Self-Consistent Green Function Embedding for Advanced Electronic Structure Methods Based on a Dynamical Mean-Field Concept

We present an embedding scheme for periodic systems that facilitates the treatment of the physically important part (here the unit cell) with advanced electronic-structure methods, that are computationally too expensive for periodic systems. The rest of the periodic system is treated with computationally less demanding approaches, e.g., Kohn-Sham density-functional theory, in a self- consistent manner. Our scheme is based on the concept of dynamical mean-field theory (DMFT) formulated in terms of Green functions. In contrast to the original DMFT formulation for correlated model Hamiltonians, we here consider the unit cell as local embedded cluster in a first-principles way, that includes all electronic degrees of freedom. Our real-space dynamical mean-field embedding (RDMFE) scheme features two nested Dyson equations, one for the embedded cluster and another for the periodic surrounding. The total energy is computed from the resulting Green functions. The performance of our scheme is demonstrated by treating the embedded region with hybrid functionals and many-body perturbation theory in the GW approach for simple bulk systems. The total energy and the density of states converge rapidly with respect to the computational parameters and approach their bulk limit with increasing cluster (i.e., unit cell) size

Thermodynamic equilibrium conditions of graphene films on SiC

First-principles surface phase diagrams reveal that epitaxial monolayer graphene films on the Si side of 3C-SiC(111) can exist as thermodynamically stable phases in a narrow range of experimentally controllable conditions, defining a path to the highest-quality graphene films. Our calculations are based on a van der Waals corrected density functional. The full, experimentally observed (6 sqrt(3)x 6 sqrt(3))-R30 supercells for zero- to trilayer graphene are essential to describe the correct interface geometries and the relative stability of surface phases and possible defects

Exact-exchange based quasiparticle energy calculations for the band gap, effective masses and deformation potentials of ScN

The band gaps, longitudinal and transverse effective masses, and deformation potentials of ScN in the rock-salt structure have been calculated employing G0W0-quasiparticle calculations using exact-exchange Kohn-Sham density functional theory one-particle wavefunctions and energies as input. Our quasiparticle gaps support recent experimental observations that ScN has a much lower indirect band gap than previously thought. The results are analyzed in terms of the influence of different approximations for exchange and correlation taken in the computational approach on the electronic structure of ScN.Comment: Comments: 9 pages including 5 figures; related publications can be found at http://www.fhi-berlin.mpg.de/th/th.htm

Renormalized Second-order Perturbation Theory for The Electron Correlation Energy: Concept, Implementation, and Benchmarks

We present a renormalized second-order perturbation theory (rPT2), based on a Kohn-Sham (KS) reference state, for the electron correlation energy that includes the random-phase approximation (RPA), second-order screened exchange (SOSEX), and renormalized single excitations (rSE). These three terms all involve a summation of certain types of diagrams to infinite order, and can be viewed as "renormalization" of the 2nd-order direct, exchange, and single excitation (SE) terms of Rayleigh-Schr\"odinger perturbation theory based on an KS reference. In this work we establish the concept of rPT2 and present the numerical details of our SOSEX and rSE implementations. A preliminary version of rPT2, in which the renormalized SE (rSE) contribution was treated approximately, has already been benchmarked for molecular atomization energies and chemical reaction barrier heights and shows a well balanced performance [Paier et al, New J. Phys. 14, 043002 (2012)]. In this work, we present a refined version of rPT2, in which we evaluate the rSE series of diagrams rigorously. We then extend the benchmark studies to non-covalent interactions, including the rare-gas dimers, and the S22 and S66 test sets. Despite some remaining shortcomings, we conclude that rPT2 gives an overall satisfactory performance across different chemical environments, and is a promising step towards a generally applicable electronic structure approach.Comment: 16 pages, 11 figure

Density-functional Theory for f electron Systems: the {\alpha}-{\gamma} Phase Transition in Cerium

The isostructural {\alpha}-{\gamma} phase transition in cerium is analyzed using density-functional theory with different exchange-correlation functionals, in particular the PBE0 hybrid functional and the exact- exchange plus correlation in the random-phase approximation [(EX+cRPA)@PBE0] approach. We show that the Hartree-Fock exchange part of the hybrid functional actuates two distinct solutions at zero temperature that can be associated with the {\alpha} and {\gamma} phases of cerium. However, despite the relatively good structural and magnetic properties, PBE0 predicts the {\gamma} phase to be the stable phase at ambient pressure and zero temperature, in contradiction with low temperature experiments. EX+cRPA reverses the energetic ordering, which emphasizes the importance of correlation for rare- earth systems

Unified description of ground and excited states of finite systems: the self-consistent GW approach

GW calculations with fully self-consistent G and W -- based on the iterative solution of the Dyson equation -- provide an approach for consistently describing ground and excited states on the same quantum mechanical level. We show that for the systems considered here self-consistent GW reaches the same final Green function regardless of the initial reference state. Self-consistency systematically improves ionization energies and total energies of closed shell systems compared to G_0W_0 based on Hartree-Fock and (semi)local density-functional theory. These improvements also translate to the electron density as exemplified by an improved description of dipole moments and permit us to assess the quality of ground state properties such as bond lengths and vibrational frequencies.Comment: 5 pages, 4 figures, supplemental materia

