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E J Baerends - One of the best experts on this subject based on the ideXlab platform.
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the kohn sham gap the fundamental gap and the optical gap the physical meaning of occupied and virtual kohn sham Orbital energies
Physical Chemistry Chemical Physics, 2013Co-Authors: O V Gritsenko, E J Baerends, R Van Der MeerAbstract:A number of consequences of the presence of the exchange–correlation hole potential in the Kohn–Sham potential are elucidated. One consequence is that the HOMO–LUMO Orbital energy difference in the KS-DFT model (the KS gap) is not “underestimated” or even “wrong”, but that it is physically expected to be an approximation to the excitation energy if electrons and holes are close, and numerically proves to be so rather accurately. It is physically not an approximation to the difference between ionization energy and electron affinity I − A (fundamental gap or chemical hardness) and also numerically differs considerably from this quantity. The KS virtual Orbitals do not possess the notorious diffuseness of the Hartree–Fock virtual Orbitals, they often describe excited states much more closely as simple Orbital transitions. The Hartree–Fock model does yield an approximation to I − A as the HOMO–LUMO Orbital energy difference (in Koopmans' frozen Orbital approximation), if the anion is bound, which is often not the case. We stress the spurious nature of HF LUMOs if the Orbital energy is positive. One may prefer Hartree–Fock, or mix Hartree–Fock and (approximate) KS operators to obtain a HOMO–LUMO gap as a Koopmans' approximation to I − A (in cases where A exists). That is a different one-electron model, which exists in its own right. But it is not an “improvement” of the KS model, it necessarily deteriorates the (approximate) excitation energy property of the KS gap in molecules, and deteriorates the good shape of the KS virtual Orbitals.
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physical interpretation and evaluation of the kohn sham and dyson components of the epsilon i relations between the kohn sham Orbital energies and the ionization potentials
Journal of Chemical Physics, 2003Co-Authors: O V Gritsenko, B Braida, E J BaerendsAbstract:Theoretical and numerical insight is gained into the e–I relations between the Kohn–Sham Orbital energies ei and relaxed vertical ionization potentials (VIPs) Ij, which provide an analog of Koopmans’ theorem for density functional theory. The Kohn–Sham Orbital energy ei has as leading term −niIi−∑j∈Ωs(i)njIj, where Ii is the primary VIP for ionization (φi)−1 with spectroscopic factor (proportional to the intensity in the photoelectron spectrum) ni close to 1, and the set Ωs(i) contains the VIPs Ij that are satellites to the (φi)−1 ionization, with small but non-negligible nj. In addition to this “average spectroscopic structure” of the ei there is an electron-shell step structure in ei from the contribution of the response potential vresp. Accurate KS calculations for prototype second- and third-row closed-shell molecules yield valence Orbital energies −ei, which correspond closely to the experimental VIPs, with an average deviation of 0.08 eV. The theoretical relations are numerically investigated in cal...
R Van Der Meer - One of the best experts on this subject based on the ideXlab platform.
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the kohn sham gap the fundamental gap and the optical gap the physical meaning of occupied and virtual kohn sham Orbital energies
Physical Chemistry Chemical Physics, 2013Co-Authors: O V Gritsenko, E J Baerends, R Van Der MeerAbstract:A number of consequences of the presence of the exchange–correlation hole potential in the Kohn–Sham potential are elucidated. One consequence is that the HOMO–LUMO Orbital energy difference in the KS-DFT model (the KS gap) is not “underestimated” or even “wrong”, but that it is physically expected to be an approximation to the excitation energy if electrons and holes are close, and numerically proves to be so rather accurately. It is physically not an approximation to the difference between ionization energy and electron affinity I − A (fundamental gap or chemical hardness) and also numerically differs considerably from this quantity. The KS virtual Orbitals do not possess the notorious diffuseness of the Hartree–Fock virtual Orbitals, they often describe excited states much more closely as simple Orbital transitions. The Hartree–Fock model does yield an approximation to I − A as the HOMO–LUMO Orbital energy difference (in Koopmans' frozen Orbital approximation), if the anion is bound, which is often not the case. We stress the spurious nature of HF LUMOs if the Orbital energy is positive. One may prefer Hartree–Fock, or mix Hartree–Fock and (approximate) KS operators to obtain a HOMO–LUMO gap as a Koopmans' approximation to I − A (in cases where A exists). That is a different one-electron model, which exists in its own right. But it is not an “improvement” of the KS model, it necessarily deteriorates the (approximate) excitation energy property of the KS gap in molecules, and deteriorates the good shape of the KS virtual Orbitals.
