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A.1 molecular dynamics 75a.1.2The thermodynamic ensemblesThe correct numerical integration of the Newton’s equationof motion must provide the conservation of the totalenergy of the system (potential plus kinetic energy). If thesystem is composed by a constant number of particles N, ithas a constant volume V and a constant energy E, the statisticalsystem (ensemble) is called microcanonical (NVE).If the simulation requires constant temperature o pressure,different ensembles can be used. In a canonical ensemble(NVT) the temperature is fixed by coupling the systemwith a thermal bath (the energy fluctuating aroundthe average value). In a NPT ensemble also the pressure iskept constant by using a suitable barostat.a.1.3Temperature controlSince, tipically, the stability and the control of the temperatureis a key issue in a simulation, is important to finda method to control it. The temperature of the system canbe related to the microscopic quantity of the system by theequipartition energy theorem12N∑im i v 2 i = 1 2 N f k B T(A.10)The temperature T can be expressed as function of theatomic velocitiesT = 1N f k B TN∑im i v 2 i(A.11)where N is the number of atoms, N f is the number ofdegrees of freedom, k B is the Boltzmann constant and m iand v i are the mass and the velocity of the atom i. For amolecule composed by N atoms the total degrees of freedomare N f = 3N − N b where N b is the number of thebonds.A rough method to control the temperature in a MD simulationis given by the velocity rescaling method. If thetemperature at the time t is T(t), it is possible to drive thesystem to a target temperature T 0 by rescaling the veloc-