Correlation energy functional and potential from time-dependent exact-exchange theory

In this work we have studied a new functional for the correlation energy obtained from the exact-exchange (EXX) approximation within time-dependent density functional theory (TDDFT). Correlation energies have been calculated for a number of different atoms showing excellent agreement with results from more sophisticated methods. These results loose little accuracy by approximating the EXX kernel by its static value, a procedure which enormously simplifies the calculations. The correlation potential, obtained by taking the functional derivative with respect to the density, turns out to be remarkably accurate for all atoms studied. This potential has been used to calculate ionization potentials, static polarizabilities and van der Waals coefficients with results in close agreement with experiment.Comment: 6 pages, 2 figure

Exact-exchange kernel of time-dependent density functional theory: Frequency dependence and photoabsorption spectra of atoms

In this work we have calculated excitation energies and photoionization cross sections of Be and Ne in the exact-exchange (EXX) approximation of time-dependent density functional theory (TDDFT). The main focus has been on the frequency dependence of the EXX kernel and on how it affects the spectrum as compared to the corresponding adiabatic approximation. We show that for some discrete excitation energies the frequency dependence is essential to reproduce the results of time-dependent Hartree-Fock theory. Unfortunately, we have found that the EXX approximation breaks down completely at higher energies, producing a response function with the wrong analytic structure and making inner-shell excitations disappear from the calculated spectra. We have traced this failure to the existence of vanishing eigenvalues of the Kohn-Sham non-interacting response function. Based on the adiabatic TDDFT formalism we propose a new way of deriving the Fano parameters of autoionizing resonances.Comment: 14 pages, 7 figure

Correlation potentials for molecular bond dissociation within the self-consistent random phase approximation

Self-consistent correlation potentials for H$_2$ and LiH for various inter-atomic separations are obtained within the random phase approximation (RPA) of density functional theory. The RPA correlation potential shows a peak at the bond midpoint, which is an exact feature of the true correlation potential, but lacks another exact feature: the step important to preserve integer charge on the atomic fragments in the dissociation limit. An analysis of the RPA energy functional in terms of fractional charge is given which confirms these observations. We find that the RPA misses the derivative discontinuity at odd integer particle numbers but explicitly eliminates the fractional spin error in the exact-exchange functional. The latter finding explains the accurate total energy in the dissociation limit.Comment: 9 pages, 10 figure

Bond Breaking and Bond Formation: How Electron Correlation is Captured in Many-Body Perturbation Theory and Density-Functional Theory

For the paradigmatic case of H2-dissociation we compare state-of-the-art many-body perturbation theory (MBPT) in the GW approximation and density-functional theory (DFT) in the exact-exchange plus random-phase approximation for the correlation energy (EX+cRPA). For an unbiased comparison and to prevent spurious starting point effects both approaches are iterated to full self-consistency (i.e. sc-RPA and sc-GW). The exchange-correlation diagrams in both approaches are topologically identical, but in sc-RPA they are evaluated with non-interacting and in sc-GW with interacting Green functions. This has a profound consequence for the dissociation region, where sc-RPA is superior to sc-GW. We argue that for a given diagrammatic expansion, the DFT framework outperforms the many-body framework when it comes to bond-breaking. We attribute this to the difference in the correlation energy rather than the treatment of the kinetic energy.Comment: 6 pages, 4 figure

Beyond the random phase approximation with a local exchange vertex

With the aim of constructing an electronic structure approach that systematically goes beyond the GW and random phase approximation (RPA) we introduce a vertex correction based on the exact-exchange (EXX) potential of time-dependent density functional theory. The EXX vertex function is constrained to be local but is expected to capture similar physics as the Hartree-Fock vertex. With the EXX vertex, we then unify different beyond-RPA approaches such as the various resummations of RPA with exchange and the second-order screened exchange approximation. The theoretical analysis is supported by numerical studies on the hydrogen dimer and the electron gas, and we discuss the role of including the vertex correction in both the screened interaction and the self-energy. Finally, we give details on our implementation within the plane-wave pseudo potential framework and demonstrate the excellent performance of the different RPA with exchange methods in describing the energetics of hydrogen and van der Waals bonds

