[Show abstract][Hide abstract] ABSTRACT: The accuracy of the many-body perturbation theory GW formalism to calculate
electron-phonon coupling matrix elements has been recently demonstrated in the
case of a few important systems. However, the related computational costs are
high and thus represent strong limitations to its widespread application. In
the present study, we explore two less demanding alternatives for the
calculation of electron-phonon coupling matrix elements on the many-body
perturbation theory level. Namely, we test the accuracy of the static
Coulomb-hole plus screened-exchange (COHSEX) approximation and further of the
constant screening approach, where variations of the screened Coulomb potential
W upon small changes of the atomic positions along the vibrational eigenmodes
are neglected. We find this latter approximation to be the most reliable,
whereas the static COHSEX ansatz leads to substantial errors. Our conclusions
are validated in a few paradigmatic cases: diamond, graphene and the C60
fullerene. These findings open the way for combining the present many-body
perturbation approach with efficient linear-response theories.
Physical Review B 01/2015; 91(15). DOI:10.1103/PhysRevB.91.155109 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Density Functional Theory calculations traditionally suffer from an inherent
cubic scaling with respect to the size of the system, making big calculations
extremely expensive. This cubic scaling can be avoided by the use of so-called
linear scaling algorithms, which have been developed during the last few
decades. In this way it becomes possible to perform ab-initio calculations for
several tens of thousands of atoms or even more within a reasonable time frame.
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 systems
with only a moderate demand of computing resources.
Physical Chemistry Chemical Physics 01/2015; DOI:10.1039/C5CP00437C · 4.49 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: 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.
Journal of Chemical Theory and Computation 10/2014; 10(10):4548-4556. DOI:10.1021/ct500552e · 5.50 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: 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 Delta SCF approach within density functional theory, in the description of the ionization energy and electronic affinity. Mean average errors of 0.20.3 eV with respect to experiment are found when using the PBE0 functional for Delta SCF and as a starting point for GW. The effect of partial self-consistency at the GW level is explored. Further, for optical excitations, the BetheSalpeter 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 BetheSalpeter formalisms for this class of systems, opening the way to the study of large clusters containing transition metal atoms of interest for photovoltaic applications.
Journal of Chemical Theory and Computation 09/2014; 10(9):3934-3943. DOI:10.1021/ct5003658 · 5.50 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The renormalization of electronic eigenenergies due to electron-phonon
interactions (temperature dependence and zero-point motion effect) is important
in many materials. We address it in the adiabatic harmonic approximation, based
on first principles (e.g. Density-Functional Theory), from different points of
view: directly from atomic position fluctuations or, alternatively, from
Janak's theorem generalized to the case where the Helmholtz free energy,
including the vibrational entropy, is used. We prove their equivalence, based
on the usual form of Janak's theorem and on the dynamical equation. We then
also place the Allen-Heine-Cardona (AHC) theory of the renormalization in a
first-principle context. The AHC theory relies on the rigid-ion approximation,
and naturally leads to a self-energy (Fan) contribution and a Debye-Waller
contribution. Such a splitting can also be done for the complete harmonic
adiabatic expression, in which the rigid-ion approximation is not required. A
numerical study within the Density-Functional Perturbation theory framework
allows us to compare the AHC theory with frozen-phonon calculations, with or
without the rigid-ion terms. For the two different numerical approaches without
rigid-ion terms, the agreement is better than 7 $\mu$eV in the case of diamond,
which represent an agreement to 5 significant digits. The magnitude of the non
rigid-ion terms in this case is also presented, distinguishing specific phonon
modes contributions to different electronic eigenenergies.
Physical Review B 08/2014; 90(21). DOI:10.1103/PhysRevB.90.214304 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We compute the zero-point renormalization (ZPR) of the optical band gap of diamond from many-body perturbation theory using the perturbative ${G}_{0}{W}_{0}$ approximation as well as quasiparticle self-consistent $GW$. The electron-phonon coupling energies are found to be more than 40% higher than standard density functional theory when many-body effects are included with the frozen-phonon calculations. A similar increase is observed for the zero-point renormalization in GaAs when ${G}_{0}{W}_{0}$ corrections are applied. We show that these many-body corrections are necessary to accurately predict the temperature dependence of the band gap. The frozen-phonon method also allows us to validate the rigid-ion approximation which is always present in density functional perturbation theory.
[Show abstract][Hide abstract] ABSTRACT: 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.
