Bulletin of the American Physical Society
2005 APS March Meeting
Monday–Friday, March 21–25, 2005; Los Angeles, CA
Session P32: Computational Methods Classical and Quantum Monte Carlo |
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Sponsoring Units: DCOMP Chair: Alice Kolakowska, Mississippi State University Room: LACC 507 |
Wednesday, March 23, 2005 11:15AM - 11:27AM |
P32.00001: Quantum Monte Carlo Study on NiO crystal Ryo Maezono, M.D. Towler, R.J. Needs Quantum Monte Carlo (QMC) calculations using the variational (VMC) and diffusion (DMC) methods is performed on NiO crystal with gaussian basis and pseudo potentials. We report calculations of energy-volume plots obtained by VMC and DMC with 2*2*2 (16 ions) and 4*4*4 (128 ions) simulation cells. In order to obtain smooth dependences careful optimizations of the basis set at each lattice constant turned out to be indispensable, as well as the larger (4*4*4) simulation cell. The cohesive energy obtained by VMC (without Jastrow function) is around 6.6 eV, while DMC gives around 9.3 eV (near to the experimental value as 9.5 eV, though the present QMC is assuming ferromagnetic ordering). [Preview Abstract] |
Wednesday, March 23, 2005 11:27AM - 11:39AM |
P32.00002: Interpretation of Hund's multiplicity rule for the atomic systems Kenta Hongo, Takayuki Oyamada, Ryo Maezono, Yoshiyuki Kawazoe, Hiroshi Yasuhara, M.D. Towler, R.J. Needs We have studied Hund's multiplicity rule for the carbon atom using quantum Monte Carlo methods[1]. Our calculations give a high-level description of electron correlation and satisfy the virial theorem to high accuracy. This allows us to obtain accurate and reliable values for each of the energy terms and therefore to give a convincing explanation of the mechanism by which Hund's rule operates in carbon. We obtain the following results: (1) the energy gain in the triplet with respect to the singlet state is due to the greater electron-nucleus attraction in the higher spin state, and (2) the electron-electron repulsion in the triplet is greater than that in the singlet, in accordance with Hartree-Fock results and studies including correlation. Although our main topic is the carbon atom, we would also like to show our current results of the nitrogen atom.[1]K. Hongo, \textit{et al}., J. Chem. Phys. \textbf{121}, 7144 (2004). [Preview Abstract] |
Wednesday, March 23, 2005 11:39AM - 11:51AM |
P32.00003: Pfaffian wavefunctions with pairing orbitals for electronic structure quantum Monte Carlo Michal Bajdich, Gabriel Drobny, Lucas K. Wagner, Kevin E. Schmidt, Lubos Mitas The trial wavefunction nodal structure determines the accuracy of electronic structure calculations by the fixed-node quantum Monte Carlo (QMC). Wavefunctions based on Hatree-Fock (HF) or multi-reference HF provide about 95\% of correlation energy in real systems such as molecules and solids. On the other hand, antisymmetrized product of pairing orbitals (geminals) is a variationally richer form which can describe effects absent in HF such as electron singlet and triplet pairing. One of such forms is the BCS pairing wavefunction with singlet pairing which can be expressed as a determinant. An extension of BCS includes also triplet pairing and therefore requires a pfaffian. We explore the variational freedom of pfaffian wavefunctions and evaluate improvements of fixed-node QMC energies for cases of atomic, molecular and solid systems. [Preview Abstract] |
Wednesday, March 23, 2005 11:51AM - 12:03PM |
P32.00004: Nodes of fermionic wavefunctions: coordinate transformations and topologies Lubos Mitas, Michal Bajdich, Gabriel Drobny, Lucas K. Wagner We study fermion nodes for both spin-polarized and spin-unpolarized states of a few-electron ions and molecules with $s,p,d$ one-particle orbitals. We find exact nodes for some cases of two electron atomic and molecular states and also the first exact node for the three-electron atomic system in $^4S(p^3)$ state using appropriate coordinate maps and wavefunction symmetries. We analyze the cases of nodes for larger number of electrons in the Hartree-Fock approximation and for some cases we find transformations for projecting the high-dimensional node manifolds into 3D space. The node topologies and other properties are studied using these projections. We also propose a general coordinate transformation as an extension of Feynman-Cohen backflow coordinates to both simplify the nodal description and as a new variational freedom for quantum Monte Carlo trial wavefunctions. [Preview Abstract] |
