arXiv subjects

Tim Gould

Publications and source records attributed to Tim Gould.

At least 37 records · Page 2Linked to original sources

arXiv2019

A simple self-interaction correction to RPA-like correlation energies

The random phase approximation (RPA) is exact for the exchange energy of a many-electron ground state, but RPA makes the correlation energy too negative by about 0.5 eV/electron. That large short-range error, which tends to cancel out of iso-electronic energy differences, is largely corrected by an exchange-correlation kernel, or (as in RPA+) by an additive local or semilocal correction. RPA+ is by construction exact for the homogeneous electron gas, and it is also accurate for the jellium surface. RPA+ often gives realistic total energies for atoms or solids in which spin-polarization corrections are absent or small. RPA and RPA+ also yield realistic singlet binding energy curves for H2 and N2, and thus RPA+ yields correct total energies even for spin-unpolarized atoms with fractional spins and strong correlation, as in stretched H2 or N2. However, RPA and RPA+ can be very wrong for spin-polarized one-electron systems (especially for stretched H2+), and also for the spin-polarization energies of atoms. The spin-polarization energy is often a small part of the total energy of an atom, but important for ionization energies, electron affinities, and the atomization energies of molecules. Here we propose a computationally efficient generalized RPA+ (gRPA+) that changes RPA+ only for spin-polarized systems by making gRPA+ exact for all one-electron densities, in the same simple semilocal way that the correlation energy densities of many meta-generalized gradent approximations are made self-correlation free. By construction, gRPA+ does not degrade the exact RPA+ description of jellium. gRPA+ is found to greatly improve upon RPA and RPA+ for the ionization energies and electron affinities of light atoms. Many versions of RPA with an approximate exchange-correlation kernel fail to be exact for all one-electron densities, and they can also be self-interaction corrected in this way.

physics.comp-ph↗

arXiv2019

Density-driven correlations in many-electron ensembles: theory and application for excited states

Density functional theory can be extended to excited states by means of a unified variational approach for passive state ensembles. This extension overcomes the restriction of the typical density functional approach to ground states, and offers useful formal and demonstrated practical benefits. The correlation energy functional in the generalized case acquires higher complexity than its ground state counterpart, however. Little is known about its internal structure nor how to effectively approximate it in general. Here we show that such a functional can be broken down into natural components, including what we call "state-" and "density-driven" correlations, with the former amenable to conventional approximations, and the latter being a unique feature of ensembles. Such a decomposition, summarised in eq. (6), provides us with a pathway to general approximations that are able to routinely handle low-lying excited states. The importance of density-driven correlations is demonstrated, an approximation for them is introduced and shown to be useful.

physics.chem-ph↗

arXiv2019

Bridging molecular dynamics and correlated wave-function methods for accurate finite-temperature properties

We introduce the "selPT" perturbative approach, based on ab initio molecular dynamics (AIMD), for computing accurate finite-temperature properties by efficiently using correlated wave-function methods. We demonstrate the power of the method by computing prototypical molecular enthalpies of adsorption in zeolite (CH$_4$ and CO$_2$ on protonated chabazite at 300~K) using the random phase approximation. Results are in excellent agreement with experiment. The improved accuracy provided by selPT represents a crucial step towards the goal of truly quantitative AIMD prediction of experimental observables at finite temperature.

cond-mat.mtrl-sci↗

arXiv2018

Polymorphism of Bulk Boron Nitride

Boron nitride (BN) is a material with outstanding technological promise because of its exceptional thermochemical stability, structural, electronic and thermal conductivity properties, and extreme hardness. Yet, the relative thermodynamic stability of its most common polymorphs (diamond-like cubic and graphite-like hexagonal) has not been resolved satisfactorily because of the crucial role played by kinetic factors in the formation of BN phases at high temperatures and pressures (experiments), and by competing bonding, electrostatic and many-body dispersion forces in BN cohesion (theory). This lack of understanding hampers the development of potential technological applications, and challenges the boundaries of fundamental science. Here, we use high-level first-principles theories that correctly reproduce all important electronic interactions (the adiabatic-connection fluctuation-dissipation theorem in the random phase approximation) to estimate with unprecedented accuracy the energy differences between BN polymorphs, and thus overcome the accuracy hurdle that hindered previous theoretical studies. We show that the ground-state phase of BN is cubic and that the frequently observed hexagonal polymorph becomes entropically stabilized over the cubic at temperatures slightly above ambient conditions ($T_{\rm c \to h} = 335 \pm 30$ K). We also reveal a low-symmetry monoclinic phase that is extremely competitive with the other low-energy polymorphs and which could explain the origins of the experimentally observed "compressed h-BN" phase. Our theoretical findings therefore should stimulate new experimental efforts in bulk BN as well as promote the use of high-level theories in modelling of technologically relevant van der Waals materials.

