Bulletin of the American Physical Society
2009 APS March Meeting
Volume 54, Number 1
Monday–Friday, March 16–20, 2009; Pittsburgh, Pennsylvania
Session L13: Computational Methods: Quantum Monte Carlo |
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Sponsoring Units: DCOMP Chair: Jeff Grossman, University of California, Berkeley Room: 309 |
Tuesday, March 17, 2009 2:30PM - 2:42PM |
L13.00001: ABSTRACT WITHDRAWN |
Tuesday, March 17, 2009 2:42PM - 2:54PM |
L13.00002: PIMC Simulation of Thermal Dissociation of Dipositronium Ilkka Kyl\"anp\"a\"a, Tapio Rantala Positronium is a hydrogen atom like pair of a positron and an electron, and correspondingly, dipositronium is a four-particle molecule formed by two positronium atoms. Stability of the dipositronium molecule was established by Hylleraas in 1947 [1], already, but not experimentally observed until recently [2]. This system of four light particles sets challenges for both theoretical and experimental consideration and in finite temperature, in particular. The experimental observations are based on the observation of positronium decay rate and the changes related to dipositronium formation or dissociation. The finite-temperature modeling of such light quantum particles has to done fully nonadiabatically, that we have accomplished with the Path-Integral Monte Carlo (PIMC) method for the thermal equilibrium. As the dissociation energy of dipositronium is about 0.4 eV, the recent observation of the thermal activation energy of about 0.07 eV was interpreted follow from the experiment related desorption process [2]. With our quantum statistical simulation we show, however, that the observed low energy obviously relates to the dissociation of the molecule, directly. [1] Hylleraas, E.A. and Ore A., Phys. Rev.71, 493 (1947). [2] Cassidy D.B. and Mills A.P. Jr., Nature 449, 195 (2007). [Preview Abstract] |
Tuesday, March 17, 2009 2:54PM - 3:06PM |
L13.00003: Convergence of the variational parameter without convergence of the energy in Quantum Monte Carlo (QMC) calculations using the Stochastic Gradient Approximation Daniel Nissenbaum, Hsin Lin, Bernardo Barbiellini, Arun Bansil To study the performance of the Stochastic Gradient Approximation (SGA) for variational Quantum Monte Carlo methods, we have considered lithium nano-clusters [1] described by Hartree-Fock wavefunctions multiplied by two-body Jastrow factors with a single variational parameter $b$. Even when the system size increases, we have shown the feasibility of obtaining an accurate value of $b$ that minimizes the energy without an explicit calculation of the energy itself. The present SGA algorithm is so efficient because an analytic gradient formula is used and because the statistical noise in the gradient is smaller than in the energy [2]. Interestingly, in this scheme the absolute value of the gradient is less important than the sign of the gradient. Work supported in part by U.S. DOE. \\ \mbox{[1] D. Nissenbaum {\em et al.}, Phys. Rev. B {\bf 76}, 033412 (2007).} \\ \mbox{[2] A. Harju, J. Low. Temp. Phys. {\bf 140}, 181 (2005).} [Preview Abstract] |
Tuesday, March 17, 2009 3:06PM - 3:18PM |
L13.00004: Effective one-body potential fitted for many-body interactions associated with a Jastrow function: application to the quantum Monte Carlo calculations Naoto Umezawa, Brian Austin, William A. Lester, Jr An efficient method of optimizing a Slater determinant, $D$, in the Jastrow-Slater-type wave function, $FD$, is suggested. Here, the so-called transcorrelated Hamiltonian, $\frac{1}{F}{\cal H} F$, which is a similarity transformation of the usual Hamiltonian of an electronic system with respect to a Jastrow function $F$, is fitted to an effective Hamiltonian, ${\cal H}_{\rm eff} = \sum_{i}^{N} \left( -\frac{1}{2} \nabla^2_i + v({\mathbf r_i}) \right)$, in which all the electron-electron and electron-neucleus interactions are represented by a one-body potential, $v({\mathbf r})$. A single-particle Schr\"odinger equation is then solved by using $v({\mathbf r})$ to determine the orbitals, of which the Slater determinant consists. The obtained orbitals improve the atomic total energies in the variational Monte Carlo calculations compared to those given by the density-functional-based orbitals. Advantages of using the optimized orbitals in the diffusion Monte Carlo calculations are also discussed. [Preview Abstract] |
