A computational study of radiationless deactivation mechanisms of furan

Chemical Physics 379 (2011) 6–12

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A computational study of radiationless deactivation mechanisms of furan M. Stenrup ⇑, Å. Larson 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 13 September 2010 In final form 2 October 2010 Available online 16 December 2010 Keywords: Radiationless deactivation Conical intersections Heterocyclic compounds Photophysics

a b s t r a c t Possible mechanisms for the radiationless deactivation of photo-excited furan have been investigated using high-level electronic structure methods. Two different conical intersections between the S0 and S1 electronic states have been characterized, both involving various degrees of CO bond cleavage. One of these corresponds to a planar ring-opened structure and the other to an asymmetric ring-puckered structure. Calculations have been performed in order to establish the vertical electronic spectrum and to investigate the behaviour of the potential energy surfaces as the intersections are approached. The present results indicate that both crossings can be accessed through exothermic and barrierless processes after vertical excitation into the optically bright S2(pp*) state. These features make them good candidates to account for efficient radiationless deactivation in furan. The deactivation pathways considered in the present work are close analogues of those previously described for other five-membered heterocycles. Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction Furan is a five-membered heterocyclic aromatic compound that occurs in nature as well as in synthesis [1]. It is a fundamental unit of many organic and biologically active compounds, and serves as a prototype for more extended heterocycles. It is structurally related to pyrrole and thiophene, but differs by the incorporation of oxygen instead of nitrogen or sulphur into the ring. The electronic spectrum of furan has been the subject of many experimental as well as theoretical investigations (see Refs. [2–17] and references therein). These studies have provided a detailed picture of the lowest singlet and triplet excited states and, in particular, the transitions contributing to the absorption spectrum. However, only a few studies have considered the relaxation processes taking place after the initial excitation step. The absorption spectrum of furan in the gas phase has been recorded by Palmer et al. [6], among others. The low energy region shows a diffuse band around 6 eV with additional peak-like structures superimposed. The current view (see, e.g., Ref. [15]) is that the diffuse band is due primarily to a singlet state with pp* valence character and a large oscillator strength (the S2 state at the equilibrium geometry), and the peaks to one or several Rydberg states. The most intense peak at 6.47 eV has been assigned to a singlet state with p3p character lying energetically above the S2(pp*) state. The gas phase photodissociation of furan has been investigated by Sorkhabi et al. [18] using ultraviolet radiation at 193 nm wavelength (6.42 eV). Excitation at this wavelength should presumably ⇑ Corresponding author. E-mail addresses: [email protected] (M. Stenrup), [email protected] (Å. Larson). 0301-0104/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2010.10.002

lead to population of either the 1pp* state or the 1p3p state. Three primary dissociation processes were observed. The dominant one was found to take place directly on an excited state potential energy surface (PES) and lead to the formation of radical products. The other two were found to give carbon monoxide + propyne and ketene + acetylene. The authors conclude that these latter two product channels are associated with the electronic ground state of the system and that rapid population transfer from the initially excited state to the ground state must occur. From a theoretical perspective, the most direct way to account for this type of population transfer is by a radiationless deactivation mechanism involving easily accessible conical intersections (CIs) [19]. As a first step, deactivation from the initially excited state to the lowest excited state must take place. This type of process has been considered in detail by Köppel and co-workers [13– 15] using wave packet propagation techniques and a model Hamiltonian based on equation-of-motion coupled cluster singles and doubles (EOM-CCSD) energy data. The S1 through S4 states of furan were found to be connected by several low-lying CIs. For a system initially in the S2(pp*) state, deactivation into the S1(p3s) state was found to occur on a time scale as short as 25 fs. An intersection between the lowest excited state and the ground state must eventually be reached in order for the deactivation process to be completed. In furan, such an S0/S1 CI is promoted by an in-plane dissociation of one of the CO bonds [20]. This ringopened type of CI has been characterized at the state-averaged complete active space self-consistent field (SA-CASSCF) level by Wilsey et al. [21], although in the context of photorearrangement of acylcyclopropene to furan. The role of the ring-opened CI in photo-excited furan was investigated in the density functional theory/multi-reference configuration interaction (DFT/MRCI) study of

