The configuration of an *N*-particle system in 3-dimensional space can be described classically by a point in a *3N* dimensional configuration space. Only a few, very small parts of this *3N* dimensional configuration space, termed "phase space", possess favorable (low) potential energies and make significant contributions to the average properties of the *N*-particle system. In contrast, the overwhelming part of configuration space is characterized by high potential energies and makes only a negligible contribution to the average properties. Sampling problems arise when the important regions of phase space are separated from each other by large free energy barriers. These large barriers cause sampling bottlenecks resulting in very long relaxation times. A prime challenge for particle-based simulations is to develop algorithms that allow the system to jump directly from one important region to another. This is usually achieved by special Monte Carlo algorithms that use specific biasing schemes to locate configurations that make significant contributions to the phase space averages. Over the past several years, the Siepmann group has contributed to the development of the following algorithms:

### Configurational-Bias Monte Carlo (CBMC)

allows for the efficient sampling of the conformational space of linear chain molecules in condensed phases

- J.I. Siepmann, "A method for the direct calculation of chemical potentials for dense chain systems",
*Mol. Phys.***70**, 1145-1158 (1990). - J.I. Siepmann and D. Frenkel, "Configurational-bias Monte Carlo - A new sampling scheme for flexible chains",
*Mol. Phys.***75**, 59-70 (1992).

### Coupled-Decoupled Configurational-Bias Monte Carlo (CD-CBMC)

allows for the efficient sampling of the conformational space of branched chain molecules

- M.G. Martin, and J.I. Siepmann, "Novel configurational-bias Monte Carlo method for branched molecules. Transferable Potentials for Phase Equilibria. 2. United-atom description of branched alkanes",
*J. Phys. Chem. B***103**, 4508-4517 (1999).

### Self-Adapting Fixed-Endpoint Configurantional-Bias Monte Carlo (SAFE-CBMC)

allows for the efficient sampling of the conformational space of cyclic molecules and high-molecular-weight polymers

- C.D. Wick and J.I. Siepmann, "Self-adapting fixed-endpoint configurational-bias Monte Carlo method for the regrowth of interior segments of chain molecules with strong intramolecular interactions",
*Macromolecules***33**, 7207-7218 (2000).

### Aggregation-Volume-Bias Monte Carlo (AVBMC)

allows for the efficient sampling of the spatial distribution of aggregating (hydrogen-bonding) molecules

- B. Chen and J.I. Siepmann, "A novel Monte Carlo algorithm for simulating strongly associating fluids: Applications to water, hydrogen fluoride, and acetic acid",
*J. Phys. Chem. B***104**, 8725-8734 (2000). - B. Chen and J.I. Siepmann, "Improving the efficiency of the aggregation-volume-bias Monte Carlo algorithm,"
*J. Phys. Chem. B***105**, 11275-11282 (2001).

### Adiabatic Nuclear Electronic Sampling Monte Carlo (ANES-MC)

allows for the efficient sampling of polarizable force fields

- B. Chen, and J.I. Siepmann, "Monte Carlo algorithms for simulating systems with adiabatic separation of electronic and nuclear degrees of freedom",
*Theor. Chem. Acc.***103**, 87-104 (1999). - B. Chen, J.J. Potoff, and J.I. Siepmann, "Adiabatic nuclear and electronic sampling Monte Carlo simulations in the Gibbs ensemble: Application to polarizable force fields for water",
*J. Phys. Chem. B***104**, 2378-2390 (2000).

### Aggregation-Volume-Bias Monte Carlo with Self-Adaptive Umbrella Sampling and Histogram Reweighting (AVUS-HR)

allows for the exceedingly efficient sampling of nucleation phenomena

- B. Chen, J.I. Siepmann, and M.L. Klein, "Simulating vapor-liquid nucleation of water: A combined histogram-reweighting and aggregation-volume-bias Monte Carlo investigation for fixed-charge and polarizable models,"
*J. Phys. Chem. A*,**109**, 1137-1145 (2005).