Stereographic Projection Path Integral Simulations of Diatomic Clusters

40946-B6
Stereographic Projection Path Integral Simulations of Diatomic Clusters

Emanuele Curotto, Arcadia University

We have investigated the structural and thermodynamic properties of hydrogen bonded clusters (HX)_n where X = Cl, F. The activities have created data that will guide future experiments, and have been important for the establishment of stereographic projection path integral methods and other algorithms that the group has produced. The work on (HF)_n clusters in particular, [J. Chem. Phys., 124, 174305 (2006).] has sparked the interests of three separate research groups which are now collaborating with us to simulate important molecular assemblies such as those of water [J. Chem. Phys., 126, 084506 (2007).], ammonia, mixed water - hydrogen clusters, and water chlathrates hydrates. The time scale difference between the intramolecular stretching degrees of freedom in the (HX)_n systems and the translations - rotations of the moieties make conventional Euclidean space quantum Monte Carlo methods based on Cartesian Coordinates highly inefficient. Therefore, the stereographic projection path integral for the curved spaces associated with the rotations of n rigid tops allows us, along with a growing community of molecular physicists, to perform otherwise formidable finite temperature quantum simulations of molecular assemblies. At this point, not only have we completed the proposed investigations: a) We have found theoretical expressions that simplify substantially the implementation of Reweighted Random Series Path Integrals (RRSPI) with Stereographic Projection Coordinates (SPC). b) We have generalized the use of SPCs to perform Diffusion Monte Carlo (DMC) simulations in manifolds, [J. Phys. Chem. A., 111,2610 (2007).] and we are currently in the process of developing and testing numerical strategies to include importance sampling, improve the statistical quality and convergence properties of SPC-DMC simulations. These developments will allow us to compute accurately and efficiently the ground state wavefunctions, energy, and related properties for molecular clusters.

The undergraduate student supported by the present grant is the third to graduate from the group with the desire to pursue a Ph.D. in theoretical chemistry. He has been supported by the present grant for the last three summers, has coauthored two articles, and he will begin his graduate work at Berkley in the fall of 2007. Two more students will graduate from the group in the spring of 2008 with the intent to pursue graduate work.

In detail during 2006-2007:

We have developed a potential energy surface (PES) model for (HCl)_n clusters by summing over the interactions between pairs. The pair interaction are obtained using the function optimized for the dimer by M. J. Elrod, and R. J. Saykally, [J. Chem. Phys. 103, 933, (1995).] using high resolution spectroscopy data. A student was trained to implement the genetic algorithm and use this to perform global minima searches in the n = 2 through 19 range.
We have carried out classical and path integral simulations of few HCl clusters, from the dimer through the pentamer.
We produce a number of configuration distributions for the random walks of the pentamer in order to understand the peculiar features of the quantum heat capacity. A student was trained to perform Classical and SPC-RRSPI simulations and to use the structural comparison algorithm. The student performed a number of parallel tempering simulations, and used the comparison algorithm to produce distributions of D₀ , where D₀ is the sum of the distance from atom of configuration 1 to atom of configuration 2. D₀ is measured between a given configuration during the random walk and the global minimum after a set of translations and rotations are performed to find the optimal superposition of the two structures.
Classical parallel tempering simulations for (HCl)_n in the n = 6 through 19 have been carried out. We detect no melting features in any of the heat capacity of these systems. The classical thermodynamic behavior is consistent with the spacing between isomeric energies at the various sizes investigated. There does not seem to be "magic numbers" in the stability patterns.
The presence of bimodal distributions for the pentamer at 10K causes us to wonder if the possibility exists for the two structure involved to coexists at these temperatures because of thermal excitations, or whether the ground state wavefunction of the pentamer is delocalized over the configuration space represented by the two peaks in the configuration distribution. For this purpose we have engaged in the development of DMC methods that can be applied to curved spaces. We concentrated our efforts to extend efficient DMC approaches, like the importance sampling, quadratically converging branching algorithms etc, and we test a novel kind of variational wavefunctions designed to overcome possible quasiergodicity problems.

