MSc Chemistry
Molecular Sciences
Literature Thesis
Controlling Ultrafast Photochemistry
Towards Rational Design of Conical Intersections
by
Yorrick Boeije
10774831
10/2020
12 EC
July 2020 – September 2020
Supervisor/Examiner:
Examiners:
Prof. dr. Massimo Olivucci Prof. dr. A.M. Brouwer Prof. dr. Evert Jan Meijer
Laboratory for Computational
Photochemistry and Photobiology
2
Abstract
During the last few decades, conical intersections (CIs) have grown from theoretical curiosities into common mechanistic features of ultrafast photochemical reactions, funneling excited molecules back to the ground state at points where the adiabatic potential energy surface (PES) of two or more electronic states become degenerate. Analogously to transition states in thermal chemistry, such a critical structure in the reaction path offers the opportunity for a rational design approach to either promote or inhibit photochemistry, which can be measured through the quantum yield (QY). Due to the inherently more complex structure of CIs and the dynamics involved in the nonadiabatic decay, such an approach is not obvious. Therefore, the aim of this study was to understand what factors control the QY in ultrafast photochemical reactions. Although the energetic accessibility of a CI can be controlled through an activation barrier on the excited state (ES) PES that separates an ES minimum from the CI, the main focus of this literature study was to understand what factors control the branching of photoproducts and reactants that occur at the CI. It was found that the basic one-dimensional Landau-Zener (LZ) predicts an increase in nonadiabatic decay rate and QY for a smaller wavepacket width and larger wavepacket velocity towards the CI. Both of these dynamical properties may be explained by a steeper slope on the ES PES that biases the wavepacket in that direction and after passage through the CI, to the photoproduct. These dynamical arguments imposed by the static ES PES explains the greater nonadiabatic decay efficiencies typically found in peaked CIs compared to sloped CIs as well. Such a topological feature can be synthetically tuned, e.g. by shifting the energetic position of the CI with respect to the Franck-Condon (FC) point. Alternatively, the velocity can be altered by tuning the normal mode frequency of the reactive coordinate. In contrast to these one-dimensional rationalizations, recent research on the photoisomerization of rhodopsin points towards a multimodal explanation that controls the branching at the CI. This modern view involves the phase-matching of multiple modes near the CI that should be optimized if one wishes to increase the QY. Hence, rational design of ultrafast photochemical processes should go beyond the LZ model by focusing on maintaining intramolecular vibrational coherence throughout the complete reaction, and on tuning the relative phase of the relevant normal modes. It is anticipated that such a strategy will impact photocatalysis and solar energy conversion research, where it is crucial to control vibronically coherent ultrafast ES processes, including electron transfer, energy transfer and singlet fission.
3
| Contents
List of Abbreviations 5
Chapter 1 |
Introduction
6
1.1 Photochemistry Basics 7 1.2 A Paradigm Shift in Ultrafast Photochemistry 8 1.3 Excited State Analogue of the Transition State 10 1.4 Aim and Outline Thesis 12 1.5 Theory of Conical Intersections 13 1.5.1 Mathematical and Computational Characterization 13 1.5.2 Chemical Understanding using Valence Bond Theory 16
Chapter 2 |
The Landau-Zener Model
19
2.1 Landau-Zener Formula 19
2.2 Static Factors 20
2.2.1 Excited State and Funnel Topographies 20 2.2.2 Static Tuning through Chemical Substitution 24
2.3 Dynamical Factors 27
2.3.1 Trajectory Distribution Properties 27 2.3.2 Dynamical Tuning through Chemical Substitution 28 2.4 Limitations of the Landau-Zener Model 30
Chapter 3 |
Beyond the Landau-Zener Model:
Vibrational Motion in Concert
32
3.1 Ultrafast Double Bond Photoisomerization of Rhodopsin 32 3.1.1 Spectroscopic Evidence (I) Vibrational Coherence 33 3.1.2 Computational Evidence: Cooperative Motion of
Three Relevant Vibrational Modes 34 3.1.3 Spectroscopic Evidence (II) Vibrational Phase Isotope
Effect 38
3.1.4 Related Studies on Rhodopsin Analogues 39 3.2 Other Ultrafast Double Bond Photoisomerizations 41 3.2.1 Biological Systems 41 3.2.2 Molecular Switches 43 3.3 Other Photochemical and Photophysical Processes 44 3.3.1 Singlet Fission in Organic Photovoltaics 44
4 3.3.2 Energy Transfer, Charge Transfer and Internal
Conversion in Photovoltaics and Nanomaterials 47
3.3.3 Photodissociation 48
3.3.4 Pericyclic Reactions 48 3.3.5 Internal Conversion in Transition Metal Complexes 51 3.4 Synergy with Coherent Control 52
Chapter 4 |
Conclusion and Outlook
54
5
List of Abbreviations
2DES 2D Electronic Spectroscopy
bathoRh bathorhodopsin
BLA Bond Length Altnernation
BO Born-Oppenheimer
CAS-MP2 Complete Active Space Møller-Plesset second order
CASSCF Complete Active Space SCF
CC Coherent Control
CI Conical Intersection
COOP Carbon Out-Of-Plane
CT Charge Transfer
DFT Density Functional Theory
DICI Defect-induced CI
ES Excited State
ESPT Excited State Proton Transfer
FC Franck-Condon
GFP Green Fluorescent Protein
GS Ground State
IC Internal Conversion
IRC Intrinsic Reaction Coordinate
IVR Intramolecular Vibrational Relaxation
IS Intersection Space
ISC Inter-System Crossing
HOOP Hydrogen Out-Of-Plane
LED Light-emitting Diode
LZ Landau-Zener
MEP Minimum Energy Path
MLCT Metal-to-Ligand Charge Transfer
NAIP N-Alkylated Indanylidene–Pyrroline
OPV Organic Photovoltaics
PES Potential Energy Surface
QY Quantum Yield
QM/MM Quantum Mechanics/Molecular Mechanics
PV Photovoltaics
Rh Rhodopsin
rPSB11 protonated Schiff base of 11-cis retinal
rPSBAT protonated Schiff base of all-trans retinal
SCF Self Consistent Field
STC singlet-triplet crossing
TD-DFT Time-dependent DFT
TICT Twisted Intramolecular Charge Transfer
TS Transition State
6
1
Introduction
Photochemistry is about the world of excited states that lies on top of the ground state world in which all of thermal chemistry takes place. The interaction of a molecule with light opens up a gate to this energetically higher world, which is not necessarily long-lived. Indeed there are regions where these two worlds meet in the form of a conical intersection (CI, sometimes also indicated by theoreticians as ‘’CoIn’’ or ‘’ConIn’’, not to confuse the acronym with the popular Configuration Interaction of electronic structure theory), that is capable of funnelling the molecule from the excited state (ES) back into the ground state (GS), which could either result in regeneration of the starting molecule (internal conversion, IC) or formation of a new molecule (photochemical reaction).1 It depends critically on the situation, whether it is
favorable or unfavorable to have quick access to a CI to facilitate nonradiative decay. An elegant example in nature where it is favorable, is the primary event in vision. Here, the protonated Schiff base of 11-cis retinal (rPSB11) undergoes a highly efficient and fast photoisomerization, triggering a signal-transduction pathways to carry over the information to the brain without any delay due to reaction dynamics.2–4 Whenever a long lifetime is
required, such as in photovoltaics (PVs) or light-emitting diodes (LEDs), nonradiative decay through a CI should be inhibited.5,6 In any case, it is important to understand the exact nature
of CIs, what factors control the photochemical outcome resulting from passage through a CI, and how these factors can be (chemically) tuned.