cond-mat.mtrl-sci↗

arXiv2018

Faraday-cage screening reveals intrinsic aspects of the van der Waals attraction

General properties of the recently observed screening of the van der Waals (vdW) attraction between a silica substrate and silica tip by insertion of graphene are predicted using basic theory and first-principles calculations. Results are then focused on possible practical applications, as well as an understanding of the nature of vdW attraction, considering recent discoveries showing it competing against covalent and ionic bonding. The traditional view of the vdW attraction as arising from pairwise-additive London dispersion forces is considered using Grimme's "D3" method, comparing results to those from Tkatchenko's more general many-body dispersion (MBD) approach, all interpreted in terms of Dobson's general dispersion framework. Encompassing the experimental results, MBD screening of the vdW force between two silica bilayers is shown to scale up to medium separations as 1.25 de/d, where d is the bilayer separation and de its equilibrium value, depicting antiscreening approaching and inside de. Means of unifying this correlation effect with those included in modern density functionals are urgently required.

cond-mat.mtrl-sci↗

arXiv2018

Quantum heat engine operating between thermal and spin reservoirs

Landauer's erasure principle is a cornerstone of thermodynamics and information theory. According to this principle, erasing information incurs a minimum energy cost. Recently, Vaccaro and Barnett [Proc. R. Soc {\bf 467}, 1770 (2011)] explored information erasure in the context of multiple conserved quantities and showed that the erasure cost can be solely in terms of spin angular momentum. As Landauer's erasure principle plays a fundamental role in heat engines, their result considerably widens the possible configurations that heat engines can have. Motivated by this, we propose here a novel optical heat engine that operates under a single thermal reservoir and a spin angular momentum reservoir coupled to a three level system with an energy-degenerate ground state. The proposed heat engine operates without producing waste heat and goes beyond the traditional Carnot engine where the working fluid is subjected to two thermal baths at different temperatures.

quant-ph↗

arXiv2018

Evaluation of van der Waals density functionals for layered materials

In 2012, Bjorkman et al. posed the question "Are we van der Waals ready?" [J. Phys.: Condens. Matter, 2012, 24, 424218] about the ability of ab initio modelling to reproduce van der Waals (vdW) dispersion forces in layered materials. The answer at that time was no, however. Here we report on a new generation of vdW dispersion models and show that one, fractionally-ionic atom (FIA) theory, offers close to quantitative predictions for layered structures. Furthermore, it does so from a qualitatively correct picture of dispersion forces. Other methods, such as D3 and optB88vdW also work well, albeit with some exceptions. We thus argue that we are nearly vdW ready, and that some modern dispersion methods are accurate enough to be used for nanomaterial prediction, albeit with some caution required.

cond-mat.mtrl-sci↗

arXiv2018

Charge transfer excitations from exact and approximate ensemble Kohn-Sham theory

By studying the lowest excitations of an exactly solvable one-dimensional molecular model, we show that components of Kohn-Sham ensembles can be used to describe charge transfers. Furthermore, we compute the approximate excitation energies obtained by using thee exact ensemble densities in the recently formulated ensemble Hartree-exchange theory [Gould and Pittalis, Phys. Rev. Lett. 119, 243001 (2017)]. Remarkably, our results show that triplet excitations are accurately reproduced across a dissociation curve in all cases tested, even in systems where ground state energies are poor due to strong static correlations. Singlet excitations exhibit larger deviations from exact results but are still reproduced semi-quantitatively.

physics.chem-ph↗

arXiv2017

'Hartree-exchange' in ensemble density functional theory: Avoiding the non-uniqueness disaster

Ensemble density functional theory is a promising method for the efficient and accurate calculation of excitations of quantum systems, at least if useful functionals can be developed to broaden its domain of practical applicability. Here, we introduce a guaranteed single-valued 'Hartree-exchange' ensemble density functional, $E_{Hx}[n]$, in terms of the right derivative of the universal ensemble density functional with respect to the coupling constant at vanishing interaction. We show that $E_{Hx}[n]$ is straightforwardly expressible using block eigenvalues of a simple matrix [equation (14)]. Specialized expressions for $E_{Hx}[n]$ from the literature, including those involving superpositions of Slater determinants, can now be regarded as originating from the unifying picture presented here. We thus establish a clear and practical description for Hartree-exchange in ensemble systems.

