The aim of these lectures is to introduce the students to the practical computational investigation of photochemical reaction mechanisms. During the last decade or so, the speed of the computers available at academic sites has grown considerably and the computational investigation of “realistic” models of organic compounds is becoming a standard practice. Current applications range from the investigation of the mechanism of synthetically useful reactions to the study of short lived organic intermediates detected in the interstellar medium. For thermal reactions, state-of-the-art ab initio quantum chemical methods (see below) provide a complete description of what happens at the molecular level during the bond-breaking bond-forming processes. In particular, it is possible to compute, the transition structure which connects a reactant to a product and the associated energy barrier with nearly chemical accuracy (ca. 1 kcal mol-1 error). Furthermore the reaction path, ie. the progression of the molecular structure towards the transition state and the product, can be determined, in a fully unbiased way, by computing the minimum energy path connecting the reactant to the product along the 3N-6 dimensional potential energy surface of the system.
Until recently reaction path computations were limited to the investigation of thermal reactions or, in general, to reactions occurring on a single potential energy surface. Photochemical processes, where, typically, the reactant resides on an excited state potential energy surface and the products accumulate on the ground state could not be easily investigated. In fact, the reaction path is expected to have two branches; one located on the excited state and the other located on the ground state energy surface. The main difficulty associated with such computation lies in the correct definition and practical computation of the “funnel” where the excited state reactant or intermediate is delivered to the ground state. In fact, while the progression on excited state energy surface, ie. the excited state “branch” of the reaction path, may be investigated with the same type of methods used for thermal reactions there was no general way of defining the “locus” where this reaction path branch would be connected to the ground state branch.
During the last decade, computational chemists have been able to develop tools and learn strategies to explore electronically excited state species. As a result of an intensive computational and experimental work, new aspects of the behaviour of photoexcited organic molecules have emerged which have allowed for a more systematic investigation of photochemical reaction pathways. The most general of these is that the nature of the funnel, ie. the point along the reaction co-ordinate where decay from the excited to the ground state begins, has been clarified. In general, this point takes the form of a low-lying intersection. In fact, it has been shown that low-lying intersections (crossings) between the photochemically relevant excited state and the ground state occur with a previously unsuspected frequency [1]. Thus, an excited state intermediate has a high probability of entering a region where the excited state crosses the ground state during its motion. Thus, such crossings, ie. conical intersections in the case of two singlet (or two triplet) states, or singlet-triplet intersections, provide a very efficient “funnel” for radiationless deactivation (internal conversion and intersystem crossing) and, in turn, prompt photoproduct formation.
The deactivation of an electronically excited intermediate by internal conversion (IC) is usually discussed in terms of the interaction between the vibrational energy levels of the ground and excited state potential energy surfaces (represented by the S0 and S1 curves in the Scheme below) using the Fermi Golden Rule. The traditional view of singlet photochemical reactions (mainly due to the work of Van der Lugt and Oosteroff [2]) assumes that the absorption of a photon results in the generation of an excited state species (M*). This intermediate represents the precursor of the photoproducts (P) which are generated by decay to the ground state. This decay was predicted to take place in the region of an avoided crossing of the excited and ground state potential energy surfaces. At such an avoided crossing, if the energy gap is larger than few kcal mol-1, M* will rapidly thermalize and the decay probability (ie. the IC rate) will be determined by the Fermi Golden Rule. Accordingly, such processes are supposed to occur on the same timescale (several molecular vibrations) close to that of fluorescence.
The rate and the energy thresholds controlling IC can now be experimentally measured by exploiting the advances in laser spectroscopic techniques, treated in other parts of this Lecture Course, which have pushed the time resolution of various experimental techniques below the picosecond time-scale. Several results indicate that the Van der Lugt and Oosteroff model has to be refined by replacing the “avoided crossing” with an “unavoided crossing” ie. a conical intersection. Indeed, femtosecond excited state lifetimes have been observed, for instance, for simple dienes [3], cyclohexadienes [4], hexatrienes [5], and in both free [6] and opsin-bound [7] retinal protonated Schiff bases.
