Helen H.
Fielding
* and
Graham A.
Worth
*
Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, UK. E-mail: h.h.fielding@ucl.ac.uk; g.a.worth@ucl.ac.uk
First published on 23rd November 2017
Time-resolved photoelectron spectroscopy measurements combined with quantum chemistry and dynamics calculations allow unprecedented insight into the electronic relaxation mechanisms of photoexcited molecules in the gas-phase. In this Tutorial Review, we explain the essential concepts linking photoelectron spectroscopy measurements with electronic structure and how key features on the potential energy landscape are identified using quantum chemistry and quantum dynamics calculations. We illustrate how time-resolved photoelectron spectroscopy and theory work together using examples ranging in complexity from the prototypical organic molecule benzene to a pyrrole dimer bound by a weak N–H⋯π interaction and the green fluorescent protein chromophore.
Key learning points• Use of time-resolved photoelectron spectroscopy to track excited state dynamics• Use of quantum chemistry and quantum dynamics calculations to characterise potential energy landscapes • Calculation of parameters related to experimental observables • Interpretation of time-resolved photoelectron spectra of molecules |
When a molecule absorbs ultraviolet (UV) light, it is promoted to an electronically excited state in which the nuclei are no longer in their equilibrium positions. The resulting excess vibrational energy is subsequently redistributed within the molecule in a variety of ways. The coupling between vibrational modes leads to intramolecular vibrational energy redistribution (IVR), typically on a timescale of 10−12–10−10 s. The molecule may then relax back to the ground electronic state by emitting a photon; the timescales for fluorescence, from a singlet excited state to a singlet ground state, or phosphorescence, from a triplet excited state to a singlet ground state, are approximately 10−10–10−7 s and 10−6–1 s, respectively. Non-radiative electronic relaxation processes often compete with these radiative electronic relaxation processes, e.g., an excited singlet state may undergo internal conversion (IC) to a lower lying singlet state, on a timescale of 10−14–10−11 s, or it may undergo intersystem crossing (ISC) to a lower lying triplet state, typically on a timescale of 10−10–10−8 s, depending on the strength of the coupling between the states. The electronic energy lost during IC or ISC is transferred to nuclear degrees of freedom. These photophysical processes are all illustrated in Fig. 1.
Fig. 1 Jablonski diagram illustrating the photophysical relaxation pathways open to a molecule following photoexcitation from S0 to vibrationally excited levels of S1. |
Alternatively, the molecule may undergo a photochemical reaction in its excited electronic state, e.g. dissociation, isomerisation, electron-transfer or proton-transfer, before relaxing back to the ground electronic state. These processes typically take place on timescales of 10−15–10−12 s. Although radiative processes almost always take place at, or near to, minimum energy configurations on the excited potential energy surface, non-radiative processes almost always take place at, or near to, molecular configurations in which two or more electronic states are degenerate, known as a conical intersection (CI). A CI seam between two electronic states is illustrated in Fig. 2.
Fig. 2 Schematic illustration of a conical intersection seam between excited and ground electronic states in a simple photochemical reaction (adapted from ref. 1 with the permission of the author). Following UV photoexcitation, there are two possible reaction coordinates that take population to different regions of the conical intersection seam where it undergoes internal conversion back to the ground electronic state (red path) or photochemistry on the excited state before returning to the ground electronic state (blue path). |
The outcome of a photoreaction depends on the shapes of the potential energy surfaces and the molecular configurations where the electronic relaxation occurs on the CI seam. There are two limiting cases: the reaction path may cross through the seam near the reactants, which corresponds to a photophysical process, or a reaction may occur on the excited state and the reaction path crosses the seam near the products. In order to understand how energy flows in molecules following the absorption of a photon, it is necessary to understand the relationship between the molecular structure, the topography of the potential energy landscape and the outcome of a photochemical reaction, i.e. the structure–dynamics–function relationship. This requires experimental measurements to track the excited state dynamics of molecules and theory to determine the electronic energies and nuclear geometries of key features on the potential energy landscape, e.g., conical intersections and avoided crossings, minima and transition states, and parameters related to experimental observables. The aim of this tutorial review is to explain how to combine time-resolved photoelectron spectroscopy measurements with quantum chemistry and quantum dynamics calculations to unravel the relaxation mechanisms of photoexcited molecules in the gas-phase.
In the independent electron approximation, photoionisation of an outer electron occurs without any reorganisation of the remaining electrons – this is known as the ‘molecular orbital’ or Koopmans picture. Measuring the electron kinetic energy (eKE) distribution of photoelectrons emitted following photoionisation allows us to determine the electron binding energy (eBE) of the molecular orbital from which the electron is ionised, with respect to the electronic state of the cation that is left behind, using eBE = hν − eKE where hν is the photon energy. The propensity for conserving vibrational energy during photoionisation, at least in rigid molecules that do not undergo large amplitude motions, also allows us to use the Franck–Condon distribution of photoelectron eKEs to identify non-resonant and resonant two-photon ionisation processes (Fig. 3).