Answers to these questions are relevant for a wide variety of research fields. In bio(physical) chemistry, researchers aim to understand how photochemical processes, such as electron transfer in photosynthesis7,8 or the biosynthesis of vitamin D9–11 are controlled by CIs.
Improved knowledge on these photochemical processes in biological systems could help chemists to design artificial systems, such as molecular motors. For example, Feringa’s motor is heavily dependent on two photoexcited ultrafast double bond isomerizations proceeding through CIs.12–14 For future exploitation of light-driven molecular motors in molecular
machines or devices, it is essential to control these photoisomerization reactions. Similarly, optimizing the performance of light-driven molecular rotors and switches relies on increased understanding of the CIs involved in their ES decay.15–18
Synthetic organic chemistry is another research field that makes tremendous use of photochemical reactions. Amongst these, light-induced pericyclic reactions in particular, such as the photochemically allowed [2+2] cycloaddition to make cyclobutanes, are widely applied.19 In these reactions, exciting the reactants with light makes an otherwise
symmetry-forbidden reaction allowed, with the help of a CI that bypasses the GS activation barrier.20–24
Although the list of photochemical reactions applied in synthetic chemistry is exhaustive, the photochemical reactions involving carbonyl groups, including Norrish types 1 and 2, should not be omitted.25 The importance of CIs that drive these photochemical reactions has been
recognized as well.26,27 Gaining mechanistic insights into these reactions is highly desirable in
order to increase (stereo)selectivity, as CIs have a well-defined stereochemistry, similar to transition states (TSs).
In general, molecules become more reactive when they are excited. Although this feature can be of synthetic purpose, it can become disastrous when thymine DNA base pairs undergo
7 a photochemical [2+2] cycloaddition, which could lead to skin cancer.28 Nature has figured out
a way to dissipate the excess energy very efficiently through a CI, limiting the cell damage.29
Sunscreen researchers thrive for the same goal by designing the molecule such that it absorbs the UV light from the sun, but gets rid of the excess energy very rapidly.30
Before explaining how the concept of CIs entered the standard vocabulary of photochemists, photophysicists and even photobiologists and discuss more thoroughly what they actually are, some preliminaries of photochemistry are shortly reviewed to provide context to CIs.
1.1
Photochemistry Basics
Photochemistry is the result of a tough competition that takes place in the ES.31 Whether a
photochemical reaction takes place upon excitation, depends critically on the efficiency of other competitive decay pathways. These pathways can be both radiative and nonradiative. Radiative decay is called fluorescence when the emission occurs from an electronically excited singlet state, whereas it is called phosphorescence when a triplet state is emitting. Nonradiative pathways include the earlier mentioned IC and photochemical reaction, next to inter-system crossing (ISC), which is the mechanism capable of switching between singlet and triplet states. In Section 1.5 it will become clear that a photochemical reaction and IC are intimately related decay processes. Usually, these photophysical decay pathways are visualized in a so-called Jablonski diagram. Also implied in the Jablonski diagram is Kasha’s rule, which states that the emitting level of a given multiplicity is the lowest excited level of that multiplicity.32 This is the result of an effective IC for higher-lying ESs and can often be
translated to photochemistry as well, meaning that photochemical reactions often take place from S1 or T1, although exceptions exist.33
To visualize a photochemical reaction, a Jablonski diagram can be rewritten in terms of adiabatic potential energy surfaces (PESs), as shown in Fig 1.1.31 These PESs are the
eigenvalues of the Born-Oppenheimer (BO) electronic Hamiltonian summed to the nuclear repulsion energy. Hence, each electronic state of a molecule is represented by a PES that shows the energy as a function of molecular coordinates. These PESs are often visualized in 2D or 3D, despite the fact that molecules are 3N-6 dimensional objects (also called ‘’nuclear coordinates’’), where N is the number of nuclei. It is important to note that the maxima and minima appearing on two different PESs may appear at different geometries. Assuming the BO approximation, these PESs are adiabatic, meaning that they only cross at CIs (crossings of states with same spin multiplicity) or singlet/triplet crossings (STCs).34 However, at these
crossing points the BO approximation fails and therefore they are not strictly parts of physically correct reaction paths, as those that involve a single PES. The reason why this visualization works so much better for discussing photochemistry, is that (i) it naturally incorporates the classical forces (slope of energy vs. geometrical distortion) when the molecule is excited to the Franck-Condon (FC) point, which significantly influences the temporal evolution of the wavepacket and hence its decay dynamics and (ii) it defines a region where nonadiabatic phenomena such as a transition from one surface to the other may occur with a nonnegligible probability.35
Furthermore, this representation is helpful for the rough classification of photochemical reactions in the following three groups.31,36 The first is an adiabatic reaction, in which the
reaction takes place on an ES surface, after which the molecule decays to the GS without entering any intersection region (a in Fig 1.1). Since an ES intermediate appears in this reaction,
8 fluorescence (indicated with a red line) can be observed. Excited state proton transfer (ESPT) reactions belong to this class.37,38 The diabatic photoreaction proceeds either via a CI (where
surfaces really cross, b in Fig 1.1) or an avoided crossing (where surfaces nearly cross, c in Fig
1.1. Especially in the first situation, there is a strong nonadiabatic coupling at the regions of
degeneracy, resulting in a failure of the BO approximation. This strong coupling is manifested in both a strong coupling between the two electronic states and local vibrational modes due to a pronounced anharmonicity in the CI region.39 As a consequence, CIs features modulate the
nonadiabatic dynamics of diabatic photoreactions at timescales as short as femtoseconds. No intermediate can be detected in such a reaction. There is a growing consensus that the majority of ultrafast (<10 ps) diabatic photoreactions proceeds through a CI. Therefore, the first sentence of this Thesis should be slightly adapted to: Photochemistry is about the world of excited states that
lies on top of the ground state world and the regions where these worlds cross.
