Resolution-of-identity approach to Hartree–Fock, hybrid density functionals, RPA, MP2 and<i>GW</i>with numeric atom-centered orbital basis functions

Ren, Xinguo; Rinke, Patrick; Blüm, Volker; Wieferink, Jürgen; Tkatchenko, Alexandre; Sanfilippo, Andrea G.; Reuter, Karsten; Scheffler, Matthias

doi:10.1088/1367-2630/14/5/053020

Cited by 679 publications

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“…However, as indicated above, We have implemented sc-GW in the all-electron electronicstructure code FHI-AIMS. 29,30 Equations (1)-(4) and (6) are solved in a numerical atomic orbital (NAO) basis using the resolution of identity technique to treat all two-particle operators efficiently. 30,31 All calculations are performed on the imaginary frequency axis and the spectral function is obtained by analytic continuation to the real frequency axis.…”

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confidence: 99%

“…29,30 Equations (1)-(4) and (6) are solved in a numerical atomic orbital (NAO) basis using the resolution of identity technique to treat all two-particle operators efficiently. 30,31 All calculations are performed on the imaginary frequency axis and the spectral function is obtained by analytic continuation to the real frequency axis. 30 The analytic continuation constitutes the only approximation of our implementation of the sc-GW method.…”

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confidence: 99%

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Unified description of ground and excited states of finite systems: The self-consistentGWapproach

et al. 2012

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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 G 0 W 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. Many-body perturbation theory (MBPT) 1 in the GW approximation of the electronic self-energy 2,3 is presently the state-of-the-art method for describing the spectral properties of solids. 4,5 Recently, it has steadily gained popularity for molecules and nanosystems. 6 In addition, MBPT provides a prescription to extract total energies and structural properties from the GW approximation and therefore is a consistent theoretical framework for single-particle spectra and total energies.Due to its numerical cost and algorithmic difficulties, the GW method has only recently been applied self-consistently (i.e., nonperturbatively) to atoms, 7 molecules, 8 and molecular transport. 6 Predominantly, GW calculations are still performed perturbatively (one-shot G 0 W 0 ) on a set of singleparticle orbitals and eigenvalues obtained from a preceding density-functional theory 9 (DFT) or Hartree-Fock (HF) calculation. This procedure introduces a considerable starting-point dependence, 10-12 which can be eliminated by iterating the Dyson equation to self-consistency. [6][7][8]13 The resulting selfconsistent GW (sc-GW ) framework is a conserving approximation in the sense of Baym and Kadanoff 14 (i.e., it satisfies momentum, energy, and particle number conservation laws). sc-GW gives total energies 15 free from the ambiguities of the G 0 W 0 scheme, in which the results depend on the chosen total energy functional. 7 However, as in any self-consistent theory, the question remains if the self-consistent solution of the Dyson equation is unique. This issue is fundamentally different from the initial-state dependence of G 0 W 0 . For HF (Ref. 16) and local-density approximation (LDA)/generalized gradient approximation + U (GGA + U ) (Ref. 17) calculations, it is well known that the self-consistency cycle can reach many local minima instead of the global minimum. Moreover, a previous sc-GW study for the Be atom showed that normconserving pseudopotential calculations do not produce the same final GW Green's function (and the corresponding ionization potential) as all-electron calculations. 18 In this Rapid Communication, we demonstrate certain key aspects of the sc-GW approximation for closed-shell molecules that make...

