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Theoretical study on a corrole-azafullerene dyad: Electronic structure, spectra and photoinduced electron transfer
Chemical Physics Letters 610–611 (2014) 50–55
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Theoretical study on a corrole-azafullerene dyad: Electronic structure, spectra and photoinduced electron transfer Ioannis D. Petsalakis ∗ , Giannoula Theodorakopoulos Theoretical and Physical Chemistry Institute, The National Hellenic Research Foundation, 48 Vassileos Constantinou Avenue, Athens 116 35, Greece
a r t i c l e
i n f o
Article history: Received 28 May 2014 In final form 8 July 2014 Available online 15 July 2014
a b s t r a c t Density Functional Theory and Time-Dependent Density Functional Theory calculations have been carried out on a recently synthesized amino-corrole and a corrole–azafullerene dyad which exhibits photoinduced electron transfer (PET). Good agreement of the theoretical results with experiment is obtained regarding the absorption and emission spectra of the corrole, the absorption spectra of the corrole–azafullerene dyad and the transient anionic and cationic radicals of azafullerene and corrole respectively. Application of Mulliken’s theory for charge-transfer states yields the excitation energy of the charge-separated state of the dyad very close to the S1 excitation of amino-corrole, consistent with a PET process. © 2014 Elsevier B.V. All rights reserved.
1. Introduction In the quest for novel materials appropriate for organic photovoltaic devices, electron donor–acceptor conjugates involving azafullerene C59 N as the electron acceptor and different chromophores as donor have been investigated [1–6]. An example for such a conjugate is dyad 3 (cf. Figure 1), which was synthesized by reaction of azafullerene acid 1 with amino-corrole 2 (cf. Figure 1) [6]. Dyad 3 was considered to be a promising candidate for photoinduced electron transfer (PET) because corroles have lower oxidation potentials and more favorable optical properties than other chromophores, namely higher absorption intensity in the low energy region of the spectrum. Furthermore, C59 N derivatives are reported to be better electron acceptors than corresponding derivatives of C60 [7]. Indeed, the formation of a photoinduced charge-separated state, corrole+ -C59 N− , was indicated, in addition to the observed suppression of corrole emission in 3, by the presence of new peaks in the femptosecond transient absorption spectra of the systems 1–3 which were assigned to charged radical fragments, corrole+ and C59 N− [6]. In the present work, density functional theory (DFT) [8] and time dependent DFT (TDDFT) [9] calculations are presented on systems 1–3 of Figure 1, in an effort to obtain information on their electronic structure and spectra, which have not been calculated previously for the corrole 2 and the dyad 3. Of particular interest and the main
∗ Corresponding author. E-mail address: [email protected] (I.D. Petsalakis). http://dx.doi.org/10.1016/j.cplett.2014.07.019 0009-2614/© 2014 Elsevier B.V. All rights reserved.
scope of the present calculations is the determination of the chargetransfer state of 3, which might be involved in a PET process, in relation to the absorbing states of the corrole donor moiety. The absorption spectrum of the corrole 2 as reported in [6] is typical in the general features of those of porphyrins with a relatively low intensity band (but significantly higher intensity than the corresponding band in porphyrins) starting at 645 nm and a high intensity band at 422 nm. In porphyrins the so called Q-bands are found in the region 500–700 nm and the sharp and intense Soret band in the region around 400 nm [10,11], which are considered in a simplified picture to arise from transitions between the highest two occupied orbitals (HOMO and HOMO − 1) and the two lowest unoccupied (LUMO, LUMO + 1). Perhaps due to this multi-reference aspect of the excited states it is generally very challenging to calculate accurately the excitation energies of porphyrins and related systems [12,13]. Furthermore, DFT/MRCI calculations indicate the necessity to include excitations from lower-lying occupied orbitals, below HOMO − 1, for an accurate determination of the excited states of porphyrin-related systems [14]. Thus in the present work the aim is to determine and assign the main features observed experimentally, rather than the accurate determination of specific bands of the amino-corrole 2. It is well known that calculation of photoinduced charge transfer states of systems of the size such as the dyad 3 is rather difficult because configuration interaction methods cannot be applied. Provided that appropriate functionals are employed, e.g. CAM-B3LYP [15], MO62X [16], BNL [17,18] it may be possible to calculate by TDDFT the charge-transfer type of excited states at the ground state minimum geometry, corresponding to the absorption spectrum of
I.D. Petsalakis, G. Theodorakopoulos / Chemical Physics Letters 610–611 (2014) 50–55
51
of excitations. In systems such that of the present work where the geometry of the excited state is generally close to that of the ground state, it is sufficient to calculate only the orbital energies of the ground state of the separate D and A [20–23]. In systems where there is significant difference between the ground and excitedstate geometries, calculation on the orbital levels at the excited state geometries of D and A may be required [24]. Furthermore, the excitation energy of the CT state may be estimated without actually calculating it by TDDFT, by making use of Mulliken’s theory for charge transfer states [25] and in particular the simplified Eq. (1). ECT = IPD − EAA −
1 RD–A
(1)
In (1), IPD stands for the ionization potential of the donor (here amino-corrole), EAA stands for the electron affinity of the acceptor (azafullerene), RD–A for the distance between D and A and 1/RD–A is the Coulomb attraction in vacuum [17]. An investigation of the applicability of this approach toward estimations of the energy of CT states resulting from PET as well as ICT processes is in progress [26]. There are many different applications of Mulliken’s theory for charge-transfer states in the literature e.g. [27] as well as in combinations with other theories [28]. Eq. (1) has been recently employed as a benchmark of the behavior of the calculated energies of chargetransfer states at large R [29]. In the present work, the orbital level-diagrams as well as Eq. (1) will be employed, in addition to the TDDFT calculations, for theoretical information on the PET state of dyad 3 and comparison with the experimental results [6]. 2. Calculations and results
Figure 1. Optimized ground state geometries of the azzafulerene acceptor 1, the amino-corrole donor 2 and the amino-corrole azafullerene dyad 3 as well as of a fulleropyrrolidene-porphyrin dyad 4.
