As reported the introductory section, real crossings (such as conical intersections and singlet-triplet crossings) have been demonstrated to occur with a previously unsuspected frequency in organic systems. Thus decay at a real crossing provides a valid alternative mechanism for excited state radiationless and, in particular for the generation of photoproducts. While there are, in principle, at least three different ways of generating a photoproduct (via an adiabatic reaction, via decay at an avoided crossing and via decay at a real crossing) here we will deal exclusively with the last type of process. In particular we will deal with photoproduct formation via decay at a conical intersection between two singlet potential energy surfaces (see framed region in the Scheme below).
Thus the investigation of the mechanism of a photochemical reaction requires, as a primary step, the investigation of the structure and energetics of the low-lying real crossings for the system under investigation. The computational results reported during the last decade indicate some general features of such crossings and of the related photochemical reaction paths. In this Lecture we make an attempt to classify these features from a chemical point of view. Furthermore we will compare the computational results in order to establish how far the present computational technology can go along the way to a complete understanding of a photochemical reaction mechanism.
The general features that we are going to discuss below will be illustrated through the analysis of a group of selected case-studies. Thus, we will discuss:
The application of different spectroscopic techniques to low temperature samples of “isolated” conjugated molecules has begun to provide very detailed information on the excited state dynamics of these organic systems and to indicate that there is a small threshold energy to ultrafast radiationless decay. State-of-the-art ab initio computations have been used here to demonstrate that the general mechanism which “triggers” the decay is a displacement of the electronically excited equilibrium structure towards a “critical” configuration where the excited and ground states cross at a conical intersection.
The molecular geometry at the point of decay shows, invariably, a sharp “kink” located at a -(CH)3- segment in the middle of the molecule. In Figure 1 we compare the structure of this -(CH)3- segment for all-trans octatetraene (all-trans-OT), S1 benzene and S1 cyclohexadiene intersections. Comparison of these structures reveals common structural and electronic features. Each structure contains a triangular arrangement of three carbon centres corresponding to a -(CH)3- kink of the carbon skeleton in all-trans OT [1] and benzene [2] and to a triangular arrangement of the -CH2 and -CH-CH2 terminal fragments in cyclohexadiene [3]. The electronic structure in each case corresponds to three weakly interacting electrons in a triangular arrangement which are loosely coupled to an isolated radical centre (this is delocalised on an allyl fragment in all-trans OT and benzene and localised in cyclohexadiene).
This type of conical intersection has been proved to be general for a series of linear polyenes and polyene radicals. These intersections are located at the end of excited state reaction path (the minimum energy path) [1] on the S1 potential energy surface and this decay path for s-trans butadiene is illustrated in Figure 2. The conical intersection is reached by twisting about two C-C bonds and decreasing of one of the C-C-C angles. As we shall now discuss, this type of decay route and the “kink” in the carbon backbone associated with the small C-C-C angle is a general feature for conjugated hydrocarbons with formula CnHn+2. This is related to the fact that in these molecules the first excited state as a π-π* doubly excited, diradical nature.
We now proceed to compare the structure and energetics of the excited state decay path for six (n=3,...,8) all-trans conjugated hydrocarbons: three polyenes (butadiene, hexatriene and octatetraene) and three polyene radicals (allyl, pentadienyl and heptatrienyl) [1]. The potential energy surfaces of these molecules have been computed using the ab initio CAS-SCF method with the DZ+d basis set and an active space including all π and π* orbitals and electrons (see Appendix A).
The lowest energy excited state reaction paths, connecting the optimised planar S1 or D1 equilibrium structures to a conical intersection, via the transition structure at the top of the energy profile, have been computed using the intrinsic reaction co-ordinate method implemented in the Gaussian 94 program package (see Section 1 and Lecture 2). The barrier heights have been corrected for dynamic correlation effects by single point computations using second order multi-reference Møller Plesset perturbation methods (see Lecture 2 and Appendix A). For n=3 and 4 the existence of a conical intersection at the end of the computed reaction path was also demonstrated by direct search and optimisation of the conical intersection point using the methodology implemented in the Gaussian 94.
In order to “calibrate” the accuracy of our computed results, the values of the energy barriers associated with the eight reaction paths are given in Table 1. The computed barriers heights are slightly larger than experiment and are correct to within 1 kcal mol-1 where the comparison with the experimental results is possible. However one has confidence that the computed reaction paths correspond to the paths populated at the range of low vibrational excess energies used in the jet experiments [7,8]. In Figure 3 we have superimposed the structure of the conical intersection of all six species. Clearly the -(CH)3- kink is a general feature. As already discussed in Lecture 1, the origin of this feature can be understood by comparison with H3, where any equilateral triangle configuration corresponds to a point on the S0/S1 conical intersection in which the three H electrons have identical pairwise interactions [9].
