Simulation Details

The simulations follow the pattern described in previous sections. The CPMD program is used with Born-Oppenheimer MD and a time step of 3.0236 fs (125 a.u.). We employ an NVT ensemble with cubic simulation cell, periodic boundary conditions, and a single point (k = 0) in the Brillouin zone. Simulations have been performed on two samples of a-GST (Fig. 17.1), with 460 and 648 atoms, respectively. We embedded in both a crystalline seed of 4 x 4 x 4 sites (13 Ge, 13 Sb, and 32 Te atoms, 6 vacancies) in a rock salt structure with lattice constant of 3.0 A. The structure of the crystallite adopted the model of Yamada [7], which assumed that one sublattice of the rock salt structure comprises Te atoms, the other a random arrangement of Ge, Sb, and vacancies. We removed the atoms of the amorphous structure inside this volume, fixed the coordinates of the seed, and optimized the resulting structure. 

For the 460-atom model, the initial geometry used was the structure of a-GST that gave excellent agreement between DF simulations and experimental x-ray diffraction (XRD) and x-ray photoemission spectroscopy (XPS) measurements [26]. With fixed coordinates of the seed, we performed DF/MD simulations at 500, 600, and 700 K over 600 ps (500/600 K) and 350 ps (700 K). The path to crystallization at 600 K is shown in Fig. 17.13(a-d). The amorphous and crystalline densities of GST differ, and the size of the cubic simulation cell was changed from 24.629 A (amorphous density of 0.0308 atoms/A ) to 24.060 A (crystalline density of 0.0330 atoms/A ) in five steps of 0.114 A. 

For the 648-atom structure, the initial coordinates of the 648-atom sample were obtained from a previous computer-aided deposition simulation [25], The size of the cubic box was reduced in two steps from 27.736 A (amorphous density) to 27.150 A (density 0.0324 atoms/A ), which is incommensurate with the rock salt stmcture with this number of atoms. Complete crystallization was not expected and was not found at 600 K (see Fig. 17.13f), but the crystallite grew until making contact with its replica at the simulation cell boundaries. 

The simulation details such as force and energy calculation including the potential models of H2O and HsO are similar to the teehniques and methods described in the earher discussion. Unlike other simulations of an exeess proton in bulk water we 

Three systems were stndied at these temperatures  

The Polak-Ribiere conjugate gradient method was used in RSll to perform the non-linear mnlhvariate optimization of the objective function with the weighing factors, Wj = 1 and W2 = 10. 

The protein systems were equilibrated by a 20 ps stepwise heating scheme and thereafter 50 ps simulation at a constant temperature of 300 K. The water systems were equilibrated by directly simulating them for 50 ps at 300 K. The MD trajectories were run using a time step of 1 fs and energy data were collected every fifth step. The free energy perturbations were sampled using 47-83. -points and 5 ps simulation for each value of X,. Data from the first 2 ps of each step were discarded for equilibration. 

To study the efficiency of the continuous-potential RG method, we have performed N VT -Monte Carlo simulations of M linear chains (length N) with truncated Lennard-Jones interactions between the non-bonded segments. In reduced units (well depth e = 1, Lennard-Jones diameter 

Recoil growth algorithm for chain molecules with continuous interactions 

We have used tcut = 2.5. The bond-length between two successive segments was chosen to be 1.0. Three successive segments of a molecule have a constant bond-angle of 2.0 rad. Intramolecular non-bonded interactions were taken into account for segments that are separated by more than two bonds. 

To enhance the efficiency of both the CBMC and the RG scheme, we have divided the inter-molecular potential energy into short-range and long-range parts 

The system contains amphiphihc lipid molecules, each of which consists of a head-group containing three linearly connected hydrophiUc beads (H) and two tails, connected to adjacent head beads, of three hydrophobic beads (T). The Upids are immersed in solvent (S). The amphiphilic nature of the Upids derives from the repulsive interactions. For any two beads of the same type, we take the repulsion 

Bonds are represented by the harmonic spring potential = fQ, d((r- h)/ry, where Ki, is the bond constant and b the equihbrium bond length here, we use Khond = 64 and h = 0.5. We also insert a weaker bond (Ki, = 10) between the first beads on the two tails to keep the tails oriented in the same direction. Additionally, we include a three-body stiffness potential along the tails of the form E = i ng e(l + cos 6), where 0 is the angle formed by three adjacent beads, and set the coefficient to = 10. This stiffness term increases the stabiUty and bending rigidity of the bilayers. 