a donor–acceptor (or D–A) dyad. However, it is extremely difficult to calculate directly the PET process as the evolution of the absorbing state of the D–A dyad into the charge-separated one (and determine the emission properties) for technical reasons: geometry optimization of the particular excited state of the dyad, i.e. the one corresponding to the absorbing state of D, is very challenging because there exist several lower-lying excited states of A (here azafullerene) and the optimization cascades to these lower states. As noted above, even experimentally the photoinduced chargetransfer state is not observed directly in the spectrum, but its existence is inferred by suppression of the donor emission as well as the observation of transient spectra of the corresponding charged fragments [6]. Therefore it is difficult to establish its position in the spectrum and compare theoretical predictions to experimental data, something that is possible to do in intramolecular charge transfer (ICT) systems [19], where the CT state corresponds normally to the lowest energy absorption of the combined system. Information on the photoinduced charge transfer states may also be obtained by approaches not requiring TDDFT calculations on the full dyad system but by considerations of the separated donor and acceptor moieties: Orbital level diagrams of the separate donor (D) and acceptor (A) may be employed for information on the possibility of a charge-transfer state in a donor–acceptor (D–A) dyad as inferred by the existence of degeneracy of D→D* and D→A* types
The present calculations employed the DFT and TDDFT methods in conjunction with the B3LYP [30] and the M062X [16] functionals along with the 6-31G (d,p) and the 6-311G(d,p) basis sets available in Gaussian-09 [31]. The B3LYP functional has been employed for determination of geometries, ionization potentials, electron affinities as well as the absorption spectra of the separate donor and acceptor moieties and of the dyad 3. The M062X functional was also employed for the determination of the excited states and in particular of 3 where the B3LYP calculations may not be appropriate for the charge-transfer state [17]. Inclusion of toluene solvent employed the PCM [32] method. Such computational procedure has been found to be adequate for similar donor–acceptor complexes [22,33]. Geometry optimization of systems 1, 2 and 3 of Figure 1, in their ground electronic state has been carried out by DFT/B3LYP/6-31G (d,p) calculations. TDDFT/B3LYP and TDDFT/M062X calculations employing both the 6-31G (d,p) and the 6-311G(d,p) basis set were subsequently carried out at the ground state minimum energy geometry for all three systems (however the TDDFT/M062X/6311G(d,p) on 3 did not converge), relevant to their absorption spectra. In addition, for the amino-corrole 2, optimization of the geometry of its lowest excited singlet state was carried out, in order to obtain information on its emission spectra. Furthermore, TDDFT/B3LYP/6-31G (d,p) calculations have been carried out on the absorption spectra of the radical anion of 1 and the radical cation of 2, in order to compare these with the experimental femptosecond transient spectroscopy data [6]. The calculated spectra are shown in Figure 2. 2.1. Amino-corrole, system 2 The experimental absorption spectrum of the amino-corrole 2 shows a strong band at 422 nm and minor bands at lower energies starting at 645 nm, while the emission spectrum upon photoexcitation at 530 nm shows a maximum at 622 nm [6]. The theoretical absorption and emission spectra of amino-corrole are
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I.D. Petsalakis, G. Theodorakopoulos / Chemical Physics Letters 610–611 (2014) 50–55
Figure 2. Calculated UV–vis spectra, by both B3LYP and M062X, (a) absorption of the amino-corrole 2, (b) emission of the amino-corrole 2, (c) absorption of the dyad 3, (d) absorption, of azafullerene 1, (e) absorption of the azafullerene radical anion (B3LYP only), (f) absorption of the amino-corrole radical cation (B3LYP only).
