DFT and TD-DFT Study on the Structural and

DFT and TD-DFT Study on the Structural and Optoelectronic Characteristics of Chemically Modified Donor-Acceptor Conjugated Oligomers for Organic Polymer Solar Cells Francisco C. Franco Jr.*a, and Allan Abraham B. Padamab a

Chemistry Department, De La Salle University, Taft Avenue, Manila, Philippines Institute of Mathematical Sciences and Physics, College of Arts and Sciences, University of the Philippines Los Baños, Laguna, Philippines b

Abstract The structural and optoelectronic properties of several substituted poly[N-9’heptadecanyl-2,7-carbazole-alt-5,5-(4’,7’-di-2-thienyl-2’,1’,3’-benzothiadiazole) (PCDTBT) conjugated oligomers have been investigated by density functional theory (DFT) and time-dependent density functional theory (TD-DFT). Various electronwithdrawing and electron-donating groups were attached to the 5’ position of the benzothiadiazole unit in the PCDTBT oligomers. HOMO energies (EHOMO), LUMO energies (ELUMO), and the fundamental energy gaps (EGap) were calculated using DFT while the first singlet excited states (EOpt) were calculated using TD-DFT. Results show that the structural properties of the oligomers greatly affect the optoelectronic properties. Results also show that both electron-withdrawing and electron-donating groups are capable of lowering the EGap of PCDTBT. Several properties of substituted PCDTBT, which may affect the solar cell properties, were then calculated and compared with the calculated values for PCDTBT. From the calculated properties, PCDTBT-F showed improvement in the EGap, open-circuit voltage (VOC), and ionization potential (IP), which may lead to solar cells with improved power conversion efficiency (PCE) compared to PCDTBT. Keywords: density functional theory, PCDTBT, optoelectronic properties

1

1.

Introduction Organic photovoltaics (OPVs) have attracted a great deal of attention due to their

various potential advantages, such as lightweight, easily fabricated, flexible, and low-cost devices [1-5]. Recent developments in organic polymer solar cell devices have led to power conversion efficiencies (PCE) close to 10% [6-8]. However, with Si-based commercial solar cells reaching 25% [9,10], significant improvement in material and device engineering must be made in order for organic polymer solar cells to be commercially attractive. Therefore, in order to synthesize new materials that may eventually lead to higher solar cell device performance, the study of organic polymer material design and intrinsic properties is indispensable. Conversion of light energy to electrical energy in OPVs involves a series of steps as shown in Figure 1. (1) Bound electron-hole pair (exciton) is generated via absorption of photon in the donor material. (2) The exciton diffuses to the donor-acceptor interface (typical diffusion length for organic polymers ~10 nm [11,12]). (3) The bound electron is transferred to the acceptor at the interface. (4) The exciton is dissociated into free charge carriers (i.e., well separated electron and hole) and transported to the electrodes.

Donor

LUMO

EB EGap

e

-

Acceptor

(2)

e

-

(3)

e

(1)

EOpt

HOMO

h

(4)

ELL

e

-

LUMO

ELH + (2)

+

-

h

+

h

EHH

(4)

HOMO Interface 2

Fig. 1. Schematic diagram of the electron and hole transport mechanism in organic photovoltaic solar cells. Bound electron-hole pairs (excitons) are represented by the shaded regions.

The amount of light absorbed by the OPV device largely depends on the fundamental energy gap (EGap) and the optical energy gap (EOpt) of the donor material. EGap is the difference between the LUMO (ELUMO) and HOMO (EHOMO) energies for well-separated electrons and holes, i.e., overcoming Coulombic attraction, which can be observed via electrochemical [35,48] and photoemission measurements [47]. On the other hand, EOpt is the minimum energy required for electronic transition to occur, producing bound electron-hole pair (excitons) due to Coulombic attraction, and measured experimentally as the onset of optical absorption, S0  S1, [35,47]. Due to this, the fundamental energy gap is usually larger than the optical gap. The difference between EGap and EOpt is called the exciton binding energy (EB), the energy required to dissociate excitons into mobile electrons and holes in the donor material [42,43,47]. The driving force for the exciton dissociation in the donor-acceptor interface is the difference in the LUMO energies of the donor (polymer) and acceptor (typically fullerene based) materials (ELL). After dissociation, ELL together with the difference between the HOMO energies of the donor and acceptor materials (EHH) prevents the recombination of the dissociated electrons and holes. Therefore, in order for exciton dissociation to be favored and to reduce recombination of electron-hole pairs after dissociation, both ELL and EHH must be greater than the EB of the donor material which is typically ~0.3 eV to 0.5 eV [14]. Another important property is the difference between the LUMO energy of the acceptor material and the HOMO energy of the donor material (ELH in Figure 1). ELH is related to the open-circuit voltage (VOC) of the OPV device. The VOC of the device can be approximated from the empirical equation [5,15]:

1 DONOR ACCEPTOR VOC = éë EHOMO - ELUMO - 0.3 eVùû e

(1)

DONOR ACCEPTOR where e is the elementary charge, EHOMO = ELH, and 0.3 eV is an empirical - ELUMO

factor arising from the quasi Fermi energies of electrons and holes within the EHOMO and 3

ELUMO energies of the acceptor and donor materials, and is subtracted from ELH [41]. VOC together with the short-circuit voltage (ISC), which mainly depends on EGap, are two main factors contributing to the photovoltaic power conversion efficiency (PCE). The PCE of an organic solar cell can be calculated from the equation [14]:

