Exchange-correlation density functionals at the meta-generalised gradient approximation level typically use the Kohn-Sham orbitals as an ingredient to create the isoorbital indicator
, where
is the ...von Weizsäcker kinetic energy density and
is the kinetic energy density of the Kohn-Sham orbitals. When a magnetic field is included in the treatment, the Kohn-Sham orbitals vary with the vector-potential gauge, as does
and implicitly the exchange-correlation energy. However, it is a known result in current density functional theory that the exact exchange-correlation energy is gauge independent. Three different gauge-independent replacements for
have been proposed by other authors. Only one of these is, however, known to stay between 0 and 1. We modify one of the others, the Maximoff-Scuseria isoorbital indicator, so that it also stays between 0 and 1. We investigate the ability of the isoorbital indicators evaluated in a system with density
and paramagnetic current density
to reproduce the value of
in a system having no paramagnetic current, but the same density
. We provide the first example known to us where the Tao-Perdew isoorbital indicator goes outside of the interval from 0 to 1.
Phosphoric acid anodization (PAA) is a candidate for replacement of toxic chromates during the surface treatment of aluminum prior to gluing in the aerospace industry. During PAA, a layer of AlPO4 ...forms on top of the alumina layer. We apply density functional theory computations to investigate how the AlPO4 surface reorganizes and how it bonds to water and adhesives. As our AlPO4 model, we use the α-berlinite (0001) surface. Taking the structure of the α-quartz (0001) surface reported by Rignanese et al. (Rignanese, G.-M.; De Vita, A.; Charlier, J.-C.; Gonze, X.; Car, R., Phys. Rev. B 2000, 61, 13250–13255) as a starting point, we find that the α-berlinite surface reconstructs. The lowest energy structure for α-berlinite (0001) is found to have a buckled configuration, with three-coordinated phosphorus protruding out of the surface and a neighboring aluminum atom binding to five oxygens. Different structures for the hydrated surface AlPO4·0.25H2O are presented, of which the most stable involves hydroxylation of the aforementioned buckle and of a new phosphorus buckle, accompanied by formation of a P–Al dative bond. We report results for the adhesion of a glue fragment derived from bisphenol A to the surface. The lowest energy is found for a covalently bonded structure, mimicking the most stable hydroxylated structure. The adhesion energy of the glue increases strongly when it is covalently bonded to the surface rather than being hydrogen bonded, providing superior adhesion to the material.
We investigate the S 1 state potential energy surface of 2-pyridone dimer (2PY)2 using time-dependent density functional and coupled cluster theory. Although the ground and S 2 excited states of ...(2PY)2 have C 2h symmetry, the S 1 state shows symmetry breaking and localization of the excitation on one of the two monomers upon relaxation of the geometry. This localization is rationalized using a simple diabatic curve crossing model. As a consequence of the symmetry breaking, S 1 to S 0 transitions become optically allowed. We hypothesize that the band at 30 776 cm−1 observed in the excitation spectrum of (2PY)2 might be attributed to the S 1 state rather than the S 2 state; the S 2 state origin is predicted 3000−4000 cm−1 above the S 1 state by hybrid density functional and coupled cluster methods. Asymmetric transfer of one hydrogen atom leads to a second S 1 state minimum that can rapidly decay to the ground state. This suggests that photoinduced tautomerization of (2PY)2 occurs in a stepwise fashion, with only one hydrogen transfer taking place on the S 1 surface.
Tensile tests on Al–Mn–Si ternary alloys show that a small amount of Si increases significantly the strength compared to Al–Mn binary alloys with the same concentration of Mn. This cannot be ...explained by classical theories for multi-element substitutional solid solution hardening under the assumption of no interaction between different alloying elements. A new simplified cluster strengthening model which addresses both the chemical and size misfit effects of atom dimers is proposed this work. The binding energies and misfit of dimers were estimated by first principles atomistic simulations. The prediction results of the model are reasonably consistent with the experimental results. It shows that the main strengthening contribution is due to the misfit of dimers.