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Figure 3. Orbital level diagram of (a) the azzafulerene acceptor 1, (b) the amino-corrole donor 2, and (c) the amino-corrole azafullerene dyad 3.
given in Figure 2a and b, where both the TDDFT/B3LYP and the TDDFT/M062X (and 6-31G(d,p) basis set) results are given. As shown, there is generally good agreement between the results of the two functionals and of the theoretical with the experimental spectra [6], both the absorption and the emission. As found previously the M062X results overestimate the excitation energies and the B3LYP are in closer agreement with experiment for states that are not of charge-transfer type [34]. For the particular corrole, in toluene, the B3LYP lowest energy transition is at 2.11 eV, the M062X at 2.23 eV with 1.96 eV the experimental. For the intense band at 422 nm, two very intense transitions calculated at 424 nm and 389 nm by B3LYP and at 390 and 366 nm by M062X (cf. spectra in Figure 2a) may be assigned. Calculations employing B3LYP/6-311 G(d,p) lead to slightly better agreement with experiment for the lowest energy transition, at 594 nm or 2.07 eV and the two intense peaks at 430 and 392 nm. For comparison, test calculations on the excited states of the amino-corrole 2 with WB97XD [35] and 6-311G(d,p) gave similar results as the B3LYP, with the lowest absorption at 586 nm (2.16 eV) and the two intense peaks at 390 nm and 366 nm. Optimization of the geometry of the lowest excited state of the amino-corrole 2 leads to a minimum energy structure for the excited state at 668 nm (by B3LYP) above the ground state, (627 nm obtained with M062X), in good agreement with the observed emission at 622 nm. The present B3LYP calculations, therefore, are shown to be reasonably accurate for the electronic spectra of the amino-corrole compound 2. It might be also noted that all functionals determine the lowestenergy transition in amino corrole around 2.16–2.23 eV to have f-value of 0.35–0.37, whereas the analogous transition in a porphyrin [22] has been calculated at 2.13 eV with f-value of 0.04, showing that indeed the corrole has higher intensity absorption in the low-energy region, in agreement with experiment [6]. The experimental absorption spectrum of compound 3 in toluene is basically a superposition of the UV–visual spectra of the reference materials 2 and the ethyl ester of 1 [6]. The absorption spectra of 3 obtained by TDDFT calculations are given in Figure 2c and for system 1 in Figure 2d. As shown, very low intensity absorption is obtained for the azafullerene compound 1 (cf. Figure 2d) and the absorption of the dyad 3 in the long wavelength
region is basically the same as the absorption spectrum of the amino-corrole chromophore (cf. Figure 2c and a). The calculated absorption spectra of the anionic radical of azafullerene (Figure 2e) and the cationic radical of amino-corrole (Figure 2f) show maxima in the region 800–1000 nm and from 400 to 100 nm, respectively, with the observed new sets of transient absorptions reported at 470, 635, 790 and 1040 nm, with the latter being assigned to the radical anion of azafullerene [6]. The present calculations show that basically all the observed bands above may be attributed to the radical cation of the corrole since the intensity of the spectra of the radical anion of azafullerene calculated in the region 800–1100 nm, is lower than in the radical cation of the corrole by an order of magnitude cf. Figure 2e and f. As noted in Section 1, the occurrence of PET in the dyad 3 has been manifested by the suppression of the corrole emission and by the observation of new transient absorption maxima [6]. Direct calculation of the minimum energy structure of the absorbing state, relevant to emission of corrole in 3, is not practical since the absorbing state of the chromophore is not the lowest excited state of the dyad and it is not possible to carry out geometry optimization of this state, see above, which would be required in order to determine the possible evolution of the absorbing state into the charge-separated one cf. [20]. Simple rules along with orbital energy diagrams of the separate donor and acceptor moieties have been employed in different PET systems and offer rationalization for the occurrence of PET in those systems. For the donor and acceptor systems of the present work a diagram of the orbital levels of the separate acceptor (1) and donor (2) moieties along with those of the dyad (3) are given in Figure 3a–c, respectively. Indicated in Figure 3b are the excitations contributing to the lowest energy absorption of corrole, showing three additional excitations as well as the more important HOMO → LUMO. As shown in Figure 3, there is near degeneracy between the LUMO + 5 unoccupied orbital of the azafullerene compound (acceptor) and the LUMO + 1 orbital of the amino-corrole donor and the possibility exists of a contribution to the excited state of the dyad of a charge-transfer type of excitation, HOMOdonor → LUMO + 5acceptor . Considering the orbital levels of the dyad, the occupied orbitals belonging to the amino-corrole moiety are HOMO and HOMO − 2,
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Figure 4. A schematic of the calculation of the excitation energy of the chargetransfer state of 3, using the IP of 2, the EA of 1, RD–A = 14 A˚ and application of Eq. (1).