PCE(%) =

I SC ´VOC ´ FF ´100% Pm

(2)

where FF is called the fill factor which is related to the series and parallel resistances in the device, and Pm is the light intensity. In order to achieve high PCE, several key considerations must be made regarding the intrinsic properties of donor materials: small EGap to have a broader range of absorption in the solar spectrum, and good combinations between the EHOMO and ELUMO of the donor and acceptor materials. poly[N-9’-heptadecanyl-2,7-carbazole-alt-5,5-(4’,7’-di-2-thienyl-2’,1’,3’benzothiadiazole) (PCDTBT) replaced poly(3-hexylthiophene-2,5-diyl) (P3HT) as the most used organic material for organic solar cells in the recent years due to its superior properties [16]. PCDTBT has a large VOC vs. PC61BM (0.9 V) [35], low energy gap (1.85 eV), and high stability from oxidation (ionization potential, IP) = 5.45 eV) [50]. One main advantage of organic semiconductor materials over inorganic materials is that the physical properties of organic materials can be easily adjusted by attaching different substituents. The solubility of organic polymers can be enhanced by attaching long chained alkyl substituents; while, the electronic energy levels can be adjusted by doping [13,37,46] and attaching electron-withdrawing or electron-donating substituents [14,17,25,26,56]. With this, it is therefore important to identify and investigate the changes in the properties and performance of this organic material in the presence of these attached substitutents. It is worth mentioning that there are other conjugated materials that can be used as alternative for conjugated polymers for solar cells such as 2D-materials: graphene- [61-63], and silicene- [64] based materials. Density functional theory (DFT) based calculations have been significant in understanding electronic properties of different systems in atomic scale [18,19]. It is also commonly used to determine properties of π-conjugated systems [17,29,33,36,59]. Even 4

though DFT calculations have been commonly found to have deviations from experimentally determined values especially for semiconductor systems, the trends for the calculated values are normally the same with the experiments [20,23,44,49]. Moreover, changes on the electronic and geometric properties of modified systems are conveniently addressed using this method. Performing studies using DFT, therefore, will aid experimentalists in the design, prediction and functionalization of different materials necessary for a specific application. In this study, we investigated the effects of substitution of various electronwithdrawing and electron-donating substituents on the structural and optoelectronic properties of poly[N-9’-heptadecanyl-2,7-carbazole-alt-5,5-(4’,7’-di-2-thienyl-2’,1’,3’benzothiadiazole) (PCDTBT), a high-performance donor material in OPVs [16], using quantum-mechanical calculations based on DFT and (Time dependent–density functional theory) TD-DFT. The hydrogen in the 5’ position of PCDTBT was replaced with several substituents (-X). The HOMO energy (EHOMO), LUMO energy (ELUMO), and energy gap (EGap) were calculated from DFT. The first excited singlet state, (EOpt) was calculated by TD-DFT calculations. The solar cell characteristics of the new PCDTBT derivatives (PCDTBT-X) were then predicted and compared with the calculated values for PCDTBT. This study also aims to provide new insights on the structural and optoelectronic properties of modified conjugated polymers, and propose new organic polymer material designs for OPVs with improved solar cell properties.

2.

Materials and methods The chemical structures of the PCDTBT derivatives (PCDTBT-X) used in the

study are shown in Figure 2. Various electron-withdrawing (i.e., prefers to gain e-): acetyl (-COCH3), cyano (-CN), fluoro (-F), nitro (-NO2), trifluoromethyl (-CF3); and electron-donating (i.e., prefers to transfer e-): amino (-NH2), isopropyl (-CH(CH3)2), dimethylamino (-N(CH3)2), ethenyl (-CH=CH2), hydroxy (-OH), methyl (-CH3), and methoxy (-OCH3), substituents (-X) were attached to the 5’ position of the benzothiadiazole unit of the PCDTBT oligomers. The heptadecanyl chain attached to the nitrogen atom of the carbazole unit in PCDTBT was replaced with isopropyl in order to 5

reduce computational costs, but still approximate the electron-withdrawing and steric effects of the heptadecanyl chain. Also, the terminals of the repeating units for all the oligomers were saturated with hydrogen atoms.

Fig. 2. The chemical structures of the PCDTBT derivatives (PCDTBT-X) used in this study. (-X) represents the attached substituent to PCDTBT.

All calculations were carried out with PC-GAMESS / Firefly QC package which is partially based from GAMESS (US) source code [27,28]. Density functional theory (DFT) and time-dependent density functional theory (TD-DFT) [21-24] were performed to investigate the effects of substitution to the structure and optoelectronic properties of the substituted PCDTBT. Geometry optimizations for PC61BM and substituted PCDTBT oligomers (n = 1 to 4 units) were performed using the Becke three parameter (exchange), Lee, Yang, and Parr (B3LYP) as the generalized gradient approximation (GGA) functional; and 6-31G(d) as the basis set. B3LYP/6-31G(d) has been successful in predicting trends in conjugated systems without significant computational costs [20,36,54,59]. All geometry optimizations were carried out in gas phase, without any symmetry constraints, and with all atoms allowed to relax. Total energy calculations to obtain the HOMO (EHOMO) and LUMO (ELUMO) energies were performed with 6311G(d,p) basis set in order to have better accuracy without substantially increasing the computational costs. The fundamental gap (EGap) was calculated from the energy 6

difference between EHOMO and ELUMO. First singlet excited states (EOpt) were calculated using TD-DFT, also at the B3LYP/6-311G(d,p) level. Exciton binding energies (EB) were estimated from the difference between EGap and EOpt [29,30]. The open-circuit voltage (VOC) of the substituted PCDTBT derivatives were evaluated from the calculated values for ELUMO of PC61BM and EHOMO of the PCDTBT derivatives using equation 1. The ionization potentials (IP) were estimated from the negative of EHOMO based from Koopman’s Theorem [31].

3.

Results and discussion

3.1.

Structural analysis of PCDTBT derivatives

Fig. 3. Schematic representation of the relevant dihedral angles (Φ) and Δr determined for various PCDTBT derivatives (PCDTBT-X) in this study. Δr is the difference between the adjacent carbon-carbon double and single bond lengths as shown by bold lines. Φ1, and Φ2 are the dihedral angles between thiophene and benzothiadiazole units. The dihedral angle (Φ) and Δr between units in the polymer backbone has significant effects on the conjugation of the polymer, thus, on the optoelectronic properties [17,29,59,60]. It was observed that the structural properties of the optimized oligomer structures showed large dependency on the substituent attached to the benzothidiazole unit. Figure 3 illustrates the significant dihedral angles and Δr 7

influenced by substitution at the 5’ position of the benzothiadiazole unit. Table 1 summarizes the dihedral angles observed for the PCDTBT derivatives studied. It was expected that Φ1 will have large deviation from coplanarity upon substitution since the presence of any substituent in the 5’ position of the benzothiadiazole unit may interact with the sulfur atom of the thiopene unit. The optimized structure for the unsubstituted PCDTBT (-H) was observed to have coplanar thiophene and benzothiadiazole units, similar to previous computational work [55]. Several PCDTBT derivatives also produced coplanar structures: PCDTBT-CN, PCDTBT-F-, PCDTBT-OH, PCDTBT-CH3, and PCDTBT-OCH3. On the other hand, the derivatives: PCDTBT-COCH3 (43.6°), PCDTBT-CH(CH3)2 (72.5°), PCDTBT-CH=CH2 (41.7°), PCDTBT-NO2 (44.3°), and PCDTBT-CF3 (49.1°), produced structures with large deviations from coplanarity (i.e., Φ > 40°). Large deviations were observed due to the steric repulsion of the bulky substituents with the sulfur atom of the adjacent thiophene unit. Φ2 was mostly unaffected since the substituent in the 5’ position doesn’t significantly interact with the other thiophene unit (non-adjacent to substitution).

