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Theoretical study on the electronic structure of triphenyl sulfonium salts: Electronic excitation and electron transfer processes
Chemical Physics Letters 601 (2014) 63–68
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Theoretical study on the electronic structure of triphenyl sulfonium salts: Electronic excitation and electron transfer processes Ioannis D. Petsalakis a,⇑, Giannoula Theodorakopoulos a, Nektarios N. Lathiotakis a, Dimitra G. Georgiadou b, Maria Vasilopoulou b, Panagiotis Argitis b a b
Theoretical and Physical Chemistry Institute, The National Hellenic Research Foundation, 48 Vassileos Constantinou Avenue, 116 35 Athens, Greece Institute of Microelectronics, NCSR ‘Demokritos’, 15310 Athens, Greece
a r t i c l e
i n f o
Article history: Received 16 February 2014 In final form 28 March 2014 Available online 4 April 2014
a b s t r a c t Density functional theory (DFT) and Time Dependent DFT calculations on triphenyl sulfonium cation (TPS) and the salts of TPS with triflate, nonaflate, perfluoro-1-octanesulfonate and hexafluoro antimonate anions are presented. These systems are widely used as cationic photoinitiators and as electron ejection layer for polymer light-emitting diodes. While some differences exist in the electronic structure of the different salts, their lowest energy intense absorption maxima are calculated at nearly the same energy for all systems. The first excited state of TPS and of the TPS salts is dissociating. Electron addition to the TPS salts lowers their energy by 1.0–1.33 eV. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction Triphenyl sulfonium (TPS) salts are well known ionic compounds, widely applied in the past decades in photoresist technology either as photoinitiators of cationic polymerizations or as photoacid generators in chemically amplified lithography systems [1,2]. Their functionality is based on their direct or sensitized photolysis, which induces the cleavage of the C–S bond in the triphenyl sulfonium cation and the subsequent release of a reactive proton, which in turn induces solubility-changing reactions, such as acid catalyzed cleavage or cationic polymerization/cross-linking in polymeric matrices [3]. The photoacid-generation function of the sulfonium salts has been also exploited for promoting desirable changes of properties of materials, as for instance, the conductivity in poly-aniline films [4] or the dielectric properties of organic films used in radiation sensors [5]. Moreover, sulfonium salts have been involved in organic optoelectronic applications, especially in OLEDs technology, in order to facilitate stacked device fabrication [6] or RGB definition [7]. The role of selected salts of this family, in particular triphenyl sulfonium triflate and nonaflate, in the device performance has been investigated, when incorporated in the green emitting conjugated copolymer poly[(9,9-dioctylfluorenyl-2,7-diyl)-co-(1,4-benzo-{2,1,3}-thiadiazole)] (F8BT) [8] or in the blue emitting poly[2-(6-cyano-6-methyl-heptyloxy)-1,4-phenylene] (CN-PPP) [9]. It was shown that addition of these salts can increase the luminescence and decrease the turn-on and ⇑ Corresponding author. Fax: +30 210 7273794. E-mail address: [email protected] (I.D. Petsalakis). http://dx.doi.org/10.1016/j.cplett.2014.03.086 0009-2614/Ó 2014 Elsevier B.V. All rights reserved.
operating voltage, thus considerably improving device performance. Although the nature of the anion does not seem to influence the photosensitivity of TPS-salts, their size is critical to their reactivity when applied as photoinitiators of cationic polymerizations [10] and, more importantly, it has been found that it may also affect the injection, transport and emission properties of organic light-emitting diodes [11]. Recently sulfonium salts bearing different counter-anions were introduced as spin-coatable all-organic cathode interfacial layers (CILs), improving substantially the luminous efficiency and brightness of F8BT-based PLEDs [12]. This improvement was attributed mainly to the favourable decrease of the polymer/Al injection barrier, which was also assisted by the conduction of electrons through the triphenyl sulfonium salt sites. These recent studies necessitated a more detailed theoretical analysis of the electronic structure of sulfonium salts. The dissociation of TPS salts upon electronic excitation leading to photoacid generation and the dissociative reduction of the TPS cation have been previously studied [13,14] and rationalized in terms of the character of the highest occupied (HOMO or H here) and lowest unoccupied (LUMO or L here) molecular orbitals of the cation, according to semiempirical, AM1, calculations [15]. These rationalizations have been generally invoked in subsequent reports [16], but it should be noted that the labels r⁄ and p⁄, employed in [15], are not appropriate in the absence of a plane of symmetry in the TPS cations. In our previous publication [12] we have presented some preliminary results from calculations on the anionic forms of TPS-triflate and TPS-nonaflate, i.e., [TPS-triflate] and [TPS-nonaflate] , to rationalize the functionality of these TPS salts as cathode interfacial layers (CILs). It was found that
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the acquisition of an electron by TPS salts lowers their total energy with respect to the neutral, rendering them attractive compounds to be used as electron injecting layers. The effect of stabilisation of sulfonium salts upon electron addition has been also reported by Endo and Tagawa [17], since improving the efficiency of photoacid generators is critical for increasing sensitivity of EUV resists [18]. However, no distinction on the stability of the isolated cation versus the cation in the presence of the anion was made. In the present report, theoretical calculations are presented on the electronic structure of four TPS salts, differing in the degree of fluorination, chemical nature (organic/inorganic) and size of the anions, namely hexafluoro antimonate, triflate, nonaflate and PFOS. The ground and excited electronic states of the neutral and anionic forms are calculated in an effort to determine the effect of the different counter anions on the electronic structure of the salt. 2. Calculations The method of calculation employed is DFT [19] for the ground electronic states and TDDFT [20] for the excited, both in conjunction with the M062X [21] functional, which has been reported to perform well for weak interactions and for non-covalent bonding [21] and it has been also found to be the case in previous work by the present authors [22]. In addition, the B3LYP functional [23,24] and the long-range corrected functionals CAM-B3LYP [25] have been employed for some of the calculations, see below, for comparison with the M062X results. While some preliminary calculations employed the 6-31G (d,p) basis set, all the other calculations, except where otherwise stated in what follows, employed basis set 6-311+G (d,p), provided by GAUSSIAN 09 [26]. For Sb the LAN2DZdp ECP basis set [27] was employed. Geometry optimization DFT calculation have been carried out on the ground electronic state of the TPS cation and the neutral salts of TPS with the anions hexafluoro antimonate, trifluoromethanesulfonate (triflate), perfluoro-1-butanesulfonate (nonaflate) and perfluoro-l-octanesulfonate (PFOS). The optimum ground state structures calculated in the present work, are given in Figure 1.