Journal of Chemical Theory and Computation 02/2014; 10(3):1212–1218. DOI:10.1021/ct401101u · 5.50 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Many-body Green's function perturbation theories, such as the GW and Bethe-Salpeter formalisms, are starting to be routinely applied to study charged and neutral electronic excitations in molecular organic systems relevant to applications in photovoltaics, photochemistry or biology. In parallel, density functional theory and its time-dependent extensions significantly progressed along the line of range-separated hybrid functionals within the generalized Kohn-Sham formalism designed to provide correct excitation energies. We give an overview and compare these approaches with examples drawn from the study of gas phase organic systems such as fullerenes, porphyrins, bacteriochlorophylls or nucleobases molecules. The perspectives and challenges that many-body perturbation theory is facing, such as the role of self-consistency, the calculation of forces and potential energy surfaces in the excited states, or the development of embedding techniques specific to the GW and Bethe-Salpeter equation formalisms, are outlined.
Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences 02/2014; 372(2011):20130271. DOI:10.1098/rsta.2013.0271 · 2.15 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We demonstrate that Daubechies wavelets can be used to construct a minimal
set of optimized localized 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 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 DFT 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 contracted basis functions for closely
related environments, e.g. in geometry optimizations or combined calculations
of neutral and charged systems.
The Journal of Chemical Physics 01/2014; 140(20). DOI:10.1063/1.4871876 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study within the many-body Green's function GW and Bethe-Salpeter formalisms the excitation energies of a paradigmatic model dipeptide, focusing on the four lowest-lying local and charge-transfer excitations. Our GW calculations are performed at the self-consistent level, updating first the quasiparticle energies, and further the single-particle wavefunctions within the static Coulomb-hole plus screened-exchange approximation to the GW self-energy operator. Important level crossings, as compared to the starting Kohn-Sham LDA spectrum, are identified. Our final Bethe-Salpeter singlet excitation energies are found to agree, within 0.07 eV, with CASPT2 reference data, except for one charge-transfer state where the discrepancy can be as large as 0.5 eV. Our results agree best with LC-BLYP and CAM-B3LYP calculations with enhanced long-range exchange, with a 0.1 eV mean absolute error. This has been achieved employing a parameter-free formalism applicable to metallic or insulating extended or finite systems.
The Journal of Chemical Physics 11/2013; 139(19):194308. DOI:10.1063/1.4830236 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: With the ever-increasing sophistication of codes, the verification of the
implementation of advanced theoretical formalisms becomes critical. In
particular, cross comparison between different codes provides a strong hint in
favor of the correctness of the implementations, and a measure of the
(hopefully small) possible numerical differences. We lead a rigorous and
careful study of the quantities that enter in the calculation of the zero-point
motion renormalization of the direct band gap of diamond due to electron-phonon
coupling, starting from the total energy, and going through the computation of
phonon frequencies and electron-phonon matrix elements. We rely on two
independent implementations : Quantum Espresso + Yambo and ABINIT. We provide
the order of magnitude of the numerical discrepancies between the codes, that
are present for the different quantities: less than $10^{-5}$ Hartree per atom
on the total energy (-5.722 Ha/at), less than 0.07 cm$^{-1}$ on the
$\Gamma,L,X$ phonon frequencies (555 to 1330 cm$^{-1}$), less than 0.5% on the
square of the electron-phonon matrix elements and less than 4 meV on the
zero-point motion renormalization of each eigenenergies (44 to 264 meV). Within
our approximations, the DFT converged direct band gap renormalization in
diamond due to the electron-phonon coupling is -0.409 eV (reduction of the band
gap).
[Show abstract][Hide abstract] ABSTRACT: 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.
The Journal of Chemical Physics 05/2013; 138(18):184302. DOI:10.1063/1.4802775 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Magnetism in two dimensional atomic sheets has attracted considerable interest as its existence could allow the development of electronic and spintronic devices. The existence of magnetism is not sufficient for devices, however, as states must be addressable and modifiable through the application of an external drive. We show that defects in hexagonal boron nitride present a strong interplay between the N-N distance in the edge and the magnetic moments of the defects. By stress-induced geometry modifications, we change the ground state magnetic moment of the defects. This control is made possible by the triangular shape of the defects as well as the strong spin localisation in the magnetic state.
[Show abstract][Hide abstract] ABSTRACT: The modifications of the electronic band structure of solids due to electron-phonon interactions (temperature and zero-point motion effects) have been explored by Manuel Cardona from both the experimental and theoretical sides. In the present contribution, we focus on the theoretical approaches to such effects. Although the situation has improved since the seventies, the wish for a fully developed theory (and associated efficient implementations) is not yet fulfilled. We review noticeable semi-empirical and first-principle studies, with a special emphasis on the Allen-Heine-Cardona (AHC) approach. We then focus on the non-diagonal Debye-Waller contribution, appearing beyond the rigid-ion approximation, in a Density-Functional Theory (DFT) approach. A numerical study shows that they can be sizeable (10%–50%) for diatomic molecules. We also present the basic idea of a new formalism, based on Density-Functional Perturbation Theory, that allows one to avoid the sums over a large number of empty states, and speed up the calculation by one order of magnitude, compared to the straightforward implementation of the AHC approach within DFT.