Table 1. Dihedral angles between the substituted benzothiadiazole unit and the adjacent thiophene units of the optimized structures (DFT/B3LYP/6-31G(d)) for n = 4 PCDTBT derivatives (PCDTBT-X). Φ1, and Φ2 are the dihedral angles shown in Figure 3. PCDTBT-X -H -COCH3 -NH2 -CH(CH3)2 -CN -N(CH3)2 -CH=CH2 -F -OH -CH3 -NO2 -CF3 -OCH3

Φ1 0.2 43.6 37.1 72.5 0.1 20.5 41.7 0.1 0.1 0.4 44.3 49.1 0.1

Φ2 0.3 2.3 1.2 0.2 0.1 3.6 0.4 0.1 0.1 0.2 3.3 0.4 0.1

The PCDTBT derivative with the bulky -N(CH3)2, group was observed to have smaller Φ1 (20.5°) compared to the less bulky -NH2 group with large Φ1 (37.1°). The 8

observed structure is due to the higher π-bonding character for H2N–C(5’) bond than the (CH3)2N–C(5’) bond. This can be verified quantitatively by comparing the bond energies (B.E.) of the two N-C bonds using the equation: B.E. = EPCDTB-X – Eisolated PCDTBT – EX, where EPCDTBT-X corresponds to the total energy of the substituted PCDTBT, Eisolated PCDTBT represents

the total energy of isolated PCDTBT, and EX is the total energy of

isolated substituent. The B.E. for H2N-C(5’) and (CH3)2N-C(5’) were observed to be 4.55 eV and 3.72 eV, respectively. Therefore, the methyl groups of PCDTBT-N(CH3)2 were observed to be out-of-plane from the benzothiadiazole unit resulting to less interaction with sulfur from the adjacent thiophene unit. On the other hand, hydrogens in PCDTBT-NH2 are in plane with the benzothiadiazole ring, and as a result, one of the hydrogens can interact with the sulfur atom of the adjacent thiophene unit, resulting to large dihedral angle. Figure 4 summarizes the Δr values determined and compared with PCDTBT. The largest Δr were observed for the derivatives: PCDTBT-COCH3, PCDTBT-NH2, PCDTBT-CH(CH3)2, PCDTBT-CH=CH2, PCDTBT-NO2, and PCDTBT-CF3. These derivatives were also the same derivatives with the largest increase in dihedral angles. The increase in Δr values can be attributed to the loss of planarity between the benzothiadiazole and thiophene units which results to less π-conjugation. On the other hand, most coplanar PCDTBT derivatives have similar Δr values with PCDTBT except for PCDTBT-CN which was observed to have significant decrease in Δr (≈ 0.01Å). One possible reason for the decrease in Δr is the increase of the quinoid character of the ground state of the polymer when substituted with the highly electron withdrawing cyano group [25,26] similar to previous theoretical studies [56].

9

0.12

PCDTBT

0.11

Δr (Å)

0.10

0.09 0.08 0.07

0.06 -OCH123

-CF113

-NO102

-CH39

-OH8

-F7

-CH=CH26

-N(CH3)25

-CN4

-CH(CH3)23

-NH22

-COCH31

0.05

PCDTBT-X Fig. 4. Δr (Å) determined by DFT/B3LYP/6-31G(d) for various PCDTBT derivatives (PCDTBT-X). Δr is the difference between the adjacent carbon-carbon single and double bond lengths as shown by the arrows in Figure 3. The Δr for PCDTBT is also shown (dotted line).

3.2.

Optoelectronic properties of PCDTBT derivatives

Electronic properties: EHOMO, ELUMO, and EGap of PCDTBT of various PCDTBT oligomers were calculated at the DFT/B3LYP/6-311G(d,p) level. (The variation of electronic properties with respect to the number of monomer units is shown in Supplementary Material Fig. S.1) Various fitting methods were previously used to approximate the polymer energy values calculated from their oligomer values, e.g., linear fit [33,59], exponential fit [32-34], polynomial fit [29]. (The polymer values extrapolated using Meier fit, an exponential fitting method is shown in Supplementary Material, Fig. S.2) The energy values calculated in this study seem to converge at n = 4, therefore, we used the n = 4 values to approximate the polymer values. The n = 4 electronic energy values for the PCDTBT are: EHOMO = -4.98 eV, ELUMO = -2.95 eV, and EGap = 2.02 eV.

10

Comparing the calculated values with the experimental values, the calculated values were observed to have large deviations of up to: 8.62 %, 18.05 %, and 9.19 % for the EHOMO, ELUMO, and EGap, respectively, compared to previously determined experimental values: -5.45 eV, -3.60 eV, and 1.85, for the EHOMO, ELUMO, and EGap, respectively [35]. These calculated values at the B3LYP/6-311G(d,p) level are similar with previously calculated values for PCDTBT dimer [57], and PBC-DFT method performed at DFT/B3LYP [58]. The DFT/B3LYP method offers satisfactory results for conjugated polymer systems [29,36-38,56-58] without having significant computational costs. In spite of this, large deviations (up to 10%) were still observed for the EHOMO energies, and up to 1 eV for ELUMO energies [39,40]. However, since we are only interested in the trends of substituted PCDTBT and how their electronic and optical

HOMO/LUMO Energy (eV)

properties compare with PCDTBT, the DFT/B3LYP method is sufficient for this study.

