diff --git a/src/koopmans/references.bib b/src/koopmans/references.bib index 98275e3f4..0f1189ff0 100644 --- a/src/koopmans/references.bib +++ b/src/koopmans/references.bib @@ -101,7 +101,7 @@ @article{Colonna2022 doi = {10.1021/acs.jctc.2c00161}, urldate = {2022-08-09}, abstract = {Koopmans spectral functionals aim to describe simultaneously ground-state properties and charged excitations of atoms, molecules, nanostructures, and periodic crystals. This is achieved by augmenting standard density functionals with simple but physically motivated orbital-density-dependent corrections. These corrections act on a set of localized orbitals that, in periodic systems, resemble maximally localized Wannier functions. At variance with the original, direct supercell implementation (Phys. Rev. X 2018, 8, 021051), we discuss here (i) the complex but efficient formalism required for a periodic boundary code using explicit Brillouin zone sampling and (ii) the calculation of the screened Koopmans corrections with density functional perturbation theory. In addition to delivering improved scaling with system size, the present development makes the calculation of band structures with Koopmans functionals straightforward. The implementation in the open-source Quantum ESPRESSO distribution and the application to prototypical insulating and semiconducting systems are presented and discussed.}, - copyright = {\textcopyright{} 2022 American Chemical Society}, + copyright = {{\textcopyright} 2022 American Chemical Society}, langid = {english} } @@ -142,7 +142,7 @@ @article{Dabo2013 issn = {14639076}, doi = {10.1039/c2cp43491a}, urldate = {2019-11-14}, - abstract = {Accurate and efficient approaches to predict the optical properties of organic semiconducting compounds could accelerate the search for efficient organic photovoltaic materials. Nevertheless, predicting the optical properties of organic semiconductors has been plagued by the inaccuracy or computational cost of conventional first-principles calculations. In this work, we demonstrate that orbital-dependent density-functional theory based upon Koopmans' condition [Phys. Rev. B, 2010, 82, 115121] is apt for describing donor and acceptor levels for a wide variety of organic molecules, clusters, and oligomers within a few tenths of an electron-volt relative to experiment, which is comparable to the predictive performance of many-body perturbation theory methods at a fraction of the computational cost. \textcopyright{} the Owner Societies 2013.} + abstract = {Accurate and efficient approaches to predict the optical properties of organic semiconducting compounds could accelerate the search for efficient organic photovoltaic materials. Nevertheless, predicting the optical properties of organic semiconductors has been plagued by the inaccuracy or computational cost of conventional first-principles calculations. In this work, we demonstrate that orbital-dependent density-functional theory based upon Koopmans' condition [Phys. Rev. B, 2010, 82, 115121] is apt for describing donor and acceptor levels for a wide variety of organic molecules, clusters, and oligomers within a few tenths of an electron-volt relative to experiment, which is comparable to the predictive performance of many-body perturbation theory methods at a fraction of the computational cost. {\textcopyright} the Owner Societies 2013.} } @article{DeGennaro2022, @@ -190,7 +190,7 @@ @article{Hamann2013 issn = {10980121}, doi = {10.1103/PhysRevB.88.085117}, urldate = {2020-06-23}, - abstract = {Fully nonlocal two-projector norm-conserving pseudopotentials are shown to be compatible with a systematic approach to the optimization of convergence with the size of the plane-wave basis. A reformulation of the optimization is developed, including the ability to apply it to positive-energy atomic scattering states and to enforce greater continuity in the pseudopotential. The generalization of norm conservation to multiple projectors is reviewed and recast for the present purposes. Comparisons among the results of all-electron and one- and two-projector norm-conserving pseudopotential calculations of lattice constants and bulk moduli are made for a group of solids chosen to represent a variety of types of bonding and a sampling of the periodic table. \textcopyright{} 2013 American Physical Society.} + abstract = {Fully nonlocal two-projector norm-conserving pseudopotentials are shown to be compatible with a systematic approach to the optimization of convergence with the size of the plane-wave basis. A reformulation of the optimization is developed, including the ability to apply it to positive-energy atomic scattering states and to enforce greater continuity in the pseudopotential. The generalization of norm conservation to multiple projectors is reviewed and recast for the present purposes. Comparisons among the results of all-electron and one- and two-projector norm-conserving pseudopotential calculations of lattice constants and bulk moduli are made for a group of solids chosen to represent a variety of types of bonding and a sampling of the periodic table. {\textcopyright} 2013 American Physical Society.