Frequency calculations ensured that these structures are indeed energy minima, while some variations in the starting geometries lead to the same optimum structures. The excited states were calculated at the ground state minimum geometry and are relevant to the absorption spectra, by TDDFT/M062X and for the TPS-triflate salt by TDDFT/B3LYP and TDDFT/CAM-B3LYP as well. Subsequent geometry optimization of the lowest excited state in each case was carried out by TDDFT/ MO62X in order to obtain information on the geometry of the excited state of each system. 3. Results and discussion The TPS cation was calculated first, cf. (i) in Figure 1, and found to be non-planar in the ground electronic state. The absorption spectrum of the cation obtained by TDDFT is given in Figure 2i (see also below), however, geometry optimization of the first excited state did not converge to a stable geometry but indicated a dissociated system. Similarly, the lowest excited state of the neutral salts (ii)–(v) in Figure 1, obtained by TDDFT calculations, are found to be dissociating. However, even though addition of an electron to the cation leads to its dissociation, in agreement with the previous reports on the dissociative reduction of aryl- and alkyl– aryl TPS cations [13,14], addition of an electron to the salts (ii)– (v) leads to stable structures for the resulting anions, at lower energy than the corresponding neutral salt, as will be described in detail below. This result has been found to be critical when these compounds are used as electron injecting layers in organic optoelectronic devices [12]. 3.1. Absorption spectra The absorption spectra of systems (i)–(v), calculated by TDDFT/ M062X at the ground-state geometry are shown in Figure 2 while in Table 1 the results are summarized in terms of kmax, f-values for the transitions from the ground state and the most significant excitations characterizing the excited state. As shown in Figure 2i for the TPS cation, significant absorption probability is found at 222
Figure 1. Ground-state optimized geometries for TPS cation (i) and the salts with hexafluoro-antimonate (ii), triflate (iii), nonaflate (iv) and PFOS (v).
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Figure 2. Calculated absorption spectra of the TPS cation (i) and the salts of TPS with hexafluoro antimonate (ii), triflate (iii), nonaflate (iv) and PFOS (v).
and 223 nm, corresponding to two close lying excited states which are the fourth and fifth calculated excited electronic states of the cation, whereas the lowest three excited states around 232– 230 nm have smaller values of oscillator strength. Looking at the
character of the excited states, cf. Table 1, the lowest three states are characterized mainly by excitations from occupied orbitals below the HOMO (or H in Table 1). Conversely, the two states corresponding to significant f-values are characterized by excitations
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I.D. Petsalakis et al. / Chemical Physics Letters 601 (2014) 63–68
Table 1 Results of the TDDFT calculations on systems (i)–(v) of Figure 1: Characterizing excitations, kmax (nm) and f-values for the lower-lying transitions from the ground state.
a
System, state No.
Main excitationsa
kmax (nm)
f-Value
System, state no
Main excitations
kmax (nm)
f-Value
(i) (i) (i) (i) (i)
H-2 ? L, H ? L+2, H-1 ? L+1 H-3 ? L, H ? L, H-1 ? L H-3 ? L+1, H ? L+1,H-1 ? L+1 H?L H ? L+1
232 230 230 223 222
0.01 0.03 0.03 0.19 0.19
(ii) (ii) (ii) (ii) (ii)
1 2 3 4 5
H-2 ? L, H ? L+2, H-1 ? L+1 H-3 ? L, H ? L, H-2 ? L H-3 ? L+1, H ? L+1 H?L H ? L+1
232 230 230 221 220
0.01 0.05 0.04 0.17 0.18
(v) (v) (v) (v) (v) (v) (v)
1 2 3 4 5 6 7
H-3 ? L+1, H-3 ? L H-4 ? L+1, H-2 ? L+1 H-7 ? L, H-8 ? L+2 H-2 ? L, H ? L, H-1 ? L H ? L+1 H-2 ? L+1, H ? L, H-1 ? L+1 H ? L+1, H ? L
234 232 229 225 223 220 217
0.03 0.03 0.01 0.14 0.04 0.11 0.03
1 2 3 4 5
(iii) (iii) (iii) (iii) (iii) (iii) (iii)
1 2 3 4 5 6 7
H-3 ? L+1, H-1 ? L H-5 ? L+1, H-2 ? L+1 H-7 ? L, H-8 ? L+2 H ? L+1, L,L+2 H?L H-2 ? L, H ? L, H-1 ? L, L+1 H-1 ? L+1, H ? L, H-2 ? L+1
234 231 229 227 225 222 219
0.02 0.04 0.01 0.04 0.06 0.09 0.12
(iv) (iv) (iv) (iv) (iv) (iv) (iv)
1 2 3 4 5 6 7
H-3 ? L+1, H-3 ? L H-3 ? L+1, H-2 ? L+1 H-7 ? L, H-8 ? L+2, L+3 H-2 ? L, H ? L, H-1 ? L H ? L+1 H-2 ? L+1, H ? L, H-1 ? L+1 H-1 ? L, H ? L+1, H ? L
234 230 229 225 222 220 218
0.03 0.03 0.03 0.13 0.03 0.11 0.04
The excitations which contribute with the largest coefficients to the excited state.
