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Theoretical study of the radiationless deactivation mechanisms of photo-excited thiophene
Chemical Physics 397 (2012) 18–25
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Theoretical study of the radiationless deactivation mechanisms of photo-excited thiophene M. Stenrup Department of Physics, Stockholm University, AlbaNova University Center, SE-106 91 Stockholm, Sweden
a r t i c l e
i n f o
Article history: Received 12 August 2011 In final form 7 December 2011 Available online 23 December 2011 Keywords: Radiationless deactivation Conical intersections Heterocyclic compounds Photophysics
a b s t r a c t The radiationless deactivation mechanisms of photo-excited thiophene have been studied using the multi-reference second-order perturbation theory and linear response coupled cluster methods. The electronic spectrum has been established and various minimum energy structures and conical intersections involving the ground and lowest singlet excited states have been characterized. Simplified reaction paths connecting the optimized geometries have been calculated as well. Based on these investigations, several deactivation mechanisms have been identified leading from the lowest bright 1pp⁄ states back to the electronic ground state. The excited state depletion in each case is possible due to the existence of low-lying conical intersections formed by either cleavage of one of the CS bonds or out-of-plane deformations of the aromatic ring. The deactivation mechanisms suggested in this work should provide some very efficient decay channels after excitation into the first UV absorption band of thiophene, and are good candidates to explain why this compound is non-fluorescent. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Thiophene belongs to the class of five-membered aromatic heterocyclic compounds [1]. It occurs sporadically in nature (e.g., in certain plants) and has found widespread use in areas ranging from pharmaceutical to material sciences. The photophysical properties of thiophene based materials are utilized in a variety of different applications [2]. In particular, recent interest has been focused on the incorporation of thiophene units into light emitting devices [3], biological labels [4], and dye-sensitized [5] as well as polymer-based [6] organic solar cells. The UV absorption spectrum of thiophene has been measured under various conditions [7–9] and several theoretical studies have been performed to aid in its interpretation [7,9–16]. The low-energy part of the gas phase spectrum shows a broad and asymmetric band in the region 5.0–6.5 eV, with a maximum near 5.5 eV [9]. The band is very diffuse but has some vibrational structure superimposed. Quantum dynamics simulations performed by Köppel et al. [14] suggest that the spectral shape is due to significant vibronic coupling among the lowest singlet excited states. Most of the band intensity can be attributed to transitions to two low-lying singlet states of pp⁄ character. Labelling the occupied valence p orbitals of thiophene in increasing order of energy as pi (i = 1, 2, 3) and the unoccupied as pi ði ¼ 4; 5Þ, the states of interest can be written as 1 p2 p4 and 1 p3 p4 . A schematic illustration of the relevant molecular orbitals is given in Fig. 1. E-mail address: [email protected] 0301-0104/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2011.12.004
The monomer form of thiophene (unlike its oligomers and polymers) is non-fluorescent [17], which points towards the existence of one or several efficient radiationless deactivation mechanisms. This hypothesis is supported by the time-resolved pump–probe experiment of Weinkauf et al. [18] carried out at an excitation wavelength of 238.4 nm (5.20 eV). The experimental data were found to be consistent with population and subsequent ultrafast decay of the lowest vibrational level of the 1 p2 p4 state. Based on electronic structure calculations performed by Salzmann et al. [16], a likely decay mechanism was suggested to be ring-opening via a dissociative 1 p3 rCS state, which forms a conical intersection (CI) with the closed shell ground state at large CS distances. The notion of CIs as means for radiationless and ultrafast deactivation of polyatomic molecules is by now well established in the literature (see for example Ref. [19] and references therein). In the particular case of thiophene, excited state decay by ring-opening has also been suggested in a recent study by Wu et al. [20] combining resonance Raman spectroscopy and electronic structure calculations. A somewhat different behavior was observed by Köppel et al. [14], who found the excited state population to oscillate between the 1 p2 p4 and 1 p3 p4 states on a femtosecond timescale. However, the model Hamiltonian employed in their simulations did not allow for dissociation via the 1 p3 rCS state to occur. The ring-opened type of CI is not unique for thiophene, but has also been characterized for related compounds such as furan [21], pyrrole [22] and imidazole [23]. Indeed, it can be considered as part of a much wider class of CIs taking place between states of
M. Stenrup / Chemical Physics 397 (2012) 18–25
pr⁄ character and the closed shell ground state [24]. As an example, the major deactivation pathway of pyrrole has been found to involve cleavage of the NH bond via a repulsive 1 prNH state [22,25]. A similar mechanism is note possible in thiophene. However, other types of CIs relevant for five-membered heterocycles can be formed by out-of-plane deformation of specific ring atoms [26]. In particular, CIs with a puckered heteroatom have been characterized for furan [27], pyrrole [22] and imidazole [23], and have been found to involve the closed shell ground state and a 1pp⁄ state analogous to the bright 1 p3 p4 state discussed above. The same type of CIs, as well as those with a puckered CH group, have been located for various kinds of substituted thiophenes [28] and must also exist for the parent compound itself. It is the aim of the present study to give a broader view of the photophysics of thiophene by considering ring-puckering, in addition to ring-opening, as a means for excited state depletion. Particular attention is focused on the decay processes following excitation into the first diffuse band of the UV spectrum and the role played by the singlet electronic states (denoted in energetic order as S0, S1, S2, etc.) in bringing these about. An additional goal is to provide an accurate set of geometries and energies that can be used to evaluate reduced computational models relevant to future molecular dynamics studies. The computational results presented in this paper have been obtained using the multi-state complete active space second-order perturbation theory (MS-CASPT2) and linear response coupled cluster (LR-CC) methods. The vertical electronic spectrum has been investigated in some detail and several minimum energy structures and CIs as well as the reaction paths connecting them have been characterized. Based on the results of these calculations, deactivation mechanisms for the lowest bright 1pp⁄ states of thiophene are proposed.
2. Computational details The study of the vertical electronic spectrum of thiophene was performed at the experimental equilibrium geometry of Bak et al. [29]. Excited state energies and oscillator strengths were calculated using the LR-CC singles (CCS), iterative approximate doubles (CC2), singles and doubles (CCSD), and non-iterative triples [CCSDR(3)] models [30–32]. In the latter case, transition dipole moments were not available and had to be taken from the corresponding CCSD calculation. The aug-cc-pVTZ basis set was used for the heavy atoms and cc-pVTZ for the hydrogen atoms. In order to properly describe Rydberg states, an auxiliary set of diffuse s and p functions was placed on the heavy atoms. The exponents of these basis functions were obtained by dividing those of the most diffuse aug-cc-pVTZ functions by three. The resulting basis set is referred to as aug-ccpVTZ+sp in the text. The convergence with respect to diffuse basis functions was examined at the CCSD level by placing an additional set of s and p functions or a set of d functions on the heavy atoms, or by changing the hydrogen basis from cc-pVTZ to aug-cc-pVTZ. In order to investigate the influence of the basis set size on the calculated quantities, a smaller double zeta basis of the aug-cc-pVDZ+sp type was also constructed. Unfortunately, an extension to quadruple zeta quality basis sets was not computationally feasible. All LR-CC calculations were carried out with the DALTON 2.0 package [33] using C2v symmetry restriction and frozen core orbitals. Relevant minimum energy structures and CIs were characterized at the MS-CASPT2 level [34–36] using a state-averaged complete active space self-consistent field (SA-CASSCF) wave function as reference. A single point calculation using this method was also carried out at the experimental equilibrium geometry in order to facilitate comparison with the LR-CC results. The active space in each case was composed of ten electrons distributed in eight orbitals. In addition to the p,p⁄ and rCS orbitals discussed above, a rCS
19
bonding and a rS non-bonding orbital were taken as active. The latter orbital was needed in order to avoid symmetry broken solutions at the SA-CASSCF level. Five electronic states were included in the state-averaging procedure and no symmetry constrains were imposed. In the correlation treatment, all core orbitals were kept doubly occupied and a level shift [37] of 0.2 a.u. as well as an IPEA shift [38] of 0.25 a.u. were employed. The 6-311G⁄ basis set was used throughout. Energy gradients were calculated numerically and used in the geometry optimizations. As an exception to this, the minimum energy CIs were located using the sequential penalty algorithm of Levine et al. [39], which requires neither gradients nor non-adiabatic couplings to be supplied. Transition dipole moments were computed from the perturbation modified CAS reference functions [36] and used to construct the corresponding oscillator strengths. The MS-CASPT2 calculations were performed with the MOLCAS 7.2 program [40]. Simplified reaction paths were constructed from a series of linear interpolations carried out between the optimized geometries. The interpolations connecting the ground state equilibrium geometry to the next structure along each reaction path were done in Cartesian coordinates, whereas all others were done in internal (Z-matrix) coordinates. This procedure was chosen to avoid certain energetically less favorable deformations of the geometry resulting if a single set of coordinates (Cartesian or internal) was used throughout. Potential energy profiles were initially calculated along the generated reaction paths using the MS-CASPT2 approach described above, but were found to be discontinuous at a few specific points. The most severe discontinuities could be traced back to the second-order perturbation treatment, and were thus not caused by singularities in the reference function itself. The potential energy profiles were subsequently re-calculated using the CCSD method and cc-pVTZ basis set. For technical reasons, these calculations were performed with the equation-of-motion (EOM) formulation of CCSD [41] as implemented in the MOLPRO 2010 package [42,43]. As far as electronic energies are concerned, this formulation is completely equivalent to LR-CC.
