ORCID Profile
0000-0002-7191-9124
Current Organisation
Griffith University
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Quantum Chemistry | Theoretical and Computational Chemistry | Statistical Mechanics in Chemistry | Quantum Physics | Quantum Information, Computation and Communication | Condensed Matter Modelling and Density Functional Theory | Thermodynamics and Statistical Physics
Expanding Knowledge in the Physical Sciences | Expanding Knowledge in the Chemical Sciences | Energy Storage (excl. Hydrogen) | Energy Conservation and Efficiency in Transport |
Publisher: CSIRO Publishing
Date: 2020
DOI: 10.1071/CH19504
Abstract: Ensemble density functional theory extends the usual Kohn-Sham machinery to quantum state ensembles involving ground- and excited states. Recent work by the authors [Phys. Rev. Lett. 119, 243001 (2017) 123, 016401 (2019)] has shown that both the Hartree-exchange and correlation energies can attain unusual features in ensembles. Density-driven (DD) correlations – which account for the fact that pure-state densities in Kohn-Sham ensembles do not necessarily reproduce those of interacting pure states – are one such feature. Here we study atoms (specifically S–P and S–S transitions) and show that the magnitude and behaviour of DD correlations can vary greatly with the variation of the orbital angular momentum of the involved states. Such estimations are obtained through an approximation for DD correlations built from relevant exact conditions, Kohn-Sham inversion, and plausible assumptions for weakly correlated systems.
Publisher: AIP Publishing
Date: 05-03-2021
DOI: 10.1063/5.0040447
Abstract: Two important extensions of Kohn–Sham (KS) theory are generalized KS theory and ensemble KS theory. The former allows for non-multiplicative potential operators and greatly facilitates practical calculations with advanced, orbital-dependent functionals. The latter allows for quantum ensembles and enables the treatment of open systems and excited states. Here, we combine the two extensions, both formally and practically, first via an exact yet complicated formalism and then via a computationally tractable variant that involves a controlled approximation of ensemble “ghost interactions” by means of an iterative algorithm. The resulting formalism is illustrated using selected ex les. This opens the door to the application of generalized KS theory in more challenging quantum scenarios and to the improvement of ensemble theories for the purpose of practical and accurate calculations.
Publisher: American Chemical Society (ACS)
Date: 24-08-2020
DOI: 10.26434/CHEMRXIV.12846836.V1
Abstract: Two important extensions of Kohn-Sham (KS) theory are generalized KS theory and ensemble KS theory. The former allows for non-multiplicative potential operators and greatly facilitates practical calculations with advanced, orbital-dependent functionals. The latter allows for quantum ensembles and enables the treatment of, e.g., open systems and excited states. Here, we combine the two extensions, both formally and practically, first via an exact yet complicated formalism, then via a computationally tractable variant that involves a controlled approximation of ensemble "ghost interactions" by means of an approach inspired by optimized effective potential theory. The resulting formalism is illustrated using selected ex les. This opens the door to the application of generalized KS theory in more challenging quantum scenarios and to the improvement of ensemble theories for the purpose of practical and accurate calculations.
Publisher: American Chemical Society (ACS)
Date: 15-12-2020
DOI: 10.26434/CHEMRXIV.12846836.V2
Abstract: Two important extensions of Kohn-Sham (KS) theory are generalized KS theory and ensemble KS theory. The former allows for non-multiplicative potential operators and greatly facilitates practical calculations with advanced, orbital-dependent functionals. The latter allows for quantum ensembles and enables the treatment of, e.g., open systems and excited states. Here, we combine the two extensions, both formally and practically, first via an exact yet complicated formalism, then via a computationally tractable variant that involves a controlled approximation of ensemble "ghost interactions" by means of an iterative algorithm. The resulting formalism is illustrated using selected ex les. This opens the door to the application of generalized KS theory in more challenging quantum scenarios and to the improvement of ensemble theories for the purpose of practical and accurate calculations.
Publisher: American Chemical Society (ACS)
Date: 27-01-2021
DOI: 10.26434/CHEMRXIV.12846836.V3
Abstract: Two important extensions of Kohn-Sham (KS) theory are generalized KS theory and ensemble KS theory. The former allows for non-multiplicative potential operators and greatly facilitates practical calculations with advanced, orbital-dependent functionals. The latter allows for quantum ensembles and enables the treatment of, e.g., open systems and excited states. Here, we combine the two extensions, both formally and practically, first via an exact yet complicated formalism, then via a computationally tractable variant that involves a controlled approximation of ensemble "ghost interactions" by means of an iterative algorithm. The resulting formalism is illustrated using selected ex les. This opens the door to the application of generalized KS theory in more challenging quantum scenarios and to the improvement of ensemble theories for the purpose of practical and accurate calculations.
Publisher: American Chemical Society (ACS)
Date: 07-07-2022
Publisher: IOP Publishing
Date: 12-01-2016
DOI: 10.1088/0953-8984/28/4/045201
Abstract: The energy and gradient expressions for the many-body dispersion scheme (MBD@rsSCS) of Ambrosetti et al (2014 J. Chem. Phys. 140 18A508) needed for an efficient implementation of the method for systems under periodic boundary conditions are reported. The energy is expressed as a sum of contributions from points s led in the first Brillouin zone, in close analogy with planewave implementations of the RPA method for electrons in the dielectric matrix formulation. By avoiding the handling of large supercells, considerable computational savings can be achieved for materials with small and medium sized unit cells. The new implementation has been tested and used for geometry optimization and energy calculations of inorganic and molecular crystals, and layered materials.
Publisher: American Chemical Society (ACS)
Date: 20-03-2020
Publisher: AIP Publishing
Date: 08-02-2023
DOI: 10.1063/5.0134330
Abstract: Kohn–Sham (KS) inversion, in which the effective KS mean-field potential is found for a given density, provides insights into the nature of exact density functional theory (DFT) that can be exploited for the development of density functional approximations. Unfortunately, despite significant and sustained progress in both theory and software libraries, KS inversion remains rather difficult in practice, especially in finite basis sets. The present work presents a KS inversion method, dubbed the “Lieb-response” approach, that naturally works with existing Fock-matrix DFT infrastructure in finite basis sets, is numerically efficient, and directly provides meaningful matrix and energy quantities for pure-state and ensemble systems. Some additional work yields potential. It thus enables the routine inversion of even difficult KS systems, as illustrated in a variety of problems within this work, and provides outputs that can be used for embedding schemes or machine learning of density functional approximations. The effect of finite basis sets on KS inversion is also analyzed and investigated.
Publisher: Elsevier BV
Date: 02-2016
Publisher: IOP Publishing
Date: 18-08-2006
Publisher: Elsevier BV
Date: 02-2016
Publisher: American Physical Society (APS)
Date: 12-2020
Publisher: American Chemical Society (ACS)
Date: 30-01-2019
DOI: 10.26434/CHEMRXIV.6964874.V2
Abstract: 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.8, 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.
Publisher: American Chemical Society (ACS)
Date: 14-08-2018
DOI: 10.26434/CHEMRXIV.6964874.V1
Abstract: 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 demonstrate that such a functional can be broken down into natural components, including what we call "state-" and "density-driven" correlations, with the latter being a unique feature of ensembles. Such a decomposition, summarised in eq. (10), is exact and also provides us with a pathway to general approximations.
Publisher: American Physical Society (APS)
Date: 10-11-2014
Publisher: American Chemical Society (ACS)
Date: 17-04-2019
DOI: 10.26434/CHEMRXIV.6964874.V4
Abstract: 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.
Publisher: American Chemical Society (ACS)
Date: 16-04-2019
DOI: 10.26434/CHEMRXIV.6964874.V3
Abstract: 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.
Publisher: AIP Publishing
Date: 03-08-2016
DOI: 10.1063/1.4959126
Abstract: The Hohenberg-Kohn density functional was long ago shown to reduce to the Thomas-Fermi (TF) 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 support the conjecture that this is also true for correlation, but much less relevant to atoms. We illustrate how expansions around a 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 EC → −AC ZlnZ + BCZ as Z → ∞, where Z is the atomic number, AC is known, and we estimate BC to be about 37 mhartree. The local density approximation yields AC exactly, but a very incorrect value for BC, showing that the local approximation is less relevant for the 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 BC a functional of the TF density for the system. The implications for the construction of approximate density functionals are discussed.
Publisher: AIP Publishing
Date: 14-02-2018
DOI: 10.1063/1.5018818
Abstract: Seven methods, including three van der Waals density functionals (vdW-DFs) and four different variants of the Tkatchenko-Scheffler (TS) methods, are tested on the A24, L7, and Taylor et al.’s “blind” test sets. It is found that for these systems, the vdW-DFs perform better that the TS methods. In particular, the vdW-DF-cx functional gives binding energies that are the closest to the reference values, while the many-body correction of TS does not always lead to an improvement in the description of molecular systems. In light of these results, several directions for further improvements to describe van der Waals interactions are discussed.