Fig 1.1 Three classes of photochemical reactions. (a) adiabatic (b) diabatic via CI and (c) diabatic via avoided crossing. Blue arrows indicate light absorption. Red arrows indicate light emission. Dotted lines represent chemical reactions, whereas curly lines represent nonradiative decay with nonzero energy gaps. R indicates reactant, P and P’ indicate photoproducts. Adapted from ref 31.31
1.2
A Paradigm Shift in Ultrafast Photochemistry
CIs have not always been recognized as such a general mechanism for ultrafast photochemical reactions and IC and have remained theoretical curiosities for a long time.40 On
the other hand, avoided crossings were believed to be more ubiquitous, which was rationalized by the non-crossing rule, that states that electronic states of the same symmetry can not cross.41
However, Teller showed in 1937 that for polyatomic molecules, same-symmetry levels can cross as well to form CIs, allowing for efficient non-adiabaticity.42 He also pointed out that
nonradiative decay occurs within a single vibrational period when the molecules travels along this CI. Importantly, his results showed that the non-crossing rule is rigorously valid only for diatomic molecules, as was later confirmed by Longuet-Higgins.43 Furthermore,
Longuet-Higgins contributed to the understanding of CIs by the discovery of the geometric phase effect, also known as Berry’s phase.44 This effect is referred to the change of sign of a wavefunction
when it is transported along a closed loop that contains a CI.
Parallel to these discoveries, Van der Lugt, Oosteroff and Devaquet found in the electrocyclic ring closure of butadiene that the point that brings the molecule back to the GS is
9 an avoided crossing minimum.45,46 Zimmerman and Michl were the first to propose that in
organic photochemical reactions this point may correspond to a CI, which they called a
photochemical funnel.47,48 These interpretations were in line with the state correlation diagrams
that Salem developed, which showed how carbonyl photochemistry relied on surface touchings and surface crossings.49 Increased computational power and new algorithms in the 80s were
required to fully embrace these ideas. First, the geometric phase effect was used to locate CIs between two electronic states of the same symmetry in the triatomic molecules O3 and
HeH2.50,51 With the advance of ab initio computational methods, it became even possible to
predict geometrical structures for CIs using symmetry-constraints in some small molecules.52– 55 Bernardi, Olivucci and Robb however, showed the importance of full geometry optimization
to locate CIs in some pericyclic reactions and developed a valence bond (VB) model to provide a chemically intuitive model to understand this.20,56 Crucially, they showed that the Van der
Lugt and Oosteroff mechanism for the butadiene ring closure involving an avoided crossing is implausible when the symmetry constraints are relaxed.57 It appeared that the mechanism
that proceeds via an avoided crossing is a 2D slice through the double cone of the reaction path that follows the CI, as shown in Fig 1.2.58
Fig 1.2 Schematic overview of the relation between an avoided crossing (left) and conical intersection (right) mechanism for the photochemical ring closure of cis-butadiene. The mechanism through the avoided crossing (the Van der Lught and Oosteroff mechanism) is a 2D-slice of the 3D CI mechanism. Hence, the Van der Lught and Oosteroff mechanism is based on a symmetry coordinate and proceeds through an ES minimum, M*. By relaxing this symmetry constraint, and allowing the molecule to follow the steepest gradient on the S1
surface, the mechanism through a CI is obtained. Also shown here is the CI structure of butadiene.58
This mechanistic transition from considering CIs instead of avoided crossings evolved parallel to the notion that Fermi’s Golden rule, which is a perturbation theory approach that assumes weak coupling in the vibrational manifold of states, is not always sufficient to describe ultrafast nonradiative decay.57,59 In this model, the overlap of vibrational
10 nonradiative decay after vibrational relaxation has taken place.31 Since the decay via an
avoided crossing takes place via a vibrationally relaxed energy minimum, Fermi’s Golden Rule has been used often to calculate the rate of nonradiative decay. However, the development of laser spectroscopic techniques allowed detection of ultrafast ES decay processes faster than the picosecond timescale. The speed of many of these processes was observed to be higher than Fermi’s Golden rule could account for. For example, femtosecond lifetimes have been measured for alkenes and aromatic compounds.60–63 These spectroscopic
results hint towards a description of nonradiative decay that does not proceed via an ES intermediate, yet a CI (unavoided crossing or real crossing).57 As more examples followed, the
concept of a CI rapidly transformed into a common mechanistic feature for photochemical processes rather than a theoretical curiosity.21,22,60,63,64
This distinction has several important implications.57 Firstly, in contrast with passage
through an avoided crossing that has to compete with other decay mechanisms such as fluorescence, the transition probability at a CI is 100% as a result of the diminishing electronic energy gap. Hence, any delay in IC or a photochemical reaction rate reflects an ES barrier. Secondly, multiple GS relaxation pathways are possible leading to different photoproducts, when the reaction proceeds through a CI. This latter point will be clarified in Section 1.5, where the nature and shape of the CI will be explained that allows for such a branching of products.
Lastly, the molecular structure of the CI has some photoproduct character. This last implication is similar to Hammond’s postulate that describes the geometrical structure of the TS in thermal reactions.65 Therefore, it seems reasonable to draw similarities between the
description of TSs in thermal chemistry and CIs in photochemistry.
1.3 Excited State Analogue of the Transition State
A primary goal of synthetic chemists is to selectively make one molecular structure with the greatest yield possible. Usually in close connection with theory, chemists are able to rationally design their experiment in order to achieve this.66 When the thermal reaction is
under kinetic control, the reaction rate can be increased by lowering the activation barrier of a specific reaction path with respect to other paths.67 Understanding the geometrical structure
and energetics of the corresponding TS is crucial in this respect. With electronic and steric tuning in their toolbox, chemists are world champion in taking control of the kinetics. They may thank transition state theory for its quantitative prediction of reaction rates and branching ratios, as well as its qualitative description of reaction coordinates in terms of energy barriers.68
In addition, statistical energy redistribution,69 phase-space dynamics70 and the
Bell-Evans-Polanyi principle71 are guiding rules for predicting and designing GS chemical reactivity.
By exciting a molecule with light, the rules of the game are changed. The holy grail in the field of photochemistry is to understand what these rules are. To start, some analogies can be made between kinetic control in ES and GS reactions, as in both cases the product is formed after the reaction proceeds through a critical structure, as illustrated in Fig 1.3. In the GS reaction, this structural bottleneck is the TS, whereas a CI forms this bottleneck in an ES reaction, whose access can be controlled by a TS on the ES surface (not shown in Fig 1.3).
