Chapter 1 Introduction 1 General Introduction
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- 4.6 Thermostating and Mass Rescaling Thermostating
Figure 4.1. Schematic representation of the hysteresis in a slow growth free energy plot. The arrows designate the direction of the scan in terms of the reaction coordinate. It should be noted that although the forces at each time step are determined from a full quantum mechanical electronic structure calculation, the dynamics itself is still classical. Therefore, quantum dynamical effects such as the tunneling are not included in the estimates of the reaction free energy barriers. Since the classical vibrational energy levels are continuous, Hvib = RT/2 for all states, the zero point energy correction and ∆Hvib are also not included in the free energy barriers derived from the AIMD simulation. 4.6 Thermostating and Mass Rescaling Thermostating. When a the nuclei of a molecular simulation follow Newton's equations of motion, the total energy of the system is conserved. Furthermore, when the volume is held constant (cell size fixed) then the simulation will generate a microcanonical (NVE) ensemble. When studying chemical reactions, this type of dynamics may be undesirable because the excess heat that is dissipated or absorbed during a reaction could alter the temperature of the system to unwanted values. For this reason the temperature of a molecular dynamics simulation is often controlled, or thermostated, such that a canonical or NVT ensemble is generated. A common thermostating procedure is to coupling the molecular system to a heatbath through the method of Nosé147. In this method,◊ an extra degree of freedom corresponding to the heatbath is added to the existing degrees of freedom of the molecular system. A kinetic energy and a potential energy term representing the heatbath are added to the Hamiltonian which allows energy to flow dynamically back and forth between the system and the heatbath. The Nosé thermostat effects the nuclear motion via a velocity dependent friction term in the equations of motion as expressed in equation 4-12.  (4-12)
The friction term is governed by the variable which obeys its own equation of motion as given by equation 4-13.  (4-13)
In this way, the kinetic energy of the nuclei fluctuates about the mean value  , where g is the number of degrees of freedom of the nuclear system, kB is the Boltzmann constant and T is the desired physical temperature of the simulation. Q in equation 4-13 is an inertial parameter which controls the time scale of the thermal fluctuations. It should be noted that a simulation that is Nosé thermostated also conserves energy if the thermostat potential,  , and kinetic energy,  , are added to the total energy.
It has recently been shown by Blöchl and Parrinello149 that the Nosé thermostating method for maintaining constant temperature molecular dynamics can be extended to the fictitious kinetic energy of the wave function in the Car-Parrinello methodology. In this context the thermostat acts to prevent the electronic wave function from slowly drifting away from the Born-Oppenheimer potential surface. The thermostating of the wave function in this way allows stable Car-Parrinello molecular dynamics to be performed for long periods of time without the need of periodically quenching the wave function to the Born-Oppenheimer potential surface. Directory: wp-content -> uploads uploads -> 587 Return function, r i(X) r i(0) r i(1) r i(2) r i(3) 1 0 2 4 6 Thermal Station, I 2 0 1 5 6 3 0 3 5 6 10 uploads -> The Case Against the nypd’s Quota-Driven ‘Broken Windows’ Policing What Is It? uploads -> For want of a nail uploads -> Police Militarization uploads -> Stop Militarizing Law Enforcement Act of 2014 uploads -> 2017 afoCo Landmark Scholarship Program uploads -> Instructions for the Preparation of Camera-Ready Contributions to the Conference Proceedings uploads -> Medical Radiography Program uploads -> Ihbb asian Championships 2014 middle school bowl Round 4 First Quarter uploads -> Ihbb european Championships 2014 Bowl Round 4 First Quarter Download 4.36 Mb. Share with your friends:
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