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C. Attaccalitea, C. Fabera, P. Boulangera, I. Ducheminb, V. Olevanoa and X. Blasea
a) Institute Neel, CNRS/UGA, Grenoble (France)
b) INAC, SP2M/L_sim, CEA cedex 09, 38054 Grenoble, France
FIESTA: French Initiative for Electronic Simulations with Thousands of Atoms
The Fiesta code implements the GW and Bethe-Salpeter formalisms using Gaussian bases. Dynamical screening contribution to the self-energy is explicitly accounted for through a contour deformation approach. Self-consistency on the wave-functions is implemented at the static COHSEX level. Tamm-Dancoff approximation (TDA) or full Bethe-Salpeter calculations can be performed. The code presently reads input Kohn-Sham eigenstates from the open-source Siesta and NWChem package.
Introduction
The quasi-particle formalism, namely the mapping of the true many-body problem onto a single (quasi-)particle framework, allows to draw fruitful correspondence between the KS approach within DFT, and the self-energy formulation eigenvalue problem within many-body perturbation theory (MBPT):
Electronic properties
Electron-phonon coupling
Optical properties
(3-fold)
LUMO
Changes in electronic structure
EPC ~ |slope|2
Structural deformation
Stepwise deformation
LDA 73 meV
evGW 101 meV
Exp. 107 meV
DFT: J. Laflamme-Janssen, PRB 2010;
GW: C. Faber, PRB 84, 155104, 2011;
Exp: Wang, JCP 2005; Hands, PRB 2008;
Electron-phonon potential
ev-GW
DFT-LDA
Electron–phonon coupling and charge-transfer excitations in organic systems
from many-body perturbation theory
C. Faber et al., J. of Material Science, 47, 7472(2012)
All correlation effects are included in the self-energy operator S
the we approximate as:
Where G is the single particle electronic Green's function
and W is the screened electron-electron interaction
The GW method
F. Aryasetiawan, and O. Gunnarsson
Reports on Progress in Physics, 61(3), 237. (1998)
It is now well documented that the KS band gap of semiconductors or insulators is significantly underestimated when using standard semilocal functionals (LDA, PBE, etc..)
In many-body perturbation theory excitation energies associated with adding or removing an electron from the system can be properly defined as the poles in the energy representation of one-particle Green's function G, and can be obtained as:
HOMO–LUMO gaps for C60, pentacene and H2TPP calculated within DFT–LDA, Hartree–Fock, hybrid B3LYP, OT-BNL, α-NKC0, ‘single-shot’ G0W0@LDA and self-consistent on the eigenvalues ev-GW@LDA and experimental results. We got HOMO–LUMO gaps that are within one-tenth of an electron volt from the experiments
GW approach leads not only to a much better description of the ionization energy and electronic affinity, but also corrects as well the ordering of levels which, for organic molecules presenting π and σ states of different nature and localization, can be wrong within LDA or PBE. This effect is illustrated in the above figure for thee case of DNA and RNA nucleobases.
First-principles GW calculations for DNA and RNA nucleobases.
C. Faber, C. Attaccalite, V. Olevano, E. Runge, X. Blase. Phys. Rev. B 83, 115123 (2011)
First-principles GW calculations for fullerenes, porphyrins, phtalocyanine, and other molecules of
interest for organic photovoltaic applications.
X. Blase, C. Attaccalite, V. Olevano, Phys. Rev. B 83, 115103 (2011)
The calculation of electron–phonon matrix elements can be very straightforwardly related, using the Helmann–Feynman theorem, to the evolution of the electronic energy level (here the three-fold t1u LUMO) with respect to the vibrational mode deformation.
In the C60 case at the GW level the coupling is significantly larger than the DFT-LDA one and in close agreement with the latest experimental value
The Bethe–Salpeter formalism tackles the problem of the neutral optical excitations,
namely excitations where the electron does not leave the system and interacts through
the (screened) Coulomb potential with the hole left in the occupied manifold.
The BSE formalism can be recast in an eigenvalues problem similar to TDDFT
in the so-called Casida's formulation:
Conclusions
Experimental and theoretical lowest-lying CT
excitation energies in a family of gas phase
donor–acceptor complexes composed on TCNE with benzene, toluene, o-xylene and
naphthalene donors. The inset shows the HOMO and LUMO localized respectively on the donor and the acceptor (TCNE/anthracene dimer).
Evolution as a function of the ZnBC–BC distance of the energy of the intramolecular Q and B (Soret) excitations and of the CT excitations. Charge-transfer excitations verify a simple asymptotic behaviour in the so-called ‘Mulliken limit’ of a large distance D between the donor and the acceptor, not well described in TDDFT.
Charge-transfer excitations in molecular donor-acceptor complexes within the many-body Bethe-Salpeter approach
X. Blase and C. Attaccalite, Applied Physics Letters, 99(17), 171909 (2011)
Short-range to long-range charge-transfer excitations in the zincbacteriochlorin-bacteriochlorin complex: a Bethe-Salpeter study
I. Duchemin, T. Deutsch, & X. Blase, PRL 109(16), 167801 (2012)
Excited states properties of organic molecules: from density functional theory to the GW and Bethe–Salpeter Green's function formalisms
C. Faber, P. Boulanger, C. Attaccalite, I. Duchemin, X. Blase Phil. Trans. A, 372, 20130271(2014)
FIESTA code: http://perso.neel.cnrs.fr/xavier.blase/fiesta/
Charge-transfer excitations in molecular donor-acceptor complexes within the many-body Bethe-Salpeter approach
X. Blase and C. Attaccalite, Applied Physics Letters, 99(17), 171909 (2011)
Short-range to long-range charge-transfer excitations in the zincbacteriochlorin-bacteriochlorin complex: a Bethe-Salpeter study
I. Duchemin, T. Deutsch, & X. Blase, PRL 109(16), 167801 (2012)
After decades of expertise in applying the GW-BSE formalism to inorganic semiconducting or insulating systems, there is an emerging line of work devoted to extending such techniques to organic molecular systems for applications in electronics, photovoltaics, photocatalysis and biology.