11 Fig 1.3 Left: PES of a thermal reaction showing the reactant (A), transition state (TS) and product (B). The red arrow indicates the transition vector, x1. Right: PESs of a diabatic
photochemical reaction showing the excited reactant (A*), conical intersection (CI), GS reactant (A) and two photoproducts (B and C). The red arrows indicate the branching plane vectors x1
and x2.57
Needless to say, there are some important qualitative differences between the TS and CI. In a thermal reaction, the TS connects the reactant (A) to a single product (B) via a single reaction path (Fig 1.3). A CI on the other hand, forms a spike on the GS PES that connects the ES reactant (A*) to two or more GS products (A, B and C) via multiple reaction paths.57 The GS reaction paths
that are accessible from this CI determine the nature of the photoproducts (or GS reactant) that might be generated. To put this distinction in more mathematical terms, the TS is a stationary point, whereas the CI is a singularity.1 Hence, the TS can be represented by a single vector
indicating a single reactive motion (which is the eigenvector of the imaginary vibrational frequency), yet the CI should be represented by two vectors forming the branching plane indicating all possible reactive directions of motion formed by combination of these two vectors.57 Section 1.5 will further elaborate on the nature of these branching plane vectors.
Secondly, GS dynamics towards the TS is frequently energetically uphill. In contrast, although there could be an activation barrier separating A* from the CI, ES dynamics towards the CI may be energetically downhill once this barrier has been transpassed.59 As will be clear
in Chapter 2, this steep gradient on the ES PES has important implications for the dynamical factors that controls the photochemistry through a CI.
A last difference that should be mentioned here is related to the dimensionality of both structures. CIs are not isolated structures as TSs, rather they are high-dimensional seams, i.e. collections of structures that are all CIs, usually of different energies.72 This will be clarified in
Section 1.5, where the electronic origin of CIs is discussed more thoroughly.
As previously mentioned, tuning of the barrier heights is the most common tactic in thermal chemistry to increase selectivity and yield. Because of the increased complexity of the (nonadiabatic) dynamics, the geometrical structure of the critical structure and the number of possible ES reaction paths, controlling ultrafast ES reactivity is less obvious.73 Still, the
12 barriers, similar to thermal reactions. Another practical complication that has to be considered for kinetic control in photochemical reactions in general is that the photoproduct might absorb at the irradiation wavelength as well, resulting in a photostationary state.31 Assuming that the
photoproduct does not absorb at this wavelength and the reaction takes place under kinetic control, it is the photochemical quantum yield (QY) that determines the reaction yield and selectivity. Also assuming that a certain photochemical reaction proceeds via one ES path through a single CI, it is the reactant/product branching ratio (A:B:C) at that CI that should be controlled to obtain higher yields and selectivities.74
This simple CI topology is present in the photoisomerization of the visual pigment rhodopsin (Fig 3.1).75 Hence, the branching ratio of reactant and product at the single CI
determines the photochemical QY and therefore controls the selectivity and yield. In this computational study, the QY is defined as the ratio of nonadiabatic trajectories leading to the product (Np) over the total number of computed trajectories launched (Nt).75 In agreement with
experiment, rhodopsin shows an excellent quantum yield of 0.67, meaning that the branching ratio at the CI is strongly in favor of the isomerized product.
1.4
Aim and Outline Thesis
Apparently, CIs are general mechanistic features in ES processes, which is why it makes sense to utilize CIs in order to rationally design molecules to control photophysical and photochemical reactions. Such ambitious goals would imply greater yields and selectivity for synthetic chemists, enhanced photostability for sunscreen developers or extended ES lifetimes for solar cell researcher or photocatalysis. Although the focus in this Thesis is on the control of ultrafast photochemical reactions, insights into the rational design of CIs to drive photochemical reactions should translate to IC and other ES processes as well, because of their common mechanistic origin.76 The aim of this Thesis can now be formulated as follows:
What factors control the quantum yield in ultrafast excited state reactions?
In line with the previous Section, in which it was stated that the branching at the CI determines the QY of a photochemical reaction under certain circumstances, rational design should consider the factors that control the branching there. Therefore, the above aim can be specified to:
What factors control the branching at a conical intersection in ultrafast excited state reactions?
This Thesis will aim to provide answers to both these questions, with special emphasis on the second one. Before diving into these questions, it is desirable to first obtain a better understanding of CIs (Section 1.5). This has been attached to this Chapter, as it does not directly answer the research question, but is required knowledge to understand Chapters 2 and 3.
Chapter 2 aims to answer these research questions within the Landau-Zener (LZ) model,
which is a basic and widely employed model to explain a majority of photochemistry.77 It takes
into account both static and dynamic aspects regarding the CI, allowing already a rational design approach to control the QY by chemical substitution.
Multiple recent research papers point towards a failure of the LZ model in describing certain ES phenomena.75,78–80 Hence, Chapter 3 is an addition to Chapter 2 to gain enhanced
13 relevant normal modes. A prominent part of Chapter 3 will be spent on rPSB11 photoisomerization in rhodopsin, to explain why its QY is so great, i.e. how the branching at the CI is controlled, and whether these insights can be applied to other ultrafast ES processes, such as singlet fission, for an optimization of QYs. Hence, rhodopsin photoisomerization forms an important framework to control ES reactivity, as it so well studied and a great illustration from nature of how photochemical reactivity can be designed so efficiently. The finishing Section of this Chapter will aim to connect coherent control experiments, where laser pulses are tuned to optimize QYs, with the relevance of the relative phase of vibrational modes in achieving this.
The Thesis will be concluded with Chapter 4, in which the factors controlling ultrafast photochemistry will be summarized. Implications for future rational design of CIs to control photochemical processes will be provided here as well.
1.5 Theory of Conical Intersections
1.5.1 Mathematical and Computational Characterization
The cone shape of CIs (when two PESs really cross) can only be visualized if the energy is plotted as a function of two specific internal geometrical coordinates of the molecule, which are combinations of bond distances and angles (Fig 1.4). For an intersection between states of the same (spin)symmetry, these geometrical coordinates, x1 and x2,are the gradient difference
vector (also called the g-vector) and the gradient of the interstate coupling vector respectively.81
They are defined as follows:55,57
𝐱𝟏 {or 𝑔(𝐪)} =
𝜕(𝐸0− 𝐸1)
𝜕𝐪 Eqn (1) 𝐱𝟐= ⟨𝟎|𝜕𝐇𝜕𝐪 |𝟏⟩ qn ()
In which the symbols in bold indicate that they represent vectors or matrices. q indicates an infinitesimal nuclear displacement. 𝟎 and 𝟏 are the adiabatic wavefunctions of the lower and upper PES respectively (S0 and S1) and H is the configuration interaction hamiltonian.
