CECAM/Psi-k Workshop


Diffusion Monte Carlo

CECAM, Lyon, 19-21 September 2002

Abstracts for Saturday, 21 September 2002

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Fixed-node Monte Carlo for fermions on a lattice: applications to the doped fullerenes

Erik Koch
Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany

Fullerides are crystals made from C60 molecules. Doping these crystals with electrons puts charge carriers into the band derived from the lowest unoccupied molecular orbital of C60, doping with holes adds carriers to the band derived from the highest unoccupied level. Since the Coulomb repulsion between charges on the same C60 molecule is strong, it is essential to include correlation effects for understanding the behavior of the induced charges. We show how the correlated hopping of the induced carriers between the C60 molecules can be described using a multi-band Hubbard model. Such a lattice model can be treated using the fixed-node approximation adapted for lattice models. We demonstrate the importance of choosing appropriate trial functions and describe efficient ways for optimizing their parameters. As applications we discuss results for the Mott transition as a function of orbital degeneracy and dimensionality of the system. In addition we show calculations of response-functions that help understanding the metallic and superconducting properties of the doped Fullerenes.


QMC studies of 2D and 3D Wigner crystals

J. R. Trail , M. D. Towler, N. D. Drummond and R. J. Needs
TCM Group, Cavendish Laboratory, Madingley Road, Cambridge, CB3 0HE, UK

We have developed new trial wave functions for 2D and 3D Wigner crystals based on a mean-field approach. These wave functions give new insights into the physics of the crystalline state and provide an excellent starting point for QMC calculations. This approach leads to improved accuracy and efficiency of VMC and DMC studies of Wigner crystals. Our scheme should allow the development of better trial wave functions for more complicated systems such as defective Wigner crystals and Wigner molecules.


Energy optimization of variational wave functions in solids: general theory and calculation of the van der Waals energy in graphite

Stephen Fahy
University of Cork, Ireland

We will review recently developed variational Monte Carlo methods for the minimization of energy with respect to the parameters in a general class of Jastrow-Slater wave functions that are suitable for periodic solids. We will demonstrate their use in explicitly calculating the contribution of van der Waals correlation to the interlayer binding of graphite, as follows: Using a modified many-body Hamiltonian, long-range instantaneous electron interactions are replaced by a static Hartree potential, thereby eliminating van der Waals correlations. This produces an optimal groundstate trial wave function which, in combination with the true fully-interacting Hamiltonian, determines the energy of the system when long-range correlation is removed.

This talk is based on work over a number of years with David Prendergast, Claudia Filippi, Friedemann Schautz, David Bevan, Antonella Malatesta, and Giovanni Bachelet. We acknowledge support from Enterprise Ireland, The Irish Higher Education Authority, and Science Foundation Ireland.


Optimization of trial wave functions for excited states of bosonic clusters

Peter Nightingale
Department of Physics, University of Rhode Island, Kingston, Rhode Island, USA

I shall discuss progress in the optimization of excited state trial wavefunctions,[1,2] in addition to applications of this method, using correlation function Monte Carlo approach, of ground and excited state energies of bosonic van der Waals clusters. The calculations are performed employing trial wavefunctions with general four-body correlations.

  1. M. P. Nightingale and Vilen Melik-Alaverdian, ``Optimization of ground and excited state wavefunctions and van der Waals clusters'', Phys. Rev. Lett. 87, 43401 (2001).
  2. M. P. Nightingale and Vilen Melik-Alaverdian, ``Trial function optimization for excited states of van der Waals clusters'', in ``Recent Advances in Quantum Monte Carlo Methods - Part II'', edited by William A. Lester, Jr., Stuart M. Rothstein and Shigenori Tanaka, World Scientific (Singapore 2002), p. 127.

Optimization of CI coefficients in multideterminant Jastrow-Slater wave functions

Friedemann Schautz
Instituut-Lorentz for Theoretical Physics, Universiteit Leiden, The Netherlands

A quantum Monte Carlo method for obtaining multi-determinant Jastrow-Slater wave functions for which the energy is stationary with respect to variations of CI coefficients is presented. The single particle orbitals can also be optimized simultaneously. Using ground state calculations of atoms and small molecules as illustrative examples, the method is shown to converge rapidly and to significantly lower the energy in most cases. Additionally, we discuss preliminary results obtained using this optimized multi-determinant trial wave functions for the ground state and low excited states within fixed-node diffusion Monte Carlo.

This work was done in collaboration with Stephen Fahy (University College Cork, Ireland) and Claudia Filippi (Universiteit Leiden, The Netherlands)


Electronic structure of nanosystems and solids by quantum Monte Carlo methods

Lubos Mitás , P. Sen, L. K. Wagner, Z. Helms
Department of Physics, North Carolina State University, USA

We report on our recent Quantum Monte carlo calculations of the electronic structure for several types of nanosystems and solids such as Si nanoclusters with embedded transition metal atoms, molecules involving transition metal atoms and transition metal oxide solids. We focus on calculations of ground and excited states in order to elucidate the electronic gaps and some optical properties. Several approaches were tried such as combination of diffusion Monte Carlo and Configuration Interaction, correlated sampling and direct state-by-state calculations. This enabled us to identify the ground states in TM@Six nanoclusters with competing d-states localized on the TM atom and more extended states from p-orbitals of the Si skeleton. We also attempt to predict band gaps of solid materials for which the experimental results are contradictory or inconclusive.


Distributed Multipole Moments and Polarizabilities with DMC

Arne Lüchow
University of Dusseldorf, Germany

Distributed Multipoles can be calculated routinely with standard ab initio methods. They provide an important ab initio tool for the construction of intermolecular potentials. Since multipole moments are sensitive to correlation effects, they are a good candidates for property calculation with DMC. It is shown how distributed multipole moments and polarizabilities can be calculated easily with DMC. The effect of the node location error on the results is analysed.


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