M. Stenrup, Å. Larson / Chemical Physics 379 (2011) 6–12

Gavrilov et al. [17]. A similar investigation has also been carried out for thiophene [17,22]. Recently, Gromov et al. [23] have extended their previous works [13–15] on the photophysics of furan by characterizing several key structures along the ring-opening pathway. Multi-dimensional PESs have been constructed with the aim of using these in quantum dynamics simulations. The radiationless deactivation of pyrrole has been extensively studied by both Domcke and co-workers [24–29] and Lischka and co-workers [30–33]. Two distinct S0/S1 CIs have been found for this molecule in addition to the ring-opened type of CI [31]. One of these is reached by stretching the NH bond [24] and the other by puckering the ring and simultaneously stretching one of the CN bonds [30]. Ab initio molecular dynamics simulations seem to indicate that the NH stretching mechanism is the most important one, although a non-negligible fraction of deactivation events was also observed for various ring-puckered geometries [31]. For obvious reasons an equivalent to the NH stretching mechanism is not present in furan. However, the ring-puckered type of CI found in pyrrole also should exist in furan. It appears that this CI has not been characterized in the literature to date, although it is briefly mentioned in Refs. [17,34]. In the present study, we have considered both the ring-opening and ring-puckering deactivation mechanisms of furan, focusing on the corresponding S0/S1 CIs and the paths through which they can be reached. Singlet states have been considered exclusively and attention directed mainly towards the radiationless decay of the S2(pp*) state. The CIs have been identified as stationary points on the crossing ‘‘seam’’, i.e. as energy minima or various order saddle points in the multi-dimensional intersection space [19]. The optimizations have been carried out using the multi-state complete active space second-order perturbation theory (MS-CASPT2). In addition, linear response coupled cluster (LR-CC) and MS-CASPT2 calculations have been performed in order to establish the vertical electronic spectrum. At the LR-CC level we have also calculated potential energy profiles along paths leading from the S0 minimum to the S0/S1 CIs. Besides providing information on the deactivation mechanisms, this gives an insight into the utility of coupled cluster methods when used near the S0/S1 crossing seam. 2. Electronic structure A schematic view of the furan molecule along with the coordinate system and atomic labels used in this work are shown in Fig. 1. The molecule is planar and belongs to the C2v point group. The px orbitals on the carbon and oxygen atoms can be used to construct three bonding p and two antibonding p* molecular orbitals, which are labelled in order of increasing energy as pi (i = 1, 2, 3) and pi ði ¼ 4; 5Þ. The p electron configuration of the closed shell ground state is given by (p1)2(p2)2(p3)2. The promotion of electrons from the p to p* orbitals gives rise to low-lying excited states of valence character. Several transitions into diffuse Rydberg orbitals can be expected in the same energy

Fig. 1. Schematic view of the furan molecule. Also shown in the figure are the coordinate system and atomic labels used in the present work.

7

range. A survey of the literature [5–13,16,17] shows quite conclusively that the S1 through S6 states comprise two valence states of p3 p4 and p2 p4 þ p3 p5 character, and four Rydberg states of p33s and p33pa (a = x, y, z) character. The 1 p3 p4 state is ionic in nature [7] and corresponds to the optically bright state discussed in the
introduction. The 1 p2 p4 þ p3 p5 state is covalent and is dominated by two excited configurations of similar weights. Excitations into antibonding r* orbitals give rise to states of much higher energies but which are strongly repulsive along certain coordinates. Dissociation of one of the CO bonds leads to the ring-opened CI discussed earlier, which is a crossing between a repulsive 1 p3 rCO state and the ground state [17]. The ring-puckered CI, as found in pyrrole, occurs between the 1 p3 p4 state and the ground state [30]. Calculations on the lowest excited states of furan have proven surprisingly challenging. This should be attributed partly to the ionic nature of the 1 p3 p4 state. The polarity of this state may be strongly overestimated and the energy artificially raised if dynamical electron correlation is not properly accounted for [16,35]. Complications also arise because the valence and Rydberg states are close in energy and mixing can easily occur. In particular, the 1 p3 p4 state shows a high affinity to mix with the 1p33px state [11,16], which belongs to the same symmetry species in C2v. In general, it is thus not possible to separate the valence from the Rydberg states, for example by excluding diffuse functions from the basis set. The problems associated with the 1 p3 p4 state are less severe near the S0/S1 crossing seam, but here the ground state wave function is multi-configurational and multi-reference based methods in general are required. We have not been able to find a computational method that alone could meet all of the above requirements and simultaneously provide smooth PESs in between the S0 minimum and the S0/S1 crossing seam. A combination of different wave function methods was therefore employed.

