ARTICLE pubs.acs.org/JPCA
Isolated and Solvated Thioxanthone: A Photophysical Study Vidisha Rai-Constapel, Susanne Salzmann,† and Christel M. Marian* †
Institute of Theoretical and Computational Chemistry, Heinrich Heine University D€usseldorf, Universit€atsstr. 1, D-40225 D€usseldorf, Germany ABSTRACT: Quantum chemical methods have been employed to study the photophysics of thioxanthone in vacuum and various solvents. Structurally, the solvation leads to a lengthening of the carbonyl bond, whereas the benzene skeleton is mostly unaffected. This is mirrored by the larger blue shift of the (nOπ*) states as compared to the red shift which the (ππ*) states undergo. For a proper understanding of the radiative and radiationless processes occurring, the excitation energy profile along a linearly interpolated path has been determined in various cases. The interesting interplay of excited states thus revealed, has been investigated to qualitatively suggest the relaxation pathways available (or dominant) in the cases under study. Rates for these processes have also been computed wherever possible.
’ INTRODUCTION There is a wide range of application for thioxanthone (TX; Figure 1) and its derivatives, for example, as type II1 photoinitiators for commercial-free radical polymerization25 or as antitumoric, antiparasitic, and anticarcinogenic agents.6,7 Recently, the advantage of utilizing TX in synthesizing photolabile protecting groups used in DNA chip synthesis has excited considerable interest.8,9 In such a moiety TX acts as a sort of intramolecular antenna and enhances the photosensitivity of the photolabile protecting group. As all these applications are initiated by means of UV radiation, the photophysical and photochemical processes of TX triggered by illumination are of utmost interest. Therefore, it is hardly surprising that TX has been extensively studied both experimentally and theoretically. Experimentally, it has been revealed that the spectroscopic properties of TX are strongly dependent on the nature of the solvent.915 This phenomenon has been first observed for the lifetime τF and quantum yield ϕF of fluorescence. While in apolar solvents, for example, benzene, τF is of the order of several picoseconds and ϕF is smaller than 0.001, in polar and protic solvents τF is prolonged to the order of several nanoseconds and ϕF rises to 0.40.6.10,13 This is an indication that nonradiative photophysical processes, such as internal conversion (IC) and intersystem crossing (ISC), are solvent dependent. With regard to its role as triplet sensitizer, ISC is of major importance for the photophysics and photochemistry of TX. Experimental studies in various solvents (apolar, polar/aprotic, and polar/protic) have shown that the quantum yield of triplet formation ϕT is substantial in TX and ranges from 0.84 in benzene to about 0.6 in water.13 In addition, kinetic studies have revealed that the triplet population kinetics consist of two components, namely, a fast component of 1011 s1 and a slow component that is highly solvent dependent.9,12 This theoretical work aims at throwing r 2011 American Chemical Society
Figure 1. Chemical structure and labeling of thioxanthone.
