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Cff EIMICAL PHYSICS LETTERS Volume 55 number 3 ON A NOVEL MONTE CARLO C PANGALI SCHEME FDR SLMULATING I May 1978 WATER AND AQUEOUS SOLUTiONS M RAO and B J BERNE CbiumBk Wiiversity New York New York fUU27 US 4 Received 3 February I978 The usual hfetropolis ltfonte Carlo afgorithm when applied to highiy associated liquids iike ST 2 water is Ehownto be very siow in establishing equilibrium and often Ieads to bottlenecks in configuration space A new Jfgorithm is presented in which the Monte Carfo moves are biased in the direction of the forces and torques acting on tbe individual molecule Comparison with the hfetropoiis scheme shows that this new method is mush more rapidly convergent En this note we introduce a novel rapid convergent Monte Carlo technique and apply it to the study of water where the common Metropolis procedure is very slowly convergent and often leads to bottlenecks in configuration space In the Monte Carlo method 1 2 various configurations of the system are sampled according to the I3oltzmann distributions exp HW t I k qip II where Rj is a vector specifying bo the positions and o entations of molecule j For rigid linear molecufes Ri is a five component vector whereas for rigid noniinear molecuies is a Six component vector is the appropriate volume element To generate a set of contigurations that are distributed according to eq I Metropolis et al 1 2J devised a scheme according to which a new configuration R R t Rh is generated from an aid conf r o R 42 1 RN by sampling a prescribed transition probabihty T R lR and this new configuration is accepted with probability Rj dRj and rejected with probab ty 4 I p In tbls way a random walk over con guratiou space is generated Averages over the distribution 1 are obtained by weighting old configurations with Q and new configurations by p f3 Up to this point the method is quite general Usually the configuration is changed by single particie moves First particle 1 is moved and this move is either accepted or rejected according to eq 3 then this is repeated for psrtiele 2 3 K The full cycle of moves is then repeated Thus aI1 that need be specified is the transition probability for a single particfe move For atomic fluids particlei is dispiaced from Rj to Ri where Ri is randomly sampfed between Ri ARo andRj t A The maximum value of the move is ARu fhuu qAyu A and the larger this parameter the Isrger the region of configuration space sampled in 3 fixed number of iterations but AR0 cannot be made arbitrariiy large because most of the moves will then be rejected The transition probability for the single particle move is then QR Research supported by National Science Foundation under grant NSF CHE 76 02414 and NIH ROi NS 1271402 In partial fulf nent of the Ph D in Chemistry at Cohenbia University Ax0 Ayu AZ i3Rj



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