3. Results and discussion 3.1. Vertical electronic spectrum The vertical excitation energies and oscillator strengths of several low-lying singlet states of thiophene are collected in Table 1. The present results, obtained with the LR-CC and MS-CASPT2 methods at the experimental equilibrium geometry [29], are displayed along with some previous theoretical results for comparison. Four valence states are considered, which are primarily due to single excitations from the p2 and p3 to the p4 and rCS orbitals. Two Rydberg states involving excitations to a diffuse 3s orbital are included as well. These together were found to be the six lowest singlet excited states at all LR-CC levels. The CC2, CCSD and CCSDR(3) models even agree on the state order within this group, except for the order of the 1 p3 p4 and 1p33s states that is reversed at the CC2 level. It is noted that the changes in the excitation energies on going from CCSD to CCSDR(3) are rather small. At the same time, the corresponding wave functions are largely dominated by singly excited configurations (92–95%). Taken together, these findings indicate that the present CCSDR(3) results should be fairly well converged with respect to the excitation level and that the effects of including higher order excitations (e.g. iterative triples or quadruples) should be minor. The results of the basis set study are favorable as well. Addition of diffuse functions to the aug-cc-pVTZ+sp basis set led to negligible changes in the excitation energies, whereas the reduction of the basis set to double zeta quality led to changes on the order of 0.1 eV. The most profound
20
M. Stenrup / Chemical Physics 397 (2012) 18–25
Table 1 Vertical excitation energies (eV) and oscillator strengths (given in parentheses) of low-lying singlet states of thiophene. The present results were obtained at the LR-CC/aug-ccpVTZ+sp and MS-CASPT2/6-311G⁄ levels using the experimental equilibrium geometry [29]. The C2v symmetry designation of each state is indicated in the heading. Method
Present study CCS CC2 CCSD CCSDR(3) MS-CASPT2 Previous studies DFT/MRCIa NEVPT2b CCSDR(3)b ADC(2)c TDDFTd CASPT2d,e a b c d e
Ref. Ref. Ref. Ref. Ref.
21A1
11B2
1
1
p2 p4
p3 p4
11A2 1 p33s
11B1
21A2
1
1
p3 rCS (0.027) (0.015) (0.014) (0.013) (0.000)
p2 rCS
6.70 6.39 6.37 6.33 6.65
(0.000) (0.000) (0.000) (0.000) (0.000)
21B1 1 p23s
6.61 5.75 5.78 5.69 5.85
(0.122) (0.078) (0.076) (0.075) (0.067)
6.04 6.08 6.13 6.01 6.14
(0.075) (0.094) (0.077) (0.076) (0.109)
6.22 6.04 6.19 6.15
(0.000) (0.000) (0.000) (0.000)
6.58 6.18 6.33 6.23 6.57
6.81 6.45 6.53 6.49
(0.007) (0.000) (0.000) (0.000)
5.39 5.80 5.70 5.73 5.64 5.33
(0.114) (0.153) (0.082) (0.099) (0.058) (0.089)
5.54 6.14 6.10 6.09 5.65 5.72
(0.112) (0.107) (0.080) (0.129) (0.074) (0.070)
5.88 6.15 6.05 5.88 5.94 5.93
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
5.86 (0.004) 6.10 (0.004) 6.30 (0.015)
6.10 (0.000) 6.22 (0.000) 6.28 (0.000)
6.52 (0.001) 6.36 (0.002)
5.67 (0.005) 6.20 (0.002)
6.04 (0.000) 6.26 (0.000)
6.32 (0.002) 6.23 (0.000)
[16]. [15]. [14]. [11]. [10].
differences occurred for the two Rydberg states that were lowered in energy by 0.13 eV upon reducing the size of the basis set. Certainly, the effect of going from triple to quadruple zeta quality is expected to be smaller than this. The present CCSDR(3) results clearly suggest that the 1 p2 p4 and 1 p3 p4 states should be identified as S1 and S2, respectively, and that the transitions to these states are the only ones with considerable oscillator strengths. The same picture is obtained at the MS-CASPT2 level, although the excitation energies in this case are shifted upwards by approximately 0.15 eV compared to at the CCSDR(3) level. It is noted that the S1 state, in addition to the p2 p4 configuration, has minor contributions from a configuration of the p3 p5 type. Conversely, the S2 state is almost exclusively of p3 p4 character. In analyzing the higher excited states it should be recognized that diffuse functions are not included in the 6-311G⁄ basis set. A direct consequence is that the pair of 1p3s states is missing at the MS-CASPT2 level. More subtle effects occur for states that are primarily valence like in nature but which contain admixtures of Rydberg excitations. In particular, the two 1 prCS states have significant contributions from 3p and 3d Rydberg components [12,15,16]. The MSCASPT2 calculations accordingly overestimate the energies of these states with more than 0.3 eV in comparison with the CCSDR(3) results. Fortunately, this problem is not very severe in the present context because the 1pr⁄ states become important only at rather distorted geometries where the valence-Rydberg mixing anyway is small. A discussion of the present results in view of the measured absorption spectrum is postponed until Section 3.2, noting for the moment that the they are fully consistent with the interpretation of the spectrum put forward in Section 1. However, two comments concerning previous theoretical results are in order. As is evident from Table 1, the present CCSDR(3) results differ from those of Pastore et al. [15]. The deviations can only be due to basis set effects because the same equilibrium geometry was used in both studies. Unfortunately, an investigation of such effects was not presented in Ref. [15], which makes the exact origin of the deviations somewhat unclear. As can also be seen from Table 1, the 1pp⁄ excitation energies calculated by Serrano-Andrés et al. [10] using the CASTP2 method are significantly lower than those obtained at the present MS-CASPT2 level. Partly these differences should be due to the lack of diffuse functions in the 6-311G⁄ basis set, and partly due to the present use of the level shift technique and multi-state version of CASPT2, which were not available at the time of the earlier study.
3.2. Minimum energy structures and conical intersections The remainder of this paper will be concerned mainly with features of the S0–S2 potential energy surfaces (PESs) of thiophene, which should be sufficient to account for the decay of the lowest 1 pp⁄ states. Critical structures have been located on those surfaces using the MS-CASPT2 method and 6-311G⁄ basis set as already described. The resulting geometries are displayed in Fig. 2 and the Cartesian coordinates given in Table S1 in the Supplementary Material. The corresponding energies of the S0 through S2 states are collected in Table 2, where the dominant electronic configuration of each state is given as well. The global minimum of the S0 PES, which is referred to simply as S0 min, is taken as the zero of the energy scale. Note that the geometry of S0 min is in very good agreement with the experimental equilibrium geometry of Bak et al. [29]. The bond lengths differ by 0.007 Å and the bond angles by 0.5° at the most. The vertical excitation energies calculated at the optimized and experimental equilibrium geometries are also very similar (cf. Table 1). For completeness, the energies of the 1 p3 rCS and 1 p2 rCS states at S0 min (not shown in Table 2) are noted to be 6.50 and 6.58 eV, respectively. Two excited state minima have been located in this work, both on the S1 PES. One of these, denoted as S1 min-a, is associated with the p2 p4 electronic configuration. The corresponding geometry has approximate Cs symmetry with the S and H2 (H5) atoms displaced out of the molecular plane in the same direction. The promotion of an electron from p2 to p4 causes also a lengthening of the C2–C3 (C4–C5) and C2–S (C5–S) bonds with respect to S0 min. The absorption spectrum of thiophene shows a weak feature at 5.16 eV, which has been assigned as the 0–0 band of the S0 ! 1 p2 p4 transition [9].
Fig. 1. Schematic illustration of the structure and relevant molecular orbitals of thiophene. The atomic numbering used in the present work is shown as well.
21
M. Stenrup / Chemical Physics 397 (2012) 18–25
Table 2 Energies (eV) and dominant electronic configurations (characters) of the S0–S2 states of thiophene at various optimized geometries. The calculations were performed using the MS-CASPT2 method and 6-311G⁄ basis set. The energies are given relative to the energy of S0 min. CS denotes the closed shell electronic configuration. Structure
S0 Energy
S1 Character
Energy
S0 min S1 min-a S1 min-b
0.00 1.40 3.69
CS CS CS
5.82 5.12 4.20
S1 TS S1/S2 CI S0/S1 CI-a
1.76 0.96 4.26
CS CS CS
5.22 5.53 4.26
S0/S1 CI-b S0/S1 CI-c
4.61 4.97
CS CS
4.61 4.97
S2 Character 4 4 CS
p2 p p2 p p3 r p3 p4 p2 p4 p3 rCS p3 p4 p3 p4
Energy
Character
6.10 6.46 6.21
p3 p4 p3 p4 2 ðp3 Þ0 rCS p2 p4 p3 p4 2 ðp3 Þ0 rCS p3 p5 p2 p4
6.03 5.53 6.17 7.50 7.63
The adiabatic excitation energy obtained in the present work, i.e., the energy of S1 min-a relative to that of S0 min, deviate from the measured 0–0 energy by only 0.04 eV (zero-point corrections not included). Good agreement is also found with the adiabatic excitation energy and geometry reported by Salzmann et al. [16], which were obtained using a combination of the time-dependent density functional theory (TDDFT) and density functional/multireference configuration interaction (DFT/MRCI) methods. The other excited state minimum located in this work, denoted as S1 min-b, is associated with the p3 rCS electronic configuration and has a planar Cs geometry with an almost completely broken
7.0 Electronic energy (eV)
Fig. 2. Optimized geometries of thiophene as obtained with the MS-CASPT2 method and 6-311G⁄ basis set. The heavy atom bond lengths (Å) are indicated in the figure. In the case of non-planar geometries, the most important torsion angles are also shown.
C5–S bond. The inter-chain bond lengths are consistent with a diradical species possessing C2–S and C4–C5 double bonds and unpaired electrons at C3 and C5. Notably, the adiabatic excitation energy of this structure is more than 2 eV lower than the vertical excitation energy of the 1 p3 rCS state. Most geometrical parameters are in reasonable agreement with those reported by Salzmann et al. [16], although the respective C5–S distances differ by 0.35 Å. A deviation of this size is perhaps not surprising considering that the rCS and rCS orbitals are practically non-bonding in the vicinity of S1 min-b. Because of a very unfavorable Franck–Condon overlap, direct comparison of the calculated adiabatic excitation energy with the measured absorption spectrum is not possible. However, an energy difference of 0.39 eV is noted compared to the computational results of Ref. [16]. Despite considerable efforts, a potential energy minimum associated with the p3 p4 electronic configuration could not be found, although such a minimum was reported by Salzmann et al. [16]. At the present level of theory, a structure geometrically similar to that in Ref. [16] was located only after initializing a transition state (TS) search on the S1 PES. The structure in question, denoted as S1 TS, is of approximate Cs symmetry and has the S atom brought out of the plane in one direction and H2 (H5) in the other. A substantial lengthening of the C2–C3 (C4–C5) bond and a shortening of the C3–C4 bond are also observed with respect to S0 min. The energy of S1 TS is only slightly higher than that of S1 min-a. A numerical evaluation of the Hessian confirmed the presence of one imaginary frequency (i1927 cm1). The corresponding normal mode is a combination of asymmetric CS stretch and CH bend. It is recognized that the calculation of numerical Hessians at the MS-CASPT2 level could potentially lead to large errors. To this end, a PES scan along the imaginary frequency normal mode of S1 TS is displayed in Fig. 3. The shape of the S1 potential energy profile firmly establish S1 TS as a saddle point at the present level of theory. To investigate this matter further, the same structure was also characterized using the CCSD method and aug-cc-pVDZ+sp basis set. The imaginary frequency obtained at this level is substantially smaller (i354 cm1) and some of the CH bending is damped out in the corresponding normal mode. The saddle point nature of S1 TS is nevertheless confirmed. It appears that the 0–0 band of the S0 ! 1 p3 p4 transition has not been identified in the measured absorption spectrum. However, a group of peaks in the region 5.05–5.15 eV were proposed by Weinkauf et al. [18] to be due to transitions into excited levels of the 1 p3 p4 state. Such an interpretation is apparently not consistent with the present results, which suggest that the p3 p4 branch of the S1 PES supports no bound states. A more extensive theoretical investigation, paying
6.0 5.0 4.0 3.0 2.0 1.0 −0.50
−0.25
0.00
0.25
Displacement (amu
0.50
1/2
Å)
Fig. 3. Potential energy profiles of the S0–S2 states of thiophene along the imaginary frequency normal mode of S1 TS. The calculations were performed using the MSCASPT2 method and 6-311G⁄ basis set. The displacement is given with respect to the optimized S1 TS geometry.
