Michael W. MahoneyMy Ph.D. was completed in 2000 in statistical physics, and my dissertation was written under William L. Jorgensen on the computational chemistry of the liquid state. It is entitled "The Computational Statistical Mechanics of Simple Models of Liquid Water," and it is described below.
Among other things, my dissertation introduced the TIP5P model of liquid water, and it resulted in the following four papers:
The Computational Statistical Mechanics of Simple Models of Liquid Water
The computational statistical mechanics of simple models of liquid water has been studied, with particular attention being paid to improving the understanding of the properties of liquid water at a range of thermodynamic state points. A new model, TIP5P, has been developed and describes the density anomaly of liquid water better than previously existing models. Classical statistical mechanical Monte Carlo calculations have been performed to optimize the parameters, especially the position of the negative charges along the lone-pair directions. Calculations performed for 512 molecules with TIP5P demonstrate that the density maximum near 4 C at 1 atm is reproduced and the average error in the density over the 100 degree temperature range from -37.5 C to 62.5 C is only 0.006 g cm-3, while high-quality structural and thermodynamic results are maintained. Its behavior at a wide range of temperatures and pressures has been characterized and it has been found to reproduce the dielectric constant and diffusion constant better than many of the commonly used alternatives.
Other efforts to improve the behavior of simple models of water under at a range of temperatures and pressures have also been performed. For example, the inclusion of electronic polarization and classical flexibility within simple four site models has been examined. Calculations on the four site flexible model TIP4F and the four site polarizable model Dang97 indicate that the behavior of the density as a function of temperature is not improved upon relative to the four site rigid model TIP4P. In addition, quantum mechanical effects on both the rigid TIP5P and the flexible TIP4F models have been examined by performing path integral Monte Carlo calculations. The modification of the behavior of TIP4F and TIP5P relative to the classical results has been characterized at both low and high temperatures. These calculations demonstrate that although the inclusion of quantum effects does not improve the description of the rigid model at a range of state points, it does improve the description of the flexible model relative to classical calculations.
With two exceptions, all of these calculations have been performed with a standard isothermal-isobaric (NPT) ensemble Monte Carlo algorithm. For such an algorithm the temperature and pressure controls are exact and the method of single particle moves permits rapid sampling of phase space for molecules with pairwise decomposable potential functions. The first exception to this is that certain dynamical quantities for TIP5P have been calculated with molecular dynamics. The other exception is that the calculations on Dang97 at a range of temperatures have been performed with a standard molecular dynamics algorithm with a Berendsen coupling scheme. The reason is that for non-pairwise decomposable dipole polarizable potentials there are technical difficulties with the implementation of a rapid Monte Carlo algorithm.
The technical difficulties have been examined in detail. For polarizable models the calculations are orders of magnitude slower than for similar nonpolarizable models not only since an expensive matrix iteration must be performed at each step of the Markov chain but also since the calculations converges more slowly as a function of Markov chain length. Several commonly used approximation methods have been examined and better ones have been developed. These have been characterized by how well they reproduce various electronic, thermodynamic and structural properties for Monte Carlo calculations on two polarizable water models, Dang93 and Dang97. The most promising method involves a modification of the dipoles on molecules near the moved molecule following an initial perturbative modification of the dipoles on every molecule. This has been found to be superior to much more computationally expensive approximation methods.