Bulletin of the American Physical Society
2006 APS March Meeting
Monday–Friday, March 13–17, 2006; Baltimore, MD
Session U27: Computational Methods: Monte Carlo/Molecular Dynamics I |
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Sponsoring Units: DCMP Chair: Andrew Williamsom, Lawrence Livermore National Laboratory Room: Baltimore Convention Center 324 |
Thursday, March 16, 2006 8:00AM - 8:12AM |
U27.00001: Density-Matrix Based Fixed-Node and Fixed-Phase Approximation for Quantum Monte Carlo John Shumway We have generalized the fixed-node and fixed-phase approximations to use density matrices. For a given trial density matrix, we generate a quantum Monte Carlo algrithm that minimizes the free energy, subject to the nodal or phase restriction. This method has enabled us to perform efficient fermion path-integral simulations at all temperatures. In the T=0 limit the algorithm simulates two copies of the system that do not interact, but which are entangled through the nodal constraint. We illustrate the advantages of this density matrix formalism in applications to semiconductor nanostructures and small molecules. We are currently investigating the use of the Kubo formula and other linear response theories within the fixed-node approximation. (For simulation codes, preprints, and other information, see http://phy.asu.edu/shumway.) [Preview Abstract] |
Thursday, March 16, 2006 8:12AM - 8:24AM |
U27.00002: Worm algorithm for continuous-space Path Integral Monte Carlo simulations Massimo Boninsegni, Nikolay Prokof'ev, Boris Svistunov We present a new approach to Path Integral Monte Carlo (PIMC) simulations based on the ``worm" algorithm, originally developed for lattice models,\footnote{N. V. Prokof'ev, B. V. Svistunov, and I. S. Tupitsyn, Phys. Lett. {\bf 238}, 253 (1998)} and recently extended to continuous-space many-body systems.\footnote{M. Boninsegni, N. Prokof'ev and B. Svistunov, cond-mat/0510214} The scheme allows for efficient computation of thermodynamic properties, including winding numbers and off-diagonal correlations, for systems of much greater size than that accessible to conventional PIMC. We present results for the superfluid transition of Helium-four in two and three dimensions. Using systems comprising several thousand particles, a very accurate determination of the superfluid transition temperature is feasible. [Preview Abstract] |
Thursday, March 16, 2006 8:24AM - 8:36AM |
U27.00003: Green's function analysis of path integral Monte Carlo molecular simulations Daejin Shin, John Shumway We demonstrate the direct determination of molecular properties from path integral Monte Carlo simulations. By sampling Matsubura Green's functions, we have calculated several linear response properties of the hydrogen molecule (H$_2$) directly from quantum Monte Carlo. We show that the vibration frequency of H$_2$ as calculated directly from the phonon temperature Green's function is in very good agreement with the calculated Born-Oppenheimer potential energy surface. We have also obtained the polarizability from the polarization correlation function, and we are looking at Raman spectra. For the high-accuracy simulations needed in chemical physics, we have developed new, fast and accurate techniques for the tabulation of Coulomb density matrices. This work motivates future path integral Monte Carlo simulations on larger molecules and could also be immediately useful in simulations of hydrogen storage materials. [Preview Abstract] |
Thursday, March 16, 2006 8:36AM - 8:48AM |
U27.00004: Energy Optimization of Many-Body Wave Functions: Application to Silicon Interstitial Defects W. D. Parker, K. P. Driver, R. G. Hennig, J. W. Wilkins, C. J. Umrigar Energy minimization [1], as opposed to the standard variance minimization [2], of the Jastrow factor results not only in lower variational Monte Carlo (VMC) energies but also in lower diffusion Monte Carlo (DMC) energies for systems that employ a nonlocal pseudopotential. We apply this approach to solids: single-interstitials in silicon. Allowing the Jastrow for the defect atom(s) to differ from that for bulk atoms lowers the VMC energy but not the DMC energy, indicating the pseudopotential locality error is small. DMC energies from 8 and 64 atom cells (plus interstitial) computed with energy-optimized trial wave functions estimate a 0.2 eV finite-size error in the formation energy. Cubic spline and Lagrange polynomial representations of orbitals have comparable efficiency in memory usage, run time and accuracy. [1] C. J. Umrigar and C. Filippi, Phys. Rev. Lett. 94, 150201 (2005). [2] C. J. Umrigar, K. G. Wilson and J. W. Wilkins, Phys. Rev. Lett. 60, 1719 (1988). [Preview Abstract] |
Thursday, March 16, 2006 8:48AM - 9:00AM |