M. Stenrup / Chemical Physics 397 (2012) 18–25
3.3. Radiationless deactivation pathways A number of deactivation pathways can be deduced from the energetic and structural data presented in the previous section. The following discussion aims at identifying the most important of these and characterize them in some detail. To facilitate this goal, a series of one dimensional cuts through the S0–S2 PESs along selected reaction coordinates are displayed in Figs. 4 and 5. The potential energy profiles were obtained at the CCSD/cc-pVTZ level and the reaction coordinates generated by linear interpolation between the MS-CASPT2 optimized geometries. The single-reference based CCSD method has previously been used in a similar study on
Electronic energy (eV)
a
S0 min S1 min−a 8.0 π3π4*
S1 min−b
S0/S1 CI−a
6.0 π2π4*
π3σCS*
4.0 2.0
0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
b Electronic energy (eV)
particular attention to the interaction of the S1 state with the neighboring S2 state, may be required to clarify this point. Inspection of Table 2 reveals that the characters of the S1 and S2 states (p2 p4 and p3 p4 ) are exchanged on going from S0 min to S1 TS. A crossing between the corresponding PESs must therefore take place. The search for such a crossing resulted in the minimum energy CI denoted as S1/S2 CI. The geometry of this structure resembles in many respects a less symmetric version of S1 TS, but with the H2 and H5 atoms kept closer to the molecular plane. The crossing takes place energetically below both of the vertically excited 1 pp⁄ states. The work of Salzmann et al. [16] do not include any optimized CIs for comparison. However, Wu et al. [20] have located several excited state structures at the CASSCF level, among them a CI involving the two 1pp⁄ states. The geometry reported in that work appears substantially more distorted than the present one, but some similarities can also be found. The observed differences should at least partly be due to an inability of the CASSCF method to treat the (covalent) 1 p2 p4 and (zwitterionic) 1 p3 p4 states in a balanced way. The remaining minimum energy CIs considered in this work all belong to the S0/S1 crossing seam. The structure denoted as S0/S1 CI-a corresponds to the ring-opened CI discussed in Section 1. It is associated with a crossing of the 1 p3 rCS and ground state PESs, and is geometrically almost identical to the ring-opened species S1 min-b, but distinguished by an even larger C5–S distance. The CI is of the symmetry allowed type since the participating states belong to different irreducible representations of the Cs point group. Energetically, it takes place only 0.06 eV above S1 min-b, and is accordingly situated far below the vertically excited 1pp⁄ states. Salzmann et al. [16] provide an estimate of the CI energy that is a few tenths of an eV lower than obtained in the present work, whereas the approximate C5–S distance quoted in their paper is practically identical with the present one. The structures referred to as S0/S1 CI-b and CI-c are both associated with intersections of the 1 p3 p4 and ground state PESs. The corresponding geometries are characterized by puckering at different sites of the heavy atom framework. In the case of S0/S1 CI-b, the puckering is mainly concentrated to the S atom. The out-of-plane deformation is accompanied by substantial lengthening of the C5–S, C2–C3 and C4–C5 bonds, as well as asymmetric twisting of the C2–H2 and C5–H5 bonds with respect to S0 min. The geometry of S0/S1 CI-c shows puckering almost exclusively at the C2 site, but also in this case the out-of-plane deformation is associated with asymmetric ring-expansion and hydrogen twist. The structural deformations described above cause a partial decoupling of the p3 and p4 orbitals to take place, which tend to stabilize the 1 p3 p4 state and destabilize the ground state [26]. As a consequence, the ring-puckered CIs appear significantly below the vertically excited 1pp⁄ states, although not as low as the ring-opened CI. Out-of-plane deformation at the S site is energetically somewhat more favorable than at C2. The ring-puckered CIs characterized in this work are qualitatively similar to those reported for various substituted thiophenes [28].
S0 min 8.0
c
S1 min−a
S0/S1 CI−b
π3π4* 6.0 π2π4*
π3π4*
4.0 2.0 0.0 0.0
Electronic energy (eV)
22
0.1
S0 min 8.0
0.2
0.3
0.4
S1 min−a
S0/S1 CI−c
π3π4* 6.0
π3π4*
π2π4* 4.0 2.0 0.0 0.0
0.1
0.2
0.3
Displacement (amu
0.4
0.5
1/2
Å)
Fig. 4. Cuts through the S0–S2 PESs of thiophene along reaction paths leading to radiationless deactivation of the 1 p2 p4 state; (a) ring-opening pathway; (b) ringpuckering pathway, deformation at the S site; (c) ring-puckering pathway, deformation at the C2 site. The energy calculations were carried out using the CCSD method and cc-pVTZ basis set, and the reaction coordinates generated by linear interpolation between the MS-CASPT2 optimized geometries. The positions of relevant minimum energy structures and CIs as well as the dominant electronic configurations are indicated along each path.
the deactivation pathways of furan [27], and was found give energies of surprisingly good quality even in situations of nearly degenerate S0 and S1 states. The small energy gaps that can be observed at some of the CI points in Figs. 4 and 5 result since the geometry and energy calculations were carried out at different levels. For the same reason, the positions of some crossings appear slightly shifted relative to the expected ones. However, the main purpose of the PES diagrams is to give only a qualitative picture of the various reaction paths. With the exception of some barrier heights, all relevant numbers will be extracted from the MS-CASPT2 results. The deactivation mechanisms proposed in the present work are schematically illustrated in Fig. 6. Assume first that the system is vertically excited from the S0 to the S1 PES. The S1 state is primarily of p2 p4 character and the initial motion after excitation should be directed from the Franck–Condon region towards the minimum energy structure S1 min-a, which is associated with the same electronic configuration. The relaxation process is accompanied by an energy release of 0.70 eV and is expected to be barrierless, as is indicated also by the appearance of the potential energy profiles in Fig. 4. The present results now suggest three different deactivation pathways
M. Stenrup / Chemical Physics 397 (2012) 18–25
Electronic energy (eV)
a
S0 min 8.0 6.0
S1/S2 CI
S1 min−b
S0/S1 CI−a
π3π4* π2π4*
π3σCS*
4.0 2.0
0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Electronic energy (eV)
b
S0 min 8.0
S1/S2 CI π 3 π4 *
6.0
π 2 π4 *
Electronic energy (eV)
π3π4*
4.0 2.0 0.0 0.0
c
S0/S1 CI−b
0.1
S0 min 8.0 6.0
0.2
0.3
S1/S2 CI
S0/S1 CI−c
π 3 π4 * π3π4*
π2π4* 4.0 2.0 0.0 0.0
0.1
0.2
0.3
Displacement (amu
1/2
0.4 Å)
Fig. 5. Cuts through the S0–S2 PESs of thiophene along reaction paths leading to radiationless deactivation of the 1 p3 p4 state; (a) ring-opening pathway; (b) ringpuckering pathway, deformation at the S site; (c) ring-puckering pathway, deformation at the C2 site. The energy calculations were carried out using the CCSD method and cc-pVTZ basis set, and the reaction coordinates generated by linear interpolation between the MS-CASPT2 optimized geometries. The positions of relevant minimum energy structures and CIs as well as the dominant electronic configurations are indicated along each path.
leading away from S1 min-a. One of these corresponds to the ringopening pathway described by Salzmann et al. [16], and proceeds from S1 min-a to S1 min-b, and subsequently from S1 min-b to
23
S0/S1 CI-a. The formation of the ring-opened species S1 min-b is associated with an energy release of 0.92 eV relative to S1 min-a. During this reaction step, the character of the S1 state is changed from p2 p4 to p3 rCS , which can be understood as a consequence of an avoided crossing taking place between the S1 and S2 PESs. The lower ‘‘cone’’ of this crossing becomes the transition state separating the two minima, as shown in Fig. 4a. From the present CCSD results, the corresponding barrier height is estimated to be 0.26 eV with respect to S1 min-a. This value is most likely an upper limit for the real one since the transition state was not strictly optimized. The final part of the ring-opening pathway, going from S1 min-b to S0/S1 CI-a, involves only a small destabilization of the S1 state by 0.06 eV. In addition, the corresponding geometries are very similar. It is therefore reasonable to assume that the rate-limiting step for the overall process is the passage from S1 min-a to S1 min-b, and once the barrier separating these minima has been passed, deactivation to the electronic ground state can occur with high efficiency. As an alternative means of going from S1 min-a to the electronic ground state, consider now the ring-puckered intersections S0/S1 CI-b and CI-c, which are formed by out-of-plane deformations at the S and C2 sites, respectively. The former CI is situated 0.51 eV and the latter 0.15 eV below S1 min-a. Proceeding from the excited state minimum towards any of these CIs leads to a change of character of the S1 state from p2 p4 to p3 p4 . The character change in each case is associated with an avoided crossing of the S1 and S2 states, as well as a barrier emerging on the S1 PES. The absence of a minimum energy structure possessing the p3 p4 electronic configuration suggest that the barriers link S1 min-a directly to the S0/ S1 crossing seam. The situation is illustrated by the potential energy profiles in Fig. 4b and c. The barrier heights for puckering at the S and C2 sites are estimated to be 0.54 and 0.45 eV, respectively. These values are approximately twice as large as the barrier height for ring-opening. The present results thus favor ring-opening as the major deactivation channel after excitation to the bright 1 p2 p4 state, with perhaps smaller contributions coming from the two ring-puckering pathways. It is noted again, however, that these conclusions are based only on very rough estimates of the relevant barrier heights. They also assume that the excess energy being released at S1 min-a is redistributed over many vibrational modes; that is, the system behaves to some extent statistically. In the time-resolved pump–probe experiment of Weinkauf et al. [18], the decay of the lowest vibrational level of the 1 p2 p4 state was found to be characterized by two time constants of 25 and 80 fs. The larger of these two was associated with the vibrational motion in the 1 p2 p4 state itself, and the smaller with the formation of the ring-opened diradical species. Although the modeling done
Fig. 6. Schematic illustration of proposed radiationless deactivation mechanisms of thiophene. Deactivation pathways originating from the 1 p2 p4 and 1 p3 p4 states are represented by red and blue arrows, respectively. Potential energy profiles are drawn for the states S0 through S2. The dotted line indicates the Franck–Condon point and the dashed curve the S1 PES along an alternative reaction coordinate. Relevant geometries and electronic configurations are indicated as well. (For interpretation of the references in colour in this figure legend, the reader is referred to the web version of this article.)