Interface dipoles of organic molecules on Ag(111) in hybrid density-functional theory

We investigate the molecular acceptors 3,4,9,10-perylene-tetracarboxylic acid dianhydride (PTCDA), 2,3,5,6-tetra uoro-7,7,8,8-tetracyanoquinodimethane (F4TCNQ), and 4,5,9,10-pyrenetetraone (PYTON) on Ag(111) using densityfunctional theory. For two groups of the HSE(\alpha, \omega) family of exchange-correlation functionals (\omega = 0 and \omega = 0.2\AA) we study the isolated components as well as the combined systems as a function of the amount of exact-exchange (\alpha). We find that hybrid functionals favour electron transfer to the adsorbate. Comparing to experimental work-function data, we report for (\alpha) ca. 0.25 a notable but small improvement over (semi)local functionals for the interface dipole. Although Kohn-Sham eigenvalues are only approximate representations of ionization energies, incidentally, at this value also the density of states agrees well with the photoelectron spectra. However, increasing (\alpha) to values for which the energy of the lowest unoccupied molecular orbital matches the experimental electron affinity in the gas phase worsens both the interface dipole and the density of states. Our results imply that semi-local DFT calculations may often be adequate for conjugated organic molecules on metal surfaces and that the much more computationally demanding hybrid functionals yield only small improvements.Comment: submitted to New Journal of Physics (2013). More information can be found at http://th.fhi-berlin.mpg.de/site/index.php?n=Publications.Publication

First-Principles Description of Charge Transfer in Donor-Acceptor Compounds from Self-Consistent Many-Body Perturbation Theory

We investigate charge transfer in prototypical molecular donor-acceptor compounds using hybrid density functional theory (DFT) and the GW approximation at the perturbative level (G0W0) and at full self-consistency (sc-GW). For the systems considered here, no charge transfer should be expected at large intermolecular separation according to photoemission experiment and accurate quantum-chemistry calculations. The capability of hybrid exchange-correlation functionals of reproducing this feature depends critically on the fraction of exact exchange $\alpha$, as for small values of $\alpha$ spurious fractional charge transfer is observed between the donor and the acceptor. G0W0 based on hybrid DFT yields the correct alignment of the frontier orbitals for all values of $\alpha$. However, G0W0 has no capacity to alter the ground-state properties of the system, because of its perturbative nature. The electron density in donor-acceptor compounds thus remains incorrect for small $\alpha$ values. In sc-GW, where the Green's function is obtained from the iterative solution of the Dyson equation, the electron density is updated and reflects the correct description of the level alignment at the GW level, demonstrating the importance of self-consistent many-body approaches for the description of ground- and excited-state properties in donor-acceptor systems.Comment: 8 pages, 7 figure

Length Dependence of Ionization Potentials of Trans-Acetylenes: Internally-Consistent DFT/GW Approach

We follow the evolution of the Ionization Potential (IP) for the paradigmatic quasi-one-dimensional trans-acetylene family of conjugated molecules, from short to long oligomers and to the infinite polymer trans-poly-acetylene (TPA). Our results for short oligomers are very close to experimental available data. We find that the IP varies with oligomer length and converges to the given value for TPA with a smooth, coupled inverse-length-exponential behavior. Our prediction is based on an "internally-consistent" scheme to adjust the exchange mixing parameter $\alpha$ of the PBEh hybrid density functional, so as to obtain a description of the electronic structure consistent with the quasiparticle approximation for the IP. This is achieved by demanding that the corresponding quasiparticle correction, in the GW@PBEh approximation, vanishes for the IP when evaluated at PBEh($\alpha^{ic}$). We find that $\alpha^{ic}$ is also system-dependent and converges with increasing oligomer length, allowing to capture the dependence of IP and other electronic properties.Comment: 22 pages with 9 figures, submitted to Physical Review

Beyond the Random Phase Approximation for the Electron Correlation Energy: The Importance of Single Excitations

The random phase approximation (RPA) for the electron correlation energy, combined with the exact-exchange energy, represents the state-of-the-art exchange-correlation functional within density-functional theory (DFT). However, the standard RPA practice -- evaluating both the exact-exchange and the RPA correlation energy using local or semilocal Kohn-Sham (KS) orbitals -- leads to a systematic underbinding of molecules and solids. Here we demonstrate that this behavior is largely corrected by adding a "single excitation" (SE) contribution, so far not included in the standard RPA scheme. A similar improvement can also be achieved by replacing the non-self-consistent exact-exchange total energy by the corresponding self-consistent Hartree-Fock total energy, while retaining the RPA correlation energy evaluated using Kohn-Sham orbitals. Both schemes achieve chemical accuracy for a standard benchmark set of non-covalent intermolecular interactions.Comment: 5 pages, 4 figures, and an additional supplementary materia