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Reports: B6 48146-B6: Can Nitrogen Offer a Different Perspective on the Hydrogen Storage Problem? (NH3)n-(H2)m Clusters from Cryogenic Storage as Novel Fuels
Work carried out from September 2009 through August 2010
An analytical model has been developed to describe the interaction between rigid ammonia and rigid hydrogen molecules. The model includes electrostatic terms, atom to atom repulsive terms, induction terms, and polarization terms. The description of polarization effects is introduced by using a non iterative form of the "charge on spring model". The parameters of the model potential are chosen by fitting high quality ab initio data obtained at the MP2 level, with extended basis sets, and where deemed necessary MP4. A total of 19 radial scans are performed to construct a grid of ab initio points. The accuracy of the fit between the model and the ab initio data is approximately 10%. To improve the accuracy of the model we add a Gaussian correction term and we optimize five additional parameters for each of the radial scans. The resulting table is used to compute the parameters for the Gaussian correction for any relative orientation of the two molecules.
Variational Monte Carlo, Diffusion Monte Carlo , and Stereographic Projection Path Integral simulations are performed on eight selected species from the (NH3)n, (ND3)n, (NH2D)n, and (NH3)n-1-ND3 clusters. Each monomer is treated as a rigid body, with the rotation spaces mapped by stereographic projection coordinates. We compare the energy obtained from Path Integral simulations at several low temperatures with those obtained by diffusion Monte Carlo, for two dimers, and we find that at 4 K, the fully deuterated dimer energy is in excellent agreement with the ground state energy of the same. The ground state wavefunction for the (NH3)2-5 clusters is predominantly localized in the global minimum of the potential energy. In all simulations of mixed isotopic substitutions, we find that the heavier isotope is almost exclusively the participant in the hydrogen bond. An article summarizing all these results has been submitted to the Journal of Chemical Physics.
During the past year we tested exhaustively the sampling strength of Parallel Tempering against a set of increasingly complex multi-funneled potential energy surfaces over a wide range of temperatures. We have found a completely deterministic, yet sufficiently complicated system to cause parallel tempering employed with an arbitrarily chosen standard move block size of one million to fail. This is the n-dimensional Decoupled Double Wells [(DDW)n] potential energy surfaces (PES). This investigation has helped elucidate one of the potential problems that are encountered when simulating sufficiently complex systems with Parallel Tempering such as (NH3)11 and Ar38. We have used this system to establish the superiority of the Smart Darting procedure, and to develop Bijective Darting, a method related to Smart Darting that does not require the knowledge of the minima.
Parallel Tempering and Smart Darting are compared using a set of n-dimensional Decoupled Double Wells [(DDW)n] potential energy surfaces (PES) for which we can obtain deterministic results. The (DDW)n family is sufficiently complicated to make Parallel Tempering unfeasible for n > 20 dimensions. Attempts to scale the number of moves with n, optimize temperature schedules, optimize swapping rates, develop alternative swapping strategies, use bias sampling, and introduce seeding methods, fail to improve the overall performance of Parallel Tempering significantly. The Smart Darting method succeeds at reducing quasiergodicity for n >> 100 using just one million moves. Motivated by the success of Smart Darting for the (DW)n family, we study the geometric properties of Eckart spaces. We find a set of transformations from relative coordinates that yield flat nonorthogonal manifolds that contain the Eckart space, and a flat parametrization of the orthogonal rotation group. We demonstrate that classical Monte Carlo simulations do not require the implementation of rotation matrices, Jacobians, or complicated mixtures of moves. Establishing Bijective Darting as an equally valid enhancement to Parallel Tempering was outside of the scope of the article in preparation to be submitted to the Journal of Chemical Physics. We plan on carefully quantifying the enhancement Bijective Darting makes to Parallel Tempering with ammonia clusters starting with the hendecamer. These challenging systems have provided the impetus for the work, however, further development of the theory presented here is necessary and is in progress.
We have developed importance sampling functions for the stochastic evaluation of Feynman Path Integrals in real time. The short-time evolution operator is split into a potential and kinetic local action contributions. The exponential of the kinetic action is remapped with a single stereographic projection coordinate onto the curved, multiply connected space, S1, with unit radius. This summer we have extended the theoretical development to the position - position autocorrelation function and we have discovered that the expression is significantly simpler to implement numerically. We are testing code for the evaluation of the thermally averaged position - position autocorrelation function with a family of quartic potentials. We use the code to produce data that can be readily compared with the results obtained employing vector spaces and explore the efficiency of the algorithms we have generated.
We have optmized two parameter trial wave functions for the evaluation of the ground state of clusters with Variational Monte Carlo, and eventually to improve the efficiency of Diffusion Monte Carlo for atomic and molecular clusters. We tested our approaches with the n-dimensional Decoupled Double Wells [(DDW)n] potential energy surfaces (PES).
We are developing the analytical surfaces for the para-H2 - (NH3)n and ortho-H2 - (NH3)n systems using the analytical surface fitted to the ab initio calculations. The resulting surfaces are used to study properties of the dimer and of the corresponding clusters. We are in the process of writing the code for these calculations.