physics.chem-ph↗

arXiv2017

Casimir-Polder size consistency -- a constraint violated by some dispersion theories

A key goal in quantum chemistry methods, whether ab initio or otherwise, is to achieve size consistency. In this manuscript we formulate the related idea of "Casimir-Polder size consistency" that manifests in long-range dispersion energetics. We show that local approximations in time-dependent density functional theory dispersion energy calculations violate the consistency condition because of incorrect treatment of highly non-local "xc kernel" physics, by up to 10% in our tests on closed-shell atoms.

physics.chem-ph↗

arXiv2017

Moiré pattern interlayer potentials in van der Waals materials from random-phase approximation calculations

Stacking-dependent interlayer interactions are important for understanding the structural and electronic properties in incommensurable two dimensional material assemblies where long-range moiré patterns arise due to small lattice constant mismatch or twist angles. Here, we study the stacking-dependent interlayer coupling energies between graphene (G) and hexagonal boron nitride (BN) homo- and hetero-structures using high-level random-phase approximation (RPA) ab initio calculations. Our results show that although total binding energies within LDA and RPA differ substantially between a factor of 200%-400%, the energy differences as a function of stacking configuration yield nearly constant values with variations smaller than 20% meaning that LDA estimates are quite reliable. We produce phenomenological fits to these energy differences, which allows us to calculate various properties of interest including interlayer spacing, sliding energetics, pressure gradients and elastic coefficients to high accuracy. The importance of long-range interactions (captured by RPA but not LDA) on various properties is also discussed. Parameterisations for all fits are provided.

cond-mat.mes-hall↗

arXiv2017

A fractionally ionic approach to polarizability and van der Waals many-body dispersion calculations

By explicitly including fractionally ionic contributions to the polarizability of a many-component system we are able to significantly improve on previous atom-wise many-body van der Waals approaches with essentially no extra numerical cost. For non-ionic systems our method is comparable in accuracy to existing approaches. However, it offers substantial improvements in ionic solids, e.g. producing better polarizabilities by over 65% in some cases. It has particular benefits for two-dimensional transition metal dichalcogenides, and interactions of H$_2$ with modified coronenes - ionic systems of nanotechnological interest. It thus offers an efficient improvement on existing approaches, valid for a wide range of systems.

physics.chem-ph↗

arXiv2016

How polarizabilities and $C_6$ coefficients actually vary with atomic volume

In this work we investigate how atomic $C_6$ coefficients and static dipole polarizabilities $α$ scale with effective volume. We show, using confined atoms covering rows 1-5 of the periodic table, that $C_6/C_6^R\approx (V/V^R)^{p_Z}$ and $α/α^R\approx (V/V^R)^{p'_Z}$ (for volume $V=\int dr \frac{4π}{3}r^3 n(r)$) where $C_6^R$, $α^R$ and $V^R$ are the reference values and effective volume of the free atom. The scaling exponents $p_Z$ and $p'_Z$ vary substantially as a function of element number $Z=N$, in contrast to the standard "rule of thumb" that $p_Z=2$ and $p'_Z=1$. Remarkably, We find that the polarizability and $C_6$ exponents $p'$ and $p$ are related by $p'\approx p-0.615$ rather than the expected $p'\approx p/2$. Results are largely independent of the form of the confining potential (harmonic, cubic and quartic potentials are considered) and kernel approximation, justifying this analysis.

physics.chem-ph↗

arXiv2016

Locality of correlation in density functional theory

The Hohenberg-Kohn density functional was long ago shown to reduce to the Thomas-Fermi approximation in the non-relativistic semiclassical (or large-$Z$) limit for all matter, i.e, the kinetic energy becomes local. Exchange also becomes local in this limit. Numerical data on the correlation energy of atoms supports the conjecture that this is also true for correlation, but much less relevant to atoms. We illustrate how expansions around large particle number are equivalent to local density approximations and their strong relevance to density functional approximations. Analyzing highly accurate atomic correlation energies, we show that the correlation energy tends to $-A_c Z ln Z + B_c Z$ as $Z$ tends to infinity, where $Z$ is the atomic number, $A_c$ is known, and we estimate $B_c$ to be about 37 millihartrees. The local density approximation yields $A_c$ exactly, but a very incorrect value for $B_c$, showing that the local approximation is less relevant for correlation alone. This limit is a benchmark for the non-empirical construction of density functional approximations. We conjecture that, beyond atoms, the leading correction to the local density approximation in the large-$Z$ limit generally takes this form, but with $B_c$ a functional of the TF density for the system. The implications for construction of approximate density functionals are discussed.

