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Julien Toulouse - One of the best experts on this subject based on the ideXlab platform.
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Basis convergence of range-separated density-Functional Theory
Journal of Chemical Physics, 2015Co-Authors: Odile Franck, Bastien Mussard, Eleonora Luppi, Julien ToulouseAbstract:Range-separated density-Functional Theory is an alternative approach to Kohn-Sham density-Functional Theory. The strategy of range-separated density-Functional Theory consists in separating the Coulomb electron-electron interaction into long-range and short-range components, and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-Functional approximation. Among the advantages of using many-body methods for the long-range part of the electron-electron interaction is that they are much less sensitive to the one-electron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of range-separated density-Functional Theory. We study the convergence of the partial-wave expansion of the long-range wave function near the electron-electron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum L for the long-range wave function, whereas it is polynomial for the case of the Coulomb interaction. We also study the convergence of the long-range second-order Møller-Plesset correlation energy of four systems (He, Ne, N2, and H2O) with the cardinal number X of the Dunning basis sets cc-p(C)VXZ, and find that the error in the correlation energy is best fitted by an exponential in X. This leads us to propose a three-point complete-basis-set extrapolation scheme for range-separated density-Functional Theory based on an exponential formula.
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Basis convergence of range-separated density-Functional Theory
The Journal of chemical physics, 2015Co-Authors: Odile Franck, Bastien Mussard, Eleonora Luppi, Julien ToulouseAbstract:Range-separated density-Functional Theory (DFT) is an alternative approach to Kohn-Sham density-Functional Theory. The strategy of range-separated density-Functional Theory consists in separating the Coulomb electron-electron interaction into long-range and short-range components and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-Functional approximation. Among the advantages of using many-body methods for the long-range part of the electron-electron interaction is that they are much less sensitive to the one-electron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of range-separated density-Functional Theory. We study the convergence of the partial-wave expansion of the long-range wave function near the electron-electron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum L for the long-range wave func...
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basis convergence of range separated density Functional Theory
Journal of Chemical Physics, 2015Co-Authors: Odile Franck, Bastien Mussard, Julien Toulouse, Eleonora LuppiAbstract:Range-separated density-Functional Theory (DFT) is an alternative approach to Kohn-Sham density-Functional Theory. The strategy of range-separated density-Functional Theory consists in separating the Coulomb electron-electron interaction into long-range and short-range components and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-Functional approximation. Among the advantages of using many-body methods for the long-range part of the electron-electron interaction is that they are much less sensitive to the one-electron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of range-separated density-Functional Theory. We study the convergence of the partial-wave expansion of the long-range wave function near the electron-electron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum L for the long-range wave function, whereas it is polynomial for the case of the Coulomb interaction. We also study the convergence of the long-range second-order Moller-Plesset correlation energy of four systems (He, Ne, N2, and H2O) with cardinal number X of the Dunning basis sets cc − p(C)V XZ and find that the error in the correlation energy is best fitted by an exponential in X. This leads us to propose a three-point complete-basis-set extrapolation scheme for range-separated density-Functional Theory based on an exponential formula.
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combining density Functional Theory and density matrix Functional Theory
Physical Review A, 2010Co-Authors: Daniel R Rohr, Julien Toulouse, Katarzyna PernalAbstract:We combine density-Functional Theory with density-matrix-Functional Theory to draw the best from both worlds. This is achieved by range separation of the electronic interaction which permits one to rigorously combine a short-range density Functional with a long-range density-matrix Functional. The short-range density Functional is approximated by the short-range version of the Perdew-Burke-Ernzerhof Functional (srPBE). The long-range density-matrix Functional is approximated by the long-range version of the Buijse-Baerends Functional (lrBB). The obtained srPBE+lrBB method accurately describes both the static and dynamic electron correlation at a computational cost similar to that of standard density-Functional approximations. This is shown for the dissociation curves of the H{sub 2}, LiH, BH, and HF molecules.
Kieron Burke - One of the best experts on this subject based on the ideXlab platform.
