Article pubs.acs.org/JPCA
Theoretical Characterization of Absorption and Emission Spectra of an Asymmetric Porphycene Zhenggang Lan,*,† Santi Nonell,‡ and Mario Barbatti*,§ †
Qingdao Institute of Bioenergy and Bioprocess Technology, Chinese Academy of Sciences, Qingdao, 266101, People’s Republic of China ‡ Grup d’Enginyeria Molecular, Institut Quimic de Sarria, Universitat Ramon Llull, Via Augusta 390, E-08017, Barcelona, Spain § Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim, Germany S Supporting Information *
ABSTRACT: The electronic ground and excited states of an asymmetric porphycene, 9-amino-2,7,12,17-tetraphenylporphycene (9-ATPPo), are investigated by electronic structure calculations. Different tautomers are considered to address their contributions to the photophysics of 9-ATPPo. Tautomerization pathways on the ground and excited states are constructed between different isomers. It is found that two trans tautomers are mainly responsible for the absorption and emission spectra of 9-ATPPo. These calculations provide a molecular mechanism to explain recent experimental observations, which show a highly complex Q-band structure in the absorption spectrum and pronounced dual fluorescence in the emission spectrum. Furthermore, the current work shows that tautomerization takes place under the assistance of cavity deformations and that a nonradiative process occurs through weak interstate nonadiabatic couplings near the S1 minimum rather than strong ones near conical intersections.
1. INTRODUCTION Porphyrins and their derivatives play important roles in many biological and chemical systems, such as photosynthetic complexes,1,2 dye-sensitized solar cells,3 red blood cells,4 and phototherapy drugs.5 As the first series of constitutional isomers of porphyrins, porphycenes were synthesized by Vogel et al. in 1986.6 Since then, they have also been widely investigated to understand their structure−functionality relationships and to explore their potential as secondgeneration agents for photodynamic therapies.7−18 In both base-free porphyrins and base-free porphycenes, four nitrogen atoms form an inner cavity that allows migration of two inner hydrogen atoms. As a result, different tautomers can be formed by attaching hydrogen atoms at different nitrogen sites. The conversion between these tautomers, constrained within the well-defined inner cavity, is isolated from the environment, making porphyrins and porphycenes a great prototype for studying many important chemical processes associated with tautomeric effects, such as proton transfer, vibronic coupling, cooperativity, tunneling, and intersystem crossing.12,13,17−19 Such tautomerization can take place in the electronic ground state, which has been proven by nuclear magnetic resonance (NMR) experiments.12 Alternatively, it can also be initialized by light absorption, which leads to photoinduced intramolecular proton transfers in molecular excited states.20 Although extensive studies on base-free porphycenes have been performed, most of them have focused on the symmetric structures with a limited number of tautomers. The © 2012 American Chemical Society
introduction of functional groups attached to porphycene ring may result in asymmetric structures, lifting the tautomeric degeneracy.18,20 Recently, Duran-Frigola and co-workers20 have investigated the photophysics of 9-amino-2,7,12,17-tetraphenylporphycene (9-ATPPo), in which the NH2 group is attached at the C9 site (meso) of the porphycene ring. The asymmetry results in six tautomers, which are illustrated in Figure 1. The absorption spectrum of 9-ATPPo shows a low-energy Q-band with complex structure and a high-energy Soret band with pronounced peak splitting.20 Furthermore, dual fluorescence bands have been observed, which are separated clearly by a significant energy gap of ∼84 nm.20 The intensity of dual fluorescence is dependent on excitation wavelength and experimental temperatures, and there is evidence suggesting that nonradiative decay processes are in competition with radiative processes. These features have been related to the existence of different tautomers and the conversion processes between them.20 Theoretical calculations can help in understanding the tautomerization of 9-ATPPo and in assigning its absorption and emission spectra at the molecular level. With this purpose, we have employed quantum-chemical methods to investigate the ground and excited states of 9-ATPPo. Ground- and excited-state stationary structures along with tautomerization pathways have been characterized. Moreover, absorption and Received: January 27, 2012 Revised: March 6, 2012 Published: March 6, 2012 3366
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Figure 1. The six tautomers of 9-ATPPo.
expense of much higher computational costs and convergence problems, we opted for employing conventional PCM in the remaining calculations. The reaction pathway between different tautomers in the ground state and the excited state was constructed by constrained optimization along proton-transfer coordinates. Two minima of the ground (or excited) state were set as the starting and ending points of the reaction pathway. Then, linear interpolation between these two geometries was performed to obtain starting geometries along the pathway. For each geometry, the proton-transfer coordinates were fixed and all other coordinates were optimized to get the final tautomerization pathway. Complementary calculations were performed with the multireference configuration interaction (MRCI) based on the semiempirical OM2 (Orthogonalization Model 2) Hamiltonian.30−32 The MRCI expansion was built from three reference configurations (close-shell ground-state configuration, single and double HOMO−LUMO excitations from the closedshell configuration). Several active spaces were employed to check consistence, combining five to six occupied orbitals and four to five unoccupied orbitals. The CI treatment included all
emission spectra have also been simulated. On the basis of these calculations, we discuss molecular mechanisms lying behind the experimentally observed complexity of the 9-ATPPo spectra.
