Molecular dynamics temperatures

Bartell and co-workers have made significant progress by combining electron diffraction studies from beams of molecular clusters with molecular dynamics simulations [14, 51, 52]. Due to their small volumes, deep supercoolings can be attained in cluster beams however, the temperature is not easily controlled. The rapid nucleation that ensues can produce new phases not observed in the bulk [14]. Despite the concern about the appropriateness of the classic model for small clusters, its application appears to be valid in several cases [51]. 

Andersen H C 1980 Molecular dynamics simulations at constant pressure and/or temperature J. Chem. 

Nose S 1984 A unified formulation of the constant-temperature molecular dynamics methods J. Chem. Phys. 81 511-19... 

The parameter /r tunes the stiffness of the potential. It is chosen such that the repulsive part of the Leimard-Jones potential makes a crossing of bonds highly improbable (e.g., k= 30). This off-lattice model has a rather realistic equation of state and reproduces many experimental features of polymer solutions. Due to the attractive interactions the model exhibits a liquid-vapour coexistence, and an isolated chain undergoes a transition from a self-avoiding walk at high temperatures to a collapsed globule at low temperatures. Since all interactions are continuous, the model is tractable by Monte Carlo simulations as well as by molecular dynamics. Generalizations of the Leimard-Jones potential to anisotropic pair interactions are available e.g., the Gay-Beme potential [29]. This latter potential has been employed to study non-spherical particles that possibly fomi liquid crystalline phases. 

Monte Carlo simulations generate a large number of confonnations of tire microscopic model under study that confonn to tire probability distribution dictated by macroscopic constrains imposed on tire systems. For example, a Monte Carlo simulation of a melt at a given temperature T produces an ensemble of confonnations in which confonnation with energy E. occurs witli a probability proportional to exp (- Ej / kT). An advantage of tire Monte Carlo metliod is tliat, by judicious choice of tire elementary moves, one can circumvent tire limitations of molecular dynamics techniques and effect rapid equilibration of multiple chain systems [65]. Flowever, Monte Carlo... 

Nose, S. A molecular dynamics method for simulations in the canonical ensemble. Mol. Phys. 52 (1984) 255-268 ibid. A unified formulation of the constant temperature molecular dynamics method. J. Chem. Phys. 81 (1984) 511-519. 

Given this effective potential, it is possible to define a constant temperature molecular dynamics algorithm such that the trajectory samples the distribution Pg(r ). The equation of motion then takes on a simple and suggestive form... 

A typical molecular dynamics simulation comprises an equflibration and a production phase. The former is necessary, as the name imphes, to ensure that the system is in equilibrium before data acquisition starts. It is useful to check the time evolution of several simulation parameters such as temperature (which is directly connected to the kinetic energy), potential energy, total energy, density (when periodic boundary conditions with constant pressure are apphed), and their root-mean-square deviations. Having these and other variables constant at the end of the equilibration phase is the prerequisite for the statistically meaningful sampling of data in the following production phase. 

The relative molecular dynamics fluctuations shown in Figure 7-17 can be compared with the crystallographic B-factors, which are also called temperature factors. The latter name, especially, indicates the information content of these factors they show how well defined within the X-ray structure the position of an atom is. Atoms with high temperature have an increased mobility. In principle, this is the same information as is provided by the molecular dynamics fluctuations. Using Eq. (48), the RMS fluctuation of an atom j can be converted into a B-factor... 

A molecular system at room temperature is accurately characterized hy its tnoLiori. Molecular dynamics simulations calculate the future position s an d velocities of atom s based upon their current values. You can obtain qiialitative and quantitative data from HyperCh etn molecular dytiatn ics sirn ulation s. 

In a molecular dynamics calculation, you can add a term to adjust the velocities, keeping the molecular system near a desired temperature. During a constant temperature simulation, velocities are scaled at each time step. This couples the system to a simulated heat bath at Tq, with a temperature relaxation time of "r. The velocities arc scaled bv a factor X. where... 

Quenched dynamics is a combination of high temperature molecular dynamics and energy minimization. This process determines the energy distribution of con formational families produced during molecular dynamics trajectories. To provide a better estimate of conformations, you should combine quenched dynamics with simulated annealing. 

Successful molecular dynamics simulations should have a fairly stable trajectory. Instability and lack of ec uilibratioii can result from a large time step, treatment of long-range cutoffs, or unrealistic coiiplin g to a temperature bath. ... 

The heating phase is used to take a molecular system smoothly from lower tern peratiires, indicative of a static initial (possibly optim i/ed ) structure, to th e temperature T at which it is desired to perform the molecular dynamics simulation. The run phase then consLitn tes a sim n lation at tern peratnre T. If th e heating h as been done carefully, it may be possible to skip the equilibration phase... 

For free dynam ics wdierc the constant temperature check box in the Molecular Dynam ics dialog box is not checked, the total energy K l OT should remain constant,, A fhictuation of the total... 

Fig. 6.2 Radial distribution function determined from a lOOps molecular dynamics simulation of liquid argon at a temperature of 100K and a density of 1.396gcm. ...

The correct treatment of boundaries and boundary effects is crucial to simulation methods because it enables macroscopic properties to be calculated from simulations using relatively small numbers of particles. The importance of boundary effects can be illustrated by considering the following simple example. Suppose we have a cube of volume 1 litre which is filled with water at room temperature. The cube contains approximately 3.3 X 10 molecules. Interactions with the walls can extend up to 10 molecular diameters into the fluid. The diameter of the water molecule is approximately 2.8 A and so the number of water molecules that are interacting with the boundary is about 2 x 10. So only about one in 1.5 million water molecules is influenced by interactions with the walls of the container. The number of particles in a Monte Carlo or molecular dynamics simulation is far fewer than 10 -10 and is frequently less than 1000. In a system of 1000 water molecules most, if not all of them, would be within the influence of the walls of the boundary. Clecirly, a simulation of 1000 water molecules in a vessel would not be an appropriate way to derive bulk properties. The alternative is to dispense with the container altogether. Now, approximately three-quarters of the molecules would be at the surface of the sample rather than being in the bulk. Such a situation would be relevcUit to studies of liquid drops, but not to studies of bulk phenomena. 

Just as one may wish to specify the temperature in a molecular dynamics simulation, so may be desired to maintain the system at a constant pressure. This enables the behavior of the system to be explored as a function of the pressure, enabling one to study phenomer such as the onset of pressure-induced phase transitions. Many experimental measuremen are made under conditions of constant temperature and pressure, and so simulations in tl isothermal-isobaric ensemble are most directly relevant to experimental data. Certai structural rearrangements may be achieved more easily in an isobaric simulation than i a simulation at constant volume. Constant pressure conditions may also be importai when the number of particles in the system changes (as in some of the test particle methoc for calculating free energies and chemical potentials see Section 8.9). 

Fig. 9.19 Schematic illustration of an energy surface. A high-temperature molecular dynamics simulation may be ah to ooercome very high energy barriers and so explore conformational space. On minimisation, the appropriate minimum energy conformation is obtained (arrcrws).

---