Publisher: American Chemical Society (ACS)
Date: 23-10-2020
DOI: 10.26434/CHEMRXIV.12382595
Abstract: Recent theory developments in ensemble density functional theory (EDFT) promise to bring decades of work for ground-states to the practical resolution of excited-states - provided newly-discovered "density-driven correlations" can be dealt with and adequate effective potentials can be found. This Letter introduces simple theories for both and shows that EDFT using these theories outperforms ΔSCF DFT and time-dependent DFT for low-lying gaps in most of the small atoms and molecules tested, even when all use the same density functional approximations. It thus establishes EDFT as a promising tool for low-cost studies of excited states and provides a clear route to practical EDFT implementation of arbitrary functional approximations. br br
Publisher: Royal Society of Chemistry (RSC)
Date: 2020
DOI: 10.1039/D0CP04137H
Abstract: Biomolecules have complex structures, and noncovalent interactions are crucial to determine their conformations and functionalities.
Publisher: American Physical Society (APS)
Date: 25-04-2019
Publisher: AIP Publishing
Date: 21-09-2012
DOI: 10.1063/1.4755286
Abstract: The “ACFD-RPA” correlation energy functional has been widely applied to a variety of systems to successfully predict energy differences, and less successfully predict absolute correlation energies. Here, we present a parameter-free exchange-correlation kernel that systematically improves absolute correlation energies, while maintaining most of the good numerical properties that make the ACFD-RPA numerically tractable. The radial exchange hole kernel is constructed to approximate the true exchange kernel via a carefully weighted, easily computable radial averaging. Correlation energy errors of atoms with 2–18 electrons show a 13-fold improvement over the RPA and a threefold improvement over the related Petersilka, Gossmann, and Gross kernel, for a mean absolute error of 13 mHa or 5%. The average error is small compared to all but the most difficult to evaluate kernels. van der Waals C6 coefficients are less well predicted, but still show improvements on the RPA, especially for highly polarisable Li and Na.
Publisher: AIP Publishing
Date: 28-05-2012
DOI: 10.1063/1.4721269
Abstract: In this paper we further explore and develop the quantum continuum mechanics (QCM) of Tao et al. [Phys. Rev. Lett. 103, 086401 (2009)] with the aim of making it simpler to use in practice. Our simplifications relate to the non-interacting part of the QCM equations, and primarily refer to practical implementations in which the groundstate stress tensor is approximated by its Kohn-Sham (KS) version. We use the simplified approach to directly prove the exactness of QCM for one-electron systems via an orthonormal formulation. This proof sheds light on certain physical considerations contained in the QCM theory and their implication on QCM-based approximations. The one-electron proof then motivates an approximation to the QCM (exact under certain conditions) expanded on the wavefunctions of the KS equations. Particular attention is paid to the relationships between transitions from occupied to unoccupied KS orbitals and their approximations under the QCM. We also demonstrate the simplified QCM semianalytically on an ex le system.
Publisher: American Chemical Society (ACS)
Date: 02-2018
DOI: 10.26434/CHEMRXIV.5840883.V1
Abstract: Seven methods, including three van der Waals density functionals (vdW-DFs) and four different variants of the Tkatchenko-Scheffler (TS) methods, are tested on the A24, L7, and Taylor et al. 's "blind" test sets. It is found that for these systems, the vdW-DFs perform better that the TS methods. In particular, the vdW-DF-cx functional gives binding energies that are the closest to the reference values, while the many body correction of TS does not always lead to an improvement in the description of molecular systems. In light of these results, several directions for further improvements to describe van der Waals interactions are discussed.
Publisher: American Chemical Society (ACS)
Date: 19-07-2019
DOI: 10.26434/CHEMRXIV.8869460.V1
Abstract: p.p1 {margin: 0.0px 0.0px 0.0px 0.0px line-height: 18.0px font: 15.8px Helvetica color: #000000 -webkit-text-stroke: #000000 background-color: #ffffff} span.s1 {font-kerning: none} span.s2 {font-kerning: none color: #000000} Hybrid functionals have proven to be of immense practical value in density functional theory calculations. While they are often thought to be a heuristic construct, it has been established that this is in fact not the case. Here, we present a rigorous and formally exact generalized Kohn-Sham (GKS) density functional theory of hybrid functionals, in which exact remainder exchange-correlation potentials combine with a fraction of Fock exchange to produce the correct ground state density. Specifically, we generalize the well-known adiabatic con- nection theorem to the case of exact hybrid functional theory and use it to provide a rigorous distinction between multiplicative exchange and correlation components. We examine the exact theory by inverting reference electron densities to obtain exact GKS potentials for hybrid functionals, showing that an equivalent description of the many-electron problem is obtained with any arbitrary global fraction of Fock exchange. We establish the dependence of these exact components on the fraction of Fock exchange and use the observed trends to shed new light on the results of approximate hybrid functional calculations.
Publisher: Wiley
Date: 07-08-2022
Abstract: Electrochromic materials can tune the illumination and heat exchange of a building with the environment and thereby save energy in lighting, heating, and air conditioning in a cost‐effective way, which is vital in realizing carbon neutrality. 2D frameworks such as coordination nanosheets (CONASHs) that are widely explored for a wide range of applications in energy storage and conversion can be a cluster of novel electrochromic materials. In this work, a series of transition metal benzenehexathiol (TM‐BHT) CONASHs are theoretically investigated via first‐principles simulations. During ion intercalation and deintercalation in TM‐BHTs, changes in lattice structures, lithium diffusion barriers, atomic charges, bond strength, and electronic properties are explored in‐depth. The incurred changes are then correlated with critical electrochromic properties, including the transmittance adjustment ranges in the visible light, near‐infrared, solar spectrum, and mid‐infrared. Among the various TM‐BHT systems, Cu‐BHT and Ag‐BHT are the most promising broadband electrochromic materials for optical and thermal management in the wavelength range from visible to mid‐infrared. The theoretical guidance from this work paves a new path toward electrochromic applications of CONASHs that exploit the versatility of these 2D materials.
Publisher: American Chemical Society (ACS)
Date: 18-12-2019
DOI: 10.26434/CHEMRXIV.9917948
Abstract: The classical turning radius Rt of an atom can be defined as the radius where the KS potential is equal to the negative ionisation potential of the atom, i.e. where v_s(R_t)=\\epsilon_h. It was recently shown [P.N.A.S. 115, E11578 (2018)] to yield chemically relevant bonding distances, in line with known empirical values. In this work we show that extension of the concept to non-integer electron number yields additional information about atomic systems, and can be used to detect the difficulty of adding or subtracting electrons. Notably, it reflects the ease of bonding in open p-shells, and its greater difficulty in open s-shells. The latter manifests in significant discontinuities in the turning radius as the electron number changes the principal quantum number of the outermost electronic shell (e.g. going from Na to Na^{2+}). We then show that a non-integer picture is required to correctly interpret bonding and dissociation in H_2^+. Results are consistent when properties are calculated exactly, or via an appropriate approximation. They can be interpreted in the context of conceptual density functional theory.
Publisher: Royal Society of Chemistry (RSC)
Date: 2018
DOI: 10.1039/C8CP05554H
Abstract: The GMTKN55 benchmarking protocol allows comprehensive analysis and ranking of density functional approximations with erse chemical behaviours. This work reports diet versions of GMTKN55 which reproduce key properties of the full protocol at substantially reduced numerical cost. ‘Diet GMTKN55’ can thus be used for benchmarking expensive methods, or in combination with solid state benchmarks.
Publisher: American Chemical Society (ACS)
Date: 18-12-2019
DOI: 10.26434/CHEMRXIV.9917948.V2
Abstract: The classical turning radius Rt of an atom can be defined as the radius where the KS potential is equal to the negative ionisation potential of the atom, i.e. where v_s(R_t)=\\epsilon_h. It was recently shown [P.N.A.S. 115, E11578 (2018)] to yield chemically relevant bonding distances, in line with known empirical values. In this work we show that extension of the concept to non-integer electron number yields additional information about atomic systems, and can be used to detect the difficulty of adding or subtracting electrons. Notably, it reflects the ease of bonding in open p-shells, and its greater difficulty in open s-shells. The latter manifests in significant discontinuities in the turning radius as the electron number changes the principal quantum number of the outermost electronic shell (e.g. going from Na to Na^{2+}). We then show that a non-integer picture is required to correctly interpret bonding and dissociation in H_2^+. Results are consistent when properties are calculated exactly, or via an appropriate approximation. They can be interpreted in the context of conceptual density functional theory.
Publisher: American Chemical Society (ACS)
Date: 10-2019
DOI: 10.26434/CHEMRXIV.9917948.V1
Abstract: The classical turning radius Rt of an atom can be defined as the radius where the KS potential is equal to the negative ionisation potential of the atom, i.e. where v_s(R_t)=\\epsilon_h. It was recently shown [P.N.A.S. 115, E11578 (2018)] to yield chemically relevant bonding distances, in line with known empirical values. In this work we show that extension of the concept to non-integer electron number yields additional information about atomic systems, and can be used to detect the difficulty of adding or subtracting electrons. Notably, it reflects the ease of bonding in open p-shells, and its greater difficulty in open s-shells. The latter manifests in significant discontinuities in the turning radius as the electron number changes the principal quantum number of the outermost electronic shell (e.g. going from Na to Na^{2+}). We then show that a non-integer picture is required to correctly interpret bonding and dissociation in H_2^+. Results are consistent when properties are calculated exactly, or via an appropriate approximation. They can be interpreted in the context of conceptual density functional theory.
