Interpretation of the Kohn–Sham orbital energies as approximate vertical ionization potentials (original) (raw)
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The Journal of Chemical Physics, 2003
Theoretical and numerical insight is gained into the ⑀-I relations between the Kohn-Sham orbital energies ⑀ i and relaxed vertical ionization potentials ͑VIPs͒ I j , which provide an analog of Koopmans' theorem for density functional theory. The Kohn-Sham orbital energy ⑀ i has as leading term Ϫn i I i Ϫ ͚ j⍀ s (i) n j I j , where I i is the primary VIP for ionization (i) Ϫ1 with spectroscopic factor ͑proportional to the intensity in the photoelectron spectrum͒ n i close to 1, and the set ⍀ s (i) contains the VIPs I j that are satellites to the (i) Ϫ1 ionization, with small but non-negligible n j. In addition to this ''average spectroscopic structure'' of the ⑀ i there is an electron-shell step structure in ⑀ i from the contribution of the response potential v resp. Accurate KS calculations for prototype second-and third-row closed-shell molecules yield valence orbital energies Ϫ⑀ i , which correspond closely to the experimental VIPs, with an average deviation of 0.08 eV. The theoretical relations are numerically investigated in calculations of the components of the ⑀-I relations for the H 2 molecule, and for the molecules CO, HF, H 2 O, HCN. The derivation of the ⑀-I relations employs the Dyson orbitals ͑the n i are their norms͒. A connection is made between the KS and Dyson orbital theories, allowing the spin-unrestricted KS xc potential to be expressed with a statistical average of individual xc potentials for the Dyson spin-orbitals as leading term. Additional terms are the correction v c,kin, due to the correlation kinetic effect, and the ''response'' v resp, , related to the correction to the energy of (NϪ1) electrons due to the correlation with the reference electron.
Zeitschrift für Physikalische Chemie, 2003
In the present work we study the properties of Kohn-Sham orbitals used in subsequent CI methods for the computation of electronic excitation energies in terms of orbital relaxation, static and dynamical correlation effects. As model systems, we use the water and the ethene molecule. As sets of orbitals, we use orbitals from an effective exact exchange Kohn-Sham method, the localized Hartree-Fock (LHF) method, as well as BLYP and HF orbitals. Our study shows that the use of LHF orbitals leads to negligible static correlation effects and thus facilitates assignments of excitation spectra, but it also shows that the remaining correlation contributions have to be taken into account carefully since error cancellation is only found in some fortitious cases. The comparison of LHF and BLYP orbitals shows that the BLYP orbitals are less suited for the description of the cationic system and as a consequence for the computation of Rydberg states.
International Journal of Quantum Chemistry, 1997
An approximation scheme was developed for the Kohn᎐Sham exchange᎐correlation potential v , making use of a partitioning of v into a long-range screening v and xc x c scr a short-range response v component. For the response part, a model v mod was used, res p res p which represents v as weighted orbital density contributions, the weights being res p determined by the orbital energies. v mod possesses the proper short-range behavior and res p the atomic-shell stepped structure characteristic for v . For the screening part, two res p model potentials v mod were used, one with the accurate Slater potential; the other one scr Ž . with the generalized gradient approximation GGA for the exchange part. Both use the GGA for the Coulomb correlation contribution to v . The scheme provides an adequate scr approximation to v in the outer-valence region with both the proper asymptotics and xc a rather accurate estimate of the ionization potential from the highest one-electron energy and a reasonable estimate of atomic E and total energies E .ᮊ 1997 John Wiley & xc tot
Journal of Electron Spectroscopy and Related Phenomena, 2009
In this paper, ionization energies of gas-phase atoms and molecules are calculated by energy-difference method and by approximate transition-state models with density functional theory (DFT). To determine the best functionals for ionization energies, we first study the H to Ar atoms. An approximation is used in which the electron density is first obtained from Kohn-Sham computations with an exchangecorrelation potential V xc known as statistical average of orbital potentials (SAOP), after which the energy is computed from that density with 59 different exchange-correlation energy functionals E xc . For the 18 atoms, the best E xc functional providing an average absolute deviation (AAD) of only 0.110 eV is one known as the Krieger-Chen-Iafrate-Savin functional modified by Krieger, Chen, Iafrate, and Kurth, if one uses the spin-polarized spherical atom description. On the other hand, if one imposes the condition of integer-electrons, the best functional is the Becke 1997 functional modified by Wilson, Bradley, and Tozer, with an AAD of 0.107 eV, while several other functionals perform almost as well. For molecules, we can achieve an accuracy of AAD = 0.21 eV for valence VIPs of nonperhalo molecules with E(V xc = SAOP;PBE0) using integer-electron description. For perhalo molecules our best approach is E(V xc from either E xc or SAOP;mPW1PW) with full symmetry to obtain an AAD = 0.24 eV.
