57th Annual Report on Research 2012 Under Sponsorship of the ACS Petroleum Research Fund

We have initiated a systematic exploration of the classical minima and the ground state properties of (NH₃)_n-cH₂ and (NH₃)_n-pH₂, where cH₂ is the classical hydrogen molecule and pH₂ is para-hydrogen. The classical minima are systematically searched for (NH₃)_8-20-cH₂ and (NH₃)_8-20-pH₂, whereas the ground state properties are computed for n = 8,12,16,17 , for c-H₂ and pH₂. The sizes above are chosen after a dominant pattern of adsorption for the hydrogen molecule on the ammonia clusters in this size range is observed and first emerges with the octamer: Both the classical and para-hydrogen prefer the site with four ammonia molecules arranged in a rhombic pattern. The sizes 12 and 16 are chosen because of their higher symmetry and increased stability. Both the dodecamer and the hexadecamer of ammonia have cage - like structures. However, neither of them have a cavity sufficiently large to contain a molecule of hydrogen inside. Therefore, the systematic search for the minima is performed by placing the hydrogen molecule randomly on the surface of a sphere with sufficiently large radius to contain comfortably the cluster inside. A large number of Brownian trajectories are generated over the first five minima of the bare ammonia clusters. Comparing the classical minima with the 0K quantum energies allows us to quantify the zero point energy for the systems. We find this to be greater than 90% of the classical energy in many cases. For the n = 17 case we find that neither the classical, nor para-hydrogen are bound when quantum effects are considered. At the same time, our exploration of the minima of bare ammonia clusters continues to seek possible large cages inside which hydrogen can be potentially stored. At the present time, we are performing genetic algorithm minima searches for n = 22 and n = 23. The structure of the global minimum of the former provides insightful information to elucidate the growth pattern of ammonia clusters. With the structure of the global minimum of n = 22 we predict that the n = 27 will be the first cluster to have an ammonia molecule in the center fully coordinated like the bulk ammonia ice, namely, the central molecule is the donor of three hydrogen bonds and the acceptor of three hydrogen bonds simultaneously.

We have formulated an extension of the Ring Polymer dynamics approach to curved spaces using stereographic projection coordinates. We test the theory by simulating the particle in a ring, mapped by a stereographic projection using three potentials. Two of these are quadratic, and one is a nonconfining sinusoidal model. We propose a new class of algorithms for the integration of the Ring Polymer Hamilton equations in curved spaces. These are designed to improve the energy conservation of symplectic integrators based on the split operator approach. For manifolds, the position - position autocorrelation function can be formulated in numerous ways. We find that the position - position autocorrelation function computed from configurations in the Euclidean space, that contains, as a submanifold, the configuration space has the best statistical properties.

We have continued to explore the Smart Darting approach, using the n-dimensional Decoupled Double Wells [(DDW)_n] potential energy surfaces for which we can obtain deterministic results. In previously reported efforts we had found that Smart Darting far outperforms Parallel Tempering for the computations of the classical heat capacity for these systems. The drawback for Smart Darting, as implemented for classical thermodynamic simulations, is that its implementation involves transformations of coordinates. Therefore, the proper Jacobian has to be computed and included in the algorithm that generates the random walk. This is nontrivial for atomic clusters and becomes very complicated to implement for systems of rigid molecules. This year we have extended our exploration of the Decoupled Double Wells [(DDW)_n] for the computation of its thermodynamic properties using several Infinite Swapping and Partial Infinite Swapping algorithms [c.f. N. Plattner, J. D. Doll, P. Dupuis, H. Wang, Y. Liu, and J. E. Gubernatis J. Chem. Phys. 135, 134111 (2011)]. Infinite Swapping (IS) is a technique for rare event sampling that uses, as the sampling distribution, the sum of all possible permutations of the product of n individual distributions, each term associating a set of n walkers with a set of n temperatures. N. Plattner, et. al. demonstrate that such sums symmetrized over all the possible permutations are connected in regions of configuration space where rare events manifest themselves, whereas the individual distributions are not connected and hence, much harder to sample. We have coded a Smart Monte Carlo algorithm for classical simulations in (DDW)_n, we have formulated a generic algorithm for producing all n! permutation operators for up to n = 7 and we have combined this code with the Smart Monte Carlo algorithm code to perform a number of tests. Because the full IS formalism grows factorially over a set of chosen temperatures, and these may not be sufficiently numerous to cover the important regions, a set of partial "shuffle" strategies have been considered by N. Plattner, et. al. We test a 18 - temperature PIS(1-3|3-1) scheme for (DDW)_1-80. We note that the approach works no better than Parallel Tempering. We are in the process of coding and testing a PIS(5|4) and a PIS(6|5) scheme with 20 and 30 temperatures respectively.