9 Molecular Dynamics Simulations in Biology,Chemistry and Physics 183 value of 2(2/3)1/2=1.633 in an ice Ih-type lattice.The increasing width with increasing distance is an indication of increasing disorder in the liquid.The first two peaks in gon(r)and gHH(r)correspond to the average intramolecu- lar distances of O-H and H-H,respectively.For further discussions we refer to[9.27]. The RDFs of water and ice from 220 to 673 K and at pressures up to 400 MPa have recently been discussed on the basis of neutron scattering data 9.26.It is interesting to note that in the ice formation there is still substantial disorder in the hydrogen bonding pattern as can be checked from the width of the RDFs.MD simulations of the phase transition,i.e.,freezing of water to ice,are more difficult to achieve than melting of ice.There have only been a few successful MD runs of free (i.e.,not confined)water which show ice nucleation and subsequent percolation of the nucleus throughout the simulation box containing 512 water molecules [9.34].Due to the complex global potential-energy surface,a large number of possible network config- urations are possible.This causes large structural fluctuations showing up in the simulations hindering the system to find an easy pathway from the liquid to the frozen state (in spite of the fact that water molecules forming tiny ice-like clusters with four-coordinated hydrogen bonds have by 2 kJ/mol lower potential energy than that of other water molecules 9.34).Results of MD simulations of ice nucleation are shown in Fig.9.2. The constant-temperature MD simulations have been done for 512 mole- cules in the simulation box with a time step of 1 fs.The TIP4P model for water has been employed,which is a flat 4-center model with a potential energy consisting of Coulomb and Lennard-Jones terms,whereby the oxygen charge is shifted to a fourth site located closer but equidistant from the two hydrogen atoms 9.35. The essential four stages in the freezing process are discussed in detail in [9.34].The simulations show that the number of six-member rings N6R fuctuates during the simulations but only increases after an initial nucleus has formed and the ice-growth process has set in,see Fig.9.2b and following. The authors investigated also the so-called Q6 parameter [9.36,which may serve to characterize in how far the hydrogen bonds are coherently (icosa- hedrally)ordered.From the simulations it seems to follow that neither N6R nor Q6 are suitable order parameters to describe the entire freezing process. Obviously coherent icosahedral orientational correlations are an imperfect so- lution to characterize tetrahedral packing of water molecules as in ice [9.36. The reverse process,melting of ice,is easier to simulate.In the following we briefly present results of melting of water clusters simulated by our group. Numerous studies have been devoted to understand the dynamics of small clusters of water since the beginning of simulation studies in the 1970s and to elucidate the nature of the pseudo-first order melting transition. Our aim is to simulate the melting of water clusters (H2O)n of selected sizes (shown in Fig.9.3)and how their properties evolve with size from ab initio type of calculations using the DFTB method [9.37].Some of the bigger9 Molecular Dynamics Simulations in Biology, Chemistry and Physics 183 value of 2(2/3)1/2 = 1.633 in an ice Ih-type lattice. The increasing width with increasing distance is an indication of increasing disorder in the liquid. The first two peaks in gOH(r) and gHH(r) correspond to the average intramolecu￾lar distances of O–H and H–H, respectively. For further discussions we refer to [9.27]. The RDFs of water and ice from 220 to 673 K and at pressures up to 400 MPa have recently been discussed on the basis of neutron scattering data [9.26]. It is interesting to note that in the ice formation there is still substantial disorder in the hydrogen bonding pattern as can be checked from the width of the RDFs. MD simulations of the phase transition, i.e., freezing of water to ice, are more difficult to achieve than melting of ice. There have only been a few successful MD runs of free (i.e., not confined) water which show ice nucleation and subsequent percolation of the nucleus throughout the simulation box containing 512 water molecules [9.34]. Due to the complex global potential-energy surface, a large number of possible network config￾urations are possible. This causes large structural fluctuations showing up in the simulations hindering the system to find an easy pathway from the liquid to the frozen state (in spite of the fact that water molecules forming tiny ice-like clusters with four-coordinated hydrogen bonds have by 2 kJ/mol lower potential energy than that of other water molecules [9.34]). Results of MD simulations of ice nucleation are shown in Fig. 9.2. The constant-temperature MD simulations have been done for 512 mole￾cules in the simulation box with a time step of 1 fs. The TIP4P model for water has been employed, which is a flat 4-center model with a potential energy consisting of Coulomb and Lennard-Jones terms, whereby the oxygen charge is shifted to a fourth site located closer but equidistant from the two hydrogen atoms [9.35]. The essential four stages in the freezing process are discussed in detail in [9.34]. The simulations show that the number of six-member rings N6R fluctuates during the simulations but only increases after an initial nucleus has formed and the ice-growth process has set in, see Fig. 9.2b and following. The authors investigated also the so-called Q6 parameter [9.36], which may serve to characterize in how far the hydrogen bonds are coherently (icosa￾hedrally) ordered. From the simulations it seems to follow that neither N6R nor Q6 are suitable order parameters to describe the entire freezing process. Obviously coherent icosahedral orientational correlations are an imperfect so￾lution to characterize tetrahedral packing of water molecules as in ice [9.36]. The reverse process, melting of ice, is easier to simulate. In the following we briefly present results of melting of water clusters simulated by our group. Numerous studies have been devoted to understand the dynamics of small clusters of water since the beginning of simulation studies in the 1970s and to elucidate the nature of the pseudo-first order melting transition. Our aim is to simulate the melting of water clusters (H2O)n of selected sizes (shown in Fig. 9.3) and how their properties evolve with size from ab initio type of calculations using the DFTB method [9.37]. Some of the bigger