Regional self-interaction correction of density functional theory

We propose a new simple scheme for self-interaction correction (SIC) of exchange functionals in the density functional theory. In the new scheme, exchange energies are corrected by substituting exchange self-interactions for exchange functionals in regions of self-interaction. To classify the regions of self-interaction, we take advantage of the property of the total kinetic energy density approaching the Weizs?cker density in the case of electrons in isolated orbitals. The scheme differs from conventional SIC methods in that it produces optimized molecular structures. Applying the scheme to the calculation of reaction energy barriers showed that it provides a clear improvement in cases where the barriers are underestimated by conventional "pure" functionals. In particular, we found that this scheme even reproduces a transition state that is not given by pure functionals.     

The self-interaction error and the description of non-dynamic electron correlation in density functional theory

The self-interaction error (SIE) plays a central role in density functional theory (DFT) when carried out with approximate exchange-correlation functionals. Its origin, properties, and consequences for the development of standard DFT to a method that can correctly describe multi-reference electron systems by treating dynamic and non-dynamic electron correlation on an equal footing, is discussed. In this connection, the seminal work of Colle and Salvetti on wave function-based correlation functionals that do no longer suffer from a SIE is essential. It is described how the Colle–Salvetti correlation functional is an anchor point for the derivation of a functional multi-reference DFT method.     

Many-electron self-interaction and spin polarization errors in local hybrid density functionals

Errors for systems with noninteger occupation have been connected to common failures of density functionals. Previously, global hybrids and pure density functionals have been investigated for systems with noninteger charge and noninteger spin state. Local hybrids have not been investigated for either of those systems to the best of our knowledge. This study intends to close this gap. We investigate systems with noninteger charge to assess the many-electron self-interaction error and systems with noninteger spin state to assess the spin polarization error of recently proposed local hybrids and their range-separated variants. We find that long-range correction is very important to correct for many-electron self-interaction error in cations, whereas most full-range local hybrids seem to be sufficient for anions, where long-range-corrected density functionals tend to overcorrect. On the other hand, while all hitherto proposed long-range-corrected density functionals show large spin polarization errors, the Perdew-Staroverov-Tao-Scuseria (PSTS) functional performs best of all local hybrids in this case and shows an outstanding behavior for the dependence of the energy on the spin polarization.     

On Koopmans' theorem in density functional theory

This paper clarifies why long-range corrected (LC) density functional theory gives orbital energies quantitatively. First, the highest occupied molecular orbital and the lowest unoccupied molecular orbital energies of typical molecules are compared with the minus vertical ionization potentials (IPs) and electron affinities (EAs), respectively. Consequently, only LC exchange functionals are found to give the orbital energies close to the minus IPs and EAs, while other functionals considerably underestimate them. The reproducibility of orbital energies is hardly affected by the difference in the short-range part of LC functionals. Fractional occupation calculations are then carried out to clarify the reason for the accurate orbital energies of LC functionals. As a result, only LC functionals are found to keep the orbital energies almost constant for fractional occupied orbitals. The direct orbital energy dependence on the fractional occupation is expressed by the exchange self-interaction (SI) energy through the potential derivative of the exchange functional plus the Coulomb SI energy. On the basis of this, the exchange SI energies through the potential derivatives are compared with the minus Coulomb SI energy. Consequently, these are revealed to be cancelled out only by LC functionals except for H, He, and Ne atoms.     

Accurate calculation of transport properties for organic molecular semiconductors with spin-component scaled MP2 and modern density functional theory methods

At ambient temperatures, intermolecular hopping of charge carriers dominates the field effect mobility and thus the performance of organic molecular semiconductors for organic-based electronic devices. We have used a wide variety of modern and accurate computational methods to calculate the main parameters associated with charge transport, taking oligoacenes, and its derivatives as the exemplary organic materials. We tackle the problem from a combined inter- and intramolecular approach, in which the parameters are calculated for an isolated single molecule concomitantly with the stability of the dimers found in experimentally determined crystalline structures. Considering that most of the future applications within the field would need a full understanding of the transport mechanism, we assess the reliability of the methods to be employed according to the nature of the problem. Finally, we perform a computationally guided molecular engineering of a new set of materials derived from tetracene (rubrene and highly twisted oligoacenes) which allows to robustly anticipate the reasons for their expected performance in organic-based electronic devices.     

