Energy-configuration criterion

The validity of both MHP and MPP has been tested in various physico-chemical processes [128,186-191]. The maximum hardness and minimum polarizability criteria complement the minimum energy criterion for stability. In general, a stable state (minimum energy configuration) or a favorable process is associated with the maximum hardness and minimum polarizability, and transition state is associated with the minimum hardness and maximum polarizability. 

In the standard HMC method two ingredients are combined to sample states from a canonical distribution efficiently. One is molecular dynamics propagation with a large time step and the other is a Metropolis-like acceptance criterion [76] based on the change of the total energy. Typically, the best sampling of the configuration space of molecular systems is achieved with a time step of about 4 fs, which corresponds to an acceptance rate of about 70% (in comparison with 40-50% for Metropolis MC of pure molecular liquids). 

We present an improved model for the flocculation of a dispersion of hard spheres in the presence of non-adsorbing polymer. The pair potential is derived from a recent theory for interacting polymer near a flat surface, and is a function of the depletion thickness. This thickness is of the order of the radius of gyration in dilute polymer solutions but decreases when the coils in solution begin to overlap. Flocculation occurs when the osmotic attraction energy, which is a consequence of the depletion, outweighs the loss in configurational entropy of the dispersed particles. Our analysis differs from that of De Hek and Vrij with respect to the dependence of the depletion thickness on the polymer concentration (i.e., we do not consider the polymer coils to be hard spheres) and to the stability criterion used (binodal, not spinodal phase separation conditions). 

At the end of one annealing step the new conformation was accepted if its energy difference to the current configuration was no higher than a given threshold energy ex, an approach recently proven optimal for certain optimization problems [34]. Throughout this study we use a threshold acceptance criterion of 1 kcal/mol. 

The energies and structural details of the best ten resulting conformations are summarized in Table (2). Again the best conformation had approached the native conformation to about 4.6 A RMSB deviation. In total six of the lowest ten conformations approach the native structure, while four others misfolded. Note that the selection criterion for the active population (see methods section) precludes the occurrence of the same configuration to within 3 A RMSB, this dominance of near native conformations of the total ensemble is particularly encouraging. 

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