Publisher: American Physical Society (APS)
Date: 15-12-2011
Publisher: American Chemical Society (ACS)
Date: 11-09-2019
DOI: 10.26434/CHEMRXIV.7938137.V2
Abstract: Materials design increasingly relies on first-principles calculations for screening important candidates and for understanding quantum mechanisms. Density functional theory (DFT) is by far the most popular first-principles approach due to its efficiency and accuracy. However, to accurately predict structures and thermodynamics, DFT must be paired with a van der Waals (vdW) dispersion correction. Therefore, such corrections have been the subject of intense scrutiny in recent years. Despite significant successes in organic molecules, no existing model can adequately cover the full range of common materials, from metals to ionic solids, h ering the applications of DFT for modern problems such as battery design. Here, we introduce a universally optimized vdW-corrected DFT method that demonstrates an unbiased reliability for predicting molecular, layered, ionic, metallic, and hybrid materials without incurring a large computational overhead. We use our method to accurately predict the intercalation potentials of layered electrode materials of a Li-ion battery system – a problem for which the existing state-of-the-art methods fail. Thus, we envisage broad use of our method in the design of chemo-physical processes of new materials.
Publisher: Wiley
Date: 25-10-2022
Abstract: Electrochromic effect has been discovered in many materials with a wide range of applications from visible to infrared, such as smart windows, electronic displays, infrared camouflage, and color‐changeable tactile sensor. However, conventional electrochromic materials cannot meet the growing demand for electrochromic performance in terms of optical contrast, response time, durability, color ersity, and flexibility, which slows down developments in this area. This is mainly due to the limited number and variety of electrochromic materials. In strong contrast, nanoarchitectonics of 2D materials with atomically thin thickness, large lateral size, and ersified series can be an effective way to address these issues and improve the electrochromic performances. This review highlights the recent achievements of emerging 2D electrochromic materials, namely covalent organic frameworks, coordination nanosheets, and transition metal carbides/nitrides/carbonitrides (MXenes). The structures, electrochromic performances and their structure–performance relationship, and future challenges of these materials have been systematically explored. This review can pave a new avenue for the promotion of the nanoarchitectonic 2D materials for the up‐scaled practical electrochromic applications.
Publisher: IOP Publishing
Date: 09-10-2004
Publisher: American Chemical Society (ACS)
Date: 03-04-2019
DOI: 10.26434/CHEMRXIV.7938137.V1
Abstract: Materials design increasingly relies on first-principles calculations for screening important candidates and for understanding quantum mechanisms. Density functional theory (DFT) is by far the most popular first-principles approach due to its efficiency and accuracy. However, to accurately predict structures and thermodynamics, DFT must be paired with a van der Waals (vdW) dispersion correction. Therefore, such corrections have been the subject of intense scrutiny in recent years. Nevertheless, no existing model can adequately cover the full range of common materials, from metals to ionic solids, h ering the applications of DFT for modern problems such as battery design. Here, we introduce a universally optimized vdW-correction that demonstrates an unbiased reliability for predicting molecular, layered, ionic, metallic, and hybrid materials without incurring a large computational overhead. We use our method to accurately predict the intercalation potentials of layered electrode materials of a Li-ion battery system – a problem for which the existing state-of-the-art methods fail. Thus, we envisage broad use of our method in the design of chemo-physical processes of new materials.
Publisher: American Chemical Society (ACS)
Date: 07-02-2019
DOI: 10.26434/CHEMRXIV.7685651.V1
Abstract: Li 4 Ti 5 O 12 (LTO) has been experimentally proven as a promising electrochromic material in applications of smart windows, thermal management and infrared camouflage. However, the fundamental mechanism on these phenomena is still lacking. For the first time, we fill this knowledge gap via quantitative matching the LTO's optical properties and electronic structure during charging/discharging using density functional theory. Our study suggests that the absorption of infrared is highly sensitive to intercalation of Li in the LTO lattice, in contrast with the adsorption of visible wavelengths. This unique property of LTO offers the practical ability in controlling infrared-induced heating with minimal effect on transmission of visible light. Furthermore, we also conclude that electrochemically controlled intercalation of Li causes donor states to appear, expand and move to deeper levels in the forbidden band, leading to better conductivity and lower transmittance, which is in line with the experimental results in the literature.
Publisher: American Chemical Society (ACS)
Date: 20-03-2020
DOI: 10.26434/CHEMRXIV.8869460.V2
Abstract: Hybrid functionals have proven to be of immense practical value in density functional theory calculations.While they are often thought to be a heuristic construct, it has been established that this is in fact not thecase. Here, we present a rigorous and formally exact generalized Kohn-Sham (GKS) density functional theoryof hybrid functionals, in which exact remainder exchange-correlation potentials combine with a fraction ofFock exchange to produce the correct ground state density. First, we extend formal GKS theory by proving ageneralized adiabatic connection theorem. We then use this extension to derive two different definitions for arigorous distinction between multiplicative exchange and correlation components - one new and one previouslypostulated. We examine their density-scaling behavior and discuss their similarities and differences. We thenpresent a new algorithm for obtaining exact GKS potentials by inversion of accurate reference electron densitiesand employ this algorithm to obtain exact potentials for simple atoms and ions. We establish that an equivalentdescription of the many-electron problem is indeed obtained with any arbitrary global fraction of Fock exchangeand we rationalize the Fock-fraction dependence of the computed remainder exchange-correlation potentials interms of the new formal theory. Finally, we use the exact theoretical framework and numerical results to shedlight on the exchange-correlation potential used in approximate hybrid functional calculations and to assess theconsequences of different choices of fractional exchange.
Publisher: American Chemical Society (ACS)
Date: 31-03-2020
DOI: 10.26434/CHEMRXIV.8869460.V3
Abstract: Hybrid functionals have proven to be of immense practical value in density functional theory calculations. While they are often thought to be a heuristic construct, it has been established that this is in fact not the case. Here, we present a rigorous and formally exact analysis of generalized Kohn-Sham (GKS) density functional theory of hybrid functionals, in which exact remainder exchange-correlation potentials combine with a fraction of Fock exchange to produce the correct ground state density. First, we extend formal GKS theory by proving a generalized adiabatic connection theorem. We then use this extension to derive two different definitions for a rigorous distinction between multiplicative exchange and correlation components - one new and one previously postulated. We examine their density-scaling behavior and discuss their similarities and differences. We then present a new algorithm for obtaining exact GKS potentials by inversion of accurate reference electron densities and employ this algorithm to obtain exact potentials for simple atoms and ions. We establish that an equivalent description of the many-electron problem is indeed obtained with any arbitrary global fraction of Fock exchange and we rationalize the Fock-fraction dependence of the computed remainder exchange-correlation potentials in terms of the new formal theory. Finally, we use the exact theoretical framework and numerical results to shed light on the exchange-correlation potential used in approximate hybrid functional calculations and to assess the consequences of different choices of fractional exchange.
Publisher: AIP Publishing
Date: 03-01-2013
DOI: 10.1063/1.4773284
Abstract: By exploiting freedoms in the definitions of “correlation,” “exchange,” and “Hartree” physics in ensemble systems, we better generalise the notion of “exact exchange” (EXX) to systems with fractional occupations of the frontier orbitals, arising in the dissociation limit of some molecules. We introduce the linear EXX (“LEXX”) theory whose pair distribution and energy are explicitly piecewise linear in the occupations \\documentclass[12pt]{minimal}\\begin{document}$f^{\\sigma }_{i}$\\end{document}fiσ. We provide explicit expressions for these functions for frontier s and p shells. Used in an optimised effective potential (OEP) approach the LEXX yields energies bounded by the piecewise linear “ensemble EXX” (EEXX) energy and standard fractional optimised EXX energy: EEEXX ⩽ ELEXX ⩽ EEXX. Analysis of the LEXX explains the success of standard OEP methods for diatoms at large spacing, and why they can fail when both spins are allowed to be non-integer so that “ghost” Hartree interactions appear between opposite spin electrons in the usual formula. The energy ELEXX contains a cancellation term for the spin ghost case. It is evaluated for H, Li, and Na fractional ions with clear derivative discontinuities for all cases. The p-shell form reproduces accurate correlation-free energies of B-F and Al-Cl. We further test LEXX plus correlation energy calculations on fractional ions of C and F and again we find both derivative discontinuities and good agreement with exact results.
Publisher: IOP Publishing
Date: 03-01-2012
DOI: 10.1088/0953-8984/24/7/073201
Abstract: We summarize the theory of van der Waals (dispersion) forces, with emphasis on recent microscopic approaches that permit the prediction of forces between solids and nanostructures right down to intimate contact and binding. Some connections are pointed out between microscopic theory and macroscopic Lifshitz theory.