more light on the complex photophysical channels discussed in the aforementioned experimental works. The solvent effect on the fluorescence properties of TX was tentatively interpreted in terms of the proximity effect,10,1618 which attributes the change in the efficiency of the 1(ππ*) f S0 internal conversion to the varying strength of vibronic coupling between the 1(nπ*) and 1(ππ*) excited states of TX. In nonpolar solvents 1(nπ*) and 1(ππ*) are very close together. In such a case, the vibronically active out-of-plane modes are the most important coupling modes for the radiationless deactivation of the lowest excited state, causing the rate of internal conversion from the latter to S0 to be high.17 Hence, small fluorescence quantum yield and longer lifetime are observed in such solvents. In a polar, hydroxylic environment the two involved states move further apart and vibronic interaction between them is weakend. The 1(nπ*) state is destabilized in such solvents, leading to a decrease in the rate of internal conversion from the 1(ππ*) state to S0. Hence, higher fluorescence quantum yield and slower fluorescence decay are observed in polar, hydroxylic solvents. Received: March 9, 2011 Revised: June 20, 2011 Published: June 28, 2011 8589
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While experimentally, the energetic position of the 1(ππ*) state is easily accessible, conventional one-photon absorption spectroscopy cannot always determine the exact energetic position of the optically dark 1(nπ*) state. All the experimental results report the 1(ππ*) to be the first excited singlet state (S1), independent of the environment, and the 1(nπ*) to be the S2 state. The exact ordering of the low-lying excited singlet states has also been the matter of theoretical studies, including our own work. Rubio-Pons et al. mention a so-called butterfly motion19 that characterizes the dynamical change between the planar and nonplanar conformers of TX. It has been stated that the energetic order of the 1(nπ*) and 1(ππ*) states is different in the two conformations. A recent reinvestigation of the energetic order of these two low-lying excited singlet states along the butterfly motion reaction coordinate by us could not corroborate these findings, which could be tentatively attributed to the shortcomings in the choice of the CAS space in ref 19. Our results in vacuum show the 1(nπ*) to be the S1 state, whereas the optically bright (ππ*) state is found about 0.07 eV higher.20 In fact, as early as 1981, Lai and Lim17 had suggested the possibility that the (nπ*) state could lie lower than the (ππ*) state in nonpolar solvents and had suggested performing experiments on jet-cooled TX.18 Unfortunately, such an experimental work was not to be found in literature to date. In this study, the photophysics of TX is under investigation. For this purpose, the minimum nuclear arrangements of the lowTable 1. Comparison between the Ground State Equilibrium Nuclear Arrangements of TX in Vacuum and Various Solvent Models [pm]/[deg]
a
vacuum
AcN
MeOH
H2O
exp.a
r(C1C2)
138.2
138.2 138.1
138.1
140.1((0.1)
r(C2C3)
139.9
140.1 140.1
140.1
140.1((0.1)
r(C3C4)
138.0
138.0 137.9
137.9
140.1((0.1)
r(C4C5)
140.6
140.8 140.9
141.0
140.1((0.1)
r(C5C6) r(C6C1)
140.3 140.3
140.5 140.6/140.7 140.8/140.7 140.1((0.1) 140.4 140.4 140.4 140.1((0.1)
r(C6S)
175.6
175.3 175.0/175.1 174.7
r(C5Cc)
148.6
148.1 147.5
175.1((0.2)
147.5/147.4 149.8((0.4)
r(Cc-O)
122.5
123.3 123.8
124.3
123.2((0.6)
— (C6SC06)
103.8
103.8 103.7
103.6
103.4((0.3)
— (C5CcC05)
119.5
120.0 120.3
120.1
119.4((0.6)
— (C6C5SC06)
180.0
180.0 178.6
177.1
169.0((1.6)
Gas phase electron-diffraction data.31
lying excited states have been obtained and, if possible, rate constants for decay processes out of these states have been determined. A comparison of our vacuum results with experimental data is only meaningful for apolar solvents such as (cyclo)hexane or benzene. In addition, three different solvents have been modeled, namely, acetonitrile (AcN), methanol (MeOH), and water. The choice of the solvents was based on their polarity and hydrogen-bonding ability, as experimental results indicate that the ability of the solvent to form hydrogen bonds has a larger effect on the photophysical behavior of TX than the polarity of the solvent.12,13