We use the settings and procedures described above to prepare a lipid bilayer membrane in a solvent The membrane has a near-zero interfacial tension, as will be discussed below. The membrane thickness h is defined as the distance between the two peaks in the lipid head density profile here, h = 4tc. 

A soHd, near-spherical nanoparticle is formed from particle beads (P) arranged on an FCC lattice with a number density of p = 3/r/. The beads comprising a single particle are constrained to move as a rigid body. It has been verified that the solvent and lipid beads do not penetrate the interior of the particle under these conditions. The particle is chosen to have a hydrophilic surface, so the interaction between the beads composing the particle (P) and the lipid tail beads is taken to be apj= 100. To induce an adhesive interaction between the particle and the membrane, we make the particle compatible with the lipid head beads by setting UpH = 25, and vary the particle-solvent interaction in the range 25 aps 60. 

The free energy of a membrane formed from self-assembled lipids includes contributions from a number of different factors. In general, the area per lipid Uj within the membrane is close to the equihbrium value Ui o- For small deviations of Oi, the membrane is accurately modeled as a hnear elastic material Then, the elastic free energy term is  

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Although water structure and sidechain flexibilities are useful gauges for the simulation protocol, more quantitative measures are needed for reliable QM/MM simulations of enzyme systems. In this regards, we have found that reduction potential [78] and pKa [73,91] calculations are particularly useful benchmark calculations because the results are likely very sensitive to the simulation details. 

Table 3. The important factors found from sequential bifurcation under two meta-models for the Old supply chain simulation. Details of the factors are given in Table 2...

Constant Pressure MD. The conventional MD technique uses a fixed size for the simulation box, that is, the calculation is performed under constant volume conditions. Using methods developed by Parrinello and Rahman and by Berendsen and coworkers, it is now possible to undertake constant pressure simulations by allowing cell dimensions to vary dnring the simulation. Detailed discussions are given in Referenced . The most obvious field of application of this technique is to the study of phase transitions, and useful applications have been reported to the study of melting and glass formation as discussed below. 

Adsorption isotherms and heats of adsorption were calculated using Grand Canonical Monte Carlo simulations. Details of the simulation are described in a previous publication [11]. Surface excess amount adsorbed was calculated by subtracting the bulk density from the pore density at the conditions of the simulation. The pore volume is necessary to calculate the pore density. In this work, the helium pore volume using ane= 0.264nm was determined by MC integration, similar to the procedure used for the PSD. 

Using the presents used manometric set-up coupled with a NIR spectrometer produced results that are in agreement with literature data, and in agreement with simulations ( simulations details are provided on ref [4]). 

We recall however that a much better, actually quantitative, agreement with experimental data of surface tension has been obtained with SPC/E [173] and TIP4P [174]. Also, surface tension calculations are less straightforward than for other properties, so that a careful evaluation of simulation details such as run length is required before the role of the potential model can safely be assessed. 

Figure 1 shows the computational domain used in the simulations. Details of the micro and macro regions are also shown in Fig. 1. In these simulations, the gravity vector is oriented in the -z direction (i.e., the bubble is growing on an upwards facing heated surface). The simulations are carried out on a uniform grid Ax = Ay = Az).

Fig. 26.9. Comparison of the energetic separation and the relative orientation of the transition-dipole moments of the k = 1 and k = 2 exciton states from individual RC-LHl complexes with results from numerical simulations for three different arrangements of the BChl a molecules in the pigment-protein complex. The top row shows the model structures A-C that have been used for the numerical simulations. Details are given in the text. The second row compares the experimental ensemble absorption spectrum (black line) with the ensemble spectrum that results from numerical simulation (gray line) for the three model structures. The third row compares the experimentally obtained energetic separations between the k = 1 and k = 2 exciton states (gray columns) with numerical simulations (black squares) for the three model structures. The fourth row compares the experimentally obtained relative orientations of the transition-dipole of the A = 1 and k = 2 exciton states (gray columns) with numerical simulations (black squares) for the three model structures. Adapted from [62]...

For dispersed systems the interfacial tension terms are generally more important in the high resolution models simulating details of the local flow close to each individual interface. 

In order to extract the configurations to be analyzed in the next section, we have both taken the results obtained in a previous Molecular D5mamics (MD) simulation (details on the simulation are given elsewhere", and also... 

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