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

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

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

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

Linear density response function within the time-dependent exact-exchange approximation

We have calculated the frequency-dependent exact exchange (EXX) kernel of time-dependent (TD) density functional theory employing our recently proposed computational method based on cubic splines. With this kernel we have calculated the linear density response function and obtained static polarizabilites, van der Waals coefficients and correlation energies for all spherical spin compensated atoms up to Argon. Some discrete excitation energies have also been calculated for Be and Ne. As might be expected, the results of the TDEXX approximation are close to those of TD Hartree-Fock theory. In addition, correlation energies obtained by integrating over the strength of the Coulomb interaction turn out to be highly accurate.Comment: 10 pages, 5 figure

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

Transient Calcium and Dopamine Increase PKA Activity and DARPP-32 Phosphorylation

Reinforcement learning theorizes that strengthening of synaptic connections in medium spiny neurons of the striatum occurs when glutamatergic input (from cortex) and dopaminergic input (from substantia nigra) are received simultaneously. Subsequent to learning, medium spiny neurons with strengthened synapses are more likely to fire in response to cortical input alone. This synaptic plasticity is produced by phosphorylation of AMPA receptors, caused by phosphorylation of various signalling molecules. A key signalling molecule is the phosphoprotein DARPP-32, highly expressed in striatal medium spiny neurons. DARPP-32 is regulated by several neurotransmitters through a complex network of intracellular signalling pathways involving cAMP (increased through dopamine stimulation) and calcium (increased through glutamate stimulation). Since DARPP-32 controls several kinases and phosphatases involved in striatal synaptic plasticity, understanding the interactions between cAMP and calcium, in particular the effect of transient stimuli on DARPP-32 phosphorylation, has major implications for understanding reinforcement learning. We developed a computer model of the biochemical reaction pathways involved in the phosphorylation of DARPP-32 on Thr34 and Thr75. Ordinary differential equations describing the biochemical reactions were implemented in a single compartment model using the software XPPAUT. Reaction rate constants were obtained from the biochemical literature. The first set of simulations using sustained elevations of dopamine and calcium produced phosphorylation levels of DARPP-32 similar to that measured experimentally, thereby validating the model. The second set of simulations, using the validated model, showed that transient dopamine elevations increased the phosphorylation of Thr34 as expected, but transient calcium elevations also increased the phosphorylation of Thr34, contrary to what is believed. When transient calcium and dopamine stimuli were paired, PKA activation and Thr34 phosphorylation increased compared with dopamine alone. This result, which is robust to variation in model parameters, supports reinforcement learning theories in which activity-dependent long-term synaptic plasticity requires paired glutamate and dopamine inputs