3. Computational details The LR-CC method [36] was used to determine the vertical excitation energies of the S1 through S6 states of furan. Calculations were performed with the LR-CC singles (CCS), iterative approximate doubles (CC2), singles and doubles (CCSD), and non-iterative triples [CCSDR(3)] models [37–39]. The experimental equilibrium geometry of Mata et al. [40] was employed and the symmetry restricted to the C2v point group. The aug-cc-pVTZ basis set appended with a set of diffuse s and p functions was used for the heavy atoms and the cc-pVTZ basis set for the hydrogen atoms. This basis is denoted as aug-cc-pVTZ+sp in the text. Test calculations with one additional set of diffuse s and p functions or one set of diffuse d functions placed on the heavy atoms were performed at the CCSD level. The effects of changing the hydrogen basis from cc-pVTZ to aug-cc-pVTZ were also examined at the same level. The exponents of the diffuse s, p and d functions were generated by dividing each preceding exponent of the same kind by three. All LR-CC calculations were performed with the DALTON 2.0 program [41]. The MS-CASPT2 method [42–44] was used to locate the S0 minimum and stationary point CIs, and to provide ground and excited state energies at these geometries. The S0 minimum was optimized using C2v symmetry and an active space composed of all five p and p* orbitals. The 6-311G* basis set was used and the computational model is accordingly written as CASPT2(6, 5)/6-311G*, where the number of active electrons and orbitals are given in parenthesis. The S0/S1 CIs were optimized using an active space composed of all p and p* orbitals, the bonding rCO orbital and antibonding rCO orbital. Two roots were included in the state-averaging procedure and the 6-311G* basis set was used. The model is denoted as MS-CASPT2(8, 7)/6-311G*. A single point calculation using this model was also carried out at the S0 minimum in order to assign

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M. Stenrup, Å. Larson / Chemical Physics 379 (2011) 6–12

relative energies to the intersecting states. Vertical excitation energies were calculated at the S0 minimum and experimental equilibrium geometry using, in addition to the p and p* orbitals, the 3s and 3p orbitals to build the active space. The 6-311+G* basis set augmented with a set of diffuse s and p functions placed on the heavy atoms was used. The exponents of the diffuse functions were derived in the even tempered manner described above. The energy of the 1 p3 p4 state is strongly overestimated at the SA-CASSCF level and we had to include as many as 11 roots in the state-averaging procedure. A level shift of 0.3 a.u. was used in order to reduce the influence of intruder states [45]. The computational model is denoted as MS-CASPT2(6, 9)/6-311+G*+sp. All MS-CASPT2 calculations were performed with the MOLCAS 7.2 program [46] employing an IPEA shift [47] of 0.25 a.u. The search for stationary point CIs at the MS-CASPT2 level was made possible using the sequential penalty algorithm described in Ref. [48], which can be operated without analytical gradients and non-adiabatic couplings. A maximal energy separation of 0.0001 a.u. was used as the criterion to determine if a particular geometry should be considered part of the intersection space or not. Paths leading from the S0 minimum to the S0/S1 CIs were constructed by linear interpolation in internal coordinates. Energy calculations using the CCSD method and 6-311+G*+sp basis set were performed along these paths. The PESs should preferably be calculated with the multi-reference based MS-CASPT2 method, but significant difficulties were encountered in retaining a consistent set of active orbitals over all geometries. Thus, MS-CASPT2 calculations were performed only along the final parts of the paths. These calculations were carried out with the same type of computational model as was used in the CI optimizations.

4. Results and discussion 4.1. Vertical electronic spectrum We begin by examining in some detail the vertical excitation energies and oscillator strengths of furan listed in Table 1. This will help to estimate the quality of the methods used and provide support for the subsequent discussions on the deactivation mechanisms. The results presented in this section were obtained at the LR-CC/aug-cc-pVTZ+sp and MS-CASPT2(6, 9)/6311+G*+sp levels using the experimental equilibrium geometry of Mata et al. [40]. The MS-CASPT2 calculations performed at the optimized equilibrium geometry are considered in Section 4.2. An interesting trend in the LR-CC results can be discerned. The energies of the 1 p3 p4 state and all Rydberg states increase for every step going from CCS to CC2 to CCSD and decrease on going from CCSD to CCSDR(3). The energy stabilization in the final step is 0.12 eV for the 1 p3 p4 state and around 0.07 eV for the Rydberg states. A somewhat larger stabilization effect is observed for the
1 p2 p4 þ p3 p5 state, which can be attributed to the fact that this state has a larger contribution of doubly excited configurations compared to the others [10]. The use of additional diffuse basis functions, as described in Section 3, was found to change the excitation energies of all states by less than 0.01 eV. These observations in combination with the small stabilization effects due to triple excitations indicate that the present CCSDR(3) energies are of good quality and in most cases should predict the state order correctly. In particular, the 1p33s and 1 p3 p4 states are the lowest excited states at all excitation levels and may be confidently associated with the S1 and S2 PESs, respectively. The largest oscillator strength is obtained for the 1 p3 p4 state, as expected. The only other state with a non-negligible oscillator strength is the 1p33py state, which

