The instantaneous normal mode (INM) approach to liquid state dynamics is presented. INM is put in historical context, and the underlying physical ideas, including the importance of the potential energy landscape, are explained. It is shown that INM can be the basis of a general starting point for dynamical calculations in liquids, and the theoretical developments necessary for future development are indicated. New results are given for the general INM formalism, as well as for depolarized light scattering, the "Boson peak" in supercooled liquids, friction on a vibrating bond, nonadiabatic solvent induced transitions of a quantum system coupled to a liquid, and diffusion in supercooled liquids.

A simulation method is presented that achieves a flat energy distribution by updating the statistical temperature instead of the density of states in Wang-Landau sampling. A novel molecular dynamics algorithm (STMD) applicable to complex systems and a Monte Carlo algorithm are developed from this point of view. Accelerated convergence for large energy bins, essential for large systems, is demonstrated in tests on the Ising model, the Lennard-Jones fluid, and bead models of proteins. STMD shows a superior ability to find local minima in proteins and new global minima are found for the 55 bead AB model in two and three dimensions. Calculations of the occupation probabilities of individual protein inherent structures provide new insights into folding and misfolding.

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We present a powerful replica exchange method, particularly suited to first-order phase transitions associated with the backbending in the statistical temperature, by merging an optimally designed generalized ensemble sampling with replica exchanges. The key ingredients of our method are parametrized effective sampling weights, smoothly joining ordered and disordered phases with a succession of unimodal energy distributions by transforming unstable or metastable energy states of canonical ensembles into stable ones. The inverse mapping between the sampling weight and the effective temperature provides a systematic way to design the effective sampling weights and determine a dynamic range of relevant parameters. Illustrative simulations on Potts spins with varying system size and simulation conditions demonstrate a comprehensive sampling for phase-coexistent states with a dramatic acceleration of tunneling transitions. A significant improvement over the power-law slowing down of mean tunneling times with increasing system size is obtained, and the underlying mechanism for accelerated tunneling is discussed.

Normal mode analysis of the velocity correlation function in supercooled liquids J. Chem. Phys. 94, 6762 (1991); 10.1063/1.460252 Modecoupling theory of the dynamics of polymer liquids: Qualitative predictions for flexible chain and ring melts Harmonic normal-mode analysis is applied to Lennard-Jones (U) liquids. The configurationaveraged density of (vibrational) states is obtained via numerical eigenanalysis of the forceconstant matrices appropriate to an ensemble of liquid configurations; the configurations are generated by computer simulation. The contribution of unstable modes is included and plays a crucial role in the analysis. It is argued that the density of states contains information which may be used to construct theories of liquid-state dynamics. The argument is pursued at two levels. First, it is demonstrated that a glance at the density of states conveys a powerful, intuitive understanding of several aspects of the dynamics. Second, a theory of the selfdiffusion constant is constructed which may be regarded as a preliminary attempt to base systematic transport theory upon normal-mode quantities.