A view of photochemical reactions, that is consistent with recent experiments, was suggested more than 30 years ago by the physicist Edward Teller [8] at the 20th Farkas Memorial Symposium. He suggested that it was the electronic factors that may play the dominant role in the efficiency of radiationless decay. Teller made two general observations:
On the basis of these observations, Teller proposed that conical intersections may provide a common and very fast decay channel from the lowest excited states of polyatomics. In the field of photochemistry, Zimmerman [9] and Michl [10] were the first to suggest, independently, that certain photoproducts originate from IC at a conical intersection. Zimmerman and Michl use the term “funnel” for this feature. This hypothesis has been supported by
The suggestions of Teller, Zimmerman and Michl has been fully supported by recent computational work [11,12]. When taken in conjunction with modern experimental results, this indicates that the radiationless decay process occurs via a conical intersection between excited and ground states. Radiationless decay at a conical intersection implies that: (a) the IC process will be 100% efficient (ie. the Landau-Zener [13] decay probability will be unity), (b) any observed retardation in the IC or reaction rate (ie. the competition with fluorescence) must reflect the presence of some excited state energy barrier which separates M* from the intersection structure and (c) in the case where the decay leads to a chemical reaction, the molecular structure at the intersection must be related to the structure of the photoproducts. Points a-c provide the theoretical basis for the computational modelling of photochemical reactions. According to this approach the excited state motion is determine by the structure of the relevant excited and ground state potential energy surfaces. In simple terms, information on the excited state lifetime and on the type of photoproducts generated is obtained by following the detailed relaxation and reaction paths of the molecule along the potential energy surfaces from the FC point, or excited state intermediate, to the ground state. This approach is part of a more general way of considering photochemistry which is already employed in the textbooks [14]; it follows the pathway on the potential energy surfaces, and pays attention to local details such as slopes, barriers, saddle points, collecting funnels, etc. To have a short term we call this method the pathway approach, following the suggestion of Fuss et al. [15].
A particularly clear illustration of the pathway approach is given by the result of recent computational studies on polyene photochemistry. Experiments on isolated molecules in cold-matrices, expanding-jets and in solution have revealed the presence of “thermally activated” fast radiationless decay channels in hexatrienes, octatetraenes., aromatic compounds such as benzene and azulene (see references collected in ref. 12) an azoalkanes. For instance, the application of different spectroscopic techniques to low temperature samples of “isolated” conjugated molecules has begun to provide detailed information on the excited state dynamics of these organic systems and recent spectroscopic low-temperature investigations of isolated polyene molecules show evidence that photoinduced double-bond trans → cis isomerization may occur non-adiabatic reaction path where the excited state intermediate decay to the ground state at a highly twisted molecular geometry. In Figure 1 we illustrate the results of two different experiments on all-trans octa-1,3,5,7-tetraene (all-trans OT).
The first experiment (Figure 1a) is due to Kohler and co-workers [16] who recorded the fluorescence lifetime of S1 (2Ag) all-trans OT as a function of the temperature. In this experiment the all-trans OT molecules are isolated in a molecular cavity of frozen n-hexane and do not interact with each other. From Figure 1a, one can see that, at temperatures above 200 K, the fluorescence lifetime drops dramatically indicating fast decay of the excited state molecules to the ground state. This event was assigned to the opening of a thermally activated efficient radiationless decay channel with a barrier height of ~1500 cm-1 (4.3 kcal mol-1). Anyway, matrix isolation studies by Kohler, indicate that the photoisomerization on the S1 state occurs adiabatically (ie. prior to decay to the ground state S0) by overcoming a ~870 cm-1 (2.5 kcal mol-1) barrier. This adiabatic reaction is activated ~150 K below the temperature required for efficient radiationless deactivation [2a], [14]. The second experiment (Figure 1b) is due to Christensen, Yoshihara, Petek and co-workers [17], who reported the fluorescence decay rate of S1 all-trans OT molecules measured in free jet expansion as a function of the excitation energy. In contrast these authors propose that (under isolated conditions in a cool-jet) trans → cis motion in all-trans OT is responsible for the observed radiationless decay channel on S1 (2Ag) which opens up at ~2100 cm-1 (~6 kcal mol-1) excess energy.
In both experiments the fluorescence lifetime decreases slowly and almost linearly by increasing the S1 excess vibrational energy until an energy threshold is reached and a dramatic decrease in excited state lifetime is observed. Quantum chemical computations of the S1 reaction path of all-trans OT have revealed that the energy threshold corresponds to a transition state which connects an excited state intermediate to a conical intersection funnel. This result is schematically illustrated in Figure 2. The computation predicts a 7.5 kcal mol-1 barrier in good agreement with the experiment.