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Warming Up Density Functional Theory
Frontiers of Quantum Chemistry, 2018Co-Authors: Justin C. Smith, Francisca Sagredo, Kieron BurkeAbstract:Density Functional Theory (DFT) has become the most popular approach to electronic structure across disciplines, especially in material and chemical sciences. In 2016, at least 30,000 papers used DFT to make useful predictions or give insight into an enormous diversity of scientific problems, ranging from battery development to solar cell efficiency and far beyond. The success of this field has been driven by usefully accurate approximations based on known exact conditions and careful testing and validation. In the last decade, applications of DFT in a new area, warm dense matter, have exploded. DFT is revolutionizing simulations of warm dense matter including applications in controlled fusion, planetary interiors, and other areas of high energy density physics. Over the past decade or so, molecular dynamics calculations driven by modern density Functional Theory have played a crucial role in bringing chemical realism to these applications, often (but not always) in excellent agreement with experiment. This chapter summarizes recent work from our group on density Functional Theory at nonzero temperatures, which we call thermal DFT. We explain the relevance of this work in the context of warm dense matter, and the importance of quantum chemistry to this regime. We illustrate many basic concepts on a simple model system, the asymmetric Hubbard dimer.
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Warming Up Density Functional Theory
arXiv: Chemical Physics, 2017Co-Authors: Justin Smith, Francisca Sagredo, Kieron BurkeAbstract:Density Functional Theory (DFT) has become the most popular approach to electronic structure across disciplines, especially in material and chemical sciences. Last year, at least 30,000 papers used DFT to make useful predictions or give insight into an enormous diversity of scientific problems, ranging from battery development to solar cell efficiency and far beyond. The success of this field has been driven by usefully accurate approximations based on known exact conditions and careful testing and validation. In the last decade, applications of DFT in a new area, warm dense matter, have exploded. DFT is revolutionizing simulations of warm dense matter including applications in controlled fusion, planetary interiors, and other areas of high energy density physics. Over the past decade or so, molecular dynamics calculations driven by modern density Functional Theory have played a crucial role in bringing chemical realism to these applications, often (but not always) with excellent agreement with experiment. This chapter summarizes recent work from our group on density Functional Theory at non-zero temperatures, which we call thermal DFT. We explain the relevance of this work in the context of warm dense matter, and the importance of quantum chemistry to this regime. We illustrate many basic concepts on a simple model system, the asymmetric Hubbard dimer.
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Connection formulas for thermal density Functional Theory
Physical Review B, 2016Co-Authors: Aurora Pribram-jones, Kieron BurkeAbstract:We show that the adiabatic connection formula of ground-state density Functional Theory relates the correlation energy to a coupling-constant integral over a purely potential contribution, and is widely used to understand and improve approximations. The corresponding formula for thermal density Functional Theory is cast as an integral over temperatures instead, ranging upward from the system's physical temperature. We also show how to relate different correlation components to each other, either in terms of temperature or coupling-constant integrations. Lastly, we illustrate our results on the uniform electron gas.
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Connection formulas for thermal density Functional Theory
Physical Review B, 2016Co-Authors: Aurora Pribram-jones, Kieron BurkeAbstract:The adiabatic connection formula of ground-state density Functional Theory relates the correlation energy to a coupling-constant integral over a purely potential contribution, and is widely used to understand and improve approximations. The corresponding formula for thermal density Functional Theory is cast as an integral over temperatures instead, ranging upward from the system's physical temperature. We also show how to relate different correlation components to each other, either in terms of temperature or coupling-constant integrations. We illustrate our results on the uniform electron gas.
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Thermal Density Functional Theory in Context
Lecture Notes in Computational Science and Engineering, 2014Co-Authors: Aurora Pribram-jones, E. K. U. Gross, Stefano Pittalis, Kieron BurkeAbstract:This chapter introduces thermal density Functional Theory, starting from the ground-state Theory and assuming a background in quantum mechanics and statistical mechanics. We review the foundations of density Functional Theory (DFT) by illustrating some of its key reformulations. The basics of DFT for thermal ensembles are explained in this context, as are tools useful for analysis and development of approximations. This review emphasizes thermal DFT’s strengths as a consistent and general framework.
Odile Franck - One of the best experts on this subject based on the ideXlab platform.