24
M. Stenrup / Chemical Physics 397 (2012) 18–25
by those authors did not include the ring-puckering pathways explicitly, the proposal of ring-opening as a primary deactivation channel is nevertheless in line with the present findings. Notably, Salzmann et al. [16] from their calculations estimate the barrier height for ring-opening to be as low as 0.04 eV. This further supports the notion that the true barrier height is smaller than that found in the present work. A quite different picture emerges if a vertical transition to the S2 state is assumed. In particular, consider the two deactivation pathways connecting the vertically excited S2 state to the ring-puckered intersections S0/S1 CI-b and CI-c via a radiationless transition at S1/S2 CI. The initial reaction step in each case is exoergic by 0.57 eV and the final by 0.92 or 0.56 eV depending on if the puckering takes place at the S or C2 sites, respectively. The two pathways are direct in the sense that no intermediates are involved. In addition, they both preserve the p3 p4 character of the initially populated state (i.e., they are diabatic). Taken together, these facts raise the possibility of a more or less barrierless connection between the vertically excited S2 state and the electronic ground state. The potential energy profiles to help explore this idea are displayed in Fig. 5b and c. The situation is somewhat complicated by the fact that the S1 and S2 PESs do not exactly coincide at the optimized S1/S2 CI point. Nevertheless, the overall behavior of these profiles is consistent with the pathways indeed being barrierless. The significance of the two direct mechanisms can be further appreciated by exploring the connection to the transition state structure S1 TS. Although this structure is technically a saddle point on the p3 p4 branch of the S1 PES, it is at the same time a minimum in all but one coordinates. The geometrical similarities between S1 TS and S1/S2 CI noted in Section 3.2 thus suggest the existence of a favorable energy gradient pointing from the Franck–Condon region towards the latter structure. This should tend to focus the population in the direction of the crossing point during the initial part of the photodynamics. Interestingly, the only coordinate along which S1 TS is not a minimum is made up of several of those vibrational modes expected to reach S0/S1 CI-b. In particular, this involves the lengthening of the C5–S bond, the shortening of the C2–S bond, and the asymmetric twisting of the C5–H5 and C2–H2 bonds. It appears as if this CI is a particularly low-lying structure possessing the p3 p4 electronic configuration. The information presented so far indicates that the direct pathways of thiophene provide two efficient channels for deactivation of the bright S2 state. Out-of-plane deformation at the sulfur atom appears to be particularly favorable in this respect. Nevertheless, it is of interest to speculate whether also other deactivation pathways might be important after excitation to the S2 state. Among others, the ring-opened structure S1 min-b could be reached from the vertically excited S2 state via a radiationless transition at S1/ S2 CI. Deactivation to the ground state would then be possible via S0/S1 CI-a as described before. However, in passing from S1/S2 CI to S1 min-b the character of the S1 state has to be changed from p3 p4 to p3 rCS , which should require an energy barrier on the S1 PES to be traversed. That this is the case is confirmed by the behavior of the potential energy profiles shown in Fig. 5a, which reveals a small energy barrier situated at 0.25 amu1/2 Å along the reaction path. In principle, the necessary change of character from p3 p4 to p3 rCS could also take place directly in the S2 state and be followed by a diabatic type of relaxation to S1 min-b. Unfortunately, however, a more detailed investigation of this possibility was hampered by difficulties in locating the relevant excited state crossing point. As yet another alternative, ring-opening could result if the decay at S1/S2 CI is followed by relaxation to S1 min-a, in which case the available deactivation pathways should resemble those previously discussed in connection with excitation to the S1 state. Although the occurrence of ring-opening thus cannot be excluded based on the present results, the diabatic, and presumably
barrierless, character of the direct pathways are clear factors speaking in favor of them. Moreover, if the decay of the 1 p3 p4 state do occur via any of those pathways, it is likely to be very fast (i.e., take place on a femtosecond timescale). These ideas are in line with a recent study by Fuji et al. [44] indicating that the analogous 1 p3 p4 state of furan deactivates by ring-puckering to the ground state within 60 fs. Before concluding this paper, the possible role played by triplet electronic states in the non-radiative decay of thiophene should be considered briefly. Deactivation via triplet states was investigated in Refs. [16,18] as an alternative explanation for the observed ultrafast depletion of the 1 p2 p4 state. A mechanism involving population transfer to the p3 p4 branch of the S1 PES followed by intersystem crossing to the second triplet excited (T2) state was examined in particular. However, although this pathway was not ruled out completely, it was regarded as less likely. The participation of a triplet mechanism appears even more doubtful in view of the present findings. This is so since the intersystem crossing has to compete not only with deactivation by ring-opening as suggested earlier, but also by ring-puckering. Thus, even if one of the singlet decay channels are temporarily blocked, fast deactivation via the others may still be possible. In particular, an excited state population residing on the p3 p4 branch of the S1 PES is likely to be removed through the ring-puckered CIs considerably before conversion to T2 can occur. The present results thus support the hypothesis that photo-excited thiophene decays primarily via its singlet electronic states, and that this is the main reason for the observed lack of fluorescence.
4. Conclusions This paper has considered the radiationless deactivation mechanisms of thiophene with particular emphasis on the decay processes following excitation into the first diffuse band of its UV absorption spectrum. The analysis has been based on computational results obtained with multi-reference second-order perturbation theory and coupled cluster based methods. An extensive set of calculations has been carried out to establish the vertical transition energies and order of the lowest singlet excited states. With some confidence, the first and second of these can be identified as the 1 p2 p4 and 1 p3 p4 states, respectively. The corresponding transitions from the electronic ground state both have appreciable oscillator strengths and should be the main sources of intensity of the first absorption band. Several minimum energy structures and CIs involving the S0 through S2 states have been characterized in order to identify the relevant decay mechanisms. In particular, three low-lying CIs of the S0/S1 type have been located. One of these is a planar ringopened structure with an almost completely broken C5–S bond, and involves the 1 p3 rCS state and the closed shell ground state. The other two are ring-puckered structures formed by out-of-plane deformations at the S or C2 sites, and involve the 1 p3 p4 state and the closed shell ground state. The deactivation mechanisms proposed in this paper can be summarized as follows. If the excitation is to the S1 state, relaxation to a local minimum on the S1 PES should follow promptly. From this point, the system can either relax to a second minimum on the same PES and deactivate through the ring-opened CI situated nearby, or proceed to and deactivate through any of the ring-puckered CIs. Each of these pathways involves a change of character of the S1 state from p2 p4 to p3 rCS or p3 p4 , and requires an associated energy barrier on the S1 PES to be traversed. A rough estimate of the corresponding barrier heights suggests that the ring-opening pathway is the major deactivation channel after excitation to the S1 state, which is consistent with previous theoretical
M. Stenrup / Chemical Physics 397 (2012) 18–25
and experimental findings. If, on the other hand, the excitation is to the S2 state, the two ring-puckered CIs can be directly reached via a CI of the S1/S2 type. No intermediates are involved and the p3 p4 character of the initially populated state is retained throughout. Moreover, these pathways are presumably free of barriers and subject to favorable energy gradients. Although additional decay channels cannot be excluded for the S2 state, deactivation by ring-puckering is likely to be a significant process. In conclusion, it appears that the mechanisms outlined above make possible efficient radiationless deactivation throughout the entire first absorption band of thiophene. As such, they are good candidates to explain why this compound is non-fluorescent. A more detailed understanding of the relevant processes may require dynamics simulations to be carried out. In addition to information on what deactivation pathways are the most important, and what are the associated time scales, such simulations could also provide insights into the photochemical events being initiated once the electronic ground state has been reached. A study along these lines, focusing to begin with on the dynamics starting in the 1 p2 p4 state, is currently undertaken and the results will be published elsewhere. Note added in proof After this manuscript was submitted for publication, Cui and Fang [45] reported on a mixed quantum-classical dynamics study of the radiationless deactivation of thiophene. The results of that study support the hypothesis that excitation to the first singlet excited state is followed by ring-opening on a femtosecond timescale. Acknowledgements The author is grateful to Å. Larson for useful discussions and comments on the manuscript. Fig. 2 was partly prepared using the XYZViewer program written by S. de Marothy. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.chemphys.2011.12.004. References [1] T. Eicher, S. Hauptmann, The Chemistry of Heterocycles: Structures, Reactions, Syntheses, and Applications, second ed., Wiley-VCH GmbH & Co. KGaA, Weinheim, Germany, 2003. [2] G. Barbarella, M. Melucci, G. Sotgiu, Adv. Mater. 17 (2005) 1581. [3] A.C. Grimsdale, K.L. Chan, R.E. Martin, P.G. Jokisz, A.B. Holmes, Chem. Rev. 109 (2009) 897. [4] M. Zambianchi, F.D. Maria, A. Cazzato, G. Gigli, M. Piacenza, F.D. Sala, G. Barbarella, J. Am. Chem. Soc. 131 (2009) 10892.
