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Emanuele Curotto
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, Arcadia University

Work carried out from September 2010 through August 2011

The analytical model developed during the 2009 - 2010 year for the interaction between rigid ammonia and rigid hydrogen molecules has been substantially revised and significantly improved. The earlier model was too costly to use in simulations of para and ortho-hydrogen - ammonia since the expectation values for parts of the model over the rotational states of hydrogen had to be evaluated numerically. In the new version of the model, we make use of distributed multipole expansions, with four sources on the ammonia molecule and one source on the hydrogen molecule. The model is ten times more accurate than its earlier version without the need to employ additional artificial terms. We develop a general procedure to compute ortho and para hydrogen surfaces using both the ground rotational state for the respective species, or if one so chooses, for the "hindered rotor" treatment. Algorithms for these surfaces now can be easily implemented. We use the three surfaces: a) oH

_{2}- NH_{3}, b) pH_{2}- NH_{3}and c) classical H_{2}- NH_{3}to compare the structure each model predicts for the global minimum, and to compute the second virial coefficient for each. We find that the classical hydrogen - ammonia model places the hydrogen molecule as the "hydrogen" bond donor as it orients itself along the axis of symmetry of ammonia and coordinates the nitrogen lone pair. By contrast, the global minima of oH_{2}- NH_{3}, and pH_{2}- NH_{3}have the ammonia molecule as the hydrogen bond donor. The minimum energy for the classical hydrogen - ammonia dimer is at -1.1164 mhartree. The minimum energy obtained for the para-hydrogen - ammonia is -0.287 mhartree, and for ortho-hydrogen - ammonia is -0.516 mhartree. An article detailing the functional form of the model, containing the parameters and the general procedure to compute ortho and para hydrogen - ammonia surfaces using both the ground rotational state for the respective species, or the "hindered rotor" treatment has been submitted for publication.Using a distributed multipole expansion, and several ab initio calculations at the MP2 level with a converged basis set size and the counterpoise correction, we formulate a model for water - water interaction that includes the important polarization effects without using empirical data. To achieve this, we formulate a distributed multipole expansion with three sources on each water molecule, we include as radial functions physically meaningful expressions for the electrostatic, the repulsive, and the dispersive interaction. We then add a non recursive polarization energy by placing a charge on the spring on each oxygen atom. We compute the zero order electrostatic field on each oxygen atom using the distributed multipole expression for the field, and after displacing the charge on the spring along the resulting direction of the zero order field, we compute a first order electrostatic field. The sum of the square of these is used to compute the polarization energy. We are in the process of generating important configurations of the trimer to be used for further MP2 level theory training data to refine all the parameters. The aim of the work is to produce a reasonable model for water clusters with three body interactions included that does not contain empirically fitted parameters. Empirically fitted potential and not adequate for the quantum simulation of clusters, and often, these surfaces fail to reproduce classical results for clusters that are well established in the literature. The three body potential for water by Kumar and Skinner has been implemented to study the relative importance of cooperative and anti-cooperative contributions from multiple hydrogen bonds in the TIP4P trimer at finite temperature. These simulations will soon yield the most important configurations needed to generate additional training data for our own model. However, we believe that the analysis will be deeply insightful in our investigations of the hydrogen bond networks.

We have continued to explore the Smart Darting approach, using the n-dimensional Decoupled Double Wells [(DDW)

_{n}] potential energy surfaces (PES) for which we can obtain deterministic results for both classical and quantum particles. 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 the actions involved in properly comparing structures, assigning these to neighborhoods surrounding minima, and the action of darting to another neighborhood, involve transformations of coordinates. Therefore, the proper Jacobian has to be computed and included in the acceptance rejection algorithm that generates the random walk. These steps are nontrivial for atomic clusters and become very complicated to implement for systems of rigid molecules. This year we have extended our exploration to the Diffusion Monte Carlo algorithm. With the parameters we have chosen for the (DDW)_{n}potential energy surface, we find that a mass of 200 atomic units or higher creates significant convergence issues for both guided and unguided DMC when n > 10 dimensions. We develop a method to incorporate Smart Darting into the Diffusion Monte Carlo algorithm that can substantially improve the convergence of the random walk to the proper ground state wavefunction, or the product of this with the variational trial wavefunction if the guided version is implemented. We show that the Smart Darting procedure introduces a bias into the resulting energy, but this can be easily controlled without impacting the effectiveness of the approach. We believe this to be a significant finding because, as we have demonstrated in the past, the Diffusion Monte Carlo algorithm does not need Jacobian terms, and the ground state wavefunction for clusters is usually dominated by one or only few relevant structures. The approach we have developed promises to extend the determination of ground states of clusters to sizes that are currently intractable. An article detailing our method and our results is in preparation.