’ METHODS AND COMPUTATIONAL DETAILS The calculation of the ground and excited state geometries, vibrational frequencies, vertical and adiabatic excitation energies, dipole (transition) moments, and oscillator strengths follows the procedures as described in ref 20. As long as not stated otherwise, the C2v symmetry constraints have been imposed for the calculation of the excited state nuclear arrangements and the obtained stationary points are found to be true minima on their respective PEHs in vacuum. To estimate spectral shifts due to solutesolvent interaction, environmental effects have been modeled for AcN, MeOH, and H2O. In this connection, electrostatic interaction has been taken into account by the conductor-like screening model (COSMO), which is implemented in the Turbomole package.21,22 Dielectric constants of ε = 78, 36, and 33 were chosen,23 corresponding to water, acetonitrile, and methanol, respectively, at ambient temperatures. Because COSMO cannot properly model hydrogen bonding, this effect was mimicked by additional microhydration for MeOH and H2O solution. For this purpose, we placed two solvent molecules next to the carbonyl group of the TX ring (Figure 4). Specific solvent molecules placed at the sulfur atom simply drift away as optimization progresses, indicating that no specific solutesolvent interaction has to be taken account of at this ring position. When COSMO was applied, the MRCI expansion was built up from the one-particle basis of COSMO optimized KohnSham orbitals. Due to technical reasons, C1 symmetry had to be used for all calculations involving COSMO and DFT/MRCI. In the Condon approximation, electronic spinorbit coupling matrix elements and vibrational overlaps are required for the theoretical determination of the ISC rates. Spinorbit matrix elements (SOMEs) between the correlated DFT/MRCI wave functions are calculated using the SPOCK program developed in
Table 2. Selected Vertical DFT/MRCI Excitation Energies of TX [eV] in Acetonitrile (AcN), Methanol (MeOH), and Water in Comparison to Earlier Results in Vacuum (DFT/MRCI and CASPT2/CASSCF) and Experimental Band Maxima ΔEDFT/MRCIa state (C2v)
vacuum
AcN
MeOH
H2O
vacuum
1 A2
nO f π*L
3.37
3.57
3.67
3.83
3.49
21A1
πH f π*L
3.44
3.36
3.29
3.22
3.59
1 B2
πH f π*L+1, πH3 f π*L
4.29
4.25
4.22
4.18
13A1
πH f π*L
2.96
2.88
2.81
2.75
3.19
13A2
nO f π*L
3.20
3.41
3.52
3.67
3.32
23A1 13B2
πH2 f π*L, πH f π*L+2 πH f π*L+1, πH1 f π*L
3.49 3.52
3.48 3.53
3.47 3.50
3.46 3.49
1
1
a
electronic structure
ΔECASPT2/CASSCFb
ΔEexptc n-hex.
AcN
MeOH
H2O
3.28d
3.28
3.28
3.21
Ref 20. b Ref 34. c Ref 13. d Burget and Jacques report the absorption maximum for TX in n-hexane to be at 3.43 eV.16 8590
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our group.24,25 For reasons of efficiency, the one-center meanfield approximation to the BreitPauli Hamiltonian is used for the description of the spinorbit coupling. This nonempirical effective one-electron operator treats the expensive two-electron terms of the full Hamiltonian in a Fock-like manner.26,27 The vibrational frequencies are determined with the program SNF.28 These frequencies are used as input for the program VIBES,29 which calculates the ISC rate constants. In vacuum, only the 22 totally symmetric serve as accepting modes and excitations were allowed to these modes. To calculate the indirect ISC rates due to vibronic coupling, first-order derivatives of the SOMEs are calculated numerically by finite difference techniques, as described in ref 30. For a qualitative interpretation of the photophysics of this chromophore, a linearly interpolated path (LIP) between the minima of the ground and the optically bright 1(πHπ*L) states was calculated using the program package DISTORT.29 At each of the 10 coordinate displacement increments, a single-point DFT/ MRCI calculation was carried out to determine the vertical excitation energies of the singlet and triplet manifolds.
’ RESULTS AND DISCUSSION As the ordering of the low-lying excited states depends on various factors, for example, geometry or solvent environment, we shall henceforth denote the electronic states according to their predominant electronic structure (diabatic representation). Ground State Geometry and Vertical Excitation Energies.
