Exact Density Functionals for Ground‐State Energies. I. General Results

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Dispersion, static correlation, and delocalisation errors in density functional theory: An electrostatic theorem perspective J. Chem. Phys. 135, 164110 (2011) Evaluation of coupling terms between intra-and intermolecular vibrations in coarse-grained normal-mode analysis: Does a stronger acid make a stiffer hydrogen bond? J. Chem. Phys. 135, 154111 (2011) Calculating dispersion interactions using maximally localized Wannier functions J. Chem. Phys. 135, 154105 (2011) A theoretical study of Ne3 using hyperspherical coordinates and a slow variable discretization approach J. Chem. Phys. 135, 134312 (2011) Additional information on J. Chem. Phys. The frozen-density embedding ͑FDE͒ scheme ͓Wesolowski and Warshel, J. Phys. Chem. 97, 8050 ͑1993͔͒ relies on the use of approximations for the kinetic-energy component v T ͓ 1 , 2 ͔ of the embedding potential. While with approximations derived from generalized-gradient approximation kinetic-energy density functional weak interactions between subsystems such as hydrogen bonds can be described rather accurately, these approximations break down for bonds with a covalent character. Thus, to be able to directly apply the FDE scheme to subsystems connected by covalent bonds, improved approximations to v T are needed. As a first step toward this goal, we have implemented a method for the numerical calculation of accurate references for v T . We present accurate embedding potentials for a selected set of model systems, in which the subsystems are connected by hydrogen bonds of various strength ͑water dimer and F-H-F − ͒, a coordination bond ͑ammonia borane͒, and a prototypical covalent bond ͑ethane͒. These accurate potentials are analyzed and compared to those obtained from popular kinetic-energy density functionals.

Section: Theory and Computational Methodologymentioning

confidence: 99%

Accurate frozen-density embedding potentials as a first step towards a subsystem description of covalent bonds

Fux

Jacob

Neugebauer

et al. 2010

199

278

“…To rectify the above situation, KS-DFT has been extended to ensemble DFT [59,60], wherein ρ(r) is assumed to be noninteracting ensemble v s -representable, as it is associated with an ensemble of pure determinantal states of the noninteracting KS system at zero temperature. Accordingly, the orbital occupation numbers in ensemble DFT are 0, 1, and fractional (between 0 and 1) for the orbitals above, below, and at the Fermi level, respectively.…”

Section: Tao-dft a Rationale For Fractional Orbital Occupationsmentioning

confidence: 99%

Role of exact exchange in thermally-assisted-occupation density functional theory: A proposal of new hybrid schemes

Chai

2017

138

We propose hybrid schemes incorporating exact exchange into thermally-assisted-occupation density functional theory (TAO-DFT) [J.-D. Chai, J. Chem. Phys. 136, 154104 (2012)] for an improved description of nonlocal exchange effects. With a few simple modifications, global and range-separated hybrid functionals in Kohn-Sham density functional theory (KS-DFT) can be combined seamlessly with TAO-DFT. In comparison with global hybrid functionals in KS-DFT, the resulting global hybrid functionals in TAO-DFT yield promising performance for systems with strong static correlation effects (e.g., the dissociation of H 2 and N 2 , twisted ethylene, and electronic properties of linear acenes), while maintaining similar performance for systems without strong static correlation effects. Besides, a reasonably accurate description of noncovalent interactions can be efficiently achieved through the inclusion of dispersion corrections in hybrid TAO-DFT. Relative to semilocal density functionals in TAO-DFT, global hybrid functionals in TAO-DFT are generally superior in performance for a wide range of applications, such as thermochemistry, kinetics, reaction energies, and optimized geometries.

“…It has been argued [22][23][24][25] that such a potential indeed will always exist, or at least that a local potential can be constructed whose corresponding Kohn-Sham density approaches the target density arbitrarily closely. These arguments for the total density and spin-restricted Kohn-Sham potential carry over unmodified to the separate spin densities and potentials (r), where each spin potential is determined up to a constant.…”

Section: ͑23͒mentioning

confidence: 99%

The spin-unrestricted molecular Kohn–Sham solution and the analogue of Koopmans’s theorem for open-shell molecules

Gritsenko

Baerends

2004

Spin-unrestricted Kohn-Sham ͑KS͒ solutions are constructed from accurate ab initio spin densities for the prototype doublet molecules NO 2 , ClO 2 , and NF 2 with the iterative local updating procedure of van Leeuwen and Baerends ͑LB͒. A qualitative justification of the LB procedure is given with a ''strong'' form of the Hohenberg-Kohn theorem. The calculated energies i of the occupied KS spin orbitals provide numerical support to the analogue of Koopmans' theorem in spin-density functional theory. In particular, the energies Ϫ i␤ of the minor spin ͑␤͒ valence orbitals of the considered doublet molecules correspond fairly well to the experimental vertical ionization potentials ͑VIPs͒ I i 1 to the triplet cationic states. The energy Ϫ H␣ of the highest occupied ͑spin-unpaired͒ ␣ orbital is equal to the first VIP I H 0 to the singlet cationic state. In turn, the energies Ϫ i␣ of the major spin ͑␣͒ valence orbitals of the closed subshells correspond to a fifty-fifty average of the experimental VIPs I i 1 and I i 0 to the triplet and singlet states. For the Li atom we find that the exact spin densities are represented by a spin-polarized Kohn-Sham system which is not in its ground state, i.e., the orbital energy of the lowest unoccupied ␤ spin orbital is lower than that of the highest occupied ␣ spin orbital ͑''a hole below the Fermi level''͒. The addition of a magnetic field in the Ϫz direction will shift the ␤ levels up so as to restore the Aufbau principle. This is an example of the nonuniqueness of the mapping of the spin density on the KS spin-dependent potentials discussed recently in the literature. The KS potentials may no longer go to zero at infinity, and it is in general the differences s (ϱ)Ϫ i that can be interpreted as ͑averages of͒ ionization energies. In total, the present results suggest the spin-unrestricted KS theory as a natural one-electron independent-particle model for interpretation and assignment of the experimental photoelectron spectra of open-shell molecules.