crystals, melts, and amorphous systems. Also described are methods for characterizing the normal mode vectors that are especially useful for larger systems, in which a large amount of data must be analyzed or where visualization or animation fails. Finally, a recently developed method for eliminating negative eigenvalues in systems with tens of thousands of atoms, trajectory averaging, is presented. Also described are several advances in numerical linear algebra for speeding up the diagonalization phase and for computing physical properties without requiring full diagonalization of the Hessian matrix. A mixed rotation-translation mode (number 2) of a 6000-atom polymer droplet, calculated from trajectory-averaged normal coordinate analysis.