Microscopic Insight into the Electronic Structure of BCF-Doped Oligothiophenes from \textit{Ab initio} Many-Body Theory
MMicroscopic Insight into the Electronic Structureof BCF-Doped Oligothiophenes from Ab initioMany-Body Theory
Richard Schier, † Ana M. Valencia, † , ‡ and Caterina Cocchi ∗ , † , ‡ † Humboldt-Universit¨at zu Berlin, Physics Department and IRIS Adlershof, 12489 Berlin,Germany ‡ Carl von Ossietzky Universit¨at Oldenburg, Institute of Physics, 26129 Oldenburg, Germany
E-mail: [email protected] a r X i v : . [ c ond - m a t . m t r l - s c i ] J u l bstract Lewis acids like tris(pentafluorophenyl)borane (BCF) offer promising routes for effi-cient p -doping of organic semiconductors. The intriguing experimental results achievedso far call for a deeper understanding of the underlying doping mechanisms. In a first-principles work, based on state-of-the-art density-functional theory and many-bodyperturbation theory, we investigate the electronic and optical properties of donor/acceptorcomplexes formed by quarterthiophene (4T) doped by BCF. For reference, hexafluo-robenzene (C F ) and BF are also investigated as dopants for 4T. Modelling theadducts as bimolecules in vacuo , we find negligible charge transfer in the ground stateand frontier orbitals either segregated on opposite sides of the interface (4T:BCF)or localized on the donor (4T:BF , 4T:C F ). In the optical spectrum of 4T:BCF,a charge-transfer excitation appears at lowest-energy, corresponding to the transitionbetween the frontier states, which exhibit very small but non-vanishing wave-functionoverlap. In the other two adducts, the absorption is given by a superposition of thefeatures of the constituents. Our results clarify that the intrinsic electronic interactionsbetween donor and acceptor are not responsible for the doping mechanisms induced byBCF and related Lewis acids. Extrinsic factors, such as solvent-solute interactions, in-termolecular couplings, and thermodynamic effects, have to be systematically analyzedfor this purpose. ntroduction Doping represents a crucial process to enable the application of organic semiconductors inoptoelectronics.
A consolidated consensus acknowledges the formation of charge-transfercomplexes and ion-pairs as the dominant doping mechanisms in organic semicon-ductors.
The emergence of Lewis acids like tris(pentafluorophenyl)borane, B(C F ) (inshort BCF) as novel dopant species has opened new routes for efficient p -doping of or-ganic polymers and oligomers. The pioneering study by Pingel et al. , has identifiedinteger charge transfer between poly(3-hexylthiophen-2,5-diyl) (P3HT) and BCF, but hasnot been able to fully disclose the underlying physical processes. The recent work by Yurash et al. has demonstrated that the doping mechanisms induced by BCF and other Lewis acidsis largely mediated by the protonation of a portion of the polymer in solution. Mansour andcoworkers have just shown that BCF promotes in P3HT the formation of polarons withdifferent characteristics depending on the morphology and aggregation of the donor species.The complexity unraveled by these observations calls for an in-depth understanding ofthe quantum-mechanical interactions that characterize these complexes. This is a necessarystep to gain insight into intrinsic properties of the materials, such as orbital hybridization,wave-function overlap, and, more generally, electronic interactions, which strongly affect thebehavior of the system in the actual experimental and device conditions, but are not straight-forward to be detected in the measurements. In order to disclose and rationalize these effects,we present in this paper a state-of-the-art first-principles investigation of the electronic andoptical properties of the donor/acceptor complex formed by a quaterthiophene (4T) oligomerdoped by BCF. In our analysis, performed in the framework of hybrid density-functional the-ory and many-body perturbation theory ( GW approximation and Bethe-Salpeter equation),we investigate isolated adducts in vacuo . In this way, we are able to pinpoint the electronicinteractions within the complex and to understand the underlying quantum-mechanical ef-fects. For comparison, we investigate two additional complexes formed by the Lewis acidBF and by hexafluorobenzene (C F ). In the ground state, we focus on the charge transfer,3he level alignment between the donor and acceptor, and the character of the frontier orbitalsin the adducts. Furthermore, we compute the optical absorption spectra of the complexesand quantitatively determine the spatial distribution of the electron and hole densities. Withthis analysis we are able to provide relevant information about the intrinsic characteristicsof these prototypical donor/acceptor complexes, which is necessary for an improved under-standing of the fundamental doping mechanisms induced by BCF and related Lewis acids. Methodology