is most likely the origin of the sharp peak found at 6.47 eV in the spectrum (see, e.g., Ref. [15] for a more detailed discussion). Our MS-CASPT2 excitation energies are found to be consistently lower than those obtained at the CCSDR(3) level. However, the differences are rather small and in no case larger than 0.2 eV, which supports the reliability of the present MS-CASPT2 approach. Relative energies among the excited states are reproduced with high accuracy and the energy order of most states is preserved compared to at the CCSDR(3) level. An exception is the order of the
close-lying 1p33py and 1 p2 p4 þ p3 p5 states, which is reversed at the MS-CASPT2 level. The oscillator strengths of the 1 p3 p4 and 1 p33py states are within a few tens of percent of the corresponding CCSDR(3) values. Christiansen et al. [9,10] have performed a series of LR-CC calculations that differ from ours mainly in the choice of basis sets and the additional use of the iterative triples (CC3) model. A very good agreement is found between the present CCSDR(3) results and those obtained using the CCSD method and a CC3 correction calculated in a smaller basis set [10]. The n-electron valence state perturbation theory (NEVPT2) results of Pastore et al. [16] agree with our CCSDR(3) results within 0.1 eV and give the same state order as our MS-CASPT2 calculations. The latter is true also for the DFT/MRCI results of Gavrilov et al. [17], although their excitation energies are somewhat lower than ours. Note that a CASPT2 study on the excited states of furan was carried out by Serrano-Andrés et al. [5] nearly two decades ago. However, this was prior to the advent of both the level shift technique [45] and the multi-state version of CASPT2 [44], which could at least partly explain the discrepancies with the present results. 4.2. S0 minimum and S0/S1 conical intersections The geometries of the S0 minimum and S0/S1 CIs of furan determined in this work are shown in Fig. 2. The corresponding bond lengths, bond angles and torsional angles for the heavy atoms are given in Table 2, and the full set of Cartesian coordinates in Table S1 in the supplementary information. The ground and excited state energies calculated at the optimized geometries can be found in Table 3. All results in this section were obtained with the MS-CASPT2 method (see Section 3 for details). We note the close agreement found between the S0 minimum located in this work and the experimental equilibrium geometry of Mata et al. [40]. The bond lengths deviate by less than 0.005 Å and the bond angles by less than 0.5 degrees. Likewise, the vertical excitation energies show only minor differences when calculated at the optimized compared to the experimental geometry (cf. Table 1). The S0/S1 ring-opened CI of furan corresponds to a planar Cs structure with an almost completely broken C5–O1 bond. From the present results, we infer an increase in the C5–O1 distance of 1.224 Å relative to its equilibrium value. Less dramatic structural changes involve a contraction of the O1–C2 bond and a lengthening of the C2–C3 bond with respect to the S0 minimum. The high-lying 1 p3 rCO state is stabilized considerably as the C5–O1 distance is increased and the crossing with the ground state occurs at an energy of only 4.05 eV. This is most likely a true minimum on the S0/S1 crossing seam. The states participating in the crossing belong to different Cs irreducible representations (A0 and A00 ). The intersection is therefore of the symmetry allowed type and its existence could in principle have been anticipated on purely energetical grounds. The largest structural differences with respect to the SA-CASSCF geometry of Wilsey et al. [21] occurs for the C5–O1 and C2–C3 bonds, which are 0.08 and 0.05 Å shorter, respectively, in their study compared to ours. From their tabulated absolute energies we infer a CI energy of 3.91 eV. The agreement with the present energy is remarkably good in view of the generally poor performance of the SA-CASSCF method near the equilibrium geometry. Good

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M. Stenrup, Å. Larson / Chemical Physics 379 (2011) 6–12

Table 1 Vertical excitation energies (eV) and oscillator strengths (given in parenthesis) of the S1 through S6 states of furan. The present results were obtained at the LR-CC/aug-cc-pVTZ+sp and MS-CASPT2(6, 9)/6-311+G*+ sp levels using the experimental equilibrium geometry of Mata et al. [40]. The C2v symmetry designation of each state is indicated in the heading. 11A2 p33s

11B2

Present study CCS CC2 CCSD CCSDR(3) MS-CASPT2

5.96 6.01 6.13 6.06 5.97

6.28 6.39 6.45 6.33 6.19

Previous studies CCSD/CC3a EOM-CCSDb NEVPT2c CASPT2d DFT/MRCIe TDDFTf

6.04 6.01 (0.000) 6.13 5.92 (0.000) 5.81 (0.000) 5.97

Method

1

a b c d e f

Ref. Ref. Ref. Ref. Ref. Ref.