} } @article{Kraisler2013, @@ -222,7 +222,7 @@ @article{Kronik2012 issn = {1549-9618}, doi = {10.1021/ct2009363}, urldate = {2022-10-17}, - abstract = {Excitation gaps are of considerable significance in electronic structure theory. Two different gaps are of particular interest. The fundamental gap is defined by charged excitations, as the difference between the first ionization potential and the first electron affinity. The optical gap is defined by a neutral excitation, as the difference between the energies of the lowest dipole-allowed excited state and the ground state. Within many-body perturbation theory, the fundamental gap is the difference between the corresponding lowest quasi-hole and quasi-electron excitation energies, and the optical gap is addressed by including the interaction between a quasi-electron and a quasi-hole. A long-standing challenge has been the attainment of a similar description within density functional theory (DFT), with much debate on whether this is an achievable goal even in principle. Recently, we have constructed and applied a new approach to this problem. Anchored in the rigorous theoretical framework of the generalized Kohn\textendash Sham equation, our method is based on a range-split hybrid functional that uses exact long-range exchange. Its main novel feature is that the range-splitting parameter is not a universal constant but rather is determined from first principles, per system, based on satisfaction of the ionization potential theorem. For finite-sized objects, this DFT approach mimics successfully, to the best of our knowledge for the first time, the quasi-particle picture of many-body theory. Specifically, it allows for the extraction of both the fundamental and the optical gap from one underlying functional, based on the HOMO\textendash LUMO gap of a ground-state DFT calculation and the lowest excitation energy of a linear-response time-dependent DFT calculation, respectively. In particular, it produces the correct optical gap for the difficult case of charge-transfer and charge-transfer-like scenarios, where conventional functionals are known to fail. In this perspective, we overview the formal and practical challenges associated with gap calculations, explain our new approach and how it overcomes previous difficulties, and survey its application to a variety of systems.} + abstract = {Excitation gaps are of considerable significance in electronic structure theory. Two different gaps are of particular interest. The fundamental gap is defined by charged excitations, as the difference between the first ionization potential and the first electron affinity. The optical gap is defined by a neutral excitation, as the difference between the energies of the lowest dipole-allowed excited state and the ground state. Within many-body perturbation theory, the fundamental gap is the difference between the corresponding lowest quasi-hole and quasi-electron excitation energies, and the optical gap is addressed by including the interaction between a quasi-electron and a quasi-hole. A long-standing challenge has been the attainment of a similar description within density functional theory (DFT), with much debate on whether this is an achievable goal even in principle. Recently, we have constructed and applied a new approach to this problem. Anchored in the rigorous theoretical framework of the generalized Kohn{\textendash}Sham equation, our method is based on a range-split hybrid functional that uses exact long-range exchange. Its main novel feature is that the range-splitting parameter is not a universal constant but rather is determined from first principles, per system, based on satisfaction of the ionization potential theorem. For finite-sized objects, this DFT approach mimics successfully, to the best of our knowledge for the first time, the quasi-particle picture of many-body theory. Specifically, it allows for the extraction of both the fundamental and the optical gap from one underlying functional, based on the HOMO{\textendash}LUMO gap of a ground-state DFT calculation and the lowest excitation energy of a linear-response time-dependent DFT calculation, respectively. In particular, it produces the correct optical gap for the difficult case of charge-transfer and charge-transfer-like scenarios, where conventional functionals are known to fail. In this perspective, we overview the formal and practical challenges associated with gap calculations, explain our new approach and how it overcomes previous difficulties, and survey its application to a variety of systems.