U27.00005: Study of Atoms and Molecules with Auxiliary-Field Quantum Monte Carlo Wirawan Purwanto, Malliga Suewattana, Henry Krakauer, Shiwei Zhang, Eric J. Walter We study the ground-state properties of second-row atoms and molecules using the phaseless auxiliary-field quantum Monte Carlo (AF QMC) method.\footnote{S. Zhang and H. Krakauer, Phys. Rev. Lett. \textbf{90}, 136401 (2003)} This method projects the many-body ground state from a trial wave function by means of random walks in the Slater-determinant space. We use a single Slater-determinant trial wave function obtained from density-functional theory (DFT) or Hartree-Fock (HF) calculations. The calculations were done with a plane-wave basis and supercells with periodic boundary condition. We investigate the finite-size effects and the accuracy of pseudopotentials within DFT, HF, and AF QMC frameworks. Pseudopotentials generated from both LDA (OPIUM\footnote{\texttt{http://opium.sourceforge.net}}) and HF\footnote{I. Ovcharenko, A. Aspuru-Guzik, and W. A. Lester, J. Chem. Phys. \textbf{114}, 7790 (2001)} are employed. We find that the many-body QMC calculations show a greater sensitivity to the accuracy of the pseudopotentials. With reliable pseudopotentials, the ionization potentials and dissociation energies obtained using AF QMC are in excellent agreement with the experimental results. [Preview Abstract] |
Thursday, March 16, 2006 9:00AM - 9:12AM |
U27.00006: Auxiliary field quantum Monte Carlo study of transition metal and post-d group atoms and molecules Henry Krakauer , Wissam A. Al-Saidi, Shiwei Zhang We applied the phaseless auxiliary field quantum Monte Carlo [1] to the study of several transition metal and post-d atoms and molecules. The transition metal study includes both all-electron and pseudopotential calculations, while the post-d group elements are studied using the consistent correlated basis which employs a small core relativistic pseudopotential [2]. The obtained electron affinities, dissociation energies, and equilibrium geometries compare favorably with experiment and with coupled cluster results. [1] S. Zhang and H. Krakauer, Phys. Rev. Lett. {\bf 90}, 136401 (2003). [2] Kirk A. Peterson, J. Chem. Phys. {\bf 119}, 11099 (2003); Kirk A. Peterson {\emph et al.}, J. Chem. Phys. {\bf 119}, 11113 (2003) [Preview Abstract] |
Thursday, March 16, 2006 9:12AM - 9:24AM |
U27.00007: Accuracy of the pseudopotential and fixed-node approximations for C$_2$, Si$_2$ and defects in crystalline Si Richard G. Hennig, Cyrus J. Umrigar, Julien Toulouse, John W. Wilkins Quantum Monte Carlo calculates binding energies and atomic structures for molecules and defect energies in solids. Accurate QMC calculations require the control of the pseudopotential and the fixed-node approximation. The calculated binding energies and bond lengths for the Si and C dimer and the energies of defects in crystalline Si test the accuracy of a range of pseudopotentials and optimized trial-wave functions. For the Si dimer and defects in crystalline Si different pseudopotentials provide similar results. The results for the Si dimer are comparable with experiments with HF pseudopotentials being most accurate. While a single determinant wave functions is sufficient for the Si dimer, the C dimer requires an optimized multi-determinant trial-wave function to achieve experimental accuracy. [Preview Abstract] |
Thursday, March 16, 2006 9:24AM - 9:36AM |
U27.00008: Structure of fermion nodes and nodal cells for QMC wave functions Lubos Mitas We study nodes of fermionic ground state wave functions. For $2D$ and higher we analytically prove that spin-polarized, noninteracting fermions in a harmonic well have two nodal cells for arbitrary system size. The result extends to other noninteracting/mean-field models such as fermions on a sphere, in a periodic box or in Hartree-Fock atomic states. Spin-unpolarized noninteracting states have multiple nodal cells, however, interactions and many-body correlations generally relax the multiple cells to the minimal number of two. This is again analytically proved, with some restrictions, for general interactions in $2D$ and higher-dimensional harmonic fermions of arbitrary size using the Bardeen-Cooper-Schrieffer variational wave function. We discuss implications and limits of the proofs for more complicated systems. The results offer an elegant and unifying framework for several previously conjectured or numerically investigated ideas and open exciting perspectives for studies of many-body effects which are beyond the usual fixed-node quantum Monte Carlo limits. [Preview Abstract] |
Thursday, March 16, 2006 9:36AM - 9:48AM |
U27.00009: Multi-pfaffian pairing wave functions for quantum Monte Carlo Michal Bajdich, Lubos Mitas, Kevin E. Schmidt We investigate the limits of accuracy of trial wave function for quantum Monte Carlo based on pfaffian functional form with singlet and triplet pairing. Using a set of first row atoms and molecules we find that this wave function provides very consistent and systematic behaviour in recovering the correlation energies on the level of 95\% . In order to get beyond this limit we have explored the possibilities of multi-pfaffian pairing wave functions. We show that small number of pfaffians recovers another large fraction of the missing correlation energy comparable to the larger-scale configuration iteraction wave functions. The trade-offs between the size of the underlying optimization problem and amounts correlation energy recovered will be discussed. [Preview Abstract] |
