Bulletin of the American Physical Society
APS March Meeting 2011
Volume 56, Number 1
Monday–Friday, March 21–25, 2011; Dallas, Texas
Session T21: Classical and Quantum Monte Carlo |
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Sponsoring Units: DCOMP Chair: Bruce Miller, Texas Christian University Room: D161 |
Wednesday, March 23, 2011 2:30PM - 2:42PM |
T21.00001: Steps beyond the fixed-phase approximation in diffusion Monte Carlo Fernando Reboredo The self-healing diffusion Monte Carlo algorithm (SHDMC) [Reboredo, Hood and Kent, Phys. Rev. B {\bf 79}, 195117 (2009); Reboredo, {\it ibid.} {\bf 80}, 125110 (2009)] is extended to study the ground and excited states of magnetic and periodic systems. The method converges to exact eigenstates as the statistical data collected increases if the wave function is sufficiently flexible. A recursive optimization algorithm is derived from the time evolution of the mixed probability density, which is given by an ensemble of electronic configurations (walkers) with complex weight. This complex weight allows the amplitude of the fixed-node wave function to move away from the trial wave function phase. This novel approach is both a generalization of SHDMC and the fixed-phase approximation [Ortiz, Ceperley and Martin, Phys Rev. Lett. {\bf 71}, 2777 (1993)]. The algorithm is demonstrated to converge to nearly exact solutions of model systems with periodic boundary conditions or applied magnetic fields for the ground state and low energy excitations. The computational cost is proportional to the number of independent degrees of freedom of the phase. [Preview Abstract] |
Wednesday, March 23, 2011 2:42PM - 2:54PM |
T21.00002: Understanding framework flexibility of periodic structures by Monte Carlo simulation An Ghysels, Veronique Van Speybroeck, Michel Waroquier, Berend Smit Metal Organic Frameworks (MOFs) are a new class of porous materials synthesized from metal clusters connected by organic linkers. Most crystalline solids are fairly rigid, and undergo small changes in volume when stress is applied. Although most MOFs are rigid, some have an unexpectedly high flexibility, and swell under pressure, temperature or adsorption changes. A well-known structure showing volume changes of over 50\% is MIL-53. A better understanding of the process will allow to design materials with improved properties for carbon capture, i.e. the framework captures CO2 from fuel gasses. In this presentation, we explore framework flexibility effects induced by gas adsorption using Monte Carlo techniques. For instance, when MIL-53 is brought into contact with a gas at increasing pressure, the framework's pores constrict, while at even higher pressures, the pores return to their original geometry. To study this phenomenon, it is essential to incorporate framework flexibility into the Monte Carlo free energy calculation. [Preview Abstract] |
Wednesday, March 23, 2011 2:54PM - 3:06PM |
T21.00003: Quantum Monte Carlo studies of solvated systems Kathleen Schwarz, Kendra Letchworth Weaver, T.A. Arias, Richard G. Hennig Solvation qualitatively alters the energetics of diverse processes from protein folding to reactions on catalytic surfaces. An explicit description of the solvent in quantum-mechanical calculations requires both a large number of electrons and exploration of a large number of configurations in the phase space of the solvent. These problems can be circumvented by including the effects of solvent through a rigorous classical density-functional description of the liquid environment, thereby yielding free energies and thermodynamic averages directly, while eliminating the need for explicit consideration of the solvent electrons. We have implemented and tested this approach within the CASINO Quantum Monte Carlo code. Our method is suitable for calculations in any basis within CASINO, including b-spline and plane wave trial wavefunctions, and is equally applicable to molecules, surfaces, and crystals. For our preliminary test calculations, we use a simplified description of the solvent in terms of an isodensity continuum dielectric solvation approach, though the method is fully compatible with more reliable descriptions of the solvent we shall employ in the future. [Preview Abstract] |
Wednesday, March 23, 2011 3:06PM - 3:18PM |
T21.00004: Fast evaluation of multideterminant wavefunctions in quantum Monte Carlo Miguel A. Morales, Bryan K. Clark, Jeremy McMinis, Jeongnim Kim, Gustavo Scuseria Quantum Monte Carlo (QMC) methods such as variational and diffusion Monte Carlo depend heavily on the quality of the trial wave function. Although Slater-Jastrow wave functions are the most commonly used variational ansatz, more sophisticated wave functions are critical to ascertaining new physics. One such wave function is the multislater- Jastrow wave function which consists of a Jastrow function multiplied by the sum of slater determinants. In this talk we describe a method for working with these wave functions in QMC codes that is easy to implement, efficient, and easily parallelized. The algorithm computes the multi determinant ratios of a series of particle hole excitations in time O(n$^{2})$+O(n$_{s}$n)+O(n$_{e})$ where n, n$_{s}$ and n$_{e}$ are the number of particles, single particle excitations, and total number of excitations, respectively. This is accomplished by producing a (relatively) compact table that contains all the information required to read off the excitation ratios. In addition we describe how to compute the gradients and laplacians of these multi determinant terms. [Preview Abstract] |
Wednesday, March 23, 2011 3:18PM - 3:30PM |