Theoretical Background
The results presented in this work are carried out from first principles in the frameworkof density functional theory (DFT) and many-body perturbation theory (MBPT), in-cluding the GW approximation and the solution of the Bethe-Salpeter equation (BSE). InDFT, the many-body system is mapped into the fictitious Kohn-Sham (KS) system of non-interacting electrons. The electronic states are described by the wavefunctions φ j , whichare the solutions of the secular equation with effective Hamiltonian ˆ h :ˆ hφ j = ( ˆ T + ˆ V eff ) φ j = ( ˆ T + ˆ V ext + ˆ V H + ˆ V xc ) φ j = (cid:15) j φ j (1)The eigenvalues (cid:15) j correspond to the energies of the respective φ j . ˆ T is the kinetic energyoperator and V eff the effective KS potential. This term is given by the sum of the externalpotential V ext , corresponding to the interaction between the electrons and the nuclei, theHartree potential V H , and the exchange-correlation potential V xc , describing the exchange-correlation interaction between the electrons. We recall that the exact form of the last termis unknown and, therefore, has to be approximated.The DFT results represent the starting point for the calculation of the quasi-particle(QP) electronic structure within the GW approximation, where the electronic self-energy4s given by Σ = iGW . Here, we use the perturbative G W approach to solve the QPequation (cid:15) QPj = (cid:15) KSj + (cid:104) φ KSj | Σ( (cid:15) QPj ) − ˆ V xc | φ KSj (cid:105) (2)and obtain the QP energies (cid:15)
QPj . Finally, to compute the optical excitations, we solve theBSE, which is the equation of motion of the two-particle polarizability: L = L + L Ξ L, (3)where L is the interacting electron-hole correlation function related to the two-particleGreen’s function, L is its non-interacting counterpart, and Ξ is the electron-hole interactionkernel including the statically screened Coulomb interaction as well as the exchange poten-tial between the positively-charged hole and the negatively-charged electron. In practice,the problem is mapped into a secular equation with an effective two-particle Hamiltonianincluding the BSE kernel. Computational Details
Equilibrium geometries are calculated by force minimization in the framework of DFT. Forthese calculations we use the all-electron code FHI-aims. The Perdew-Burke-Ernzerhofsemi-local functional is used to approximate the exchange-correlation potential, togetherwith tight integration grids and TIER2 basis sets. The Tkatchenko-Scheffler scheme isadopted to include van der Waals interactions. The optimization procedure is carried outuntil the Hellmann-Feynman forces are smaller than 10 − eV/˚A.To calculate the electronic and optical properties in the framework of DFT and MBPT, weuse the MOLGW code. Gaussian-type cc-pVDZ basis sets are used and the resolution-of-identity approximation is applied. Here, the hybrid exchange-correlation functional usingthe Coulomb-attenuating method CAM-B3LYP is chosen. The Bader charge analysisscheme is used to compute the partial charges. The G W and the BSE calculations5re performed including all the occupied states and with approximately three time as manyunoccupied states. The total number of occupied and unoccupied states is determined by thenumber of basis functions used to calculate the KS wave-functions. In the case of 4T:BCF,this amounts to a total of 822 KS states, including 209 occupied and 613 virtual orbitals.For 4T:C F
130 occupied and 384 virtual orbitals are used, while in 4T:BF , 101 occupiedand 301 virtual ones are adopted. The BSE is solved in the Tamm-Dancoff approximation.The spatial distribution of the λ th electron-hole pair is evaluated from the electron and holedensities, defined as: ρ λh ( r ) = (cid:88) αβ A λαβ | φ α ( r ) | (4)and ρ λe ( r ) = (cid:88) αβ A λαβ | φ β ( r ) | , (5)respectively, where φ α and φ β are the occupied and the unoccupied QP states con-tributing to the λ th excitation, respectively. The weighting coefficients A λαβ are the absolutesquares of the normalized BSE eigenvectors. Results
Structural properties (a) (b) (c) (b) y x z 1 2 3 4
Figure 1: Ball-and-stick representation of the adducts considered in this work: (a) 4T:BCF,(b) 4T:C F and (c) 4T:BF complexes. Sulphur, carbon, hydrogen, fluorine, and boronatoms are represented in yellow, grey, white, green, and pink, respectively. The number ofthe 4T rings in panel (b) is used in Table 1. 6o study the impact of BCF on the electronic and optical properties of organic semicon-ductors, we consider a model system formed by 4T interacting with one BCF molecule in thegas phase, in absence of any reference of such a system in the solid state. It is worth mention-ing, however, that in co-crystals the geometries of faced 4T and tetracyanoquinodimethaneis not significantly affected compared to the charge-transfer complex in the gas phase.