1.00

CB LUMO CB HOMO

0.00 -1.00 -2.00 -3.00 -4.00 -5.00 -6.00 -7.00

PC61BM

-OCH -OCH3 3

-CF -CF3 3

-NO 2 -NO2

-CH -CH3 3

-OH -OH

-F-F

-CH=CH -CH=CH2 2

-N(CH 3)2 -N(CH3)2

-CN -CN

-CH(CH 3)2 -CH(CH3)2

-NH 2 -NH2

-COCH 3 -COCH3

-HH

-8.00

PCDTBT-X Fig. 5. Calculated energy values (n = 4) of the PCDTBT derivatives: EHOMO (bottom of rectangular box), ELUMO (top of rectangular box), and EGap (length of rectangular box) using DFT at the B3LYP/6-311G(d,p) level. The EHOMO (dotted line) and ELUMO (dashed line) for an isolated carbazole (CB) unit; and the EHOMO (black segment) and ELUMO (red 11

segment) for the isolated substituted benzothiadiazole (BT-X) units are also shown. The EHOMO (thick black segment) and ELUMO (thick red segment) for PC61BM are included for reference.

In the frontier molecular orbital diagram for PCDTBT, well-delocalized HOMO wavefunctions are observed along the conjugated backbone (i.e., carbazole (CB) thiophene (T) – benzothiadiazole (BT) – thiopehene (T)). On the other hand, the LUMO wavefunctions are generally localized on the thiophene and benzothiadiazole (T-BT-T) units of the PCDTBT. (Frontier molecular orbitals for PCDTBT and its derivatives are shown in Supplementary Material, Fig. S.3 and S.4) These observations are due to the differences in the HOMO and LUMO energies of the isolated carbazole (CB) and dithienyl-benzothiadiazole (T-BT-T). The EHOMO and ELUMO values for the isolated CB (dotted and dashed lines, respectively), T-BT-X-T (black and red segments, respectively) units are shown in Figure 5. The EHOMO (-6.11 eV) and ELUMO (-3.51 eV) for PC61BM were also calculated at the DFT/B3LYP/6-311G(d,p) level and included in Figure 5 (shown as thick black and red segments, respectively). The experimental energy values for PC61BM are: EHOMO = -6.0 eV and ELUMO = -4.3 eV [15] which corresponds to 1.8 % and 18.3 % deviations for the calculated EHOMO, and ELUMO values, respectively. The EHOMO and ELUMO for the isolated unsubstitued T-BT-T unit are: -5.53 eV and -2.85 eV, respectively, similar to previously calculated values in [20]. As shown in Figure 5, the differences between the HOMO energies of CB and T-BT-X-T units ranges from 0.01 eV up to 0.56 eV, and results to good orbital mixing. On the other hand, the differences between the LUMO energies of CB and T-BT-X-T ranges from 1.5 – 2.4 eV which results to less orbital mixing of the LUMO wavefunctions, resulting to LUMO wavefunctions closer to the LUMO of T-BT-X-T. From the isolated T-BT-X-T derivatives, it can be observed that the derivatives with electron withdrawing substituents have lower EHOMO and ELUMO than PCDTBT. This observation can be attributed to the stabilization of the HOMO and LUMO of the isolated fragments due to withdrawal of e- charge by the substituent [14], which results to lower energy values. On the other hand, lower EHOMO but higher ELUMO values were observed for isolated fragments with large dihedral angles (i.e., Φ > 40°) and electron 12

donating substituents. This observation can be attributed to the loss of π-conjugation in the fragment as observed from Δr values. The bond energy between the -CH(CH3)2 and CH=CH2 substituted benzothiadiazole unit and adjacent thiophene unit was observed to decrease to 4.97 eV and 5.06 eV, respectively, compared to the bond energy for the unsubstituted benzothiadiazole which is 5.40 eV. Electron donating substituents with dihedral angles less than 40° have EHOMO and ELUMO values greater than the isolated unsubstituted T-BT-X-T. This is attributed to the destabilization of the HOMO and LUMO, owing to the release of e- charge of the substituent leading to higher energy values [14,17]. From the n = 4 energy values, PCDTBT derivatives with electron-withdrawing substituents: PCDTBT-COCH3, PCDTBT-CN, PCDTBT-F, PCDTBT-NO2, and PCDTBT-CF3 have lower EHOMO and ELUMO levels. On the other hand, PCDTBT derivatives with electron-donating substituents: PCDTBT-CH3, PCDTBT-NH2, PCDTBT-OH, and PCDTBT-OCH3 have higher EHOMO and ELUMO levels. The EGap values were observed to be in the range between 1.85 eV to 2.47 eV. Several derivatives with electron-withdrawing and electron-donating substituents have lower EGap compared to PCDTBT: PCDTBT-COCH3, PCDTBT-N(CH3)2, PCDTBT-NO2, PCDTBT-CN, PCDTBT-F, PCDTBT-OH, and PCDTBT-OCH3. For electron-withdrawing substituents, ELUMO decreases more than EHOMO, while for electron-donating substituents, EHOMO increases more than ELUMO. Larger EGap values were observed for several PCDTBT derivatives compared to PCDTBT: PCDTBT-NH2, PCDTBT-CH(CH3)2, PCDTBTCH=CH2, PCDTBT-CH3, and PCDTBT-CF3. With the exception of PCDTBT-CH3, these PCDTBT derivatives were also observed to have the largest dihedral angles. Deviation from planarity reduces the π-conjugation in the polymer thus widening the EGap. For PCDTBT-CH3, it was observed that the electron-donating effect resulted to slightly larger increase in ELUMO than EHOMO resulting slight to increase in EGap. Table 2 summarizes the calculated n = 4 electronic and optical properties at the DFT and TD-DFT at the B3LYP/6-311G(d,p) level. The EHOMO, ELUMO, and EGap values are listed as mentioned in Figure 5. According to previous calculations for P3HT, increase in dihedral angles to about 16° from planarity does not have significant effects on the energy values, EHOMO, ELUMO, and EGap [65]. The first singlet excitation energy, 13

EOpt value for PCDTBT was 1.69 eV, a 10.1 % deviation from the experimentally determined value of 1.88 eV, measured from the onset of absorption in solution [51]. (The evolution of the excitation energies and oscillator strengths for n = 1 to n = 4 oligomers with their corresponding configurations are shown in Supplementary Material, Table S.1) The EOpt values were observed to have the same trends with EGap, that is, PCDTBT derivatives with large dihedral angles have larger EOpt values. It must be noted that the EGap values are all greater than the EOpt values since it takes additional energy to fully separate electrons and holes into free carriers. The difference in EGap and EOpt is called the exciton binding energy (EB), also shown in Table 2. EB values were observed to be in the range between 0.29 eV to 0.35 eV, consistent with exciton binding energies for conjugated polymers [14]. The largest increases in EB, i.e., 0.02 eV – 0.04 eV from PCDTBT, were observed for the PCDTBT derivatives with large deviation from planarity, i.e., Φ > 40° similar to previous observations for P3HT. It was observed previously that less than 30° increase in the dihedral angles does not have significant effects on the binding energy of P3HT [45].