starting from HOMO, and more specifically the fourth state is characterized mainly by the HOMO ? LUMO excitation, or H ? L, and the fifth by H ? L+1 excitation (cf. Table 1). Nearly identical absorption spectrum as that of the TPS cation is calculated for the salt of TPS with hexafluoro antimonate, cf. (ii) in Figure 2 and Table 1, where again the fourth and fifth at 221 and 220 nm states have significant oscillator strengths and are characterized by the same types of excitations as the corresponding states of the cation (cf. (i)). The similarity in the electronic structure of TPS cation (i) and of the TPS-hexafluoro antimonate salt (ii), is also reflected in the frontier molecular orbitals of these systems, cf. (i) and (ii) in Figure 3, where electron density plots are given for the MO of TPS and the neutral salts. It is noteworthy that the counter-anion is not involved in the frontier orbitals of the TPS-hexafluoro antimonate salt (ii) (cf. Figure 3). The absorption spectra of the three other salts, (iii)–(v) have different appearance, cf. Figure 2, and this is also reflected in their MOs: As shown in Figure 3, the occupied frontier orbitals of the three larger salts include electron density on the anions, and in particular their HOMO is located solely on the corresponding anion moiety. Conversely, the LUMO in all cases involves solely the TPS group, cf. Figure 3. In TPS-triflate, cf. (iii) Table 1 and Figure 2, the lowest five excited states have low oscillator strength, with states 1, 2 and 3 at 234–229 nm characterized by excitations from inner occupied orbitals to the lowest two unoccupied (i.e. L and L+1). State four, at 227 nm with 0.04 oscillator strength is characterized mainly by excitations H ? L, H ? L+1 and H ? L+2 and state five at 225 nm, with oscillator strength 0.06, has the main contribution from the H ? L excitation. The two significant absorptions, at 221 nm and 219 nm, correspond to excited states number six and seven and in these states the most important excitations involve the two highest occupied orbitals below H, i.e. H-1 ? L, H-1 ? L+1, H-2 ? L+1 and with a smaller contribution H ? L. As noted above, the unoccupied frontier orbitals, including the LUMO, involve the TPS group while HOMO lies on the anion and accordingly the H ? L excitation does not have large oscillator strength. The HOMO-1 and HOMO-2 orbitals are now the ones with electron density on the TPS, cf. (iii) in Figure 3, and accordingly excitations from these occupied orbitals correspond to transitions with significant oscillator strengths, cf. the transitions at 221 nm and 219 nm calculated for the TPS-triflate salt, cf. Table 1.
The calculated absorption spectra of TPS-nonaflate and TPSPFOS (cf. (iv) and (v) in Figure 2 are nearly identical and show different ordering of states than TPS-triflate, with significant oscillator strengths corresponding to the fourth and sixth excited states at 225 nm and 220 nm, respectively, in both salts. Significant contributions to these states are found from H-2 ? L, H-2 ? L+1, H1 ? L+1, H ? L and H ? L+1 excitations. These two salts have nearly identical molecular orbitals (cf. (iv) and (v) in Figure 3). It might be noted that while the details of the molecular orbitals and the ordering of the electronic states changes in the different salts calculated here, (ii)–(v), the lowest energy significant absorption is calculated in the region 220–225 nm in all these systems. Low intensity absorption is also predicted in all cases at 234 nm (232 nm in TPS-hexafluoro antimonate). This reflects a similar energy gap for all TPS-salts. However, these values are overestimating the excitation energy by about 1.0 eV, since the experimental absorption spectra obtain the lowest energy absorption at 285 nm (corresponding to an energy gap of 4.35 eV) for the triflate and nonaflate salts [12]. The calculated TDDFT/CAM-B3LYP excitation energies are only slightly smaller (by <0.1 eV) than the TDDFT/ M062X for the TPS-triflate salt, and this agreement of the excitation energies obtained with these two functionals has been generally observed [e.g., 22]. Given the large size of the systems calculated in the present work, it is not possible to employ more elaborate methods, which might lead to better numerical agreement with experiment. The overestimation of the excitation energy of the calculations with M062X (and the CAM-B3LYP) functional is also found for the ionization energy (calculated as the difference in the total energies of the neutral and the cation) of the TPS triflate salt, calculated at 8.6 eV (8.4 eV by CAM-B3LYP) with experimental estimate at 7.7 eV and similarly for the ionization energy of the nonaflate salt with calculated at 8.7 eV and experimental at 7.6 eV [5]. Even higher IP values are calculated for the salts (ii) at 9.4 eV and (v) at 9.2 eV. This trend shows that the ionisation energies of the TPS salts increase with increasing degree of fluorination of the anion, indicating an enhanced electron withdrawing character of the salt as the number of fluorine atoms in the anion increases. This is of particular importance in the case when these compounds are being used as electron injecting layers, since electron-withdrawing character is beneficial for the injection of electrons from the cathode of an OLED device. It should be also noted here that
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calculations on the triflate salt employing the B3LYP functional [24,25] yield ionization energy 7.9 eV but underestimates the excitation energy with calculated value at 3.38 eV. 3.2. Electron addition The materials that are employed as electron injecting layers should be stable as anions, and for this reason, addition of an electron to systems (i)–(v) of Figure 1 has been investigated by DFT/M06X geometry optimization of the anion salts, i.e. [TPS-X] and for [TPS-triflate] by CAM-B3LYP as well and of neutral TPS. These calculations resulted in stable minimum energy structures for the anions of (ii)–(v) but found neutral TPS to be
67
dissociating, in accord with the dissociative reduction of TPS [13,14]. The calculated minimum energies of the anions of the salts are lower than the energy of the corresponding neutral salts by 1.0 eV for (ii), 1.24 eV for (iii) (1.3 eV by CAM-B3LYP), 1.32 eV for (iv) and 1.33 for (v). This means that TPS-nonaflate and TPSPFOS have the highest electron affinity and are, thus, expected to be the most suitable – in terms of electronic profile – to act as injecting layer in OLEDs. The electron affinity of substituted TPS-triflate for different substituents on the phenyl groups of TPS has been calculated previously by DFT/6-31G polarization [17], where they too calculate lower energies for the anions than the corresponding neutrals of the different salts, ranging between 30 and 40 kcal/mol, in vacuum.
Figure 3. Electron density plots of the frontier orbitals (from HOMO-2 to LUMO+1) of TPS cation (i) and salts of TPS with hexafluoro antimonate (ii), triflate (iii), nonaflate (iv) and PFOS (v).
Figure 4. Ground-state optimized geometries and electron density plots of the HOMO and LUMO orbitals of the anions of salts (ii)–(v) of Figure 1.
