Langevin modes of macromolecules

The standard gas phase normal mode analysis is generalized to condensed phases within the framework of the classical Langevin equation. The solution of this equation for a system of 3N atoms moving on a harmonic potential surface and subject to viscous damping described by a friction matrix (which is nondiagonal in the presence of hydrodynamic interactions) is reduced to the diagonalization of a 6N×6N real nonsymmetric matrix obtained from the mass‐weighted force constant and friction matrices. Alternative formulations of the problem requiring either the diagonalization of a complex symmetric matrix or the solution to a generalized eigenvalue problem involving real symmetric matrices are also considered. The resulting eigenvalues, in general complex, are real when the motion is overdamped and occur in complex conjugate pairs in the underdamped case. It is shown that when the eigenvectors are normalized in a particular way, all quantities of interest (e.g., correlation functions) have simple spectral repre...

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