Table 2. Calculated energy values EHOMO, ELUMO, and EGap of the PCDTBT derivatives using the n = 4 oligomer values with DFT at the B3LYP/6-311G(d,p) level. EOPT was calculated from the n = 4 oligomer values of the PCDTBT derivatives with TD-DFT at the B3LYP/6-311G(d,p) level. EB values were calculated from the difference between EGap and EOpt. PCDTBT-X -H -COCH3 -NH2 -CH(CH3)2 -CN -N(CH3)2 -CH=CH2 -F -OH -CH3 -NO2 -CF3 -OCH3

EHOMO (eV) -4.98 -5.10 -4.93 -5.19 -5.18 -4.88 -5.05 -5.02 -4.86 -4.94 -5.28 -5.19 -4.82

ELUMO (eV) -2.95 -3.11 -2.68 -2.72 -3.32 -2.87 -2.87 -3.02 -2.88 -2.88 -3.37 -3.13 -2.86 14

EGap (eV) 2.02 1.99 2.25 2.47 1.86 2.01 2.18 1.99 1.97 2.07 1.91 2.06 1.96

Eopt (eV) 1.71 1.69 1.91 2.12 1.56 1.69 1.84 1.69 1.69 1.75 1.58 1.73 1.67

EB (eV) 0.32 0.30 0.34 0.36 0.30 0.32 0.34 0.30 0.28 0.32 0.33 0.33 0.29

Figure 6 shows the evolution of the oscillator strengths for all substituted PCDTBT oligomers; an important property related to the absorption coefficient of materials, thus, also an important parameter for OPVs. Coplanar oligomer PCDTBT derivatives generally have large oscillator strengths, which result from highly extended πconjugation due to good spacial overlap of the wavefunctions [20]. Conversely, the derivatives that have the lowest oscillator strengths are the PCDTBT derivatives with

-OCH13 3

-CF12 3

-NO11 2

-CH10 3

-OH9

-F8

-CH=CH27

-N(CH3)26

-CN5

-CH(CH3)24

-NH23

-COCH32

4.50 4.00 3.50 3.00 2.50 2.00 1.50 1.00 0.50 0.00

-H1

Oscillator Strength, ƒ

large dihedral angles (Φ > 40°), which result to less spacial overlap of the wavefunctions.

PCDTBT-X Fig. 6. Oscillator strengths for the first singlet excitation transitions, S0  S1, of the n = 4 oligomers used in this study calculated at the TD-DFT/B3LYP/6-311G(d,p).

3.3.

Solar cell characteristics

Figure 7 summarizes the trends in the predicted solar cell properties: ED-R, IP, VOC, and EGap values. Figure 7(a) shows the ability of the polymer to dissociate excitons and prevent recombination, ED-R, calculated using the difference between the ELL (from Figure 1) and EB. It can be observed that there are two polymers with negative values: PCDTBT-CN and PCDTBT-NO2. This will negatively impact the dissociation of excitons to charge carriers and will favor electron-hole recombinations. The rest of the 15

polymers show positive ED-R which will drive the dissociation of excitons and prevent electron-hole recombinations. From the calculated values, PCDTBT derivatives that will result to higher VOC, from equation 1, and IP, calculated from the negative of EHOMO, compared to PCDTBT are the electron-withdrawing substituted polymers with stabilized EHOMO: PCDTBTCOCH3, PCDTBT-F, PCDTBT-CN, PCDTBT-NO2, and PCDTBT-CF3. The calculated VOC for PCDTBT/PCB61M was 1.16 V, compared to the experimentally determined VOC for PCDTBT/PC61BM solar cells which was 0.9 V [35]. The deviation resulted from the large deviations observed from the calculated (more positive) ELUMO values, i.e., 18.3% for PC61BM. The estimated VOC values for the PCDTBT derivatives are shown in Figure 7(b). Other PCDTBT derivatives with large Φ: PCDTBT-CH(CH3)2, and PCDTBTCH=CH2, also produced higher VOC and IP due to stabilized HOMO energies. Higher VOC suggest that these PCDTBT derivatives may have improved power conversion efficiency compared to PCDTBT, i.e., PCE proportional to VOC. Since IP is approximated to be equal to the negative of the EHOMO, the lower is the EHOMO (more negative), the higher is the IP (shown in Figure 7(d)). Larger IP may result to a polymer material more stable to oxidation and which may result to higher device lifetime.

16

(a)

(b)

(c)

(d)

Fig. 7. Summary of the predicted solar cell characteristics of the polymers in this study: (a) ability of the polymer to dissociate excitons and prevent recombination, ED-R, (b) 17

open circuit voltage, VOC, (c) energy gap, EGap, and (d) ionization potential, IP. The dashed lines in (b), (c), and (d) represents the calculated values for PCDTBT. Filled circles and cross marks represent positive and negative values for ED-R, respectively, in (a); while the filled circles and cross marks represent better and worse predicted properties than PCDTBT, respectively, in (b), (c), and (d). Several PCDTBT derivatives will result to a lower EGap (Figure 7c) compared to PCDTBT namely: PCDTBT-COCH3, PCDTBT-N(CH3)2, PCDTBT-CN, PCDTBT-F, PCDTBT-OH, PCDTBT-CF3, and PCDTBT-OCH3. Electron-withdrawing substituents: COCH3, -CN, -F, and -CF3, lower the EGap by mainly lowering the ELUMO. Electrondonating substituents: -OH, -N(CH3)2, and –OCH3 lower the EGap by mainly increasing the EHOMO. The results suggest that these PCDTBT derivatives may increase the shortcircuit density (ISC) of the solar cell compared to PCDTBT since lower EGap will result to a broader absorption range for the polymer which will increase the amount of charge carriers generated, thus, leading to higher PCE.