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The calculated minimum energy geometries of the salt anions, [TPS-X] by DFT/M062X are not drastically different from those of the corresponding neutrals (cf. Figure 4). Generally, in the salt anions the S–S distance is elongated by 0.44–1.1 Å, two of the three C–S distances in TPS are elongated by 0.03 Å and the third shortened by 0.06 Å. Similarly, two of the three C–S–C bond angles are enlarged by 2–10°, while one is lessened by 5–7°. Conversely, the geometry of [TPS-triflate] obtained by CAM-B3LYP has significantly longer S–S distance than in the neutral salt, by 1.9 Å. The HOMO and LUMO molecular orbitals of the anions (cf. Figure 4) involve almost entirely the TPS part and in particular the HOMO of the anion (for each salt), cf. Figure 4, is similar to the LUMO of the corresponding neutral, cf. Figure 3, suggestive of a simple addition of the electron into the LUMO of the neutral. Similarly, the LUMO of the anion is similar to the LUMO+1 orbital of the corresponding neutral, cf. Figures 3 and 4, indicating that the addition of the electron to the TPS salts, (ii)–(v) does not lead to drastic differences in the electronic structure, just as in the case of the geometries above. This attribute is highly beneficial for electron injection during device operation. Further investigation on the anions (iii)–(v) involved TDDFT calculations in order to determine their excited electronic states. The lowest excited state at the ground state geometry (corresponding to absorption) is calculated at 1.26 eV for TPS-triflate anion, 1.35 eV for TPS-nonaflate anion and 1.37 eV for TPS-PFOS anion. Optimization of the excited state geometry of the salt anions find an avoided crossing with the ground state at which point the optimizations stopped, and therefore it was not possible to determine a stable geometry for the excited state of the anions. 4. Conclusions Triphenyl sulfonium (TPS) salts are well known ionic compounds, widely applied as functional additives in photoresist technology, in the active layer of OLEDs and more recently as efficient electron injection layer for PLEDs. Theoretical calculations have been presented on the electronic structure of the TPS cation and four TPS salts, namely, hexafluoro antimonate, triflate, nonaflate and PFOS. The results show some differences in the electronic structure of TPS cation and TPS-hexafluoro antimonate as compared with all-organic TPS-salts with the perfluorinated anions (triflate, nonanflate, PFOS). In particular, the electron density of the HOMO of the latter salts is located on the anions, whereas that of the former on the TPS cation. This results in differences in the nature of the dominant excitations and also in the ordering of the electronic states in the different TPS-salts calculated here, (ii)–(v), but the lowest energy significant absorption is calculated in the region 220–225 nm in all these systems indicating a similar energy gap. The ionisation potential of the TPS-salts, (ii)–(v), increases with increasing degree of fluorination of the anion,
implying – taking into account the similar optical gap – enhanced electron withdrawing character of the highly fluorinated TPS-salts (nonaflate, PFOS). The first excited state of the TPS cation and also that of the different TPS-salts is found to be dissociating. Finally, while acquisition of an electron by TPS cation leads to its dissociation, it was found to be favourable in the case of the salts, with calculated electron affinities ranging between 1.0 and 1.33 eV. The results derived from this Letter give a deeper insight to the electronic structure of TPS-salts that may be useful for their further implementation in lithographic or organic electronic applications. Acknowledgement Financial support of this work by the General Secretariat for Research and Technology, Greece (project Polynano-Kripis 447963) is gratefully acknowledged. References [1] J.V. Crivello, Adv. Polym. Sci. 62 (1984) 1. [2] E. Reichmanis, F.M. Houlihan, O. Nalamasu, T.X. Neenan, Chem. Mater. 39 (1991) 394. [3] J.L. Dektar, N.P. Hacker, J. Am. Chem. Soc. 112 (1990) 6004. [4] M. Angelopoulos, J.M. Shaw, W.-S. Huang, R.D. Kaplan, Mol. Cryst. Liq. Cryst. 189 (1990) 221. [5] E. Kapetanakis, A.M. Douvas, P. Argitis, P. Normand, ACS Appl. Mater. Interfaces 5 (2013) 5667. [6] C.D. Müller et al., Nature 421 (2003) 829. [7] M. Vasilopoulou, D.G. Georgiadou, G. Pistolis, P. Argitis, Adv. Funct. Mater. 17 (2007) 3477. [8] D.G. Georgiadou, L.C. Palilis, M. Vasilopoulou, G. Pistolis, D. Dimotikali, P. Argitis, RSC Adv. 2 (2012) 11786. [9] D.G. Georgiadou, L.C. Palilis, M. Vasilopoulou, G. Pistolis, D. Dimotikali, P. Argitis, J. Mater. Chem. 21 (2011) 9296. [10] J.V. Crivello, J.H.W. Lam, J. Polym. Sci. A Polym. Chem. 17 (1979) 1047. [11] D.G. Georgiadou, L.C. Palilis, M. Vasilopoulou, G. Pistolis, D. Dimotikali, P. Argitis, Synth. Met. 181 (2013) 37. [12] D.G. Georgiadou et al., ACS Appl. Mater. Interfaces 5 (2013) 12346. [13] P.S. McKinney, S. Rosenthal, J. Electroanal. Chem. 16 (1968) 261. [14] D. Franklin, F.D. Saeva, B.P. Morgan, J. Am. Chem. Soc. 106 (1984) 4121. [15] F.D. Saeva, D.T. Breslin, P.A. Martic, J. Am. Chem. Soc. 111 (1989) 1328; F.D. Saeva, D.T. Breslin, P.A. Martic, J. Photochem. Photobiol. A 86 (1995) 149. [16] R. Xia et al., Chem. Mater. 24 (2012) 237. [17] M. Endo, S. Tagawa, J. Photopolym. Sci. Technol. 24 (2011) 205. [18] T. Itani, T. Kosawa, Jpn. J. Appl. Phys. 52 (2013) 010002. [19] R.G. Parr, Annu. Rev. Phys. Chem. 46 (1995) 701. [20] M.A.L. Marques, E.K.U. Gross, Annu. Rev. Phys. Chem. 55 (2004) 427. [21] (a) Y. Zhao, D. Truhlar, Theor. Chem. Acc. 120 (2008) 215; (b) Y. Zhao, D. Truhlar, Acc. Chem. Res. 41 (2008) 157. [22] D. Tzeli, I.D. Petsalakis, G. Theodorakopoulos, Phys. Chem. Chem. Phys. 13 (25) (2011) 11965; I.D. Petsalakis, D. Tzeli, Ioannis S.K. Kerkines, G. Theodorakopoulos, Comp. Theor. Chem. 965 (2011) 168. [23] A.D. Becke, Phys. Rev. A 38 (1988) 3098. [24] C. Lee, W. Yang, Phys. Rev. B 37 (1988) 785. [25] M.J.G. Peach, P. Benfield, T. Helgaker, D.J.J. Tozer, Chem. Phys. 128 (2008). [26] M.J. Frisch et al., GAUSSIAN 09, Revision A.1, Gaussian Inc., Wallingford CT, 2009. [27] P.J. Hay, W.R. Wadt, J. Chem. Phys. 82 (1985) 270 (284–298; 299–310).
