Energy minima sampling

The time that the trajectory must spend at / max to ensure that the equilibrium distribution is sampled is at least Tmin, the time required to surmount the largest barrier separating the global energy minimum from other thermodynamically important states. Using Eq. (39) we find... 

Due to scientific and public concern about environmental pollution, new developments in environmental analysis are focused on the implementation of environmental-friendly practices in the laboratories. Main strategies are addressed to saving energy and to reduce solvent consumption with the minimum sample manipulation by using on-site, online, and direct analysis (e.g., biosensors) [42],... 

An important difficulty of this simulation is the fact that, once the two helices are close to each other, it is very difficult to slide one with respect to the other or change their relative orientation because of steric clashes. This means that a simulation where the helix-helix distance is constrained would not be able to sample phase space efficiently but rather would remain near the local energy minimum where it started. In contrast, using ABF, the helices have the opportunity to move closer and farther apart so that their relative position can vary more freely. 

The equilibrium dimensions rm and lm of the inverted domain correspond to the minimum of the total free energy of the tip array-sample system, Wtotai The calculated domain sizes at the energy minimum are shown in Figure 10.17 as a function of the distance p0 between two adjacent tips. 

Molecular mechanics (MM) and dynamics (MD) are useful tools to investigate the conformational properties of organic molecules. (75) In particular, the combined use of MM and MD can be very effective in sampling the potential energy hypersurface (PES) when structurally constrained molecules are considered. In the present work, the PES has been described using the MM+ forcefield (16) and MM optimizations were followed by short MD runs (10 ps) carried out at different temperature (from 300 to 700 K) in order to sample the PES efficiently. Usually, due to the steric properties of the molecules investigated, no more than 10 MM/MD cycles were necessary to localize all the relevant energy minimum structures. 

Eg between the valence band and the conduction band. The band structure of a direct II-VI intrinsic semiconductor like CdSe can be represented reasonably well by a parabolic band model like that shown schematically in Fig. 2. Here, k = 7r/ris the wave vector and r is the radial distance from an arbitrary origin in the center of the crystal. The kinetic energy of the electron is proportional to E- and the energy minimum of the conduction band and the maxima of the valence bands occur at k = 0 (corresponding to r = co in a bulk sample). 

Using the MCY potential at constant pressure and temperature the system became structurally unstable as described in ref. [74], even though the first nearest neighbour distance was preserved at about 2.9 A. A considerable distribution was found for the local tetrahedral symmetry. This behaviour is reasonable since a simple 6-12 potential has no preference for a tetrahedral ly bonded structure. However, with a fixed cell volume the simulation became stable. Nearest neighbour molecules move within the energy minimum created by the pair-potential and the pair-wise additive electrostatic forces. At low temperatures, these molecules only sample the parabolic part of the potential... 

In the multiple copy MD [77] or locally enhance sampling (LES) [78] method, part of the system simulated is replicated multiple times, e.g. 20 copies of a peptide are simulated in the presence of 1 copy of the solvent. There are no interactions between the multiple copies. The unreplicated atoms feel the mean force of all the copies of the replicated atoms. The mean field generated by the multiple copy ensemble reduces the energy barriers but conserves the global energy minimum [78]. The number of degrees of freedom is reduced in the sense that one simulation with m copies of a subset of the atoms samples to a similar extent to m standard simulations (without multiple copies) in approximately l/m times the simulation time. Applications to peptides in solvent have shown improved sampling of phase space [79, 66]. 

We then performed several metadynamics runs with different choices of w, 5s and tq and, since the exact free energy for the system has been computed by umbrella sampling explicitly, we estimate the error with (11). In total, we tested more than fifty different combinations of parameters, for a total of almost 200 ns of molecular dynamics. All the simulations are started from the same initial condition in which the naphthalene is inserted in the catenane, and are stopped when the system escapes this free energy minimum. 

---