} } @article{Lejaeghere2016, @@ -250,20 +250,19 @@ @article{Li2018 urldate = {2020-04-04} } -@misc{Linscott2023, - title = {Koopmans: An Open-Source Package for Accurately and Efficiently Predicting Spectral Properties with {{Koopmans}} Functionals}, +@article{Linscott2023, + title = {Koopmans: {{An Open-Source Package}} for {{Accurately}} and {{Efficiently Predicting Spectral Properties}} with {{Koopmans Functionals}}}, shorttitle = {Koopmans}, - author = {Linscott, Edward and Colonna, Nicola and De Gennaro, Riccardo and Nguyen, Ngoc Linh and Borghi, Giovanni and Ferretti, Andrea and Dabo, Ismaila and Marzari, Nicola}, + author = {Linscott, Edward B. and Colonna, Nicola and De Gennaro, Riccardo and Nguyen, Ngoc Linh and Borghi, Giovanni and Ferretti, Andrea and Dabo, Ismaila and Marzari, Nicola}, year = {2023}, - month = feb, - number = {2302.07759}, - eprint = {2302.07759}, - primaryclass = {cond-mat, physics:physics}, - publisher = {{arXiv}}, - abstract = {Over the past decade we have developed Koopmans functionals, a computationally efficient approach for predicting spectral properties with an orbital-density-dependent functional formulation. These functionals address two fundamental issues with density functional theory (DFT). First, while Kohn-Sham eigenvalues can loosely mirror experimental quasiparticle energies, they are not meant to reproduce excitation energies and there is formally no connection between the two (except for the HOMO for the exact functional). Second, (semi-)local DFT deviates from the expected piecewise linear behavior of the energy as a function of the total number of electrons. This can make eigenvalues an even poorer proxy for quasiparticle energies and, together with the absence of the exchange-correlation derivative discontinuity, contributes to DFT's underestimation of band gaps. By enforcing a generalized piecewise linearity condition to the entire electronic manifold, Koopmans functionals yield molecular orbital energies and solid-state band structures with comparable accuracy to many-body perturbation theory but at greatly reduced computational cost and preserving a functional formulation. This paper introduces "koopmans", an open-source package that contains all of the code and workflows needed to perform Koopmans functional calculations without requiring expert knowledge. The theory and algorithms behind Koopmans functionals are summarized, and it is shown how one can easily use the koopmans package to obtain reliable spectral properties of molecules and materials.}, - archiveprefix = {arxiv}, - copyright = {All rights reserved}, - keywords = {Condensed Matter - Materials Science,Physics - Chemical Physics,Physics - Computational Physics} + month = aug, + journal = {J. Chem. Theory Comput.}, + publisher = {{American Chemical Society}}, + issn = {1549-9618}, + doi = {10.1021/acs.jctc.3c00652}, + urldate = {2023-08-24}, + abstract = {Over the past decade we have developed Koopmans functionals, a computationally efficient approach for predicting spectral properties with an orbital-density-dependent functional framework. These functionals impose a generalized piecewise linearity condition to the entire electronic manifold, ensuring that orbital energies match the corresponding electron removal/addition energy differences (in contrast to semilocal DFT, where a mismatch between the two lies at the heart of the band gap problem and, more generally, the unreliability of Kohn{\textendash}Sham orbital energies). This strategy has proven to be very powerful, yielding molecular orbital energies and solid-state band structures with comparable accuracy to many-body perturbation theory but at greatly reduced computational cost while preserving a functional formulation. This paper reviews the theory of Koopmans functionals, discusses the algorithms necessary for their implementation, and introduces koopmans, an open-source package that contains all of the code and workflows needed to perform Koopmans functional calculations and obtain reliable spectral properties of molecules and materials.}, + copyright = {All rights reserved} } @article{Ma2016, @@ -326,7 +325,7 @@ @article{Nguyen2015 publisher = {{American Physical Society}}, doi = {10.1103/PhysRevLett.114.166405}, urldate = {2021-06-16}, - abstract = {The determination of spectral properties from first principles can provide powerful connections between microscopic theoretical predictions and experimental data, but requires complex electronic-structure formulations that fall outside the domain of applicability of common approaches, such as density-functional theory. We show here that Koopmans-compliant functionals, constructed to enforce piecewise linearity and the correct discontinuity derivative in energy functionals with respect to fractional occupation\textemdash i.e., with respect to charged excitations\textemdash provide molecular photoemission spectra and momentum maps of Dyson orbitals that are in excellent agreement with experimental ultraviolet photoemission spectroscopy and orbital tomography data. These results highlight the role of Koopmans-compliant functionals as accurate and inexpensive quasiparticle approximations to the spectral potential.