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John P Perdew - One of the best experts on this subject based on the ideXlab platform.
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when does static correlation scale to the High Density Limit as exchange does
Journal of Molecular Structure-theochem, 2010Co-Authors: John P Perdew, Jianmin TaoAbstract:Abstract In Density functional theory, the exchange–correlation energy is usually decomposed as the sum of exchange and correlation contributions. In the absence of static correlation, this decomposition can be made by uniform coordinate scaling to the High-Density Limit, because the exchange part dominates in this Limit. The estimate of static correlation provided by semilocal, global hybrid, and some more-advanced approximate exchange–correlation functionals scales up as exchange does in this Limit. Here we argue that a proper estimate of static correlation should scale up in magnitude less strongly than exchange in the High-Density Limit, except in special circumstances. Such a special circumstance can occur when there is an exact degeneracy at the non-interacting Fermi level, or when another Limit is taken first, in which a degeneracy develops between occupied and unoccupied Kohn–Sham orbital energies. Examples of the latter case are the H 2 molecule as the bond length is stretched to infinity, and the four-electron atomic ion as the nuclear charge tends to infinity.
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correlation energy of the uniform electron gas from an interpolation between High and low Density Limits
Physical Review B, 2010Co-Authors: Jianwei Sun, John P Perdew, Michael SeidlAbstract:We show that known or knowable information about the High-$({r}_{s}\ensuremath{\rightarrow}0)$ and low-Density $({r}_{s}\ensuremath{\rightarrow}\ensuremath{\infty})$ asymptotes can be used to predict the correlation energy per electron, ${e}_{c}({r}_{s},\ensuremath{\zeta})$, of the three-dimensional uniform gas over the whole range of the Density parameter $(0\ensuremath{\le}{r}_{s}l\ensuremath{\infty})$ and relative spin polarization $(0\ensuremath{\le}|\ensuremath{\zeta}|\ensuremath{\le}1)$, without quantum Monte Carlo or other input. For $\ensuremath{\zeta}=0$, the High-Density Limit through order ${r}_{s}$ is known exactly from many-body perturbation theory, and for all $\ensuremath{\zeta}$, the low-Density Limit through order $1/{r}_{s}^{2}$ is known accurately from a simple, intuitive, and accurate model. We propose a single interpolation formula with the expected analytic structure to all orders in both Limits, and use it to predict ${e}_{c}({r}_{s},0)$ in excellent agreement with quantum Monte Carlo data. For $|\ensuremath{\zeta}|g0$, we derive the $\ensuremath{\zeta}$ dependence of the coefficient ${a}_{1}(\ensuremath{\zeta})$ of the ${r}_{s}\text{ }\text{ln}\text{ }{r}_{s}$ term, previously known only for $|\ensuremath{\zeta}|=0$ and 1. For ${b}_{1}(\ensuremath{\zeta})$, the coefficient of the ${r}_{s}$ term (not yet derived for $\ensuremath{\zeta}\ensuremath{\ne}0$), we approximately extend the known ${b}_{1}(0)$ by using a simplification of the available quantum Monte Carlo information that replaces the second-order transition over $50l{r}_{s}l100$ by a sudden transition to full spin polarization at ${r}_{s}=75$.
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energy densities of exchange and correlation in the slowly varying region of the airy gas
2009Co-Authors: John P Perdew, Lucian A Constantin, Adrienn RuzsinszkyAbstract:In Kohn–Sham theory, where the integrated exchange and correlation energies are functionals of the electron Density, several recent approximate functionals make use of the energy densities of exchange and correlation for nonuniform reference systems or of exchange for the real system of interest. A relevant case in which to examine these energy densities is the Airy gas. Here we evaluate the conventional exact-exchange energy Density from the occupied orbitals, and the conventional correlation energy Density within the random phase approximation using the occupied and unoccupied orbitals. We find, as expected, that the exchange energy Density in the region of slowly varying electron Density demonstrates a mostly negative small correction to the local Density approximation (LDA) but has no second-order Density-gradient expansion (although the integrated exchange energy of a finite system has one). We also find, as expected, that the exchange-correlation energy Density demonstrates a positive small correction to the LDA in the region of High and slowly varying electron Density. It too appears to have no second-order Density-gradient expansion. An appendix shows that a slowly varying Density, scaled uniformly to the High-Density Limit in which exchange dominates, remains slowly varying only for exchange and not for correlation.