In Figure 4 we show (heptatrienyl radical), the π-electron density is localized along the three equivalent pairwise interactions (i.e. along the lines of the triangle illustrated) of the -(CH)3- kink.
Moving from conjugated hydrocarbons to other classes of organic molecules, the electronic structure of the lowest lying intersection changes. We now have detailed results on the olefin-carbonyl Paterno-Buchi system [10], α,β-enones [11], β,γ-enones [12], azo-compounds (diazomethane [13] and cyclic diazoalkenes [14]) and acylcyclopropenes [15] photorearrangements. While hydrocarbon photochemistry typically involves a low energy π-π* doubly-excited covalent state, the singlet photochemistry of carbonyl and azo-compounds is dominated by n to π* excitations. In Figure 5, we show the molecular and electronic structure of the diazabicyclo[2.1.1]hept-2-ene (DBH) and its conical intersection.
The DBH conical intersection is entered after C-N α-cleavage on the S1 state and leads to production of a diazenyl diradical. Thus the S1 photochemical reaction path is similar to the one of benzene and all-trans OT and illustrated in Lecture 1. As shown in Figure 5 the novel feature of the azoalkane S1/S0 conical intersection is that these are molecular structures where four states are degenerate: S0, S1, T1, T2. The accuracy of the methodology used in these studies has been tested against other azoalkane spectroscopic data [16]. For instance the computed 0-0 singlet excitation energies are 84.0 kcal mol-1 (82.7 including ZPE correction) for pyrazoline (exp. value 82 kcal mol-1) and 73.7 kcal mol-1 for 2,3-diazabicyclo[2.2.2]oct-2-ene (DBO) (exp. value 76 kcal mol-1). Second, the energy barriers for α C-N bond cleavage of singlet-excited pyrazoline and DBO afforded values of 7.6 (6.4 including ZPE correction) and 11.4 kcal mol-1, which compares with experimental values of 6-9 for a pyrazoline derivative and 8.6-10.2 kcal mol-1 for DBO derivatives.
The photochemistry of bichromophoric (C=O and C=C) compounds is, as in the azoalkanes, complicated by the competition between triplet 3(π-π) pathways and singlet 1(n-π) and triplet 3(n-π) pathways. This can be illustrated with the structure of the S0/S1 conical intersections found in α,β-enones. In this case, the first singlet excited state is not a π-π* state but an n-π* state where the lone-pair orbital n becomes singly occupied. This results in an electronic and molecular structure which is very different from the -(CH)3- kink seen in conjugated hydrocarbons. The case of cis-acrolein [16d] is instructive (see Figure 6a). The S1/S0 conical intersection has a 90° twisted terminal CH2 and corresponds to a diradical with radical centres on CH2 and O with a central C-C double-bond (1.34 Å). This structure corresponds to a point of degeneracy between the n-π* and ground state because the radical centres do not interact with each other and with the central π-bond. Thus, in this structure the S0 state and the 1(n-π*) state differ only in a 90° rotation of the position of the singly-occupied orbital on the oxygen. Since the position of this radical centre is isolated from the CH2 radical centre, the states have the same energy.
The structure of the S1/S0 conical intersection in acrolein rationalises the observed wavelength dependent photochemistry of α,β-enones. Direct irradiation with 310 nm light produces cis-trans double-bond isomerisation exclusively. In contrast irradiation with 250 nm light produces a mixture of isomerisation and ring-closure products. The 310 nm photochemistry comes from the enone T1 triplet state. Computations on acrolein demonstrate that this state is populated by ISC from the initial S1 (n-π*) excited state molecule to a T1 (π-π*) diradical intermediate whose structure is shown in Figure 6b. The 3(π-π*) diradical intermediate is not generated directly but involves decay through successive S1/T2 and a T2/T1 intersections. The T1 intermediate is located at a T1/S0 intersection and is the precursor of the photoproducts which are generated via a slow ISC process. The stability and structure of this diradical correlates nicely with the observed phosphorescence [17] and lack of production of the four-member ring oxetene upon <300 nm irradiation [18]. In fact, while the two radical centres are located on two vicinal carbons, the carbonyl bond is fully formed. Consequently, relaxation to the S0 state can only result in α,β-enone formation structure via cis-trans motion. The production of oxetane requires a very different decay point which is assigned to the S1/S0 conical intersection described above. The fact that 250 nm radiation is required for populating this decay channel is consistent with the fact that this is located at least 40 kJ mol-1 above the initial S1 structure.