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Home > Reports Back to Table of Contents 40946-B6 Stereographic Projection Path Integral Simulations of Diatomic Clusters Emanuele Curotto, Arcadia University We have investigated the structural and thermodynamic properties of hydrogen bonded clusters (HX)_n where X = Cl, F. The activities have created data that will guide future experiments, and have been important for the establishment of stereographic projection path integral methods and other algorithms that the group has produced. The work on (HF)_n clusters in particular, [J. Chem. Phys., 124, 174305 (2006).] has sparked the interests of three separate research groups which are now collaborating with us to simulate important molecular assemblies such as those of water [J. Chem. Phys., 126, 084506 (2007).], ammonia, mixed water - hydrogen clusters, and water chlathrates hydrates. The time scale difference between the intramolecular stretching degrees of freedom in the (HX)_n systems and the translations - rotations of the moieties make conventional Euclidean space quantum Monte Carlo methods based on Cartesian Coordinates highly inefficient. Therefore, the stereographic projection path integral for the curved spaces associated with the rotations of n rigid tops allows us, along with a growing community of molecular physicists, to perform otherwise formidable finite temperature quantum simulations of molecular assemblies. At this point, not only have we completed the proposed investigations: a) We have found theoretical expressions that simplify substantially the implementation of Reweighted Random Series Path Integrals (RRSPI) with Stereographic Projection Coordinates (SPC). b) We have generalized the use of SPCs to perform Diffusion Monte Carlo (DMC) simulations in manifolds, [J. Phys. Chem. A., 111,2610 (2007).] and we are currently in the process of developing and testing numerical strategies to include importance sampling, improve the statistical quality and convergence properties of SPC-DMC simulations. These developments will allow us to compute accurately and efficiently the ground state wavefunctions, energy, and related properties for molecular clusters. The undergraduate student supported by the present grant is the third to graduate from the group with the desire to pursue a Ph.D. in theoretical chemistry. He has been supported by the present grant for the last three summers, has coauthored two articles, and he will begin his graduate work at Berkley in the fall of 2007. Two more students will graduate from the group in the spring of 2008 with the intent to pursue graduate work. In detail during 2006-2007: We have developed a potential energy surface (PES) model for (HCl)_n clusters by summing over the interactions between pairs. The pair interaction are obtained using the function optimized for the dimer by M. J. Elrod, and R. J. Saykally, [J. Chem. Phys. 103, 933, (1995).] using high resolution spectroscopy data. A student was trained to implement the genetic algorithm and use this to perform global minima searches in the n = 2 through 19 range. We have carried out classical and path integral simulations of few HCl clusters, from the dimer through the pentamer. We produce a number of configuration distributions for the random walks of the pentamer in order to understand the peculiar features of the quantum heat capacity. A student was trained to perform Classical and SPC-RRSPI simulations and to use the structural comparison algorithm. The student performed a number of parallel tempering simulations, and used the comparison algorithm to produce distributions of D₀ , where D₀ is the sum of the distance from atom of configuration 1 to atom of configuration 2. D₀ is measured between a given configuration during the random walk and the global minimum after a set of translations and rotations are performed to find the optimal superposition of the two structures. Classical parallel tempering simulations for (HCl)_n in the n = 6 through 19 have been carried out. We detect no melting features in any of the heat capacity of these systems. The classical thermodynamic behavior is consistent with the spacing between isomeric energies at the various sizes investigated. There does not seem to be "magic numbers" in the stability patterns. The presence of bimodal distributions for the pentamer at 10K causes us to wonder if the possibility exists for the two structure involved to coexists at these temperatures because of thermal excitations, or whether the ground state wavefunction of the pentamer is delocalized over the configuration space represented by the two peaks in the configuration distribution. For this purpose we have engaged in the development of DMC methods that can be applied to curved spaces. We concentrated our efforts to extend efficient DMC approaches, like the importance sampling, quadratically converging branching algorithms etc, and we test a novel kind of variational wavefunctions designed to overcome possible quasiergodicity problems. Back to top Terms of Use Security Privacy Contact Copyright © 2008 American Chemical Society

40946-B6 Stereographic Projection Path Integral Simulations of Diatomic Clusters

40946-B6
Stereographic Projection Path Integral Simulations of Diatomic Clusters