Wednesday, March 23, 2005 12:03PM - 12:15PM |
P32.00005: Dielectric Response of Periodic Systems from Quantum Monte Carlo Paolo Umari, Andrew J. Willamson, Giulia Galli, Nicola Marzari We introduce a novel approach to study the response of periodic systems to finite homogeneous electric fields using the diffusion Quantum Monte Carlo method. The interaction with the electric field is expressed through a generalized many-body electric-enthalpy functional; a Hermitian local potential is then constructed that determines the evolution towards the ground state. This local potential depends self-consistently on the Berry-phase polarization, and is evolved ``on-the-fly'' in the course of the simulation, with the polarization operator evaluated using forward-walking. To validate this approach we calculated the dielectric susceptibility of simple molecular chains, greatly over-estimated by standard density-functional approaches, and found good agreement with the results obtained with correlated quantum-chemistry calculations. [Preview Abstract] |
Wednesday, March 23, 2005 12:15PM - 12:27PM |
P32.00006: Coupled Electron-Ion Monte Carlo Study of Hydrogen Kris Delaney, David Ceperley, Carlo Pierleoni We present details of the Coupled Electron-Ion Monte Carlo method (CEIMC) [1,2] applied to the problem of the equation of state of pure hydrogen. The aim is to develop a method that can predict state information outside the range of temperatures and pressures that are accessible with other existing methods, such as PIMC. \\ The CEIMC method centers on exploring the configuration space of the hydrogen nuclei (classical or quantum path integrals) using a modified Metropolis algorithm, with configurational energy differences computed from Born-Oppenheimer energies. Energy differences are computed with VMC or Reptation quantum Monte Carlo, both of which supply unbiased estimates of energy differences, the latter within a projector framework. New developments include a fast band-structure calculation for the trial function which should improve the localization of molecule-atom phase transitions. \\ (1) D. Ceperley, M. Dewing and C. Pierleoni, in Bridging Time Scales: Molecular Simulations for the Next Decade, eds. P. Nielaba, M. Mareschal and G. Ciccotti, Springer-Verlag, pgs. 473-500 (2002). \\ (2) C. Pierleoni, D. M. Ceperley and M. Holzmann, Phys. Rev. Lett. 93, 146402 (2004) [Preview Abstract] |
Wednesday, March 23, 2005 12:27PM - 12:39PM |
P32.00007: Auxiliary Field Quantum Monte Carlo in Continuum Systems Luke Shulenburger, Richard Martin The auxiliary field Quantum Monte Carlo method allows Monte Carlo to be performed in any basis. This is accomplished by using the Hubbard-Stratonavich transformation to transform two body interactions into an integral over one body interactions. In practice this method has been difficult to use because while exact, it suffered from a phase problem more severe than the sign problem encountered in Diffusion Monte Carlo. Recent work has suggested a phase free approximation that allows this phase problem to be overcome while sacrificing the exact nature of the method$^1$. We have implemented the auxiliary field Quantum Monte Carlo algorithm with the phase free approximation in a plane wave basis. The results of this code for the total energy of jellium and silicon are compared to previous work to assess the accuracy of the method and its approximation. We also discuss results obtained for the energy of jellium with a gap caused by modifying the kinetic energy operator. Results from this study may prove useful in developing more accurate functionals for density functional calculations$^2$. We conclude with a brief discussion of the strengths and weaknesses of the auxiliary field method within the phase free approximation. \begin{itemize} \item[{[1]}] S. Zhang, and H. Krakauer. Phys. Rev. Lett. {\bf 90}, 136401 (2003) \item[{[2]}] C. Gutle, et. al., Int. J. Quant. Chem. {\bf 75}, 885 (1999) \end{itemize} [Preview Abstract] |
Wednesday, March 23, 2005 12:39PM - 12:51PM |
