arXiv subjects

Ali Alavi

Publications and source records attributed to Ali Alavi.

95 records · Page 6Linked to original sources

arXiv2012

Convergence of many-body wavefunction expansions using a plane wave basis: from the homogeneous electron gas to the solid state

Using the finite simulation-cell homogeneous electron gas (HEG) as a model, we investigate the convergence of the correlation energy to the complete basis set (CBS) limit in methods utilising plane-wave wavefunction expansions. Simple analytic and numerical results from second-order Møller-Plesset theory (MP2) suggest a 1/M decay of the basis-set incompleteness error where M is the number of plane waves used in the calculation, allowing for straightforward extrapolation to the CBS limit. As we shall show, the choice of basis set truncation when constructing many-electron wavefunctions is far from obvious, and here we propose several alternatives based on the momentum transfer vector, which greatly improve the rate of convergence. This is demonstrated for a variety of wavefunction methods, from MP2 to coupled-cluster doubles theory (CCD) and the random-phase approximation plus second-order screened exchange (RPA+SOSEX). Finite basis-set energies are presented for these methods and compared with exact benchmarks. A transformation can map the orbitals of a general solid state system onto the HEG plane wave basis and thereby allow application of these methods to more realistic physical problems.

physics.comp-ph↗

arXiv2012

Investigation of the Full Configuration Interaction Quantum Monte Carlo Method Using Homogeneous Electron Gas Models

Using the homogeneous electron gas (HEG) as a model, we investigate the sources of error in the `initiator' adaptation to Full Configuration Interaction Quantum Monte Carlo (i-FCIQMC), with a view to accelerating convergence. In particular we find that the fixed shift phase, where the walker number is allowed to grow slowly, can be used to effectively assess stochastic and initiator error. Using this approach we provide simple explanations for the internal parameters of an i-FCIQMC simulation. We exploit the consistent basis sets and adjustable correlation strength of the HEG to analyze properties of the algorithm, and present finite basis benchmark energies for N=14 over a range of densities $0.5 \leq r_s \leq 5.0$ a.u. A \emph{single-point extrapolation} scheme is introduced to produce complete basis energies for 14, 38 and 54 electrons. It is empirically found that, in the weakly correlated regime, the computational cost scales linearly with the plane wave basis set size, which is justifiable on physical grounds. We expect the fixed shift strategy to reduce the computational cost of many \iFCIQMC calculations of weakly correlated systems. In addition, we provide benchmarks for the electron gas, to be used by other quantum chemical methods in exploring periodic solid state systems.

physics.comp-ph↗

arXiv2011

A Full Configuration Interaction Perspective on the Homogeneous Electron Gas

Highly accurate results for the homogeneous electron gas (HEG) have only been achieved to date within a diffusion Monte Carlo (DMC) framework. Here, we introduce a newly developed stochastic technique, Full Configuration Interaction Quantum Monte Carlo (FCIQMC), which samples the exact wavefunction expanded in plane wave Slater determinants. Despite the introduction of a basis set incompleteness error, we obtain a finite-basis energy which is significantly, and variationally lower than any previously published work for the 54-electron HEG at $r_s$ = 0.5 a.u., in a Hilbert space of $10^{108}$ Slater determinants. At this value of $r_s$, as well as of 1.0 a.u., we remove the remaining basis set incompleteness error by extrapolation, yielding results comparable or better than state-of-the-art DMC backflow energies. In doing so, we demonstrate that it is possible to yield highly accurate results with the FCIQMC method in sizable periodic systems.

cond-mat.quant-gas↗

arXiv2010

Dispersion interactions between semiconducting wires

The dispersion energy between extended molecular chains (or equivalently infinite wires) with non-zero band gaps is generally assumed to be expressible as a pair-wise sum of atom-atom terms which decay as $R^{-6}$. Using a model system of two parallel wires with a variable band gap, we show that this is not the case. The dispersion interaction scales as $z^{-5}$ for large interwire separations $z$, as expected for an insulator, but as the band gap decreases the interaction is greatly enhanced; while at shorter (but non-overlapping) separations it approaches a power-law scaling given by $z^{-2}$, \emph{i.e.} the dispersion interaction expected between \emph{metallic} wires. We demonstrate that these effects can be understood from the increasing length scale of the plasmon modes (charge fluctuations), and their increasing contribution to the molecular dipole polarizability and the dispersion interaction, as the band gaps are reduced. This result calls into question methods which invoke locality assumptions in deriving dispersion interactions between extended small-gap systems.

cond-mat.mes-hall↗

arXiv2000

Equilibrium and adhesion of Nb/sapphire: the effect of oxygen partial pressure

We derive a formula, useful for first-principles calculations, which relates the free energy of an oxide/metal interface to the free energies of surfaces and the work of separation of the interface. We distinguish the latter {\it mechanical} quantity from the {\it thermodynamic} work of adhesion, and we describe explicitly how both may be calculated. Our formulae for interfacial and surface energies are cast in terms of quantities which can be calculated or looked up in tables, and include as additional parameters the ambient temperature and partial pressure of oxygen $P_{O_2}$. From total energy calculations for the Nb(111)/alpha-alumina(0001) interface, free Nb and alumina surfaces, we obtain firstly numerical estimates of the works of separation, which are independent of $P_{O_2}$. We then obtain surface energies, interfacial energies and the equilibrium work of adhesion as a function of $P_{O_2}$.

cond-mat.mtrl-sci↗