The photoisomerization of protonated Schiff bases (protonated imines) occurs along a fully barrierless reaction path which resembles that of butadiene (see Figure 2 above). Nevertheless we will now see that, again, due to the different electronic nature of the S1 state the molecular structure and electronic distribution of the lowest-lying conical intersection is completely different from that of polyene hydrocarbons. The S1 state of cis C5H6NH 2+, a short protonated Schiff base analogue of tZt hexa-1,3,5-triene, is ionic 1Bu-like whereas the S1 energy surface of the corresponding polyene [19] is the covalent 2Ag state. The evolution of the shortcis C5H6NH 2+ along the interstate MEP (see Lecture 2) connecting the FC structure of the cis isomer to the S1 trans and cis product wells is illustrated in Figure 7.
Along this path the energy difference between the S1 and S2 (covalent 2Ag-like) states is large (> 25 kcal mol-1) and thus it appears that covalent S2 is not involved in the reaction. The S1 relaxation path ends at a point where the S1 (1Bu-like) and S0 potential energy surfaces cross at a conical intersection (CI). The intersection point (CI) has a ~80° twisted central double bond which provides a route for fully efficient non-adiabatic cis-trans isomerization. Starting from this point we have located two S0 relaxation paths. The first path is a continuation of the excited state path and ends at the all-trans C5H6NH 2+ well. The second path describes the back-formation of the reactant.
While both the doubly excited π-π* of polyenes and singly excited n-π* state of azoalkanes and carbonyl compounds are diradicals in nature and do not involve charge transfer from a region of the molecule to another, the singly excited π-π* state of protonated Schiff bases does. Figure 8 shows the evolution of the Mulliken charges [20] (with hydrogens summed into heavy atoms) along the reaction co-ordinate. The cis S0-S1 FC excitation results in a partial single electron transfer towards the NH2 end of the molecule which is consistent with the charge transfer associated with the HOMO-LUMO singly excited 1Bu-like nature of S1 [21,22]. Accordingly, the positive charge migrates towards the -CH2 molecular end. The most striking feature is the large, but regular, increase (from ~0.0 to +0.39) of the charge at the γ carbon centre along the S1 path. This centre is adjacent to the rotating bond and a stabilization of its positive charge must have an important effect on the stability of the twisted configuration. Along the isomerization co-ordinate the excited state charge distribution is smoothly changed and this change continues into the ground state branch of the reaction (i.e. after CI) where the positive charge is shifted back towards the -NH2 molecular end. As shown in Figure 8, in the vicinity of the CI point about 70% of the positive charge is localized on the allyl fragment due to depopulation of its singly occupied molecular orbital (SOMO). It must be noticed that in cis C5H6NH 2+ the increase in polarization along the computed MEP is gradual and a polarization corresponding to the migration of ~0.5 electrons towards the -CH-CH=NH2 is already present in the untwisted FC region. This situation is described by the four resonance formulae reported in Scheme 1.
The existence of a conical intersection point and the charge motion observed along the computed isomerization co-ordinate can be rationalized using the “two-electron two-orbital model” of Michl, Bonacic-Koutecky et al. [23b,24]. According to this theory the twisted CI structure corresponds to a “critically heterosymmetric biradicaloid”. A heterosymmetric biradicaloid is a structure where two localized orbitals have different energies but do not interact. This is the situation found in the CI structure presented above where one has that the SOMO π-orbital of the allyl fragment and the SOMO π-orbital of the -CHCH2NH2 + fragment are not overlapping. In this condition the energy separation of the “ionic” S1 and “covalent” S0 states depends on the difference between the electron affinity of the allyl SOMO and the ionization potential of the -CHCH2NH2 + SOMO.
These quantities can be changed as a function of the fragment structure. Thus along the last part of the S1 reaction co-ordinate the geometry of the two fragments is such that these energies become equal. Consequently, the S1 energy is lowered and ultimately the S1 surface crosses with the S0 surface. This interpretation is strongly supported by the π electron densities for the degenerate S0 and S1 states reported in Figure 9 (see also appendix B for a more detailed discussion on such twisted conical intersections).