T21.00005: ABSTRACT WITHDRAWN |
Wednesday, March 23, 2011 3:30PM - 3:42PM |
T21.00006: Wave Function Optimization in QMCPACK Jeremy McMinis, Miguel Morales, Jeongnim Kim, David Ceperley Wave function optimization is essential for both the accuracy and efficiency of diffusion, reptation, and variational quantum Monte Carlo (QMC). In this talk we outline the wave function optimization strategy used in the QMC software package QMCPACK developed at the University of Illinois. We use an extension of the linear optimization method originally developed by Umrigar et. al.[1] to optimize parameters in Slater-Jastrow, multi-determinant Slater-Jastrow, and Backflow-Jastrow trial wave functions. The efficiency and accuracy of this method is presented for bulk Silicon, Jellium, and the Nitrogen dimer.\\[4pt] [1] Umrigar et al. PRL 98, 110201 (2007) [Preview Abstract] |
Wednesday, March 23, 2011 3:42PM - 3:54PM |
T21.00007: Testing of He-core pseudopotentials for 3d elements in quantum Monte Carlo Minyi Zhu, Lubos Mitas We construct He-core pseudopotentials for several elements in the 3rd row such as for V, Cr, Mn, Fe and Zn, with the goal of using these in high-accuracy quantum Monte Carlo (QMC) calculations. We study the accuracy of constructed pseudopotentials on MnO molecular states with different spin polarizations. We compare these results also with Density Functional Theory and Hartree-Fock approaches since we previously found noticeable differences between Ne-core pseudopotential and relativistic all-electron calculations in high-spin vs. low-spin state comparisons. The result indicates that these discrepancies stem from method biases related to the presence of core states, as we conjectured earlier. Additionally, we also discuss the computational cost of the He-core pseudopotentials in QMC calculations. [Preview Abstract] |
Wednesday, March 23, 2011 3:54PM - 4:06PM |
T21.00008: Spin-orbit interaction in quantum Monte Carlo Lubos Mitas, Rene Derian, Shi Guo For spinless Hamiltonians (ie, no explicit spin operators), real space quantum Monte Carlo (QMC) methods such as variational and fixed-node diffusion Monte Carlo are well established. In these cases the electron spins and their components commute with the Hamiltonian and therefore are conserved quantities. This implies that spins can be fixed as given by the symmetry of a considered state and one solves only for the spatial part of the corresponding wave function. Indeed, this is a common practice in electronic structure QMC and also in most quantum chemical calculations. However, many systems require treating spins as quantum dynamical variables. We will present progress of our studies in this direction both in variational and diffusion Monte Carlo for heavy atoms with spin-orbit operators. One possibility is to use possibilities offered by various formulations of Hubbard-Stratonovitch transformation as realized in QMC for nuclear systems. We explore also other options both in variational and diffusion Monte Carlo framework. In particular, we define new representation for spinors which enable to formulate the diffusion Monte Carlo along the lines of fixed-phase approximation. We compare the results for the considered approaches also from the point of computational efficiency. [Preview Abstract] |
Wednesday, March 23, 2011 4:06PM - 4:18PM |
T21.00009: A quantum Monte Carlo study of molecular systems with heavy elements Shi Guo, Kevin Rasch, Lubos Mitas, Enrique Batista, Richard Martin We use quantum Monte Carlo method to study the bis-cyclopentadienyl Hafnium dichloride molecule $Cp_2HfCl_2$. There are two Cl dissociation channels for $Cp_2HfCl_2$: one is to break into neutral fragments, the other one into charged fragments. We employ the Stuttgart pseudopotential to represent the Hf atom and optimized Slater-Jastrow trial wave function at the variational Monte Carlo level. The calculations of the dissociation energies are carried out by the fixed-node diffusion Monte Carlo. We observe that for the heavy elements the low valence density in the core region can generate large energy fluctuations and we address this by improvements of the correlation factor. Alternatively, we construct Hf pseudopotentials with different core sizes and test for the accuracy of such pseudopotential Hamiltonians. We compare the QMC results also with DFT calculations with hybrid functionals. [Preview Abstract] |
Wednesday, March 23, 2011 4:18PM - 4:30PM |
T21.00010: Fixed-Node Errors in Diffusion Monte Carlo Study of Li Molecular and Solid Systems Kevin Rasch, Lubos Mitas We study the fixed-node bias in the Diffusion Monte Carlo calculations of Li systems such as Li dimer, Li clusters, and Li body-centered cubic crystal at the equilibrium lattice constant. The calculations include both core and valence electrons in order to avoid any possible impact by pseudopotentials. We examine the fixed-node errors for different types of orbitals and wave-function forms. We use estimations of exact total energies from alternative approaches such as correlated basis set methods or from experiment. The results suggest that for Li systems it is possible to construct accurate wave-functions which recover correlation energy at 97-99 \% of correlation energy in the full many-body framework. [Preview Abstract] |
Wednesday, March 23, 2011 4:30PM - 4:42PM |
