Xinguo Ren

Ab initio molecular simulations with numeric atom-centered orbitals

We describe a complete set of algorithms for ab initio molecular simulations based on numerically tabulated atom-centered orbitals (NAOs) to capture a wide range of molecular and materials properties from quantum-mechanical first principles. The full algorithmic framework described here is embodied in the Fritz Haber Institute “ab initio molecular simulations” (FHI-aims) computer program package. Its comprehensive description should be relevant to any other first-principles implementation based on NAOs. The focus here is on density-functional theory (DFT) in the local and semilocal (generalized gradient) approximations, but an extension to hybrid functionals, Hartree–Fock theory, and MP2/GW electron self-energies for total energies and excited states is possible within the same underlying algorithms. An all-electron/full-potential treatment that is both computationally efficient and accurate is achieved for periodic and cluster geometries on equal footing, including relaxation and ab initio molecular dynamics. We demonstrate the construction of transferable, hierarchical basis sets, allowing the calculation to range from qualitative tight-binding like accuracy to meV-level total energy convergence with the basis set. Since all basis functions are strictly localized, the otherwise computationally dominant grid-based operations scale as O(N) with system size N. Together with a scalar-relativistic treatment, the basis sets provide access to all elements from light to heavy. Both low-communication parallelization of all real-space grid based algorithms and a ScaLapack-based, customized handling of the linear algebra for all matrix operations are possible, guaranteeing efficient scaling (CPU time and memory) up to massively parallel computer systems with thousands of CPUs.

Random-phase approximation and its applications in computational chemistry and materials science

The random-phase approximation (RPA) as an approach for computing the electronic correlation energy is reviewed. After a brief account of its basic concept and historical development, the paper is devoted to the theoretical formulations of RPA, and its applications to realistic systems. With several illustrating applications, we discuss the implications of RPA for computational chemistry and materials science. The computational cost of RPA is also addressed which is critical for its widespread use in future applications. In addition, current correction schemes going beyond RPA and directions of further development will be discussed.

Structure and energetics of benzene adsorbed on transition-metal surfaces: density-functional theory with van der Waals interactions including collective substrate response

The adsorption of benzene on metal surfaces is an important bench- mark system for hybrid inorganic/organic interfaces. The reliable determination of the interface geometry and binding energy presents a significant challenge for both theory and experiment. Using the Perdew-Burke-Ernzerhof (PBE), PBE+vdW (van der Waals) and the recently developed PBE+vdW surf (density- functional theory with vdW interactions that include the collective electronic response of the substrate) methods, we calculated the structures and energet- ics for benzene on transition-metal surfaces: Cu, Ag, Au, Pd, Pt, Rh and Ir. Our calculations demonstrate that vdW interactions increase the binding en- ergy by more than 0.70eV for physisorbed systems (Cu, Ag and Au) and by an even larger amount for strongly bound systems (Pd, Pt, Rh and Ir). The collective response of the substrate electrons captured via the vdW surf method plays a significant role for most substrates, shortening the equilibrium dis- tance by 0.25A for Cu and decreasing the binding energy by 0.27eV for Rh. The reliability of our results is assessed by comparison with calculations using the random-phase approximation including renormalized single excitations,

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

GW calculations with a fully self-consistent Green’s function G and screened interaction W —based on the iterative solution of the Dyson equation—provide a consistent framework for the description of groundand excited-state properties of interacting many-body systems. We show that for closed-shell systems selfconsistent GW reaches the same final Green’s function regardless of the initial reference state. Self-consistency systematically improves ionization energies and total energies of closed-shell systems compared to G0W0 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.