Supporting premature infants’ oral feeding in the NICU—a qualitative study of nurses’ perspectives

One major task in the neonatal intensive care unit (NICU) involves ensuring adequate nutrition and supporting the provision of human milk. The aim of this study was to explore nurses’ experiences of the oral feeding process in the NICU when the infant is born extremely or very preterm. We used a qualitative inductive approach. Nine nurses from three family-centered NICUs were interviewed face-to-face. The interviews were transcribed verbatim and analyzed using content analysis. Five sub-categories and two generic categories formed the main category: ‘A complex and long-lasting collaboration.’ The nurses wished to contribute to the parents’ understanding of the feeding process and their own role as parents in this process. The nurses’ intention was to guide and support parents to be autonomous in this process. They saw the family as a team in which the preterm infant was the leader whose needs and development directed the feeding and the parents’ actions in this process. Written and verbal communication, seeing all family members as important members of a team and early identification of the most vulnerable families to direct the emotional and practical feeding support accordingly can strengthen the feeding process in the NICU

The correlation potential in density functional theory at the GW-level: spherical atoms

As part of a project to obtain better optical response functions for nano materials and other systems with strong excitonic effects we here calculate the exchange-correlation (XC) potential of density-functional theory (DFT) at a level of approximation which corresponds to the dynamically- screened-exchange or GW approximation. In this process we have designed a new numerical method based on cubic splines which appears to be superior to other techniques previously applied to the "inverse engineering problem" of DFT, i.e., the problem of finding an XC potential from a known particle density. The potentials we obtain do not suffer from unphysical ripple and have, to within a reasonable accuracy, the correct asymptotic tails outside localized systems. The XC potential is an important ingredient in finding the particle-conserving excitation energies in atoms and molecules and our potentials perform better in this regard as compared to the LDA potential, potentials from GGA:s, and a DFT potential based on MP2 theory.Comment: 13 pages, 9 figure

Discontinuities of the exchange-correlation kernel and charge-transfer excitations in time-dependent density functional theory

We identify the key property that the exchange-correlation (XC) kernel of time-dependent density functional theory must have in order to describe long-range charge-transfer excitations. We show that the discontinuity of the XC potential as a function of particle number induces a space -and frequency-dependent discontinuity of the XC kernel which diverges as $r\to\infty$. In a combined donor-acceptor system, the same discontinuity compensates for the vanishing overlap between the acceptor and donor orbitals, thereby yielding a finite correction to the Kohn-Sham eigenvalue differences. This mechanism is illustrated to first order in the Coulomb interaction.Comment: 6 pages, 3 figures (expanded version, accepted in Phys. Rev. A

Electronic structure of TiSe2 from a quasi-self-consistent G0W0 approach

n a previous work, it was shown that the inclusion of exact exchange is essential for a first-principles description of both the electronic and the vibrational properties of TiSe2, M. Hellgren et al. [Phys. Rev. Lett. 119, 176401 (2017)]. The GW approximation provides a parameter-free description of screened exchange but is usually employed perturbatively (G0W0), making results more or less dependent on the starting point. In this work, we develop a quasi-self-consistent extension of G0W0 based on the random phase approximation (RPA) and the optimized effective potential of hybrid density functional theory. This approach generates an optimal G0W0 starting point and a hybrid exchange parameter consistent with the RPA. While self-consistency plays a minor role for systems such as Ar, BN, and ScN, it is shown to be crucial for TiS2 and TiSe2. We find the high-temperature phase of TiSe2 to be a semimetal with a band structure in good agreement with experiment. Furthermore, the optimized hybrid functional agrees well with our previous estimate and therefore accurately reproduces the low-temperature charge-density-wave phase