able free of charge,are,e.g.,Amber/Sander8,CHARMM,NAMD10,NWCHEM!1 and LAMMPS!2」 2 Models for Particle Interactions A system is completely determined through it's Hamiltoian =Hto +H1,where Ho is the internal part of the Hamiltonian,given as N 0=+∑4，)+u,,r)+ (2) =1 i<j i<j where p is the momentum,m the mass of the particles and u and u(3)are pair and three- body interaction potentials.H is an external part,which can include time dependent effects or external sources for a force.All simulated objects are defined within a model description.Often a precise knowledge of the interaction between atoms,molecules or sur- faces are not known and the model is constructed in order to describe the main features of some observables.Besides boundary conditions.which are imposed.it is the model which completely determines the system from the physical point of view.In classical simulations the objects are most often described by point-like centers which interact through pair-or multibody interaction potentials.In that way the highly complex description of electron dynamics is abandoned and an effective picture is adopted where the main features like the hard core of a particle,electric multipoles or internal degrees of freedom of a molecules are modeled by a set of parameters and(most often)analytical functions which depend on the mutual position of particles in the configuration.Since the parameters and functions give a complete information of the system's energy as well as the force acting on each particle through F=-VU,the combination of parameters and functions is also called a force field.Different types of force field were developed during the last ten years.Among them are e.g.MM313,MM414,Dreiding15,SHARP6,VALBON7,UFFI8,CFF9519 AMBER20 CHARMM21,OPLS22 and MMFF23.Typical examples for force field functions are summerized in Fig.2. There are major differences to be noticed for the potential forms.The first distinction is to be made between pair-and multibody potentials.In systems with no constraints,the interaction is most often described by pair potentials,which is simple to implement into a program.In the case where multibody potentials come into play,the counting of interaction partners becomes increasingly more complex and dramatically slows down the execution of the program.Only for the case where interaction partners are known in advance,e.g. in the case of torsional or bending motions of a molecule can the interaction be calculated efficiently by using neighbor lists or by an intelligent way of indexing the molecular sites. A second important difference between interactions is the spatial extent of the potential, classifying it into short and long range interactions.If the potential drops down to zero faster than r-d,where r is the separation between two particles and d the dimension of the problem,it is called short ranged,otherwise it is long ranged.This becomes clear by considering the integral drd oo:n≤d finite n>d (3) 215able free of charge, are, e.g., Amber/Sander8 , CHARMM9 , NAMD10 , NWCHEM11 and LAMMPS12 . 2 Models for Particle Interactions A system is completely determined through it’s Hamiltoian H = H0 + H1, where H0 is the internal part of the Hamiltonian, given as H0 = X N i=1 p 2 i 2mi + X N i<j u(ri , rj ) + X N i<j u (3)(ri , rj , rk) + . . . (2) where p is the momentum, m the mass of the particles and u and u (3) are pair and three￾body interaction potentials. H1 is an external part, which can include time dependent effects or external sources for a force. All simulated objects are defined within a model description. Often a precise knowledge of the interaction between atoms, molecules or sur￾faces are not known and the model is constructed in order to describe the main features of some observables. Besides boundary conditions, which are imposed, it is the model which completely determines the system from the physical point of view. In classical simulations the objects are most often described by point-like centers which interact through pair- or multibody interaction potentials. In that way the highly complex description of electron dynamics is abandoned and an effective picture is adopted where the main features like the hard core of a particle, electric multipoles or internal degrees of freedom of a molecules are modeled by a set of parameters and (most often) analytical functions which depend on the mutual position of particles in the configuration. Since the parameters and functions give a complete information of the system’s energy as well as the force acting on each particle through F = −∇U, the combination of parameters and functions is also called a force field. Different types of force field were developed during the last ten years. Among them are e.g. MM313 , MM414 , Dreiding15 , SHARP16 , VALBON17 , UFF18 , CFF9519 , AMBER20 CHARMM21 , OPLS22 and MMFF23 . Typical examples for force field functions are summerized in Fig. 2. There are major differences to be noticed for the potential forms. The first distinction is to be made between pair- and multibody potentials. In systems with no constraints, the interaction is most often described by pair potentials, which is simple to implement into a program. In the case where multibody potentials come into play, the counting of interaction partners becomes increasingly more complex and dramatically slows down the execution of the program. Only for the case where interaction partners are known in advance, e.g. in the case of torsional or bending motions of a molecule can the interaction be calculated efficiently by using neighbor lists or by an intelligent way of indexing the molecular sites. A second important difference between interactionsis the spatial extent of the potential, classifying it into short and long range interactions. If the potential drops down to zero faster than r −d , where r is the separation between two particles and d the dimension of the problem, it is called short ranged, otherwise it is long ranged. This becomes clear by considering the integral I = Z drd r n =  ∞ : n ≤ d finite : n > d (3) 215