More often, the x2 vector is represented as the nonadiabatic coupling vector (also called the
h-vector), which is parallel to the gradient of the interstate coupling vector and is defined in Eqn
3.23
𝐱𝟐 {or ℎ(𝐪)} = ⟨𝟎|
𝜕𝟏
𝜕𝐪⟩ Eqn (3)
x1 (or g) is the vector that points along the steepest slope between the two PESs. So at a
point near the CI on the ES PES it will be directed parallel to the reaction path. Since x2 (or h)
is not parallel to x1, neither is it parallel to the reaction path. x2 is the direction of nuclear
displacement that mixes the upper adiabatic wavefunction with the lower adiabatic
wavefunction at the CI. When these two states are of different symmetry at the apex of the
cone, the symmetry-lowering x2 allows them to mix. Together, these vectors and their
14 the CI and molecular deformation along these two directions (or any combination of them) lifts the degeneracy between S1 and S0, forming the shape of a double cone.57 When moving
along any of the other n-2 vibrational degrees of freedom (n = 3N-6 in total, where N is the number of nuclei), the degeneracy is not lifted. Hence, the intersection space (IS), formed by these n-2 internal coordinates (x3,x4 …xn, which are locally orthogonal to the 2D branching
plane), is a hyperline that consists of an infinite number of CI points. It is not trivial which of these CI points in the IS space is most relevant for a certain photochemical reaction.72 Finally,
the formal definition of a CI can be stated as follows:58
Two states even with the same spatial and spin symmetry will intersect along a (n-2) hyperline as the energy is plotted against the n nuclear coordinates.
Fig 1.4 Left: graphical representation of a CI and its relation with the vectors x1 and x2. Plotting
the energy as a function of these coordinates clearly shows the double cone shape of the CI. Right: illustration of the n-2 dimensional nature of the CI, which is a hyperline if plotted against all the n nuclear degrees of freedom.
For a symmetry-allowed CI, the relevant coordinates to consider can be classified as
coupling and tuning modes.82 Analogously to the nonadiabatic coupling vector and gradient
difference vector, these modes modulate the interstate coupling through vibronic (i.e. nonadiabatic) coupling and the steepest variation in electronic energy gap respectively.83,84
Fig 1.5 illustrates how these concepts can be used to understand a photochemical reaction
path, in the case when different parts of the IS are associated with different ES processes.85
Here, photoexcitation from the GS equilibrium reactant structure, GS1, to the FC-point,
indicated with EX1, results in ES nuclear dynamics that is determined by X12 and X3. X12
indicates a vector that lies in the branching plane, while X3 denotes a vector orthogonal to the
branching space. As is in agreement with the previous discussion, motion along X12 leads to
nonradiative decay and its subsequent initial GS trajectory, because in this direction the degeneracy between S1 and S0 is lifted. In contrast, X3 directs the molecule along the IS in which
S1 and S0 remain degenerate. Indeed, several CI points, CI1 and CI2 are found in this space.
Both pathways to CI1 (full line) and CI2 (dotted line) could eventually lead to nonradiative
decay in the branching space. However, whereas the first could lead to formation of the reactant (IC), the second leads to formation of a photoproduct (GS2). In any case, it is the X12
vector that leads to passage through a CI. Because the branching plane changes along the IS, the nature of the x1 and x2 vectors is different in CI1 and CI2, which explains the different decay
processes that occur through these CIs. Furthermore, the accessibility of GS valleys upon decay controls the direction of motion during GS relaxation and hence the formed photoproducts.58
15 Fig 1.5 A hypothetical photochemical reaction pathway with energy plotted as a function of the coordinates X12 and X3. The former represents any vector of the branching plane, whereas
the latter represents any vector orthogonal to that plane. The photochemical reaction path starts by exciting from the equilibrium GS geometry, GS1, creating a wavepacket at the
FC-point, EX1. From there, this wavepacket can reach either CI1 or CI2 via the full and dotted white
trajectories respectively. Both CIs display the double cone shape as shown in the inset. Motion in this branching plane leads to nonradiative decay.85
According to the pathway approach, structural features of the ES and GS PESs, including slopes, barriers and funnels, determine the photochemical reaction path.64 This approach has
a close connection with describing the progression of excited molecules as wavepackets moving along a PES. Whenever an ES minimum (M*) is separated from the CI by a TS (a in
Fig 2.1), a minimum energy path (MEP) that connects the FC-state to M* and M* to the CI can
be computed using the intrinsic reaction coordinate (IRC) method.58 The MEP is a reasonable
measure of the progress of ES molecules, as a molecule will move along this well-defined path on average. Furthermore, the MEP is a good approximation when vibrationally cold molecules are studied.
When either M* or TS is absent, or both are absent (b in Fig 2.1), the lowest lying CI point can be located by minimizing the geometry in the n-2 IS.56 Indeed, in the branching space
neither of the gradients at the touching surfaces is zero (which would be zero at an avoided crossing), which is a necessary requirement to locate a stationary point.23 Instead, it is the
projection of the gradient of the ES PES onto the (n-2)-dimensional subspace that goes to zero when the geometry of the CI is optimized.86 Hence, in n-dimensional space the CI will not be
observed as a minimum, although it is the bottom of a funnel. This is analogous to the optimization of a TS where the energy minimization is carried out along n-1 directions orthogonal to the reaction coordinate, in combination with maximizing the energy along the reaction coordinate. Usually, both the optimization is carried out for the CI, as well as for the TS to provide a full picture of the reaction dynamics involved using the Newton-Raphson method.87 Because the optimization of CIs by definition involves two adiabatic PESs, standard
16 (TD-DFT) are not applicable.88,89 Therefore, multi-configuration SCF (Self Consistent Field)
methods, such as CAS-SCF (Complete Active Space SCF) or CAS-MP2 should be used, which are based on variational and perturbative configuration interaction theory respectively.90,91
These ab initio methods are the preferred choice when calculating the complete ES PES and CI structures, as well as excitation energies.