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Theoretical study of the radiationless deactivation mechanisms of photo-excited thiophene M. Stenrup Department of Physics, Stockholm University, AlbaNova University Center, SE-106 91 Stockholm, Sweden
a r t i c l e
i n f o
Article history: Received 12 August 2011 In final form 7 December 2011 Available online 23 December 2011 Keywords: Radiationless deactivation Conical intersections Heterocyclic compounds Photophysics
a b s t r a c t The radiationless deactivation mechanisms of photo-excited thiophene have been studied using the multi-reference second-order perturbation theory and linear response coupled cluster methods. The electronic spectrum has been established and various minimum energy structures and conical intersections involving the ground and lowest singlet excited states have been characterized. Simplified reaction paths connecting the optimized geometries have been calculated as well. Based on these investigations, several deactivation mechanisms have been identified leading from the lowest bright 1pp⁄ states back to the electronic ground state. The excited state depletion in each case is possible due to the existence of low-lying conical intersections formed by either cleavage of one of the CS bonds or out-of-plane deformations of the aromatic ring. The deactivation mechanisms suggested in this work should provide some very efficient decay channels after excitation into the first UV absorption band of thiophene, and are good candidates to explain why this compound is non-fluorescent. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Thiophene belongs to the class of five-membered aromatic heterocyclic compounds [1]. It occurs sporadically in nature (e.g., in certain plants) and has found widespread use in areas ranging from pharmaceutical to material sciences. The photophysical properties of thiophene based materials are utilized in a variety of different applications [2]. In particular, recent interest has been focused on the incorporation of thiophene units into light emitting devices [3], biological labels [4], and dye-sensitized [5] as well as polymer-based [6] organic solar cells. The UV absorption spectrum of thiophene has been measured under various conditions [7–9] and several theoretical studies have been performed to aid in its interpretation [7,9–16]. The low-energy part of the gas phase spectrum shows a broad and asymmetric band in the region 5.0–6.5 eV, with a maximum near 5.5 eV [9]. The band is very diffuse but has some vibrational structure superimposed. Quantum dynamics simulations performed by Köppel et al. [14] suggest that the spectral shape is due to significant vibronic coupling among the lowest singlet excited states. Most of the band intensity can be attributed to transitions to two low-lying singlet states of pp⁄ character. Labelling the occupied valence p orbitals of thiophene in increasing order of energy as pi (i = 1, 2, 3) and the unoccupied as pi ði ¼ 4; 5Þ, the states of interest can be written as 1 p2 p4 and 1 p3 p4 . A schematic illustration of the relevant molecular orbitals is given in Fig. 1. E-mail address: [email protected] 0301-0104/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2011.12.004
The monomer form of thiophene (unlike its oligomers and polymers) is non-fluorescent [17], which points towards the existence of one or several efficient radiationless deactivation mechanisms. This hypothesis is supported by the time-resolved pump–probe experiment of Weinkauf et al. [18] carried out at an excitation wavelength of 238.4 nm (5.20 eV). The experimental data were found to be consistent with population and subsequent ultrafast decay of the lowest vibrational level of the 1 p2 p4 state. Based on electronic structure calculations performed by Salzmann et al. [16], a likely decay mechanism was suggested to be ring-opening via a dissociative 1 p3 rCS state, which forms a conical intersection (CI) with the closed shell ground state at large CS distances. The notion of CIs as means for radiationless and ultrafast deactivation of polyatomic molecules is by now well established in the literature (see for example Ref. [19] and references therein). In the particular case of thiophene, excited state decay by ring-opening has also been suggested in a recent study by Wu et al. [20] combining resonance Raman spectroscopy and electronic structure calculations. A somewhat different behavior was observed by Köppel et al. [14], who found the excited state population to oscillate between the 1 p2 p4 and 1 p3 p4 states on a femtosecond timescale. However, the model Hamiltonian employed in their simulations did not allow for dissociation via the 1 p3 rCS state to occur. The ring-opened type of CI is not unique for thiophene, but has also been characterized for related compounds such as furan [21], pyrrole [22] and imidazole [23]. Indeed, it can be considered as part of a much wider class of CIs taking place between states of
M. Stenrup / Chemical Physics 397 (2012) 18–25
pr⁄ character and the closed shell ground state [24]. As an example, the major deactivation pathway of pyrrole has been found to involve cleavage of the NH bond via a repulsive 1 prNH state [22,25]. A similar mechanism is note possible in thiophene. However, other types of CIs relevant for five-membered heterocycles can be formed by out-of-plane deformation of specific ring atoms [26]. In particular, CIs with a puckered heteroatom have been characterized for furan [27], pyrrole [22] and imidazole [23], and have been found to involve the closed shell ground state and a 1pp⁄ state analogous to the bright 1 p3 p4 state discussed above. The same type of CIs, as well as those with a puckered CH group, have been located for various kinds of substituted thiophenes [28] and must also exist for the parent compound itself. It is the aim of the present study to give a broader view of the photophysics of thiophene by considering ring-puckering, in addition to ring-opening, as a means for excited state depletion. Particular attention is focused on the decay processes following excitation into the first diffuse band of the UV spectrum and the role played by the singlet electronic states (denoted in energetic order as S0, S1, S2, etc.) in bringing these about. An additional goal is to provide an accurate set of geometries and energies that can be used to evaluate reduced computational models relevant to future molecular dynamics studies. The computational results presented in this paper have been obtained using the multi-state complete active space second-order perturbation theory (MS-CASPT2) and linear response coupled cluster (LR-CC) methods. The vertical electronic spectrum has been investigated in some detail and several minimum energy structures and CIs as well as the reaction paths connecting them have been characterized. Based on the results of these calculations, deactivation mechanisms for the lowest bright 1pp⁄ states of thiophene are proposed.
2. Computational details The study of the vertical electronic spectrum of thiophene was performed at the experimental equilibrium geometry of Bak et al. [29]. Excited state energies and oscillator strengths were calculated using the LR-CC singles (CCS), iterative approximate doubles (CC2), singles and doubles (CCSD), and non-iterative triples [CCSDR(3)] models [30–32]. In the latter case, transition dipole moments were not available and had to be taken from the corresponding CCSD calculation. The aug-cc-pVTZ basis set was used for the heavy atoms and cc-pVTZ for the hydrogen atoms. In order to properly describe Rydberg states, an auxiliary set of diffuse s and p functions was placed on the heavy atoms. The exponents of these basis functions were obtained by dividing those of the most diffuse aug-cc-pVTZ functions by three. The resulting basis set is referred to as aug-ccpVTZ+sp in the text. The convergence with respect to diffuse basis functions was examined at the CCSD level by placing an additional set of s and p functions or a set of d functions on the heavy atoms, or by changing the hydrogen basis from cc-pVTZ to aug-cc-pVTZ. In order to investigate the influence of the basis set size on the calculated quantities, a smaller double zeta basis of the aug-cc-pVDZ+sp type was also constructed. Unfortunately, an extension to quadruple zeta quality basis sets was not computationally feasible. All LR-CC calculations were carried out with the DALTON 2.0 package [33] using C2v symmetry restriction and frozen core orbitals. Relevant minimum energy structures and CIs were characterized at the MS-CASPT2 level [34–36] using a state-averaged complete active space self-consistent field (SA-CASSCF) wave function as reference. A single point calculation using this method was also carried out at the experimental equilibrium geometry in order to facilitate comparison with the LR-CC results. The active space in each case was composed of ten electrons distributed in eight orbitals. In addition to the p,p⁄ and rCS orbitals discussed above, a rCS
19
bonding and a rS non-bonding orbital were taken as active. The latter orbital was needed in order to avoid symmetry broken solutions at the SA-CASSCF level. Five electronic states were included in the state-averaging procedure and no symmetry constrains were imposed. In the correlation treatment, all core orbitals were kept doubly occupied and a level shift [37] of 0.2 a.u. as well as an IPEA shift [38] of 0.25 a.u. were employed. The 6-311G⁄ basis set was used throughout. Energy gradients were calculated numerically and used in the geometry optimizations. As an exception to this, the minimum energy CIs were located using the sequential penalty algorithm of Levine et al. [39], which requires neither gradients nor non-adiabatic couplings to be supplied. Transition dipole moments were computed from the perturbation modified CAS reference functions [36] and used to construct the corresponding oscillator strengths. The MS-CASPT2 calculations were performed with the MOLCAS 7.2 program [40]. Simplified reaction paths were constructed from a series of linear interpolations carried out between the optimized geometries. The interpolations connecting the ground state equilibrium geometry to the next structure along each reaction path were done in Cartesian coordinates, whereas all others were done in internal (Z-matrix) coordinates. This procedure was chosen to avoid certain energetically less favorable deformations of the geometry resulting if a single set of coordinates (Cartesian or internal) was used throughout. Potential energy profiles were initially calculated along the generated reaction paths using the MS-CASPT2 approach described above, but were found to be discontinuous at a few specific points. The most severe discontinuities could be traced back to the second-order perturbation treatment, and were thus not caused by singularities in the reference function itself. The potential energy profiles were subsequently re-calculated using the CCSD method and cc-pVTZ basis set. For technical reasons, these calculations were performed with the equation-of-motion (EOM) formulation of CCSD [41] as implemented in the MOLPRO 2010 package [42,43]. As far as electronic energies are concerned, this formulation is completely equivalent to LR-CC.
