Constant volume minimization

The basis of constant pressure minimization is that both lattice vectors and coordinates are adjusted to remove forces on both the atoms and the unit cell as a whole. This is commonly performed simultaneously, using the same approach for the lattice vectors as was used in constant volume minimization for the coordinates (i.e. treating the lattice vectors as additional variables). 

During the volume adjustments, constant volume minimizations are performed to ensure that the ions stay at their potential energy minima. This reduces the possibility of an atom moving to an unstable site and giving rise to imaginary frequencies (where the solution of co2 is negative). 

A large fraction of such a material may quickly pass through the gastrointestinal tract and remain unabsorbed. Local irritation by a test substance generally decreases when the material is diluted. If the objective of the study is to establish systemic toxicity, the test substance should be administered in a constant volume to minimize gastrointestinal irritation that may, in turn, affect its absorption. If, however, the objective is to assess the irritation potential of the test substance, then it should be administered undiluted. 

However, these potentials do not yet express the second law in the form most convenient for chemical applications. Open laboratory vessels exposed to the temperature and pressure of the surroundings are subject neither to constraints of isolation (as required for entropy maximization) nor to adiabatic constant-volume conditions (as required for energy minimization). Hence, we seek alternative thermodynamic potentials that express the criteria for equilibrium under more general conditions. 

Another topic of interest is the shape that an isolated body of constant volume with an anisotropic surface energy will adopt to minimize its total interfacial energy. This can be resolved by means of the Wulff construction shown in Fig. C.4e. Here, a line has been drawn at each point on the 7-plot which is perpendicular to the n corresponding to that point. The interior envelope of these lines is then the shape of minimum energy (i.e., the Wulff shape). The Wulff shape for the 7-plot in Fig. C.4a contains sharp edges and contains only inclinations that have been shown to be stable in Fig. C.46 and c. 

To construct the moment Gibbs free energy, one can now proceed as in the constant volume case In the ideal contribution, we replace lnn(cr) —> In [n(ff)/n (o-)], with a normalized parent distribution m0 (cr), and then minimize g at fixed values of the m,. The minimum occurs for distributions n a) from the family... 

At equilibrium, with constant volume, temperature, and constant amounts of material, the free energy is minimal. At a minimum the derivatives with respect to all independent variables must be zero ... 

After the initial configuration construction, we performed a standard equilibration protocol for DNA simulations [20]. The entire structure was minimized by the steepest descent method in order to avoid close atomic contacts, followed by slow constant volume heating to 300 K over 100 ps using 2.4 kcal/mol harmonic restraints. These restraints were slowly reduced to zero during a series of energy minimization and 50 ps equilibration steps at constant temperature (300 K) and pressure (1 bar) with a 0.2 ps coupling constant for both parameters. The final equilibration step was a 100 ps constant volume run. 

Constraints are easy to implement in a second-derivative minimiza-tion. For instance, in zeolite modeling it may be required to carry out an energy minimization under the constraint of constant volume. This could be done by adding to the set of equations an equation of constraint. Because the... 

There are various techniques available for molecular dynamics simulation, i.e., adiabatic, isothermal. The constant volume, temperature (isothermal NVT) method (constant number of atoms, volume, and temperature) is most commonly used. The simulated results obtained from the molecular dynamics studies are then coordinate minimized to ensure that the global minimum has been achieved. 

In order to achieve the best possible catalyst conversion efficiency at a constant volume, while minimizing the power drain due to excessive pressure drop through the converter, one would maximize the heat and mass transfer with respect to the pressure drop. In other words, in the graph shown in Figure 7 for 100% open frontal area, where the Heat Mass Transfer Factor is on the x-axis and the Pressure Drop Factor is on the y-axis, the slope of the curve should to be as shallow as possible. All of the channel shapes evaluated here tend to fall close to the same hne. However, as the open frontal area decreases from 100%, the Pressure Drop Factor increases while the Heat Mass Transfer Factor remains constant so that the relative attractiveness of some channel structures will be improved as the OFA is taken into account. 

To directly simulate the condensed-phase chemical reactivity of HMX, we use the SCC-DFTB method to determine the interatomic forces and simulate the decomposition at constant-volume and temperature conditions. The initial condition of the simulation included six HMX molecules in a cell, corresponding to the unit cell of the S phase of HMX (Fig. 10) with a total of 168 atoms. It is well known [76] that HMX undergoes a phase transition at 436 K from the P phase (two molecules per unit cell with a chair molecular conformation, density = 1.89 g/cm ) to the 6 phase (with boat molecular conformation, density=1.50 g/cm ). We thus chose the 8 phase as the initial starting structure so as to include all the relevant physical attributes of the system prior to chemical decomposition. The calculation started with the experimental unit cell parameters and atomic positions of 8 HMX. The atomic positions were then relaxed in an energy minimization procedure. The resulting atomic positions were verified to be close to the experimental positions. 

The first stage of any lattice simulation is to equilibrate the structure, i.e. bring it to a state of mechanical equilibrum. The simplest procedure is to equilibrate under conditions of constant volume, i.e. with invariant cell dimensions. Extensions to the procedure were introduced by Parker (1982, 1983) who introduced the use of constant pressure minimization in the computer code METAPOCS, in which lattice energy minimization was performed with respect... 

---