There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The Weighted Histogram Analysis Method (WHAM), an extension of Ferrenberg and Swendsen's Multiple Histogram Technique, has been applied for the first time on complex biomolecular Hamiltonians. The method is presented here as an extension of the Umbrella Sampling method for free-energy and Potential of Mean Force calculations. This algorithm possesses the following advantages over methods that are currently employed: (1) It provides a built-in estimate of sampling errors thereby yielding objective estimates of the optimal location and length of additional simulations needed to achieve a desired level of precision; (2) it yields the “best” value of free energies by taking into account all the simulations so as to minimize the statistical errors; (3) in addition to optimizing the links between simulations, it also allows multiple overlaps of probability distributions for obtaining better estimates of the free-energy differences. By recasting the Ferrenberg–Swendsen Multiple Histogram equations in a form suitable for molecular mechanics type Hamiltonians, we have demonstrated the feasibility and robustness of this method by applying it to a test problem of the generation of the Potential of Mean Force profile of the pseudorotation phase angle of the sugar ring in deoxyadenosine. © 1992 by John Wiley & Sons, Inc.

The weighted histogram analysis method for free-energy calculations on biomolecules. I: The method

Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling

http://experimentationlab.berkeley.edu/sites/default/files/AFMImages/butt_AFM.pdf

Force measurements with the atomic force microscope: Technique, interpretation and applications

Implicit Solvation Models: Equilibria, Structure, Spectra, and Dynamics.

Gas-liquid coexistence and demixing in systems with highly directional pair potentials

The Gaussian overlap model for anisotropic particles is generalized to include ellipsoids which are not axially symmetric. Explicit analytical expressions are given for the potential and for the torques necessary in molecular dynamics (MD) simulations. Employing this model, we have obtained MD results for several systems carefully selected to determine the influence of molecular biaxiality upon the formation of uniaxial nematic phases. By comparing systems of biaxial and axially symmetric particles with the same length‐to‐breadth ratio and at the same reduced density and temperature, it is clearly shown that even relatively little molecular ‘‘flatness’’ can significantly favor the formation of a uniaxial nematic phase. For example, ellipsoids characterized by the aspect ratios 2:3:9 form a stable nematic whereas the axially symmetric counterpart (i.e., 3:3:9) has no stable liquid crystal phase.

A generalized Gaussian overlap model for fluids of anisotropic particles

Grand canonical Monte Carlo calculations are used to investigate the demixing transition in model ionic solutions where the solvent is explicitly included. Charged hard sphere ions in hard sphere, dipolar hard sphere and quadrupolar hard sphere solvents are considered and the results are compared with the primitive (continuum solvent) model. For all solvents considered, it is found that the demixing transition is in the same general region of the phase diagram and is roughly described by liquid-vapor equilibrium in the primitive model. However, details such as the precise location of the critical point and the width of the unstable region depend upon the exact nature of the solvent.

Phase behavior of ionic solutions : comparison of the primitive and explicit solvent models

In this paper the reference hypernetted-chain (RHNC) and reference linearized hypernetted-chain (RLHNC) theories for 1 : 1 electrolytes solutions are compared with molecular dynamics (MD) simulations at ∼ 1 M. It is shown that the theoretical results and MD calculations are generally in good agreement for the solvent-solvent and ion-solvent correlation functions. For the solutions considered the full RHNC theory does not greatly improve upon the RLHNC approximation, but it does give significantly more accurate results for the ion-solvent correlations and for the dielectric constant. Convergence difficulties in the MD calculations prevent an unambiguous evaluation of the theoretical predictions for the ion-ion structure and a discussion of this problem is given.

A comparison between computer simulation and theoretical results for ionic solutions

Grand Canonical Monte Carlo calculations are used to examine the phase behavior of model binary liquid mixtures confined between parallel plates. The stable and metastable states are identified by direct evaluation of the grand potential. It is shown that demixing transitions can lead to long-range attractive forces acting between the plates, verifying earlier predictions based on approximate integral equation theories. The nature of these transitions and the physical origin of the accompanying attractive forces are discussed.

G. N. Patey

Papers

Gas-liquid coexistence and demixing in systems with highly directional pair potentials

A generalized Gaussian overlap model for fluids of anisotropic particles

Phase behavior of ionic solutions : comparison of the primitive and explicit solvent models

A comparison between computer simulation and theoretical results for ionic solutions

Demixing and the force between parallel plates immersed in binary liquid mixtures