4T is a representative thiophene oligomer absorbing visible light, which is often usedto mimic short segments of polythiophene chains. In the relaxed geometry obtained for4T:BCF and reported in Figure 1a), the acceptor is adsorbed on one side of the donor. Thisgeometry resembles the adduct formation proposed by Pingel et al. , with the boron atomaligned to the sulphur on one of the outer rings of 4T. An alternative geometry with BCFon the center of the 4T backbone was also explored but turned out to be energetically lessfavorable than the one in Figure 1a).For reference, we also investigate the adducts formed by 4T doped by the Lewis acidBF , as well as by hexafluorobenzene (C F ). The optimized geometries of the energeticallymost favorable configurations are shown in Figure 1b)-c). Additional information about thestructural properties of the adducts is given in Table 1, where the values of the dihedral angleS-C-C-S are reported for each ring of 4T, according to the labeling in Figure 1b). We recallthat in the isolated 4T molecule each angle is equal to 180 ◦ . It is evident that the interactionwith BCF causes a significant distortion in the 4T backbone such that the thiophene ringdirectly below the acceptor (ring 4), is subject to a 40 ◦ torsion with respect to the adjacentring 3 (see Table 1), which is facing the C F unit adsorbed directly above it. The rest ofthe 4T molecule also experiences a distortion ranging from 25 ◦ to 13 ◦ further away from thedopant adsorption site. Also the adsorption of BF causes a pronounced distortion of thethiophene backbone with a torsion angle of approximately 20 ◦ between the rings. On theother hand, when interacting with C F , the 4T backbone remains almost planar except fora twist of about 25 ◦ of the side rings (see Table 1). In all adducts, the bond lengths undergonegligible changes compared to isolated 4T, which are therefore not reported herein.7 able 1: Dihedral angle between the different 4T rings (as labeled in Figure 1). F ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ The mutual distance between donor and acceptor varies in the three adducts, due to thedifferent nature of the dopant molecule involved. In the case of 4T:BCF, the shortest B-Sdistance amounts to 3.75 ˚A while in 4T:BF it is equal to 3.83 ˚A. The F atoms in the lattersystem are separated by 3.42 ˚A from the underlying C atoms in 4T. In the 4T:C F complex,the carbon and fluorine atoms of the acceptor lie on the same plane, about 3.4 ˚A above the4T backbone. This distance is comparable with the separation between the C F ring andthe donor in 4T:BCF. Electronic properties
Table 2: Bader charges on the acceptors in the considered adducts. The meanvalues of the charges on the C F rings in BCF and on the F atoms in BF arereported. Charges are given in units of electrons with positive (negative) valuesindicating change depletion (accumulation). Species 4T:BCF 4T:C F Tot. charge -0.068 -0.027 -0.032B +2.955 - +2.957C F / F -1.008 - -0.996As the next step in our analysis, we examine the electronic properties of the adducts,starting from inspecting the charge transfer in the ground state. For this purpose, we makeuse of the Bader charge analysis, partitioning the system between the donor and the acceptorunits (see Table 2). In all three adducts we find a negligible charge transfer between 4T andthe respective acceptor species, of the order of 10 − electrons. In the case of the 4T:BCF and4T:BF , a significant charge transfer occurs within the acceptor molecules. This behavior isnot driven by the interacting 4T molecule but is an intrinsic property of the Lewis acids BF F rings, donates almostin full its three valence electrons (see Table 2). The absence of ground-state charge transferin 4T:BCF, modeled here as an isolated bimolecule in vacuo , is in perfect agreement witha previous calculation performed in an idealized thiophene polymer doped by BCF. Thisfinding reveals that the doping mechanism between 4T and BCF does not result from directcharge transfer, but is driven by external factors, such as polaron formation, integer chargetransfer with consequent protonation of the donor, and solution environment thatare not included in these calculations. -2 -4 -6 -8 -10 +2 0 -2 -4 -6 -8 -10 +4 +2 -2 -4 -6 -8 -10 -12 -14 -16 E ne r g y [ e V ] BCF 4T-BCF 4T 4T iso (c) (b) (a) C F F