An alternative self-interaction correction in the generalized exchange local-density functional theory

The local-density functional (LDF) theory does not accurately predict the total energy and the orbital energy of an atom, because of the incomplete cancellation of the self-interaction in the Coulomb integral by that in the exchange integral. Recent investigations showed that the agreement of the total energy and one-electron eigenvalue of an atom in the LDF and Hartree–Fock (HF) theories are remarkably improved by introducing a self-interaction correction in the LDF theory. An alternative self-interaction correction (ASIC) in the generalized exchange local-density functional (GX-LSD) theory is developed by equalizing the one-electron eigenvalue with the ionization potential of the corresponding orbital. The ASIC is subsequently applied to some closed-shell atoms and shown to give numerically better results than both the self-interaction corrected (SIC) exchange-only local-spin-density functional theory (SIC-XO-LSD) and the self-interaction corrected GX-LSD theory (SIC-GX-LSD).     

On the accuracy of density functional theory for iron-sulfur clusters

A simple, yet powerful wave function manipulation method was introduced utilizing a generalized ionic fragment approach that allows for systematic mapping of the wave function space for multispin systems with antiferromagnetic coupling. The use of this method was demonstrated for developing ground state electronic wave function for [2Fe-2S] and [Mo-3Fe-4S] clusters. Using well-defined ionic wave functions for ferrous and ferric irons, sulfide, and thiolate fragments, the accuracy of various density functionals and basis sets including effective core potentials were evaluated on a [4Fe-4S] cluster by comparing the calculated geometric and electronic structures with crystallographic data and experimental atomic spin densities from X-ray absorption spectroscopy, respectively. We found that the most reasonable agreement for both geometry and atomic spin densities is obtained by a hybrid functional with 5% HF exchange and 95% density functional exchange supplemented with Perdew's 1986 correlation functional. The basis set seems to saturate only at the triple-zeta level with polarization and diffuse functions. Reasonably preoptimized structures can be obtained by employing computationally less expensive effective core potentials, such as the Stuttgart-Dresden potential with a triple-zeta valence basis set. The extension of the described calibration methodology to other biologically important and more complex iron-sulfur clusters, such as hydrogenase H-cluster and nitrogenase FeMo-co will follow.     

On the evaluation of the non-interacting kinetic energy in density functional theory

The utility of both an orbital-free and a single-orbital expression for computing the non-interacting kinetic energy in density functional theory is investigated for simple atomic systems. The accuracy of both expressions is governed by the extent to which the Kohn-Sham equation is solved for the given exchange-correlation functional and so special attention is paid to the influence of finite Gaussian basis sets. The orbital-free expression is a statement of the virial theorem and its accuracy is quantified. The accuracy of the single-orbital expression is sensitive to the choice of Kohn-Sham orbital. The use of particularly compact orbitals is problematic because the failure to solve the Kohn-Sham equation exactly in regions where the orbital has decayed to near-zero leads to unphysical behaviour in regions that contribute to the kinetic energy, rendering it inaccurate. This problem is particularly severe for core orbitals, which would otherwise appear attractive due to their formally nodeless nature. The most accurate results from the single-orbital expression are obtained using the relatively diffuse, highest occupied orbitals, although special care is required at orbital nodes.     

New link between conceptual density functional theory and electron delocalization

In this paper we give a new definition of the softness kernel based on the exchange-correlation density. This new kernel is shown to correspond to the change of electron fluctuation upon external perturbation, thus helping to bridge the gap between conceptual density functional theory and some tools describing electron localization in molecules. With the aid of a few computational calculations on diatomics we illustrate the performance of this new computational tool.     

On correlated electron-nuclear dynamics using time-dependent density functional theory

We discuss possibilities and challenges for describing correlated electron and nuclear dynamics within a surface-hopping framework using time-dependent density functional theory (TDDFT) for the electron dynamics. We discuss the recent surface-hopping method proposed by Craig et al. [Phys. Rev. Lett. 95, 163001 (2005)] that is based on Kohn-Sham potential energy surfaces. Limitations of this approach arise due to the Kohn-Sham surfaces generally having different gradients than the true TDDFT-corrected ones. Two mechanisms of the linear response procedure cause this effect: we illustrate these with examples.     

