Date of Graduation


Document Type


Degree Name

Doctor of Philosophy in Chemistry (PhD)

Degree Level



Chemistry & Biochemistry


Feng Wang

Committee Member

Peter Pulay

Second Committee Member

Colin Heyes

Third Committee Member

Jingyi Chen


Curvature, Long Time Correlation, Markov State Model, Molecular Dynamics, Nanodroplets, Surface Tension


The surface tension of nanoscale droplets of water was studied with molecular dynamics simulations using the BLYPSP-4F water potential. The internal pressure of the droplet was measured using a correlation between the pressure and density, established through a series of bulk simulations performed at pressures from 1 to 1000 bar. Such a procedure allows for reliable determination of internal pressure without the need to calculate the local Virial. The surface tension, estimated with the Young-Laplace relation, shows a good agreement with the Tolman equation with a Tolman length of -0.48 Å. The interface of a liquid water droplet is shown to be around 1.1 to 1.3 nm thick depending on radii. The fairly thick interface region put an upper limit on the size of droplets that still have a bulk-like interior.

The effect for removing weak longtime correlation is studied using a model system that contains a driven atom at liquid density under strong thermal fluctuations. The force that drives the tagged particle is about 1% the average random force experienced by the particle. The tagged particle is allowed to assume a range of masses from 1/8 to 800 times that of a surrounding particle to study the effects of inertia. The driving force is indefinitely correlated but much weaker than “random” fluctuations from the environment. From this study, it is shown that the environmental influence is not fully random leading to the force autocorrelation function being a poor metric for detecting the correlated driving force. For systems with small inertia, our study reveals that discarding longtime correlation has negligible influence on the first passage time (FPT) estimate, whereas for particles with large inertia, the deviation can indeed be appreciable. It is interesting that the Markov State Model (MSM) still produces reasonable estimates on the FPT even when a very short lag time that clearly violates the Markovianity assumption is used. This is likely a result of favorable error cancellations when the MSM transition matrices were constructed with trajectories much longer than the lag time.