3. Results and discussion 3.1. Vertical electronic spectrum The vertical excitation energies and oscillator strengths of several low-lying singlet states of thiophene are collected in Table 1. The present results, obtained with the LR-CC and MS-CASPT2 methods at the experimental equilibrium geometry [29], are displayed along with some previous theoretical results for comparison. Four valence states are considered, which are primarily due to single excitations from the p2 and p3 to the p4 and rCS orbitals. Two Rydberg states involving excitations to a diffuse 3s orbital are included as well. These together were found to be the six lowest singlet excited states at all LR-CC levels. The CC2, CCSD and CCSDR(3) models even agree on the state order within this group, except for the order of the 1 p3 p4 and 1p33s states that is reversed at the CC2 level. It is noted that the changes in the excitation energies on going from CCSD to CCSDR(3) are rather small. At the same time, the corresponding wave functions are largely dominated by singly excited configurations (92–95%). Taken together, these findings indicate that the present CCSDR(3) results should be fairly well converged with respect to the excitation level and that the effects of including higher order excitations (e.g. iterative triples or quadruples) should be minor. The results of the basis set study are favorable as well. Addition of diffuse functions to the aug-cc-pVTZ+sp basis set led to negligible changes in the excitation energies, whereas the reduction of the basis set to double zeta quality led to changes on the order of 0.1 eV. The most profound
20
M. Stenrup / Chemical Physics 397 (2012) 18–25
Table 1 Vertical excitation energies (eV) and oscillator strengths (given in parentheses) of low-lying singlet states of thiophene. The present results were obtained at the LR-CC/aug-ccpVTZ+sp and MS-CASPT2/6-311G⁄ levels using the experimental equilibrium geometry [29]. The C2v symmetry designation of each state is indicated in the heading. Method
Present study CCS CC2 CCSD CCSDR(3) MS-CASPT2 Previous studies DFT/MRCIa NEVPT2b CCSDR(3)b ADC(2)c TDDFTd CASPT2d,e a b c d e
Ref. Ref. Ref. Ref. Ref.
21A1
11B2
1
1
p2 p4
p3 p4
11A2 1 p33s
11B1
21A2
1
1
p3 rCS (0.027) (0.015) (0.014) (0.013) (0.000)
p2 rCS
6.70 6.39 6.37 6.33 6.65
(0.000) (0.000) (0.000) (0.000) (0.000)
21B1 1 p23s
6.61 5.75 5.78 5.69 5.85
(0.122) (0.078) (0.076) (0.075) (0.067)
6.04 6.08 6.13 6.01 6.14
(0.075) (0.094) (0.077) (0.076) (0.109)
6.22 6.04 6.19 6.15
(0.000) (0.000) (0.000) (0.000)
6.58 6.18 6.33 6.23 6.57
6.81 6.45 6.53 6.49
(0.007) (0.000) (0.000) (0.000)
5.39 5.80 5.70 5.73 5.64 5.33
(0.114) (0.153) (0.082) (0.099) (0.058) (0.089)
5.54 6.14 6.10 6.09 5.65 5.72
(0.112) (0.107) (0.080) (0.129) (0.074) (0.070)
5.88 6.15 6.05 5.88 5.94 5.93
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
5.86 (0.004) 6.10 (0.004) 6.30 (0.015)
6.10 (0.000) 6.22 (0.000) 6.28 (0.000)
6.52 (0.001) 6.36 (0.002)
5.67 (0.005) 6.20 (0.002)
6.04 (0.000) 6.26 (0.000)
6.32 (0.002) 6.23 (0.000)
[16]. [15]. [14]. [11]. [10].
differences occurred for the two Rydberg states that were lowered in energy by 0.13 eV upon reducing the size of the basis set. Certainly, the effect of going from triple to quadruple zeta quality is expected to be smaller than this. The present CCSDR(3) results clearly suggest that the 1 p2 p4 and 1 p3 p4 states should be identified as S1 and S2, respectively, and that the transitions to these states are the only ones with considerable oscillator strengths. The same picture is obtained at the MS-CASPT2 level, although the excitation energies in this case are shifted upwards by approximately 0.15 eV compared to at the CCSDR(3) level. It is noted that the S1 state, in addition to the p2 p4 configuration, has minor contributions from a configuration of the p3 p5 type. Conversely, the S2 state is almost exclusively of p3 p4 character. In analyzing the higher excited states it should be recognized that diffuse functions are not included in the 6-311G⁄ basis set. A direct consequence is that the pair of 1p3s states is missing at the MS-CASPT2 level. More subtle effects occur for states that are primarily valence like in nature but which contain admixtures of Rydberg excitations. In particular, the two 1 prCS states have significant contributions from 3p and 3d Rydberg components [12,15,16]. The MSCASPT2 calculations accordingly overestimate the energies of these states with more than 0.3 eV in comparison with the CCSDR(3) results. Fortunately, this problem is not very severe in the present context because the 1pr⁄ states become important only at rather distorted geometries where the valence-Rydberg mixing anyway is small. A discussion of the present results in view of the measured absorption spectrum is postponed until Section 3.2, noting for the moment that the they are fully consistent with the interpretation of the spectrum put forward in Section 1. However, two comments concerning previous theoretical results are in order. As is evident from Table 1, the present CCSDR(3) results differ from those of Pastore et al. [15]. The deviations can only be due to basis set effects because the same equilibrium geometry was used in both studies. Unfortunately, an investigation of such effects was not presented in Ref. [15], which makes the exact origin of the deviations somewhat unclear. As can also be seen from Table 1, the 1pp⁄ excitation energies calculated by Serrano-Andrés et al. [10] using the CASTP2 method are significantly lower than those obtained at the present MS-CASPT2 level. Partly these differences should be due to the lack of diffuse functions in the 6-311G⁄ basis set, and partly due to the present use of the level shift technique and multi-state version of CASPT2, which were not available at the time of the earlier study.
3.2. Minimum energy structures and conical intersections The remainder of this paper will be concerned mainly with features of the S0–S2 potential energy surfaces (PESs) of thiophene, which should be sufficient to account for the decay of the lowest 1 pp⁄ states. Critical structures have been located on those surfaces using the MS-CASPT2 method and 6-311G⁄ basis set as already described. The resulting geometries are displayed in Fig. 2 and the Cartesian coordinates given in Table S1 in the Supplementary Material. The corresponding energies of the S0 through S2 states are collected in Table 2, where the dominant electronic configuration of each state is given as well. The global minimum of the S0 PES, which is referred to simply as S0 min, is taken as the zero of the energy scale. Note that the geometry of S0 min is in very good agreement with the experimental equilibrium geometry of Bak et al. [29]. The bond lengths differ by 0.007 Å and the bond angles by 0.5° at the most. The vertical excitation energies calculated at the optimized and experimental equilibrium geometries are also very similar (cf. Table 1). For completeness, the energies of the 1 p3 rCS and 1 p2 rCS states at S0 min (not shown in Table 2) are noted to be 6.50 and 6.58 eV, respectively. Two excited state minima have been located in this work, both on the S1 PES. One of these, denoted as S1 min-a, is associated with the p2 p4 electronic configuration. The corresponding geometry has approximate Cs symmetry with the S and H2 (H5) atoms displaced out of the molecular plane in the same direction. The promotion of an electron from p2 to p4 causes also a lengthening of the C2–C3 (C4–C5) and C2–S (C5–S) bonds with respect to S0 min. The absorption spectrum of thiophene shows a weak feature at 5.16 eV, which has been assigned as the 0–0 band of the S0 ! 1 p2 p4 transition [9].
Fig. 1. Schematic illustration of the structure and relevant molecular orbitals of thiophene. The atomic numbering used in the present work is shown as well.
21
M. Stenrup / Chemical Physics 397 (2012) 18–25
Table 2 Energies (eV) and dominant electronic configurations (characters) of the S0–S2 states of thiophene at various optimized geometries. The calculations were performed using the MS-CASPT2 method and 6-311G⁄ basis set. The energies are given relative to the energy of S0 min. CS denotes the closed shell electronic configuration. Structure
S0 Energy
S1 Character
Energy
S0 min S1 min-a S1 min-b
0.00 1.40 3.69
CS CS CS
5.82 5.12 4.20
S1 TS S1/S2 CI S0/S1 CI-a
1.76 0.96 4.26
CS CS CS
5.22 5.53 4.26
S0/S1 CI-b S0/S1 CI-c
4.61 4.97
CS CS
4.61 4.97
S2 Character 4 4 CS
p2 p p2 p p3 r p3 p4 p2 p4 p3 rCS p3 p4 p3 p4
Energy
Character
6.10 6.46 6.21
p3 p4 p3 p4 2 ðp3 Þ0 rCS p2 p4 p3 p4 2 ðp3 Þ0 rCS p3 p5 p2 p4
6.03 5.53 6.17 7.50 7.63
The adiabatic excitation energy obtained in the present work, i.e., the energy of S1 min-a relative to that of S0 min, deviate from the measured 0–0 energy by only 0.04 eV (zero-point corrections not included). Good agreement is also found with the adiabatic excitation energy and geometry reported by Salzmann et al. [16], which were obtained using a combination of the time-dependent density functional theory (TDDFT) and density functional/multireference configuration interaction (DFT/MRCI) methods. The other excited state minimum located in this work, denoted as S1 min-b, is associated with the p3 rCS electronic configuration and has a planar Cs geometry with an almost completely broken
7.0 Electronic energy (eV)
Fig. 2. Optimized geometries of thiophene as obtained with the MS-CASPT2 method and 6-311G⁄ basis set. The heavy atom bond lengths (Å) are indicated in the figure. In the case of non-planar geometries, the most important torsion angles are also shown.
C5–S bond. The inter-chain bond lengths are consistent with a diradical species possessing C2–S and C4–C5 double bonds and unpaired electrons at C3 and C5. Notably, the adiabatic excitation energy of this structure is more than 2 eV lower than the vertical excitation energy of the 1 p3 rCS state. Most geometrical parameters are in reasonable agreement with those reported by Salzmann et al. [16], although the respective C5–S distances differ by 0.35 Å. A deviation of this size is perhaps not surprising considering that the rCS and rCS orbitals are practically non-bonding in the vicinity of S1 min-b. Because of a very unfavorable Franck–Condon overlap, direct comparison of the calculated adiabatic excitation energy with the measured absorption spectrum is not possible. However, an energy difference of 0.39 eV is noted compared to the computational results of Ref. [16]. Despite considerable efforts, a potential energy minimum associated with the p3 p4 electronic configuration could not be found, although such a minimum was reported by Salzmann et al. [16]. At the present level of theory, a structure geometrically similar to that in Ref. [16] was located only after initializing a transition state (TS) search on the S1 PES. The structure in question, denoted as S1 TS, is of approximate Cs symmetry and has the S atom brought out of the plane in one direction and H2 (H5) in the other. A substantial lengthening of the C2–C3 (C4–C5) bond and a shortening of the C3–C4 bond are also observed with respect to S0 min. The energy of S1 TS is only slightly higher than that of S1 min-a. A numerical evaluation of the Hessian confirmed the presence of one imaginary frequency (i1927 cm1). The corresponding normal mode is a combination of asymmetric CS stretch and CH bend. It is recognized that the calculation of numerical Hessians at the MS-CASPT2 level could potentially lead to large errors. To this end, a PES scan along the imaginary frequency normal mode of S1 TS is displayed in Fig. 3. The shape of the S1 potential energy profile firmly establish S1 TS as a saddle point at the present level of theory. To investigate this matter further, the same structure was also characterized using the CCSD method and aug-cc-pVDZ+sp basis set. The imaginary frequency obtained at this level is substantially smaller (i354 cm1) and some of the CH bending is damped out in the corresponding normal mode. The saddle point nature of S1 TS is nevertheless confirmed. It appears that the 0–0 band of the S0 ! 1 p3 p4 transition has not been identified in the measured absorption spectrum. However, a group of peaks in the region 5.05–5.15 eV were proposed by Weinkauf et al. [18] to be due to transitions into excited levels of the 1 p3 p4 state. Such an interpretation is apparently not consistent with the present results, which suggest that the p3 p4 branch of the S1 PES supports no bound states. A more extensive theoretical investigation, paying
6.0 5.0 4.0 3.0 2.0 1.0 −0.50
−0.25
0.00
0.25
Displacement (amu
0.50
1/2
Å)
Fig. 3. Potential energy profiles of the S0–S2 states of thiophene along the imaginary frequency normal mode of S1 TS. The calculations were performed using the MSCASPT2 method and 6-311G⁄ basis set. The displacement is given with respect to the optimized S1 TS geometry.