Publisher: American Chemical Society (ACS)
Date: 10-01-2022
DOI: 10.26434/CHEMRXIV-2022-786FK
Abstract: In calculations based on density functional theory, the "HOMO-LUMO gap" (difference between the highest occupied and lowest unoccupied molecular orbital energies) is often used as a low-cost, ad hoc approximation for the lowest excitation energy. Here we show that a simple correction based on rigorous ensemble density functional theory makes the HOMO-LUMO gap exact, in principle, and significantly more accurate, in practice. The introduced perturbative ensemble density functional theory approach predicts different and useful values for singlet-singlet and singlet-triplet excitations, using semi-local and hybrid approximations. Excitation energies are of similar quality to time-dependent density functional theory, especially at high fractions of exact exchange. It therefore offers an easy-to-implement and low-cost route to robust prediction of molecular excitation energies.
Publisher: American Physical Society (APS)
Date: 30-04-2008
Publisher: American Chemical Society (ACS)
Date: 10-03-2022
DOI: 10.1021/ACS.JPCLETT.2C00042
Abstract: In calculations based on density functional theory, the "HOMO-LUMO gap" (difference between the highest occupied and lowest unoccupied molecular orbital energies) is often used as a low-cost, ad hoc approximation for the lowest excitation energy. Here we show that a simple correction based on rigorous ensemble density functional theory makes the HOMO-LUMO gap exact in principle and significantly more accurate in practice. The introduced perturbative ensemble density functional theory approach predicts different and useful values for singlet-singlet and singlet-triplet excitations, using semilocal and hybrid approximations. Excitation energies are similar in quality to time-dependent density functional theory, especially at high fractions of exact exchange. The approach therefore offers an easy-to-implement and low-cost route to robust prediction of molecular excitation energies.
Publisher: American Physical Society (APS)
Date: 06-06-2012
Publisher: AIP Publishing
Date: 28-01-2013
DOI: 10.1063/1.4789581
Publisher: American Chemical Society (ACS)
Date: 28-04-2021
DOI: 10.26434/CHEMRXIV.14498238.V1
Abstract: Double excitations, which are dominated by a Slater-determinant with both electrons in the highest occupied molecular orbital promoted to the lowest unoccupied orbital(s), pose significant challenges for low-cost electronic structure calculations based on density functional theory (DFT). Here, we demonstrate that recent advances in ensemble DFT [ Phys. Rev. Lett. 125 , 233001 (2020)], which extend concepts of ground-state DFT to excited states via a rigorous physical framework based on the ensemble fluctuation-dissipation theorem, can be used to shed light on the double excitation problem. We find that the exchange physics of double excitations is reproducible by standard DFT approximations using a linear combination formula, but correlations are more complex. We then show, using selected test systems, that standard DFT approximations may be adapted to tackle double excitations based on theoretically motivated simple formulae that employ ensemble extensions of expressions that use the on-top pair density.
Publisher: AIP Publishing
Date: 21-05-2013
DOI: 10.1063/1.4804981
Abstract: We assess a variant of linear-response range-separated time-dependent density-functional theory (TDDFT), combining a long-range Hartree-Fock (HF) exchange kernel with a short-range adiabatic exchange-correlation kernel in the local-density approximation (LDA) for calculating isotropic C6 dispersion coefficients of homodimers of a number of closed-shell atoms and small molecules. This range-separated TDDFT tends to give underestimated C6 coefficients of small molecules with a mean absolute percentage error of about 5%, a slight improvement over standard TDDFT in the adiabatic LDA which tends to overestimate them with a mean absolute percentage error of 8%, but close to time-dependent Hartree-Fock which has a mean absolute percentage error of about 6%. These results thus show that introduction of long-range HF exchange in TDDFT has a small but beneficial impact on the values of C6 coefficients. It also confirms that the present variant of range-separated TDDFT is a reasonably accurate method even using only a LDA-type density functional and without adding an explicit treatment of long-range correlation.
Publisher: American Chemical Society (ACS)
Date: 10-01-2020
DOI: 10.1021/JACS.9B11589
Abstract: Materials design increasingly relies on first-principles calculations for screening important candidates and for understanding quantum mechanisms. Density functional theory (DFT) is by far the most popular first-principles approach due to its efficiency and accuracy. However, to accurately predict structures and thermodynamics, DFT must be paired with a van der Waals (vdW) dispersion correction. Therefore, such corrections have been the subject of intense scrutiny in recent years. Despite significant successes in organic molecules, no existing model can adequately cover the full range of common materials, from metals to ionic solids, h ering the applications of DFT for modern problems such as battery design. Here, we introduce a universally optimized vdW-corrected DFT method that demonstrates an unbiased reliability for predicting molecular, layered, ionic, metallic, and hybrid materials without incurring a large computational overhead. We use our method to accurately predict the intercalation potentials of layered electrode materials of a Li-ion battery system, a problem for which the existing state-of-the-art methods fail. Thus, we envisage broad use of our method in the design of chemo-physical processes of new materials.
Publisher: Wiley
Date: 12-02-2022
Abstract: A generalized adiabatic connection that applies to any type of range‐separated hybrid (RSH) functional employed within generalized Kohn–Sham (KS) theory is presented. This generalized relation is then used to derive a definition for a rigorous distinction between multiplicative exchange and correlation components. The developed adiabatic connection is defined in terms of both generalized and conventional KS orbitals. It is shown, however, that using only the KS orbitals produces an error that is , where is fully defined in terms of parameters in the RSH functional, and is found to be small in practical calculations. It is expected that this new adiabatic connection can assist in the development of new RSH functionals and the assessment of existing ones.
Publisher: American Chemical Society (ACS)
Date: 07-07-2016
Abstract: Using time-dependent density functional theory (TDDFT) with exchange kernels, we calculate and test imaginary frequency-dependent dipole polarizabilities for all atoms and many ions in rows 1-6 of the periodic table. These are then integrated over frequency to produce C6 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. Parametrizations are presented for 411+ atoms and ions, allowing results to be easily used by other researchers. A curious relationship, C6,XY ∝ [αX(0)αY(0)](0.73), is found between C6 coefficients and static polarizabilities α(0). The relationship C6,XY = 2C6,XC6,Y/[(αX/αY)C6,Y + (αY/αX)C6,X] is tested and found to work well ( 30% errors) in a small fraction of cases.
Publisher: IOP Publishing
Date: 11-10-2013
DOI: 10.1088/0953-8984/25/44/445010
Abstract: We combine high-level theoretical and ab initio understanding of graphite to develop a simple, parametrized force-field model of interlayer binding in graphite, including the difficult non-pairwise-additive coupled-fluctuation dispersion interactions. The model is given as a simple additive correction to standard density functional theory (DFT) calculations, of form ΔU(D) = f(D)[U(vdW)(D) - U(DFT)(D)] where D is the interlayer distance. The functions are parametrized by matching contact properties, and long-range dispersion to known values, and the model is found to accurately match high-level ab initio results for graphite across a wide range of D values. We employ the correction on the bigraphene binding and graphite exfoliation problems, as well as lithium intercalated graphite LiC6. We predict the binding energy of bigraphene to be 0.27 J m(-2), and the exfoliation energy of graphite to be 0.31 J m(-2), respectively slightly less and slightly more than the bulk layer binding energy 0.295 J m(-2)/layer. Material properties of LiC6 are found to be essentially unchanged compared to the local density approximation. This is appropriate in view of the relative unimportance of dispersion interactions for LiC6 layer binding.
Publisher: American Chemical Society (ACS)
Date: 10-11-2020
Publisher: American Chemical Society (ACS)
Date: 28-06-2019
DOI: 10.26434/CHEMRXIV.8340857.V1
Abstract: We report on previously unnoticed features of the exact Hartree-exchange and correlation potentials for atoms with fractional electron numbers. We show that these potentials, when treated separately, can reach non-vanishing asymptotic constant values in the outer region of spherical, spin unpolarized atoms. In the next leading order, the potentials resemble Coulomb potentials created by effective charges which have the peculiarity of not behaving as piecewise constants as a function of the electron number. We provide analytical derivations and complement them with numerical results using the inversion of the Kohn-Sham equations for interacting densities obtained by accurate quantum Monte Carlo calculations. The present results expand on the knowledge of crucial exact properties of Kohn-Sham systems, which can guide development of advanced exchange-correlation approximations.
Publisher: American Chemical Society (ACS)
Date: 27-08-2019
DOI: 10.26434/CHEMRXIV.9730250.V1
Abstract: The strongly-interacting limit of density functional theory has attracted considerable attention recently due to its ability to deal with the difficult strong correlation problem. Recent work [JPCL 8, 2799-2805 (2017)] introduced the "multiple radii functional" (MRF) approximation, inspired by this limit, which is designed to work well for strong correlations between dissociated fragments. Here, we analyse the MRF in exactly solvable one-dimensional molecules, to uncover how it matches, and deviates from, exact results and use range-separation of the Coulomb potential in both exact and approximate theory to explore how this varies in space. Our work opens a path to new approximations incorporating the MRF, amongst other ingredients.