A detailed assignment of our calculated vertical DFT/MRCI excitation energies, at the ground state minimum in vacuum, to the steady state absorption spectrum in cyclohexane in an energy range of up to 6 eV is given in ref 20. In the present work, the emphasis lies on the determination of the energetic positions of the low-lying excited singlet and triplet states in various solvents, as these states are accountable for the photophysical and photochemical behavior upon UV(A) radiation. For a compilation of our results in acetonitrile, methanol, and water, see Tables 1 and 2. To aid the discussion, previous results for TX in vacuum as well as gas-phase electron-diffraction data31 are included in the tables and briefly summarized in the following. The ordering and shape of the molecular orbitals (MO) are very similar for all environments; hence, the reader is referred to ref 20 for this information. With respect to the equilibrium ground state arrangement, solvation shows small and very localized structural changes. The outstanding variations in the ground state geometry due to solvation are listed below. • An elongation of the carbonyl bond with the effect increasing from AcN (+0.8 pm) over MeOH (+1.3 pm) to H2O (+1.8 pm). • In line with variation of the CO bond, the C5Cc and C6S bonds are stabilized (see Figure 1 for atom labeling). Otherwise, the solvent-induced bond alterations are minor. • While in AcN the nuclear arrangements are found to have C2v symmetry, with explicit solvent molecules, butterfly deformation is observed. Vacuum. As mentioned at the beginning, a detailed discussion of the vertical excitation energies in vacuum is to be found in ref 20. The interesting facts are summarized here. The first excited singlet state in vacuum is found to be the optically forbidden 1(nOπ*L) state. Almost degenerate to it the optically bright 1(πHπ*L) state is found. Energetically these two low-lying excited states are rather isolated as the S3 state is found more
Figure 2. TDDFT equilibrium structures of excited states in comparison with the ground-state geometry. All bond lengths in pm.
Figure 3. Selected frontier orbitals (isovalue = 0.02).
than 0.8 eV higher in energy. In the triplet manifold, there are two states found below these two singlet states. The T1 state is seen to be dominated by the HOMOLUMO transition, while the T2 state exhibits a nO f π*L configuration. In addition, the T3 and T4 states, both multiconfigurational 3(ππ*) states, are found in close proximity to the low-lying excited singlet states. The DFT/ MRCI energies are marginally lower than those determined by the CASPT2 method, however, the trends in the energies are in perfect agreement in both the methods (Table 2). Acetonitrile. As is to be expected, due to the medium polarity of AcN, the (nOπ*L) states demonstrate hypsochromicity, while the low-lying (πHπ*L) states show bathochromaticity. 8591
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Figure 4. Position of explicit methanol (left) and water molecules (right) around TX.
A general trend is also that the red shift experienced by the (πHπ*L) states is smaller (0.08 eV) as compared to the blue shift that the (nOπ*L) states undergo (0.20 eV). As a result the energetic order of the two low-lying excited singlet states is reversed as compared to vacuum. The vertical excitation energy of 1(πHπ*L) in AcN is computed to be 3.36 eV. Krystkowiak et al.13 find the absorption maximum for 1(πHπ*L) state in this solvent to be 3.28 eV. Kronfeld and Timpe32 find this excitation energy to be 3.25 eV. All these data are in good agreement with our calculated results, the difference being ≈0.1 eV. The multiconfigurational S3 (ππ*) state shows a stabilization in AcN by 0.04 eV (see Table 2), and the stabilization of the other (ππ*) triplet states is comparable, being within 0.04 to 0.01 eV. The effect of such energetic shifts on the photophysics in AcN as compared to vacuum is very interesting, as shall be discussed in a later section. Methanol. We find the first optically bright state 1(πHπ*L) to lie at 3.29 eV above the electronic ground state. Burget10 and Morita33 observe the first absorption band at 3.28 eV (in methanol) and 3.26 eV (in ethanol), respectively, agreeing perfectly with our results. We predict the 1(nOπ*L) state to be blue-shifted by 0.3 eV in methanol solution. In the case of the triplet manifold, we observe prominent