Table 3. Comparison of the calculated solar cell properties for the various PCDTBT derivatives vs. PCDTBT in this study: ability to dissociate and prevent recombination (ED-R), open-circuit voltage (VOC), energy gap (EGap), and ionization potential (IP). PCDTBT-X -COCH3 -NH2 -CH(CH3)2 -CN -N(CH3)2 -CH=CH2 -F -OH -CH3 -NO2 -CF3 -OCH3

ED-R (eV) o o o x o o o o o x o o

VOC (eV) o x o o x o o x x o o x

EGap(V) o x x o o x o o x o x o

IP (eV) o x o o x o o x x o o x

Table 3 presents a comparison of the predicted solar cell properties of substituted PCDTBT (PCDTBT-X) with the calculated values for PCDTBT. It is observed that two PCDTBT derivatives have better solar cell properties than PCDTBT: PCDTBT-F and 18

PCDTBT-COCH3 (labelled “o”) in all calculated properties from Table 3. However, from the structural analysis of the derivatives, it was observed that PCDTBT-COCH3 had dihedral angles as large as 43.6° as shown in Table 1. This resulted to a great decrease in the oscillator strength of the material (i.e., low absorption coefficient), which may reduce the photocurrent density of the material for a certain thickness of the active layer (typically ~1 μm [53]). The non-planar structure may also lead to problems in the morphology of the active layer when the polymer-acceptor blend is prepared which has a great impact on the solar cell electrical properties: ISC, VOC and fill-factor FF [52]. Therefore, PCDTBT-F derivative may have overall better solar cell properties than PCDTBT. PCDTBT-F showed improvements in the calculated values of some important solar cell properties, i.e., EGap, VOC, and IP compared to PCDTBT.

4.

Conclusions The structural and optoelectronic properties of various substituted poly[N-9’-

heptadecanyl-2,7-carbazole-alt-5,5-(4’,7’-di-2-thienyl-2’,1’,3’-benzothiadiazole) (PCDTBT) conjugated oligomers were studied by density functional theory (DFT) and time-dependent density functional theory (TD-DFT). Results show that structural effects, such as large increase in Φ and Δr negatively affect the EGap and EOpt which will lead to lower amount of light absorbed in solar cells. Results also suggest that several electronwithdrawing and electron-donating substituents are capable of reducing the EGap of PCDTBT, which may lead to higher ISC. Coplanar thiophene and substituted benzothiadiazole units in PCDTBT derivatives lead to higher oscillator strengths, which may lead to higher light absorption. Electron-withdrawing substituents with lowered EHOMO level may also lead to higher VOC and more stable polymer due to higher ionization potential, IP. However, for the case of PCDTBT-CN, the decrease in frontier orbitals is too great which may negatively impact the solar cell characteristics. From the PCDTBT derivatives investigated, PCDTBT-F showed higher VOC and IP, and smaller EGap compared to PCDTBT. These results suggest that PCDTBT-F may have better solar cell power conversion efficiency since PCE is proportional to both VOC and ISC. PCDTBT-F is also expected to have improved oxidation stability due to the higher IP. 19

While discrepancies in the calculated values exist in reference to existing experimental data, the conclusions and predictions based from the obtained trends for the substituted PCDBT study can aid in future designs of organic materials based on PCDTBT for solar cell application.

Acknowledgements FFJr. acknowledges funding from the University Research Coordination Office (URCO) of De La Salle University – Manila under Project No. 35N1TAY14-3TAY14.

References [1]

R. Roesch, K.-R. Eberhardt, S. Engmann, G. Gobsch, H. Hoppe, Polymer solar cells with enhanced lifetime by improved electrode stability and sealing, Sol. Energy Mater. Sol. Cells. 117 (2013) 59–66.

[2]

J. Hou, M.-H. Park, S. Zhang, Y. Yao, L.-M. Chen, J.-H. Li, et al., Bandgap and Molecular Energy Level Control of Conjugated Polymer Photovoltaic Materials Based on Benzo[1,2-b:4,5-b′]dithiophene, Macromolecules. 41 (2008) 6012–6018.

[3]

H. Hoppe, N.S. Sariciftci, Organic solar cells: An Overview, J. Mater. Res. 19 (2004) 1924–1945.

[4]

E. Zhou, K. Hashimoto, K. Tajima, Low Band Gap Polymers for Photovoltaic Device with Photocurrent Response Wavelengths over 1000 nm, Polymer. 54 (2013) 6501–6509.

[5]

T. Ameri, P. Khoram, J. Min, C.J. Brabec, Organic Ternary Solar Cells: A Review, Adv. Mater. 25 (2013) 4245–4266.

[6]

Y. Matsuo, Y. Sato, T. Niinomi, I. Soga, H. Tanaka, E. Nakamura, Columnar Structure in Bulk Heterojunction in Solution-Processable Three-Layered p-i-n Organic Photovoltaic Devices Using Tetrabenzoporphyrin Precursor and Silylmethyl[60]fullerene, J. Am. Chem. Soc. 131 (2009) 16048–16050.

[7]

M. Riede, C. Uhrich, J. Widmer, R. Timmreck, D. Wynands, G. Schwartz, et al., Efficient Organic Tandem Solar Cells based on Small Molecules, Adv. Funct. Mater. 21 (2011) 3019–3028. 20

[8]

J.M. Lobez, T.L. Andrew, V. Bulović, T.M. Swager, Improving the Performance of P3HT–Fullerene Solar Cells with Side-Chain-Functionalized Poly(thiophene) Additives: A New Paradigm for Polymer Design, ACS Nano. 6 (2012) 3044–3056.

[9]