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Unified description of ground and excited states of finite systems: The self-consistentGWapproach

et al. 2012

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“…A Γ-centered 8 × 8 × 8 k−point mesh is used for the DFT calculations. All calculations are performed using the all-electron numeric atom-centered basis code fhi-aims [40][41][42][43] and Tier 2 basis sets.…”

Section: Theorymentioning

confidence: 99%

On the Monte Carlo Description of Hot Carrier Effects and Device Characteristics of III‐N LEDs

Kivisaari

Sadi

et al. 2017

Adv Elect Materials

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of LED operation remain poorly understood, presenting an obvious bottleneck for further LED development and optimization. [5] For example, recent measurements have shown that III-N LEDs exhibit notable hot carrier distributions already close to the peak efficiency, [6][7][8][9] suggesting that hot carriers might have a more profound effect on the device characteristics than previously anticipated.To date, conventional LED simulations have mainly relied on the drift-diffusion (DD) model (see, e.g., refs. [10-13]), which cannot genuinely account for hot carriers and generally also produces larger turnon voltages for MQW LEDs than observed experimentally. [14] Many reasons have been suggested to explain this discrepancy, including charge transport through indium fluctuations, [15] V-shaped pits, [16] tunneling through traps [17] or hot carrier transport. [18] At present it is, however, unclear if the discrepancy is of a physical origin or if it arises simply because the very foundations of the widely adopted DD model make it incapable of predicting the most essential device-level characteristics of LEDs.The Monte Carlo (MC) method has been established as the standard tool to simulate hot-carrier effects in unipolar semiconductor devices such as transistors. Recently the MC method has also been expanded by Bertazzi et al. to simulate hot electron effects in GaN barriers of LEDs using full-band MC methods, [19] and ourselves, as we have recently developed a coupled Monte Carlo-drift-diffusion (MCDD) simulation method to investigate hot-electron effects in full III-N MQW LED structures. [20][21][22] More recently, we have also introduced a full MC model, [23] which can be used to carry out full MC simulations of both electrons and holes in a complete LED device. Nevertheless, the previous works have not yet provided a full analysis of the pertinent physics and differences between MC and DD. To provide more insight into the physics of MQW devices and to facilitate their further development, we now deploy our full MC simulator to answer the following questions:

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“…The effective masses of m * c = 1.4463 m 0 for the conduction and m * v = −8.3035 m 0 for the valence band have been obtain from a fit to the DFT band structure of bulk ZnO. All DFT calculations in this work have been performed with the Fritz-Haber-Institut ab initio molecular simulations (FHI-aims) code [38,39] and the Heyd-Scuseria-Ernzerhof (HSE) [40,41] exchange-correlation functional. Following our previous work on ZnO [42], the exact-exchange admixture was chosen to be 40%, which yields a band gap of E g = 3.4 eV.…”

Section: Numerical Investigationmentioning

confidence: 99%

Theory of optical excitations in dipole-coupled hybrid molecule-semiconductor layers: Coupling of a molecular resonance to semiconductor continuum states

et al. 2014

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We theoretically investigate the optical absorption of a hybrid system consisting of an organic molecular film on top of a semiconductor substrate. The electronic states of the isolated spatially separated constituents couple due to the Coulomb interaction of the optically induced charge carriers across the film-substrate interface. Focussing on the coupling of optical active molecular transitions to semiconductor continuum states, we find that the nonradiative dipole-dipole energy transfer causes the formation of coupled excitations, effectively reducing the excitation energy of the optical resonance in the molecular film and inducing a broadening of the associated absorption peak. In the framework of the Heisenberg equation of motion technique, we derive the Bloch equations for these hybrid systems. The input parameters for our model system of ladder-type quarterphenyl (L4P) molecules on the ZnO(1010) surface are taken from density functional theory calculations.

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Resolution-of-identity approach to Hartree–Fock, hybrid density functionals, RPA, MP2 andGWwith numeric atom-centered orbital basis functions

Cited by 679 publications

References 214 publications

Unified description of ground and excited states of finite systems: The self-consistentGWapproach

Unified description of ground and excited states of finite systems: The self-consistentGWapproach

On the Monte Carlo Description of Hot Carrier Effects and Device Characteristics of III‐N LEDs

Theory of optical excitations in dipole-coupled hybrid molecule-semiconductor layers: Coupling of a molecular resonance to semiconductor continuum states

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