Publisher: American Chemical Society (ACS)
Date: 23-08-2019
DOI: 10.26434/CHEMRXIV.8340857.V2
Abstract: We report on previously unnoticed features of the exact Hartree-exchange and correlation potentials for atoms and ions treated via ensemble density functional theory, demonstrated on fractional ions of Li, C, and F. We show that these potentials, when treated separately, can reach non-vanishing asymptotic constant values in the outer region of spherical, spin unpolarized atoms. In the next leading order, the potentials resemble Coulomb potentials created by effective charges which have the peculiarity of not behaving as piecewise constants as a function of the electron number. We provide analytical derivations and complement them with numerical results using the inversion of the Kohn-Sham equations for interacting densities obtained by accurate quantum Monte Carlo calculations. The present results expand on the knowledge of crucial exact properties of Kohn-Sham systems, which can guide development of advanced exchange-correlation approximations.
Publisher: Elsevier BV
Date: 09-2020
Publisher: American Chemical Society (ACS)
Date: 2018
DOI: 10.26434/CHEMRXIV.6519764
Abstract: We consider the dispersion energy between two well-separated molecules. Provided that exchange overlap effects can be neglected, the Generalized Casimir Polder (GCP) formula gives the dispersion energy exactly to second order in the inter-system Coulomb pair potential, in terms of the density response functions of the isolated molecules. One can alternatively calculate the dispersion interaction from the density response in a supramolecular (dimer) energy TDDFT/ACFD calculation. This uses the density response from Time Dependent Density Functional Theory (TDDFT) and the Adiabatic Connection (ACFD) groundtstate electronic energy formula, and treats the two systems together. Some of us recently [JCTC 13, 5829 (2017)] showed that the supramolecular TDDFT/ACFD approach can fail to reproduce the exact GCP result, when the exchange-correlation kernel ƒxc in the TDDFT calculation is assumed to be local. Here we examine ways in which a nonlocal density dependence of ƒxc might be able to remove this discrepancy. br
Publisher: American Physical Society (APS)
Date: 08-03-2023
Publisher: Royal Society of Chemistry (RSC)
Date: 2019
DOI: 10.1039/C9CP03633D
Abstract: We show that the Hartree-exchange and correlation potentials of ensemble systems can have unexpected features, including non-vanishing asymptotic constants and non-trivial screening of electrons. These features are demonstrated here on Li, C, and F.
Publisher: AIP Publishing
Date: 04-02-2020
DOI: 10.1063/1.5130693
Abstract: The classical Kohn–Sham turning radius Rt of an atom can be defined as the radius where the Kohn–Sham potential is equal to the negative ionization potential of the atom, i.e., where vs(Rt) = ϵh. It was recently shown [E. Ospadov et al., Proc. Natl. Acad. Sci. U. S. A. 115, E11578–E11585 (2018)] to yield chemically relevant bonding distances, in line with known empirical values. In this work, we show that extension of the concept to non-integer electron number yields additional information about atomic systems and can be used to detect the difficulty of adding or subtracting electrons. Notably, it reflects the ease of bonding in open p-shells and its greater difficulty in open s-shells. The latter manifests in significant discontinuities in the turning radius as the electron number changes the principal quantum number of the outermost electronic shell (e.g., going from Na to Na2+). We then show that a non-integer picture is required to correctly interpret bonding and dissociation in H2+. Results are consistent when properties are calculated exactly or via an appropriate approximation. They can be interpreted in the context of conceptual density functional theory.
Publisher: Elsevier BV
Date: 05-2021
Publisher: Elsevier
Date: 2016
Publisher: Royal Society of Chemistry (RSC)
Date: 2022
DOI: 10.1039/D2CP02827A
Abstract: In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners.
Publisher: American Physical Society (APS)
Date: 11-2010
Publisher: AIP Publishing
Date: 12-08-2019
DOI: 10.1063/1.5099330
Abstract: Recently, Li4Ti5O12 (LTO) has been experimentally proven as a promising broadband electrochromic material for applications like smart windows, thermal management, and infrared camouflage. However, a detailed understanding of the fundamental mechanism of these phenomena is still lacking, especially how and why the optical spectrum changes with lithiation. We fill this knowledge gap by performing a detailed analysis of LTO's optical properties during charging/discharging via a robust study of the density functional theory (DFT). Our study suggests that the absorption of infrared light is highly sensitive to intercalation of Li in the LTO lattice, in contrast to that of visible wavelengths. This unique characteristic of LTO offers an effective mechanism in controlling infrared radiation intensity with minimal attenuation on the transmission of visible light. Furthermore, the DFT study also reveals that the electrochemical intercalation of Li introduces donor states which will gradually expand and move to deeper levels in the forbidden band. This electronic structure change leads to better conductivity and lower transmittance, which is in line with the experimental observation in the literature.
Publisher: American Chemical Society (ACS)
Date: 21-09-2020
DOI: 10.26434/CHEMRXIV.12382595.V2
Abstract: Recent theory developments in ensemble density functional theory (EDFT) promise to bring decades of work for ground-states to the practical resolution of excited-states - provided newly-discovered "density-driven correlations" can be dealt with and adequate effective potentials can be found. This Letter introduces simple theories for both and shows that EDFT using these theories outperforms ΔSCF DFT and time-dependent DFT for low-lying gaps in most of the small atoms and molecules tested, even when all use the same density functional approximations. It thus establishes EDFT as a promising tool for low-cost studies of excited states and provides a clear route to practical EDFT implementation of arbitrary functional approximations.
Publisher: American Chemical Society (ACS)
Date: 23-10-2020
DOI: 10.26434/CHEMRXIV.12382595.V3
Abstract: Recent theory developments in ensemble density functional theory (EDFT) promise to bring decades of work for ground-states to the practical resolution of excited-states - provided newly-discovered "density-driven correlations" can be dealt with and adequate effective potentials can be found. This Letter introduces simple theories for both and shows that EDFT using these theories outperforms ΔSCF DFT and time-dependent DFT for low-lying gaps in most of the small atoms and molecules tested, even when all use the same density functional approximations. It thus establishes EDFT as a promising tool for low-cost studies of excited states and provides a clear route to practical EDFT implementation of arbitrary functional approximations.
Publisher: American Chemical Society (ACS)
Date: 30-05-2018
DOI: 10.26434/CHEMRXIV.6388637.V1
Abstract: 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 h ers 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 two-dimensional hexagonal polymorph becomes entropically stabilized over the cubic at temperatures slightly above ambient conditions (Tc = 63+-20'C). We also reveal a new 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.
Publisher: AIP Publishing
Date: 28-08-2016
DOI: 10.1063/1.4961643
Abstract: In this work, we investigate how atomic C6 coefficients and static dipole polarizabilities α scale with effective volume. We show, using confined atoms covering rows 1-5 of the periodic table, that C6/C6R≈(V/VR)pZ and α/αR≈(V/VR)pZ′ (for volume V=∫dr4π3r3n(r)), where C6R, αR, and VR are the reference values and effective volume of the free atom. The scaling exponents pZ and pZ′ vary substantially as a function of element number Z = N, in contrast to the standard “rule of thumb” that pZ = 2 and pZ′=1. Remarkably, we find that the polarizability and C6 exponents p′ and p are related by p′ ≈ p − 0.615 rather than the expected p′ ≈ 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.
Publisher: American Chemical Society (ACS)
Date: 03-01-2019
DOI: 10.26434/CHEMRXIV.6388637.V3
Abstract: 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 h ers 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 two-dimensional hexagonal polymorph becomes entropically stabilized over the cubic at temperatures slightly above ambient conditions (Tc = 63+-20'C). We also reveal a new 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.
Publisher: American Chemical Society (ACS)
Date: 29-05-2020
DOI: 10.26434/CHEMRXIV.12382595.V1
Abstract: NOTE: This manuscript has been withdrawn from consideration due to an error pointed out during review. The ozone reference calculations reported here as being for singlet-triplet gaps are actually for singlet-singlet excitations. All other results are fine so I leave the preprint with this "erratum".
Publisher: American Chemical Society (ACS)
Date: 19-09-2018
DOI: 10.26434/CHEMRXIV.6388637.V2
Abstract: 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 h ers 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 two-dimensional hexagonal polymorph becomes entropically stabilized over the cubic at temperatures slightly above ambient conditions (Tc = 63+-20'C). We also reveal a new 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.
Publisher: AIP Publishing
Date: 03-01-2013
DOI: 10.1063/1.4773066
Abstract: One of the known weaknesses of the adiabatic connection fluctuation dissipation (ACFD) correlation energy functional under the direct random-phase approximation (RPA) is its failure to accurately predict energy differences between dissimilar systems. In this work we evaluate ionisation potentials I and electron affinities A for atoms and ions with one to eighteen electrons using the ACFD functional under the RPA, and with the “PGG (Petersilka-Gossmann-Gross)” and “RXH (radial exchange hole)” model exchange kernels. All calculations are carried out using a real-space, all electron method with an exact exchange groundstate to minimise errors. As expected, the RPA is less accurate even than some regular density functional theory approaches, while the introduction of a dynamical exchange kernel improves results. In contrast to the case of atomic groundstate energies, the PGG kernel outperforms the RXH kernel for I and A. Mean absolute errors for I/A are found to be 3.27/2.38 kcal/mol, 4.38/5.43 kcal/mol, and 9.24/ 8.94 kcal/mol for the PGG, RXH, and RPA, respectively. We thus show that the inclusion of even the simple “RXH” kernel improves both quantities when compared to the RPA.