red (for 3(πHπ*L)) and blue (for 3(nOπ*L)) shifts for the two lowest-lying states, whereas the solvent shift for the higher-lying (ππ*) states is marginal. Though the polarity of this medium is comparable to AcN, a comparison of the calculated vertical energies demonstrates the importance of taking into account the H-bonding effects in the calculations. We shall see later on how the photophysics of the two systems compare with each other. Water. The low-lying states of the triplet and singlet manifold show substantial shifts in aqueous solution. The singlet and triplet (nOπ*L) states show a much larger blue shift in water due to the hydrogen bonding (see Figure 5) and the increased polarity of water as compared to methanol. The vertical excitation energy of 1(nOπ*L) in water is calculated to be 3.83 eV, which is 0.46 eV higher than in vacuum. The corresponding triplet state lies 0.43 eV higher in energy. The 1(πHπ*L) state is stabilized by 0.22 eV. Because TX is not very soluble in water, experimental data does contain some uncertainty. Krystkowiak et al.13 have reported results for TX in water and heavy water. They obtain the absorption maximum for TX in aqueous solution at 3.21 eV,
which agrees very nicely with our calculated value of 3.22 eV. Our data is further backed by the results reported by Morita et al.,33 who measured the absorption spectrum of TX in an ethanol water solution. They find an absorption maximum at 3.15 eV for the H-bonded species of TXwater. Due to the strong blue shift of the 3(nOπ*L) state in aqueous medium, three 3(ππ*) states are pushed below this state. The 3(πHπ*L) state is stabilized by 0.21 eV, whereas the other two 3(ππ*) states are red-shifted by merely 0.020.03 eV. Adiabatic Excitation Energies in Vacuum. To be able to understand the various photophysical processes occurring after photoexcitation to a higher-lying state one has to look at the minimum of this excited state. The energetic position of the various electronic states at this minimum reveals the possible pathways accessible to the molecule for the dissipation of the excess energy. In this subsection, we present the minimum geometries for chosen singlet and triplet excited states in vacuum. In a preceding paper,20 the nuclear arrangement of the first optically bright state 1(πHπ*L) has been discussed in detail. (πHπ*L) States. In the vertical excitation spectrum, the singlet and triplet (πHπ*L) states arise from the same electronic transition with similar c2 values (0.80 for the singlet state and 0.77 for the triplet state), hence, one expects these states to have nearly the same equilibrium nuclear arrangement. However, Figure 2 shows that the 3(πHπ*L) equilibrium geometry is dominated by CcO bond lengthening of 7.8 pm and a CcC5 (CcC50 , see Figure 1) bond shortening by 4.4 pm, whereas the corresponding singlet state does not show such large variations. Though only one major contribution to the electronic struture of 3(πHπ*L) has been listed in Table 2, it is the second contribution from πH1 f π*L (13%), which causes the deviation from the trend set by the 1(πHπ*L) state (this contribution being absent here). For a better understanding, the πH, πH1 and π*L orbitals at the 3(πHπ*L) minimum geometry are shown in Figure 3. The πH1 f π*L transition leads to an increase in the antibonding character of the CcO bond, thus, explaining the enhanced lengthening in the triplet state. Similarly, the bonding character in the CcC5 (CcC50 ) region is additionally enhanced due to πH1 f π*L contribution causing the extra shortening of this bond in this state. (nOπ*L) States. The equilibrium nuclear structures of the 1 (nOπ*L) and the 3(nOπ*L) states display a pronounced stretching 8592
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Figure 5. Comparison of the vertical excitation energies vacuum, acetonitrile, methanol, and water.
Table 3. Adiabatic Singlet and Triplet DFT/MRCI Excitation Energies ΔEadia [eV] and Zero-Point Vibrational Energy Corrections (ZPVE) [eV] of Low-Lying Excited States vacuum
AcN
MeOH
water
geometry ΔEadia ZPVE ΔEadia ΔEest ΔEadia ΔEest ΔEadia ΔEest (nOπ*L)
3.00
0.1
3.35
3.20
(πHπ*L)
3.34
0.15
3.26
3.25
3.19
3.19
3.11
(πHπ*L)
2.81
0.14
2.76
2.73
2.69
2.66
2.78
(nOπ*L)
2.88
0.09
3.23
3.09
3.18
3.35
(ππ*)a
3.34
0.21
3.33
3.32
3.31
(ππ*)a
3.45
0.22
3.44
3.45
3.42
1 1 3 3 3 3
a
3.30
3.46 3.12 2.60
Multiconfigurational triplet states, see Table 2.
