GW and Bethe-Salpeter study of small water clusters.

We study within the GW and Bethe-Salpeter many-body perturbation theories the electronic and optical properties of small (H2O)n water clusters (n = 1-6). Comparison with high-level CCSD(T) Coupled-Cluster at the Single Double (Triple) levels and ADC(3) Green's function third order algebraic diagrammatic construction calculations indicates that the standard non-self-consistent G0W0@PBE or G0W0@PBE0 approaches significantly underestimate the ionization energy by about 1.1 eV and 0.5 eV, respectively. Consequently, the related Bethe-Salpeter lowest optical excitations are found to be located much too low in energy when building transitions from a non-self-consistent G0W0 description of the quasiparticle spectrum. Simple self-consistent schemes, with update of the eigenvalues only, are shown to provide a weak dependence on the Kohn-Sham starting point and a much better agreement with reference calculations. The present findings rationalize the theory to experiment possible discrepancies observed in previous G0W0 and Bethe-Salpeter studies of bulk water. The increase of the optical gap with increasing cluster size is consistent with the evolution from gas to dense ice or water phases and results from an enhanced screening of the electron-hole interaction.

Accurate and efficient linear scaling DFT calculations with universal applicability.

Density functional theory calculations are computationally extremely expensive for systems containing many atoms due to their intrinsic cubic scaling. This fact has led to the development of so-called linear scaling algorithms during the last few decades. In this way it becomes possible to perform ab initio calculations for several tens of thousands of atoms within reasonable walltimes. However, even though the use of linear scaling algorithms is physically well justified, their implementation often introduces some small errors. Consequently most implementations offering such a linear complexity either yield only a limited accuracy or, if one wants to go beyond this restriction, require a tedious fine tuning of many parameters. In our linear scaling approach within the BigDFT package, we were able to overcome this restriction. Using an ansatz based on localized support functions expressed in an underlying Daubechies wavelet basis - which offers ideal properties for accurate linear scaling calculations - we obtain an amazingly high accuracy and a universal applicability while still keeping the possibility of simulating large system with linear scaling walltimes requiring only a moderate demand of computing resources. We prove the effectiveness of our method on a wide variety of systems with different boundary conditions, for single-point calculations as well as for geometry optimizations and molecular dynamics.

Daubechies wavelets for linear scaling density functional theory.

We demonstrate that Daubechies wavelets can be used to construct a minimal set of optimized localized adaptively contracted basis functions in which the Kohn-Sham orbitals can be represented with an arbitrarily high, controllable precision. Ground state energies and the forces acting on the ions can be calculated in this basis with the same accuracy as if they were calculated directly in a Daubechies wavelets basis, provided that the amplitude of these adaptively contracted basis functions is sufficiently small on the surface of the localization region, which is guaranteed by the optimization procedure described in this work. This approach reduces the computational costs of density functional theory calculations, and can be combined with sparse matrix algebra to obtain linear scaling with respect to the number of electrons in the system. Calculations on systems of 10,000 atoms or more thus become feasible in a systematic basis set with moderate computational resources. Further computational savings can be achieved by exploiting the similarity of the adaptively contracted basis functions for closely related environments, e.g., in geometry optimizations or combined calculations of neutral and charged systems.

Fast and Accurate Electronic Excitations in Cyanines with the Many-Body Bethe-Salpeter Approach.

The accurate prediction of the optical signatures of cyanine derivatives remains an important challenge in theoretical chemistry. Indeed, up to now, only the most expensive quantum chemical methods (CAS-PT2, CC, DMC, etc.) yield consistent and accurate data, impeding the applications on real-life molecules. Here, we investigate the lowest lying singlet excitation energies of increasingly long cyanine dyes within the GW and Bethe-Salpeter Green's function many-body perturbation theory. Our results are in remarkable agreement with available coupled-cluster (exCC3) data, bringing these two single-reference perturbation techniques within a 0.05 eV maximum discrepancy. By comparison, available TD-DFT calculations with various semilocal, global, or range-separated hybrid functionals, overshoot the transition energies by a typical error of 0.3-0.6 eV. The obtained accuracy is achieved with a parameter-free formalism that offers similar accuracy for metallic or insulating, finite size or extended systems.

Combining the Bethe-Salpeter Formalism with Time-Dependent DFT Excited-State Forces to Describe Optical Signatures: NBO Fluoroborates as Working Examples.

We propose to use a blend of methodologies to tackle a challenging case for quantum approaches: the simulation of the optical properties of asymmetric fluoroborate derivatives. Indeed, these dyes, which present a low-lying excited-state exhibiting a cyanine-like nature, are treated not only with the Time-Dependent Density Functional Theory (TD-DFT) method to determine both the structures and vibrational patterns but also with the Bethe-Salpeter approach to compute both the vertical absorption and emission energies. This combination allows us to obtain 0-0 energies with a significantly improved accuracy compared to the "raw" TD-DFT estimates. We also discuss the impact of various declinations of the Polarizable Continuum Model (linear-response, corrected linear-response, and state-specific models) on the obtained accuracy.

Benchmark Many-Body GW and Bethe-Salpeter Calculations for Small Transition Metal Molecules.

We study the electronic and optical properties of 39 small molecules containing transition metal atoms and 7 others related to quantum-dots for photovoltaics. We explore in particular the merits of the many-body GW formalism, as compared to the ΔSCF approach within density functional theory, in the description of the ionization energy and electronic affinity. Mean average errors of 0.2-0.3 eV with respect to experiment are found when using the PBE0 functional for ΔSCF and as a starting point for GW. The effect of partial self-consistency at the GW level is explored. Further, for optical excitations, the Bethe-Salpeter formalism is found to offer similar accuracy as time-dependent DFT-based methods with the hybrid PBE0 functional, with mean average discrepancies of about 0.3 and 0.2 eV, respectively, as compared to available experimental data. Our calculations validate the accuracy of the parameter-free GW and Bethe-Salpeter formalisms for this class of systems, opening the way to the study of large clusters containing transition metal atoms of interest for photovoltaic applications.

Selecting boron fullerenes by cage-doping mechanisms.

So far, no boron fullerenes were synthesized: more compact sp(3)-bonded clusters are energetically preferred. To circumvent this, metallic clusters have been suggested by Pochet et al. [Phys. Rev. B 83, 081403(R) (2011)] as "seeds" for a possible synthesis which would topologically protect the sp(2) sector of the configuration space. In this paper, we identify a basic pentagonal unit which allows a balance between the release of strain and the self-doping rule. We formulate a guiding principle for the stability of boron fullerenes, which takes the form of an isolated filled pentagon rule (IFPR). The role of metallic clusters is then reexamined. It is shown that the interplay of the IFPR and the seed-induced doping breaks polymorphism and its related problems: it can effectively select between different isomers and reduce the reactivity of the boron shells. The balance between self and exterior doping represents the best strategy for boron buckyball synthesis.

Theory of tunnel ionization in complex systems.

A quasianalytical theory of tunnel ionization is developed that is applicable to general complex systems, such as large molecules. Our analysis reveals strong deviations from conventional tunnel ionization theories, dependent upon the system's geometry, angular momentum, and polarizability. A comparison of our theory with recent C(60) ionization experiments yields reasonable agreement.