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Theoretical study on the electronic structure of triphenyl sulfonium salts: Electronic excitation and electron transfer processes Ioannis D. Petsalakis a,⇑, Giannoula Theodorakopoulos a, Nektarios N. Lathiotakis a, Dimitra G. Georgiadou b, Maria Vasilopoulou b, Panagiotis Argitis b a b
Theoretical and Physical Chemistry Institute, The National Hellenic Research Foundation, 48 Vassileos Constantinou Avenue, 116 35 Athens, Greece Institute of Microelectronics, NCSR ‘Demokritos’, 15310 Athens, Greece
a r t i c l e
i n f o
Article history: Received 16 February 2014 In final form 28 March 2014 Available online 4 April 2014
a b s t r a c t Density functional theory (DFT) and Time Dependent DFT calculations on triphenyl sulfonium cation (TPS) and the salts of TPS with triflate, nonaflate, perfluoro-1-octanesulfonate and hexafluoro antimonate anions are presented. These systems are widely used as cationic photoinitiators and as electron ejection layer for polymer light-emitting diodes. While some differences exist in the electronic structure of the different salts, their lowest energy intense absorption maxima are calculated at nearly the same energy for all systems. The first excited state of TPS and of the TPS salts is dissociating. Electron addition to the TPS salts lowers their energy by 1.0–1.33 eV. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction Triphenyl sulfonium (TPS) salts are well known ionic compounds, widely applied in the past decades in photoresist technology either as photoinitiators of cationic polymerizations or as photoacid generators in chemically amplified lithography systems [1,2]. Their functionality is based on their direct or sensitized photolysis, which induces the cleavage of the C–S bond in the triphenyl sulfonium cation and the subsequent release of a reactive proton, which in turn induces solubility-changing reactions, such as acid catalyzed cleavage or cationic polymerization/cross-linking in polymeric matrices [3]. The photoacid-generation function of the sulfonium salts has been also exploited for promoting desirable changes of properties of materials, as for instance, the conductivity in poly-aniline films [4] or the dielectric properties of organic films used in radiation sensors [5]. Moreover, sulfonium salts have been involved in organic optoelectronic applications, especially in OLEDs technology, in order to facilitate stacked device fabrication [6] or RGB definition [7]. The role of selected salts of this family, in particular triphenyl sulfonium triflate and nonaflate, in the device performance has been investigated, when incorporated in the green emitting conjugated copolymer poly[(9,9-dioctylfluorenyl-2,7-diyl)-co-(1,4-benzo-{2,1,3}-thiadiazole)] (F8BT) [8] or in the blue emitting poly[2-(6-cyano-6-methyl-heptyloxy)-1,4-phenylene] (CN-PPP) [9]. It was shown that addition of these salts can increase the luminescence and decrease the turn-on and ⇑ Corresponding author. Fax: +30 210 7273794. E-mail address: [email protected] (I.D. Petsalakis). http://dx.doi.org/10.1016/j.cplett.2014.03.086 0009-2614/Ó 2014 Elsevier B.V. All rights reserved.
operating voltage, thus considerably improving device performance. Although the nature of the anion does not seem to influence the photosensitivity of TPS-salts, their size is critical to their reactivity when applied as photoinitiators of cationic polymerizations [10] and, more importantly, it has been found that it may also affect the injection, transport and emission properties of organic light-emitting diodes [11]. Recently sulfonium salts bearing different counter-anions were introduced as spin-coatable all-organic cathode interfacial layers (CILs), improving substantially the luminous efficiency and brightness of F8BT-based PLEDs [12]. This improvement was attributed mainly to the favourable decrease of the polymer/Al injection barrier, which was also assisted by the conduction of electrons through the triphenyl sulfonium salt sites. These recent studies necessitated a more detailed theoretical analysis of the electronic structure of sulfonium salts. The dissociation of TPS salts upon electronic excitation leading to photoacid generation and the dissociative reduction of the TPS cation have been previously studied [13,14] and rationalized in terms of the character of the highest occupied (HOMO or H here) and lowest unoccupied (LUMO or L here) molecular orbitals of the cation, according to semiempirical, AM1, calculations [15]. These rationalizations have been generally invoked in subsequent reports [16], but it should be noted that the labels r⁄ and p⁄, employed in [15], are not appropriate in the absence of a plane of symmetry in the TPS cations. In our previous publication [12] we have presented some preliminary results from calculations on the anionic forms of TPS-triflate and TPS-nonaflate, i.e., [TPS-triflate] and [TPS-nonaflate] , to rationalize the functionality of these TPS salts as cathode interfacial layers (CILs). It was found that
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the acquisition of an electron by TPS salts lowers their total energy with respect to the neutral, rendering them attractive compounds to be used as electron injecting layers. The effect of stabilisation of sulfonium salts upon electron addition has been also reported by Endo and Tagawa [17], since improving the efficiency of photoacid generators is critical for increasing sensitivity of EUV resists [18]. However, no distinction on the stability of the isolated cation versus the cation in the presence of the anion was made. In the present report, theoretical calculations are presented on the electronic structure of four TPS salts, differing in the degree of fluorination, chemical nature (organic/inorganic) and size of the anions, namely hexafluoro antimonate, triflate, nonaflate and PFOS. The ground and excited electronic states of the neutral and anionic forms are calculated in an effort to determine the effect of the different counter anions on the electronic structure of the salt. 2. Calculations The method of calculation employed is DFT [19] for the ground electronic states and TDDFT [20] for the excited, both in conjunction with the M062X [21] functional, which has been reported to perform well for weak interactions and for non-covalent bonding [21] and it has been also found to be the case in previous work by the present authors [22]. In addition, the B3LYP functional [23,24] and the long-range corrected functionals CAM-B3LYP [25] have been employed for some of the calculations, see below, for comparison with the M062X results. While some preliminary calculations employed the 6-31G (d,p) basis set, all the other calculations, except where otherwise stated in what follows, employed basis set 6-311+G (d,p), provided by GAUSSIAN 09 [26]. For Sb the LAN2DZdp ECP basis set [27] was employed. Geometry optimization DFT calculation have been carried out on the ground electronic state of the TPS cation and the neutral salts of TPS with the anions hexafluoro antimonate, trifluoromethanesulfonate (triflate), perfluoro-1-butanesulfonate (nonaflate) and perfluoro-l-octanesulfonate (PFOS). The optimum ground state structures calculated in the present work, are given in Figure 1.
