David A. Kofke
Graduate Students
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Our research aims to improve the ability of molecular simulation to describe the properties of materials. Improvements of this type can be made in two directions:
  • simulation methods can be developed to expand the range of phenomena accessible to molecular simulation; one might view these as qualitative improvements to the field
  • molecular models studied by simulation can be constructed to yield more realistic descriptions of the systems being modeled; these are more quantitative improvements to the field

Specific application areas targeted by our group are as follows.

Understanding free-energy calculations

The free-energy perturbation (FEP) method is a core technique in computational chemistry. Despite its importance and wide use, it is frequently applied in ways that are inefficient at best, and incorrect at worst. FEP calculations can be performed in either of two directions, depending on which system is taken as the reference. It is well known that these two calculations lead to results that differ systematically. One mistake commonly made is to assume that both calculations are equally wrong, and the best result is obtained by splitting the difference. By applying modeling concepts to the simulation process itself, we have shown that this heuristic is incorrect, and we have formulated one that is much more reliable. Staged FEP calculations are usually optimized by equalizing the free-energy difference between stages. We have found that this heuristic too is incorrect, and can lead to imprecisions that are several orders of magnitude worse than an approach based on consideration of entropy differences.

Efficient evaluation of free-energies and phase equilibria in solids

Calculating the free energy of solid phases is more difficult than in fluid phases. Fluid free-energies are simpler because they can be evaluated by a process of inserting a single molecule. Because this is not such a big change (it describes a thermodynamically intensive property, the chemical potential), free-energy methods can handle it without great difficulty. In solids, molecule insertion cannot be completed without introducing a defect in the lattice, and this complicates the use of such methods. Instead, the standard method involves thermodynamic integration of the whole solid to a reference system, such as an Einstein crystal. This is a big change (involving the full extensive free energy), and so it is an expensive calculation to compute the free-energy along this path. In our research we are attempting to develop efficient free-energy methods for solids.

Molecular and engineering modeling of hydrogen fluoride

This project is concerned with the development of models that can predict and characterize a broad range of properties of hydrogen fluoride (HF) and its mixtures with water. The specific aim of the project is to develop and test molecular models appropriate for these systems, and to use the observed microscopic behaviors to formulate better engineering models. Hydrogen fluoride is an excellent candidate on which to base this development, and for many reasons:
  • HF is a very important substance commercially, but it is poorly characterized experimentally because it is extraordinarily difficult and dangerous to work with;
  • HF is a very small molecule. Thus, with He and H2, it is among the most intensively studied systems using ab initio methods;
  • despite its small size, HF exhibits behavior complex enough to elude adequate description by engineering models;
  • its associating nature leads to the formation of hydrogen-bonded chains, but because it forms few if any branched aggregates engineering modeling does not have to contend with the effects of complex hydrogen-bonded networks (prevalent, for example, in water)-thus it is reasonable to expect that a very good molecular-based engineering model for HF is within reach.
The larger aim in all of this work is the advancement of modeling techniques that bridge ab initio quantum chemistry and bulk-phase modeling via molecular simulation. Thus the specific focus of the project provides a vehicle for treating a problem of much broader impact.

Object-oriented programming in molecular simulation

This is less a research than a development project driven by an interest in applying molecular simulation as a teaching tool. More on that topic is available on the teaching page. We are investigating the feasibility of using the molecular simulation teaching tools as a basis for constructing extensible, object-oriented research-quality molecular simulation codes. Etomica is the name of the API and development environment that we are constructing. We now have a page devoted to describing and disseminating it.