The above mentioned techniques provide information about the processes involved in nonradiative decay up to the CI point. In addition to this, to determine the branching at a CI it is important to understand the evolution of GS photoproducts following decay through this CI by studying the GS relaxation process. Celani et al. developed a protocol to characterize these relaxation pathways and their corresponding photoproducts.87 Yet still, this only
provides static information about the decay process. To get a full picture of a photochemical reaction path, starting from the initially prepared wavepacket at the FC-point, passing through a CI and relaxing via GS pathways to the photoproducts, dynamical effects should be included, such as the incorporation of a vibrationally hot initial quantum state and the momentum associated with the gradient of the electronic wavefunction. In order to achieve this, on-the-fly quantum-classical dynamical studies that follow the evolution of the wavepacket according to Newtonian dynamics should be exploited.92 Nevertheless, since the ES PES structure
determines the initial molecular motion, these dynamical methods often yield the same mechanistic information as the MEP. For computation of QYs and ES lifetimes however, a nonadiabatic dynamics treatment is required, e.g. by including a semiclassical surface hopping algorithm.75 Because CAS-SCF or CAS-MP2 based PESs can not be used for trajectory
calculations in large systems based on their high computational cost, often scaled-CASSCF/AMBER trajectories are used.93
The mathematical descriptions of CIs and their classification according to the symmetry of the crossing states is much more involved than described here.39 Similarly, if the reader wishes
to gain a more detailed understanding of the models used to characterize the CIs and the involved reaction paths, this has been documented in other literature as well.94,95
1.5.2 Chemical Understanding using Valence Bond Theory
The ultimate goal in investigating the structure of CIs and the associated reaction pathways is to provide a chemical understanding, allowing for a rational design of photochemical reactions. When Bernardi, Olivucci and Robb developed the Valence Bond (VB) model that describe the electronic structure of CIs and the changes associated with them during a photochemical reaction, a chemically intuitive picture could be tied to the type of molecular motion in the branching plane to fully rationalize the decay process.20
The following discussion largely follows the review written by Olivucci and Robb, in which the type of CIs are classified into four groups according to VB arguments.73 The four
groups are:
1. Three electron H3-like triangle
2. Trans-annular -bonds 3. Charge-transfer 4. n-* re-coupling
Since groups 1 and 3 are of greatest relevance in this Thesis, these will be elaborated on, starting with group 1. CIs appearing in polyenes, benzenes and other hydrocarbons often are of type 1.58,96,97 In a type 1 CI, the electronic structure is such that there are three weakly coupled
17 unpaired electrons in a H3-like triangle (top Fig 1.6). In addition, there is another spectator
unpaired electron in a fragment -orbital. This triangle is often referred to as a kink which is indicated with the shaded atoms in the polyene example in Fig 1.6. A and B denote two linearly independent VB couplings (i.e. pairs of electrons with antiparallel spins prompting either or -bonding) of the three unpaired electrons in three orbitals. Structure C is a linear combination of these two. The white arrows interconvert these structures in a loop surrounding the CI. Moving from structure A to A’ on the GS (or C to C’) preserves the VB coupling, which provides the force driving the geometrical change. Hence, photochemical reactions are possible due to a change in spin pairing upon photoexcitation, after which (a combination of) the x1 and x2 vectors at the CI repair the spin pairing in a certain direction, which determines
which photoproducts will be formed. For example, molecular motion bringing the two non-covalently bonded carbon atoms in the triangle closer, could lead spin pairing between these carbon atoms, resulting in a cyclopropane ring.
Fig 1.6 Top: type 1 CI (three electron H3-like triangle). A, B and C represent Valence Bond (VB)
structures on the ES surface, whereas A’ and C’ represent VB structures on the GS surface. The thick stripes indicate where spin repairing will take place to form either a or -bond. Also indicated are the directions of the gradient difference vector and derivative coupling vector. Bottom: geometrical CI structure in a cyanine which is a type 3 CI (charge-transfer). Also shown at the right of this Figure are the resonance structures associated with the different charge distributions in S1 and S0. The upper structure has the positive charge located on the
left fragment, whereas in the lower structure the positive charge is located at the right of the molecule.
18 The photoisomerization of rPSB11 and related retinal chromophores follow a type 3 CI. Cyanines, which will be used as an example now, show type 3 CIs as well (bottom Fig 1.6).98
Their lowest ES is of charge transfer (CT) character. The CI appears about half-way through the isomerization coordinate, in which the two halves of the twisted molecule differ by a charge of one electron. Hence, such a CI is similar to a twisted intramolecular charge transfer (TICT) state.99 This is illustrated with the charges denoted in the resonance structures of Fig
1.6, where in the upper structure the positive charge is mainly localized at the left part of the
molecule (H2N=CH—CH-), whereas in the lower structure the positive charge is localized at
the right part (-CH=NH2). The degeneracy of the S0 and S1 states at this twisted geometry, and
hence the occurrence of the CI, can be rationalized by their heterosymmetric biradicaloid nature.73 In these biradicaloid structures, the energy of two frontier orbitals of weakly
interacting fragments at this specific geometry are equal. In this case, these frontier orbitals are the 3 filled SOMO of the (H2N—CH—CH-) fragment and the LUMO of the (-CH—NH2)
fragment with two electrons. It follows that regardless of which fragment orbital the sixth -electron populates, the same energy is obtained. If the sixth --electron populates the SOMO, the positive charge will appear on the right side, yielding the bottom structure, whereas population of the LUMO will yield the upper structure (Fig 1.6). This tactic of finding CIs by looking for geometries with two (nearly) degenerate weakly interacting orbitals (biradicaloid) has been used frequently.52,53,64,100 For example in the twisted geometry of ethene, the two
p-orbitals are weakly interacting and hence a small energy difference is expected between the three possible singlet states by filling two electrons in these two orbitals. Similar scenarios appear in molecules where these two frontier orbitals are spatially far away.
For a much more elaborate and complete review on the VB treatment of CIs, see references 53 and 73.53,73
19
2
The Landau-Zener Model
2.1
Landau-Zener Formula
The development of the Landau-Zener (LZ) formula goes back to the 1930s, where Landau and Zener were independently aiming to understand and calculate nonadiabatic processes of atomic collisions.101,102 In their semi-classical one-dimensional approach, they treated the nuclei
classically, introducing externally controlled parameters to this nonadiabatic problem. Although Landau worked out the model with an error of a factor 2 and many alternative derivations followed, the analytical solution to calculate the transition probability is now known as the LZ formula.103 Even though the LZ formula is already 88 years old, it is still being
applied widely, both when it is the only feasible way in complex systems and to provide first estimates of transition probabilities in simpler systems.77 Since it forms the framework of so
many nonadiabatic processes, including photochemical reactions, this equation and its implications will be discussed thoroughly in this Chapter.
Whereas Landau and Zener were primarily focussed on nonadiabatic transitions involving avoided crossings, Teller generalized the LZ formula to include passage through CIs by taking into account multiple dimensions.42 These ideas were picked up by other researchers, which
lead to many publications, albeit all focussing on peaked CIs.104–108 The importance of such a CI
topography on the transition probability will be discussed in Section 2.2. Although refinements to this formula are still being made to generalize for other CI topographies,109 herein the
simplest, oldest and most revealing expressions will be discussed, shown in Eqn (4) and (5).64
𝑃 = exp (−
2𝐸2
ℎ𝑣s) Eqn (4)
in which P represents the nonadiabatic transition probability, E is the energy gap between the two diabatic PESs at the geometry of closest approach, v is the speed of nuclear motion along the reaction coordinate on the upper surface (i.e. the direction of motion towards the CI) and s is the magnitude of the asymptotic slope difference between the two surfaces around the avoided crossing/CI.
A similar expression for the transition probability is shown in Eqn (5), in which represents the Massey parameter that is defined in Eqn (6).110
𝑃 = exp(−[]) qn () = (q)
ħ
|𝒗
||ℎ(𝐪)
| Eqn (6)Both Eqn (4) and (5) assume the validity of a local first order adiabatic PES model where (i) the coupling matrix element H12 = ⟨𝜙1(𝒓)|𝑯𝒆𝒍(𝒓, 𝒒)|𝜙2(𝒓)⟩, in which ϕk is the kth electronic
wavefunction in the diabatic representation, is a constant and (ii) the slopes of the intersecting diabatic states are constant. Since Eqn (5) assumes the adiabatic representation, it can show the importance of nonadiabatic coupling between the two states through h(q), which is the nonadiabatic coupling vector defined in Eqn (3). Further, it is physically more correct to represent both the magnitude of the nuclear velocity, |v|, and nuclear displacement, q, in
20 vector notation. Additionally, this expression signifies that the nonadiabatic coupling (h) and energy gap (E) depend on nuclear coordinates.