4T 4T iso BF
4T 4T iso -1.43 +4.31 -1.22 -9.33 -0.05 +0.05 +1.90 +0.28 -0.05 -6.28 -6.50 -6.55 -9.09 +0.21 +0.14 +0.23 -0.05 -6.44 -6.28 -6.51 -6.28 -6.46 -6.52 -15.10 E ne r g y [ e V ] E ne r g y [ e V ] Figure 2: Level alignment, computed from G W , of (a) 4T:BCF (b) 4T:C F (c) 4T:BF ,with respect to their constituents: The frontier states of the acceptors are referred to thegas-phase molecule, while for 4T we report both the frontier energies in the isolated molecule(4T iso ) and in the distorted geometry of the adduct.We continue with our analysis on the electronic properties of the adducts by consideringthe energy level alignment computed from G W on top of hybrid DFT, as reported inFigure 2. In each panel, from left to right, we show the frontier states of the isolated acceptor,of the adduct, of the donor in the relaxed geometry of the respective adduct, as well as in thegas phase (4T iso ). In the case of 4T:BCF, the lowest unoccupied molecular orbital (LUMO)of BCF is energetically comprised between the frontier states of the donor, resulting in a type II level alignment. A close inspection of Figure 2a) reveals that the energies of the9ighest-occupied molecular orbital (HOMO) of 4T:BCF is only a few tens meV lower thanthe HOMO of the donor in the geometry of the adduct. This difference increases up to afew hundreds meV with respect to the isolated 4T (4T iso ). The LUMO of 4T:BCF is equallyclose in energy to the LUMO of BCF alone. These correspondences are mirrored by thecharacter of the frontier orbitals in the adduct, shown in Figure 3, left panel. The HOMO islocalized on the donor, while the LUMO on the acceptor. Both states retain the character ofthe corresponding orbitals of the constituents (see Figure S1 in the Supporting Information).A careful analysis of the LUMO of 4T:BCF reveals, however, a slight hybridization betweendonor and acceptor, which will play a role in the optical properties discussed below.4T:C F and 4T:BF are instead characterized by a type I level alignment between theconstituents (see Figure 2b,c). In those cases, the relatively small size of the acceptormolecules gives rise to band gaps of the order of 11 eV for C H and almost 20 eV forBF , which largely exceed the one of 4T. As a result, the frontier orbitals of the adductscoincide with those of the donor, both in terms of energy (see Figure 2) and of spatial dis-tribution (see Figure 3b,c). Also the QP gap is almost identical to the one of 4T ( ∼ F and 4T:BF differences in the QP gaps of the adducts compared to those of the donor areascribed to polarization effects exerted by the acceptor molecule. The calculated larger gapis in agreement with previous findings for breaking the planarity of the π -conjugated 4Tmolecule. A final note about the effect of the distortion of 4T in the presence of the dopant. Con-trary to previous results obtained for edge-functionalized graphene nanoflakes, wherebackbone distortions give rise to a band-gap reduction, in the three adducts considered here,the HOMO and the LUMO of the donor in the geometry of the complex are energetically(slightly) lower and higher, respectively, compared to those of their flat and isolated counter-parts. This behavior can be interpreted as an indication that the planar geometry predictedby semi-local DFT for gas-phase 4T is not the global minimum of this configuration, as also10 F H L Figure 3: HOMO (H) and LUMO (L) of the considered D/A complexes with isosurfacesdepicted at 10% of their maximum value.suggested by earlier experimental results.