Publisher: Royal Society of Chemistry (RSC)
Date: 2014
DOI: 10.1039/C3CP54479F
Abstract: The organic-inorganic hybrid perovskite CH3NH3PbI3 is a novel light harvester, which can greatly improve the solar-conversion efficiency of dye-sensitized solar cells. In this article, a first-principle theoretical study is performed using local, semi-local and non-local exchange-correlation approximations to find a suitable method for this material. Our results, using the non-local optB86b + vdWDF functional, excellently agree with the experimental data. Thus, consideration of weak van der Waals interactions is demonstrated to be important for the accurate description of the properties of this type of organic-inorganic hybrid materials. Further analysis of the electronic properties reveals that I 5p electrons can be photo-excited to Pb 6p empty states. The main interaction between the organic cations and the inorganic framework is through the ionic bonding between CH3 and I ions. Furthermore, I atoms in the Pb-I framework are found to be chemically inequivalent because of their different chemical environments.
Publisher: American Physical Society (APS)
Date: 25-04-2016
Publisher: Beilstein Institut
Date: 23-05-2018
DOI: 10.3762/BJOC.14.99
Abstract: Modern approaches to modelling dispersion forces are becoming increasingly accurate, and can predict accurate binding distances and energies. However, it is possible that these successes reflect a fortuitous cancellation of errors at equilibrium. Thus, in this work we investigate whether a selection of modern dispersion methods agree with benchmark calculations across several potential-energy curves of the benzene dimer to determine if they are capable of describing forces and energies outside equilibrium. We find the exchange-hole dipole moment (XDM) model describes most cases with the highest overall agreement with reference data for energies and forces, with many-body dispersion (MBD) and its fractionally ionic (FI) variant performing essentially as well. Popular approaches, such as Grimme-D and van der Waals density functional approximations (vdW-DFAs) underperform on our tests. The meta-GGA M06-L is surprisingly good for a method without explicit dispersion corrections. Some problems with SCAN+rVV10 are uncovered and briefly discussed.
Publisher: CSIRO Publishing
Date: 2001
DOI: 10.1071/CH01052
Abstract: We discuss the ability of a number of standard and non-standard computational techniques to reproduce dispersion forces, using ex les from the literature as well as some new ex les. We conclude that there are still some cases where standard methods are not so far successful. There are some promising directions under study, however. Manuscript received: 15 March 2001 Final version: 26 October 2001.
Publisher: Elsevier BV
Date: 2021
Publisher: American Chemical Society (ACS)
Date: 15-05-2017
Abstract: This work proposes, justifies, and reports tests of the chemically relevant left Fukui function of Li, C, and F on a range of density functional approximations. Analysis indicates that functionals can be good at densities and bad at Fukui functions, and vice versa, analogous with energies and ionization potentials. "TPSSh", "SOGGA11X", and "B2PLYP" are star performers on both, however. Many "Minnesota functionals" fare much better here than in a recent analysis of electron densities. In this context, new optimizing strategies are mentioned.
Publisher: AIP Publishing
Date: 05-2018
DOI: 10.1063/1.5022832
Abstract: By studying the lowest excitations of an exactly solvable one-dimensional soft-Coulomb molecular model, we show that components of Kohn-Sham ensembles can be used to describe charge transfer processes. Furthermore, we compute the approximate excitation energies obtained by using the exact ensemble densities in the recently formulated ensemble Hartree-exchange theory [T. Gould and S. 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.
Publisher: American Association for the Advancement of Science (AAAS)
Date: 04-01-2019
Abstract: High-level many-body ab initio calculations reveal a strong phase competition in boron nitride near-ambient conditions.
Publisher: American Chemical Society (ACS)
Date: 15-06-2018
DOI: 10.26434/CHEMRXIV.6519764.V1
Abstract: We consider the dispersion energy between two well-separated molecules. Provided that exchange overlap effects can be neglected, the Generalized Casimir Polder (GCP) formula gives the dispersion energy exactly to second order in the inter-system Coulomb pair potential, in terms of the density response functions of the isolated molecules. One can alternatively calculate the dispersion interaction from the density response in a supramolecular (dimer) energy TDDFT/ACFD calculation. This uses the density response from Time Dependent Density Functional Theory (TDDFT) and the Adiabatic Connection (ACFD) groundtstate electronic energy formula, and treats the two systems together. Some of us recently [JCTC 13, 5829 (2017)] showed that the supramolecular TDDFT/ACFD approach can fail to reproduce the exact GCP result, when the exchange-correlation kernel ƒxc in the TDDFT calculation is assumed to be local. Here we examine ways in which a nonlocal density dependence of ƒxc might be able to remove this discrepancy.
Publisher: American Chemical Society (ACS)
Date: 10-03-2021
Publisher: American Physical Society (APS)
Date: 29-05-2014
Publisher: American Chemical Society (ACS)
Date: 19-10-2020
DOI: 10.26434/CHEMRXIV.12456146
Abstract: Density functional theory can be generalized to mixtures of ground and excited states, for the purpose of determining energies of excitations using low-cost density functional approximations. Adapting approximations originally developed for ground states to work in the new setting would fast-forward progress enormously. But, previous attempts have stumbled on daunting fundamental issues. Here we show that these issues can be prevented from the outset, by using a fluctuation dissipation theorem (FDT) to dictate key functionals. We thereby show that existing exchange energy approximations are readily adapted to excited states, when combined with a rigorous exact Hartree term that is different in form from its ground state counterpart, and counterparts based on ensemble ansatze. Applying the FDT to correlation energies also provides insights into ground state-like and ensemble-only correlations. We thus provide a comprehensive and versatile framework for ensemble density functional approximations.
Publisher: Cambridge University Press (CUP)
Date: 12-07-2021
DOI: 10.33774/CHEMRXIV-2021-KFR3S-V2
Abstract: Double excitations, which are dominated by a Slater-determinant with both electrons in the highest occupied molecular orbital promoted to the lowest unoccupied orbital(s), pose significant challenges for low-cost electronic structure calculations based on density functional theory (DFT). Here, we demonstrate that recent advances in ensemble DFT [{\\it Phys. Rev. Lett.} {\\bf 125}, 233001 (2020)], which extend concepts of ground-state DFT to excited states via a rigorous physical framework based on the ensemble fluctuation-dissipation theorem, can be used to shed light on the double excitation problem. We find that the exchange physics of double excitations is reproducible by standard DFT approximations using a linear combination formula, but correlations are more complex. In passing, to analyze correlation, we extend the random-phase approximation to ensembles. We then show, using selected test systems, that standard DFT approximations may be adapted to tackle double excitations based on theoretically motivated simple formulae that employ ensemble extensions of expressions that use the on-top pair density.
Publisher: American Chemical Society (ACS)
Date: 12-07-2021
DOI: 10.26434/CHEMRXIV-2021-KFR3S-V2
Abstract: Double excitations, which are dominated by a Slater-determinant with both electrons in the highest occupied molecular orbital promoted to the lowest unoccupied orbital(s), pose significant challenges for low-cost electronic structure calculations based on density functional theory (DFT). Here, we demonstrate that recent advances in ensemble DFT [{\\it Phys. Rev. Lett.} {\\bf 125}, 233001 (2020)], which extend concepts of ground-state DFT to excited states via a rigorous physical framework based on the ensemble fluctuation-dissipation theorem, can be used to shed light on the double excitation problem. We find that the exchange physics of double excitations is reproducible by standard DFT approximations using a linear combination formula, but correlations are more complex. In passing, to analyze correlation, we extend the random-phase approximation to ensembles. We then show, using selected test systems, that standard DFT approximations may be adapted to tackle double excitations based on theoretically motivated simple formulae that employ ensemble extensions of expressions that use the on-top pair density.
Publisher: IOP Publishing
Date: 03-2007
Publisher: American Chemical Society (ACS)
Date: 12-2016
Abstract: 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 nonionic 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
Publisher: American Chemical Society (ACS)
Date: 13-04-2018
DOI: 10.26434/CHEMRXIV.5802300.V2
Abstract: By studying the lowest excitations of an exactly solvable one-dimensional \\SP{}{soft-Coulomb} 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 the 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.
Publisher: American Chemical Society (ACS)
Date: 10-11-2017
Abstract: A key goal in quantum chemistry methods, whether ab initio or otherwise, is to achieve size consistency. In this work 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 nonlocal "xc kernel" physics, by up to 10% in our tests on closed-shell atoms.
Publisher: American Chemical Society (ACS)
Date: 19-01-2018
DOI: 10.26434/CHEMRXIV.5802300.V1
Abstract: Paper providing a proof-of-principle that ensemble DFT can reproduce difficult charge transfer physics. 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.
