arXiv subjects

R. J. Needs

Publications and source records attributed to R. J. Needs.

At least 73 records · Page 4Linked to original sources

arXiv2008

Quantum Monte Carlo study of the Ne atom and the Ne+ ion

We report all-electron and pseudopotential calculations of the ground-stateenergies of the neutral Ne atom and the Ne+ ion using the variational and diffusion quantum Monte Carlo (DMC) methods. We investigate different levels of Slater-Jastrow trial wave function: (i) using Hartree-Fock orbitals, (ii) using orbitals optimized within a Monte Carlo procedure in the presence of a Jastrow factor, and (iii) including backflow correlations in the wave function. Small reductions in the total energy are obtained by optimizing the orbitals, while more significant reductions are obtained by incorporating backflow correlations. We study the finite-time-step and fixed-node biases in the DMC energy and show that there is a strong tendency for these errors to cancel when the first ionization potential (IP) is calculated. DMC gives highly accurate values for the IP of Ne at all the levels of trial wave function that we have considered.

cond-mat.mtrl-sci↗

arXiv2008

Diffusion quantum Monte Carlo study of three-dimensional Wigner crystals

We report diffusion quantum Monte Carlo calculations of three-dimensional Wigner crystals in the density range r_s=100-150. We have tested different types of orbital for use in the approximate wave functions but none improve upon the simple Gaussian form. The Gaussian exponents are optimized by directly minimizing the diffusion quantum Monte Carlo energy. We have carefully investigated and sought to minimize the potential biases in our Monte Carlo results. We conclude that the uniform electron gas undergoes a transition from a ferromagnetic fluid to a body-centered-cubic Wigner crystal at r_s=106+/-1. The diffusion quantum Monte Carlo results are compared with those from Hartree-Fock and Hartree theory in order to understand the role played by exchange and correlation in Wigner crystals. We also study "floating" Wigner crystals and give results for their pair-correlation functions.

cond-mat.str-el↗

arXiv2008

Jastrow correlation factor for atoms, molecules, and solids

A form of Jastrow factor is introduced for use in quantum Monte Carlo simulations of finite and periodic systems. Test data are presented for atoms, molecules, and solids, including both all-electron and pseudopotential atoms. We demonstrate that our Jastrow factor is able to retrieve a large fraction of the correlation energy.

physics.comp-ph↗

arXiv2008

Exciton and biexciton energies in bilayer systems

We report calculations of the energies of excitons and biexcitons in ideal two-dimensional bilayer systems within the effective-mass approximation with isotropic electron and hole masses. The exciton energies are obtained by a simple numerical integration technique, while the biexciton energies are obtained from diffusion quantum Monte Carlo calculations. The exciton binding energy decays as the inverse of the separation of the layers, while the binding energy of the biexciton with respect to dissociation into two separate excitons decays exponentially.

cond-mat.other↗

arXiv2008

Quantum Monte Carlo, Density Functional Theory, and Pair Potential Studies of Solid Neon

We report quantum Monte Carlo (QMC), plane-wave density-functional theory (DFT), and interatomic pair-potential calculations of the zero-temperature equation of state (EOS) of solid neon. We find that the DFT EOS depends strongly on the choice of exchange-correlation functional, whereas the QMC EOS is extremely close to both the experimental EOS and the EOS obtained using the best semiempirical pair potential in the literature. This suggests that QMC is able to give an accurate treatment of van der Waals forces in real materials, unlike DFT. We calculate the QMC EOS up to very high densities, beyond the range of values for which experimental data are currently available. At high densities the QMC EOS is more accurate than the pair-potential EOS. We generate a different pair potential for neon by a direct evaluation of the QMC energy as a function of the separation of an isolated pair of neon atoms. The resulting pair potential reproduces the EOS more accurately than the equivalent potential generated using the coupled-cluster CCSD(T) method.

cond-mat.mtrl-sci↗

arXiv2008

Electron Emission from Diamondoids: A Diffusion Quantum Monte Carlo Study

We present density-functional theory (DFT) and quantum Monte Carlo (QMC) calculations designed to resolve experimental and theoretical controversies over the optical properties of H-terminated C nanoparticles (diamondoids). The QMC results follow the trends of well-converged plane-wave DFT calculations for the size dependence of the optical gap, but they predict gaps that are 1-2 eV higher. They confirm that quantum confinement effects disappear in diamondoids larger than 1 nm, which have gaps below that of bulk diamond. Our QMC calculations predict a small exciton binding energy and a negative electron affinity (NEA) for diamondoids up to 1 nm, resulting from the delocalized nature of the lowest unoccupied molecular orbital. The NEA suggests a range of possible applications of diamondoids as low-voltage electron emitters.