Self-consistent GW: an all-electron implementation with localized basis functions

This paper describes an all-electron implementation of the self-consistent GW (sc-GW) approach—i.e., based onthesolutionoftheDysonequation—inanall-electronnumericatom-centeredorbitalbasisset.WecastHedin’s equations into a matrix form that is suitable for numerical calculations by means of (i) the resolution-of-identity techniquetohandlefour-centerintegralsand(ii)abasisrepresentationfortheimaginary-frequencydependenceof dynamical operators. In contrast to perturbative G0W0 ,s c-GW provides a consistent framework for ground- and excited-state properties and facilitates an unbiased assessment of the GW approximation. For excited states, we benchmark sc-GW for five molecules relevant for organic photovoltaic applications: thiophene, benzothiazole, 1,2,5-thiadiazole, naphthalene, and tetrathiafulvalene. At self-consistency, the quasiparticle energies are found to be in good agreement with experiment and, on average, more accurate than G0W0 based on Hartree-Fock or density-functional theory with the Perdew-Burke-Ernzerhof exchange-correlation functional. Based on the Galitskii-Migdal total energy, structural properties are investigated for a set of diatomic molecules. For binding energies, bond lengths, and vibrational frequencies sc-GW and G0W0 achieve a comparable performance, which is, however, not as good as that of exact-exchange plus correlation in the random-phase approximation and its advancement to renormalized second-order perturbation theory. Finally, the improved description of dipole moments for a small set of diatomic molecules demonstrates the quality of the sc-GW ground-state density.

Bond breaking and bond formation: How electron correlation is captured in many-body perturbation theory and density-functional theory

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.

Toward Low-Temperature Dehydrogenation Catalysis: Isophorone Adsorbed on Pd(111)

Adsorbate geometry and reaction dynamics play essential roles in catalytic processes at surfaces. Here we present a theoretical and experimental study for a model functional organic/metal interface: isophorone (C9H14O) adsorbed on the Pd(111) surface. Density functional theory calculations with the Perdew-Burke-Ernzerhoff (PBE) functional including van der Waals (vdW) interactions, in combination with infrared spectroscopy and temperature-programmed desorption (TPD) experiments, reveal the reaction pathway between the weakly chemisorbed reactant (C9H14O) and the strongly chemisorbed product (C9H10O), which occurs by the cleavage of four C-H bonds below 250 K. Analysis of the TPD spectrum is consistent with the relatively small magnitude of the activation barrier derived from PBE+vdW calculations, demonstrating the feasibility of low-temperature dehydrogenation.

First-principles description of charge transfer in donor-acceptor compounds from self-consistent many-body perturbation theory

This work was supported by the European Research Council Advanced Grant DYNamo (ERC-2010-AdG-267374), the European Commission within the FP7 CRONOS project (ID 280879), Spanish Grant (FIS2010-21282-C02-01), Ikerbasque and Grupos Consolidados UPV/EHU del Gobierno Vasco (IT578-13).

GW100: Benchmarking G0W0 for Molecular Systems.

We present the GW100 set. GW100 is a benchmark set of the ionization potentials and electron affinities of 100 molecules computed with the GW method using three independent GW codes and different GW methodologies. The quasi-particle energies of the highest-occupied molecular orbitals (HOMO) and lowest-unoccupied molecular orbitals (LUMO) are calculated for the GW100 set at the G0W0@PBE level using the software packages TURBOMOLE, FHI-aims, and BerkeleyGW. The use of these three codes allows for a quantitative comparison of the type of basis set (plane wave or local orbital) and handling of unoccupied states, the treatment of core and valence electrons (all electron or pseudopotentials), the treatment of the frequency dependence of the self-energy (full frequency or more approximate plasmon-pole models), and the algorithm for solving the quasi-particle equation. Primary results include reference values for future benchmarks, best practices for convergence within a particular approach, and average error bars for the most common approximations.

Benchmark of GW methods for azabenzenes

Many-body perturbation theory in the GW approximation is a useful method for describing electronic properties associated with charged excitations. A hierarchy of GW methods exists, starting from non-self-consistent G0W0, through partial self-consistency in the eigenvalues (ev-scGW) and in the Green function (scGW0), to fully self-consistent GW (scGW). Here, we assess the performance of these methods for benzene, pyridine, and the diazines. The quasiparticle spectra are compared to photoemission spectroscopy (PES) experiments with respect to all measured particle removal energies and the ordering of the frontier orbitals. We find that the accuracy of the calculated spectra does not match the expectations based on their level of self-consistency. In particular, for certain starting points G0W0 and scGW0 provide spectra in better agreement with the PES than scGW.