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High Density Limit of the perdew burke ernzerhof generalized gradient approximation and related Density functionals
Physical Review A, 2006Co-Authors: Viktor N Staroverov, John P Perdew, Gustavo E Scuseria, Ernest R Davidson, Jacob KatrielAbstract:We point out a simplifying but mildly inconsistent assumption of the Perdew-Burke-Ernzerhof (PBE) correlation functional, which should be corrected when evaluating the High-Density Limit of the PBE energy for nonsinglet systems under uniform Density scaling. The discussion also concerns High-Density Limits of all Density functionals that use PBE as an ingredient, including the Tao-Perdew-Staroverov-Scuseria (TPSS) approximation. We revisit the nonrelativistic correlation energies of isoelectronic atomic ions in the Limit of infinite nuclear charge and explain small discrepancies between the PBE and TPSS values of these Limits existing in the literature.
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spin scaling of the electron gas correlation energy in the High Density Limit
Physical Review B, 1991Co-Authors: Yue Wang, John P PerdewAbstract:Expression de l'energie de correlation de l'etat fondamental par particule dans un gaz d'electrons uniformes avec des densites de spin n↑ et n↓. Etablissement d'une expression analytique pour le facteur d'echelle de spin dans la Limite de haute densite r s →0
Peter Gill - One of the best experts on this subject based on the ideXlab platform.
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leading order behavior of the correlation energy in the uniform electron gas
International Journal of Quantum Chemistry, 2012Co-Authors: Pierrefrancois Loos, Peter GillAbstract:We show that, in the High-Density Limit, restricted Moller-Plesset (RMP) perturbation theory yields E (2) RMP = π
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leading order behavior of the correlation energy in the uniform electron gas
arXiv: Strongly Correlated Electrons, 2011Co-Authors: Pierrefrancois Loos, Peter GillAbstract:We show that, in the High-Density Limit, restricted M{\o}ller-Plesset (RMP) perturbation theory yields $E_{\text{RMP}}^{(2)} = \pi^{-2}(1-\ln 2) \ln r_s + O(r_s^0)$ for the correlation energy per electron in the uniform electron gas, where $r_s$ is the Seitz radius. This contradicts an earlier derivation which yielded $E_{\text{RMP}}^{(2)} = O(\ln|\ln r_s|)$. The reason for the discrepancy is explained.
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correlation energy of two electrons in the High Density Limit
arXiv: Other Condensed Matter, 2010Co-Authors: Pierrefrancois Loos, Peter GillAbstract:We consider the High-Density-Limit correlation energy $\Ec$ in $D \ge 2$ dimensions for the $^1S$ ground states of three two-electron systems: helium (in which the electrons move in a Coulombic field), spherium (in which they move on the surface of a sphere), and hookium (in which they move in a quadratic potential). We find that the $\Ec$ values are strikingly similar, depending strongly on $D$ but only weakly on the external potential. We conjecture that, for large $D$, the Limiting correlation energy $\Ec \sim -\delta^2/8$ in any confining external potential, where $\delta = 1/(D-1)$.
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correlation energy of two electrons in the High Density Limit
Journal of Chemical Physics, 2009Co-Authors: Pierrefrancois Loos, Peter GillAbstract:P.M.W.G. thanks the APAC Merit Allocation Scheme for a grant of supercomputer time, and the Australian Research Council Grant Nos. DP0664466 and DP0771978 for funding.
