We develop new computational methods that can be used to carry out more effective and efficient molecular simulations. Some examples of our work in this area are given below.

**Reservoir Sampling Monte Carlo**

It is well known that flexible molecules having dependent internal coordiantes poses special problems for Monte Carlo sampling. We have developed an approach which breaks molecules into fragments, each of which is connected to another fragment via a bond about which a single dihedral angle exists. The internal coordiantes of the fragments are sampled from a known probability distribution in a "reservoir". When the time comes to either regrow a molecule (in an open ensemble simulation) or alter internal coordinates (in a normal thermal equilibration move) the fragments are reassembled in "tinker toy" fashion using configurational bias methods. The image below shows how an alkylimidazolium cation might be decomposed into fragments.

The figure below shows the probability distribution of the six dependent bond angles in neopentane sampled with the method. Brute force Boltzmann rejection methods required 25 minutes to generate 1000 successful neopentane confirmations at 300 K. With the reservoir sampling method, 1000 configurations were generated in 0.03s!

For more information, see: Jindal K. Shah and Edward J. Maginn, "A General and Efficient Monte Carlo Method for Sampling Intramolecular Degrees of Freedom of Branched and Cyclic Molecules", *Journal of Chemical Physics*, **2011**, 135, 134121.

**Continuous Fractional Component Method**

Insertions and deletions of molecules in open ensembles are notoriously difficult for large molecules and/or dense systems. Even for a relatively simple molecule like water, unbiased insertions and deletions have acceptance probabilities well below 0.1% at room temperature. We have developed a procedure that makes these moves much more efficient by performing the insertions and deletions *gradually*. We call the technique the "continuous fractional component" method; it draws upon concepts from expanded ensemble and flat histogram sampling approaches to couple or decouple molecules in a simulation box through a series of stochastic moves. When the interaction energy is completely "turned off" the molecle is "deleted" and when the molecule is fully coupled to the system, it is "inserted".

As an example, the figure above shows a schematic of a liquid-vapor Gibbs ensemble simulation. On the left is a weakly coupled fractional molecule in the liquid with coupling parameter lambda=0.2 and a vapor phase containing a fractional molecule with coupling parameter lambda=0.8. A stochastic move is made to reduce the coupling strength in the liquid box by 0.4 and increase the strength in the vapor box by 0.4. This results in the deletion of the liquid molecule and the "reassignment" of the residual -0.2 coupling to a random liquid molecule. Likewise, the fractional molecule becomes fully coupled in the vapor box and a new very weakly coupled (lambda=0.2) molecule is randomly inserted elsewhere.

More details of the method can be found here:

Wei Shi and Edward J. Maginn, “Improvement in Molecule Exchange Efficiency in Gibbs Ensemble Monte Carlo: Development and Implementation of the Continuous Fractional Component Move”, *Journal of Computational Chemistry*, **2008**, 29, 2520-2530.

Wei Shi and Edward J. Maginn, “Continuous Fractional Component Monte Carlo: An Adaptive Biasing Method for Open System Atomistic Simulations”, *Journal of Chemical Theory and Computation*, **2007**, 3, 1451-1463.