cond-mat.mtrl-sci↗

arXiv2016

Graphene as a p-type metal for ultimate miniaturization

We report macroscopic sheets of highly conductive bilayer graphene with exceptionally high hole concentrations of ~ $10^{15}$ $cm^{-2}$ and unprecedented sheet resistances of 20-25 Ω per square over macroscopic scales, and obtained in-situ over a thin cushion of molecular oxygen on a silicon substrate. The electric and electronic properties of this specific configuration remain stable upon thermal anneals and months of exposure to air. We further report a complementary ab-initio study, predicting an enhancement of graphene adhesion energy of up to a factor 20, also supported by experimental fracture tests. Our results show that the remarkable properties of graphene can be realized in a reliable fashion using a high-throughput process. In addition to providing exceptional material properties, the growth process we employed is scalable to large areas so that the outstanding conduction properties of graphene can be harnessed in devices fabricated via conventional semiconductor manufacturing processes. We anticipate that the approach will provide the necessary scalability and reliability for future developments in the graphene nanoscience and technology fields, especially in areas where further miniaturization is hampered by size effects and electrical reliability of classical conductors.

cond-mat.mtrl-sci↗

arXiv2016

$C_6$ coefficients and dipole polarizabilities for all atoms and many ions in rows 1-6 of the periodic table

Using time-dependent density functional theory (tdDFT) with exchange kernels we calculate and test imaginary frequency-dependent dipole polarizabilities for all atoms and many ns in rows 1-6 of the periodic table. These are then integrated over frequency to produce $C_6$ coefficients. Results are presented under different models: straight tdDFT calculations using two different kernels, "benchmark" tdDFT calculations corrected by more accurate quantum chemical and experimental data, and "benchmark" tdDFT with frozen orbital anions. Parametrisations are presented for 411+ atoms and ions, allowing results to be easily used by other researchers. A curious relationship, $C_{6,XY}\propto [α_X(0)α_Y(0)]^{0.73}$ is found between $C_6$ coefficients and static polarizabilities $α(0)$. The relationship $C_{6,XY}=2C_{6,X}C_{6,Y}/[α_X/α_YC_{6,Y}+α_Y/α_XC_{6,X}]$ is tested and found to work well ($<5$\% errors) in about 80\% of cases, but can break down badly ($>30$\% errors) in a small fraction of cases.

physics.comp-ph↗

arXiv2016

Layer Response Theory: Energetics of layered materials from semi-analytic high-level theory

We present a readily computable semi-analytic Layer Response Theory (LRT) for analysis of cohesive energetics involving two-dimensional layers such as BN or graphene. The theory approximates the Random Phase Approximation (RPA) correlation energy. Its RPA character ensures that the energy has the correct van der Waals asymptotics for well-separated layers, in contrast to simple pairwise atom-atom theories which fail qualitatively for layers with zero electronic energy gap. At the same time our theory is much less computationally intensive than the full RPA energy. It also gives accurate correlation energies near to the binding minimum, in contrast to Lifshitz-type theory. We apply our LRT theory successfully to graphite and to BN, and to a graphene-BN heterostructure.

cond-mat.mtrl-sci↗

arXiv2014

Kohn-Sham potentials in exact density-functional theory at non-integer electron numbers

Within exact electron density-functional theory, we investigate Kohn-Sham (KS) potentials, orbital energies, and non-interacting kinetic energies of the fractional ions of Li, C and F. We use quantum Monte Carlo densities as input, which are then fitted, interpolated at non-integer electron numbers $N$, and inverted to produce accurate KS potentials $v_s^N(r)$. We study the dependence of the KS potential on $N$, and in particular we numerically reproduce the theoretically predicted spatially constant discontinuity of $v_s^N(r)$ as $N$ passes through an integer. We further show that, for all the cases considered, the inner orbital energies and the non-interacting kinetic energy are nearly piecewise linear functions of $N$. This leads us to propose a simple approximation of the KS potential $v_s^N(r)$ at any fractional electron number $N$ which uses only quantities of the systems with the adjacent integer electron numbers.

physics.chem-ph↗