(0.000) (0.000) (0.000) (0.000) (0.000)

1

21A1 ðp2 p4 þ p3 p5 Þ

11B1 1 p33py

21A2 1 p33pz

21B2 1 p33px

6.74 6.82 6.65 6.45

6.45 6.53 6.66 6.60 6.51

6.66 6.67 6.82 6.75 6.66

(0.000) (0.000) (0.000) (0.000) (0.000)

6.72 6.83 6.95 6.89 6.74

6.73 6.69 (0.000) 6.79 6.59 (0.000)

6.86

6.69

6.83

1

p3 p4 (0.175) (0.174) (0.164) (0.161) (0.192)

6.32 6.44 (0.166) 6.41 6.04 (0.154) 6.00 (0.230) 6.12

(0.000) (0.000) (0.000) (0.008)

6.57 6.72 (0.000) 6.62 6.16 (0.002) 6.25 (0.000) 6.76

(0.039) (0.034) (0.036) (0.035) (0.023)

6.58 6.53 (0.036) 6.68 6.46 (0.031) 6.30 (0.043) 6.58

(0.002) (0.002) (0.000) (0.000) (0.001)

6.87 6.48 (0.047)

[10]. [13]. [16]. [5]. [17]. [12].

Table 3 Ground and excited state energies (eV) calculated at the S0 minimum, S0/S1 ringopened CI (ROCI) and S0/S1 ring-puckered CI (RPCI) of furan. Structure

State

Energy

Character

S0 minimum

S0 S1 S2 S3 S4 S5 S6

0.00a 5.96a 6.17a 6.40a 6.50a 6.64a 6.73a

(p3)2 p33s

S0 S1

4.05b 4.05b

(p3)2

S0 S1

b

(p3)2

S0/S1 ROCI S0/S1 RPCI Fig. 2. Geometries of the S0 minimum, S0/S1 ring-opened CI (ROCI) and S0/S1 ringpuckered CI (RPCI) of furan. All structures were optimized at the MS-CASPT2 level.

Table 2 Selected bond lengths (Å), bond angles (degrees) and torsional angles (degrees) for the S0 minimum, S0/S1 ring-opened CI (ROCI) and S0/S1 ring-puckered CI (RPCI) of furan.

a b

Parameter

S0 minimuma

S0/S1 ROCIb

S0/S1 RPCIb

O1–C2 C2–C3 C3–C4 C4–C5 C5–O1 O1–C2–C3 C2–C3–C4 C3–C4–C5 C4–C5–O1 C5–O1–C2 O1–C2–C3–C4 C2–C3–C4–C5 C3–C4–C5–O1

1.361 1.365 1.435 1.365 1.361 110.8 105.9 105.9 110.8 106.6 0.0 0.0 0.0

1.227 1.439 1.440 1.333 2.585 122.9 118.3 123.7 84.8 90.3 0.6 0.2 0.0

1.295 1.491 1.355 1.501 1.588 115.1 99.7 109.1 102.2 92.9 36.4 3.7 20.9

CASPT2(6, 5)/6-311G*. MS-CASPT2(8, 7)/6-311G*.

agreement is also found with the EOM-CCSD results of Gromov et al. [23]. Most bond lengths deviate by less than 0.015 Å

a b

4.98 4.98b

p3 p4 p2 p4 þ p3 p5 p33py p33pz p33px p3 rCO p3 p4

MS-CASPT2(6, 9)/6-311+G*+sp. MS-CASPT2(8, 7)/6-311G*.

(0.035 Å for the C5–O1 distance) and the energy of 4.17 eV obtained at the EOM-CCSD level compares very well with the present value. The S0/S1 ring-puckered CI located in this work, as with the ring-opened CI, is found to have a considerably lengthened C5–O1 bond. However, in this case, this bond is only partially broken, being 0.227 Å longer than at the equilibrium geometry. The puckering of the heavy-atom framework is primarily due to an out-ofplane rotation of the O1–C2 bond by 36.4 degrees (as measured by the O1–C2–C3–C4 torsional angle) and is accompanied by additional tuning of the hydrogen atoms. A substantial lengthening of the C2–C3 and C4–C5 bonds, and a contraction of the O1–C2 and C3–C4 bonds relative to the S0 minimum, are also observed. At the ring-puckered geometry, the p3 orbital has transformed essentially into a p-like orbital on C5, and p4 into an antibonding combination of p-like orbitals on O1 and C2. Inspection of the wave function confirms that the intersecting states are the 1 p3 p4 state and the closed shell ground state. The crossing occurs at an energy of 4.98 eV. This is well above the energy of the ring-opened CI, but still implies a stabilization of the 1 p3 p4 state by 1.19 eV with respect to its energy at the equilibrium geometry. The significant energy lowering seen for this state is closely related to its biradical nature caused by the distribution of electrons into the nearly decoupled p3 and p4 orbitals [34]. The ring-puckered CI of furan

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M. Stenrup, Å. Larson / Chemical Physics 379 (2011) 6–12

is qualitatively very similar to the analogous structures found for pyrrole [30] and imidazole [49].