P32.00008: Quantum Monte Carlo Study of Composite-Fermions in Quantum Dots Alev Devrim Guclu, Gun Sang Jeon, Cyrus Umrigar, Jainendra Jain Composite-fermion wave functions, projected onto the lowest Landau level, provide accurate wave functions for quantum dots in the limit of strong magnetic fields. We show that the range of validity of these wave functions can be greatly extended to smaller magnetic fields by incorporating Landau level mixing effects by multiplying them with a Jastrow factor, optimized using the variance minimization method. The energy and other expectation values can be further improved by projecting the wave functions onto the ground state using diffusion Monte Carlo within the fixed-phase approximation. Energies for 6-electron system are compared to energies obtained by exact diagonalization within 3 Landau levels. Excellent agreement between the two methods is obtained. We then apply our method to a 15-electron system, far beyond the capabilities of the exact diagonalization method, to study ground state properties as the magnetic field is varied. [Preview Abstract] |
Wednesday, March 23, 2005 12:51PM - 1:03PM |
P32.00009: Quantum Monte Carlo examines accuracy of density functional approximations for defects and phase transformations in silicon Richard G. Hennig, Kevin P. Driver, William D. Parker, John W. Wilkins, Cyrus J. Umrigar Silicon displays a variety of interstitial defects limiting device fabrication and performance and shows at least twelve crystallographic phases under pressure. While DFT-determined structures are reliable, defect energies and phase transformation pressures are sensitive to the specific exchange-correlation functional. Diffusion Monte Carlo calculations for silicon defects and phases test the accuracy of the current density-functional approximations LDA, PW91, PBE, and TPSS. Diffusion Monte Carlo predicts the correct cohesive energy of the diamond structure, however, the pressure for the transition to beta-tin is larger than in experiments. The transformation is sensitive to anisotropic stresses; an anisotropy of 2-3 GPa lowers the prediction to agree with experiment. Diffusion Monte Carlo for high-pressure Si phases and interstitial defect clusters shows that relative to diamond Si the energies of phases and defects are underestimated by DFT. [Preview Abstract] |
Wednesday, March 23, 2005 1:03PM - 1:15PM |
P32.00010: Auxiliary Field Quantum Monte Carlo Study of Ground State Properties of Atoms and Molecules Malliga Suewattana, Shiwei Zhang, Henry Krakauer, Eric Walter We apply a recently developed quantum Monte Carlo (QMC) method \footnote{Shiwei Zhang, Henry Krakauer, Phys. Rev. Lett. {\bf 90}. 136401 (2003).} to calculate the ground state properties of several atoms and molecules. The QMC method projects the many-body ground state from a trial state by random walks in the space of Slater determants. The Hubbard-Stratonovich transformation is employed to decouple the Coulomb interaction between electrons. A trial wave function $|\Psi_T\rangle$ is used in the approximation to control the phase problem in QMC. We also carry out Hartree-Fock (HF) and density functional theory (with the local density approximation (LDA)) calculations. The generated single Slater determinant wave functions are used as $|\Psi_T\rangle$ in QMC. The dissociation and ionization energies are calculated for Aluminum, Silicon, Phosphorous, Sulfur, Chlorine and Arsenic atoms and molecules. The results are in good agreement with experimental values. [Preview Abstract] |
Wednesday, March 23, 2005 1:15PM - 1:27PM |
P32.00011: Study of TiO and MnO using auxiliary field quantum Monte Carlo Wissam Al-Saidi, Henry Krakauer, Shiwei Zhang We study the transition metal oxide molecules TiO and MnO using the recently developed auxiliary field quantum Monte Carlo approach [1]. This method maps the interacting many-body problem into a linear combination of non-interacting problems using a complex Hubbard-Stratonovich transformation, and controls the phase/sign problem using a trial wave function. It employs a random walk approach in Slater determinant space to project the ground state of the system, and uses much of the same machinery as density functional theory such as single particle basis and non-local pseudopotentials. In our calculations, we used a single Slater determinant trial wave function obtained from a density functional calculation, with no further optimization. The calculated dissociation energies are in good agreement with experiments. These together with previous results show the robustness of the method for studying sp- as well as d-bonded atoms, and molecules. Calculations of other observables and correlation functions will also be discussed. [1] S. Zhang and H. Krakauer, Phys. Rev. Lett. 90, 126401 (2003). [Preview Abstract] |