M. Stenrup / Chemical Physics 397 (2012) 18–25
3.3. Radiationless deactivation pathways A number of deactivation pathways can be deduced from the energetic and structural data presented in the previous section. The following discussion aims at identifying the most important of these and characterize them in some detail. To facilitate this goal, a series of one dimensional cuts through the S0–S2 PESs along selected reaction coordinates are displayed in Figs. 4 and 5. The potential energy profiles were obtained at the CCSD/cc-pVTZ level and the reaction coordinates generated by linear interpolation between the MS-CASPT2 optimized geometries. The single-reference based CCSD method has previously been used in a similar study on
Electronic energy (eV)
a
S0 min S1 min−a 8.0 π3π4*
S1 min−b
S0/S1 CI−a
6.0 π2π4*
π3σCS*
4.0 2.0
0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
b Electronic energy (eV)
particular attention to the interaction of the S1 state with the neighboring S2 state, may be required to clarify this point. Inspection of Table 2 reveals that the characters of the S1 and S2 states (p2 p4 and p3 p4 ) are exchanged on going from S0 min to S1 TS. A crossing between the corresponding PESs must therefore take place. The search for such a crossing resulted in the minimum energy CI denoted as S1/S2 CI. The geometry of this structure resembles in many respects a less symmetric version of S1 TS, but with the H2 and H5 atoms kept closer to the molecular plane. The crossing takes place energetically below both of the vertically excited 1 pp⁄ states. The work of Salzmann et al. [16] do not include any optimized CIs for comparison. However, Wu et al. [20] have located several excited state structures at the CASSCF level, among them a CI involving the two 1pp⁄ states. The geometry reported in that work appears substantially more distorted than the present one, but some similarities can also be found. The observed differences should at least partly be due to an inability of the CASSCF method to treat the (covalent) 1 p2 p4 and (zwitterionic) 1 p3 p4 states in a balanced way. The remaining minimum energy CIs considered in this work all belong to the S0/S1 crossing seam. The structure denoted as S0/S1 CI-a corresponds to the ring-opened CI discussed in Section 1. It is associated with a crossing of the 1 p3 rCS and ground state PESs, and is geometrically almost identical to the ring-opened species S1 min-b, but distinguished by an even larger C5–S distance. The CI is of the symmetry allowed type since the participating states belong to different irreducible representations of the Cs point group. Energetically, it takes place only 0.06 eV above S1 min-b, and is accordingly situated far below the vertically excited 1pp⁄ states. Salzmann et al. [16] provide an estimate of the CI energy that is a few tenths of an eV lower than obtained in the present work, whereas the approximate C5–S distance quoted in their paper is practically identical with the present one. The structures referred to as S0/S1 CI-b and CI-c are both associated with intersections of the 1 p3 p4 and ground state PESs. The corresponding geometries are characterized by puckering at different sites of the heavy atom framework. In the case of S0/S1 CI-b, the puckering is mainly concentrated to the S atom. The out-of-plane deformation is accompanied by substantial lengthening of the C5–S, C2–C3 and C4–C5 bonds, as well as asymmetric twisting of the C2–H2 and C5–H5 bonds with respect to S0 min. The geometry of S0/S1 CI-c shows puckering almost exclusively at the C2 site, but also in this case the out-of-plane deformation is associated with asymmetric ring-expansion and hydrogen twist. The structural deformations described above cause a partial decoupling of the p3 and p4 orbitals to take place, which tend to stabilize the 1 p3 p4 state and destabilize the ground state [26]. As a consequence, the ring-puckered CIs appear significantly below the vertically excited 1pp⁄ states, although not as low as the ring-opened CI. Out-of-plane deformation at the S site is energetically somewhat more favorable than at C2. The ring-puckered CIs characterized in this work are qualitatively similar to those reported for various substituted thiophenes [28].
S0 min 8.0
c
S1 min−a
S0/S1 CI−b
π3π4* 6.0 π2π4*
π3π4*
4.0 2.0 0.0 0.0
Electronic energy (eV)
22
0.1
S0 min 8.0
0.2
0.3
0.4
S1 min−a
S0/S1 CI−c
π3π4* 6.0
π3π4*
π2π4* 4.0 2.0 0.0 0.0
0.1
0.2
0.3
Displacement (amu
0.4
0.5
1/2
Å)
Fig. 4. Cuts through the S0–S2 PESs of thiophene along reaction paths leading to radiationless deactivation of the 1 p2 p4 state; (a) ring-opening pathway; (b) ringpuckering pathway, deformation at the S site; (c) ring-puckering pathway, deformation at the C2 site. The energy calculations were carried out using the CCSD method and cc-pVTZ basis set, and the reaction coordinates generated by linear interpolation between the MS-CASPT2 optimized geometries. The positions of relevant minimum energy structures and CIs as well as the dominant electronic configurations are indicated along each path.
the deactivation pathways of furan [27], and was found give energies of surprisingly good quality even in situations of nearly degenerate S0 and S1 states. The small energy gaps that can be observed at some of the CI points in Figs. 4 and 5 result since the geometry and energy calculations were carried out at different levels. For the same reason, the positions of some crossings appear slightly shifted relative to the expected ones. However, the main purpose of the PES diagrams is to give only a qualitative picture of the various reaction paths. With the exception of some barrier heights, all relevant numbers will be extracted from the MS-CASPT2 results. The deactivation mechanisms proposed in the present work are schematically illustrated in Fig. 6. Assume first that the system is vertically excited from the S0 to the S1 PES. The S1 state is primarily of p2 p4 character and the initial motion after excitation should be directed from the Franck–Condon region towards the minimum energy structure S1 min-a, which is associated with the same electronic configuration. The relaxation process is accompanied by an energy release of 0.70 eV and is expected to be barrierless, as is indicated also by the appearance of the potential energy profiles in Fig. 4. The present results now suggest three different deactivation pathways
M. Stenrup / Chemical Physics 397 (2012) 18–25
Electronic energy (eV)
a
S0 min 8.0 6.0
S1/S2 CI
S1 min−b
S0/S1 CI−a
π3π4* π2π4*
π3σCS*
4.0 2.0
0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Electronic energy (eV)
b
S0 min 8.0
S1/S2 CI π 3 π4 *
6.0
π 2 π4 *
Electronic energy (eV)
π3π4*
4.0 2.0 0.0 0.0
c
S0/S1 CI−b
0.1
S0 min 8.0 6.0
0.2
0.3
S1/S2 CI
S0/S1 CI−c
π 3 π4 * π3π4*
π2π4* 4.0 2.0 0.0 0.0
0.1
0.2
0.3
Displacement (amu
1/2
0.4 Å)
Fig. 5. Cuts through the S0–S2 PESs of thiophene along reaction paths leading to radiationless deactivation of the 1 p3 p4 state; (a) ring-opening pathway; (b) ringpuckering pathway, deformation at the S site; (c) ring-puckering pathway, deformation at the C2 site. The energy calculations were carried out using the CCSD method and cc-pVTZ basis set, and the reaction coordinates generated by linear interpolation between the MS-CASPT2 optimized geometries. The positions of relevant minimum energy structures and CIs as well as the dominant electronic configurations are indicated along each path.
leading away from S1 min-a. One of these corresponds to the ringopening pathway described by Salzmann et al. [16], and proceeds from S1 min-a to S1 min-b, and subsequently from S1 min-b to
23
S0/S1 CI-a. The formation of the ring-opened species S1 min-b is associated with an energy release of 0.92 eV relative to S1 min-a. During this reaction step, the character of the S1 state is changed from p2 p4 to p3 rCS , which can be understood as a consequence of an avoided crossing taking place between the S1 and S2 PESs. The lower ‘‘cone’’ of this crossing becomes the transition state separating the two minima, as shown in Fig. 4a. From the present CCSD results, the corresponding barrier height is estimated to be 0.26 eV with respect to S1 min-a. This value is most likely an upper limit for the real one since the transition state was not strictly optimized. The final part of the ring-opening pathway, going from S1 min-b to S0/S1 CI-a, involves only a small destabilization of the S1 state by 0.06 eV. In addition, the corresponding geometries are very similar. It is therefore reasonable to assume that the rate-limiting step for the overall process is the passage from S1 min-a to S1 min-b, and once the barrier separating these minima has been passed, deactivation to the electronic ground state can occur with high efficiency. As an alternative means of going from S1 min-a to the electronic ground state, consider now the ring-puckered intersections S0/S1 CI-b and CI-c, which are formed by out-of-plane deformations at the S and C2 sites, respectively. The former CI is situated 0.51 eV and the latter 0.15 eV below S1 min-a. Proceeding from the excited state minimum towards any of these CIs leads to a change of character of the S1 state from p2 p4 to p3 p4 . The character change in each case is associated with an avoided crossing of the S1 and S2 states, as well as a barrier emerging on the S1 PES. The absence of a minimum energy structure possessing the p3 p4 electronic configuration suggest that the barriers link S1 min-a directly to the S0/ S1 crossing seam. The situation is illustrated by the potential energy profiles in Fig. 4b and c. The barrier heights for puckering at the S and C2 sites are estimated to be 0.54 and 0.45 eV, respectively. These values are approximately twice as large as the barrier height for ring-opening. The present results thus favor ring-opening as the major deactivation channel after excitation to the bright 1 p2 p4 state, with perhaps smaller contributions coming from the two ring-puckering pathways. It is noted again, however, that these conclusions are based only on very rough estimates of the relevant barrier heights. They also assume that the excess energy being released at S1 min-a is redistributed over many vibrational modes; that is, the system behaves to some extent statistically. In the time-resolved pump–probe experiment of Weinkauf et al. [18], the decay of the lowest vibrational level of the 1 p2 p4 state was found to be characterized by two time constants of 25 and 80 fs. The larger of these two was associated with the vibrational motion in the 1 p2 p4 state itself, and the smaller with the formation of the ring-opened diradical species. Although the modeling done
Fig. 6. Schematic illustration of proposed radiationless deactivation mechanisms of thiophene. Deactivation pathways originating from the 1 p2 p4 and 1 p3 p4 states are represented by red and blue arrows, respectively. Potential energy profiles are drawn for the states S0 through S2. The dotted line indicates the Franck–Condon point and the dashed curve the S1 PES along an alternative reaction coordinate. Relevant geometries and electronic configurations are indicated as well. (For interpretation of the references in colour in this figure legend, the reader is referred to the web version of this article.)
