Constant temperature molecular dynamics

Once the cell is built, a quenched molecular dynamics approach is used to optimize the positions of the atoms. This method involves running NVT molecular dynamics (constant number, volume, and temperature) at 7000 K for 20 ps, followed by another 20 ps of NPT (constant number, pressure, and temperature) molecular dynamics. The purpose of this initial two-stage process is to randomize the structure... 

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... 

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. 

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... 

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... 

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). 

Molecular dynamics calculations use equations 25-27. HyperChem integrates equations 26 and 27 to describe the motions of atoms. In the absence of temperature regulation, there are no external sources or depositories of energy. That is, no other energy terms exist in the Hamiltonian, and the total energy of the system is constant. 

If there is no external temperature control (using a simulated constant temperature bath), molecular dynamics simulations are constant energy. 

Most molecular dynamics simulations, and particularly those for proteins, use constant temperature conditions. 

For a conformation in a relatively deep local minimum, a room temperature molecular dynamics simulation may not overcome the barrier and search other regions of conformational space in reasonable computing time. To overcome barriers, many conformational searches use elevated temperatures (600-1200 K) at constant energy. To search conformational space adequately, run simulations of 0.5-1.0 ps each at high temperature and save the molecular structures after each simulation. Alternatively, take a snapshot of a simulation at about one picosecond intervals to store the structure. Run a geometry optimization on each structure and compare structures to determine unique low-energy conformations. 

If the heating time t or cooling time t are non-zero, or if the run time tj. is non-zero and constant temperature is selected, velocities are adjusted (rescaled) during the molecular dynamics run to change the temperature of the system. 

For constant temperature dynamics where the constant temperature check box in the Molecular Dynamics Options dialog box is checked, the energy will not remain constant but will fluctuate as energy is exchanged with the bath. The temperature, depending on the value set for the relaxation constant, will approach con-stan cy. 

The simplest method that keeps the temperature of a system constant during an MD simulation is to rescale the velocities at each time step by a factor of (To/T) -, where T is the current instantaneous temperature [defined in Eq. (24)] and Tq is the desired temperamre. This method is commonly used in the equilibration phase of many MD simulations and has also been suggested as a means of performing constant temperature molecular dynamics [22]. A further refinement of the velocity-rescaling approach was proposed by Berendsen et al. [24], who used velocity rescaling to couple the system to a heat bath at a temperature Tq. Since heat coupling has a characteristic relaxation time, each velocity V is scaled by a factor X, defined as... 

To construct Nose-Hoover constant-temperature molecular dynamics, an additional coordinate, s, and its conjugate momentum p, are introduced. The Hamiltonian of the extended system of the N particles plus extended degrees of freedom can be expressed... 

---