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The Kohn–Sham gap, the fundamental gap and the optical gap: the physical meaning of occupied and virtual Kohn–Sham Orbital energies
Physical Chemistry Chemical Physics, 2013Co-Authors: Evert Jan Baerends, Oleg V. Gritsenko, R Van Der MeerAbstract:A number of consequences of the presence of the exchange–correlation hole potential in the Kohn–Sham potential are elucidated. One consequence is that the HOMO–LUMO Orbital energy difference in the KS-DFT model (the KS gap) is not “underestimated” or even “wrong”, but that it is physically expected to be an approximation to the excitation energy if electrons and holes are close, and numerically proves to be so rather accurately. It is physically not an approximation to the difference between ionization energy and electron affinity I − A (fundamental gap or chemical hardness) and also numerically differs considerably from this quantity. The KS virtual Orbitals do not possess the notorious diffuseness of the Hartree–Fock virtual Orbitals, they often describe excited states much more closely as simple Orbital transitions. The Hartree–Fock model does yield an approximation to I − A as the HOMO–LUMO Orbital energy difference (in Koopmans' frozen Orbital approximation), if the anion is bound, which is often not the case. We stress the spurious nature of HF LUMOs if the Orbital energy is positive. One may prefer Hartree–Fock, or mix Hartree–Fock and (approximate) KS operators to obtain a HOMO–LUMO gap as a Koopmans' approximation to I − A (in cases where A exists). That is a different one-electron model, which exists in its own right. But it is not an “improvement” of the KS model, it necessarily deteriorates the (approximate) excitation energy property of the KS gap in molecules, and deteriorates the good shape of the KS virtual Orbitals.
Evert Jan Baerends - One of the best experts on this subject based on the ideXlab platform.
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The Kohn–Sham gap, the fundamental gap and the optical gap: the physical meaning of occupied and virtual Kohn–Sham Orbital energies
Physical Chemistry Chemical Physics, 2013Co-Authors: Evert Jan Baerends, Oleg V. Gritsenko, R Van Der MeerAbstract:A number of consequences of the presence of the exchange–correlation hole potential in the Kohn–Sham potential are elucidated. One consequence is that the HOMO–LUMO Orbital energy difference in the KS-DFT model (the KS gap) is not “underestimated” or even “wrong”, but that it is physically expected to be an approximation to the excitation energy if electrons and holes are close, and numerically proves to be so rather accurately. It is physically not an approximation to the difference between ionization energy and electron affinity I − A (fundamental gap or chemical hardness) and also numerically differs considerably from this quantity. The KS virtual Orbitals do not possess the notorious diffuseness of the Hartree–Fock virtual Orbitals, they often describe excited states much more closely as simple Orbital transitions. The Hartree–Fock model does yield an approximation to I − A as the HOMO–LUMO Orbital energy difference (in Koopmans' frozen Orbital approximation), if the anion is bound, which is often not the case. We stress the spurious nature of HF LUMOs if the Orbital energy is positive. One may prefer Hartree–Fock, or mix Hartree–Fock and (approximate) KS operators to obtain a HOMO–LUMO gap as a Koopmans' approximation to I − A (in cases where A exists). That is a different one-electron model, which exists in its own right. But it is not an “improvement” of the KS model, it necessarily deteriorates the (approximate) excitation energy property of the KS gap in molecules, and deteriorates the good shape of the KS virtual Orbitals.