2. COMPUTATIONAL DETAILS Minimum-energy geometries of ground and excited states were optimized at the density functional theory (DFT) and timedependent density functional theory (TDDFT)21 levels. The long-range corrected CAM-B3LYP functional22 was employed, since it provides a good description of both localized and delocalized excitations.23 The 6-31G(d,p) basis set was used for optimization.24−26 At optimized geometries, single-point calculations with TZVP,27 6-31G++(df,p), and 6-31G+(df,p) were also performed to check the influence of basis sets. The effect of solvation by toluene was investigated with the polarizable continuum model (PCM).28 To obtain a statespecific description of solvent effects, the self-consistent statespecific (PCM-SS) procedure described in ref 29 was applied to the vertical excitations of trans-1 and trans-2. Because little difference in comparison to conventional PCM was observed in the results (see Table S1 in the Supporting Information) at the 3367
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single and double excitations within the selected active space from the above three references. The simulation of the absorption spectrum of 9-ATPPo was based on the nuclear-ensemble method described in ref 33. In this method, ground-state geometries are sampled with a harmonic-oscillator Wigner distribution function.34 Then, at each point Rk in the ensemble, oscillator strengths f 0l and transition energies ΔE0l between the ground state (0) and all final states (l) of interest are computed. These quantities are employed to compute the absorption cross section, given by33
At S1 minima of the isomers, radiative lifetimes (τ) were computed as36 2πε mc 3 τ = 2 02 e ω01 |f10 |
where ω01 is the angular frequency for the S1−S0 vertical transition at the S1 minimum. TDDFT electronic structure calculations were performed with Gaussian 09.37 Absorption cross sections were simulated with the Newton-X38,39 program interfaced to Gaussian 09. A development version of the MNDO package was employed for the OM2/MRCI calculations.24,25
Np Nfs ⎡ πe 2ℏ 1 ⎢ σ(E) = ∑ ⎢ ∑ f0l (R k)gL 2mc ε0nr N l ⎣ p k
⎤ (E − ΔE0l(R k), δ)⎥⎥ ⎦
3. RESULTS 3.1. Ground-State Properties. The ground-state minima of six tautomers (Figure 1) were optimized, and their energies are given in Table 1. (Their Cartesian coordinates are given in
(1)
where e and m are the electron charge and mass, ε0 is the vacuum permittivity, and nr is the refractive index of the medium. Np and Nfs are the number of points in the ensembles and the number of final states, respectively. gL is a normalized Lorentzian line shape centered at ΔE0l and with full width δ. The absorption cross section given in cm2/molecule is related to the molar extinction coefficient ε (in M −1·cm−1) through
ε(E) =
10−3NA σ(E) ln(10)
Table 1. Energetic and Thermodynamics Characterization of the Ground State of 9-ATPPo Tautomersa trans-1 TZVP E (au) ΔE (kcal/mol) ΔEZP (kcal/mol) ΔG (kcal/mol)
(2)
where NA is the Avogadro constant. When more than one isomer contributes to the spectrum, the absorption cross section is given by the Boltzmann average of these tautomers:35
E (au) ΔE (kcal/mol) ΔEZP (kcal/mol) ΔG (kcal/mol)
N
σT (E) =
−ΔGi / kBT ∑i =isom 1 σi(E)e N
−ΔGi / kBT ∑i =isom 1 e
(3)
where kB is the Boltzmann constant, T is the temperature, and the sums run over each of the Nisom isomers included in the average. σi is the absorption cross section computed with eq 1 for tautomer i, whose ground-state Gibbs free energy lies ΔGi above the ground-state Gibbs free energy of the most stable tautomer included in the average. The error in the cross section due to the statistical sampling can be estimated by
E (au) ΔE (kcal/mol) ΔEZP (kcal/mol) ΔG (kcal/mol)
πe 2ℏ ∑ 1/2 1 1/2 2mc ε0nr l Np (Np − 1)
trans-2
6-31G(d,p)
TZVP
6-31G(d,p)
−1968.731 536 0.00
Gas Phase −1968.071 669 0.00
−1968.731 280 0.16
−1968.071 437 0.15
−
0.00
−
0.15
−
0.00
−
0.33
−1968.738 416 0.00
Toluene (PCM) −1968.078 −1968.738 497 132 0.00 0.18
−1968.078 269 0.14
−
0.00
−
0.17
−
0.00
−
0.40
cis-A1 6-31G(d,p)
Nfs
δσ(E) ≃
