5,656 research outputs found
Real single ion solvation free energies with quantum mechanical simulation
Single ion solvation free energies are one of the most important properties
of electrolyte solutions and yet there is ongoing debate about what these
values are. Only the values for neutral ion pairs are known. Here, we use DFT
interaction potentials with molecular dynamics simulation (DFT-MD) combined
with a modified version of the quasi-chemical theory (QCT) to calculate these
energies for the lithium and fluoride ions. A method to correct for the error
in the DFT functional is developed and very good agreement with the
experimental value for the lithium fluoride pair is obtained. Moreover, this
method partitions the energies into physically intuitive terms such as surface
potential, cavity and charging energies which are amenable to descriptions with
reduced models. Our research suggests that lithium's solvation free energy is
dominated by the free energetics of a charged hard sphere, whereas fluoride
exhibits significant quantum mechanical behavior that cannot be simply
described with a reduced model.Comment: 13 pages, 4 figure
Electrostatic solvation free energies of charged hard spheres using molecular dynamics with density functional theory interactions
Determining the solvation free energies of single ions in water is one of the
most fundamental problems in physical chemistry and yet many unresolved
questions remain. In particular, the ability to decompose the solvation free
energy into simple and intuitive contributions will have important implications
for models of electrolyte solution. Here, we provide definitions of the various
types of single ion solvation free energies based on different simulation
protocols. We calculate solvation free energies of charged hard spheres using
density functional theory interaction potentials with molecular dynamics
simulation (DFT-MD) and isolate the effects of charge and cavitation, comparing
to the Born (linear response) model. We show that using uncorrected Ewald
summation leads to unphysical values for the single ion solvation free energy
and that charging free energies for cations are approximately linear as a
function of charge but that there is a small non-linearity for small anions.
The charge hydration asymmetry (CHA) for hard spheres, determined with quantum
mechanics, is much larger than for the analogous real ions. This suggests that
real ions, particularly anions, are significantly more complex than simple
charged hard spheres, a commonly employed representation.Comment: 28 pages, 5 figure
On the existence of infinitely many closed geodesics on orbifolds of revolution
Using the theory of geodesics on surfaces of revolution, we introduce the
period function. We use this as our main tool in showing that any
two-dimensional orbifold of revolution homeomorphic to S^2 must contain an
infinite number of geometrically distinct closed geodesics. Since any such
orbifold of revolution can be regarded as a topological two-sphere with metric
singularities, we will have extended Bangert's theorem on the existence of
infinitely many closed geodesics on any smooth Riemannian two-sphere. In
addition, we give an example of a two-sphere cone-manifold of revolution which
possesses a single closed geodesic, thus showing that Bangert's result does not
hold in the wider class of closed surfaces with cone manifold structures.Comment: 21 pages, 4 figures; for a PDF version see
http://www.calpoly.edu/~jborzell/Publications/publications.htm
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