Tuesday, March 17, 2009 3:18PM - 3:30PM |
L13.00005: Improved Algorithm for Calculating Observables in Diffusion and Reptation Quantum Monte Carlo Jeremy McMinis, David Ceperley, Carlo Pierleoni By reformulating the calculation of observables using the Hellman-Feynman theorem we are able to reduce the bias on observables calculated in Diffusion and Reptation Monte Carlo. Unlike previous attempts [1], our technique assumes no knowledge about derivatives of the trial or exact ground state wavefunction with respect to the perturbation. We will outline the derivation of the operator and show examples for DMC by comparing to forward walking, and within RMC by showing faster convergence to the unbiased, ground state observable. [1]Assaraf and Caffarel, J. Chem. Phys. 119, 10536 (2003) [Preview Abstract] |
Tuesday, March 17, 2009 3:30PM - 3:42PM |
L13.00006: Analysis of fixed-nodes errors in quantum Monte Carlo calculations of atoms and molecules Shuming Hu, Kevin Rasch, Minyi Zhu, Michal Bajdich, Lubos Mitas The accuracy of fixed-node QMC calculation is determined by the fermion nodes of the trial wavefunction. We analyze the fixed-node errors for a diverse set of atoms and molecules. In some cases, our simple wavefunctions have almost the exact nodes. But in other cases, it is very difficult to find the exact nodes even with wavefunctions of correlated many-body forms, such as extensive multi-reference expansions, pairing and backflow. We try to elucidate the impact of the size and extent of the basis sets as one of the factors influencing fixed-node biases. The testing systems also include transition metal atoms with all-electron and Ne-core pseudopotential calculations. [Preview Abstract] |
Tuesday, March 17, 2009 3:42PM - 3:54PM |
L13.00007: Geometry of fermion nodes and its impact on many-body effects in quantum Monte Carlo Lubos Mitas Fermion nodes, which are zero sets of stationary fermionic many-body wavefunctions, play an important role in quantum Monte Carlo calculations. In the diffusion Monte Carlo method the so-called fixed-node approximation allows us to avoid well-known inefficiencies of the fermion sign problem and to use the method for large systems. Besides this practical importance fermion nodes are also related to spectral properties of second order differential operators and to several physical effects and quantities. In order to understand these relationships we study fermion nodal hypersurfaces, both their topologies and shapes, as determined by wavefunctions built from different types of correlations such as pairing orbitals and backflow many-body coordinates. We analyze the impact of particle interactions on the changes of nodal topologies and the conditions under which such changes can occur. We investigate impact of nodal topologies on properties of wavefunctions with periodic boundary conditions as well as relationship of the nodal surfaces to kinetic energy and some other quantities. We further attempt to elucidate the nodal properties on examples of exactly solvable models. [Preview Abstract] |
Tuesday, March 17, 2009 3:54PM - 4:06PM |
L13.00008: Hybrid DFT orbitals as a means of reduction of fixed-node errors in diffusion Monte Carlo simulations Jindrich Kolorenc, Shuming Hu, Lubos Mitas We explore possibilities to improve variational freedom of Slater-Jastrow trial wave function by using one-body orbitals from the hybrid density-functional theory (DFT) to construct its determinantal Slater part. Weight of the exact exchange term in the hybrid DFT functional serves as a variational parameter that is optimized with respect to the total energy calculated within the fixed-node diffusion Monte Carlo method. This approach is certainly less powerful than direct optimization of one-body orbitals within a basis-set expansion, but its modest computational requirements make it suitable for large-scale simulations of solids. Presented method will be illustrated on several materials with emphasis on transition-metal compounds. The weight of the exact exchange term optimized in this way can also serve as a guide for the hybrid DFT itself. For instance, it provides hints how the weight is changed/screened when a crystal is compressed. [Preview Abstract] |