Wednesday, March 23, 2005 1:27PM - 1:39PM |
P32.00012: Monte Carlo Calculations of Finite Temperature Transition Rates in Nickel Erik Welch, Kaden Hazzard, John Wilkins Experiments reveal that self diffusion for many fcc and bcc metals is enhanced at high temperatures, thereby deviating from expected Arrhenius behavior. For nickel it is expected the deviation is caused by the influence of the di-vacancy mechanism in addition to the dominant single vacancy mechanism, but zero temperature \emph{ab initio} calculations suggest this is not the case. We investigate finite temperature effects due to anharmonicity in the potential for the single vacancy mechanism in nickel using a classical EAM potential. We modify the recently developed Wang-Landau Monte Carlo method to extract the vibrational density of states along a continuous spatial reaction coordinate. This allows the calculation of the transition rate within full transition state theory at finite temperature. We find our results agree with the harmonic approximation at low temperature and we compare our high temperature results with experiment. [Preview Abstract] |
Wednesday, March 23, 2005 1:39PM - 1:51PM |
P32.00013: Numerical Interpolation of Orbitals in Periodic Systems for Diffusion Monte Carlo Calculations William Parker, Kevin Driver, Phillip Peterson, Richard Hennig, John Wilkins, Cyrus Umrigar Diffusion Monte Carlo methods provide accurate energies for complex materials, however, the algorithms are computationally intensive. Representing the orbitals of the Slater determinant numerically with splines reduces the time scaling from O($N^3$) to O($N^2$) \footnote{A. J. Williamson, R. Q. Hood, and J. C. Grossman. PRL \textbf{87}, 246406 (2001).}. We compare memory and time requirements and the accuracy dependence on the number of grid points for cubic spline and Lagrange interpolation schemes in periodic systems. Both interpolation schemes have a small prefactor, providing speedup even for small systems. For example, in bulk silicon with 256 electrons, Lagrange interpolation reduces the computation time by a factor of 70. We are currently working on the implementation of different splines routines. [Preview Abstract] |
Wednesday, March 23, 2005 1:51PM - 2:03PM |
P32.00014: A rejection-free Monte Carlo method for the hard-disk system Hiroshi Watanabe, Satoshi Yukawa, Mark A. Novotny, Nobuyasu Ito We construct a rejection-free Monte Carlo method for the hard-disk system. Rejection-free Monte Carlo methods preserve the time-evolution behavior of the standard Monte Carlo method, and it is confirmed for our method by observing nonequilibrium relaxations of a bond-orientational order parameter. The rejection-free method obtains much better performance than the standard method at high densities with new optimization methods to calculate a rejection probability and to update the system. This method should allow an efficient study of the dynamics of two-dimensional solids at high density. [Preview Abstract] |
Wednesday, March 23, 2005 2:03PM - 2:15PM |
P32.00015: Optimal Ensemble Monte Carlo Simulations: Application to dense Lennard-Jones fluids Simon Trebst, Matthias Troyer Broad-histogram Monte Carlo simulations directly calculate the density of states of a (quantum) system by sampling broad energy ranges and thereby give access to thermodynamic properties. While flat-histogram methods suffer from a critical slowing down, we have shown that the simulation of an optimized ensemble substantially speeds up equilibration and can efficiently overcome the entropic barriers which cause the slowdown [1]. In this talk, we present recent applications of the optimal ensemble method to dense Lennard-Jones fluids and particle-solvent models. Based on measurements of the local diffusivity an optimal ensemble that maximizes round-trip rates in radial coordinates can be simulated and the potential of mean force can be determined to high precision. The optimized histogram of the radial random walk reveals clear signatures of the intermediate transitions between shells of the dense fluid. [1] S. Trebst, D. A. Huse, M. Troyer, Phys. Rev. E {\bf 70}, 046701 (2004) [Preview Abstract] |
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