arXiv subjects

R. J. Needs

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

At least 55 records · Page 3Linked to original sources

arXiv2010

Quantum Monte Carlo study of the ground state of the two-dimensional Fermi fluid

We have used the variational and diffusion quantum Monte Carlo methods to calculate the energy, pair correlation function, static structure factor, and momentum density of the ground state of the two-dimensional homogeneous electron gas. We have used highly accurate Slater-Jastrow-backflow trial wave functions and twist averaging to reduce finite-size effects where applicable. We compare our results with others in the literature and construct a local-density-approximation exchange-correlation functional for 2D systems.

cond-mat.mes-hall↗

arXiv2010

Quantum Monte Carlo calculation of the energy band and quasiparticle effective mass of the two-dimensional Fermi fluid

We have used the diffusion quantum Monte Carlo method to calculate the energy band of the two-dimensional homogeneous electron gas (HEG), and hence we have obtained the quasiparticle effective mass and the occupied bandwidth. We find that the effective mass in the paramagnetic HEG increases significantly when the density is lowered, whereas it decreases in the fully ferromagnetic HEG. Our calculations therefore support the conclusions of recent experimental studies [Y.-W. Tan et al., Phys. Rev. Lett. 94, 016405 (2005); M. Padmanabhan et al., Phys. Rev. Lett. 101, 026402 (2008); T. Gokmen et al., Phys. Rev. B 79, 195311 (2009)]. We compare our calculated effective masses with other theoretical results and experimental measurements in the literature.

cond-mat.mes-hall↗

arXiv2010

Phase Diagram of the Low-Density Two-Dimensional Homogeneous Electron Gas

We have used quantum Monte Carlo methods to calculate the zero-temperature phase diagram of the two-dimensional homogeneous electron gas. We find a transition from a paramagnetic fluid to an antiferromagnetic triangular Wigner crystal at density parameter r_s=31(1) a.u. and a transition to a ferromagnetic crystal at r_s=38(5) a.u. The fully spin-polarized fluid is never stable. We searched for, but did not find, the ferromagnetic hybrid phase proposed by H. Falakshahi and X. Waintal [Phys. Rev. Lett. 94, 046801 (2005)].

cond-mat.mes-hall↗

arXiv2010

Quantum Monte Carlo for minerals at high pressure: Phase stability, equations of state, and elasticity of silica

Silica is an abundant component of the Earth whose crystalline polymorphs play key roles in its structure and dynamics. As the simplest silicates, understanding pure silica is a prerequisite to understanding the rocky part of the Earth, its majority. First principle density functional theory (DFT) methods have often been used to accurately predict properties of silicates. Here, we study silica with quantum Monte Carlo (QMC), which until now was not computationally possible for such complex materials, and find that QMC overcomes the failures of DFT. QMC is a benchmark method that does not rely on density functionals, but rather explicitly treats the electrons and their interactions via a stochastic solution of Schrodinger's equation. Using ground state QMC plus phonons within the quasiharmonic approximation from density functional perturbation theory, we obtain the thermal pressure and equations of state of silica phases up to Earth's core-mantle boundary. Our results provide the most well-constrained equations of state and phase boundaries available for silica. QMC indicates a transition to the most dense alpha-PbO2 structure above the core-insulating D" layer, suggesting the absence of significant free silica in the bulk lower mantle, which has been assumed but never proven. We also find an accurate shear elastic constant and its geophysically important softening with pressure.

cond-mat.mtrl-sci↗

arXiv2010

Fundamental high pressure calibration from all-electron quantum Monte Carlo calculations

We develop an all-electron quantum Monte Carlo (QMC) method for solids that does not rely on pseudopotentials, and use it to construct a primary ultra-high pressure calibration based the equation of state of cubic boron nitride(c-BN). We compute the static contribution to the free energy with QMC, and obtain the phonon contribution from density functional theory, yielding a high-accuracy calibration up to 900 GPa usable directly in experiment. Furthermore, we compute the anharmonic Raman frequency shift with QMC as a function of pressure and temperature, allowing optical pressure calibration in table-top experiments. In contrast to present experimental approaches, small systematic errors in the theoretical EOS do not increase with pressure, and no extrapolation is needed. This all-electron methodology is generally applicable to first-row solids, and can be used to provide a new reference for ab initio calculations of solids and to benchmark pseudopotential accuracy.