Decay through a conical intersection and the subsequent evolution on the ground state surface can be studied using quantum or semi-classical dynamics [25]. For a cold or thermalized excited state of a sizeable organic molecule, the structure of the potential energy surface is expected to play the dominant role in determining the initial molecular motion in the decay region. Thus, one expects that excited state stationary points and minimum energy paths (MEP) will provide the important mechanistic information. For a photochemical reaction involving decay at a conical intersection, the MEP co-ordinate will have two branches. The first (excited state) branch describes the evolution of the molecular structure of the excited state intermediate until a decay point is accessed. At this point, the second (ground state) branch of the reaction co-ordinate begins, which describes the relaxation process ultimately leading to product formation. The excited state MEP and low-lying conical intersections which describe the excited state reaction co-ordinate have been characterized for several systems [26]. However, the characterization of the associated ground state co-ordinate, which describes the relaxation occurring after the decay, appears to be an outstanding problem. Indeed, while the location of minima, transition states, conical intersections and MEP on the excited state potential energy surface can be accomplished with existing methods [27], the problem of determining ground state relaxation paths, starting in the vicinity of a conical intersection, does not seem to have been frequently considered. It has been shown in Lecture 2 that the ground state relaxation paths departing from a single conical intersection point can be unambiguously defined and computed with a new gradient-driven method (see also ref. 28). Such structural (i.e. non-dynamical) information should provide a description of the reaction mechanism for photoproduct formation from vibrationally “cold” excited state reactants (i.e. under conditions of low vibrational excess energy) that occur in many experiments where slow excited state motion or/and thermal equilibration is possible (such as in cool jets, in cold matrices, and in solution). We will now illustrate an application of such method to the description of the radiationless decay and competitive photoproduct formation process in CHD/cZc-hexatriene system.
Irradiation at 254 nm transforms 2,5-di-tert-butylhexa-1,3,5-triene (a hexatriene with a dominant cZc equilibrium conformation) into the corresponding cyclohexadiene with a 0.54 quantum yield. The reverse reaction transforms 1,4-di-tert-butylcyclohexa-1,3-diene into the corresponding hexatriene with a 0.46 quantum yield [29]. Consistently, the computed structure of the low-lying part of the S1 (2A1) potential energy surface of these molecules shows that both the direct (CHD → cZc-HT) and reverse (cZc-HT → CHD) photochemical reactions involve the formation and decay of a common excited state intermediate (see Scheme 2).
This intermediate corresponds to excited state cZc-HT (cZc-HT*) and it is predicted to decay to the ground (1A1) state via a conical intersection (CICHD) which has been located ~1 kcal mol-1 above cZc-HT*. The detailed structure of CICHD is given in Figure 10. This is a polyene type conical intersection showing an interchain -(CH)3- kink (see also Figure 1).
Given the tetraradical electronic nature of this structure (see also discussion in Section 4.1 above) relaxation from CICHD may occur along three different routes as illustrated in Scheme 2b. Each route is associated with a different bond formation mode which is, in turn, driven by the re-coupling of four weakly interacting electrons (Scheme 2). Accordingly, route a leads to relaxation towards cZc-HT, route b leads to CHD and route c leads to a methylenecyclopentene diradical (MCPD). The mechanism of product formation in CHD photochemistry, in the limit of a “cold” excited state, has been investigate via a systematic search for the ground state relaxation paths departing in the region of CICHD and defining the “accessible” product valleys. We assume that: (i) the photoproducts originate from an excited state intermediate which is sufficiently “cold” that the ground state trajectories lie very close to the computed MEP and (ii) the surface hop occurs in the vicinity of the optimised conical intersection point.
The initial relaxation directions from a conical intersection have been located with the method discussed in Lecture 2. The results of these computations yield a description of the ground state relaxation paths departing in the vicinity of the CICHD structure of Figure 10. The results are illustrated in Figure 11.
The excited state reaction path connecting the intermediate cZc-HT* to CICHD is that of a slightly sloped conical intersection. The excited state path (red arrows) controls the motion leading to decay at CICHD, and the ground state relaxation paths (blue arrows) control the evolution following the decay and the photoproduct formation process. In the hypothesis that significant picosecond vibrational relaxation takes place in solution at room-temperature, the IRD (see Lecture 2) computed in the region of the conical intersection provide insight into the mechanism of the CHD/cZc-HT photochemical interconversion. The cZc-HT* intermediate which is produced by either CHD or cZc-HT irradiation, decays via a facile vibrational displacement leading towards the CICHD decay point. After decay, the reaction path bifurcates along two ground state relaxation valleys leading to CHD and cZc-HT. A third relaxation valley leading to MCPD is not directly connected to the conical intersection point CICHD and originates after the energy ridge RDGMCPD splits into two new ridges (comprising the MCPD “valley”) around 1.0 amu1/2 bohr distance from the decay point.
