Constant-temperature simulation

Since many systems of interest in chemistry have intrinsic multiple time scales it is important to use integrators that deal efficiently with the multiple time scale problem. Since our multiple time step algorithm, the so-called reversible Reference System Propagator Algorithm (r-RESPA) [17, 24, 18, 26] is time reversible and symplectic, they are very useful in combination with HMC for constant temperature simulations of large protein systems. 

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 a constant temperature simulation, a molecular system is coupled to a heat bath via a Bath relaxation constant (see Temperature Control on page 72). When setting this constant, remember that a small number results in tight coupling and holds the temperature closer to the chosen temperature. A larger number corresponds to weaker coupling, allowing more fluctuation in temper-... 

To some extent you can monitor constant temperature simulations by the temperature (TEMP) and its deviation (D TEMP) or by kinetic energy (EKIN) and its deviation (D EKIN). Plot these values using the HyperChem Molecular Averages dialog box. 

Berendsen et al. [H. I. C. Berendsen, I. P. M. Postma, W. F. van Gun-steren, A. di Nola, and I. R. Haak, J. Chem. Phys. 81, 3684 (1984)] have described a simple scheme for constant temperature simulations that is implemented in HyperChem. You can use this constant temperature scheme by checking the constant temperature check box and specifying a bath relaxation constant t. This relaxation constant must be equal to or bigger than the dynamics step size D/. If it is equal to the step size, the temperature will be kept as close to constant as possible. This occurs, essentially, by rescaling the velocities used to update positions to correspond exactly to the specified initial temperature. For larger values of the relaxation constant, the temperature is kept approximately constant by superimposing a first-order relaxation process on the simulation. That is ... 

A constant-temperature simulation now consists of the following steps ... 

The classical equations of motion are solved with the velocity Verlet method [66]. The simulation is performed in the microcanonical ensemble (N,V,E) in a cubic box with length 15 A. Periodic boundary conditions are applied. The system is equilibrated by performing a constant temperature simulation [67] for 10 ps to achieve a mean temperature of 1000 K. The temperature control is then turned off to gain constant energy conditions. 

There are several reasons why we might want to maintain or otherwise control the temperature during a molecular dynamics simulation. Even in a constant NVE simulation it is common practice to adjust the temperature to the desired value during the equilibration phase. A constant temperature simulation may be required if we wish to determine how... 

Most CP simulations of clusters aimed at investigating their behavior at finite temperature are made on the microcanonical ensemble. Only rarely have constant-temperature simulations using the Nose algorithm [263] been reported. 

We note that Hoover defines y kT as the instantaneous kinetic energy per particle, KEqj /N, and for a "constant temperature simulation," Hoover constrains the kinetic energy to be strictly constant. This produces an ensemble whose weight function contains 6(KEqj - constant), and hence it is different from the MD ensemble. Several articles on nonequilibrium fluids appear in the January, 1984, issue of Physics Today, and of particular interest for nonequilibrium molecular dynamics are the articles by Evans, Hanley, and Hess, by Hoover, and by Alder and Alley. ... 

Lastly, it must be mentioned that energy is not conserved in this methodology because the Hamiltonian is time dependent. However, it is a great candidate for constant-temperature simulations, where a thermostat is used to absorb any temperature variation. 

It is usually desired to perform molecular dynamics simulations at constant temperature. In the simulations considered here, constant temperature is accomplished in one of two ways. In the first, stochastic forces and associated frictional forces are introduced which act individually on each atom of the system. This approach is hereafter referred to as stochastic dynamics (SD) simulation. The mean-square magnitude of the stochastic forces, which are purely random and Gaussian, is proportional to the temperature of the system, as described in Ref. 24. A canonical ensemble is simulated if the friction coefficient 7 for the frictional forces is chosen such that 1 /7 is much smaller than the total simulation time. The resulting damping forces do influence dynamic quantities, however, and this is the primary drawback of the SD method. The SD method was used in Refs 24, 25 and 31. The second method for constant temperature simulations involves either direct scaling of atomic velocities, as in Refs 29 and 30, or the inclusion of an additional temperature degree of freedom to the system by the Nose method,as appUed in Refs 31 and 32. Such simulations are hereafter referred to as molecular dynamics (MD) simulations. Of the MD methods considered, only the Nose method yields a true canonical ensemble. 

Nos developed a deterministic approach to constant temperature simulations based on an extended Lagrangian which does not disturb the dynamic properties of the system. Since then, modifications of this approach have been developed to generate constant pressure and temperature simulations. These extended system methods have been known to suffer from stability problems, as well as occasional failures in ergodicity. Klein and co-workers introduced the concept of Nos6-Hoover chains to overcome these problems, and used a Liouville operator formalism to obtain reversible integrators generating these chains. 

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