while of the unoccupied the orbital LUMO + 3. Thus the excitation HOMO − 2 → LUMO, LUMO + 1, LUMO + 2 in the dyad is of CT type, cf. Figure 3. However, given the multi-excitation character of the donor excitation the orbital-level diagram is not as effective in predicting the CT process in the present situation as it has been in other cases [20–24]. Next, the excitation energy of the CT state is considered: The TDDFT calculation of the excited states of the corrole-azafullerene dyad, at the ground state geometry employing the M062X functional for the better description of the CT states, obtains as fourth excited state to be the absorbing state of corrole at 2.26 eV (f-value 0.33) in toluene solvent. A charge-transfer state is calculated at 2.42 eV (seventh excited state), which might interact with the absorbing state at different geometries resulting from geometry relaxation of the absorbing state. As noted in the introduction a good estimate of the energy of the CT state may be obtained by application of Mulliken’s formula, cf. Eq. (1) [25]. Here we will apply such analysis to the azafullerene-corrole dyad, and employ for RD–A the distance from the center of C59 N and the corrole in the optimum ground-state geometry, as shown in Figure 1 for structure 3. An alternative approach would involve calculating the distance from the center of the MO of the donor to that of the acceptor involved in the charge-transfer state. In this case, cf. MO pictures in Figure 3c, the two approaches practically coincide. Furthermore, an error of 1 A˚ for the present case would lead to an error of 0.05 eV in the estimated excitation energy. A schematic diagram, showing the quantities required for application of Eq. (1) to the amino-corrole azafullerene system is given in Figure 4. The particular values of IP for amino-corrole and EA for the azafullerene compound 1, as well as the ground state geometry (and RDA ) have been determined by B3LYP/6-31G(d,p) calculations on isolated systems. As shown in Figure 4, the resulting energy of the CT state is found at 2.16 eV, coinciding with the S1 excitation energy of the donor amino-corrole moiety. The excitation energy of corrole within the azafullerene-corrole dyad calculated by B3LYP/6-31G(d,p) is 2.21 eV (f-value 0.19) and in toluene 2.17 (f-value 0.33). Thus Eq. (1) leads to the reasonable result that the CT state resulting from PET following absorption of light by the corrole, lies at energy close to that of the absorbing state. The actual numerics will depend on the basis set and the particular functional and method employed for the determination of the IP and EA quantities. For example if we use IPD and EAA values of 6.11 eV and 2.64 eV, respectively, which were calculated for the separate donor and acceptor by B3LYP/6-311G(d,p), and RD–A as above, the resulting estimated excitation energy of the CT state is 2.44 eV. Similarly,
employing MO62X/6-311G(d,p) IPD and EAA results in estimates for the energy of CT at 2.66 eV, with nearly identical results obtained using CAM-B3LYP/6-311G(d,p) quantities. It might be noted that the determination of the IP and EA can be carried out by the best method possible for the separate donor and acceptor moieties, while experimental quantities might also be used and similarly the S1 excitation energy of the donor. Similarly, DFT calculations are adequate for the geometry of the ground state required for the RD–A quantity, and in this manner it is not necessary to calculate the CT by TDDFT on the whole donor–acceptor dyad, which might be impractical, considering the requirements for large basis sets and the difficulties of TDDFT for charge-separated states. Eq. (1) will lead to reasonable estimates of the charge-transfer state for isolated donor–acceptor complexes. For comparison, calculation of the CT state of 3 by TDDFT/M062X/6-31G(d,p) isolated and in a series of solvents of different dielectric constant offered in Gaussian-09 resulted in differences in the calculated excitation energy of about 0.3 eV. For further comparison, an analogous application of Eq. (1) to a fulleropyrrolidine-porphyrin dyad (see 4 in Figure 1) previously calculated [22,33], using the distance RD–A determined from the ˚ the EA calculated ground state geometry of the dyad of about 21 A, for fulleropyrrolidine (2.40 eV) and the IP of porphyrin (6.58) by B3LYP, yields the estimated CT energy at 3.5 eV. Thus the above analysis shows that, for the particular fullerene-porphyrin dyad 4, the CT state corresponds to the higher energy absorption of porphyrin calculated (B3LYP/6-31G(d,p) at 3.10 and 3.17 eV, and not the lowest energy (and low intensity) absorption at 2.15, whereas in 3 the CT state is estimated at the energy of the lowest excited state of the amino-corrole chromophore. The above two examples show that application of Eq. (1) may lead to reasonable estimates of the excitation energy of chargetransfer states, for systems with well separated donor and acceptor, without any claims to greater accuracy that may be obtained by careful TDDFT, when such calculations are practical.
3. Conclusions Theoretical TDDFT calculations on a corrole-azafullerene dyad obtain absorption and emission spectra of the amino corrole and absorption spectra of the dyad in agreement with experimental UV–vis spectra. The existence of a charge-transfer state at excitation energy near the lowest absorbing energy of the corrole is supported by TDDFT calculations and by application of Mulliken’s theory, utilizing IP of the donor, EA of the acceptor and the distance between donor and acceptor. Thus the present calculations are in agreement with experiment on the existence of a charge-separated state of the corrole-azafullerene dyad resulting from a PET process, following excitation of the donor to the lowest excited state. Finally, it is proposed that application of Mulliken’s theory leads to reasonable estimates of the excitation energy of the CT state of a donor–acceptor dyad, using either experimental quantities or theoretical calculations on separate donor and acceptor moieties and only a ground state DFT calculation on the full donor–acceptor dyad. Application of Mulliken’s theory is of particular value when TDDFT or other accurate calculations are not practical.
Acknowledgements The authors are grateful to Dr. N. Tagmatarchis and Dr. G. Rotas of TPCI/NHRF, Athens and to Prof. R. Baer of the Hebrew University in Jerusalem for helpful discussions. Financial support of this work by the General Secretariat for Research and Technology, Greece (project Polynano-Kripis 447963) is gratefully acknowledged.
