Configurational sampling

The biasing function is applied to spread the range of configurations sampled such that the trajectory contains configurations appropriate to both the initial and final states. For the creation or deletion of atoms a softcore interaction function may be used. The standard Lennard-Jones (LJ) function used to model van der Waals interactions between atoms is strongly repulsive at short distances and contains a singularity at r = 0. This precludes two atoms from occupying the same position. A so-called softcore potential in contrast approaches a finite value at short distances. This removes the sin-... 

Pig. 2. By replacing the methyl group in p-methlyphenol with a series of softcore iiitcTaction sites it is possible to spread the range of configurations sampled to include configurations with and without a cavity in the para position. 

The mixed solvent models, where the first solvation sphere is accounted for by including a number of solvent molecules, implicitly include the solute-solvent cavity/ dispersion terms, although the corresponding tenns between the solvent molecules and the continuum are usually neglected. Once discrete solvent molecules are included, however, the problem of configuration sampling arises. Nevertheless, in many cases the first solvation shell is by far the most important, and mixed models may yield substantially better results than pure continuum models, at the price of an increase in computational cost. 

Once the selectivity is optimized, a system optimization can be performed to Improve resolution or to minimize the separation time. Unlike selectivity optimization, system cqptimization is usually highly predictable, since only kinetic parameters are generally considered (see section 1.7). Typical experimental variables include column length, particle size, flow rate, instrument configuration, sample injection size, etc. Hany of these parameters can be. Interrelated mathematically and, therefore, computer simulation and e]q>ert systems have been successful in providing a structured approach to this problem (480,482,491-493). 

His residues at configurations sampled using the popular link-host-atom exclusion scheme changes the free energy derivatives by 8-9 kcal/mol despite that the QM/MM frontiers are far from the zinc-bound water. With this effect taken into account, the calculated pKa value for the zinc-bound water in the WT CAII is in encouraging agreement with experiment the value is 7.1 (5.4) for the 20 (25) A-inner-region simulations, as compared to the experimental value of around 7 [86],... 

Here, ( )0 denotes an ensemble average over configurations sampled from the reference state. This is the fundamental FEP formula, which is the basis for all further developments in this chapter. It states that AA can be estimated by sampling only equilibrium configurations of the reference state. 

In practice, this simple formula will hardly ever work, especially if the free energy changes appreciably with . Consider, for example, two states of the systems, , and j such that A,1 f <) - AA( j) = 5/, BT. Then, on average, the former state is sampled only seven times for every 1,000 configurations sampled from the latter state. Such nonuniform sampling is undesirable, as it leads to a considerable loss of statistical accuracy. For the free energy profile shown in Fig. 3.1, transitions between... 

In previous work on enhanced configurational sampling [154, 155] it was conjectured that a method based on the Tsallis generalization of the canonical ensemble [156] would be expected to have faster convergence with P, and an application was produced to prove this conjecture [34], Here we present a pedagogical outline of the ideas behind this approach. 

After the thermalization run, configuration sampling begins to obtain RDCF and coordination number distribution. Figure 11 shows one single system configuration, mean RDCF, coordination number distribution and configuration structure factor S(q) with an example. 

Moreover, Nieber and Doltsinis [64] have studied the effect of thermal molecular motion on the fluorescence energy by averaging over 10 configurations sampled from a 300 K ROKS Sr CP-MD run. Due to the flatness of the ROKS. S, PES, the... 

Langer and Doltsinis [45] have calculated nonadiabatic surface hopping trajectories for 10 different initial configurations sampled from a ground state AIMD runs at 100 K. They later extended their study to a total of 16 trajectories [41, 42], From a mono-exponential fit to the 5) population a lifetime of 1.3 ps is obtained (see Table 10-1 the average transition probability and its standard deviation leads to the interval [0.6...1.1...3.5] ps. Thus methylation appears to result in a slightly longer excited state lifetime. 

---