Constant temperature dynamics

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... 

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. 

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... 

Temperature-dependent (dynamic) NMR studies are suited to the study of processes with rate constants between 10 and 10 s Some applications are shown in Table 2.13 and in problems 13 and 14. 

Perhaps the most common computer simulation method for nonequilibrium systems is the nonequilibrium molecular dynamics (NEMD) method [53, 88]. This typically consists of Hamilton s equations of motion augmented with an artificial force designed to mimic particular nonequilibrium fluxes, and a constraint force or thermostat designed to keep the kinetic energy or temperature constant. Here is given a brief derivation and critique of the main elements of that method. 

Here, w(xfc) is the weighting factor for any property at a given position on the fcth step xfc. For example, for a constant-temperature molecular dynamics or a Metropolis MC run, the weighting factor is unity. However, we wish to leave some flexibility in case we want to use non-Boltzmann distributions then, the weighting factor will be given by a more complicated function of the coordinates. The ergodic measure is then defined as a sum over N particles... 

Tu, K., Tobias, D. J. and Klein M. L. (1995). Constant pressure and temperature molecular dynamics simulation of a fully hydrated liquid crystal phase dipalmitoylphosphatidylcholine bilayer, Biophys. J., 69, 2558-2562. 

Weakliem, P. C. and Carter, E. A. Constant temperature molecular dynamics simulations of Si(100) and Ge(100) equilibrium structure and short-time behavior. Journal of Chemical Physics 96, 3240 (1992). 

Nose S, Constant-temperature molecular dynamics, Mol Phys, 57, 187 (1986)... 

There are many excellent reviews on the standard molecular dynamics method dealing with calculations in the microcanonical ensemble as well as on the Monte Carlo method involving calculations in the canonical, isothermal isobaric, and grand canonical ensemble (< ). In the present article, we shall limit ourselves exclusively to those developments that have taken place since the work of Andersen (4). In the molecular dynamics method, the developments are the constant-pressure, constant-temperature, constant-temperature-constant-pressure, variable shape simulation cell MD, and isostress calculations in the Monte Carlo method, it is the variable shape simulation cell calculation. 

Other methods for performing constant-temperature molecular dynamics calculations have been proposed recently. Evans (72) has introduced an external damping force in addition to the usual intermolecular force in order to keep the temperature constant in the simulation of a dissipative fluid flow. In another method, Haile and Gupta 13) have imposed the constraint of constant kinetic energy on the lagrangian equations of motion to perform calculations al constant temperature. 

From the point of view of the solvent influenee, there are three features of an electron spin resonance (ESR) speetrum of interest for an organic radical measured in solution the gf-factor of the radical, the isotropie hyperfine splitting (HFS) constant a of any nucleus with nonzero spin in the moleeule, and the widths of the various lines in the spectrum [2, 183-186, 390]. The g -faetor determines the magnetic field at which the unpaired electron of the free radieal will resonate at the fixed frequency of the ESR spectrometer (usually 9.5 GHz). The isotropie HFS constants are related to the distribution of the Ti-electron spin density (also ealled spin population) of r-radicals. Line-width effects are correlated with temperature-dependent dynamic processes such as internal rotations and electron-transfer reaetions. Some reviews on organic radicals in solution are given in reference [390]. 

S. Nose, An Extension of the Canonical Ensemble Molecular Dynamics Method, Mol. Phys. 57 (1986) 187-191 S. Nose, A Unified Formulation of the Constant Temperature Molecular Dynamics Methods, J. Chem. Phys. 81 (1984) 511-519 D. J. Evans and B. L. Holian, The Nose-Hoover Thermostat, J. Chem. Phys. 83 (1985) 4069-4074 B. L. Holian, A. F. Voter and R. Ravelo, Thermostatted Molecular Dynamics How to avoid the Toda Demon Hidden in Nose-Hoover Dynamics, Phys. Rev. E 52 (1995), 2338-2347 Luis F. Rull, J.J. Morales and F. Cuadros, Isothermal Molecular-Dynamics Calculations, Phys. Rev. B 32 (1985) 6050-6052. 

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