cond-mat.mtrl-sci↗

arXiv2009

Ultracold atoms at unitarity within quantum Monte Carlo

Variational and diffusion quantum Monte Carlo (VMC and DMC) calculations of the properties of the zero-temperature fermionic gas at unitarity are reported. The ratio of the energy of the interacting to the non-interacting gas for a system of 128 particles is calculated to be 0.4517(3) in VMC and 0.4339(1) in the more accurate DMC method. The spherically-averaged pair-correlation functions, momentum densities, and one-body density matrices are very similar in VMC and DMC, but the two-body density matrices and condensate fractions show some differences. Our best estimate of the condensate fraction of 0.51 is a little smaller than values from other quantum Monte Carlo calculations.

cond-mat.quant-gas↗

arXiv2009

Norm-conserving Hartree-Fock pseudopotentials and their asymptotic behavior

We investigate the properties of norm-conserving pseudopotentials (effective core potentials) generated by inversion of the Hartree-Fock equations. In particular we investigate the asymptotic behaviour as $\mathbf{r} \to \infty$ and find that such pseudopotentials are non-local over all space, apart from a few special special cases such H and He. Such extreme non-locality leads to a lack of transferability and, within periodic boundary conditions, an undefined total energy. The extreme non-locality must therefore be removed, and we argue that the best way to accomplish this is a minor relaxation of the norm-conservation condition. This is implemented, and pseudopotentials for the atoms H$-$Ar are constructed and tested.

cond-mat.mtrl-sci↗

arXiv2009

Smooth relativistic Hartree-Fock pseudopotentials for H to Ba and Lu to Hg

We report smooth relativistic Hartree-Fock pseudopotentials (also known as averaged relativistic effective potentials or AREPs) and spin-orbit operators for the atoms H to Ba and Lu to Hg. We remove the unphysical extremely non-local behaviour resulting from the exchange interaction in a controlled manner, and represent the resulting pseudopotentials in an analytic form suitable for use within standard quantum chemistry codes. These pseudopotentials are suitable for use within Hartree-Fock and correlated wave function methods, including diffusion quantum Monte Carlo calculations.

cond-mat.mtrl-sci↗

arXiv2009

Spectroscopic data for the LiH molecule from pseudopotential quantum Monte Carlo calculations

Quantum Monte Carlo and quantum chemistry techniques are used to investigate pseudopotential models of the lithium hydride (LiH) molecule. Interatomic potentials are calculated and tested by comparing with the experimental spectroscopic constants and well depth. Two recently-developed pseudopotentials are tested, and the effects of introducing a Li core polarization potential are investigated. The calculations are sufficiently accurate to isolate the errors from the pseudopotentials and core polarization potential. Core-valence correlation and core relaxation are found to be important in determining the interatomic potential.

cond-mat.mtrl-sci↗

arXiv2009

Unrestricted Hartree-Fock theory of Wigner crystals

We demonstrate that unrestricted Hartree-Fock theory applied to electrons in a uniform potential has stable Wigner crystal solutions for $r_s \geq 1.44$ in two dimensions and $r_s \geq 4.5$ in three dimensions. The correlation energies of the Wigner crystal phases are considerably smaller than those of the fluid phases at the same density.

cond-mat.mtrl-sci↗

arXiv2009

Hydrogen/nitrogen/oxygen defect complexes in silicon from computational searches

Point defect complexes in crystalline silicon composed of hydrogen, nitrogen, and oxygen atoms are studied within density-functional theory (DFT). Ab initio Random Structure Searching (AIRSS) is used to find low-energy defect structures. We find new lowest-energy structures for several defects: the triple-oxygen defect, {3O}, triple oxygen with a nitrogen atom, {N, 3O}, triple nitrogen with an oxygen atom, {3N,O}, double hydrogen and an oxygen atom, {2H,O}, double hydrogen and oxygen atoms, {2H,2O} and four hydrogen/nitrogen/oxygen complexes, {H,N,O}, {2H,N,O}, {H,2N,O} and {H,N,2O}. We find that some defects form analogous structures when an oxygen atom is replaced by a NH group, for example, {H,N,2O} and {3O}, and {H,N} and {O}. We compare defect formation energies obtained using different oxygen chemical potentials and investigate the relative abundances of the defects.