} + abstract = {The determination of spectral properties from first principles can provide powerful connections between microscopic theoretical predictions and experimental data, but requires complex electronic-structure formulations that fall outside the domain of applicability of common approaches, such as density-functional theory. We show here that Koopmans-compliant functionals, constructed to enforce piecewise linearity and the correct discontinuity derivative in energy functionals with respect to fractional occupation{\textemdash}i.e., with respect to charged excitations{\textemdash}provide molecular photoemission spectra and momentum maps of Dyson orbitals that are in excellent agreement with experimental ultraviolet photoemission spectroscopy and orbital tomography data. These results highlight the role of Koopmans-compliant functionals as accurate and inexpensive quasiparticle approximations to the spectral potential.} } @article{Nguyen2016, @@ -361,7 +360,7 @@ @article{Nguyen2018 } @article{Pederson1984, - title = {Local-density {{Hartree}}\textendash{{Fock}} Theory of Electronic States of Molecules with Self-interaction Correction}, + title = {Local-density {{Hartree}}{\textendash}{{Fock}} Theory of Electronic States of Molecules with Self-interaction Correction}, author = {Pederson, Mark R. and Heaton, Richard A. and Lin, Chun C.}, year = {1984}, month = mar, @@ -373,7 +372,7 @@ @article{Pederson1984 issn = {0021-9606}, doi = {10.1063/1.446959}, urldate = {2019-03-23}, - abstract = {A scheme for incorporating the self-interaction correction (SIC) to the local density approximation of the Hartree\textendash Fock theory of electronic structure of molecules is presented. This method is applied to the N2 molecule and the resulting orbital energies and total energy are in good agreement with the Hartree\textendash Fock values.}, + abstract = {A scheme for incorporating the self-interaction correction (SIC) to the local density approximation of the Hartree{\textendash}Fock theory of electronic structure of molecules is presented. This method is applied to the N2 molecule and the resulting orbital energies and total energy are in good agreement with the Hartree{\textendash}Fock values.}, keywords = {ELECTRONIC STRUCTURE,HARTREE-FOCK METHOD,MOLECULES,NITROGEN} } @@ -397,7 +396,7 @@ @article{Prandini2018 } @article{Scherpelz2016, - title = {Implementation and {{Validation}} of {{Fully Relativistic GW Calculations}}: {{Spin}}\textendash{{Orbit Coupling}} in {{Molecules}}, {{Nanocrystals}}, and {{Solids}}}, + title = {Implementation and {{Validation}} of {{Fully Relativistic GW Calculations}}: {{Spin}}{\textendash}{{Orbit Coupling}} in {{Molecules}}, {{Nanocrystals}}, and {{Solids}}}, shorttitle = {Implementation and {{Validation}} of {{Fully Relativistic GW Calculations}}}, author = {Scherpelz, Peter and Govoni, Marco and Hamada, Ikutaro and Galli, Giulia}, year = {2016}, @@ -410,7 +409,7 @@ @article{Scherpelz2016 issn = {1549-9618}, doi = {10.1021/acs.jctc.6b00114}, urldate = {2022-02-17}, - abstract = {We present an implementation of G0W0 calculations including spin\textendash orbit coupling (SOC) enabling investigations of large systems, with thousands of electrons, and we discuss results for molecules, solids, and nanocrystals. Using a newly developed set of molecules with heavy elements (called GW-SOC81), we find that, when based upon hybrid density functional calculations, fully relativistic (FR) and scalar-relativistic (SR) G0W0 calculations of vertical ionization potentials both yield excellent performance compared to experiment, with errors below 1.9\%. We demonstrate that while SR calculations have higher random errors, FR calculations systematically underestimate the VIP by 0.1 to 0.2 eV. We further verify that SOC effects may be well approximated at the FR density functional level and then added to SR G0W0 results for a broad class of systems. We also address the use of different root-finding algorithms for the G0W0 quasiparticle equation and the significant influence of including d electrons in the valence partition of the pseudopotential for G0W0 calculations. Finally, we present statistical analyses of our data, highlighting the importance of separating definitive improvements from those that may occur by chance due to a limited number of samples. We suggest the statistical analyses used here will be useful in the assessment of the accuracy of a large variety of electronic structure methods.} + abstract = {We present an implementation of G0W0 calculations including spin{\textendash}orbit coupling (SOC) enabling investigations of large systems, with thousands of electrons, and we discuss results for molecules, solids, and nanocrystals. Using a newly developed set of molecules with heavy elements (called GW-SOC81), we find that, when based upon hybrid density functional calculations, fully relativistic (FR) and scalar-relativistic (SR) G0W0 calculations of vertical ionization potentials both yield excellent performance compared to experiment, with errors below 1.9\%. We demonstrate that while SR calculations have higher random errors, FR calculations systematically underestimate the VIP by 0.1 to 0.2 eV. We further verify that SOC effects may be well approximated at the FR density functional level and then added to SR G0W0 results for a broad class of systems. We also address the use of different root-finding algorithms for the G0W0 quasiparticle equation and the significant influence of including d electrons in the valence partition of the pseudopotential for G0W0 calculations. Finally, we present statistical analyses of our data, highlighting the importance of separating definitive improvements from those that may occur by chance due to a limited number of samples. We suggest the statistical analyses used here will be useful in the assessment of the accuracy of a large variety of electronic structure methods.