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Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Theoretical study on a corrole-azafullerene dyad: Electronic structure, spectra and photoinduced electron transfer Ioannis D. Petsalakis ∗ , Giannoula Theodorakopoulos Theoretical and Physical Chemistry Institute, The National Hellenic Research Foundation, 48 Vassileos Constantinou Avenue, Athens 116 35, Greece
a r t i c l e
i n f o
Article history: Received 28 May 2014 In final form 8 July 2014 Available online 15 July 2014
a b s t r a c t Density Functional Theory and Time-Dependent Density Functional Theory calculations have been carried out on a recently synthesized amino-corrole and a corrole–azafullerene dyad which exhibits photoinduced electron transfer (PET). Good agreement of the theoretical results with experiment is obtained regarding the absorption and emission spectra of the corrole, the absorption spectra of the corrole–azafullerene dyad and the transient anionic and cationic radicals of azafullerene and corrole respectively. Application of Mulliken’s theory for charge-transfer states yields the excitation energy of the charge-separated state of the dyad very close to the S1 excitation of amino-corrole, consistent with a PET process. © 2014 Elsevier B.V. All rights reserved.
1. Introduction In the quest for novel materials appropriate for organic photovoltaic devices, electron donor–acceptor conjugates involving azafullerene C59 N as the electron acceptor and different chromophores as donor have been investigated [1–6]. An example for such a conjugate is dyad 3 (cf. Figure 1), which was synthesized by reaction of azafullerene acid 1 with amino-corrole 2 (cf. Figure 1) [6]. Dyad 3 was considered to be a promising candidate for photoinduced electron transfer (PET) because corroles have lower oxidation potentials and more favorable optical properties than other chromophores, namely higher absorption intensity in the low energy region of the spectrum. Furthermore, C59 N derivatives are reported to be better electron acceptors than corresponding derivatives of C60 [7]. Indeed, the formation of a photoinduced charge-separated state, corrole+ -C59 N− , was indicated, in addition to the observed suppression of corrole emission in 3, by the presence of new peaks in the femptosecond transient absorption spectra of the systems 1–3 which were assigned to charged radical fragments, corrole+ and C59 N− [6]. In the present work, density functional theory (DFT) [8] and time dependent DFT (TDDFT) [9] calculations are presented on systems 1–3 of Figure 1, in an effort to obtain information on their electronic structure and spectra, which have not been calculated previously for the corrole 2 and the dyad 3. Of particular interest and the main
∗ Corresponding author. E-mail address: [email protected] (I.D. Petsalakis). http://dx.doi.org/10.1016/j.cplett.2014.07.019 0009-2614/© 2014 Elsevier B.V. All rights reserved.
scope of the present calculations is the determination of the chargetransfer state of 3, which might be involved in a PET process, in relation to the absorbing states of the corrole donor moiety. The absorption spectrum of the corrole 2 as reported in [6] is typical in the general features of those of porphyrins with a relatively low intensity band (but significantly higher intensity than the corresponding band in porphyrins) starting at 645 nm and a high intensity band at 422 nm. In porphyrins the so called Q-bands are found in the region 500–700 nm and the sharp and intense Soret band in the region around 400 nm [10,11], which are considered in a simplified picture to arise from transitions between the highest two occupied orbitals (HOMO and HOMO − 1) and the two lowest unoccupied (LUMO, LUMO + 1). Perhaps due to this multi-reference aspect of the excited states it is generally very challenging to calculate accurately the excitation energies of porphyrins and related systems [12,13]. Furthermore, DFT/MRCI calculations indicate the necessity to include excitations from lower-lying occupied orbitals, below HOMO − 1, for an accurate determination of the excited states of porphyrin-related systems [14]. Thus in the present work the aim is to determine and assign the main features observed experimentally, rather than the accurate determination of specific bands of the amino-corrole 2. It is well known that calculation of photoinduced charge transfer states of systems of the size such as the dyad 3 is rather difficult because configuration interaction methods cannot be applied. Provided that appropriate functionals are employed, e.g. CAM-B3LYP [15], MO62X [16], BNL [17,18] it may be possible to calculate by TDDFT the charge-transfer type of excited states at the ground state minimum geometry, corresponding to the absorption spectrum of
I.D. Petsalakis, G. Theodorakopoulos / Chemical Physics Letters 610–611 (2014) 50–55
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of excitations. In systems such that of the present work where the geometry of the excited state is generally close to that of the ground state, it is sufficient to calculate only the orbital energies of the ground state of the separate D and A [20–23]. In systems where there is significant difference between the ground and excitedstate geometries, calculation on the orbital levels at the excited state geometries of D and A may be required [24]. Furthermore, the excitation energy of the CT state may be estimated without actually calculating it by TDDFT, by making use of Mulliken’s theory for charge transfer states [25] and in particular the simplified Eq. (1). ECT = IPD − EAA −
1 RD–A
(1)
In (1), IPD stands for the ionization potential of the donor (here amino-corrole), EAA stands for the electron affinity of the acceptor (azafullerene), RD–A for the distance between D and A and 1/RD–A is the Coulomb attraction in vacuum [17]. An investigation of the applicability of this approach toward estimations of the energy of CT states resulting from PET as well as ICT processes is in progress [26]. There are many different applications of Mulliken’s theory for charge-transfer states in the literature e.g. [27] as well as in combinations with other theories [28]. Eq. (1) has been recently employed as a benchmark of the behavior of the calculated energies of chargetransfer states at large R [29]. In the present work, the orbital level-diagrams as well as Eq. (1) will be employed, in addition to the TDDFT calculations, for theoretical information on the PET state of dyad 3 and comparison with the experimental results [6]. 2. Calculations and results
Figure 1. Optimized ground state geometries of the azzafulerene acceptor 1, the amino-corrole donor 2 and the amino-corrole azafullerene dyad 3 as well as of a fulleropyrrolidene-porphyrin dyad 4.