Thursday, March 16, 2006 9:48AM - 10:00AM |
U27.00010: Backflow transformations in inhomogeneous systems Pablo Lopez Rios, Andrea Ma, Neil D. Drummond, Richard J. Needs The quality of trial wave-functions, and of their nodal surface in particular, determines the accuracy of the results obtained within the Fixed-Node Diffusion Monte Carlo (DMC) method. Backflow transformations have been proven capable of improving the nodal surface of Slater-Jastrow (SJ) wave-functions in homogeneous systems. In this work we will present the extension of backflow to inhomogeneous systems, along with DMC results for atoms, molecules and solids which show the improved accuracy of this form of trial wave-function. We will also discuss the advantages of using electron-by-electron algorithms to enhance the computational efficiency of QMC with backflow wave-functions. [Preview Abstract] |
Thursday, March 16, 2006 10:00AM - 10:12AM |
U27.00011: The equation of state of diamond from quantum Monte Carlo calculations Ryo Maezono, Andrea Ma, Mike D. Towler, Neil D. Drummond, Richard J. Needs We describe variational and diffusion quantum Monte Carlo (VMC and DMC) calculations that have been performed to evaluate the elastic properties of diamond up to pressures of about 500 GPa. We have used a smooth, norm-conserving, Hartree-Fock carbon pseudopotential in our work. Our trial wave functions were of Slater-Jastrow form, containing orbitals generated in plane-wave DFT-GGA calculations, which were re-expanded in a blip-function basis set. We propose a new scheme for determining the cutoff lengths that occur in our Jastrow factor. Using a 512-electron simulation cell, and fitting a Vinet equation of state to our energy-volume data, we have calculated the equilibrium lattice constant (A, in Angstrom), bulk modulus (B, in GPa), and pressure derivative of the bulk modulus (B') to be (A,B,B')=(3.547, 4.83, 3.43) within VMC and (3.563, 4.52, 3.61) within DMC, as compared with the experimental values of (A,B,B')=(3.567, 4.4-4.5, 3.0-4.0). [Preview Abstract] |
Thursday, March 16, 2006 10:12AM - 10:24AM |
U27.00012: Improved estimators for quantum Monte Carlo calculation of spherically averaged intracule densities Julien Toulouse, Roland Assaraf, Cyrus Umrigar System-averaged pair densities or ``intracule densities'' are important for qualitative and quantitative descriptions of electron correlation~[1] In quantum Monte Carlo (QMC) simulations, spherically averaged intracule densities are usually calculated by means of the traditional histogram technique (i.e., by counting the number of times two electrons are found at a certain distance) that is very noisy at short electron-electron distances. We will show how previously-used improved estimators for the on-top pair density~[2,3] can be generalized to the case of non-vanishing electron-electron distances, as an application of the ``zero-variance'' procedure~[4]. The obtained estimators lead to noise several orders of magnitude smaller than the histogram technique, allowing unprecedented fast and accurate calculations of intracule densities in QMC. Illustrative calculations on simple atomic systems will be given. [1] J. M. Mercero, E. Valderrama and J. M. Ugalde, in ``NATO-ASI Series in Metal-Ligand Interaction in Molecular-, Nano-, Micro, and Macro-systems in Complex Environments'', Ed.: N. Russo, D. R. Salahub and M. Witko, Kluwer Academic Publishres, Dordrecht (2003). [2] P. Langfelder, S. M. Rothstein and J. Vrbik, J. Chem. Phys. {\bf 107}, 8525 (1997). [3] A. Sarsa, F. J. G\'alvez and E. Buend\'ia, J. Chem. Phys. {\bf 109}, 7075 (1998). [4] R. Assaraf and M. Caffarel, Phys. Rev. Lett. {\bf 83}, 4682 (1999). [Preview Abstract] |
Thursday, March 16, 2006 10:24AM - 10:36AM |
U27.00013: Accurate energy differences with Quantum Monte Carlo Simone Chiesa, David Ceperley, Jeongnim Kim, Richard Martin Computation of accurate energy differences is of primary importance in the study of transformations as those occurring in solid to solid phase transitions or chemical reactions. In stochastic quantum simulations this can be done efficiently, employing correlated sampling techniques whereby fluctuations cancel with each other leading to results with a much smaller statistical error. Although correlated sampling is very effective for variational Monte Carlo such is not the case for diffusion Monte Carlo where branching and different nodal structures force the introduction of uncontrolled approximations. Here we describe the use of reptation Monte Carlo as a method that maintains a single path for both systems and leads to energies which are exact within the fixed node approximation. We show how to combine umbrella sampling with coordinate transformations to give a simple and efficient algorithm to compute small energy differences. Application to dissociation reaction paths and weakly bound systems are presented. [Preview Abstract] |
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