A. Blakers, N. Zin, K. McIntosh, K. Fong, High Efficiency Silicon Solar Cells, Energy Procedia. 33 (2013) 1-10

[10] P.J. Cousins, D.D. Smith, H.C. Luan, J. Manning, T.D. Dennis, A. Waldhauer, et al., Generation 3: Improved Performance at Lower Cost, Conf. Rec. IEEE Photovolt. Spec. Conf. (2010) 275–278. [11] K. Feron, W. Belcher, C. Fell, P. Dastoor, Organic Solar Cells: Understanding the Role of FÖrster Resonance Energy Transfer, Int. J. Mol. Sci. 13 (2012) 17019– 17047. [12] R.R. Lunt, N.C. Giebink, A.A. Belak, J.B. Benziger, S.R. Forrest, Exciton Diffusion Lengths of Organic Semiconductor Thin Films Measured by Spectrally Resolved Photoluminescence Quenching, J. Appl. Phys. 105 (2009). [13] Y. Zhang, H. Zhou, J. Seifter, L. Ying, A. Mikhailovsky, A.J. Heeger, et al., Molecular Doping Enhances Photoconductivity in Polymer Bulk Heterojunction Solar Cells, Adv. Mater. 25 (2013) 7038–7044. [14] Y. Li, Molecular Design of Photovoltaic Materials for Polymer Solar Cells: Toward Suitable Electronic Energy Levels and Broad Absorption, Acc. Chem. Res. 45 (2012) 723–733. [15] M.C. Scharber, D. Mühlbacher, M. Koppe, P. Denk, C. Waldauf, A.J. Heeger, et al., Design Rules for Donors in Bulk-Heterojunction Solar Cells - Towards 10 % Energy-Conversion Efficiency, Adv. Mater. 18 (2006) 789–794. [16] J. Liu, S. Shao, G. Fang, B. Meng, Z. Xie, L. Wang, High-Efficiency Inverted Polymer Solar Cells with Transparent and Work-Function Tunable MoO3-Al Composite Film as Cathode Buffer Layer, Adv. Mater. 24 (2012) 2774–2779. [17] J. Roncali, Molecular Engineering of the Band Gap of π-Conjugated Systems: Facing Technological Applications, Macromol. Rapid Commun. 28 (2007) 1761– 1775. [18] F. Giustino, Materials Modelling using Density Functional Theory: Properties and Predictions, Oxford University Press, 2014. 21

[19] F. Jensen, Introduction to Computational Chemistry, Wiley, 2007. [20] L. Pandey, C. Risko, J.E. Norton, J.-L. Brédas, Donor–Acceptor Copolymers of Relevance for Organic Photovoltaics: A Theoretical Investigation of the Impact of Chemical Structure Modifications on the Electronic and Optical Properties, Macromolecules. 45 (2012) 6405–6414. [21] A.D. Laurent, C. Adamo, D. Jacquemin, Dye Chemistry with Time-Dependent Density Functional Theory, Phys. Chem. Chem. Phys. 16 (2014) 14334–14356. [22] D. Niedzialek, I. Duchemin, T.B. de Queiroz, S. Osella, A. Rao, R. Friend, et al., First Principles Calculations of Charge Transfer Excitations in Polymer–Fullerene Complexes: Influence of Excess Energy, Adv. Funct. Mater. 25 (2015) 1972–1984. [23] J.M. Granadino-Roldán, A. Garzón, G. García, M. Moral, A. Navarro, M.P. Fernández-Liencres, et al., Theoretical Study of the Effect of Alkyl and Alkoxy Lateral Chains on the Structural and Electronic Properties of π-Conjugated Polymers Consisting of Phenylethynyl-1,3,4-thiadiazole, J. Phys. Chem. C. 115 (2011) 2865–2873. [24] R.-F. Chen, L.-Y. Liu, H. Fu, C. Zheng, H. Xu, Q.-L. Fan, et al., The Influence of the Linkage Pattern on the Optoelectronic Properties of Polysilafluorenes: A Theoretical Study, J. Phys. Chem. B. 115 (2011) 242–248. [25] F.A. Carey, R.J. Sundberg, Advanced Organic Chemistry: Part A: Structure and Mechanisms, 5th ed., Springer, 2007. [26] J. Mcmurry, Organic Chemistry, 5th ed., Thomson Learning, 2000. [27] A.A. Granovsky, GAMESS/Firefly version 8.1, (2013). http://classic.chem.msu.su/gran/gamess/index.html. [28] M.W. Schmidt, K.K. Baldridge, J.A. Boatz, S.T. Elbert, M.S. Gordon, J.H. Jensen, et al., General Atomic and Molecular Electronic Structure System, J. Comput. Chem. 14 (1993) 1347–1363. [29] E.F. Oliveira, F.C. Lavarda, Molecular Design of New P3HT Derivatives: Adjusting Electronic Energy Levels for Blends with PCBM, Mater. Chem. Phys. 148 (2014) 923–932. [30] L. Zhu, Y. Yi, L. Chen, Z. Shuai, Exciton Binding Energy of Electronic Polymers: A First Principles Study, J. Theor. Comput. Chem. 7 (2008) 517–530. 22

[31] J. Luo, Z.Q. Xue, W.M. Liu, J.L. Wu, Z.Q. Yang, Koopmans’ Theorem for Large Molecular Systems within Density Functional Theory, J. Phys. Chem. A. 110 (2006) 12005–12009. [32] J. Gierschner, J. Cornil, H.J. Egelhaaf, Optical Bandgaps of π-Conjugated Organic Materials at the Polymer Limit: Experiment and Theory, Adv. Mater. 19 (2007) 173–191. [33] L. Zhang, M. Yu, H. Zhao, Y. Wang, J. Gao, Theoretical Investigations on the Electronic and Optical Characteristics of Fused-ring Homopolymers: Comparison of Oligomer Method and PBC-DFT Method, Chem. Phys. Lett. 570 (2013) 153– 158. [34] H. Meier, U. Stalmach, H. Kolshorn, Effective Conjugation Length and UV/vis Spectra of Oligomers, Acta Polym. 48 (1997) 379–384. [35] N. Blouin, A. Michaud, M. Leclerc, A Low-Bandgap Poly(2,7-Carbazole) Derivative for Use in High-Performance Solar Cells, Adv. Mater. 19 (2007) 2295– 2300. [36] L. Zhang, K. Pei, M. Yu, Y. Huang, H. Zhao, M. Zeng, et al., Theoretical Investigations on Donor–Acceptor Conjugated Copolymers Based on Naphtho[1,2-c:5,6-c]bis[1,2,5]thiadiazole for Organic Solar Cell Applications, J. Phys. Chem. C. 116 (2012) 26154–26161. [37] H. Ullah, A.-H.A. Shah, S. Bilal, K. Ayub, Doping and Dedoping Processes of Polypyrrole: DFT Study with Hybrid Functionals, J. Phys. Chem. C. 118 (2014) 17819–17830. [38] L. Zhang, N.S. Colella, B.P. Cherniawski, S.C.B. Mannsfeld, A.L. Briseno, Oligothiophene Semiconductors: Synthesis, Characterization, and Applications for Organic Devices, ACS Appl. Mater. Interfaces. 6 (2014) 5327–5343. [39] M.E. Casida, M. Huix-Rotllant, Progress in Time-Dependent Density-Functional Theory, Annu. Rev. Phys. Chem. 63 (2012) 287–323. [40] N. Kuritz, T. Stein, R. Baer, L. Kronik, Charge-Transfer-Like π→π* Excitations in Time-Dependent Density Functional Theory: A Conundrum and Its Solution, J. Chem. Theory Comput. 7 (2011) 2408–2415.