A density functional theory study of interaction between formamide and guanine

Hydrogen bonding in complexes formed between formamide and guanine molecules was completely investigated using density functional theory (DFT) at the 6-311++G(d, p) level. For comparison, the HF and MP2 methods were also used. Nine stable cyclic structures stabilized by two hydrogen bonds were found. One of these was a six-membered ring, five were seven-membered rings, and the others were eight-membered rings. The eight-membered ring is preferable to the seven-and six-membered ones as follows from H-bond lengths and interaction energies. The FG4 structure was calculated to be the most stable, and another cyclic structure, FG5, was least stable because of the six-membered ring and the weakest interaction. The infrared spectrum frequencies, intensities, and vibrational frequency shifts are also reported. The text was submitted by the authors in English.     

Multicomponent density functional theory study of the interplay between electron-electron and electron-proton correlation

The interplay between electron-electron and electron-proton correlation is investigated within the framework of the nuclear-electronic orbital density functional theory (NEO-DFT) approach, which treats electrons and select protons quantum mechanically on the same level. Recently two electron-proton correlation functionals were developed from the electron-proton pair densities obtained from explicitly correlated wavefunctions. In these previous derivations, the kinetic energy contribution arising from electron-proton correlation was neglected. In this paper, an electron-proton correlation functional that includes this kinetic energy contribution is derived using the adiabatic connection formula in multicomponent DFT. The performance of the NEO-DFT approach using all three electron-proton correlation functionals in conjunction with three well-established electronic exchange-correlation functionals is assessed. NEO-DFT calculations with these electron-proton correlation functionals capture the increase in the hydrogen vibrational stretching frequencies arising from the inclusion of electron-electron correlation in model systems. Electron-proton and electron-electron correlation are found to be uncoupled and predominantly additive effects to the total energy for the model systems studied. Thus, electron-proton correlation functionals and electronic exchange-correlation functionals can be developed independently and subsequently combined together without re-parameterization.     

Embedding wave function theory in density functional theory

We present a framework for embedding a highly accurate coupled-cluster calculation within a larger density functional calculation. We use a perturbative buffer to help insulate the coupled-cluster region from the rest of the system. Regions are defined, not in real space, but in Hilbert space, though connection between the two can be made by spatial localization of single-particle orbitals. Relations between our embedding approach and some similar techniques are discussed. We present results for small sample systems for which we can extract essentially exact results, demonstrating that our approach seems to work quite well and is generally more reliable than some of the related approaches due to the introduction of additional interaction terms.     

Dispersion, static correlation, and delocalisation errors in density functional theory: an electrostatic theorem perspective

Dispersion, static correlation, and delocalisation errors in density functional theory are considered from the unconventional perspective of the force on a nucleus in a stretched diatomic molecule. The electrostatic theorem of Feynman is used to relate errors in the forces to errors in the electron density distortions, which in turn are related to erroneous terms in the Kohn-Sham equations. For H(2), the exact dispersion force arises from a subtle density distortion; the static correlation error leads to an overestimated force due to an exaggerated distortion. For H(2)(+), the exact force arises from a delicate balance between attractive and repulsive components; the delocalisation error leads to an underestimated force due to an underestimated distortion. The net force in H(2)(+) can become repulsive, giving the characteristic barrier in the potential energy curve. Increasing the fraction of long-range exact orbital exchange increases the distortion, reducing delocalisation error but increasing static correlation error.     

A density functional study of a twisted nematic cell and its relation to the Frank-Oseen theory

The numerical results for the twist angle profile xi(z) across a slab-shaped nematic cell obtained from a density functional theory (DFT) are compared to the predictions of the macroscopic Frank-Oseen theory. The latter theory predicts that xi"(z)=0, and this is also seen to be the case for the DFT results. These do, however, verify the Frank-Oseen relation, lambda+/-W+/-=K2, between the de Gennes extrapolation length (lambda+/-), the anchoring energy per unit area of the (+/-) cell wall (W+/-), and the elastic constant of the nematic for twist deformations (K2), only if W+/- is nonlinearly related to the amplitude of the anchoring term of the DFT.