a donor–acceptor (or D–A) dyad. However, it is extremely difficult to calculate directly the PET process as the evolution of the absorbing state of the D–A dyad into the charge-separated one (and determine the emission properties) for technical reasons: geometry optimization of the particular excited state of the dyad, i.e. the one corresponding to the absorbing state of D, is very challenging because there exist several lower-lying excited states of A (here azafullerene) and the optimization cascades to these lower states. As noted above, even experimentally the photoinduced chargetransfer state is not observed directly in the spectrum, but its existence is inferred by suppression of the donor emission as well as the observation of transient spectra of the corresponding charged fragments [6]. Therefore it is difficult to establish its position in the spectrum and compare theoretical predictions to experimental data, something that is possible to do in intramolecular charge transfer (ICT) systems [19], where the CT state corresponds normally to the lowest energy absorption of the combined system. Information on the photoinduced charge transfer states may also be obtained by approaches not requiring TDDFT calculations on the full dyad system but by considerations of the separated donor and acceptor moieties: Orbital level diagrams of the separate donor (D) and acceptor (A) may be employed for information on the possibility of a charge-transfer state in a donor–acceptor (D–A) dyad as inferred by the existence of degeneracy of D→D* and D→A* types
The present calculations employed the DFT and TDDFT methods in conjunction with the B3LYP [30] and the M062X [16] functionals along with the 6-31G (d,p) and the 6-311G(d,p) basis sets available in Gaussian-09 [31]. The B3LYP functional has been employed for determination of geometries, ionization potentials, electron affinities as well as the absorption spectra of the separate donor and acceptor moieties and of the dyad 3. The M062X functional was also employed for the determination of the excited states and in particular of 3 where the B3LYP calculations may not be appropriate for the charge-transfer state [17]. Inclusion of toluene solvent employed the PCM [32] method. Such computational procedure has been found to be adequate for similar donor–acceptor complexes [22,33]. Geometry optimization of systems 1, 2 and 3 of Figure 1, in their ground electronic state has been carried out by DFT/B3LYP/6-31G (d,p) calculations. TDDFT/B3LYP and TDDFT/M062X calculations employing both the 6-31G (d,p) and the 6-311G(d,p) basis set were subsequently carried out at the ground state minimum energy geometry for all three systems (however the TDDFT/M062X/6311G(d,p) on 3 did not converge), relevant to their absorption spectra. In addition, for the amino-corrole 2, optimization of the geometry of its lowest excited singlet state was carried out, in order to obtain information on its emission spectra. Furthermore, TDDFT/B3LYP/6-31G (d,p) calculations have been carried out on the absorption spectra of the radical anion of 1 and the radical cation of 2, in order to compare these with the experimental femptosecond transient spectroscopy data [6]. The calculated spectra are shown in Figure 2. 2.1. Amino-corrole, system 2 The experimental absorption spectrum of the amino-corrole 2 shows a strong band at 422 nm and minor bands at lower energies starting at 645 nm, while the emission spectrum upon photoexcitation at 530 nm shows a maximum at 622 nm [6]. The theoretical absorption and emission spectra of amino-corrole are
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Figure 2. Calculated UV–vis spectra, by both B3LYP and M062X, (a) absorption of the amino-corrole 2, (b) emission of the amino-corrole 2, (c) absorption of the dyad 3, (d) absorption, of azafullerene 1, (e) absorption of the azafullerene radical anion (B3LYP only), (f) absorption of the amino-corrole radical cation (B3LYP only).