[Show abstract][Hide abstract] ABSTRACT: We present a first-principles study of Peierls distortions in trans-polyacetylene, polyacene, and armchair (n,n) carbon nanotubes. Our findings suggest that the ground-state geometries of armchair (n,n) carbon nanotubes, with n up to 6, exhibit a Peierls distortion as it is found for trans-polyactetylene. In contrast to previous studies in which no Peierls distortion is found with conventional local and semilocal density functionals, we use a hybrid functional whose exact-exchange admixture has been specifically optimized for the problem at hand.
[Show abstract][Hide abstract] ABSTRACT: The energy bands of semiconductors exhibit significant shifts and broadening with temperature at constant volume. This is an effect of the direct renormalization of band energies due to electron-phonon interactions. In search of an efficient linear response DFT approach to this effect, beyond semi-empirical approximation or frozen- phonon DFT, we have implemented formulas derived by Allen and Heine [J. Phys. C 9, 2305 (1976)] inside the ABINIT package. We have found that such formulas need a great number of bands, O(1000), to properly converge the thermal corrections of deep potential well atoms, i.e. elements of the first row. This leads to heavy computational costs even for simple systems like diamond. The DFPT formalism can be used to circumvent entirely the need for conduction bands by computing the first-order wave-functions using the self-consistent Sternheimer equation. We will compare the results of both formalism demonstrating that the DFPT approach reproduces the correct converged results of the formulas of Allen and Heine.
[Show abstract][Hide abstract] ABSTRACT: ABINIT [http://www.abinit.org] allows one to study, from first-principles, systems made of electrons and nuclei (e.g. periodic solids, molecules, nanostructures, etc.), on the basis of Density-Functional Theory (DFT) and Many-Body Perturbation Theory. Beyond the computation of the total energy, charge density and electronic structure of such systems, ABINIT also implements many dynamical, dielectric, thermodynamical, mechanical, or electronic properties, at different levels of approximation.The present paper provides an exhaustive account of the capabilities of ABINIT. It should be helpful to scientists that are not familiarized with ABINIT, as well as to already regular users. First, we give a broad overview of ABINIT, including the list of the capabilities and how to access them. Then, we present in more details the recent, advanced, developments of ABINIT, with adequate references to the underlying theory, as well as the relevant input variables, tests and, if available, ABINIT tutorials.Program summaryProgram title: ABINITCatalogue identifier: AEEU_v1_0Distribution format: tar.gzJournal reference: Comput. Phys. Comm.Programming language: Fortran95, PERL scripts, Python scriptsComputer: All systems with a Fortran95 compilerOperating system: All systems with a Fortran95 compilerHas the code been vectorized or parallelized?: Sequential, or parallel with proven speed-up up to one thousand processors.RAM: Ranges from a few Mbytes to several hundred Gbytes, depending on the input file.Classification: 7.3, 7.8External routines: (all optional) BigDFT [1], ETSF IO [2], libxc [3], NetCDF [4], MPI [5], Wannier90 [6]Nature of problem: This package has the purpose of computing accurately material and nanostructure properties: electronic structure, bond lengths, bond angles, primitive cell size, cohesive energy, dielectric properties, vibrational properties, elastic properties, optical properties, magnetic properties, non-linear couplings, electronic and vibrational lifetimes, etc.Solution method: Software application based on Density-Functional Theory and Many-Body Perturbation Theory, pseudopotentials, with planewaves, Projector-Augmented Waves (PAW) or wavelets as basis functions.Running time: From less than one second for the simplest tests, to several weeks. The vast majority of the >600 provided tests run in less than 30 seconds.References:[1] http://inac.cea.fr/LSim/BigDFT.[2] http://etsf.eu/index.php?page=standardization.[3] http://www.tddft.org/programs/octopus/wiki/index.php/Libxc.[4] http://www.unidata.ucar.edu/software/netcdf.[5] http://en.wikipedia.org/wiki/MessagePassingInterface.[6] http://www.wannier.org.
[Show abstract][Hide abstract] ABSTRACT: The electronic properties of ladder-type polythiophene (polythienoacene) and its derivatives are studied using density functional theory. Upon an analysis of the variation of the band gap when comparing the non-ladder and the ladder-type polymers, a discrepancy is found between the thiophene and the pyrrole(nitrogen-substituted thiophene) polymer families. The polythienoacene has a larger band gap than the polythiophene whereas the opposite is found for the pyrrole polymers. Also, it is found that a simple alternation of the sulfur atom in polythienoacene structure by nitrogen or boron atoms can lead to small band gap polymers. The excitations of these polythienoacene's derivatives are investigated using time-dependent density functional theory.