Arguably the most important result from the LZ formula (Eqn (4) and (5)) is that it relates the speed to the transition probability. When the wavepacket approaches the point of (near) degeneracy with greater speed (or momentum), the LZ formula predicts that nonradiative decay is more efficient through a larger nonadiabatic transition probability, P. In this way, the transition changes from fully adiabatic (avoided crossing) to fully diabatic (CI) with enhanced speed.111 This greater speed could be due to a steeper slope on the PES (static factor), which
implies faster molecular motion (dynamical factor). An example where this prediction was applied in an experimental context was carried out by Wang et al. who rationalized the reduced isomerization QY in isorhodopsin compared to rhodopsin by its slower reaction speed.112
The second implication from the LZ formula is that a greater difference in slopes between the upper and lower surface translates into a greater P. This is clearly a topological feature that will be touched upon in the next Section. Another topological feature that determines P, is the electronic energy gap. This value should be relatively small, in order to obtain a feasible transition probability. As an illustration, even for the maximum conceivable values of v = 1013
Å/s and s = 5 eV/Å, the LZ formula yields P = 2∙10-21 if E = 1 eV.64 Only when E approaches
values less than a few kJ/mol, P becomes significantly large to allow for nonradiative transitions.57 For nonzero values, the nonradiative decay process still involves an energetic
intermediate (avoided crossing) and always has values of P smaller than 1. Only when there is a real crossing, as in a CI (E = 0), P becomes unity, hence providing a 100% efficient funnel from the ES to the GS, within a single vibrational period and without any intermediates.
2.2
Static Factors
This Section will discuss how static factors affect the rate and trajectory of ultrafast ES processes, which can be described as a coherent wavepacket progressing along the ES surface and, after a nonadiabatic transition, along the GS surface.113 These static effects are mainly
manifested in the topography of the ES PES and the funnel that brings the excited molecule to the GS, through the variables 𝐸, s and v (Eqn 4) within the framework of the LZ model. Understanding how these factors influence the nonadiabatic decay rate and trajectory allows one to control ultrafast photochemistry through rational design, which will be discussed in
Subsection 2.2.2. It should be noted that it may be difficult to disentangle static and dynamical
effects, such as in the case of the gradient-directed effect. The slope of the excited PES towards the CI is a static consideration, yet it influences the velocity of the wavepacket as well, which is a dynamical property.
2.2.1 Excited State and Funnel Topographies
Ultrafast photochemical processes are affected by the topography of the ES PES and the CI.73 These effects, which are summarized below, are referred to as static.
➢ Barrier(less)
➢ Peaked/sloped CI (local topography)
➢ Position (and energy) CI on the reaction coordinate
21 Six different scenarios that demonstrate these feature are illustrated in Fig 2.1. In situation (a), an activation barrier separates the FC state from the CI. In this case, the photochemical process is thermally activated, resulting in wavelength and temperature dependent effects. As a consequence, these processes are typically not ultrafast, unless the barrier is sufficiently small.
Situation (b) sketches a peaked CI, whereas situation (c) illustrates a sloped CI. Important kinetic differences are observed between these two types of CIs. Whereas for the peaked CI, reaching this crossing once already results in nonradiative decay with a LZ transition probability of unity within a single vibrational period, some oscillations between the ES and GS PESs may occur near the sloped CI. Consequently, even if the CI is reached with sufficient energy, irreversible passage to the GS surface is not guaranteed as the wavepacket can travel back to the ES surface (a process called ‘’up-funneling’’), resulting in a slower reaction speed.114,115 The distinction in this local CI topography could explain the selective
photoisomerization at the C11=C12 bond in rPSB11, since the corresponding CI is peaked,
whereas isomerization around C13=C14 bond corresponds to a sloped CI.116 The same
distinction has been used to explain the faster photoisomerization of a retinal-model in aqueous solution (peaked) compared to gas-phase (sloped).117
Fig 2.1 Schematic representation of six different photochemical reaction pathways with varying PES and CI topologies. (a) path including an activation barrier, in which a transition state (TS) separates an ES minimum, M*, from the peaked CI. (b) barrierless with peaked CI, leading to either the reactant (R) or photoproduct (P). (c) path with sloped CI, that proceeds via M* and only leads to R. (d) similar to a, but CI displaced towards P. (e) similar to c, but with CI displaced towards P. (f) similar to b, now with multiple competitive GS relaxation pathways, leading to two possible photoproducts, P and P’.73
Situations (d) and (e) illustrate how the CI is displaced on the reaction coordinate towards the products, with respect to situations (a) and (b). These photochemical processes have a large adiabatic character, as a substantial part of the reaction occurs on the ES PES before the
22 nonadiabatic event occurs. This is why the ES minimum in (e) is denoted with P* instead of M*. It should be noted that the reaction path connecting FC to P* may be different (if not orthogonal) to the reaction coordinate connecting P* to CI, which would significantly complicate the dynamics and the applicability of simple 1D dynamics models, such as the LZ model described above.
As shown in situation (f), more than two GS valleys may be accessible after passage through the CI. In this specific peaked CI, three GS relaxation paths are possible, which are each characterized by (a specific combination of) the branching plane vectors. The introduction of an activation barrier on the ES PES could favor one of these GS relaxation pathways. In addition, if the evolution of the ES wavepacket is such that it points to the CI and then, without changing direction, to the photoproduct, the QY is enhanced.73 This is a qualitative
interpretation from the LZ model that implies conservation of speed through the CI.
Another situation not shown in Fig 2.1, arises when multiple accessible CIs are present. Fig
2.2 shows an example of a photoinduced C—Cl bond cleavage in diphenylmethylene chloride
where two CIs should be considered.118 In this example, the diabatic PESs are calculated at the
ONIOM(CAS(12,10)/B3LYP) level of theory, which is used to reduce the computational cost by treating the molecule at different levels of theory. After the molecule is brought to the FC-state with a laser pump, the wavepacket can evolve along two pathways leading to different photoproducts. The orange curve closest to the FC-point leads to a radical product, whereas the blue curve is only reached after a slightly larger C—Cl stretch, resulting in a cationic product. Apart from this example, in general there will be multiple CIs present, which could lead to a variety of photoproducts. Although for sloped CIs usually the lowest energy CI (which is easiest to locate computationally) dominates the photochemistry, this is not necessarily the case for peaked CIs. In fact, many structurally (and hence energetically) distinct CIs in the IS may need to be considered, as commonly encountered in QM/MM trajectory calculations.119 This also implies that a photochemical reaction is a statistical distribution of
multiple pathways with corresponding reaction times. Indeed, this dynamical aspect will be elaborated upon in Section 2.3.