The distance of the initial part of the CHD, cZc-HT, MCPD valleys (see shaded regions in Figure 11) from the decay point and the magnitude of their slope provide qualitative information on the extent of the “catchment region” associated with a specific photoproduct. A valley (i.e. a MEP determined via IRD computations) which develops close to the conical intersection point and which is lower in energy will be associated with a larger “catchment region” and therefore there will be a higher probability of populating the associated valley upon decay from the conical intersection. Figure 11 suggests that the size of the CHD and cZc-HT “catchment regions” must be similar. Thus we expect that the decay of cZc-HT* will generate the products CHD and cZc-HT with similar yields. Hence, the photolysis of CHD is predicted to generate cZc-HT with a quantum yield ΦcZc < 1 because of the competitive CHD back formation. On the other hand, the computational results suggest that MCPD can only be a very low quantum yield primary photoproduct in the photolysis of CHD. The MCPD product formation path has a higher valley with respect to the other paths. Further, the MCPD product formation path is, initially, topologically inhibited since, in the immediate vicinity of the conical intersection it corresponds to a ridge (i.e. RDGMPCD) and ridge-like paths will be only populated at very large kinetic energy. For this reason, the photolysis of either CHD or cZc-HT must have a similar outcome. In fact, since both these reactants yield the same cZc-HT* 2A1 intermediate cZc-HT is predicted to yield CHD with a quantum yield ΦcZc-HT → CHD which is related to the quantum yield of cZc-HT produced via CHD photolysis (ΦCHD → cZc-HT) by the relation ΦcZc-HT → CHD ≈ (1 - ΦCHD → cZc-HT).
The interpretation of the CHD/cZc-HT photolysis just presented is compatible with the available experimental data. The ca. 1 kcal mol-1 excited state energy barrier computed via multireference MP2 theory is consistent with the observed picosecond lifetime of the 2A1 state following CHD direct irradiation [30]. While there are no measurements of ΦCHD → CHD (i.e. CHD back-formation during photolysis of CHD) or ΦcZc-HT → CHD (i.e. CHD formation during photolysis of cZc-HT), ΦCHD → cZc-HT is 0.41 [30] i.e. suggesting efficient CHD back-formation. On the other hand, irradiation of 2,5-di-tert-butylhexa-1,3,5-triene produces 1,4-di-tert-butylcyclohexa-1,3-diene with a 0.54 quantum yield. The reverse reaction occurs with a 0.46 quantum yield [29] in agreement with the predicted relationship ΦCHD → cZc-HT ∼ (1 - ΦcZc-HT → CHD). In other substituted and polycyclic molecules [31] steric and strain effects may greatly differentiate the slopes of the CHD and cZc-HT valleys leading to values of ΦCHD, ΦcZc-HT far from 0.5. However, the relationship given above appears to hold even in these cases [32].
The all-trans epta-2,4,6-trienimminium cation (a “longer” protonated Schiff base with four conjugated double-bonds) has the S1 MEP which is similar to the MEP of Figure 7. However, in contrast to the short protonated Schiff base seen above, this molecule may undergo trans→cis isomerization at either the double-bonds in position 2 and 4 as illustrated in Scheme 3.
The presence of competing channels that are barrierless or nearly barrierless is an interesting feature of longer protonated Schiff bases. Here we characterise the S1 MEPs of both these isomerization processes.
In Figure 12 we report the two unconstrained MEPs. Again the structure of such paths is similar to the one of Figure 7 but with a longer energy plateau (from 1 to 3 au and from 1 to 5 au for the C2-C3 and C4-C5 isomerization respectively). The two paths are nearly barrierless with only a <1 kcal mol-1 energy difference along the long plateau region (in favour of the isomerization at position C2-C3). However, the initial part of the MEPs, which is dominated by double-bond expansion, is similar. Thus, in contrast with 2-cis-C5H6NH 2+, the MEP co-ordinate of this longer protonated Schiff base shows that evolution along the torsional co-ordinate (and therefore either of the two competing paths) begins only after relaxation in the vicinity of the planar stationary point SP.
The results of analytical frequency computations confirm that, in a similar fashion to the short protonated Schiff base, the FC structure evolves along a co-ordinate dominated by totally symmetric stretching modes and the structure of region I is that of a valley.
This is also confirmed by the direction of the gradient at the FC point and by the fact that at 0.73 au distance one has a real (although extremely small) frequencies (8 and 59 cm-1) along the two relevant torsional modes. As seen in the case of the shorter 2-cis-C5H6NH 2+, there is one imaginary frequency at the S1 stationary point. However, the magnitude of this imaginary frequency and of the frequency corresponding to the alternative isomerization mode are only 45 i (C2-C3 torsional mode) and 62 cm-1 (C4-C5 torsional mode), thus reflecting the existence of the energy plateau and the general flatness of region II.
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