The accessibility of the S0/S1 CIs considered in this work can be estimated from the potential energy diagrams shown in Figs. 3 and 4. In the construction of these diagrams we have made use of the simplified reaction paths described in Section 3. The energy calculations have been carried out at the CCSD/6-311+G*+sp level. As the crossing seam is approached, the S0 and S1 potential energy profiles are also shown as obtained by the MS-CASPT2(8, 7)/6-311G* method. The intermediate geometries are identified by the length of the C5–O1 bond, which is indicated on the x-axis of each diagram. The behaviour of the potential energy profiles along the ringopening pathway (Fig. 3a and b) appears somewhat complex, involving several different types of curve crossings. The energy of the 1 p3 p4 state is a nearly constant function of the reaction coordinate and is crossed by the 1p33s state, which is raised in energy as a consequence of the C5–O1 bond cleavage. The crossing (indicated as A in Fig. 3b) becomes a CI since the participating states belong to different Cs symmetry species. As the reaction coordinate is further increased, the energy of the 1 p3 rCO state is reduced substantially and an avoided crossing with the 1p33s state is formed, as well as a symmetry allowed CI with the 1 p3 p4 state (indicated as B in Fig. 3b). Additional stabilization of the 1 p3 rCO state in combination with a destabilization of S0 finally gives rise to the S0/S1 ring-opened CI. Note that the S1/S2 CIs labelled A and B have not been optimized in the present work. However, the EOM-CCSD re-

Electronic energy (eV)

a

8.0

6.0

1

π3π4*

1

π33s

S0/S1 ROCI 1

π3σCO*

4.0

2.0

S0 minimum

0.0 1.4

Electronic energy (eV)

b

1.6

1.8

2.0

2.2

2.4

6.8

6.6

B 1

A

π3π4*

6.4

1 1

π33s

π3σCO*

6.2 1.4

1.5 1.6 1.7 C5 − O1 bond length (Å)

1.8

Fig. 3. (a) Potential energy profiles of the S0 through S3 states of furan along the ring-opening pathway. Full and dashed lines correspond to the CCSD/6-311+G*+sp and MS-CASPT2(8, 7)/6-311G* results, respectively. The reaction coordinate was constructed by linear interpolation in internal coordinates between the S0 minimum and S0/S1 ring-opened CI (ROCI). The electronic energy is plotted as a function of the C5–O1 bond length. (b) Expanded view of the S1 through S3 PESs in the region 6.1 to 6.9 eV.

1

Electronic energy (eV)

4.3. Radiationless deactivation pathways

8.0 π3π4*

6.0

1

S0/S1 RPCI

π3π4*

1

π33s

4.0

2.0

S0 minimum

0.0 1.40

1.45 1.50 1.55 C5 − O1 bond length (Å)

Fig. 4. Potential energy profiles of the S0 through S2 states of furan along the ringpuckering pathway. Full and dashed lines correspond to the CCSD/6-311+G*+sp and MS-CASPT2(8, 7)/6-311G* results, respectively. The reaction coordinate was constructed by linear interpolation in internal coordinates between the S0 minimum and S0/S1 ring-puckered CI (RPCI). The electronic energy is plotted as a function of the C5–O1 bond length.

sults of Gromov et al. [23] indicate that they can be associated with two distinct stationary points on the S1/S
2 crossing seam. For a system initially in the S2 p3 p4 state, the energetically most favourable route to the ring-opened CI involves a direct change between the p3 p4 and p3 rCO configurations. The highest energy point along this route corresponds to intersection B, which is situated only 0.06 eV above the vertical S2 energy. Similar features were noted in the DFT/MRCI study of Gavrilov et al. [17]. Optimization of structure B should reduce its energy even further as indicated by the results of Gromov et al. [23]. Thus, it appears
that deactivation of the S2 p3 p4 state along the ring-opening pathway, at least in principle, can proceed without barriers. The potential energy diagram for the ring-puckering pathway (Fig. 4) turns out to be less complicated. Out-of-plane deformations of the ring system in combination with C5–O1 bond cleavage immediately begin to stabilize the 1 p3 p4 state and destabilize the 1 p33s state. An avoided crossing between these states is formed and their electronic configurations are interchanged. Further relaxation of the 1 p3 p4 state on the S1 surface leads directly to the S0/S1 ring-puckered CI. From the
present CCSD results, we find that deactivation of the S2 p3 p4 state along the ring-puckering pathway can take place without any barriers. However, for this mechanism to be efficient, additional deformations of the molecule are needed in order to tune the S1/S2
avoided crossing into a real crossing. Deactivation of the S2 p3 p4 state may then proceed in a repulsive fashion without changing the electronic character the entire way to the S0/S1 crossing seam. Somewhat schematically, we could also
think of an alternative decay mechanism in which the S1 p3 p4 intermediate state is reached via the ring-opening pathway but subsequently relaxed along the ring-puckering pathway. Also in this case, the S0/S1 crossing seam may be accessed without chang
ing the electronic character of the S2 p3 p4 state. It is essential to estimate the quality of our calculated potential energy profiles. At the S0 minimum, the present CCSD approach gives an energy of 5.98 eV for the S1 state and 6.48 eV for the S2 state. These numbers compare reasonably well with the best estimates given in Section 4.1. A much more critical issue is the performance of the single-reference based CCSD method near the S0/S1 crossing seam. In this context, it is instructive to compare our CCSD results to those obtained at the MS-CASPT2 level. The diffuse basis functions used in connection with the former but not the latter method are of less importance at these geometries and do not affect the comparison appreciably. Starting with the ring-opening pathway, the two sets of potential energy curves are found to have