cond-mat.mtrl-sci↗

arXiv2008

van der Waals Interactions Between Thin Metallic Wires and Layers

Quantum Monte Carlo (QMC) methods have been used to obtain accurate binding-energy data for pairs of parallel thin metallic wires and layers modeled by 1D and 2D homogeneous electron gases. We compare our QMC binding energies with results obtained within the random phase approximation, finding significant quantitative differences and disagreement over the asymptotic behavior for bilayers at low densities. We have calculated pair-correlation functions for metallic biwire and bilayer systems. Our QMC data could be used to investigate van der Waals energy functionals.

cond-mat.mtrl-sci↗

arXiv2007

Dissociation energy of the water dimer from Quantum Monte Carlo calculations

We report a study of the electronic dissociation energy of the water dimer using quantum Monte Carlo (QMC) techniques. We have performed variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) calculations of the electronic ground state of the water monomer and dimer using all-electron and pseudopotential approaches. We have used Slater-Jastrow trial wave functions with B3LYP-like single-particle orbitals, into which we have incorporated backflow correlations. When backflow correlations are introduced, the total energy of the water monomer decreases by about 4-5 mHa, yielding a DMC energy of -76.42830(5) Ha, which is only 10 mHa above the experimental value. In our pseudopotential DMC calculations, we have compared the total energies of the water monomer and dimer obtained using the locality approximation with those from the variational scheme recently proposed by Casula [Phys. Rev. B 74, 161102(R) (2006)]. The time step errors in the Casula scheme are larger and the extrapolation of the energy to zero time step always lies above the result obtained with the locality approximation. However, the errors cancel when energy differences are taken, yielding electronic dissociation energies within error bars of each other. The dissociation energies obtained in our various all-electron and pseudopotential calculations range between 5.03(7) and 5.47(9) kcal/mol and are in good agreement with experiment. Our calculations give monomer dipole moments which range between 1.897(2) and 1.909(4) Debye and dimer dipole moments which range between 2.628(6) and 2.672(5) Debye.

cond-mat.other↗

arXiv2006

Graphite intercalation compounds under pressure

Motivated by recent experimental work, we use first-principles density functional theory methods to conduct an extensive search for low enthalpy structures of C$_6$Ca under pressure. As well as a range of buckled structures, which are energetically competitive over an intermediate range of pressures, we show that the high pressure system ($\gtrsim 18$ GPa) is unstable towards the formation of a novel class of layered structures, with the most stable compound involving carbon sheets containing five- and eight-membered rings. As well as discussing the energetics of the different classes of low enthalpy structures, we comment on the electronic structure of the high pressure compound and its implications for superconductivity.

cond-mat.supr-con↗

arXiv2006

High-pressure phases of silane

It has been suggested that hydrogen may metallise at lower pressures if it is ``precompressed''. Here we introduce a search strategy for predicting high-pressure structures and apply it to silane using first-principles electronic structure computations. It is based on relaxing randomly chosen structures, and is demonstrated to work well for unit cells containing up to at least ten atoms. We predict that silane will metallise at higher pressures than previously anticipated, but we suggest that the metallic phase might show high-temperature superconductivity at experimentally accessible pressures.

cond-mat.mtrl-sci↗

arXiv2005

A variance-minimization scheme for optimizing Jastrow factors

We describe a new scheme for optimizing many-electron trial wave functions by minimizing the unreweighted variance of the energy using stochastic integration and correlated-sampling techniques. The scheme is restricted to parameters that are linear in the exponent of a Jastrow correlation factor, which are the most important parameters in the wave functions we use. The scheme is highly efficient and allows us to investigate the parameter space more closely than has been possible before. We search for multiple minima of the variance in the parameter space and compare the wave functions obtained using reweighted and unreweighted variance minimization.

physics.comp-ph↗

arXiv2005

Quantum Monte Carlo calculations of the structural properties and the B1-B2 phase transition of MgO

We report diffusion Monte Carlo (DMC) calculations on MgO in the rock-salt and CsCl structures. The calculations are based on Hartree-Fock pseudopotentials, with the single-particle orbitals entering the correlated wave function being represented by a systematically convergeable cubic-spline basis. Systematic tests are presented on system-size errors using periodically repeating cells of up to over 600 atoms. The equilibrium lattice parameter of the rock-salt structure obtained within DMC is almost identical to the Hartree-Fock result, which is close to the experimental value. The DMC result for the bulk modulus is also in good agreement with the experimental value. The B1-B2 transition pressure (between the rock-salt and CsCl structures) is predicted to be just below 600 GPa, which is beyond the experimentally accessible range, in accord with other predictions based on Hartree-Fock and density functional theories.

cond-mat.str-el↗

arXiv2004

Interpretation of Hund's multiplicity rule for the carbon atom

Hund's multiplicity rule is investigated for the carbon atom using quantum Monte Carlo methods. Our calculations give an accurate account of electronic correlation and obey the virial theorem to high accuracy. This allows us to obtain accurate 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 find that 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, in accordance with Hartree-Fock calculations and studies including correlation. The method used here can easily be extended to heavier atoms.