of the CcO bond by 9.9 and 10.2 pm, respectively (see Figure 2). This is accompanied by a shortening of the CcC5 and CcC50 bonds by approximately 6 pm for both geometries. The change in the structural parameters reflects the change of character in the corresponding frontier orbitals. Figure 3 shows the electron density around carbonyl bond in the nO and π*L orbitals. In both orbitals, the character is antibonding, leading to longer bond length. Similarly, it is seen that the character of the electron denstiy around the CcC5 (CcC50 ) bond changes from being anti- to bonding, thus, pictorically explaining the bond shortening here. The adiabatic excitation energies of the two states are 3.00 and 2.88 eV, respectively (Table 3). The stabilization in both states is also comparable, being 0.37 eV for 1(nOπ*L) and 0.32 eV for 3 (nOπ*L). The ground state destabilization in 1(nOπ*L) is 0.41 eV leading to a vertical emission energy of 2.59 eV. Due to its A2 symmetry radiative decay of this excited state to the electronic ground state is dipole forbidden. For 3(nOπ*L) the vertical emission energy is 2.45 eV due to 0.43 eV destabilization of the ground state. Higher-Lying 3(ππ*) States. For the next two higher-lying multiconfigurational 3(ππ*) states we calculate imaginary frequencies of v1 = i1311.22 cm1 (T3) and v1 = i792 cm1 (T4) at the C2v PEH corresponding to a B2 symmetric, in-plane mode. A distortion of the coordinate along the imaginary
modes in the two states leads to the lower Cs symmetric coordinates. In this point group the two states belong to the A0 irreducible representation. A geometry optimization at Cs level, however, reveals a root-flipping of the two energetically close lying states. Photophysics of TX: Isolated and Solvated. The discussion above paves the path to a better understanding of the photophysics of TX from vacuum to aqueous solution. We present in the follwing a qualitative picture of the various processes occurring after photoexcitation from the FranckCondon (FC) region of the groundstate to the 1(πHπ*L) excited state. Figure 6 shows the calculated linearly interpolated path from the minimum of the groundstate (zero of the geometrical axes) to the 1 (πHπ*L) minimum, at which the energetic layout of the singlet and triplet manifold determine the facile (and not so facile) photophysical processes leading to relaxation to the ground state. A qualitative description of the spin-allowed (Figure 6) and spinforbidden (Figure 7) radiationless transitions is presented in the following. Vacuum. The radiative rate is calculated to be 4.5 107 s1, which compares well to the experimental value in n-hexane (>1 107 s1) by Krystkowiak et al.13 Two ISC channels are feasible in vacuum, namely, the 1(πHπ*L) ' 3(nOπ*L) and the 1 (nOπ*L) ' 3(πHπ*L) channels. The rate for the two channels should be quite high as the involved states lie close to each other. We calculated these ISC rates to be of the order of 1010 s1. The ISC rate observed in n-hexane13 compares very well with our total ISC rate of 1010 s1 (Table 4) in vacuum, being e15 109 s1. The proximity of 1,3(nOπ*L) and 1,3(πHπ*L) states suggests that vibronic coupling should also play a part in the photophysics. We calculate the vibronic spinorbit rate to be comparable to the direct ISC rates, being ≈1010 s1 for 1(πHπ*L) ' 3(πHπ*L) and ≈109 s1 for 1(nOπ*L) ' 3(nOπ*L) channels. The derivatives of the SOMEs involved are listed in Table 5 along with the oop modes involved. Figure 6 shows that the optically dark 1(nOπ*L) lies slightly below the bright 1(πHπ*L) state in the FC region. At the minimum of the 1(πHπ*L) electronic state, the states are degenerate, which is an indication of a very fast IC between the two states, with a rate comparable to ISC. Hence, we conclude that in vacuum the radiationless processes should dominate and effectively quench fluorescence. Acetonitrile. The picture is a little altered when one moves on to the polar solvent acetonitrile. The 1,3(nOπ*L) states undergo a relatively larger blue shift as compared to the red shift of the (ππ*) states. The relaxation to the 1(πHπ*L) minimum occurs undisturbed. IC to 1(nOπ*L), being an activated process, should show temperature dependence in this solvent. The ISC from the two singlet states to the corresponding triplet states should, however, compete with the former channel, being equally favorable for relaxation. The SOMEs (Table 4) and ΔEad are close to the values calculated for vacuum and indicate comparable ISC rates. Experiments conducted at room temperature in acetonitrile13 determine comparable IC (5.5 109 s1) and ISC (10.6 109 s1) rates, thus, supporting our explanation. A recent work by Angulo et al.34 reports the ISC and IC rates in AcN to be 8 109 s1 and 4.1 109 s1, which are also in good agreement with our results and further support the qualitative picture provided by our calculations. The calculated vibronic spinorbit coupling is of the order of 107 s1. Because the indirect SO coupling borrows 8593
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Figure 6. DFT/MRCI excitation energy profiles along a linearly interpolated path between the S0 and 1(πHπ*L) minimum geometries in various cases.