Optical properties
The analysis of the electronic structure reported above provides all the ingredients to inves-tigate the optical properties of the adducts. In Figure 4 we report the absorption spectracomputed from the solution of the BSE. In each panel we show the result for the adducts to-gether with the spectra of their isolated constituents in the respective equilibrium geometries.The spectrum of 4T:BCF (Figure 4a) is dominated at the onset by an intense peakat 3.4 eV (P ), including a weak shoulder at 3.1 eV (P*). Other maxima are found atapproximately 4 eV (P**) and at 5.5 eV (P ). Deeper in the UV region between 6 eVand 7.5 eV a broad and intense feature comprises the peaks P*** and P . Comparisonbetween the spectrum of the adduct and the spectra of its individual constituents offersclear indications about the nature of the aforementioned absorption peaks. First of all wenotice that P is blue-shifted by approximately 0.5 eV with respect to the first excitation of4T, considered in its flat geometry (further details about this spectrum are in the SupportingInformation, see Figure S6). This trend is consistent with the electronic structure discussedabove, where the QP gap of distorted 4T is larger than the one of its flat counterpart(see Figure 2a). The 4T-like character of P is confirmed by the spatial distribution of11 ** P P P P P * P P P P P P *** BCF 4T iso F C F iso BF iso Energy [eV] (a) (b) (c) O S O S O S Figure 4: Optical spectra of (a) 4T:BCF, (b) 4T:C F , (c) 4T:BF and of their respectiveconstituents in the equilibrium geometries as isolated compounds. A Lorentzian broadeningwith a full width at half maximum of 0.125 eV is applied to the spectra to mimic theexcitation lifetime. The strength of all peaks is normalized to the height of first maximumin the spectrum of 4T.the electron and hole densities associated to this excitation (see Figure 5a). On the otherhand, the lowest-energy peak, P*, is a charge-transfer excitation emerging in the spectrum of4T:BCF due to the character of its frontier orbitals (see Figure 3). In fact, P* corresponds tothe transition from the HOMO of the adduct, localized on the donor, to the LUMO, mainlydistributed on the acceptor and only slightly hybridized with 4T. This minimal wave-functionoverlap explains the weak but non-vanishing oscillator strength (OS) of P*, in spite of its12lmost pure charge-transfer character. The analysis of the electron and hole densities inFigure 5a) supports this interpretation.The second bright peak in the spectrum of 4T:BCF, P**, appears at the same energyas the first maximum in the spectrum of BCF. The analysis of the corresponding electronand hole densities (Figure 5a) reveals, however, that this excitation in the adduct is ratherdelocalized across the whole complex, especially as far as the hole is concerned. P appearsin proximity of the second absorption maximum in the spectrum of 4T (for further details,see Supporting Information, Figure S6 and related discussion). However, the analysis ofthe corresponding electron and hole densities (see Figure 5), which are largely delocalizedacross the donor and the acceptor molecules, reveals that this excitation is evidently a newfeature emerging in the adduct. Finally, P*** and P appear in the UV region, where also anintense and equally broad feature is present in the spectrum of BCF alone. P*** is mainlylocalized on the acceptor and the corresponding electron and hole densities are resemblingof their counterparts in the excitation of isolated BCF at the same energy (see SupportingInformation, Figure S8). On the other hand, P is a delocalized excitation across the wholeadduct, as clearly visible through the plot of the corresponding electron and hole densitiesin Figure 5a). Its large OS is therefore a direct consequence of such a large wave-functionoverlap.We now turn to the analysis of the spectra of 4T:C F and 4T:BF , shown in Figure 4b)and c), respectively. At a glance, it is evident that they both resemble the spectrum of4T:BCF, especially in the low-energy region. The first intense peak, P , is found at ap-proximately the same energy in the spectra of all three adducts and bears the same 4T-likecharacter regardless of the dopant species, as shown by the corresponding electron and holedensity distributions in Figure 5. Also P appears in all three spectra at about the same en-ergy (5.5 eV) and with approximately the same OS. However, the character of this excitationvaries depending