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Figure 3. Orbital level diagram of (a) the azzafulerene acceptor 1, (b) the amino-corrole donor 2, and (c) the amino-corrole azafullerene dyad 3.
given in Figure 2a and b, where both the TDDFT/B3LYP and the TDDFT/M062X (and 6-31G(d,p) basis set) results are given. As shown, there is generally good agreement between the results of the two functionals and of the theoretical with the experimental spectra [6], both the absorption and the emission. As found previously the M062X results overestimate the excitation energies and the B3LYP are in closer agreement with experiment for states that are not of charge-transfer type [34]. For the particular corrole, in toluene, the B3LYP lowest energy transition is at 2.11 eV, the M062X at 2.23 eV with 1.96 eV the experimental. For the intense band at 422 nm, two very intense transitions calculated at 424 nm and 389 nm by B3LYP and at 390 and 366 nm by M062X (cf. spectra in Figure 2a) may be assigned. Calculations employing B3LYP/6-311 G(d,p) lead to slightly better agreement with experiment for the lowest energy transition, at 594 nm or 2.07 eV and the two intense peaks at 430 and 392 nm. For comparison, test calculations on the excited states of the amino-corrole 2 with WB97XD [35] and 6-311G(d,p) gave similar results as the B3LYP, with the lowest absorption at 586 nm (2.16 eV) and the two intense peaks at 390 nm and 366 nm. Optimization of the geometry of the lowest excited state of the amino-corrole 2 leads to a minimum energy structure for the excited state at 668 nm (by B3LYP) above the ground state, (627 nm obtained with M062X), in good agreement with the observed emission at 622 nm. The present B3LYP calculations, therefore, are shown to be reasonably accurate for the electronic spectra of the amino-corrole compound 2. It might be also noted that all functionals determine the lowestenergy transition in amino corrole around 2.16–2.23 eV to have f-value of 0.35–0.37, whereas the analogous transition in a porphyrin [22] has been calculated at 2.13 eV with f-value of 0.04, showing that indeed the corrole has higher intensity absorption in the low-energy region, in agreement with experiment [6]. The experimental absorption spectrum of compound 3 in toluene is basically a superposition of the UV–visual spectra of the reference materials 2 and the ethyl ester of 1 [6]. The absorption spectra of 3 obtained by TDDFT calculations are given in Figure 2c and for system 1 in Figure 2d. As shown, very low intensity absorption is obtained for the azafullerene compound 1 (cf. Figure 2d) and the absorption of the dyad 3 in the long wavelength
region is basically the same as the absorption spectrum of the amino-corrole chromophore (cf. Figure 2c and a). The calculated absorption spectra of the anionic radical of azafullerene (Figure 2e) and the cationic radical of amino-corrole (Figure 2f) show maxima in the region 800–1000 nm and from 400 to 100 nm, respectively, with the observed new sets of transient absorptions reported at 470, 635, 790 and 1040 nm, with the latter being assigned to the radical anion of azafullerene [6]. The present calculations show that basically all the observed bands above may be attributed to the radical cation of the corrole since the intensity of the spectra of the radical anion of azafullerene calculated in the region 800–1100 nm, is lower than in the radical cation of the corrole by an order of magnitude cf. Figure 2e and f. As noted in Section 1, the occurrence of PET in the dyad 3 has been manifested by the suppression of the corrole emission and by the observation of new transient absorption maxima [6]. Direct calculation of the minimum energy structure of the absorbing state, relevant to emission of corrole in 3, is not practical since the absorbing state of the chromophore is not the lowest excited state of the dyad and it is not possible to carry out geometry optimization of this state, see above, which would be required in order to determine the possible evolution of the absorbing state into the charge-separated one cf. [20]. Simple rules along with orbital energy diagrams of the separate donor and acceptor moieties have been employed in different PET systems and offer rationalization for the occurrence of PET in those systems. For the donor and acceptor systems of the present work a diagram of the orbital levels of the separate acceptor (1) and donor (2) moieties along with those of the dyad (3) are given in Figure 3a–c, respectively. Indicated in Figure 3b are the excitations contributing to the lowest energy absorption of corrole, showing three additional excitations as well as the more important HOMO → LUMO. As shown in Figure 3, there is near degeneracy between the LUMO + 5 unoccupied orbital of the azafullerene compound (acceptor) and the LUMO + 1 orbital of the amino-corrole donor and the possibility exists of a contribution to the excited state of the dyad of a charge-transfer type of excitation, HOMOdonor → LUMO + 5acceptor . Considering the orbital levels of the dyad, the occupied orbitals belonging to the amino-corrole moiety are HOMO and HOMO − 2,
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Figure 4. A schematic of the calculation of the excitation energy of the chargetransfer state of 3, using the IP of 2, the EA of 1, RD–A = 14 A˚ and application of Eq. (1).