Frequency calculations ensured that these structures are indeed energy minima, while some variations in the starting geometries lead to the same optimum structures. The excited states were calculated at the ground state minimum geometry and are relevant to the absorption spectra, by TDDFT/M062X and for the TPS-triflate salt by TDDFT/B3LYP and TDDFT/CAM-B3LYP as well. Subsequent geometry optimization of the lowest excited state in each case was carried out by TDDFT/ MO62X in order to obtain information on the geometry of the excited state of each system. 3. Results and discussion The TPS cation was calculated first, cf. (i) in Figure 1, and found to be non-planar in the ground electronic state. The absorption spectrum of the cation obtained by TDDFT is given in Figure 2i (see also below), however, geometry optimization of the first excited state did not converge to a stable geometry but indicated a dissociated system. Similarly, the lowest excited state of the neutral salts (ii)–(v) in Figure 1, obtained by TDDFT calculations, are found to be dissociating. However, even though addition of an electron to the cation leads to its dissociation, in agreement with the previous reports on the dissociative reduction of aryl- and alkyl– aryl TPS cations [13,14], addition of an electron to the salts (ii)– (v) leads to stable structures for the resulting anions, at lower energy than the corresponding neutral salt, as will be described in detail below. This result has been found to be critical when these compounds are used as electron injecting layers in organic optoelectronic devices [12]. 3.1. Absorption spectra The absorption spectra of systems (i)–(v), calculated by TDDFT/ M062X at the ground-state geometry are shown in Figure 2 while in Table 1 the results are summarized in terms of kmax, f-values for the transitions from the ground state and the most significant excitations characterizing the excited state. As shown in Figure 2i for the TPS cation, significant absorption probability is found at 222
Figure 1. Ground-state optimized geometries for TPS cation (i) and the salts with hexafluoro-antimonate (ii), triflate (iii), nonaflate (iv) and PFOS (v).
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Figure 2. Calculated absorption spectra of the TPS cation (i) and the salts of TPS with hexafluoro antimonate (ii), triflate (iii), nonaflate (iv) and PFOS (v).
and 223 nm, corresponding to two close lying excited states which are the fourth and fifth calculated excited electronic states of the cation, whereas the lowest three excited states around 232– 230 nm have smaller values of oscillator strength. Looking at the
character of the excited states, cf. Table 1, the lowest three states are characterized mainly by excitations from occupied orbitals below the HOMO (or H in Table 1). Conversely, the two states corresponding to significant f-values are characterized by excitations
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Table 1 Results of the TDDFT calculations on systems (i)–(v) of Figure 1: Characterizing excitations, kmax (nm) and f-values for the lower-lying transitions from the ground state.
a
System, state No.
Main excitationsa
kmax (nm)
f-Value
System, state no
Main excitations
kmax (nm)
f-Value
(i) (i) (i) (i) (i)
H-2 ? L, H ? L+2, H-1 ? L+1 H-3 ? L, H ? L, H-1 ? L H-3 ? L+1, H ? L+1,H-1 ? L+1 H?L H ? L+1
232 230 230 223 222
0.01 0.03 0.03 0.19 0.19
(ii) (ii) (ii) (ii) (ii)
1 2 3 4 5
H-2 ? L, H ? L+2, H-1 ? L+1 H-3 ? L, H ? L, H-2 ? L H-3 ? L+1, H ? L+1 H?L H ? L+1
232 230 230 221 220
0.01 0.05 0.04 0.17 0.18
(v) (v) (v) (v) (v) (v) (v)
1 2 3 4 5 6 7
H-3 ? L+1, H-3 ? L H-4 ? L+1, H-2 ? L+1 H-7 ? L, H-8 ? L+2 H-2 ? L, H ? L, H-1 ? L H ? L+1 H-2 ? L+1, H ? L, H-1 ? L+1 H ? L+1, H ? L
234 232 229 225 223 220 217
0.03 0.03 0.01 0.14 0.04 0.11 0.03
1 2 3 4 5
(iii) (iii) (iii) (iii) (iii) (iii) (iii)
1 2 3 4 5 6 7
H-3 ? L+1, H-1 ? L H-5 ? L+1, H-2 ? L+1 H-7 ? L, H-8 ? L+2 H ? L+1, L,L+2 H?L H-2 ? L, H ? L, H-1 ? L, L+1 H-1 ? L+1, H ? L, H-2 ? L+1
234 231 229 227 225 222 219
0.02 0.04 0.01 0.04 0.06 0.09 0.12
(iv) (iv) (iv) (iv) (iv) (iv) (iv)
1 2 3 4 5 6 7
H-3 ? L+1, H-3 ? L H-3 ? L+1, H-2 ? L+1 H-7 ? L, H-8 ? L+2, L+3 H-2 ? L, H ? L, H-1 ? L H ? L+1 H-2 ? L+1, H ? L, H-1 ? L+1 H-1 ? L, H ? L+1, H ? L
234 230 229 225 222 220 218
0.03 0.03 0.03 0.13 0.03 0.11 0.04
The excitations which contribute with the largest coefficients to the excited state.