Publisher: American Physical Society (APS)
Date: 03-07-2019
Publisher: Royal Society of Chemistry (RSC)
Date: 2022
DOI: 10.1039/D2CP00268J
Abstract: “Poison sets” introduced in this work specifically target failures of density functional approximations. They thereby offer insights into hard computational chemistry problems via novel benchmarking strategies.
Publisher: American Physical Society (APS)
Date: 12-04-2013
Publisher: American Chemical Society (ACS)
Date: 22-08-2019
DOI: 10.26434/CHEMRXIV.8141912.V2
Abstract: We study static correlation and delocalisation errors and show that even methods with good energies can yield significant delocalization errors that affect the density, leading to large errors in predicting e.g. dipole moments. We illustrate this point by comparing existing state-of-art approaches with an accurate exchange correlation functional based on a generalised valence-bond ansatz, in which orbitals and fractional occupations are treated as variational parameters via an optimized effective potential (OEP). We show that the OEP exhibits step and peak features which, similar to the exact Kohn-Sham (KS) potential of DFT, are crucial to prevent charge delocalization. We further show that the step is missing in common approximations within reduced density matrix functional theory resulting in delocalization errors comparable to those found in DFT approximations. Finally, we explain the delocalization error as coming from an artificial mixing of the ground state with a charge-transfer excited state which is avoided if occupation numbers exhibit discontinuities.
Publisher: American Chemical Society (ACS)
Date: 17-05-2019
DOI: 10.26434/CHEMRXIV.8141912.V1
Abstract: Strongly correlated electrons have been the subject of substantial theoretical interest for many years. Most work has focused on obtaining the energy in a low-cost fashion. Here, we show that even methods with good energies can yield significant "delocalization errors" that affect the orbitals and density, leading to large errors in predicting other important properties such as dipole moments. We illustrate this point by comparing existing state-of-art approaches with an accurate exchange correlation functional based on a generalised valence bond ansatz, in which orbitals and fractional occupations are treated as variational parameters via a common optimized effective potential (OEP). We show that the OEP exhibits step and peak features which, similar to the exact Kohn-Sham (KS) potential of DFT, are crucial to prevent charge delocalization. We further show that the step is missing in common approximations within reduced density matrix functional theory resulting in delocalization errors comparable to those found in DFT approximations. Finally, we explain the delocalisation error as coming from an artificial mixing of the ground state with a charge-transfer excited state which is avoided if occupation numbers exhibit discontinuities.
Publisher: American Chemical Society (ACS)
Date: 31-03-2020
DOI: 10.26434/CHEMRXIV.8869460
Abstract: Hybrid functionals have proven to be of immense practical value in density functional theory calculations. While they are often thought to be a heuristic construct, it has been established that this is in fact not the case. Here, we present a rigorous and formally exact analysis of generalized Kohn-Sham (GKS) density functional theory of hybrid functionals, in which exact remainder exchange-correlation potentials combine with a fraction of Fock exchange to produce the correct ground state density. First, we extend formal GKS theory by proving a generalized adiabatic connection theorem. We then use this extension to derive two different definitions for a rigorous distinction between multiplicative exchange and correlation components - one new and one previously postulated. We examine their density-scaling behavior and discuss their similarities and differences. We then present a new algorithm for obtaining exact GKS potentials by inversion of accurate reference electron densities and employ this algorithm to obtain exact potentials for simple atoms and ions. We establish that an equivalent description of the many-electron problem is indeed obtained with any arbitrary global fraction of Fock exchange and we rationalize the Fock-fraction dependence of the computed remainder exchange-correlation potentials in terms of the new formal theory. Finally, we use the exact theoretical framework and numerical results to shed light on the exchange-correlation potential used in approximate hybrid functional calculations and to assess the consequences of different choices of fractional exchange. br br
Publisher: American Physical Society (APS)
Date: 17-10-2022
Publisher: American Physical Society (APS)
Date: 04-08-2021
Publisher: American Chemical Society (ACS)
Date: 28-04-2021
DOI: 10.26434/CHEMRXIV.14498238
Abstract: Double excitations, which are dominated by a Slater-determinant with both electrons in the highest occupied molecular orbital promoted to the lowest unoccupied orbital(s), pose significant challenges for low-cost electronic structure calculations based on density functional theory (DFT). Here, we demonstrate that recent advances in ensemble DFT [ i Phys. Rev. Lett. /i b /b , 233001 (2020)], which extend concepts of ground-state DFT to excited states via a rigorous physical framework based on the ensemble fluctuation-dissipation theorem, can be used to shed light on the double excitation problem. We find that the exchange physics of double excitations is reproducible by standard DFT approximations using a linear combination formula, but correlations are more complex. We then show, using selected test systems, that standard DFT approximations may be adapted to tackle double excitations based on theoretically motivated simple formulae that employ ensemble extensions of expressions that use the on-top pair density. br br
Publisher: American Chemical Society (ACS)
Date: 17-08-2018
DOI: 10.26434/CHEMRXIV.6615509.V2
Abstract: 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.
Publisher: American Chemical Society (ACS)
Date: 20-06-2018
DOI: 10.26434/CHEMRXIV.6615509.V1
Abstract: 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.
Publisher: American Chemical Society (ACS)
Date: 27-01-2021
DOI: 10.26434/CHEMRXIV.12846836
Abstract: Two important extensions of Kohn-Sham (KS) theory are generalized KS theory and ensemble KS theory. The former allows for non-multiplicative potential operators and greatly facilitates practical calculations with advanced, orbital-dependent functionals. The latter allows for quantum ensembles and enables the treatment of, e.g., open systems and excited states. Here, we combine the two extensions, both formally and practically, first via an exact yet complicated formalism, then via a computationally tractable variant that involves a controlled approximation of ensemble "ghost interactions" by means of an iterative algorithm. The resulting formalism is illustrated using selected ex les. This opens the door to the application of generalized KS theory in more challenging quantum scenarios and to the improvement of ensemble theories for the purpose of practical and accurate calculations. br br
Publisher: American Physical Society (APS)
Date: 13-12-2017
Publisher: AIP Publishing
Date: 08-11-2019
DOI: 10.1063/1.5125692
Abstract: The strongly interacting limit of density functional theory has attracted considerable attention recently due to its ability to deal with the difficult strong correlation problem. Recent work [S. Vuckovic and P. Gori-Giorgi, J. Phys. Chem. Lett. 8, 2799–2805 (2017)] introduced the “multiple radii functional” (MRF) approximation, inspired by this limit, which is designed to work well for strong correlations between dissociated fragments. Here, we analyze the MRF in exactly solvable one-dimensional molecules to uncover how it matches and deviates from exact results and use range-separation of the Coulomb potential in both exact and approximate theory to explore how this varies in space. We show that range-separated treatment of the MRF can offer advantages over a full treatment, by using MRF for short-ranged and/or midranged interactions only. Our work opens a path to new approximations incorporating the MRF, amongst other ingredients.
Publisher: American Chemical Society (ACS)
Date: 03-09-2018
DOI: 10.26434/CHEMRXIV.7038428.V1
Abstract: The GMTKN55 benchmarking protocol introduced by [Goerigk et al., Phys. Chem. Chem. Phys., 2017, 19, 32184] allows comprehensive analysis and ranking of density functional approximations with erse chemical behaviours. But this comprehensiveness comes at a cost: GMTKN55's 1500 benchmarking values require energies for around 2500 systems to be calculated, making it a costly exercise. This manuscript introduces three subsets of GMTKN55, consisting of 30, 100 and 150 systems, as `diet' substitutes for the full database. The subsets are chosen via a stochastic genetic approach, and consequently can reproduce key results of the full GMTKN55 database, including ranking of approximations.
Publisher: American Chemical Society (ACS)
Date: 05-09-2018
DOI: 10.26434/CHEMRXIV.7038428.V2
Abstract: The GMTKN55 benchmarking protocol introduced by [Goerigk et al., Phys. Chem. Chem. Phys., 2017, 19, 32184] allows comprehensive analysis and ranking of density functional approximations with erse chemical behaviours. But this comprehensiveness comes at a cost: GMTKN55's 1500 benchmarking values require energies for around 2500 systems to be calculated, making it a costly exercise. This manuscript introduces three subsets of GMTKN55, consisting of 30, 100 and 150 systems, as `diet' substitutes for the full database. The subsets are chosen via a stochastic genetic approach, and consequently can reproduce key results of the full GMTKN55 database, including ranking of approximations.
Publisher: American Physical Society (APS)
Date: 12-03-2009
Publisher: American Physical Society (APS)
Date: 27-08-2019
Publisher: American Chemical Society (ACS)
Date: 05-01-2023
DOI: 10.26434/CHEMRXIV-2023-Q6VD2
Abstract: Kohn-Sham inversion, in which the effective Kohn-Sham mean-field potential is found for a given density, provides insights into the nature of exact density functional theory (DFT) that can be exploited for the development of density functional approximations. Unfortunately, and despite significant and sustained progress in both theory and software libraries, KS inversion remains rather difficult in practice, and especially in finite basis sets. The present work presents a Kohn-Sham inversion method, dubbed the "Lieb-response" approach, that naturally works with existing Fock-matrix DFT infrastructure in finite basis sets, is numerically efficient, and directly provides meaningful matrix and energy quantities for pure-state and ensemble systems. Some additional work yields potentials. It thus enables the routine inversion of KS systems, as illustrated on a variety of problems within this work and provides outputs that can be used for embedding schemes or machine learning of density functional approximations.