Figure 7. DFT/MRCI excitation energy profiles along a linearly interpolated path between the 1(πHπ*L) and 3(πHπ*L) minimum geometries in various cases.
its intensity from the SO coupling between the (nOπ*L) and (ππ*) states, the reduced rate is obvious because these states are further apart as compared to vacuum. The calculated derivatives reflect this trend (Table 5). The kF is determined to be 5.2 107 s1 and agrees well with the experimental value of 8.1 107 s1 in ref 13.
Methanol. The next case in study is methanol, which is nearly as polar as acetonitrile but undergoes specific solvent interaction with the chromophore, enhancing the blue shift of the 1,3(nOπ*L) states. The red shift of the (ππ*) states is, however, comparable to that in the nonspecific solvent. As can be seen from Figure 6, the energetics in methanol is quite different as compared to the 8594
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Table 4. Calculated SOMEs [cm1], Rate Constants kISC [s1] for (S ' T) ISC Channels (left) in TX and the Adiabatic Electronic Energy Difference ΔEad [eV] in Various Cases channel
vacuum
iff
ΔE
SOME
AcN
ad
kISC
SOME
methanol
ΔE
ad
kISC
water
SOME
ΔE
kISC
ad
SOME
ΔEad
kISC
(πHπ*L) Geometry
1
(πHπ*L) f (nOπ*L)x
0.47
0.17
∼10
2.03
0.02
NaN
+0.22
(πHπ*L) f3 (nOπ*L)y 1 (πHπ*L) f3 (nOπ*L)z
0.47 0.47
0.17 0.17
∼10 ∼1010
0.40 15.72
0.02 0.02
NaN NaN
+0.22 +0.22
1
3
1
15.60
8 109
15.26 1
(nOπ*L) Geometry
(nOπ*L) f (πHπ*L)x
0.19
0.47
∼1
1.06
0.64
∼105
0.17
0.86
(nOπ*L) f (πHπ*L)y
0.19
0.47
∼1
2.20
0.64
∼106
0.23
0.86
0.47
∼109
28.21
0.64
∼108
25.71
0.86
1
3
1
3
(nOπ*L) f3 (πHπ*L)z
1
0.19
49.80
∼1010
42.68
Table 5. Derivatives of SOMES [cm1] with Respect to the Corresponding Dimensionless Normal Coordinates at the 1 (πHπ*L) Minimum Geometry vacuum #mode
AcN
ν
deriv 17.583
#mode
ν
MeOH deriv
#mode
ν
deriv 0.959
2
87
2
100 0.850
9
90
5
220 1.744
5
219 0.406
16
220 0.076
10
363 18.841
10
367 1.807
22
359 1.164
12
401 12.492
12
404 0.439
24
407 0.685
16
466 15.617
16
465 0.001
28
464 0.693
22
727 0.047
22
730 0.158
35
733 0.240
26 28
826 20.175 879 2.055
26 28
856 0.000 902 0.605
41 43
848 0.115 907 0.818
31
944 15.923
31
951 0.653
45
947 0.597
cases discussed above. The higher lying triplet (ππ*) states are now lying below the 1(nOπ*L) state in the FC region. According to our interpretation of the calculated data, fluorescence in methanol should be stronger than in the previous two cases. In their paper, W€oll et al.9 discuss the photophysics of thioxanthone in methanol. The high fluorescence quantum yield has been explained in terms of a delayed fluorescence. According to the model presented in this work, the process involves a fast and reversible ISC between 1(πHπ*L) and 3(nOπ*L) states, which are nearly isoenergetic, followed by a slow IC from 3 (nOπ*L) to the 3(πHπ*L) state. The results of our work lend support to this model. 3(nOπ*L) and 1(πHπ*L) states are nearly degenerate. The energy difference between the crossing point of the potential energy surfaces of these two states and the adiabatic energy of the 1(πHπ*L) state gives an estimate of the activation energy, ET, required so as to make ISC between them feasible. We determine ET to be approximately 492 cm1. The value of ET presented here is for the T = 0 K limit. The experimental data obtained for the room temperature have shown that activated processes may occur.9 Hence, in view of the fact that ET is only about 2 kBT at room temperature, rapid activated ISC should be feasible. Rates for ISC between energetically near degenerate, but spatially strongly displaced potentials cannot be determined with our ansatz. The underlying golden rule approximation rests on the assumptions that the vibrational density of final states is high and that the transition is irreversible.35,36 Both requisites are not