starting from HOMO, and more specifically the fourth state is characterized mainly by the HOMO ? LUMO excitation, or H ? L, and the fifth by H ? L+1 excitation (cf. Table 1). Nearly identical absorption spectrum as that of the TPS cation is calculated for the salt of TPS with hexafluoro antimonate, cf. (ii) in Figure 2 and Table 1, where again the fourth and fifth at 221 and 220 nm states have significant oscillator strengths and are characterized by the same types of excitations as the corresponding states of the cation (cf. (i)). The similarity in the electronic structure of TPS cation (i) and of the TPS-hexafluoro antimonate salt (ii), is also reflected in the frontier molecular orbitals of these systems, cf. (i) and (ii) in Figure 3, where electron density plots are given for the MO of TPS and the neutral salts. It is noteworthy that the counter-anion is not involved in the frontier orbitals of the TPS-hexafluoro antimonate salt (ii) (cf. Figure 3). The absorption spectra of the three other salts, (iii)–(v) have different appearance, cf. Figure 2, and this is also reflected in their MOs: As shown in Figure 3, the occupied frontier orbitals of the three larger salts include electron density on the anions, and in particular their HOMO is located solely on the corresponding anion moiety. Conversely, the LUMO in all cases involves solely the TPS group, cf. Figure 3. In TPS-triflate, cf. (iii) Table 1 and Figure 2, the lowest five excited states have low oscillator strength, with states 1, 2 and 3 at 234–229 nm characterized by excitations from inner occupied orbitals to the lowest two unoccupied (i.e. L and L+1). State four, at 227 nm with 0.04 oscillator strength is characterized mainly by excitations H ? L, H ? L+1 and H ? L+2 and state five at 225 nm, with oscillator strength 0.06, has the main contribution from the H ? L excitation. The two significant absorptions, at 221 nm and 219 nm, correspond to excited states number six and seven and in these states the most important excitations involve the two highest occupied orbitals below H, i.e. H-1 ? L, H-1 ? L+1, H-2 ? L+1 and with a smaller contribution H ? L. As noted above, the unoccupied frontier orbitals, including the LUMO, involve the TPS group while HOMO lies on the anion and accordingly the H ? L excitation does not have large oscillator strength. The HOMO-1 and HOMO-2 orbitals are now the ones with electron density on the TPS, cf. (iii) in Figure 3, and accordingly excitations from these occupied orbitals correspond to transitions with significant oscillator strengths, cf. the transitions at 221 nm and 219 nm calculated for the TPS-triflate salt, cf. Table 1.
The calculated absorption spectra of TPS-nonaflate and TPSPFOS (cf. (iv) and (v) in Figure 2 are nearly identical and show different ordering of states than TPS-triflate, with significant oscillator strengths corresponding to the fourth and sixth excited states at 225 nm and 220 nm, respectively, in both salts. Significant contributions to these states are found from H-2 ? L, H-2 ? L+1, H1 ? L+1, H ? L and H ? L+1 excitations. These two salts have nearly identical molecular orbitals (cf. (iv) and (v) in Figure 3). It might be noted that while the details of the molecular orbitals and the ordering of the electronic states changes in the different salts calculated here, (ii)–(v), the lowest energy significant absorption is calculated in the region 220–225 nm in all these systems. Low intensity absorption is also predicted in all cases at 234 nm (232 nm in TPS-hexafluoro antimonate). This reflects a similar energy gap for all TPS-salts. However, these values are overestimating the excitation energy by about 1.0 eV, since the experimental absorption spectra obtain the lowest energy absorption at 285 nm (corresponding to an energy gap of 4.35 eV) for the triflate and nonaflate salts [12]. The calculated TDDFT/CAM-B3LYP excitation energies are only slightly smaller (by <0.1 eV) than the TDDFT/ M062X for the TPS-triflate salt, and this agreement of the excitation energies obtained with these two functionals has been generally observed [e.g., 22]. Given the large size of the systems calculated in the present work, it is not possible to employ more elaborate methods, which might lead to better numerical agreement with experiment. The overestimation of the excitation energy of the calculations with M062X (and the CAM-B3LYP) functional is also found for the ionization energy (calculated as the difference in the total energies of the neutral and the cation) of the TPS triflate salt, calculated at 8.6 eV (8.4 eV by CAM-B3LYP) with experimental estimate at 7.7 eV and similarly for the ionization energy of the nonaflate salt with calculated at 8.7 eV and experimental at 7.6 eV [5]. Even higher IP values are calculated for the salts (ii) at 9.4 eV and (v) at 9.2 eV. This trend shows that the ionisation energies of the TPS salts increase with increasing degree of fluorination of the anion, indicating an enhanced electron withdrawing character of the salt as the number of fluorine atoms in the anion increases. This is of particular importance in the case when these compounds are being used as electron injecting layers, since electron-withdrawing character is beneficial for the injection of electrons from the cathode of an OLED device. It should be also noted here that
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calculations on the triflate salt employing the B3LYP functional [24,25] yield ionization energy 7.9 eV but underestimates the excitation energy with calculated value at 3.38 eV. 3.2. Electron addition The materials that are employed as electron injecting layers should be stable as anions, and for this reason, addition of an electron to systems (i)–(v) of Figure 1 has been investigated by DFT/M06X geometry optimization of the anion salts, i.e. [TPS-X] and for [TPS-triflate] by CAM-B3LYP as well and of neutral TPS. These calculations resulted in stable minimum energy structures for the anions of (ii)–(v) but found neutral TPS to be
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dissociating, in accord with the dissociative reduction of TPS [13,14]. The calculated minimum energies of the anions of the salts are lower than the energy of the corresponding neutral salts by 1.0 eV for (ii), 1.24 eV for (iii) (1.3 eV by CAM-B3LYP), 1.32 eV for (iv) and 1.33 for (v). This means that TPS-nonaflate and TPSPFOS have the highest electron affinity and are, thus, expected to be the most suitable – in terms of electronic profile – to act as injecting layer in OLEDs. The electron affinity of substituted TPS-triflate for different substituents on the phenyl groups of TPS has been calculated previously by DFT/6-31G polarization [17], where they too calculate lower energies for the anions than the corresponding neutrals of the different salts, ranging between 30 and 40 kcal/mol, in vacuum.
Figure 3. Electron density plots of the frontier orbitals (from HOMO-2 to LUMO+1) of TPS cation (i) and salts of TPS with hexafluoro antimonate (ii), triflate (iii), nonaflate (iv) and PFOS (v).
Figure 4. Ground-state optimized geometries and electron density plots of the HOMO and LUMO orbitals of the anions of salts (ii)–(v) of Figure 1.