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The analog of Koopmans' theorem for virtual Kohn-Sham Orbital energies
Canadian Journal of Chemistry, 2009Co-Authors: Oleg Gritsenkoo. Gritsenko, Evert Jan BaerendsAbstract:An analog of Koopmans’ theorem is formulated for the energies, ea, of virtual Kohn–Sham (KS) molecular Orbitals (MOs) from the requirement that the KS theory provides, in principle, not only the ex...
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interpretation of the kohn sham Orbital energies as approximate vertical ionization potentials
Journal of Chemical Physics, 2002Co-Authors: Delano P Chong, O V Gritsenko, Evert Jan BaerendsAbstract:Theoretical analysis and results of calculations are put forward to interpret the energies −ek of the occupied Kohn–Sham (KS) Orbitals as approximate but rather accurate relaxed vertical ionization potentials (VIPs) Ik. Exact relations between ek and Ik are established with a set of linear equations for the ek, which are expressed through Ik and the matrix elements ekresp of a component of the KS exchange-correlation (xc) potential vxc, the response potential vresp. Although −Ik will be a leading contribution to ek, other Ij≠k do enter through coupling terms which are determined by the overlaps between the densities of the KS Orbitals as well as by overlaps between the KS and Dyson Orbital densities. The Orbital energies obtained with “exact” KS potentials are compared with the experimental VIPs of the molecules N2, CO, HF, and H2O. Very good agreement between the accurate −ek of the outer valence KS Orbitals and the corresponding VIPs is established. The average difference, approaching 0.1 eV, is about a...
O V Gritsenko - One of the best experts on this subject based on the ideXlab platform.
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the kohn sham gap the fundamental gap and the optical gap the physical meaning of occupied and virtual kohn sham Orbital energies
Physical Chemistry Chemical Physics, 2013Co-Authors: O V Gritsenko, E J Baerends, R Van Der MeerAbstract:A number of consequences of the presence of the exchange–correlation hole potential in the Kohn–Sham potential are elucidated. One consequence is that the HOMO–LUMO Orbital energy difference in the KS-DFT model (the KS gap) is not “underestimated” or even “wrong”, but that it is physically expected to be an approximation to the excitation energy if electrons and holes are close, and numerically proves to be so rather accurately. It is physically not an approximation to the difference between ionization energy and electron affinity I − A (fundamental gap or chemical hardness) and also numerically differs considerably from this quantity. The KS virtual Orbitals do not possess the notorious diffuseness of the Hartree–Fock virtual Orbitals, they often describe excited states much more closely as simple Orbital transitions. The Hartree–Fock model does yield an approximation to I − A as the HOMO–LUMO Orbital energy difference (in Koopmans' frozen Orbital approximation), if the anion is bound, which is often not the case. We stress the spurious nature of HF LUMOs if the Orbital energy is positive. One may prefer Hartree–Fock, or mix Hartree–Fock and (approximate) KS operators to obtain a HOMO–LUMO gap as a Koopmans' approximation to I − A (in cases where A exists). That is a different one-electron model, which exists in its own right. But it is not an “improvement” of the KS model, it necessarily deteriorates the (approximate) excitation energy property of the KS gap in molecules, and deteriorates the good shape of the KS virtual Orbitals.