Tuesday, March 17, 2009 4:06PM - 4:18PM |
L13.00009: Geometry optimization using Quantum Monte Carlo Lucas Wagner, Jeffrey Grossman There are many molecular and solid systems where correlation effects need to be treated very accurately to obtain correct geometries. Current density functionals often do not perform sufficiently well in excited states, weak-binding, and transition metal oxide systems. Quantum Monte Carlo (QMC) offers very accurate total energies due to explicit treatment of electron correlation, but its stochastic nature makes precise geometry optimization challenging. We present a method that uses noisy total energies to perform a stochastic series of line minimizations. This method is efficient for multiple degrees of freedom and is effective in both the excited state and when the trial function is relatively poor--two regimes in which forces in QMC have not been developed. Details of the approach will be presented as well as a number of applications. [Preview Abstract] |
Tuesday, March 17, 2009 4:18PM - 4:30PM |
L13.00010: Quantum Monte Carlo calculations of the energy-level alignment at organic-inorganic hybrid interfaces Zhigang Wu, Yosuke Kanai, Jeffrey Grossman Understanding interface properties of nano- and hybrid- materials at molecular level is of critical importance for fostering technological advancements. While the density functional theory (DFT) continues to be an important method for investigating opto-electronic and excitation properties of materials, the DFT calculations in some cases fail to provide an accurate description. One such difficult case is computing the energy-level alignment at a hybrid interface, composed of two distinct materials with very different electronic characteristics. In this work we present a quantum Monte Carlo approach to correct the Kohn-Sham (KS) level alignment, and we demonstrate this approach for hybrid interfaces between the silicon (001) surface and several organic molecules. Our calculations show that for some molecules there is a qualitative difference with the DFT-KS level alignment, completely changing the character of the heterojunctions formed. We will discuss its implication for understanding the opto-electronic behaviors of hybrid interfaces, along with some computational/theoretical challenges in extending this approach further. [Preview Abstract] |
Tuesday, March 17, 2009 4:30PM - 4:42PM |
L13.00011: QMC Study of Optical Switching of Azobenzene Molecule Rene Derian, Matus Dubecky, Lubos Mitas, Ivan Stich Optical Switching of photochromic azobenzene (AB) molecule via first excited singlet-state is studied. AB features two photoswitchable conformations, cis and trans with very different geometries and properties. Using QMC techniques we compute excitation/deexcitation ground-state -- first singlet- excited-state spectra of AB. By a careful QMC optimization of the ground/excited-state wave functions with up to 500 determinants chemical accuracy is obtained for the cis and trans conformers. Our QMC results are significantly superior to DFT results with proper spin symmetry (ROKS) and surpass also the available standard quantum chemistry results such as CAS SCF. These results open up the possibility of simulation of anchored AB opto-mechanical switches. [Preview Abstract] |
Tuesday, March 17, 2009 4:42PM - 4:54PM |
L13.00012: Multideterminant quantum Monte Carlo calculations of benzene dimers Richard G. Hennig, Kathleen A. Schwarz, Cyrus Umrigar, Julien Toulouse Benzene dimers represent the prototypical system for weak $\pi$-$\pi$ interactions that determine the bonding for various organic materials and carbon nanostructures. Several previous studies using coupled-cluster and quantum Monte Carlo methods have determined the binding energy of parallel, perpendicular and parallel-shifted configurations of the benzene dimer. Here we present multi-determinant variational and diffusion Monte Carlo calculations for the various benzene dimer configurations. The total energy of the benzene dimers depends strongly on basis set size, orbital