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Basis convergence of range-separated density-Functional Theory
Journal of Chemical Physics, 2015Co-Authors: Odile Franck, Bastien Mussard, Eleonora Luppi, Julien ToulouseAbstract:Range-separated density-Functional Theory is an alternative approach to Kohn-Sham density-Functional Theory. The strategy of range-separated density-Functional Theory consists in separating the Coulomb electron-electron interaction into long-range and short-range components, and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-Functional approximation. Among the advantages of using many-body methods for the long-range part of the electron-electron interaction is that they are much less sensitive to the one-electron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of range-separated density-Functional Theory. We study the convergence of the partial-wave expansion of the long-range wave function near the electron-electron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum L for the long-range wave function, whereas it is polynomial for the case of the Coulomb interaction. We also study the convergence of the long-range second-order Møller-Plesset correlation energy of four systems (He, Ne, N2, and H2O) with the cardinal number X of the Dunning basis sets cc-p(C)VXZ, and find that the error in the correlation energy is best fitted by an exponential in X. This leads us to propose a three-point complete-basis-set extrapolation scheme for range-separated density-Functional Theory based on an exponential formula.
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Basis convergence of range-separated density-Functional Theory
The Journal of chemical physics, 2015Co-Authors: Odile Franck, Bastien Mussard, Eleonora Luppi, Julien ToulouseAbstract:Range-separated density-Functional Theory (DFT) is an alternative approach to Kohn-Sham density-Functional Theory. The strategy of range-separated density-Functional Theory consists in separating the Coulomb electron-electron interaction into long-range and short-range components and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-Functional approximation. Among the advantages of using many-body methods for the long-range part of the electron-electron interaction is that they are much less sensitive to the one-electron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of range-separated density-Functional Theory. We study the convergence of the partial-wave expansion of the long-range wave function near the electron-electron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum L for the long-range wave func...
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basis convergence of range separated density Functional Theory
Journal of Chemical Physics, 2015Co-Authors: Odile Franck, Bastien Mussard, Julien Toulouse, Eleonora LuppiAbstract:Range-separated density-Functional Theory (DFT) is an alternative approach to Kohn-Sham density-Functional Theory. The strategy of range-separated density-Functional Theory consists in separating the Coulomb electron-electron interaction into long-range and short-range components and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-Functional approximation. Among the advantages of using many-body methods for the long-range part of the electron-electron interaction is that they are much less sensitive to the one-electron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of range-separated density-Functional Theory. We study the convergence of the partial-wave expansion of the long-range wave function near the electron-electron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum L for the long-range wave function, whereas it is polynomial for the case of the Coulomb interaction. We also study the convergence of the long-range second-order Moller-Plesset correlation energy of four systems (He, Ne, N2, and H2O) with cardinal number X of the Dunning basis sets cc − p(C)V XZ and find that the error in the correlation energy is best fitted by an exponential in X. This leads us to propose a three-point complete-basis-set extrapolation scheme for range-separated density-Functional Theory based on an exponential formula.
Miguel A. L. Marques - One of the best experts on this subject based on the ideXlab platform.
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Reduced density matrix Functional Theory for superconductors
Physical Review B, 2019Co-Authors: Jonathan Schmidt, Carlos L. Benavides-riveros, Miguel A. L. MarquesAbstract:We present an ab initio Theory for superconductors, based on a unique mapping between the statistical density operator at equilibrium, on the one hand, and the corresponding one-body reduced density matrix $\ensuremath{\gamma}$ and the anomalous density $\ensuremath{\chi}$, on the other. This formalism for superconductivity yields the existence of a universal Functional ${\mathfrak{F}}_{\ensuremath{\beta}}[\ensuremath{\gamma},\ensuremath{\chi}]$ for the superconductor ground state, whose unique properties we derive. We then prove the existence of a Kohn-Sham system at finite temperature and derive the corresponding Bogoliubov--de Gennes--type single-particle equations. By adapting the decoupling approximation from density Functional Theory for superconductors we bring these equations into a computationally feasible form. Finally, we use the existence of the Kohn-Sham system to extend the Sham-Schl\"uter connection and derive a first exchange-correlation Functional for our Theory. This reduced density matrix Functional Theory for superconductors has the potential of overcoming some of the shortcomings and fundamental limitations of density Functional Theory of superconductivity.
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A Primer in Density Functional Theory
2010Co-Authors: Carlos Fiolhais, Fernando Nogueira, Miguel A. L. MarquesAbstract:Density Functionals for Non-relativistic Coulomb Systems in the New Century.- Orbital-Dependent Functionals for the Exchange-Correlation Energy: A Third Generation of Density Functionals.- Relativistic Density Functional Theory.- Time-Dependent Density Functional Theory.- Density Functional Theories and Self-energy Approaches.- A Tutorial on Density Functional Theory.