(6)
cis-A2 6-31G(d,p)
cis-B1 6-31G(d,p)
cis-B2 6-31G(d,p)
−1968.070 425 0.78
Gas Phase −1968.067 210 2.80
−1968.022 821 30.65
−1968.028 457 27.12
0.55
2.10
31.20
27.91
0.60
2.23
30.44
27.06
DFT calculations with CAM-B3LYP functional. ΔEZP includes the zero-point vibrational energy scaled by 0.98. ΔG for 298.15 K without anharmonic corrections. a
⎤1/2
⎡ Np ⎢ (f (R )g (E − ΔE (R ), δ) − ⟨s ⟩)2 ⎥ 0l k l ⎥ ⎢∑ 0l k L ⎣ k ⎦
the Supporting Information.) Among all tautomers, the energies of the two trans tautomers are lower than those of the other four cis tautomers. In the gas phase, the most stable tautomer is trans-1, in which the two hydrogen atoms are attached at the N21 and N23 atoms. With the 6-31G(d,p) basis set, the trans-2 tautomer is located only slightly higher (∼0.15 kcal/mol) than trans-1. It is interesting to notice that cis-A1 lies 0.78 kcal/mol higher than trans-1, while cis-A2 has much higher energy (2.80 kcal/mol). Similar energy differences between cis
(4)
where Np
1 ⟨sl⟩ = ∑ ΔE0l(R k ′)f0l (R k ′)gL(E − ΔE0l(R k ′), δ) Np k′
(5) 3368
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Figure 2. (a) Main molecular orbitals involved in the excitations of 9-ATPPo (trans-1). C2h-approximated representation of the orbitals is given. (b) Main contributions to the spectrum of porphycenes (right) from which 9-ATPPo is one particular asymmetric case. The equivalent transitions for porphyrin are shown as well (left). (c) Experimental absorption spectrum (curve) and theoretical transition energies and oscillator strengths (vertical lines). Theoretical data for trans-1 tautomer at PCM/TD-CAM-B3LYP/6-31++G(2df,p) level. Experimental absorption spectrum in toluene from ref 20.
that trans-1 is blue-shifted in relation to trans-2, which is blueshifted in relation to cis-A1. 3.2. Excited-State Properties: Vertical Absorption. Before we discuss the excited states of 9-ATPPo, it is useful to address the general features of electronic transitions in basefree porphyrins and porphycenes. The electronic character of low-lying bright states of these molecules can be understood by Gouterman’s four-orbital picture40 (Figure 2b). Due to the D4h symmetry of base-free porphyrins, the LUMO and LUMO + 1 are degenerate (eg representation). At the same time, HOMO and HOMO − 1 belong to a1u and a2u representations, respectively. Two a1u → eg transitions are responsible for the weak absorption band (Q-band) in the low-energy domain. At the same time, two a2u → eg transitions give origin to the strong Soret absorption band. Due to the degeneracy of eg orbitals, the two electronic transitions in the Q-band overlap each other. The same happens for the two electronic transitions in the Soret band. From base-free porphyrins to base-free porphycenes, the symmetry of the system is lowered from D4h to C2h (Figure 2b). Then, HOMO and HOMO − 1 belong to au representation, while degenerate eg LUMO and LUMO + 1 orbitals split into two nondegenerate orbitals belonging to bg representation. The lifting of the orbital degeneracy leads to a peak splitting in the Q-band, as well as in the Soret band.14 As noticed by DuranFrigola et al.,20 the addition of the NH2 group to produce the asymmetric 9-ATPPo leads to even more pronounced peak splitting of the bands. Based on Gouterman’s four-orbital picture and ab initio results, the absorption spectra of 9-ATPPo can be assigned. For illustration, let us start from the most stable tautomer, trans-1. The vertical excitation energy at S0 equilibrium geometry of trans-1 in the gas phase is given in Table 2 (obtained with the