24
M. Stenrup / Chemical Physics 397 (2012) 18–25
by those authors did not include the ring-puckering pathways explicitly, the proposal of ring-opening as a primary deactivation channel is nevertheless in line with the present findings. Notably, Salzmann et al. [16] from their calculations estimate the barrier height for ring-opening to be as low as 0.04 eV. This further supports the notion that the true barrier height is smaller than that found in the present work. A quite different picture emerges if a vertical transition to the S2 state is assumed. In particular, consider the two deactivation pathways connecting the vertically excited S2 state to the ring-puckered intersections S0/S1 CI-b and CI-c via a radiationless transition at S1/S2 CI. The initial reaction step in each case is exoergic by 0.57 eV and the final by 0.92 or 0.56 eV depending on if the puckering takes place at the S or C2 sites, respectively. The two pathways are direct in the sense that no intermediates are involved. In addition, they both preserve the p3 p4 character of the initially populated state (i.e., they are diabatic). Taken together, these facts raise the possibility of a more or less barrierless connection between the vertically excited S2 state and the electronic ground state. The potential energy profiles to help explore this idea are displayed in Fig. 5b and c. The situation is somewhat complicated by the fact that the S1 and S2 PESs do not exactly coincide at the optimized S1/S2 CI point. Nevertheless, the overall behavior of these profiles is consistent with the pathways indeed being barrierless. The significance of the two direct mechanisms can be further appreciated by exploring the connection to the transition state structure S1 TS. Although this structure is technically a saddle point on the p3 p4 branch of the S1 PES, it is at the same time a minimum in all but one coordinates. The geometrical similarities between S1 TS and S1/S2 CI noted in Section 3.2 thus suggest the existence of a favorable energy gradient pointing from the Franck–Condon region towards the latter structure. This should tend to focus the population in the direction of the crossing point during the initial part of the photodynamics. Interestingly, the only coordinate along which S1 TS is not a minimum is made up of several of those vibrational modes expected to reach S0/S1 CI-b. In particular, this involves the lengthening of the C5–S bond, the shortening of the C2–S bond, and the asymmetric twisting of the C5–H5 and C2–H2 bonds. It appears as if this CI is a particularly low-lying structure possessing the p3 p4 electronic configuration. The information presented so far indicates that the direct pathways of thiophene provide two efficient channels for deactivation of the bright S2 state. Out-of-plane deformation at the sulfur atom appears to be particularly favorable in this respect. Nevertheless, it is of interest to speculate whether also other deactivation pathways might be important after excitation to the S2 state. Among others, the ring-opened structure S1 min-b could be reached from the vertically excited S2 state via a radiationless transition at S1/ S2 CI. Deactivation to the ground state would then be possible via S0/S1 CI-a as described before. However, in passing from S1/S2 CI to S1 min-b the character of the S1 state has to be changed from p3 p4 to p3 rCS , which should require an energy barrier on the S1 PES to be traversed. That this is the case is confirmed by the behavior of the potential energy profiles shown in Fig. 5a, which reveals a small energy barrier situated at 0.25 amu1/2 Å along the reaction path. In principle, the necessary change of character from p3 p4 to p3 rCS could also take place directly in the S2 state and be followed by a diabatic type of relaxation to S1 min-b. Unfortunately, however, a more detailed investigation of this possibility was hampered by difficulties in locating the relevant excited state crossing point. As yet another alternative, ring-opening could result if the decay at S1/S2 CI is followed by relaxation to S1 min-a, in which case the available deactivation pathways should resemble those previously discussed in connection with excitation to the S1 state. Although the occurrence of ring-opening thus cannot be excluded based on the present results, the diabatic, and presumably
barrierless, character of the direct pathways are clear factors speaking in favor of them. Moreover, if the decay of the 1 p3 p4 state do occur via any of those pathways, it is likely to be very fast (i.e., take place on a femtosecond timescale). These ideas are in line with a recent study by Fuji et al. [44] indicating that the analogous 1 p3 p4 state of furan deactivates by ring-puckering to the ground state within 60 fs. Before concluding this paper, the possible role played by triplet electronic states in the non-radiative decay of thiophene should be considered briefly. Deactivation via triplet states was investigated in Refs. [16,18] as an alternative explanation for the observed ultrafast depletion of the 1 p2 p4 state. A mechanism involving population transfer to the p3 p4 branch of the S1 PES followed by intersystem crossing to the second triplet excited (T2) state was examined in particular. However, although this pathway was not ruled out completely, it was regarded as less likely. The participation of a triplet mechanism appears even more doubtful in view of the present findings. This is so since the intersystem crossing has to compete not only with deactivation by ring-opening as suggested earlier, but also by ring-puckering. Thus, even if one of the singlet decay channels are temporarily blocked, fast deactivation via the others may still be possible. In particular, an excited state population residing on the p3 p4 branch of the S1 PES is likely to be removed through the ring-puckered CIs considerably before conversion to T2 can occur. The present results thus support the hypothesis that photo-excited thiophene decays primarily via its singlet electronic states, and that this is the main reason for the observed lack of fluorescence.
4. Conclusions This paper has considered the radiationless deactivation mechanisms of thiophene with particular emphasis on the decay processes following excitation into the first diffuse band of its UV absorption spectrum. The analysis has been based on computational results obtained with multi-reference second-order perturbation theory and coupled cluster based methods. An extensive set of calculations has been carried out to establish the vertical transition energies and order of the lowest singlet excited states. With some confidence, the first and second of these can be identified as the 1 p2 p4 and 1 p3 p4 states, respectively. The corresponding transitions from the electronic ground state both have appreciable oscillator strengths and should be the main sources of intensity of the first absorption band. Several minimum energy structures and CIs involving the S0 through S2 states have been characterized in order to identify the relevant decay mechanisms. In particular, three low-lying CIs of the S0/S1 type have been located. One of these is a planar ringopened structure with an almost completely broken C5–S bond, and involves the 1 p3 rCS state and the closed shell ground state. The other two are ring-puckered structures formed by out-of-plane deformations at the S or C2 sites, and involve the 1 p3 p4 state and the closed shell ground state. The deactivation mechanisms proposed in this paper can be summarized as follows. If the excitation is to the S1 state, relaxation to a local minimum on the S1 PES should follow promptly. From this point, the system can either relax to a second minimum on the same PES and deactivate through the ring-opened CI situated nearby, or proceed to and deactivate through any of the ring-puckered CIs. Each of these pathways involves a change of character of the S1 state from p2 p4 to p3 rCS or p3 p4 , and requires an associated energy barrier on the S1 PES to be traversed. A rough estimate of the corresponding barrier heights suggests that the ring-opening pathway is the major deactivation channel after excitation to the S1 state, which is consistent with previous theoretical
M. Stenrup / Chemical Physics 397 (2012) 18–25
and experimental findings. If, on the other hand, the excitation is to the S2 state, the two ring-puckered CIs can be directly reached via a CI of the S1/S2 type. No intermediates are involved and the p3 p4 character of the initially populated state is retained throughout. Moreover, these pathways are presumably free of barriers and subject to favorable energy gradients. Although additional decay channels cannot be excluded for the S2 state, deactivation by ring-puckering is likely to be a significant process. In conclusion, it appears that the mechanisms outlined above make possible efficient radiationless deactivation throughout the entire first absorption band of thiophene. As such, they are good candidates to explain why this compound is non-fluorescent. A more detailed understanding of the relevant processes may require dynamics simulations to be carried out. In addition to information on what deactivation pathways are the most important, and what are the associated time scales, such simulations could also provide insights into the photochemical events being initiated once the electronic ground state has been reached. A study along these lines, focusing to begin with on the dynamics starting in the 1 p2 p4 state, is currently undertaken and the results will be published elsewhere. Note added in proof After this manuscript was submitted for publication, Cui and Fang [45] reported on a mixed quantum-classical dynamics study of the radiationless deactivation of thiophene. The results of that study support the hypothesis that excitation to the first singlet excited state is followed by ring-opening on a femtosecond timescale. Acknowledgements The author is grateful to Å. Larson for useful discussions and comments on the manuscript. Fig. 2 was partly prepared using the XYZViewer program written by S. de Marothy. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.chemphys.2011.12.004. References [1] T. Eicher, S. Hauptmann, The Chemistry of Heterocycles: Structures, Reactions, Syntheses, and Applications, second ed., Wiley-VCH GmbH & Co. KGaA, Weinheim, Germany, 2003. [2] G. Barbarella, M. Melucci, G. Sotgiu, Adv. Mater. 17 (2005) 1581. [3] A.C. Grimsdale, K.L. Chan, R.E. Martin, P.G. Jokisz, A.B. Holmes, Chem. Rev. 109 (2009) 897. [4] M. Zambianchi, F.D. Maria, A. Cazzato, G. Gigli, M. Piacenza, F.D. Sala, G. Barbarella, J. Am. Chem. Soc. 131 (2009) 10892.
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