Fig 2.2 Diabatic PESs involved in the photodissociation of C—Cl in diphenylmethylene chloride, calculated at the ONIOM(CAS(12,10)/B3LYP) level of theory. The black, red, orange and blue curves represent the S0, S1, S2 and S3 PESs respectively.118
23 Especially the influence of the local topography on P (Eqn 4) has been studied intensively. As mentioned before, it is typically well understood that peaked CIs result in higher reaction speeds and hence greater transition probabilities, compared to sloped CIs.72,115,116,120,121
Interestingly, Malhado et al. showed that this difference in efficiency is not due to a topographical difference, but rather due to dynamical factors.109 Specifically, peaked CIs act as
more efficient funnels, because the wavepacket is brought towards the CI, whereas sloped CIs steer it away from it. Additionally, in peaked CIs nonadiabatic transfer frequently occurs without any wavepacket fragmentation as the transition takes place in the first passage.121
Hence, it can be argued that it is not the CI topography, but the dynamical effects resulting from this topography that affect nonadiabatic decay efficiencies when comparing peaked and sloped CIs. As a result, if the velocity is kept artificially constant for trajectories reaching either a peaked or sloped CI, P is equal for both trajectories. It should be noted that these local topography differences do play a larger role when the kinetic energy of the wavepacket is low, which is more common for energetically higher CIs.109
Fuß et al. highlight the importance of the slope of the ES PES in deciding both which photochemical pathway is reached and the efficiency of nonradiative decay.64,122 Herein, it is
emphasized that the slope of a PES equals the classical force acting on a molecule. This has been called the gradient-directed effect, which implies that the excited molecule will follow the path of steepest descent.59 Because of the relation between surface gradient and velocity, some
formulations of LZ theory use surface gradients instead of velocities to calculate P.77 The
gradient-directed effect for a barrierless double bond photoisomerization reaction of a chiral molecule (a) and an asymmetrically substituted derivative (b) is illustrated in Fig 2.3. In both cases, the molecule is accelerated from the FC-region because of the asymmetry of the reaction coordinate, which is a torsion angle distortion.
Fig 2.3 Schematic representation of initially barrierless double bond photoisomerization reactions for two symmetry-equivalent conformers such as in a chiral molecule (a) and inequivalent conformers, as for an asymmetrically substituted derivative (b). The blue line represents the light absorption to the FC-state, whereas the red line indicates the direction of acceleration due to the slope of the S1 surface along the torsional reaction coordinate, q. Based
on only p-orbital interactions, q=0 (planar) would correspond to a minimum on the S0 surface.
(dotted line). Including s-orbital and steric interactions, leads to energy minima deviating from q=0 (full line). Excitation from these GS equilibrium minima to S1 () antibonding
contributions of the p-orbitals dominate, leading to a repulsive interaction, which motion along the torsional coordinate partially relieves.122
24
2.2.2 Static Tuning through Chemical Substitution
Chemists often use chemical substitution as a strategy for understanding GS reactivity trends that can eventually assist in the optimization of reaction rate and selectivity. Although this same strategy can be used to optimize photochemical reactions, it is less obvious how chemical substitution impacts the reactivity. This is because more factors are involved in photochemistry that can be altered upon substitution. For example, Oesterling et al. performed a joint theoretical and experimental study on the relaxation dynamics in furan derivatives by introducing an aldehyde group in different positions.123 Compared to furan, the aldehyde
substituted molecules had a different FC-state, impacting the relaxation dynamics through structurally different decay channels.
In this Section, the focus will be on chemical substitutions that leave the spectroscopic properties of the chromophore largely unperturbed, but primarily alter particular regions of the ES PES. In this way, the effect of chemical substituents on the nonadiabatic dynamics outside of the FC region can be studied. Schuurman and Stolow called these potential effects, since these substitutions primarily affect the branching between different relaxation pathways by either shifting relative energies of the CI with respect to the FC-point or tilting the PES towards a certain direction.59
Systematically adding methyl substituents to ethylene results in the former effect. As shown in Fig 2.4, the addition of methyl substituents alters the relative energies between the Rydberg 3s and * states, as was confirmed by a combined femtosecond time-resolved photoelectron spectroscopy (TR-PES) and ab initio quantum chemical model study.124 The
crossing between these states is relevant as the ES wavepacket needs to pass through this CI in order to decay to the GS. The CI topography is of type a (see Fig 2.1), hence having an activation barrier between the FC-point and CI. From this Figure, it can be observed that the Rydberg 3s state, being the S1 state at the equilibrium geometry, is lowered in energy upon
increasing substitution. This does not only increase the activation barrier to reach the 3s/* CI, which decreases the decay rate, yet displaces the CI further in the reaction coordinate as well. Hence, the tetramethyl substituted ethylene has the CI with the largest torsional angle (63°). Remarkably, this correlation between an increasing barrier and later critical structure is reminiscent of Polanyi rules for thermal chemistry.65
Another illustrative example from the same research group are the methyl substituted acrylonitrile derivatives that they studied using the same combination of spectroscopy and quantum chemical calculations. This example is different from the previous one, because now it is the competition between different CI channels that is tuned upon chemical substitution. Three different structures were studied by the Canadian group, one being acrylonitrile (AN), another being cis-2-metharylonitrile (MeAN) and the last one being cis-3-metharylonitrile (CrCN), as shown in Scheme 1.125 Population of the * state results in a twist around the central
double bond followed by pyramidalization leading to a CI that is similar to the one in ethylene (see Fig 2.4). If dynamical effects (Section 2.3) would have been dominant in driving the nonadiabatic dynamics, it would be expected that CrCN would have the largest ES lifetime, since both carbon atoms are hindered to perform a pyramidalization as they both carry high mass substituents that retard nuclear motion. In addition, it would then be expected that MeAN would approximately have the same lifetime as AN, since pyramidalization could still occur at the unsubstituted carbon atom. In contrast, MeAN has the largest lifetime (97 fs), followed by CrCN (86 fs) and AN (60 fs), which the authors explained by a potential effect. They rationalized this trend by the electronic behaviour of CN, being capable of stabilizing
25 Fig 2.4 Impact of methyl substituents on the relative energies of the Rydberg 3s and * states in ethylene as a function of the twist reaction coordinate. The red dot indicates the position of the CI, together with its geometrical structure.124
Scheme 1. Chemical structures of acrylonitrile (AN), cis-3-metharylonitrile (CrCN) and cis-2-metharylonitrile (MeAN). Also indicated are their lifetimes ’’’’ as measured with TRPES.125