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The calculated minimum energy geometries of the salt anions, [TPS-X] by DFT/M062X are not drastically different from those of the corresponding neutrals (cf. Figure 4). Generally, in the salt anions the S–S distance is elongated by 0.44–1.1 Å, two of the three C–S distances in TPS are elongated by 0.03 Å and the third shortened by 0.06 Å. Similarly, two of the three C–S–C bond angles are enlarged by 2–10°, while one is lessened by 5–7°. Conversely, the geometry of [TPS-triflate] obtained by CAM-B3LYP has significantly longer S–S distance than in the neutral salt, by 1.9 Å. The HOMO and LUMO molecular orbitals of the anions (cf. Figure 4) involve almost entirely the TPS part and in particular the HOMO of the anion (for each salt), cf. Figure 4, is similar to the LUMO of the corresponding neutral, cf. Figure 3, suggestive of a simple addition of the electron into the LUMO of the neutral. Similarly, the LUMO of the anion is similar to the LUMO+1 orbital of the corresponding neutral, cf. Figures 3 and 4, indicating that the addition of the electron to the TPS salts, (ii)–(v) does not lead to drastic differences in the electronic structure, just as in the case of the geometries above. This attribute is highly beneficial for electron injection during device operation. Further investigation on the anions (iii)–(v) involved TDDFT calculations in order to determine their excited electronic states. The lowest excited state at the ground state geometry (corresponding to absorption) is calculated at 1.26 eV for TPS-triflate anion, 1.35 eV for TPS-nonaflate anion and 1.37 eV for TPS-PFOS anion. Optimization of the excited state geometry of the salt anions find an avoided crossing with the ground state at which point the optimizations stopped, and therefore it was not possible to determine a stable geometry for the excited state of the anions. 4. Conclusions Triphenyl sulfonium (TPS) salts are well known ionic compounds, widely applied as functional additives in photoresist technology, in the active layer of OLEDs and more recently as efficient electron injection layer for PLEDs. Theoretical calculations have been presented on the electronic structure of the TPS cation and four TPS salts, namely, hexafluoro antimonate, triflate, nonaflate and PFOS. The results show some differences in the electronic structure of TPS cation and TPS-hexafluoro antimonate as compared with all-organic TPS-salts with the perfluorinated anions (triflate, nonanflate, PFOS). In particular, the electron density of the HOMO of the latter salts is located on the anions, whereas that of the former on the TPS cation. This results in differences in the nature of the dominant excitations and also in the ordering of the electronic states in the different TPS-salts calculated here, (ii)–(v), but the lowest energy significant absorption is calculated in the region 220–225 nm in all these systems indicating a similar energy gap. The ionisation potential of the TPS-salts, (ii)–(v), increases with increasing degree of fluorination of the anion,
implying – taking into account the similar optical gap – enhanced electron withdrawing character of the highly fluorinated TPS-salts (nonaflate, PFOS). The first excited state of the TPS cation and also that of the different TPS-salts is found to be dissociating. Finally, while acquisition of an electron by TPS cation leads to its dissociation, it was found to be favourable in the case of the salts, with calculated electron affinities ranging between 1.0 and 1.33 eV. The results derived from this Letter give a deeper insight to the electronic structure of TPS-salts that may be useful for their further implementation in lithographic or organic electronic applications. Acknowledgement Financial support of this work by the General Secretariat for Research and Technology, Greece (project Polynano-Kripis 447963) is gratefully acknowledged. References [1] J.V. Crivello, Adv. Polym. Sci. 62 (1984) 1. [2] E. Reichmanis, F.M. Houlihan, O. Nalamasu, T.X. Neenan, Chem. Mater. 39 (1991) 394. [3] J.L. Dektar, N.P. Hacker, J. Am. Chem. Soc. 112 (1990) 6004. [4] M. Angelopoulos, J.M. Shaw, W.-S. Huang, R.D. Kaplan, Mol. Cryst. Liq. Cryst. 189 (1990) 221. [5] E. Kapetanakis, A.M. Douvas, P. Argitis, P. Normand, ACS Appl. Mater. Interfaces 5 (2013) 5667. [6] C.D. Müller et al., Nature 421 (2003) 829. [7] M. Vasilopoulou, D.G. Georgiadou, G. Pistolis, P. Argitis, Adv. Funct. Mater. 17 (2007) 3477. [8] D.G. Georgiadou, L.C. Palilis, M. Vasilopoulou, G. Pistolis, D. Dimotikali, P. Argitis, RSC Adv. 2 (2012) 11786. [9] D.G. Georgiadou, L.C. Palilis, M. Vasilopoulou, G. Pistolis, D. Dimotikali, P. Argitis, J. Mater. Chem. 21 (2011) 9296. [10] J.V. Crivello, J.H.W. Lam, J. Polym. Sci. A Polym. Chem. 17 (1979) 1047. [11] D.G. Georgiadou, L.C. Palilis, M. Vasilopoulou, G. Pistolis, D. Dimotikali, P. Argitis, Synth. Met. 181 (2013) 37. [12] D.G. Georgiadou et al., ACS Appl. Mater. Interfaces 5 (2013) 12346. [13] P.S. McKinney, S. Rosenthal, J. Electroanal. Chem. 16 (1968) 261. [14] D. Franklin, F.D. Saeva, B.P. Morgan, J. Am. Chem. Soc. 106 (1984) 4121. [15] F.D. Saeva, D.T. Breslin, P.A. Martic, J. Am. Chem. Soc. 111 (1989) 1328; F.D. Saeva, D.T. Breslin, P.A. Martic, J. Photochem. Photobiol. A 86 (1995) 149. [16] R. Xia et al., Chem. Mater. 24 (2012) 237. [17] M. Endo, S. Tagawa, J. Photopolym. Sci. Technol. 24 (2011) 205. [18] T. Itani, T. Kosawa, Jpn. J. Appl. Phys. 52 (2013) 010002. [19] R.G. Parr, Annu. Rev. Phys. Chem. 46 (1995) 701. [20] M.A.L. Marques, E.K.U. Gross, Annu. Rev. Phys. Chem. 55 (2004) 427. [21] (a) Y. Zhao, D. Truhlar, Theor. Chem. Acc. 120 (2008) 215; (b) Y. Zhao, D. Truhlar, Acc. Chem. Res. 41 (2008) 157. [22] D. Tzeli, I.D. Petsalakis, G. Theodorakopoulos, Phys. Chem. Chem. Phys. 13 (25) (2011) 11965; I.D. Petsalakis, D. Tzeli, Ioannis S.K. Kerkines, G. Theodorakopoulos, Comp. Theor. Chem. 965 (2011) 168. [23] A.D. Becke, Phys. Rev. A 38 (1988) 3098. [24] C. Lee, W. Yang, Phys. Rev. B 37 (1988) 785. [25] M.J.G. Peach, P. Benfield, T. Helgaker, D.J.J. Tozer, Chem. Phys. 128 (2008). [26] M.J. Frisch et al., GAUSSIAN 09, Revision A.1, Gaussian Inc., Wallingford CT, 2009. [27] P.J. Hay, W.R. Wadt, J. Chem. Phys. 82 (1985) 270 (284–298; 299–310).