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electron correlation in hooke s law atom in the High Density Limit
Journal of Chemical Physics, 2005Co-Authors: Peter Gill, Darragh P OneillAbstract:The authors also thank Professor John D. Morgan III for advice concerning Eq. s1d and both EPSRC sGrant No. GR/R81121d and the Research School of Chemistry at ANU for funding.
P R Young - One of the best experts on this subject based on the ideXlab platform.
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High precision Density measurements in the solar corona i analysis methods and results for fe xii and fe xiii
Astronomy and Astrophysics, 2009Co-Authors: P R Young, T Watanabe, Hirohisa Hara, J T MariskaAbstract:Aims. The EUV Imaging Spectrometer (EIS) instrument on board the Hinode satellite has access to some of the best coronal Density diagnostics, and the High sensitivity of the instrument now allows electron number Density, Ne, measurements to an unprecedented precision of up to ±5% in active regions. This paper gives a thorough overview of data analysis issues for the best diagnostics of Fe xii and Fe xiii and assesses the accuracy of the measurements. Methods. Two Density diagnostics each from Fe xii (λ186.88/λ195.12 and λ196.64/λ195.12) and Fe xiii (λ196.54/λ202.04 and λ203.82/λ202.04) are analysed in two active region datasets from 2007 May 3 and 6 that yield densities in the range 8.5 ≤ log (Ne/cm −3 ) ≤ 11.0. The densities are derived using v5.2 of the CHIANTI atomic database. Blending, line fitting, and instrumental issues are discussed, and line fit parameters presented. Results. The Fe xii and Fe xiii diagnostics show broadly the same trend in Density across the active region, consistent with their similar temperatures of formation. However, the High precision of the EIS measurements demonstrates significant discrepancies of up to 0.5 dex in derived log Ne values, with Fe xii always giving Higher densities than Fe xiii. The discrepancies may partly be due to real physical differences between the emitting regions of the two plasmas, but the dominant factor lies in the atomic models of the two ions. Two specific problems are identified for Fe xii λ196.64 and Fe xiii λ203.82: the former is found to be underestimated in strength by the CHIANTI atomic model, while the High-Density Limit of the λ203.82/λ202.04 ratio appears to be inaccurate in the CHIANTI atomic model. The small grating tilt of the EIS instrument is found to be very significant when deriving densities from emission lines separated by more than a few angstroms. Revised wavelengths of 196.518 ± 0.003 A and 196.647 ± 0.003 A are suggested for the Fe xiii λ196.54 and Fe xii λ196.64 lines, respectively.
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High precision Density measurements in the solar corona i analysis methods and results for fe xii and fe xiii
arXiv: Astrophysics, 2008Co-Authors: P R Young, T Watanabe, Hirohisa Hara, J T MariskaAbstract:The EUV Imaging Spectrometer (EIS) instrument on board the Hinode satellite has access to some of the best coronal Density diagnostics and the High sensitivity of the instrument now allows electron number Density, N_e, measurements to an unprecedented precision of up to +/-5 % in active regions. This paper gives a thorough overview of data analysis issues for the best diagnostics of Fe XII and Fe XIII and assesses the accuracy of the measurements. Two Density diagnostics each from Fe XII (186.88/195.12 and 196.64/195.12) and Fe XIII (196.54/202.04 and 203.82/202.04) are analysed in two active region data-sets from 2007 May 3 and 6 that yield densities in the range 8.5 < log N_e < 11.0. The densities are derived using v5.2 of the CHIANTI atomic database. The Fe XII and Fe XIII diagnostics show broadly the same trend in Density across the active region, consistent with their similar temperatures of formation. However the High precision of the EIS measurements demonstrates significant discrepancies of up to 0.5 dex in derived log N_e values, with Fe XII always giving Higher densities than Fe XIII. The discrepancies may partly be due to real physical differences between the emitting regions of the two plasmas, but the dominant factor lies in the atomic models of the two ions. Two specific problems are identified for Fe XII 196.64 and Fe XIII 203.82: the former is found to be under-estimated in strength by the CHIANTI atomic model, while the High Density Limit of the 203.82/202.04 is suggested to be inaccurate in the CHIANTI atomic model. The small grating tilt of the EIS instrument is found to be very significant when deriving densities from emission lines separated by more than a few angstroms.