Publisher: American Physical Society (APS)
Date: 15-07-2009
Publisher: American Physical Society (APS)
Date: 27-11-2017
Publisher: Royal Society of Chemistry (RSC)
Date: 2021
DOI: 10.1039/D1CP03888E
Abstract: We test a number of dispersion corrected Generalized Gradient Approximation (GGA) and meta-GGA functionals for their ability to predict the interactions of ionic liquids, and show that most can achieve energies within 1 kcal mol −1 of benchmarks.
Publisher: American Chemical Society (ACS)
Date: 11-06-2020
DOI: 10.26434/CHEMRXIV.12456146.V1
Abstract: Density functional theory can be generalized to mixtures of ground and excited states, for the purpose of determining energies of excitations using low-cost density functional approximations. Adapting approximations originally developed for ground states to work in the new setting would fast-forward progress enormously. But, previous attempts have stumbled on daunting fundamental issues. Here we show that these issues can be prevented from the outset, by working from a fluctuation dissipation theorem (FDT). We thereby show that existing exchange energy approximations are readily adapted to excited states, when combined with a rigorous exact Hartree term that is different in form from its ground state counterpart, and counterparts based on ensemble ansatze. Applying the FDT to correlation energies also provides insights into ground state-like and ensemble-only correlations. We thus provide a comprehensive and versatile framework for ensemble density functional approximations.
Publisher: American Chemical Society (ACS)
Date: 07-09-2020
DOI: 10.26434/CHEMRXIV.12456146.V2
Abstract: Density functional theory can be generalized to mixtures of ground and excited states, for the purpose of determining energies of excitations using low-cost density functional approximations. Adapting approximations originally developed for ground states to work in the new setting would fast-forward progress enormously. But, previous attempts have stumbled on daunting fundamental issues. Here we show that these issues can be prevented from the outset, by using a fluctuation dissipation theorem (FDT) to dictate key functionals. We thereby show that existing exchange energy approximations are readily adapted to excited states, when combined with a rigorous exact Hartree term that is different in form from its ground state counterpart, and counterparts based on ensemble ansatze. Applying the FDT to correlation energies also provides insights into ground state-like and ensemble-only correlations. We thus provide a comprehensive and versatile framework for ensemble density functional approximations.
Publisher: American Chemical Society (ACS)
Date: 27-01-2023
DOI: 10.26434/CHEMRXIV-2023-Q6VD2-V2
Abstract: Kohn-Sham inversion, in which the effective Kohn-Sham mean-field potential is found for a given density, provides insights into the nature of exact density functional theory (DFT) that can be exploited for the development of density functional approximations. Unfortunately, and despite significant and sustained progress in both theory and software libraries, KS inversion remains rather difficult in practice, and especially in finite basis sets. The present work presents a Kohn-Sham inversion method, dubbed the “Lieb-response” approach, that naturally works with existing Fock-matrix DFT infrastructure in finite basis sets, is numerically efficient, and directly provides meaningful matrix and energy quantities for pure-state and ensemble systems. Some additional work yields potentials. It thus enables the routine inversion of even difficult KS systems, as illustrated on a variety of problems within this work and provides outputs that can be used for embedding schemes or machine learning of density functional approximations. The effect of finite basis sets on Kohn-Sham inversion is also analysed and investigated.
Publisher: AIP Publishing
Date: 11-12-2013
DOI: 10.1063/1.4839615
Abstract: Via a novel experiment, Liu et al. [Phys. Rev. B 85, 205418 (2012)] estimated the graphite binding energy, specifically the cleavage energy, an important physical property of bulk graphite. We re-examine the data analysis and note that within the standard Lennard-Jones model employed, there are difficulties in achieving internal consistency in the reproduction of the graphite elastic properties. By employing similar models which guarantee consistency with the elastic constant, we find a wide range of model dependent binding energy values from the same experimental data. We attribute some of the difficulties in the determination of the binding energy to: (i) limited theoretical understanding of the van der Waals dispersion of graphite cleavage, (ii) the mis-match between the strong bending stiffness of the graphite-SiO2 cantilever and the weak asymptotic inter-layer forces that are integrated over to produce the binding energy. We find, however, that the data do support determination of a maximum inter-layer force that is relatively model independent. We conclude that the peak force per unit area is 1.1 ± 0.15 GPa for cleavage, and occurs at an inter-layer spacing of 0.377 ± 0.013 nm.
Publisher: American Chemical Society (ACS)
Date: 20-08-2019
Abstract: We study static correlation and delocalization errors and show that even methods with good energies can yield significant delocalization errors that affect the density, leading to large errors in predicting, e.g., dipole moments. We illustrate this point by comparing existing state-of-the-art approaches with an accurate exchange-correlation functional based on a generalized valence-bond ansatz in which orbitals and fractional occupations are treated as variational parameters via an optimized effective potential (OEP). We show that the OEP exhibits step and peak features that, similar to the exact Kohn-Sham potential of density functional theory (DFT), are crucial to prevent charge delocalization. We further show that the step is missing in common approximations within reduced density matrix functional theory, resulting in delocalization errors comparable to those found in DFT approximations. Finally, we explain the delocalization error as coming from artificial mixing of the ground state with a charge-transfer excited state that is avoided if the occupation numbers exhibit discontinuities.
Publisher: Elsevier BV
Date: 09-2023
Publisher: American Chemical Society (ACS)
Date: 08-05-2020
DOI: 10.26434/CHEMRXIV.12268991.V1
Abstract: Functional oxide perovskites are the pillar of cutting-edge technological applications. Density functional theory (DFT) simulations are the theoretical methods of choice to understand and design perovskite materials. However, tests on the reliability of DFT to describe fundamental properties of oxide perovskites are scarce and mostly ill-defined due to a lack of rigorous theoretical benchmarks for solids. Here, we present a quantum Monte Carlo benchmark study of DFT on the archetypal perovskite BaTiO3 (BTO). It shows that no DFT approximation can simultaneously reproduce the energy, structure, and electronic density of BTO. Traditional protocols to select DFT approximations are empirical and fail to detect this shortcoming. An approach combining two different non-empirical DFT schemes, "SCAN" [1] and "HSE06" [2], is able to holistically describe BTO with accuracy. Combined DFT approaches should thus be considered as a promising alternative to standard methods for simulating oxide perovskites.
Publisher: American Physical Society (APS)
Date: 20-05-2020
Publisher: Proceedings of the National Academy of Sciences
Date: 16-10-2018
Abstract: How the van der Waals dispersion interaction relates to chemical electron-correlation effects presents a critical challenge to density functional theory development. Here, recently observed screening of the dispersion force between two insulating objects caused by the insertion of an intermediary graphene layer is explained in terms of Dobson’s general description of dispersion. This then provides a much-needed handle concerning how density functional approaches relate such long-range dispersion interactions to the subtleties of covalent bonding. Screening at intermediate distances appears to change the London expression from r −6 to r −7 , an effect that becomes antiscreening (dispersion enhancement) at distances shorter than van der Waals contact. This provides basic insight into modern revelations that dispersion forces can outcompete covalent forces to control chemical structure.
Publisher: AIP Publishing
Date: 11-2013
DOI: 10.1063/1.4828724
Publisher: American Chemical Society (ACS)
Date: 23-02-2018
DOI: 10.26434/CHEMRXIV.5917114.V1
Abstract: Modern approaches to modelling dispersion forces are becoming increasingly accurate, and can predict accurate binding distances and energies. However, it is possible that these successes reflect a fortuitous cancellation of errors at equilibrium. Thus, in this work we investigate whether a selection of modern dispersion methods agree with benchmark calculations across several potential-energy curves of the benzene dimer to determine if they are capable of describing forces and energies outside equilibrium. We find the exchange-hold dipole moment (XDM) model describes most cases with the highest overall agreement with reference data for energies and forces, with many-body dispersion (MBD) and its fractionally ionic (FI) variant performing essentially as well. Popular approaches, such as Grimme-D and van der Waals density functional approximations (vdW-DFAs) underperform on our tests. The meta-GGA M06-L is surprisingly good for a method without explicit dispersion corrections. Some problems with SCAN+rVV10 are uncovered and briefly discussed.
Location: United Kingdom of Great Britain and Northern Ireland
Location: United Kingdom of Great Britain and Northern Ireland
Start Date: 06-2022
End Date: 06-2026
Amount: $920,537.00
Funder: Australian Research Council
View Funded ActivityStart Date: 10-2019
End Date: 10-2023
Amount: $390,000.00
Funder: Australian Research Council
View Funded ActivityStart Date: 06-2020
End Date: 06-2025
Amount: $450,000.00
Funder: Australian Research Council
View Funded Activity