Rapid Equilibration by algorithmic quenching the ringing mode in molecular dynamics
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Rapid Equilibration by algorithmic quenching the ringing mode in molecular dynamics Graeme J.Ackland School of Physics and Astronomy, The University of Edinburgh, JCMB, Kings Buildings, Mayfield Road, Edinburgh EH9 3FD ABSTRACT Long wavelength acoustic phonons are normally weakly coupled to other vibrational modes in a crystalline system. This is particularly problematic in molecular dynamics calculations where vibrations at the system-size scale are typically excited at initiation. The equilibration time for these vibrations depends on the strength of coupling to other modes, so is typically very long. A very simple deterministic method is presented which removes this problem. Examples of equilibration in lithium and a martensitic phase transition in sodium are used to demonstrate the method. INTRODUCTION Molecular dynamics is a very powerful method for simulating the behaviour of a manyatom system. It is particularly useful and flexible when used for studying phase transitions, since it makes no assumption about the preferred crystal structure. However if the system is not initiated in an equilibrium structure, it may take some time to equilibrate. There is no good theory that enables one to say how long the equilibration will take. Indeed, within statistical mechanics, it is difficult to define what a non-equilibrium state even means. Provided the molecular dynamics is based on some underlying Lagrangian, any simulation will be initiated in a valid microstate of the appropriate ensemble. The reason why this microstate is ``non-equilibrium'' lies outside the realm of statistical mechanics. Probably the only sensible way to address this is via the equipartition theorem, which holds that each degree of freedom has, on average, an equal amount of energy. One might then argue that if a single degree of freedom in a microstate has a macroscopic amount of energy - i.e. a finite fraction of the total energy – then the microstate is atypical and ``non-equilibrium''. One can think here of non-equilibrium situations in the Cartesian coordinate system ri, e.g. a radiation damage simulation where the primary knock-on atom has keV of energy, or of non-equilibrium in the normal modes ui, a simulation in which one phonon mode is massively excited. Unfortunately, even this definition fails in general because of the nonunique definition of degrees of freedom. One can always recast the degrees of freedom in any linear combination - including a linear combination qi, chosen such that all the kinetic energy is in one degree of freedom qi. It is likely that such a perverse choice would have entangled degrees of freedom very far from the normal modes, which describe a typical near-harmonic crystal system. As such, the energy in qi, would disperse quickly into the other qj modes.
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