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.

IntroductionThe 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

Electron­phonon coupling

Optical properties

(3-fold)

LUMO

Changes in electronic structure

EPC ~ |slope|2

Structural deformation

Stepwise deformation

LDA 73 meVevGW 101 meVExp. 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 charge­transfer excitations in organic systems from many­body perturbation theory

C. Faber et al.,  J. of Material Science, 47, 7472(2012) 

All correlation effects are included in the self-energy operator the we approximate as:

Where G is the single particle electronic Green's function and W is the screened electron-electron interaction

The GW methodF. 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 many­body 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  one­particle 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, OT­BNL,  ­NKC0, ‘single­shot’ Gα

0W

0@LDA and self­

consistent on the eigenvalues ev­GW@LDA and experimental results. We got HOMO–LUMO gaps that are within one­tenth 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   and   states of different nature and localization, can be wrong π σwithin LDA or PBE.  This effect  is illustrated in the above figure  for thee case of DNA 

and RNA nucleobases.

●  First­principles GW calculations for DNA and RNA nucleobases.         C. Faber, C. Attaccalite, V. Olevano, E. Runge, X. Blase. Phys. Rev. B 83, 115123 (2011)

●  First­principles 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 three­fold t1u

 LUMO) with respect to the vibrational 

mode deformation. 

In the C60

 case at the GW level the coupling is significantly larger than the DFT­LDA 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. 

Charge­transfer excitations verify a simple asymptotic behaviour in the so­called ‘Mulliken limit’  of a large distance D between the donor and the acceptor, not well described in TDDFT.

●  Charge­transfer excitations in molecular donor­acceptor complexes within the many­body Bethe­Salpeter approach X. Blase and C. Attaccalite, Applied Physics Letters, 99(17), 171909 (2011)

● Short­range to long­range charge­transfer excitations in the zincbacteriochlorin­bacteriochlorin complex: a Bethe­Salpeter 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/

●  Charge­transfer excitations in molecular donor­acceptor complexes within the many­body Bethe­Salpeter approach X. Blase and C. Attaccalite, Applied Physics Letters, 99(17), 171909 (2011)

● Short­range to long­range charge­transfer excitations in the zincbacteriochlorin­bacteriochlorin complex: a Bethe­Salpeter study I. Duchemin, T. Deutsch, & X. Blase, PRL 109(16), 167801 (2012)

After decades of expertise in applying the GW­BSE 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.