and trans forms have been also observed by Quartarolo et al. in their investigation of brominated porphycenes.18 The different stabilities of the two cis-A tautomers can be understood by the introduction of an amino group. It distorts the inner cavity of the porphycene ring in such a way that the N22···H hydrogen bond in cis-A2 (N22HN23 = 157°) is destabilized in comparison to the equivalent N23···H hydrogen bond in cis-A1 (N22HN23 = 152°). The last two tautomers (cis-B) have rather high energies. Their low stability is due to the strong H−H interaction, which distorts the phenyl−pyrrole groups and brings the inner H atoms out of the porphycene plane. This distortion has been also reported by Sobolewski et al.10 When toluene solution is included by the PCM model, trans1 is still the most stable tautomer. The relative energies of other tautomers with respect to trans-1 do not change significantly. Therefore, under experimental conditions similar to those reported in ref 20, similar concentrations of the two trans tautomers should coexist at room temperature, while cis-A1 may also give a minor contribution. On the other hand, cis-A2, cis-B1, and cis-B2 should not be observed. Similar conclusions have also been reached in ref 18. Vibrational analysis was performed for all tautomers in the gas phase and in toluene solution. The IR spectra for the three more stable tautomers (trans-1, trans-2, and cis-A1) are given in the Supporting Information, and we only outline the main features here. The solvent effects have almost no influence on the IR spectra. Moreover, the three tautomers display rather similar IR spectra. The main difference is in the NH-stretching modes inside the cavity. While for trans-1 and trans-2 the two cavity modes are almost degenerate (the frequency difference is around 30 cm−1), these modes for cis-A1 are separated by about 130 cm−1. Another noticeable trend concerning these modes is 3369
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Table 2. Characterization of the Vertical Spectrum of trans-1 in Terms of the Main Orbital Transitions and of the State Charactera
Table 3. Characterization of the Q Band in Gas Phase for the Six Tautomers at TD-CAM-B3LYP/6-31G(d,p) S0
trans-1 state
main orbital transition
S0 S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15
cs πpo(H)−πpo(L)* πpo(H−1)−πpo(L)* πph(17)/po−πpo(L)* πph(7)/po−πpo(L)* πpo(H)−πpo(L+1)* πph(2)/po−πpo(L)* πph(12)/po−πpo(L)* πpo(H−1)−πpo(L+1)* πpo(H−6)−πpo(L)* πph(17)/po−πpo(L)* πph(7)−πpo(L)* πpo(H)−πph(12)* πpo(H−1)−πph(12)* πph(17)−πpo(L)* πpo(H−1)−πph(12)*
LE-Q1 LE-Q2 LE LE LE-Sr1 LE LE LE-Sr2 LE LE CT CT CT CT CT
ΔE (eV)
f
0.00 1.93 2.32 3.29 3.48 3.69 3.75 3.81 3.92 4.13 4.17 4.34 4.45 4.72 4.75 4.82
− 0.390 0.326 0.038 0.042 0.916 0.044 0.035 1.124 0.105 0.269 0.029 0.011 0.022 0.002 0.004
trans-1 trans-2 cis-A1 cis-A2 cis-B1 cis-B2
S1−S0 (Q1)
S2−S0 (Q2)
E (eV)
E (eV)
f
E (eV)
f
0.00 0.01 0.03 0.12 1.33 1.18
1.93 1.93 2.13 1.90 2.08 2.23
0.390 0.524 0.490 0.374 0.369 0.312
2.32 2.19 2.31 2.22 2.52 2.46
0.326 0.191 0.261 0.295 0.201 0.141
Because the results show a very weak dependence on basis sets and solvation conditions, the following discussions based on data obtained by using the 6-31+G(df,p) basis set and the PCM model are in general valid for the other levels as well. The absorption energy of the first Q transition (Q1) gives trans-1 (1.86 eV) ∼ trans-2 (1.88 eV) < cis-A1 (2.03 eV). For the Q2 transition, a different energy order is observed: trans-2 (2.20 eV) < cis-A1 (2.26 eV) ∼ trans-1 (2.26 eV). The order of vertical energies for the three tautomers in the first Soret transition (Sr1) is similar to those in the Q2 transition, while the Sr2 transitions display trans-1 < cis-A1 < trans-2. The energies of the Q1 and Q2 transitions agree within 0.3 eV with the experimental work, which can be considered a good agreement given the uncertainties of the theoretical methods. However, a larger deviation is observed for the Soret band and all calculated energies are ∼0.5 eV higher than experimental values. Such a large deviation is often observed in calculations of high-lying excited states41 and can be attributed to deficiencies in the quantum-chemical levels and lack of vibronic energy corrections. The inclusion of the toluene solvent does not modify the relative energy ordering of electronic states of three tautomers, but causes a small red shift of all absorption bands. The red shift exists for the Q-band (0.06−0.07 eV) and Soret band (0.10−0.12 eV) for both trans-1 and cis-A1, while this red shift becomes very small (