cond-mat.str-el↗

arXiv2004

Diamond and $β$-tin structures of Si studied with quantum Monte Carlo calculations

We have used diffusion quantum Monte Carlo (DMC) calculations to study the pressure-induced phase transition from the diamond to $β$-tin structure in silicon. The calculations employ the pseudopotential technique and systematically improvable B-spline basis sets. We show that in order to achieve a precision of 1 GPa in the transition pressure the non-cancelling errors in the energies of the two structures must be reduced to 30 meV/atom. Extensive tests on system size errors, non-local pseudopotential errors, basis-set incompleteness errors, and other sources of error, performed on periodically repeated systems of up to 432 atoms, show that all these errors together can be reduced to well below 30 meV/atom. The calculated DMC transition pressure is about 3-4 GPa higher than the accepted experimental range of values, and we argue that the discrepancy may be due to the fixed-node error inherent in DMC techniques.

cond-mat.mtrl-sci↗

arXiv2004

Structural relaxations in electronically excited poly(para-phenylene)

Structural relaxations in electronically excited poly(para-phenylene) are studied using many-body perturbation theory and density-functional-theory methods. A sophisticated description of the electron-hole interaction is required to describe the energies of the excitonic states, but we show that the structural relaxations associated with exciton formation can be obtained quite accurately within a constrained density-functional-theory approach. We find that the structural relaxations in the low-energy excitonic states extend over about 8 monomers, leading to an energy reduction of 0.22 eV and a Stokes shift of 0.40 eV.

cond-mat.mtrl-sci↗

arXiv2000

Excitons in T-shaped quantum wires

We calculate energies, oscillator strengths for radiative recombination, and two-particle wave functions for the ground state exciton and around 100 excited states in a T-shaped quantum wire. We include the single-particle potential and the Coulomb interaction between the electron and hole on an equal footing, and perform exact diagonalisation of the two-particle problem within a finite basis set. We calculate spectra for all of the experimentally studied cases of T-shaped wires including symmetric and asymmetric GaAs/Al$_{x}$Ga$_{1-x}$As and In$_{y}$Ga$_{1-y}$As/Al$_{x}$Ga$_{1-x}$As structures. We study in detail the shape of the wave functions to gain insight into the nature of the various states for selected symmetric and asymmetric wires in which laser emission has been experimentally observed. We also calculate the binding energy of the ground state exciton and the confinement energy of the 1D quantum-wire-exciton state with respect to the 2D quantum-well exciton for a wide range of structures, varying the well width and the Al molar fraction $x$. We find that the largest binding energy of any wire constructed to date is 16.5 meV. We also notice that in asymmetric structures, the confinement energy is enhanced with respect to the symmetric forms with comparable parameters but the binding energy of the exciton is then lower than in the symmetric structures. For GaAs/Al$_{x}$Ga$_{1-x}$As wires we obtain an upper limit for the binding energy of around 25 meV in a 10 Å wide GaAs/AlAs structure which suggests that other materials must be explored in order to achieve room temperature applications. There are some indications that In$_{y}$Ga$_{1-y}$As/Al$_{x}$Ga$_{1-x}$As might be a good candidate.

cond-mat.mes-hall↗

arXiv2000

Quantum Monte Carlo Analysis of Exchange and Correlation in the Strongly Inhomogeneous Electron Gas

We use variational quantum Monte Carlo to calculate the density-functional exchange-correlation hole n_{xc}, the exchange-correlation energy density e_{xc}, and the total exchange-correlation energy E_{xc}, of several electron gas systems in which strong density inhomogeneities are induced by a cosine-wave potential. We compare our results with the local density approximation and the generalized gradient approximation. It is found that the nonlocal contributions to e_{xc} contain an energetically significant component, the magnitude, shape, and sign of which are controlled by the Laplacian of the electron density.

cond-mat.mtrl-sci↗

arXiv2000

Many-Electron Trial Wave Functions for Inhomogeneous Solids

Quantum Monte Carlo simulations of interacting electrons in solids often use Slater-Jastrow trial wave functions with Jastrow factors containing one- and two-body terms. In uniform systems the long-range behavior of the two-body term may be deduced from the random-phase approximation (RPA) of Bohm and Pines. Here we generalize the RPA to nonuniform systems. This gives the long-range behavior of the inhomogeneous two-body correlation term and provides an accurate analytic expression for the one-body term. It also explains why Slater-Jastrow trial wave functions incorporating determinants of Hartree-Fock or density-functional orbitals are close to optimal even in the presence of an RPA Jastrow factor. After adjusting the inhomogeneous RPA Jastrow factor to incorporate the known short-range behavior, we test it using variational Monte Carlo calculations. We find that the most important aspect of the two-body term is the short-range behavior due to electron-electron scattering, although the long-range behavior described by the RPA should become more important at high densities.

cond-mat.mtrl-sci↗