23

[41] R.A. Street, S.A. Hawks, P.P. Khlyabich, G. Li, B.J. Schwartz, B.C. Thompson, et al., Electronic Structure and Transition Energies in Polymer–Fullerene Bulk Heterojunctions, J. Phys. Chem. C. 118 (2014) 21873–21883. [42] A. Dkhissi, Excitons in Organic Semiconductors, Synth. Met. 161 (2011) 1441– 1443. [43] B.-G. Kim, C.-G. Zhen, E.J. Jeong, J. Kieffer, J. Kim, Organic Dye Design Tools for Efficient Photocurrent Generation in Dye-Sensitized Solar Cells: Exciton Binding Energy and Electron Acceptors, Adv. Funct. Mater. 22 (2012) 1606–1612. [44] S. Radhakrishnan, R. Parthasarathi, V. Subramanian, N. Somanathan, Quantum Chemical Studies on Polythiophenes Containing Heterocyclic Substituents: Effect of Structure on the Band Gap, J. Chem. Phys. 123 (2005) 164905. [45] R.S. Bhatta, M. Tsige, Chain Length and Torsional Dependence of Exciton Binding Energies in P3HT and PTB7 Conjugated Polymers: A First-Principles Study, Polym. 55 (2014) 2667–2672. [46] T.P. Kaloni, G. Schreckenbach, M.S. Freund, Structural and Electronic Properties of Pristine and Doped Polythiophene: Periodic versus Molecular Calculations, J. Phys. Chem. C. 119 (2015) 3979–3989. [47] C. Deibel, D. Mack, J. Gorenflot, A. Schöll, S. Krause, F. Reinert, et al., Energetics of Excited States in the Conjugated Polymer poly(3-hexylthiophene), Phys. Rev. B. 81 (2010) 85202. [48] N. Banerji, E. Gagnon, P.-Y. Morgantini, S. Valouch, A.R. Mohebbi, J.-H. Seo, et al., Breaking Down the Problem: Optical Transitions, Electronic Structure, and Photoconductivity in Conjugated Polymer PCDTBT and in Its Separate Building Blocks, J. Phys. Chem. C. 116 (2012) 11456–11469. [49] C. Risko, M.D. McGehee, J.-L. Brédas, A quantum-chemical perspective into low optical-gap polymers for highly-efficient organic solar cells, Chem. Sci. 2 (2011) 1200–1218. [50] J.H. Seo, S. Cho, M. Leclerc, A.J. Heeger, Energy level alignments at poly[N-9′′hepta-decanyl-2,7-carbazole-alt-5,5-(4′,7′-di-2-thienyl-2′,1′,3′-benzothiadiazole)] on metal and polymer interfaces, Chem. Phys. Lett. 503 (2011) 101–104.

24

[51] B. Kim, H.R. Yeom, M.H. Yun, J.Y. Kim, C. Yang, A Selenophene Analogue of PCDTBT: Selective Fine-Tuning of LUMO to Lower of the Bandgap for Efficient Polymer Solar Cells, Macromolecules. 45 (2012) 8658–8664. [52] B. Ray, M. Alam, Random vs Regularized OPV: Limits of Performance Gain of Organic Bulk Heterojunction Solar Cells by Morphology Engineering, Sol. Energy Mater. Sol. Cells. 99 (2012) 204–212. [53] L. Zeng, C.W. Tang, S.H. Chen, Effects of Active Layer Thickness and Thermal Annealing on Polythiophene: Fullerene Bulk Heterojunction Photovoltaic Devices, Appl. Phys. Lett. 97 (2010) 053305. [54] S.S. Zade, N. Zamoshchik, M. Bendikov, From Short Conjugated Oligomers to Conjugated Polymers. Lessons from Studies on Long Conjugated Oligomers, Acc. Chem. Res. 44 (2011) 14–24. [55] X. Lu, H. Hlaing, D.S. Germack, J. Peet, W.H. Jo, D. Andrienko, et al., Bilayer Order in a Polycarbazole-conjugated Polymer, Nat Commun. 3 (2012) 795. [56] J.M. Toussaint, J.L. Brédas, Novel Low Bandgap Polymers: polydicyanomethylene-cyclopentadithiophene and -dipyrrole, Synth. Met. 61 (1993) 103–106. [57] F. Wu, L. Chen, H. Wang, Y. Chen, Experimental Investigation and Theoretical Calculation of Molecular Architectures on Carbazole for Photovoltaics, J. Phys. Chem. C. 117 (2013) 9581–9589. [58] T.M. Pappenfus, J.A. Schmidt, R.E. Koehn, J.D. Alia, PBC-DFT Applied to Donor−Acceptor Copolymers in Organic Solar Cells: Comparisons between Theoretical Methods and Experimental Data, Macromolecules. 44 (2011) 2354– 2357. [59] H. Sahu, A.N. Panda, Computational Study on the Effect of Substituents on the Structural and Electronic Properties of Thiophene–Pyrrole-Based π-Conjugated Oligomers, Macromolecules. 46 (2013) 844–855. [60] S.P. Rittmeyer, A. Groß, Structural and Electronic Properties of oligo- and polythiophenes Modified by Substituents, Beilstein J. Nanotechnol. 3 (2012) 909– 919.

25

[61] Y.C. Cheng, T.P. Kaloni, Z.Y. Zhu, and U. Schwingenschlogl, Oxidation of Graphene in Ozone Under Ultraviolet Light, Appl. Phys. Lett. 101 (2012) 073110 [62] N. Singh, T.P. Kaloni, U. Schwingenschlogl, A First-Principles Investigation of the Optical Spectra of Oxidized Graphene, Appl. Phys. Lett. 102 (2013) 023101 [63] T.P. Kaloni, M.U. Kahaly, R. Faccio, and U. Schwingenschlogl, Modelling Magnetism of C at O and B Monovacancies in Graphene, Carbon 64 (2012) 281287 [64] T.P. Kaloni, G. Schreckenbach, and M. Freund, Large Enhancement and Tunable Band Gap in Silicene by Small Organic Molecule Adsorption, J. Phys. Chem. C. 118 (2014) 23361-23367 [65] S.S. Zade, M. Bendikov, Twisting of Conjugated Oligomers and Polymers: Case Study of Oligo- and Polythiophene, Chem. Eur. J. 13 (2007) 3688

26