coefficients and number of determinants in the trial wave function. The binding energy converges faster than the total energy with basis set size and number of determinants due to partial cancellation of errors. While orbital optimization lowers the total energy, the large number of orbital parameters and hence large computational cost limits orbital optimizations to wave functions with small basis sets and small numbers of determinants. In comparison the optimization of the Jastrow and determinant coefficients can efficiently converge the energy of benzene dimers and enables accurate predictions of the binding energies. [Preview Abstract] |
Tuesday, March 17, 2009 4:54PM - 5:06PM |
L13.00013: A Quantum Monte Carlo investigation of dispersion interactions in graphite Leonardo Spanu, Giulia Galli, Sandro Sorella We present a series of Quantum Monte Carlo (QMC) calculations of graphite, aimed at describing on the same footing the strong C-C covalent bonds and the weaker interlayer interactions. In particular, we carried out calculations of binding energies, bond lengths and compressibility by using the Variational Monte Carlo and Lattice Regularized Diffusion Monte Carlo techniques [1]. We use as a variational ansatz the Jastrow Antisymmetrical Wave function, including a pairing determinant and a Jastrow correlation factor [2]. Our results allow for a detailed analysis of dispersion forces between graphite layers, including their behavior at long distances, and yield a quantitative estimate of the layer binding energy. \vspace{0.3cm} \newline [1] Casula M. et al. Phys. Rev. Lett. 95 100201 (2005) \newline [2] Casula M. et al. J. Chem. Phys. 119, 6500 (2003) [Preview Abstract] |
Tuesday, March 17, 2009 5:06PM - 5:18PM |
L13.00014: Auxiliary-Field Quantum Monte Carlo Studies of Pressure-Induced Phase Transitions in Silicon and MnO Wirawan Purwanto, Henry Krakauer, Eric Walter, Shiwei Zhang Accurate theoretical predictions across structural phase transitions are challenging, as they typically involve different electronic structures on the two sides of the transition. We use the phaseless auxiliary-field quantum Monte Carlo (AFQMC) method---which yields accurate many-body wave functions by means of importance sampled random walks in the space of Slater determinants---to calculate the equation of state near two phase transitions: in Si, from the diamond to metallic $\beta$-tin transition at $\sim 11$ GPa; and in MnO, the volume and magnetic moment collapse at $\sim 100$ GPa. The Si phase transition serves as a test case to study the accuracy of the AFQMC method; the calculated transition pressure is in good agreement with the experiment. Applications to the MnO phase transition will then be presented. [Preview Abstract] |
Tuesday, March 17, 2009 5:18PM - 5:30PM |
L13.00015: A Quantum Monte Carlo Study of Molecular Titanium Dihydride$^\dag$ Todd D. Beaudet, Jeongnim Kim, Kenneth Esler, Richard M. Martin Recently there has been interest in the possibility of reversibly storing molecular hydrogen on titanium decorated carbon-nanostructures$^1$. As part of our research$^2$ in this area, we present DFT and QMC results for molecular TiH$_2$ using pseudopotentals. We identify the low energy symmetry-classified states and compare with previous work$^{3,4}$, where there is not a consensus on the symmetry and geometry of the ground state. At the DFT level, the TiH$_2$ d-states are nearly decoupled from the molecular geometry so that several d-state orderings are very close in energy. In our work we use diffusion Monte Carlo with the fixed-node approximation where the symmetry and nodal structure are determined by a trial function constructed of molecular orbitals from DFT. We will also discuss progress on Ti-carbon systems pertaining to hydrogen adsorption. \\ \\ $^1$ E. Durgun \textit{et al.}, Phys. Rev. Lett. \textbf{97}, 226102 (2006). \\ $^2$ T. D. Beaudet \textit{et al.}, J. Chem. Phys. \textbf{129}, 164711 (2008). \\ $^3$ J. A. Platts, J. Mol. Struct. \textbf{545}, 111 (2001). \\ $^4$ B. Ma, C. L. Collins, H. F. Schaefer, J. Am. Chem. Soc. \textbf{118}, 870 (1996). \\ $^\dag$ Supported by NSF DMR03-25939. [Preview Abstract] |
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