} } @article{Schlipf2015, @@ -424,7 +423,7 @@ @article{Schlipf2015 issn = {0010-4655}, doi = {10.1016/j.cpc.2015.05.011}, urldate = {2021-07-09}, - abstract = {We present an optimization algorithm to construct pseudopotentials and use it to generate a set of Optimized Norm-Conserving Vanderbilt (ONCV) pseudopotentials for elements up to Z=83 (Bi) (excluding Lanthanides). We introduce a quality function that assesses the agreement of a pseudopotential calculation with all-electron FLAPW results, and the necessary plane-wave energy cutoff. This quality function allows us to use a Nelder\textendash Mead optimization algorithm on a training set of materials to optimize the input parameters of the pseudopotential construction for most of the periodic table. We control the accuracy of the resulting pseudopotentials on a test set of materials independent of the training set. We find that the automatically constructed pseudopotentials (http://www.quantum-simulation.org) provide a good agreement with the all-electron results obtained using the FLEUR code with a plane-wave energy cutoff of approximately 60 Ry.}, + abstract = {We present an optimization algorithm to construct pseudopotentials and use it to generate a set of Optimized Norm-Conserving Vanderbilt (ONCV) pseudopotentials for elements up to Z=83 (Bi) (excluding Lanthanides). We introduce a quality function that assesses the agreement of a pseudopotential calculation with all-electron FLAPW results, and the necessary plane-wave energy cutoff. This quality function allows us to use a Nelder{\textendash}Mead optimization algorithm on a training set of materials to optimize the input parameters of the pseudopotential construction for most of the periodic table. We control the accuracy of the resulting pseudopotentials on a test set of materials independent of the training set. We find that the automatically constructed pseudopotentials (http://www.quantum-simulation.org) provide a good agreement with the all-electron results obtained using the FLEUR code with a plane-wave energy cutoff of approximately 60 Ry.}, keywords = {All-electron calculation,Condensed matter,Density functional theory,Plane wave,Pseudopotential} } @@ -440,7 +439,7 @@ @article{Schubert2023 issn = {0021-9606}, doi = {10.1063/5.0138610}, urldate = {2023-04-20}, - abstract = {Koopmans spectral functionals are a class of orbital-density-dependent functionals designed to accurately predict spectroscopic properties. They do so markedly better than their Kohn\textendash Sham density-functional theory counterparts, as demonstrated in earlier works on benchmarks of molecules and bulk systems. This work is a complementary study where\textemdash instead of comparing against real, many-electron systems\textemdash we test Koopmans spectral functionals on Hooke's atom, a toy two-electron system that has analytical solutions for particular strengths of its harmonic confining potential. As these calculations clearly illustrate, Koopmans spectral functionals do an excellent job of describing Hooke's atom across a range of confining potential strengths. This work also provides broader insights into the features and capabilities of Koopmans spectral functionals more generally.} + abstract = {Koopmans spectral functionals are a class of orbital-density-dependent functionals designed to accurately predict spectroscopic properties. They do so markedly better than their Kohn{\textendash}Sham density-functional theory counterparts, as demonstrated in earlier works on benchmarks of molecules and bulk systems. This work is a complementary study where{\textemdash}instead of comparing against real, many-electron systems{\textemdash}we test Koopmans spectral functionals on Hooke's atom, a toy two-electron system that has analytical solutions for particular strengths of its harmonic confining potential. As these calculations clearly illustrate, Koopmans spectral functionals do an excellent job of describing Hooke's atom across a range of confining potential strengths. This work also provides broader insights into the features and capabilities of Koopmans spectral functionals more generally.} } @article{Skone2016, @@ -477,7 +476,7 @@ @article{vanSetten2018 } @article{Wing2021, - title = {Band Gaps of Crystalline Solids from {{Wannier-localization}}\textendash Based Optimal Tuning of a Screened Range-Separated Hybrid Functional}, + title = {Band Gaps of Crystalline Solids from {{Wannier-localization}}{\textendash}Based Optimal Tuning of a Screened Range-Separated Hybrid Functional}, author = {Wing, Dahvyd and Ohad, Guy and Haber, Jonah B. and Filip, Marina R. and Gant, Stephen E. and Neaton, Jeffrey B. and Kronik, Leeor}, year = {2021}, month = aug,