David Mitrouskas - One of the best experts on this subject based on the ideXlab platform.
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High Density Limit of the fermi polaron with infinite mass
Letters in Mathematical Physics, 2019Co-Authors: Ulrich Linden, David MitrouskasAbstract:We analyze the ground state energy for N identical fermions in a two-dimensional box of volume $$L^2$$ interacting with an external point scatterer. Since the point scatterer can be considered as an impurity particle of infinite mass, this system is a Limit case of the Fermi polaron. We prove that its ground state energy in the Limit of High Density $$N/L^2\gg 1$$ is given by the polaron energy. The polaron energy is an energy estimate based on trial states up to first order in particle-hole expansion, which was proposed by Chevy (Phys Rev A 74:063628, 2006) in the physics literature. The relative error in our result is shown to be small uniformly in L. Hence, we do not require a gap of fixed size in the spectrum of the Laplacian on the box. The strategy of our proof relies on a twofold Birman–Schwinger type argument applied to the many-particle Hamiltonian of the system.
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High Density Limit of the fermi polaron with infinite mass
arXiv: Mathematical Physics, 2018Co-Authors: Ulrich Linden, David MitrouskasAbstract:We analyze the ground state energy for $N$ identical fermions in a two-dimensional box of volume $L^2$ interacting with an external point scatterer. Since the point scatterer can be considered as an impurity particle of infinite mass, this system is a Limit case of the Fermi polaron. We prove that its ground state energy in the Limit of High Density $N/L^2 \gg 1$ is given by the polaron energy. The polaron energy is an energy estimate based on trial states up to first order in particle-hole expansion, which was proposed by F. Chevy in the physics literature. The relative error in our result is shown to be small uniformly in $L$. Hence, we do not require a gap of fixed size in the spectrum of the Laplacian on the box. The strategy of our proof relies on a twofold Birman-Schwinger type argument applied to the many-particle Hamiltonian of the system.
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Free Time Evolution of a Tracer Particle Coupled to a Fermi Gas in the High-Density Limit
Communications in Mathematical Physics, 2017Co-Authors: Maximilian Jeblick, David Mitrouskas, Sören Petrat, Peter PicklAbstract:The dynamics of a particle coupled to a dense and homogeneous ideal Fermi gas in two spatial dimensions is studied. We analyze the model for coupling parameter g = 1 (i.e., not in the weak coupling regime), and prove closeness of the time evolution to an effective dynamics for large densities of the gas and for long time scales of the order of some power of the Density. The effective dynamics is generated by the free Hamiltonian with a large but constant energy shift which is given at leading order by the spatially homogeneous mean field potential of the gas particles. Here, the mean field approximation turns out to be accurate although the fluctuations of the potential around its mean value can be arbitrarily large. Our result is in contrast to a dense bosonic gas in which the free motion of a tracer particle would be disturbed already on a very short time scale. The proof is based on the use of strong phase cancellations in the deviations of the microscopic dynamics from the mean field time evolution.