The Davydov or exciton splitting of vertical excitation energies is commonly used to estimate the excitation energy transfer rate between chromophores. Here we investigate the S1-S2 Davydov splitting ...in 2-pyridone dimer as a function of the monomer separation, R. We assess the ability of various functionals to reproduce the Davydov splitting at finite R predicted by the approximate coupled cluster singles doubles method CC2. While semilocal functionals fail qualitatively because of spurious charge-transfer intruder states, global hybrids with a large fraction of exact exchange, such as BHandH-LYP, reproduce the CC2 splittings within few wavenumbers. We analyze our results by comparison to lowest-order intermolecular perturbation theory in the spirit of Förster and Dexter. At equilibrium hydrogen bond distance, the Förster-Dexter splittings are too small by up to a factor of 2.
We present an analysis of the dispersion interaction energy and forces in density-functional theory from the point of view of the adiabatic connection between the Kohn-Sham non-interacting and fully ...interacting systems. Accurate coupled-cluster singles-doubles-perturbative-triples CCSD(T) densities are computed for the helium dimer and used to construct the exchange-correlation potential of Kohn-Sham theory, showing agreement with earlier results presented for the Hartree-Fock-Kohn-Sham method M. Allen and D. J. Tozer, J. Chem. Phys. 117, 11113 (2002). The accuracy of the methodology utilized to determine these solutions is checked by calculation of the Hellmann-Feynman forces based on the Kohn-Sham densities, which are compared with analytic CCSD(T) forces. To ensure that this comparison is valid in a finite atomic-orbital basis set, we employ floating Gaussian basis functions throughout and all results are counterpoise corrected. The subtle charge-rearrangement effects associated with the dispersion interaction are highlighted as the origin of a large part of the dispersion force. To recover the exchange-correlation components of the interaction energy, adiabatic connections are constructed for the supermolecular system and for its constituent atoms; subtraction of the resulting adiabatic-connection curves followed by integration over the interaction strength recovers the exchange-correlation contribution relevant to the density-functional description of the dispersion interaction. The results emphasize the long-ranged, dynamically correlated nature of the dispersion interaction between closed-shell species. An alternative adiabatic-connection path is also explored, where the electronic interactions are introduced in a manner that emphasizes the range of the electronic interactions, highlighting their purely long-ranged nature, consistent with the success of range-separated hybrid approaches in this context.
The exact exchange-correlation potential of Kohn-Sham density functional theory is known to jump discontinuously by a spatial constant as the average electron number, N, crosses an integer in an open ...system of fluctuating electron number, with important physical consequences for charge transfers and band gaps. We have recently constructed an essentially exact exchange-correlation potential v
xc
for N electrons (0 ≤ N ≤ 2) in the presence of a -1/r external potential, i.e., for a ground ensemble of H
+
ion, H atom, and H
-
ion densities. That construction illustrates the discontinuity at N = 1, where it equals I
H
- A
H
, the positive difference between the ionization energy and the electron affinity of the hydrogen atom. Here we construct the corresponding essentially exact spin-up and spin-down exchange-correlation potentials v
xc,↑
and v
xc,↓
of the Kohn-Sham spin-density functional theory, more commonly used for electronic structure calculations, for the ground ensemble with most-negative z-component of spin (or equivalently in the presence of a uniform magnetic field of infinitesimal strength). The potentials v
xc
, v
xc,↑
, and v
xc,↓
, which vanish as r → ∞ (except when N approaches an integer from above), are identical for 0 ≤ N ≤ 1 and for N = 2 but not for 1 < N < 2. We find that the majority or spin-down potential has a spatially constant discontinuity at N = 1 equal to I
H
- A
H
. The minority or spin-up potential has a discontinuity which is this constant in one order of limits, but is a spatially varying function in a different order of limits. This order-of-limits problem is a consequence of a special circumstance: the vanishing of the spin-up density at N = 1.
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