44 research outputs found
Diffusion Quantum Monte Carlo Calculations of Excited States of Silicon
The band structure of silicon is calculated at the Gamma, X, and L wave
vectors using diffusion quantum Monte Carlo methods. Excited states are formed
by promoting an electron from the valence band into the conduction band. We
obtain good agreement with experiment for states around the gap region and
demonstrate that the method works equally well for direct and indirect
excitations, and that one can calculate many excited states at each wave
vector. This work establishes the fixed-node DMC approach as an accurate method
for calculating the energies of low lying excitations in solids.Comment: 5 pages, 1 figur
Finite size errors in quantum many-body simulations of extended systems
Further developments are introduced in the theory of finite size errors in
quantum many-body simulations of extended systems using periodic boundary
conditions. We show that our recently introduced Model Periodic Coulomb
interaction [A. J. Williamson et al., Phys. Rev. B 55, R4851 (1997)] can be
applied consistently to all Coulomb interactions in the system. The Model
Periodic Coulomb interaction greatly reduces the finite size errors in quantum
many-body simulations. We illustrate the practical application of our
techniques with Hartree-Fock and variational and diffusion quantum Monte Carlo
calculations for ground and excited state calculations. We demonstrate that the
finite size effects in electron promotion and electron addition/subtraction
excitation energy calculations are very similar.Comment: 15 pages, 6 figures. To appear in Phys. Rev.
Quantum Monte Carlo calculation of Compton profiles of solid lithium
Recent high resolution Compton scattering experiments in lithium have shown
significant discrepancies with conventional band theoretical results. We
present a pseudopotential quantum Monte Carlo study of electron-electron and
electron-ion correlation effects on the momentum distribution of lithium. We
compute the correlation correction to the valence Compton profiles obtained
within Kohn-Sham density functional theory in the local density approximation
and determine that electronic correlation does not account for the discrepancy
with the experimental results. Our calculations lead do different conclusions
than recent GW studies and indicate that other effects (thermal disorder,
core-valence separation etc.) must be invoked to explain the discrepancy with
experiments.Comment: submitted to Phys. Rev.
Quantum Monte Carlo calculations of the one-body density matrix and excitation energies of silicon
Quantum Monte Carlo (QMC) techniques are used to calculate the one-body
density matrix and excitation energies for the valence electrons of bulk
silicon. The one-body density matrix and energies are obtained from a
Slater-Jastrow wave function with a determinant of local density approximation
(LDA) orbitals. The QMC density matrix evaluated in a basis of LDA orbitals is
strongly diagonally dominant. The natural orbitals obtained by diagonalizing
the QMC density matrix resemble the LDA orbitals very closely. Replacing the
determinant of LDA orbitals in the wave function by a determinant of natural
orbitals makes no significant difference to the quality of the wave function's
nodal surface, leaving the diffusion Monte Carlo energy unchanged. The Extended
Koopmans' Theorem for correlated wave functions is used to calculate excitation
energies for silicon, which are in reasonable agreement with the available
experimental data. A diagonal approximation to the theorem, evaluated in the
basis of LDA orbitals, works quite well for both the quasihole and
quasielectron states. We have found that this approximation has an advantageous
scaling with system size, allowing more efficient studies of larger systems.Comment: 13 pages, 4 figures. To appear in Phys. Rev.
Variational quantum Monte Carlo calculations for solid surfaces
Quantum Monte Carlo methods have proven to predict atomic and bulk properties
of light and non-light elements with high accuracy. Here we report on the first
variational quantum Monte Carlo (VMC) calculations for solid surfaces. Taking
the boundary condition for the simulation from a finite layer geometry, the
Hamiltonian, including a nonlocal pseudopotential, is cast in a layer resolved
form and evaluated with a two-dimensional Ewald summation technique. The exact
cancellation of all Jellium contributions to the Hamiltonian is ensured. The
many-body trial wave function consists of a Slater determinant with
parameterized localized orbitals and a Jastrow factor with a common two-body
term plus a new confinement term representing further variational freedom to
take into account the existence of the surface. We present results for the
ideal (110) surface of Galliumarsenide for different system sizes. With the
optimized trial wave function, we determine some properties related to a solid
surface to illustrate that VMC techniques provide standard results under full
inclusion of many-body effects at solid surfaces.Comment: 9 pages with 2 figures (eps) included, Latex 2.09, uses REVTEX style,
submitted to Phys. Rev.
Cohesive properties of alkali halides
We calculate cohesive properties of LiF, NaF, KF, LiCl, NaCl, and KCl with
ab-initio quantum chemical methods. The coupled-cluster approach is used to
correct the Hartree-Fock crystal results for correlations and to systematically
improve cohesive energies, lattice constants and bulk moduli. After inclusion
of correlations, we recover 95-98 % of the total cohesive energies. The lattice
constants deviate from experiment by at most 1.1 %, bulk moduli by at most 8 %.
We also find good agreement for spectroscopic properties of the corresponding
diatomic molecules.Comment: LaTeX, 10 pages, 1 figure, accepted by Phys. Rev.
Carbon clusters near the crossover to fullerene stability
The thermodynamic stability of structural isomers of ,
, and , including
fullerenes, is studied using density functional and quantum Monte Carlo
methods. The energetic ordering of the different isomers depends sensitively on
the treatment of electron correlation. Fixed-node diffusion quantum Monte Carlo
calculations predict that a isomer is the smallest stable
graphitic fragment and that the smallest stable fullerenes are the
and clusters with and
symmetry, respectively. These results support proposals that a
solid could be synthesized by cluster deposition.Comment: 4 pages, includes 4 figures. For additional graphics, online paper
and related information see http://www.tcm.phy.cam.ac.uk/~prck
Diffusion Monte Carlo Study of Para -Diiodobenzene Polymorphism Revisited
We revisit our investigation of the diffusion Monte Carlo (DMC) simulation of p-DIB molecular crystal polymorphism. [J. Phys. Chem. Lett. 2010, 1, 1789-1794] We perform, for the first time, a rigorous study of finite-size effects and choice of nodal surface on the prediction of polymorph stability in molecular crystals using fixed-node DMC. Our calculations are the largest which are currently feasible using the resources of the K computer and provide insights into the formidable challenge of predicting such properties from first principles. In particular, we show that finite-size effects can influence the trial nodal surface of a small (1×1×1) simulation cell considerably. We therefore repeated our DMC simulations with a 1×3×3 simulation cell, which is the largest such calculation to date. We used a DFT nodal surface generated with the PBE functional and we accumulated statistical samples with ∼6.4×105 core-hours for each polymorph. Our final results predict a polymorph stability consistent with experiment, but indicate that results in our previous paper were somewhat fortuitous. We analyze the finite-size errors using model periodic Coulomb (MPC) interactions and kinetic energy corrections, according to the CCMH scheme of Chiesa, Ceperley, Martin, and Holzmann. We investigate the dependence of the finite-size errors on different aspect ratios of the simulation cell (k-mesh convergence) in order to understand how to choose an appropriate ratio for the DMC calculations. Even in the most expensive simulations currently possible, we show that the finite size errors in the DMC total energies are far larger than the energy difference between the two polymorphs, although error cancellation means that the polymorph prediction is accurate. Finally, we found that the T-move scheme is essential for these massive DMC simulations in order to circumvent population explosions and large time-step biases.Chemistry and Chemical Biolog