T21.00011: Comparison of the Angular Dependence of Monte Carlo Particle Transport Modeling Software Jeff Chancellor, Stephen Guetersloh Modeling nuclear interactions is relevant to cancer radiotherapy, space mission dosimetry and the use of heavy ion research beams. In heavy ion radiotherapy, fragmentation of the primary ions has the unwanted effect of reducing dose localization, contributing to a non-negligible dose outside the volume of tissue being treated. Fragmentation in spaceship walls, hardware and human tissue can lead to large uncertainties in estimates of radiation risk inside the crew habitat. Radiation protection mandates very conservative dose estimations, and reduction of uncertainties is critical to avoid limitations on allowed mission duration and maximize shielding design. Though fragment production as a function of scattering angle has not been well characterized, experimental simulation with Monte Carlo particle transport models have shown good agreement with data obtained from on-axis detectors with large acceptance angles. However, agreement worsens with decreasing acceptance angle, attributable in part to incorrect transverse momentum assumptions in the models. We will show there is an unacceptable angular discrepancy in modeling off-axis fragments produced by inelastic nuclear interaction of the primary ion. The results will be compared to published measurements of 400 MeV/nucleon carbon beams interacting in C, CH2, Al, Cu, Sn, and Pb targets. [Preview Abstract] |
Wednesday, March 23, 2011 4:42PM - 4:54PM |
T21.00012: A Quantum Monte Carlo study of Hydrogen Adsorption on Carbon and Transition Metal Systems Todd D. Beaudet, Jeongnim Kim, Richard M. Martin We present a quantum Monte Carlo study of many molecular structures of Ti-ethylene with up to 5 H$_{2}$ molecules. These structures have been of recent interest due to energetics favorable for reversibly storing hydrogen.\footnote{E. Durgun \textit{et al}., Phys. Rev. Lett. \textbf{97}, 226102 (2006).} Diffusion Monte Carlo is employed with the fixed node approximation and pseudopotentials that have been tested for H$_{2}$ adsorbed on benzene and calculations on TiH$_{2}$ molecules.\footnote{T. D. Beaudet, Doctoral Dissertation, University of Illinois at Urbana-Champaign (2010).} Many low energy configurations were studied by calculation of ground and excited states energy surfaces. The formation energies are comparable to other work\footnote{Y. Y. Sun \textit{et al}., Phys. Rev. B \textbf{82}, 073401 (2010).} and indicate that at least 3 hydrogen molecules can be adsorbed with energies in the range considered relevant for practical hydrogen storage. [Preview Abstract] |
Wednesday, March 23, 2011 4:54PM - 5:06PM |
T21.00013: Release-Node quantum Monte Carlo studies for molecules Norm Tubman, Jonathan Dubois, Randolph Hood, Berni Alder Release-Node quantum Monte Carlo (RN-QMC) is a method that calculates unbiased ground-state energies of fermionic systems. However, while RN-QMC has been successfully applied to the homogeneous electron gas with more than one hundred electrons, obtaining converged results for molecular systems has proven to be problematic for all but the smallest systems. A promising route to extending the method's success to a wider class of physically interesting Hamiltonians lies in the application of projection techniques such as Maximum Entropy (MaxEnt) which, in principle, allows for extrapolation to the converged ground-state energy. Direct application of MaxEnt to higher Z elements is, however, not entirely straightforward. We propose strategies for optimizing MaxEnt analysis of short time RN-QMC data and demonstrate their effectiveness in obtaining ground state energies for the first row dimers. Attention is given to the determination of statistical errors in the resulting extrapolations as well as an attempt to characterize the minimum decay time required for unbiased results. [Preview Abstract] |
Wednesday, March 23, 2011 5:06PM - 5:18PM |
T21.00014: Melting transition of Lennard-Jones particles in two dimensions Keola Wierschem, Efstratios Manousakis The melting transition of Lennard-Jones particles in two dimensions is investigated along a single isochore using classical Monte Carlo methods. A finite-size scaling analysis is conducted for the second moments of the translational and bond-orientational order parameters, and their critical exponents are determined. The behavior of these exponents is consistent with the predictions of the two-stage Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory of melting in two dimensions. The translational and bond-orientational correlation lengths are also studied, with evidence of a divergence in the bond-orientational correlation length while the translational correlation length remains finite. This provides further support for the KTHNY melting scenario, although we cannot rule out possible phase co-existence due to a first order phase transition. [Preview Abstract] |
Wednesday, March 23, 2011 5:18PM - 5:30PM |
T21.00015: Micro-canonical Monte Carlo study of spin wave excitations in 2D XY model Smita Ota We have carried out micro-canonical Monte Carlo simulation of 2D XY model in a 30x30 lattice using periodic boundary conditions. In this micro-canonical Monte Carlo simulation, the energy is the input quantity and the temperature of the system is obtained from the simulations. Spin waves and bound vortex excitations dominate in the 2D XY model below the topological vortex unbinding transition. We have studied the spin waves from the energy distribution of an individual spin in the 2D XY model. The most probable spin wave energy corresponds to the maximum in the energy distribution. The probability of the spin wave excitation is found to be reduce exponentially, by an order of magnitude as the temperature increases to the topological transition. [Preview Abstract] |
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