Nowadays, features like excited state intermediates and funnels are conveniently computed as points on the potential energy surface associated with the photochemically relevant excited state (usually the first singlet or triplet excited state). The computation of the excited state potential energy surface requires suitable quantum chemical methods which will be discussed in this Lecture Course by others. The detailed knowledge of the molecular structure of the funnel appears to be of vital importance for the rationalization and prediction of the observed photoproduct distribution. In fact, as mentioned above, we expect the photoproduct molecular structure to be related to the molecular structure of the decay channel more or less in the same way in which the structure of a thermal product is related to that of the corresponding transition state. Similarly, the detailed knowledge of the energetic stability of the decay channel relative, for instance, to the excited state equilibrium structure of the reactant is expected to be related to the excited state lifetime. In other, words excited state energy barriers may control the time taken by the system to reach the decay channel. Thus, in the first lecture we revise the theoretical concepts required for investigating chemical reactions by computing the potential energy surface. These include:
The goal of a computational approach to the study of photochemical mechanism is the complete description of what happens along the reaction co-ordinate from the absorptive act to the photoproduct formation. In thermal chemistry this problem is tackled by mapping of the reaction path which connects the reactant to the product (ie. two energy minima) through the transition state (ie. a saddle point). In practice this is done by computing the minimum energy path (MEP) connecting the reactant and product wells. The strategy used in photochemistry is similar. This is based on the mapping of the photochemical reaction path followed by following the MEP from the excited state intermediate (or from the Frack-Condon structure) to the ground state photoproduct through a conical intersection. This method (recently named pathway approach by Fuss et al. [14]) pays attention to local details and properties like slopes, saddle points, barriers and funnels (such as conical intersections) and has an intimate connection to the approach using the motion of wavepackets or semi-classical trajectories on potential surfaces to describe ultrafast photochemical processes. This description is now receiving new impact by recent advances in femtosecond spectroscopy and ultrafast techniques. Thus, in Lecture 2 we illustrate the computational tools and strategies which are being used to compute a photochemical reaction path. These include:
In Lecture 3 we illustrate few “general results” which have been obtained in the field of mechanistic organic photochemistry and compare them with modern (time resolved) and traditional experimental data. In particular we will show that, in agreement with the suggestions of Teller [8], Zimmerman [9] and Michl [10], recent computational [12] work, when taken in conjunction with modern experimental studies, indicates that in several cases the radiationless decay process does not occur via decay an excited state intermediate M* in many cases, but rather through a conical intersection (ie. a “real” surface crossing) between excited and ground states. While laser experiments provide information on the structure and energetics of the excited state potential energy surfaces controlling fast decay, more traditional photochemistry, such as quantum yield measurements, provide information on the molecular structure of the decay channel and on the product formation paths. The detailed characterisation of the stereo- and regio-chemistry of the primary photoproducts and transient intermediates, their quantum yields and the effect of specifically designed sterically and rotationally hindered reactants on these quantities [18] is now possible. As consequence the observed stereoselectivity and photoproduct distribution of a photochemical organic reaction must depend on either:
The study of photochemical mechanisms presents a considerable challenge for computational chemistry. Standard methods for the evaluation of the potential energy at an arbitrary molecular geometry such as SCF and DFT cannot describe excited states (see appendix A for details). Thus multi-reference methods such as CASSCF [19], multi-reference MP2 [20] and multireference CI [21] for the evaluation of the potential energy must be employed. While standard methods for molecular structure optimization can be used to find minima (ie. reactant, product and intermediates) and saddle points (ie. transition states) for ground or excited states, the description of the crossing region requires special methods because the Born-Oppenheimer approximation breaks down. Thus, as we will discuss in Lecture 2, special methods are required for the location and optimization of crossing structures. In addition, the inter-state nature of photochemical reaction paths requires special methodologies to locate the energy valleys describing the ground state relaxation occurring after the decay at the crossing. Further as we shall see the efficiency of radiationless processes is intimately connected to the velocity along the reaction path. Dynamics methods, which yield trajectories rather than paths, such as the wavepacket or semi-classical dynamics must be used in this case.
Methodologies such as CASSCF, multireference MP2 and multireference-CI (MR-CI [19, 21]) are now available in both commercial and free software [22, 23]. Methodologies for locating and optimising crossings between two potential energy surface is available in Gaussian [22a]. Methods for computing ground state relaxation paths starting from a crossing point as well as methods for computing semi-classical trajectories are still matter of research and to our knowledge are not publically available.
Copyright ©2000 Università di Siena , All Rights
Reserved.
Please report errors in this document to Prof. Olivucci.