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very similar shapes and to be shifted in energy by approximately 0.2 eV. True crossings are obtained at both levels of theory since the participating states are, by symmetry, non-interacting. A similar energy shift is observed along the ring-puckering pathway, although here the CCSD potential energy curves do not become fully degenerate. This behaviour is not surprising given the fact that the CIs were optimized at the MS-CASPT2 level. The apparently good performance of the CCSD method in this region of configuration space is remarkable since the presence of same symmetry states as well as a partially broken CO bond should combine to give a truly multi-configurational ground state wave function. In summary, it appears that both the ring-opened and ringpuckered CIs of furan are accessible after vertical excitation into
the bright S2 p3 p4 state. Deactivation through the ring-opened CI is very favourable from an energetic point of view. However, it requires relatively large distortions of the atomic framework. Conversely, deactivation through the ring-puckered CI is energetically less favourable but requires considerably smaller deformations of the molecular skeleton. Additional differences exist with respect to the excited state transitions that have to be induced in order for the S0/S1 CIs to be reached. The situation is similar to that previously described for pyrrole [31] and imidazole [49]. It is notable that in the case of imidazole, the ring-opened and ring-puckered CIs have been shown to be connected by the same crossing seam [49]. This is most likely also true in the case of furan considering the strong similarity between the electronic structures of these compounds. From the present results alone we can not conclude which part of this seam should be most efficient in promoting transitions back to the electronic ground state. In favour of the ring-puckering mechanism is the observed preference for deactivation at ring-puckered over planar ring-opened geometries in the dynamics simulations on pyrrole [31]. However, the efficiency of both types of pathways may in fact be enhanced in furan due to the absence of an equivalent to the NH stretching mechanism.

5. Concluding remarks In this study we have investigated some radiationless deactivation mechanisms of furan using the MS-CASPT2 and LR-CC electronic structure methods. Two different stationary points on the S0/S1 crossing seam have been characterized and the corresponding deactivation pathways explored. One of these points corresponds to a planar ring-opened structure with an almost completely broken CO bond and arises from a degeneracy of the 1 p3 rCO state and the closed shell ground state. The other resembles a ring-puckered structure with a partially broken CO bond and occurs between the 1 p3 p4 state and the closed shell ground state. Both of the S0/S1 CIs considered in this work are
situated below the vertical excitation energy of the bright S2 p3 p4 state and are reachable from this state essentially without barriers. From this point of view, they are both good candidates to account for ultrafast radiationless deactivation in furan. At the present moment, we can not conclude which, if any, of these mechanism is the preferred one. The ring-opened and ring-puckered CIs may in fact belong to the same branch of the S0/S1 crossing seam, in which case the distinction between the two pathways could be lost completely. Explicit dynamics simulations are probably needed in order to clarify these issues. Ultimately, such dynamics simulations should also provide insights into the influence of the S0/S1 CIs on the photo-products formed. This is of particular interest in the present context because several reaction mechanisms proposed for the photochemistry of furan involve CO bond cleavage as an intermediate step (see, e.g., Ref. [50]).

