Monte-Carlo method Rosenbluth

The essence of the configurational bias Monte Carlo method is that a growing molecule is preferentially directed (i.e. biased) towards acceptable structures The effects of these biases can then be removed by modifying the acceptance rules The configurational bias methods are based upon work published in 1955 by Rosenbluth and Rosenbluth... 

Let us now consider how the configurational bias Monte Carlo method would deal with this problem. Again, the first site (S) is chosen at random. We next consider where to place the second unit. The sites adjacent to S are examined to see which are free. In this case, only two of the four sites are free. One of these free sites is chosen at random. Note that the conventional Monte Carlo procedure selected from all four adjoining sites at random, irrespective of whether it is occupied or not. A Rosenbluth weight for the move is then calculated. The Rosenbluth weight for each step i is given by ... 

Martin M G and J I Siepmann 1999. Novel Configurational-bias Monte Carlo Method tor Branched Molecules Transferable Potentials for Phase Equilibria. 2 United-atom Description of Branched Alkanes Journal of Physical Chemistry 103 4508-4517 Metropolis N, A W Rosenbluth, M N Rosenbluth, A H Teller and E Teller 1953 Equation of State Calculations by Fast Computing Machines. Journal of Chemical Physics 21 1087-1092 Okamoto Y and U H E Hansmann 1995. Thermodynamics of HeUx-coU Transitions Studied by Multicanomcal Algorithms. Journal of Physical Chemistry 99 11276-11287 Panagiotopoulos A Z 1987. Direct Determination of Phase Coexistence Properties of Fluids by Monte Carlo Simulation in a New Ensemble. Molecular Physics 61.813-826 Pangali C, M Rao and B J Berne 1978 On a Novel Monte Carlo Scheme for Simulating Water and Aqueous Solutions Chemical Physics Letters 55 413-417. 

The first molecular simulations were performed almost five decades ago by Metropolis et al. (1953) on a system of hard disks by the Monte Carlo (MC) method. Soon after, hard spheres (Rosenbluth and Rosenbluth, 1954) and Lennard-Jones (Wood and Parker, 1957) particles were also studied by both MC and molecular dynamics (MD). Over the years, the simulation techniques have evolved to deal with more complex systems by introducing different sampling or computational algorithms. Molecular simulation studies have been made of molecules ranging from simple systems (e.g., noble gases, small organic molecules) to complex molecules (e.g., polymers, biomolecules). 

Chai J-D, Head-Gordon M (2008) Long-range corrected hybrid density functionals with damped atom-atom dispersion corrections. Phys Chem Chem Phys 10 6615-6620 Pacchioni G (2008) Modeling doped and defective oxides in catalysis with density functional theory methods room for improvtanent. J Chem Phys 128 182505 Metropolis NA, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equation of state calculations by fast computing machines. J Chem Phys 21 1087-1092 Anderson JB (2007) Quantum Mrmte Carlo. Oxford Uruversity Press, Oxford Hammond BL, Lester WA, Reynolds PJ (1994) Monte Carlo in ab mitio quantum cheirristry. World Scientific, Singapore... 

---