Molecular dynamics global minima

The most serious problem with MM as a method to predict molecular structure is convergence to a false, rather than the global minimum in the Born-Oppenheimer surface. The mathematical problem is essentially still unsolved, but several conformational searching methods for approaching the global minimum, and based on either systematic or random searches have been developed. These searches work well for small to medium-sized molecules. The most popular of these techniques that simulates excitation to surmount potential barriers, has become known as Molecular Dynamics [112]. 

Figure 5.6 A representation of the change in the value of is-rotai demonstrating how the computation could stop at a local (X) rather than the true (global) minimum value. The use of molecular dynamics gives the structure kinetic energy which allows it to overcome energy barriers, such as Y, to reach the global minimum energy structure of the molecule...

The AMBER-based approach used to model cyclic polyethers and cryptands has also been applied to the study of the Li+, Na+ and K+ complexes of three spherands (Fig. 15.3)14941. Experimentally determined metal ion selectivities were successfully reproduced. A similar AMBER-based model, used for molecular mechanics and dynamics of a cyclic urea-based spherand was also successful in reproducing its metal ion selectivity14951. A number of new conformations of the spherand, including the global energy minimum, were located using molecular dynamics [4951. 

PCFF force fields, alternatively with molecular dynamics, in order to identify the global minimum of the energy value). The investigated single chain has a polymerization degree DP=25, similar to the results obtained by synthesis. 

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 determine whether the move in the latter case will be made, one calculates then a random number in the interval [0 1] and from its value, compared to P above, it is decided whether the move is realized. Through this approach it is, as above, possible for the system to move around in the structure space, and by gradually reducing T, it is hoped, as for the simulated annealing and molecular dynamics, that the system ultimately ends in the global total-energy minimum. 

In principle, the substrate provides an external medium on which the cluster is either grown or deposited. In the first case, the methods we have discussed in Section 2 can still be applied with the modification that the presence of the medium shall be included first of all as providing an external (structured) potential in which the cluster grows. The structure of the substrate may be optimized, too, but without searching for its global total-energy minimum. When the cluster is deposited on the substrate, some molecular-dynamics approach is most useful. 

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