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physical interpretation and evaluation of the kohn sham and dyson components of the epsilon i relations between the kohn sham Orbital energies and the ionization potentials
Journal of Chemical Physics, 2003Co-Authors: O V Gritsenko, B Braida, E J BaerendsAbstract:Theoretical and numerical insight is gained into the e–I relations between the Kohn–Sham Orbital energies ei and relaxed vertical ionization potentials (VIPs) Ij, which provide an analog of Koopmans’ theorem for density functional theory. The Kohn–Sham Orbital energy ei has as leading term −niIi−∑j∈Ωs(i)njIj, where Ii is the primary VIP for ionization (φi)−1 with spectroscopic factor (proportional to the intensity in the photoelectron spectrum) ni close to 1, and the set Ωs(i) contains the VIPs Ij that are satellites to the (φi)−1 ionization, with small but non-negligible nj. In addition to this “average spectroscopic structure” of the ei there is an electron-shell step structure in ei from the contribution of the response potential vresp. Accurate KS calculations for prototype second- and third-row closed-shell molecules yield valence Orbital energies −ei, which correspond closely to the experimental VIPs, with an average deviation of 0.08 eV. The theoretical relations are numerically investigated in cal...
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interpretation of the kohn sham Orbital energies as approximate vertical ionization potentials
Journal of Chemical Physics, 2002Co-Authors: Delano P Chong, O V Gritsenko, Evert Jan BaerendsAbstract:Theoretical analysis and results of calculations are put forward to interpret the energies −ek of the occupied Kohn–Sham (KS) Orbitals as approximate but rather accurate relaxed vertical ionization potentials (VIPs) Ik. Exact relations between ek and Ik are established with a set of linear equations for the ek, which are expressed through Ik and the matrix elements ekresp of a component of the KS exchange-correlation (xc) potential vxc, the response potential vresp. Although −Ik will be a leading contribution to ek, other Ij≠k do enter through coupling terms which are determined by the overlaps between the densities of the KS Orbitals as well as by overlaps between the KS and Dyson Orbital densities. The Orbital energies obtained with “exact” KS potentials are compared with the experimental VIPs of the molecules N2, CO, HF, and H2O. Very good agreement between the accurate −ek of the outer valence KS Orbitals and the corresponding VIPs is established. The average difference, approaching 0.1 eV, is about a...
Gustavo E. Scuseria - One of the best experts on this subject based on the ideXlab platform.
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self consistent generalized kohn sham local hybrid functionals of screened exchange combining local and range separated hybridization
Journal of Chemical Physics, 2008Co-Authors: Benjamin G. Janesko, Aliaksandr V Krukau, Gustavo E. ScuseriaAbstract:We present local hybrid functionals that incorporate a position-dependent admixture of short-range (screened) nonlocal exact [Hartree-Fock-type (HF)] exchange. We test two limiting cases: screened local hybrids with no long-range HF exchange and long-range-corrected local hybrids with 100% long-range HF exchange. Long-range-corrected local hybrids provide the exact asymptotic exchange-correlation potential in finite systems, while screened local hybrids avoid the problems inherent to long-range HF exchange in metals and small-bandgap systems. We treat these functionals self-consistently using the nonlocal exchange potential constructed from Kohn-Sham Orbital derivatives. Generalized Kohn-Sham calculations with screened and long-range-corrected local hybrids can provide accurate molecular thermochemistry and kinetics, comparable to existing local hybrids of full-range exchange. Generalized Kohn-Sham calculations with existing full-range local hybrids provide results consistent with previous non-self-consistent and “localized local hybrid” calculations. These new functionals appear to provide a promising extension of existing local and range-separated hybrids.
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climbing the density functional ladder nonempirical meta generalized gradient approximation designed for molecules and solids
Physical Review Letters, 2003Co-Authors: Jianmin Tao, John P Perdew, Viktor N Staroverov, Gustavo E. ScuseriaAbstract:The electron density, its gradient, and the Kohn-Sham Orbital kinetic energy density are the local ingredients of a meta-generalized gradient approximation (meta-GGA). We construct a meta-GGA density functional for the exchange-correlation energy that satisfies exact constraints without empirical parameters. The exchange and correlation terms respect two paradigms: one- or two-electron densities and slowly varying densities, and so describe both molecules and solids with high accuracy, as shown by extensive numerical tests. This functional completes the third rung of "Jacob's ladder" of approximations, above the local spin density and GGA rungs.