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effective dynamics of two tracer particles coupled to a fermi gas in the High Density Limit
Workshop on Macroscopic Limits of Quantum Systems, 2017Co-Authors: Maximilian Jeblick, David Mitrouskas, Peter PicklAbstract:In a recent paper (Jeblick, Mitrouskas, Petrat and Pickl, Commun. Math. Phys. 356(1), 143–187 (2017) [1]), we studied the dynamics of a particle coupled to a dense and homogeneous ideal Fermi gas in two spatial dimensions. In that paper, closeness of the time evolution to an effective free dynamics for large densities of the gas was proven. The main point of interest of this result was to consider coupling constants that do not scale with the Density of the gas. In the present article, we generalize this result to a system of two tracer particles coupled to the ideal Fermi gas. Naively, one might expect this to be a trivial extension of the single particle result. But this is not the case since there is an interesting additional effect: While the dynamics of both tracer particles decouple again from the Fermi gas, there are collision processes which are not present for a single tracer particle and which lead to an effective interaction between the two tracer particles. This effective interaction is mediated through the creation and immediate annihilation of electron–hole pairs, and can thus be interpreted as a Lamb shift-type effect.
Andreas Savin - One of the best experts on this subject based on the ideXlab platform.
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Scaling relations, virial theorem, and energy densities for long-range and short-range Density functionals
International Journal of Quantum Chemistry, 2015Co-Authors: Julien Toulouse, Paola Gori-Giorgi, Andreas SavinAbstract:Decomposition of the Coulomb electron- electron interaction into a long-range and a short-range part is described within the framework of Density functional theory, deriving some scaling relations and the corresponding virial theorem. We study the behavior of the local Density approximation in the High-Density Limit for the long-range and the short-range functionals by carrying out a detailed analysis of the correlation energy of a uniform electron gas interacting via a long-range-only electron- electron repulsion. Possible definitions of exchange and correlation energy densities are discussed and clarified with some examples.
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High Density Limit of two electron systems results from the extended overhauser approach
Journal of Chemical Theory and Computation, 2007Co-Authors: Paola Gorigiorgi, Andreas SavinAbstract:The "extended Overhauser model" [Overhauser, A. W. Can. J. Phys. 1995, 73, 683] for the calculation of the spherically and system-averaged pair Density (APD) has been recently combined with the Kohn-Sham equations to yield realistic APD and correlation energies. In this work we test this approach in the High-Density (weakly correlated) Limit of the He isoelectronic series and of the Hooke's atom isoelectronic series. Unlike many of the commonly used energy functionals, the Overhauser approach yields accurate correlation energies for both series.
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the High Density Limit of two electron systems results from the extended overhauser approach
arXiv: Chemical Physics, 2007Co-Authors: Paola Gorigiorgi, Andreas SavinAbstract:The ``extended Overhauser model'' [Overhauser, Can. J. Phys. 1995, 73, 683] for the calculation of the spherically and system-averaged pair Density (APD) has been recently combined with the Kohn-Sham equations to yield realistic APD and correlation energies. In this work we test this approach in the High-Density (weakly-correlated) Limit of the He isoelectronic series and of the Hooke's atom isoelectronic series. Unlike many of the commonly used energy functionals, the Overhauser approach yields accurate correlation energies for both series.
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construction of an accurate self interaction corrected correlation energy functional based on an electron gas with a gap
1999Co-Authors: J B Krieger, Jiqiang Chen, Gerald J Iafrate, Andreas SavinAbstract:The usual starting point of any first principles construction of an approximate electron correlation energy functional EC[{no.}]s the homogeneous electron gas weakly perturbed by an external potential. To lowest non-vanishing order in the gradient of the electron Density, \( \nabla \pi \) the correlation energy Density, per electron,may be written“)as the usual local spin Density (LSD) expression, \( \varepsilon _c^{LSD}\) plus a term proportional to \( |\nabla \pi {|^2}\). When perturbation theory is employed to calculate \( \varepsilon _c^{LSD}\)the result diverges in each order of the electron-electron coupling due to the zero energy gap between states at the Fermi energy and the neighboring unoccupied states in the continuum. By employing many body perturbation theory techniques, this series may besummed in the High Density Limit to eld a finite result(3). Other numerical calculations have been employed to calculate \( \varepsilon _c^{LSD}\) for arbitrary uniform Density(4)