For the paradigmatic case of H(2) dissociation, we compare state-of-the-art many-body perturbation theory in the GW approximation and density-functional theory in the exact-exchange plus random-phase approximation (RPA) for the correlation energy. 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 noninteracting 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, sc-RPA outperforms sc-GW when it comes to bond breaking. We attribute this to the difference in the correlation energy rather than the treatment of the kinetic energy.

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 dynamicallyscreened-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.

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 that diverges as r → ∞. 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.

We show that the inclusion of screened exchange via hybrid functionals provides a unified description of the electronic and vibrational properties of TiSe 2 . In contrast to local approximations in density functional theory, the explicit inclusion of exact, nonlocal exchange captures the effects of the electron-electron interaction needed to both separate the Ti-d states from the Se-p states and stabilize the charge-densitywave (CDW) (or low-T) phase through the formation of a p-d hybridized state. We further show that this leads to an enhanced electron-phonon coupling that can drive the transition even if a small gap opens in the high-T phase. Finally, we demonstrate that the hybrid functionals can generate a CDW phase where the electronic bands, the geometry, and the phonon frequencies are in agreement with experiments. DOI: 10.1103/PhysRevLett.119.176401 The charge density wave (CDW) instability is a common phenomenon in layered semimetallic transition metal dichalcogenides (TMDs) [1] and has attracted considerable interest over the years, from both the experimental and the theoretical side. The CDW phase is often found to compete with superconductivity and thus plays a similar role as the antiferromagnetic phase in strongly correlated heavy fermion systems or in high-T c cuprates [2][3][4][5]. This intriguing similarity has stimulated the search for a better understanding of the physical mechanism behind the CDW instability in TMDs [6].The CDW instability in TiSe 2 is one of the most studied and debated. On the experimental side, neutron diffraction [7] and x-ray scattering [8] have established the existence of a commensurate 2 × 2 × 2 structural transition at 200 K. This is confirmed by angle resolved photo emission spectroscopy (ARPES) as well as by transport measurements [7], where an abrupt increase in resistivity is found at the same temperature. However, upon further cooling the resistivity reaches an anomalous maximum [7], after which a weak metallic behavior is observed. By contrast, ARPES finds an insulating low-T phase, with a gap of approximately 0.15 eV [9][10][11][12][13][14]. In the high-T phase ARPES has not been able to conclude whether the system is semimetallic or semiconducting due to the very small indirect (possibly negative) gap. Theoretically, this fact makes TiSe 2 an ideal candidate to exhibit an excitonic insulator phase [9,[15][16][17] for which the CDW transition is driven by a purely electronic instability. Some recent experiments [18] partly support this scenario. On the other hand, excitonic correlations alone are insufficient as demonstrated in Ref. [19].Additional experimental evidence for the CDW instability has been provided by vibrational spectra as a function of temperature. A complete softening of an optical phonon at the L point has been observed in inelastic x-ray scattering experiments [20]. In Raman and infrared (IR) spectroscopy the transition is detected by the appearance of a large number of new modes [21,22], some of which can be related to the CDW transition ...

In this work we studied a new functional for the correlation energy obtained from the exact-exchange (EXX) approximation within time-dependent density functional theory. Correlation energies have been calculated for a number of different atoms showing excellent agreement with results from more sophisticated methods. These results lose 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.

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 improved total energy in the dissociation limit.

We have calculated the correlation energy of the homogeneous electron gas (HEG) and the dissociation energy curves of molecules with covalent bonds from an efficient implementation of the adiabatic connection fluctuation dissipation expression including the exact-exchange (EXX) kernel. The EXX kernel is defined from first-order perturbation theory and used in the Dyson equation of time-dependent density-functional theory. Within this approximation (RPAx), the correlation energies of the HEG are significantly improved with respect to the random phase approximation (RPA) up to densities of the order of r s ≈ 10. However, beyond this value, the RPAx response function exhibits an unphysical divergence and the approximation breaks down. Total energies of molecules at equilibrium are also highly accurate, but we find a similar instability at stretched geometries. Staying within an exact first-order approximation to the response function, we use an alternative resummation of the higher-order terms. This slight redefinition of RPAx fixes the instability in total energy calculations without compromising the overall accuracy of the approach.

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.