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Benchmark calculations for reduced density-matrix Functional Theory
The Journal of Chemical Physics, 2008Co-Authors: Nektarios N. Lathiotakis, Miguel A. L. MarquesAbstract:Reduced density-matrix Functional Theory (RDMFT) is a promising alternative approach to the problem of electron correlation. Like standard density Functional Theory, it contains an unknown exchange-correlation Functional, for which several approximations have been proposed in the last years. In this article, we benchmark some of these Functionals in an extended set of molecules with respect to total and atomization energies. Our results show that the most recent RDMFT Functionals give very satisfactory results compared to standard quantum chemistry and density Functional approaches.
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benchmark calculations for reduced density matrix Functional Theory
arXiv: Chemical Physics, 2008Co-Authors: Nektarios N. Lathiotakis, Miguel A. L. MarquesAbstract:Reduced density-matrix Functional Theory (RDMFT) is a promising alternative approach to the problem of electron correlation. Like standard density Functional Theory, it contains an unknown exchange-correlation Functional, for which several approximations have been proposed in the last years. In this article, we benchmark some of these Functionals in an extended set of molecules with respect to total and atomization energies. Our results show that the most recent RDMFT Functionals give very satisfactory results compared to more involved quantum chemistry and density Functional approaches.
Bastien Mussard - One of the best experts on this subject based on the ideXlab platform.
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Basis convergence of range-separated density-Functional Theory
Journal of Chemical Physics, 2015Co-Authors: Odile Franck, Bastien Mussard, Eleonora Luppi, Julien ToulouseAbstract:Range-separated density-Functional Theory is an alternative approach to Kohn-Sham density-Functional Theory. The strategy of range-separated density-Functional Theory consists in separating the Coulomb electron-electron interaction into long-range and short-range components, and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-Functional approximation. Among the advantages of using many-body methods for the long-range part of the electron-electron interaction is that they are much less sensitive to the one-electron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of range-separated density-Functional Theory. We study the convergence of the partial-wave expansion of the long-range wave function near the electron-electron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum L for the long-range wave function, whereas it is polynomial for the case of the Coulomb interaction. We also study the convergence of the long-range second-order Møller-Plesset correlation energy of four systems (He, Ne, N2, and H2O) with the cardinal number X of the Dunning basis sets cc-p(C)VXZ, and find that the error in the correlation energy is best fitted by an exponential in X. This leads us to propose a three-point complete-basis-set extrapolation scheme for range-separated density-Functional Theory based on an exponential formula.
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Basis convergence of range-separated density-Functional Theory
The Journal of chemical physics, 2015Co-Authors: Odile Franck, Bastien Mussard, Eleonora Luppi, Julien ToulouseAbstract:Range-separated density-Functional Theory (DFT) is an alternative approach to Kohn-Sham density-Functional Theory. The strategy of range-separated density-Functional Theory consists in separating the Coulomb electron-electron interaction into long-range and short-range components and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-Functional approximation. Among the advantages of using many-body methods for the long-range part of the electron-electron interaction is that they are much less sensitive to the one-electron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of range-separated density-Functional Theory. We study the convergence of the partial-wave expansion of the long-range wave function near the electron-electron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum L for the long-range wave func...
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basis convergence of range separated density Functional Theory
Journal of Chemical Physics, 2015Co-Authors: Odile Franck, Bastien Mussard, Julien Toulouse, Eleonora LuppiAbstract:Range-separated density-Functional Theory (DFT) is an alternative approach to Kohn-Sham density-Functional Theory. The strategy of range-separated density-Functional Theory consists in separating the Coulomb electron-electron interaction into long-range and short-range components and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-Functional approximation. Among the advantages of using many-body methods for the long-range part of the electron-electron interaction is that they are much less sensitive to the one-electron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of range-separated density-Functional Theory. We study the convergence of the partial-wave expansion of the long-range wave function near the electron-electron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum L for the long-range wave function, whereas it is polynomial for the case of the Coulomb interaction. We also study the convergence of the long-range second-order Moller-Plesset correlation energy of four systems (He, Ne, N2, and H2O) with cardinal number X of the Dunning basis sets cc − p(C)V XZ and find that the error in the correlation energy is best fitted by an exponential in X. This leads us to propose a three-point complete-basis-set extrapolation scheme for range-separated density-Functional Theory based on an exponential formula.