cond-mat.mtrl-sci↗

arXiv2009

Post-Cotunnite phase of TeO2

We have used first-principles density-functional-theory methods with a random-structure-searching technique to determine the structure of the previously unidentified post-cotunnite phase of TeO2. Our calculations indicate a transition from the cotunnite to post-cotunnite phase at 130 GPa. The predicted post-cotunnite structure has P2_1/m space group symmetry and its calculated x-ray diffraction pattern is in good agreement with the available experimental data. We find that the cotunnite phase re-enters at about 260 GPa.

cond-mat.mtrl-sci↗

arXiv2008

Exciton-exciton interaction and biexciton formation in bilayer systems

We report quantum Monte Carlo calculations of biexciton binding energies in ideal two-dimensional bilayer systems with isotropic electron and hole masses. We have also calculated exciton-exciton interaction potentials, and pair distribution functions for electrons and holes in bound biexcitons. Comparing our data with results obtained in a recent study using a model exciton-exciton potential [C. Schindler and R. Zimmermann, Phys. Rev. B \textbf{78}, 045313 (2008)], we find a somewhat larger range of layer separations at which biexcitons are stable. We find that individual excitons retain their identity in bound biexcitons for large layer separations.

cond-mat.str-el↗

arXiv2008

Total forces in the diffusion Monte Carlo method with nonlocal pseudopotentials

We report exact expressions for atomic forces in the diffusion Monte Carlo (DMC) method when using nonlocal pseudopotentials. We present approximate schemes for estimating these expressions in both mixed and pure DMC calculations, including the pseudopotential Pulay term which has not previously been calculated and the Pulay nodal term which has not been calculated for real systems in pure DMC simulations. Harmonic vibrational frequencies and equilibrium bond lengths are derived from the DMC forces and compared with those obtained from DMC potential energy curves. Results for four small molecules show that the equilibrium bond lengths obtained from our best force and energy calculations differ by less than 0.002 Angstrom.

cond-mat.mtrl-sci↗

arXiv2008

Hydrogen/silicon complexes in silicon from computational searches

Defects in crystalline silicon consisting of a silicon self-interstitial atom and one, two, three, or four hydrogen atoms are studied within density-functional theory (DFT). We search for low-energy defects by starting from an ensemble of structures in which the atomic positions in the defect region have been randomized. We then relax each structure to a minimum in the energy. We find a new defect consisting of a self-interstitial and one hydrogen atom (denoted by {I,H}) which has a higher symmetry and a lower energy than previously reported structures. We recover the {I,H_2} defect found in previous studies and confirm that it is the most stable such defect. Our best {I,H_3} defect has a slightly different structure and lower energy than the one previously reported, and our lowest energy {I,H_4} defect is different to those of previous studies.

cond-mat.mtrl-sci↗

arXiv2008

Scheme for adding electron-nucleus cusps to Gaussian orbitals

A simple scheme is described for introducing the correct cusps at nuclei into orbitals obtained from Gaussian basis set electronic structure calculations. The scheme is tested with all-electron variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) methods for the Ne atom, the H2 molecule, and 55 molecules from a standard benchmark set. It greatly reduces the variance of the local energy in all cases and slightly improves the variational energy. This scheme yields a general improvement in the efficiency of all-electron VMC and DMC calculations using Gaussian basis sets.

physics.comp-ph↗

arXiv2008

All-electron quantum Monte Carlo calculations for the noble gas atoms He to Xe

We report all-electron variational and diffusion quantum Monte Carlo (VMC and DMC) calculations for the noble gas atoms He, Ne, Ar, Kr, and Xe. The calculations were performed using Slater-Jastrow wave functions with Hartree-Fock single-particle orbitals. The quality of both the optimized Jastrow factors and the nodal surfaces of the wave functions declines with increasing atomic number Z, but the DMC calculations are tractable and well behaved in all cases. We discuss the scaling of the computational cost of DMC calculations with Z.

cond-mat.mtrl-sci↗

arXiv2008

Inhomogeneous backflow transformations in quantum Monte Carlo calculations

An inhomogeneous backflow transformation for many-particle wave functions is presented and applied to electrons in atoms, molecules, and solids. We report variational and diffusion quantum Monte Carlo VMC and DMC energies for various systems and study the computational cost of using backflow wave functions. We find that inhomogeneous backflow transformations can provide a substantial increase in the amount of correlation energy retrieved within VMC and DMC calculations. The backflow transformations significantly improve the wave functions and their nodal surfaces.

physics.comp-ph↗