Calculations of valence electron binding energies using Kohn–Sham theory and transition potentials
Journal of Electron Spectroscopy and Related Phenomena, 2000
Motivated by the success in computing X-ray photoelectron binding energies and chemical shifts in the core region we apply the Kohn-Sham density functional and transition potential methodology to calculations of binding energies in the valence electron region. Accurate predictions of binding energies over a large energy interval are obtained for a set of molecules for which the quasi-particle approximation holds, but which still have been considered notoriously difficult. The accuracy is found to be a few tenths of an eV in the outermost valence region, slightly poorer in the intermediate region, and seems to be maintained with increasing size of the system.
Contribution of correlation and relaxation to generalized overlaps for outer-valence ionization
Chemical Physics, 1989
In the generalized overlap approximation (GOA) and under appropriate experimental conditions, the electron momentum spectroscopy (EMS) triple differential cross section is proportional to the spherically averaged momentum distribution (MD) of the generalized overlap (GO) of the electronic wavefunctions of a parent molecule and its daughter cation. The GO is usually further approximated by the target Hartree-Fock approximation (THFA) which treats the parent wavefunction as uncorrelated. Improvements in EMS resolution have made it increasingly desirable to go beyond the THFA. This necessarily means taking parent correlation into account, but the relative importance of relaxation and ion correlation is not immediately obvious. In the present paper, finite-order nondegenerate perturbation theory (FOND PT) is used to derive explicit correction terms for the THFA. Although our result is equivalent to the previous formula of Pickup and Goscinski, our formulation is an improvement because it is easily interpreted in terms of wavefunctions. This makes the correction terms for the frozen orbital and target Hartree-Fock approximations particularly obvious. These correction terms are used to examine the relative importance of relaxation and ion correlation for outer valence ionization for a certain class of ion states which we call lone symmetry states. This symmetry restriction allows us to simplify our calculations ofgeneralized overlaps (GOs) by ignoring second-order FOND PT contributions to the ion wavefunction. Although we find ion correlation to be of negligible importance when calculating GOs to second order in FOND PT for ionization out of the lb, and lb2 orbitals of water and out of the L bonds of acetylene and ethylene, we find that these are isolated cases. In general, both relaxation and ion correlation are found to be significant for the calculation of GOs. Our work should make it quite clear that GOs are really neither purely an "initial-state" nor purely a "final-state" phenomenon, but rather involve contributions from both states. This bodes ill for the success of initial-state approximations for calculating GOs unless these approximations can in some way account for both relaxation and final-state correlation.
Journal of chemical theory and computation, 2014
In recent years, several benchmark studies on the performance of large sets of functionals in time-dependent density functional theory (TDDFT) calculations of excitation energies have been performed. The tested functionals do not approximate exact Kohn-Sham orbitals and orbital energies closely. We highlight the advantages of (close to) exact Kohn-Sham orbitals and orbital energies for a simple description, very often as just a single orbital-to-orbital transition, of molecular excitations. Benchmark calculations are performed for the statistical average of orbital potentials (SAOP) functional for the potential [J. Chem. Phys. 2000, 112, 1344; 2001, 114, 652], which approximates the true Kohn-Sham potential much better than LDA, GGA, mGGA, and hybrid potentials do. An accurate Kohn-Sham potential does not only perform satisfactorily for calculated vertical excitation energies of both valence and Rydberg transitions but also exhibits appealing properties of the KS orbitals including ...
Core ionization potentials from self-interaction corrected Kohn-Sham orbital energies
The Journal of Chemical Physics, 2007
We propose a simple self-interaction correction to Kohn-Sham orbital energies in order to apply ground state Kohn-Sham density functional theory to accurate predictions of core electron binding energies and chemical shifts. The proposition is explored through a series of calculations of organic compounds of different sizes and types. Comparison is made versus experiment and the "⌬Kohn-Sham" method employing separate state optimizations of the ground and core hole states, with the use of the B3LYP functional and different basis sets. A parameter ␣ is introduced for a best fitting of computed and experimental ionization potentials. It is found that internal parametrizations in terms of basis set expansions can be well controlled. With a unique ␣ = 0.72 and basis set larger than 6-31G, the core ionization energies ͑IPs͒ of the self-interaction corrected Kohn-Sham calculations fit quite well to the experimental values. Hence, self-interaction corrected Kohn-Sham calculations seem to provide a promising tool for core IPs that combines accuracy and efficiency.