Density functional theory: coverage of dynamic and non-dynamic electron correlation effects

Bond Stretching and Redox Behavior in Coinage Metal Complexes of the Dichalcogenide Dianions [(SPh2P)2CEEC(PPh2S)2]2− (E=S, Se): Diradical Character of the Dinuclear Copper(I) Complex (E=S)

“…The performance of the different density functionals in modeling singlet states with diradical character is related not only to the identity of the functional but also to the amount of exact, Hartree-Fock exchange used in its construction. [28] Calculations conducted for 5c at different theoretical levels give indirect support for diradical character in the ground state of this molecular complex. The Hartree-Fock optimized geometry shows a highly asymmetric S2Cu2 unit with a (C)SS(C) distance very close to a single bond, 2.211 Å.…”

Calculation of spin-densities within the context of density functional theory. The crucial role of the correlation functional

“…In the case of the NMR SSCCs one has to consider that calculated values depend on ͑a͒ the choice of the appropriate basis set ͑correct description of the core region͒, b͒ the inclusion of long-range electron correlation to avoid singlettriplet instabilities by using local exchange functionals, [14][15][16][17][18] ͑c͒ the correction for rotational-vibrational effects ͑especially important when the nuclei of light atoms participate in spinspin coupling͒, and ͑d͒ the consideration of environmental effects ͑specific and nonspecific solvation, cluster formation, temperature, pressure, etc.͒. We note that the data material presently available is not sufficient to clearly identify the role of equal-spin and opposite-spin correlation and the balanced description of these effects by the correlation functional.…”

“…[7][8][9][10][11][12] A necessary requirement for improving standard KohnSham ͑KS͒ DFT is the basic understanding of the electronic effects accounted for by the approximate exchangecorrelation ͑XC͒ functionals in use today. In recent work, we have made several steps in this direction by describing exchange and correlation effects included by a given XC functional with the help of suitable difference densities, [13][14][15][16] by analyzing the effect of the self-interaction error of X functionals via the X-hole [17][18][19] or separating intrinsic and external nondynamic correlation effects in BS-UDFT or other twoconfigurational DFT approaches. 20,21 In this work, we focus on the observations that atomic and molecular energies as well as molecular geometries and vibrational frequencies are reasonably described by the generalized gradient approximation ͑GGA͒/XC functional BLYP ͑Refs.…”

“…The performance of any XC functional is best assessed by ͑a͒ separating exchange and correlation description [13][14][15][16] and ͑b͒ investigating simple electronic systems for which the correlation effects can easily be identified and analyzed. For example, if one considers just atoms rather than molecules, then of the three basic electron pair correlation effects ͑left-right, angular, and in-out correlation͒ just in-out correlation remains.…”

Excitation Energies from Spin-Restricted Ensemble-Referenced Kohn−Sham Method: A State-Average Approach

“…Note that the 1 Σ u + excited state of H 2 has an ionic character, whereas the 1 Σ g + ground state possesses a covalent character. The overstabilization of ionic states can be traced back to the effect of electron self-interaction error in approximate density functionals, 24,61,62 which leads to somewhat too diffuse occupied KS orbitals. As more selfinteraction error free Hartree-Fock exchange energy is mixed into a hybrid HF/DFT functional, such as BH&HLYP, the overall effect of such an overstabilization subsides and the excitation energy to the ionic 1 Σ u + state obtained in REKS calculations improves (see Figure 2).…”