fulfilled for the 1(ππ*) ' 3(nπ*) radiationless transition. With regard to the S1 ' T1 transition, we expect the vibronic SO coupling to be further weakend (calculated rate being ≈106 s1) as the involved states are even further apart in energy. The radiative rate is calculated to be 5 107 s1, in perfect agreement with the reported experimental rate of 4.7 107 s1 13. Water. The trend that solvent environment causes a much larger blue shift as compared to the red shift is also seen for water. The 3(nOπ*L) state now clearly lies above the 1(πHπ*L) state. Their minima are no longer degenerate (see Figure 7). We do not expect the dynamics of the solvent molecules to effect the situation much, however, an increase in temperature might cause the 1(πHπ*L) ' 3(nOπ*L) channel to be activated. A strong fluorescence should be observed in water as the IC and ISC channels are either no longer available or too weak. The rate is calculated to be kF = 4.2 107 s1. The experimentally observed rate is kF = 4.8 107 s113, which agrees well with our data.
’ CONCLUSIONS A systematic study of TX in vacuum as well as in solution is presented in this work. DFT(TDDFT) is used to optimize the various electronic states. A continuum solvent model (COSMO) alongwith microsolvation has been used to describe the solvent environment around the chromophore. The major structural variation is seen in the bond length of the carbonyl bond, which is, for example, stretched by 1.8 pm in water as compared to the isolated TX. Both, polarity and hydrogen bonding play a decisive role in the energetics. The calculated vertical excitation spectrum in various cases reveals the blue shifts of the (nOπ*) states to be comparatively larger than the red-shift, which the (ππ*) states undergo. It also gives a glimpse as to how the photophysics can be expected to vary in these systems by providing information about the relative shifts in energies of the various singlet and triplet electronic states involved. A detailed qualitative interpretation of the radiative and radiationless channels is presented in the section on the photophysics of TX. The fluorescence and ISC rates calculated in this work agree well with the values available in literature. In vacuum and apolar solvents the radiationless processes should gain the upper hand, effectively quenching the radiative processes, as in these cases the triplet and singlet states involved in the photophysics lie very close to each other, hence, facilitating fast IC and ISC. The rates calculated for these channels are about 100 times greater than kF. As the (nOπ*) and (ππ*) states draw apart due to 8595
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The Journal of Physical Chemistry A solvent effects, the radiationless channels become less dominant, hence, fluorescence is observed in polar solvents. An important aspect should, however, be kept in mind. The thermodynamics of the solvent molecules would affect the photophysics, making certain channels available that display small energy barriers, as, for example, discussed in the section on the photophysics of TX for the case of methanol.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. Present Addresses †
Department of Chemistry, Aarhus University, Langelandsgade 140, 8000 Aarhus C, Denmark.
’ ACKNOWLEDGMENT Financial support by the Deutsche Forschungsgemeinschaft through SFB663/C1, MA 1051/12-1, and HHU Strategischer Forschungsf€orderungsfonds is gratefully acknowledged. The authors also gratefully thank P. Gilch for helpful discussions. ’ REFERENCES
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