while of the unoccupied the orbital LUMO + 3. Thus the excitation HOMO − 2 → LUMO, LUMO + 1, LUMO + 2 in the dyad is of CT type, cf. Figure 3. However, given the multi-excitation character of the donor excitation the orbital-level diagram is not as effective in predicting the CT process in the present situation as it has been in other cases [20–24]. Next, the excitation energy of the CT state is considered: The TDDFT calculation of the excited states of the corrole-azafullerene dyad, at the ground state geometry employing the M062X functional for the better description of the CT states, obtains as fourth excited state to be the absorbing state of corrole at 2.26 eV (f-value 0.33) in toluene solvent. A charge-transfer state is calculated at 2.42 eV (seventh excited state), which might interact with the absorbing state at different geometries resulting from geometry relaxation of the absorbing state. As noted in the introduction a good estimate of the energy of the CT state may be obtained by application of Mulliken’s formula, cf. Eq. (1) [25]. Here we will apply such analysis to the azafullerene-corrole dyad, and employ for RD–A the distance from the center of C59 N and the corrole in the optimum ground-state geometry, as shown in Figure 1 for structure 3. An alternative approach would involve calculating the distance from the center of the MO of the donor to that of the acceptor involved in the charge-transfer state. In this case, cf. MO pictures in Figure 3c, the two approaches practically coincide. Furthermore, an error of 1 A˚ for the present case would lead to an error of 0.05 eV in the estimated excitation energy. A schematic diagram, showing the quantities required for application of Eq. (1) to the amino-corrole azafullerene system is given in Figure 4. The particular values of IP for amino-corrole and EA for the azafullerene compound 1, as well as the ground state geometry (and RDA ) have been determined by B3LYP/6-31G(d,p) calculations on isolated systems. As shown in Figure 4, the resulting energy of the CT state is found at 2.16 eV, coinciding with the S1 excitation energy of the donor amino-corrole moiety. The excitation energy of corrole within the azafullerene-corrole dyad calculated by B3LYP/6-31G(d,p) is 2.21 eV (f-value 0.19) and in toluene 2.17 (f-value 0.33). Thus Eq. (1) leads to the reasonable result that the CT state resulting from PET following absorption of light by the corrole, lies at energy close to that of the absorbing state. The actual numerics will depend on the basis set and the particular functional and method employed for the determination of the IP and EA quantities. For example if we use IPD and EAA values of 6.11 eV and 2.64 eV, respectively, which were calculated for the separate donor and acceptor by B3LYP/6-311G(d,p), and RD–A as above, the resulting estimated excitation energy of the CT state is 2.44 eV. Similarly,
employing MO62X/6-311G(d,p) IPD and EAA results in estimates for the energy of CT at 2.66 eV, with nearly identical results obtained using CAM-B3LYP/6-311G(d,p) quantities. It might be noted that the determination of the IP and EA can be carried out by the best method possible for the separate donor and acceptor moieties, while experimental quantities might also be used and similarly the S1 excitation energy of the donor. Similarly, DFT calculations are adequate for the geometry of the ground state required for the RD–A quantity, and in this manner it is not necessary to calculate the CT by TDDFT on the whole donor–acceptor dyad, which might be impractical, considering the requirements for large basis sets and the difficulties of TDDFT for charge-separated states. Eq. (1) will lead to reasonable estimates of the charge-transfer state for isolated donor–acceptor complexes. For comparison, calculation of the CT state of 3 by TDDFT/M062X/6-31G(d,p) isolated and in a series of solvents of different dielectric constant offered in Gaussian-09 resulted in differences in the calculated excitation energy of about 0.3 eV. For further comparison, an analogous application of Eq. (1) to a fulleropyrrolidine-porphyrin dyad (see 4 in Figure 1) previously calculated [22,33], using the distance RD–A determined from the ˚ the EA calculated ground state geometry of the dyad of about 21 A, for fulleropyrrolidine (2.40 eV) and the IP of porphyrin (6.58) by B3LYP, yields the estimated CT energy at 3.5 eV. Thus the above analysis shows that, for the particular fullerene-porphyrin dyad 4, the CT state corresponds to the higher energy absorption of porphyrin calculated (B3LYP/6-31G(d,p) at 3.10 and 3.17 eV, and not the lowest energy (and low intensity) absorption at 2.15, whereas in 3 the CT state is estimated at the energy of the lowest excited state of the amino-corrole chromophore. The above two examples show that application of Eq. (1) may lead to reasonable estimates of the excitation energy of chargetransfer states, for systems with well separated donor and acceptor, without any claims to greater accuracy that may be obtained by careful TDDFT, when such calculations are practical.
3. Conclusions Theoretical TDDFT calculations on a corrole-azafullerene dyad obtain absorption and emission spectra of the amino corrole and absorption spectra of the dyad in agreement with experimental UV–vis spectra. The existence of a charge-transfer state at excitation energy near the lowest absorbing energy of the corrole is supported by TDDFT calculations and by application of Mulliken’s theory, utilizing IP of the donor, EA of the acceptor and the distance between donor and acceptor. Thus the present calculations are in agreement with experiment on the existence of a charge-separated state of the corrole-azafullerene dyad resulting from a PET process, following excitation of the donor to the lowest excited state. Finally, it is proposed that application of Mulliken’s theory leads to reasonable estimates of the excitation energy of the CT state of a donor–acceptor dyad, using either experimental quantities or theoretical calculations on separate donor and acceptor moieties and only a ground state DFT calculation on the full donor–acceptor dyad. Application of Mulliken’s theory is of particular value when TDDFT or other accurate calculations are not practical.
Acknowledgements The authors are grateful to Dr. N. Tagmatarchis and Dr. G. Rotas of TPCI/NHRF, Athens and to Prof. R. Baer of the Hebrew University in Jerusalem for helpful discussions. Financial support of this work by the General Secretariat for Research and Technology, Greece (project Polynano-Kripis 447963) is gratefully acknowledged.
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