on the acceptor. In the case of 4T:C F , the hole is distributed on both4T and C F while the electron is localized only on the donor (see Figure 5b). Conversely,13 P P P P P (a) (b) (c) P * P ** P *** P P P Figure 5: Electron (blue) and hole (red) densities of the optical excitations listed in Table 1for (a) 4T:BCF, (b) 4T:C F , and (c) 4T:BF . The isosurfaces are plotted at approximately1% of their maximum value.in 4T:BF , both the electron and hole densities are localized solely on 4T.The higher-energy excitation P is found between 6.5 eV and 7.0 eV in the spectra alladducts. However, like P , its relative OS and its character are affected by the dopant species.In 4T:C F , P is rather intense (its OS is about half of the one of P ), and its electron andhole densities are both distributed across the entire adduct, similar to its counterpart in thespectrum of 4T:BCF (see Figure 5). Note that the first peak in the spectrum of isolatedC F is energetically very close to P (see Figure 4b). On the contrary, in the spectrum of4T:BF , P is almost as weak as P and is again almost entirely distributed on the donor only(see Figure 5c). A careful inspection of Figure 4c) reveals that the spectrum of isolated BF does not feature any absorption feature in the region between 2.5 eV and 8.0 eV, consideredin this analysis. The absorption onset of this molecule is found at 12.23 eV, in line with theexisting literature, as shown in Figure S7 of the Supporting Information.14 iscussion and Conclusions The results presented in this work offer important insight into the intrinsic electronic struc-ture of BCF-doped oligothiophenes, calculated as isolated bimolecules in vacuo . This sit-uation is representative of the local interactions between donor and acceptor species.
However, it is important to consider the fact that in real samples these systems are em-bedded in an environment (either in solution or in solid-state) and are therefore subject tonon-negligible dielectric screening. In general, going from the gas- to the condensed-phaseinduces a broadening and a red-shift of the absorption features as an effect of the dielectricscreening exerted by the closely-packed molecules.
Related phenomena like excitonicdelocalization are also observed in organic crystals.
In the case of p -doped organic crys-tals in the low-doping limit, it was shown that the screening plays a role in accuratelydetermining ionization potential and electron affinity. It is therefore reasonable to ex-pect a red-shift of a few hundred meV in the computed absorption lines upon inclusion of ascreening term mimicking a realistic dielectric embedding for BCF-doped 4T.In the modeled adducts, we find negligible charge transfer in the ground state of the orderof 10 − electrons. A substantial charge redistribution occurs instead within BCF and BF ,where the C F rings and the F atoms, respectively, withdraw almost in full the three valenceelectrons of the B atom. This result supports the recent experimental findings that othermechanisms such as protonation in solution and/or polaron formation are responsiblefor the doping mechanism induced by BCF and related Lewis acids.The electronic structure of 4T:BCF is characterized by the type II level alignment be-tween its constituents, with the LUMO of BCF comprised between the frontier orbitals of4T. However, different from conventional charge-transfer complexes formed, for example,by 2,3,5,6-tetrafluoro-tetracyanoquinodimethane and 4T (see, e.g. , Refs. 9,10) the HOMOand the LUMO of 4T:BCF are localized on the donor and the acceptor, respectively, witha non-vanishing wave-function overlap between them. This behavior is the key for under-standing the doping mechanism of 4T:BCF. In the adducts 4T:C F and 4T:BF , a type I Acknowledgement
Fruitful discussions with Michele Guerrini, Ahmed Mansour, Andreas Opitz, and DieterNeher are kindly acknowledged. This work was funded by the German Research Founda-tion (DFG) through the project “FoMEDOS” – Project number 286798544 (HE 5866/2-1).Computational resources partly provided by the The North-German Supercomputing Al-liance (HLRN) – project bep00076. 16 upporting Information Available
The following files are available free of charge. Additional details about the electronic andoptical properties of the adducts and their constituents are provided.
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No ground-state charge-transfer charge-transfer excitationcharge-transfer excitation