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A surprising outcome of the present study concerns the behaviour of the single-reference based CCSD method near the S0/S1 crossing seam. We find that the potential energy profiles obtained with this method are similar to those obtained with the multi-reference based MS-CASPT2 approach. These results are remarkable considering that the electronic ground state in this region should have a rather pronounced multi-configurational character. Similar situations exist in which the CCSD approach breaks down entirely. However, the use of this method in certain favourable cases may provide an attractive alternative to more elaborate multi-reference schemes. Acknowledgements We are very thankful to E. V. Gromov and H. Köppel for enlightening discussions and warm hospitality during our visits to Heidelberg, and R. D. Thomas for reading and commenting on the manuscript. This work was financially supported by the Swedish Research Council (VR). Computational resources were provided by SNIC through Uppsala Multidisciplinary Center for Advanced Computational Science (UPPMAX) under Project p2008038. Fig. 2 was prepared using the XYZViewer program written by S. de Marothy. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.chemphys.2010.10.002. References [1] J.A. Joule, K. Mills, Heterocyclic Chemistry, fourth ed., Blackwell Science Ltd, Oxford, UK, 2000. [2] C.D. Cooper, A.D. Williamson, J.C. Miller, R.N. Compton, J. Chem. Phys. 73 (1980) 1527. [3] J.L. Roebber, D.P. Gerrity, R. Hemley, V. Vaida, Chem. Phys. Lett. 75 (1980) 104. [4] L. Nyulászi, J. Mol. Struct. 273 (1992) 133. [5] L. Serrano-Andrés, M. Merchán, I. Nebot-Gil, B.O. Roos, M. Fülscher, J. Am. Chem. Soc. 115 (1993) 6184. [6] M.H. Palmer, I.C. Walker, C.C. Ballard, M.F. Guest, Chem. Phys. 192 (1995) 111. [7] H. Nakano, T. Tsuneda, T. Hashimoto, K. Hirao, J. Chem. Phys. 104 (1996) 2312. [8] A.B. Trofimov, J. Schirmer, Chem. Phys. 224 (1997) 175. [9] O. Christiansen, A. Halkier, H. Koch, P. Jørgensen, T. Helgaker, J. Chem. Phys. 108 (1998) 2801. [10] O. Christiansen, P. Jørgensen, J. Am. Chem. Soc. 120 (1998) 3423. [11] J. Wan, J. Meller, M. Hada, M. Ehara, H. Nakatsuji, J. Chem. Phys. 113 (2000) 7853. [12] R. Burcl, R.D. Amos, N.C. Handy, Chem. Phys. Lett. 355 (2002) 8. [13] E.V. Gromov, A.B. Trofimov, N.M. Vitkovskaya, J. Schirmer, H. Köppel, J. Chem. Phys. 119 (2003) 737. [14] H. Köppel, E.V. Gromov, A.B. Trofimov, Chem. Phys. 304 (2004) 35. [15] E.V. Gromov, A.B. Trofimov, N.M. Vitkovskaya, H. Köppel, J. Schirmer, H.-D. Meyer, L.S. Cederbaum, J. Chem. Phys. 121 (2004) 4585. [16] M. Pastore, C. Angeli, R. Cimiraglia, Chem. Phys. Lett. 426 (2006) 445. [17] N. Gavrilov, S. Salzmann, C.M. Marian, Chem. Phys. 349 (2008) 269. [18] O. Sorkhabi, F. Qi, A.H. Rizvi, A.G. Suits, J. Chem. Phys. 111 (1999) 100. [19] W. Domcke, D.R. Yarkony, H. Köppel (Eds.), Conical Intersections: Electronic Structure, Dynamics & Spectroscopy, World Scientific Publishing Co. Pte. Ltd., Singapore, 2004. [20] L. Salem, J. Am. Chem. Soc. 96 (1974) 3486. [21] S. Wilsey, M.J. Bearpark, F. Bernardi, M. Olivucci, M.A. Robb, J. Am. Chem. Soc. 118 (1996) 4469. [22] S. Salzmann, M. Kleinschmidt, J. Tatchen, R. Weinkauf, C.M. Marian, Phys. Chem. Chem. Phys. 10 (2008) 380. [23] E.V. Gromov, A.B. Trofimov, F. Gatti, H. Köppel, J. Chem. Phys. 133 (2010) 164309. [24] A.L. Sobolewski, W. Domcke, Chem. Phys. Lett. 321 (2000) 479. [25] A.L. Sobolewski, W. Domcke, Chem. Phys. 259 (2000) 181. [26] V. Vallet, Z. Lan, S. Mahapatra, A.L. Sobolewski, W. Domcke, Faraday Discuss. 127 (2004) 283. [27] V. Vallet, Z. Lan, S. Mahapatra, A.L. Sobolewski, W. Domcke, J. Chem. Phys. 123 (2005) 144307. [28] Z. Lan, A. Dupays, V. Vallet, S. Mahapatra, W. Domcke, J. Photochem. Photobiol. A 190 (2007) 177. [29] Z. Lan, W. Domcke, Chem. Phys. 350 (2008) 125.

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