Measuring the photoelectron angular distribution (PAD) as well as the eKE distribution allows us to obtain additional information about the molecular orbital from which the electron is ionised.5 As the electron leaves the molecule, it scatters from the molecular potential and the scattering wave function reflects the electronic and nuclear configurations of the neutral molecule at the moment of ionization. There is a requirement that the direct product of the irreducible representations of the free electron wave function (Γe−), the electronic state of the cation (ΓM+), the transition dipole moment operator (Γμ) and the electronic state of the neutral molecule (ΓM) contains the totally symmetric irreducible representation of the molecular point group (Γs), i.e. Γe− ⊗ ΓM+ ⊗ Γμ ⊗ ΓM ⊂ Γs. The PAD is measured in the laboratory frame relative to the electric field vector of the photoionising laser and reflects the electronic symmetry of the neutral molecule and the symmetries of the contributing molecular frame transition dipole moment components. Since the relative contributions of the molecular frame transition dipole moments are determined geometrically by the orientation of the molecule relative to the ionising laser field polarisation, the form of the measured PAD will reflect the distribution of molecular axes.
In a TRPES experiment, an ultrashort pump laser pulse (typically ∼100 fs) promotes a molecule to an excited electronic state and a second ultrashort probe laser pulse then ionises the evolving excited state of the molecule (Fig. 4). The wavelength of the probe pulse is usually selected to allow access to as much of the ionisation continuum as possible whilst minimising absorption to excited electronic states to avoid the possibility of probe–pump dynamics complicating the TRPES. The eKE distributions (and PADs) are then measured at a series of precisely timed pump–probe time intervals. One of the advantages of TRPES over pump–probe methods such as transient absorption spectroscopy or time-resolved fluorescence spectroscopy, is that ionisation is always an allowed process because the selection rules are relaxed as a result of the range of possible symmetries of the outgoing electron, i.e. there are no optically dark states in photoionisation.
(1) |
To extract decay times from a set of time-resolved photoelectron spectra, the integrated areas of the photoelectron spectra recorded at each pump–probe delay are scaled to the intensity of the integrated photoelectron signal at that pump–probe delay and the set of scaled photoelectron spectra are fit to the expression
(2) |
To a first approximation, the decay associated spectra, Ci(eKE), can be understood using conservation of energy. Assuming the excess vibrational energy for a given electronic state Evib = hνpump – E(Sn) is conserved during photoionisation, eKE = hνprobe – [E(Dn) – E(Sn)]. Thus, knowing the vertical excitation energies of the electronically excited states of the neutral molecule and the ionisation energies and propensities for ionisation from each electronically excited state to each continuum (Section 3), allows us to assign the different components of the photoelectron spectra to different regions of the excited state potential energy surface.
Qualitative insight into the nature of the molecular orbitals from which the electron is photoionised can also be obtained from PADs which, for a two-photon pump–probe experiment, may be fit to the expression
I(θ) = a[1 + β2P2(cosθ) + β4P4(cosθ)], | (3) |
To calculate the potential energy at a given nuclear geometry requires us to solve the electronic Schrödinger equation at that nuclear geometry. This can be achieved using a quantum chemistry program, such as Gaussian, Molpro, Qchem or Molcas. A method and a basis set must be selected that balance computational resources and accuracy.
The method defines the way in which the wavefunction is represented and the level of approximation used to solve the Schrödinger equation. Methods can be divided into two classes: those based on molecular orbital (MO) theory and those based on density functional theory (DFT). MO methods are based on Hartree–Fock (HF) theory, which calculates the orbitals in a one-electron picture. HF theory treats each electron in the average field of the point charges representing the nuclei and the other electrons. This means that electron–electron interactions are treated only approximately and electron correlation is not described correctly. Electron correlation must be included if accurate energies are required.
For electronic ground-state calculations, there are a number of methods that include the correlation energy. The most commonly used are configuration interaction singles and doubles (CISD), coupled cluster singles and doubles (CCSD), and Moller–Plesset second-order perturbation theory (MP2). MP2 is the least computationally expensive but, as it is a correction to the HF energy, it can breakdown at geometries away from the minimum energy geometry where HF is a poor description, leading to qualitatively incorrect results. Although the correlation energy may be as much as 10% of the total energy, it often only plays a small role in properties such as the lowest energy geometry and vibrational frequencies.
For electronically excited-state calculations, there are again a number of MO based methods that can be used. The standard is complete active space self consistent field (CASSCF). In this, a set of occupied and virtual orbitals are selected (the CAS space) and the wavefunction is constructed using all possible arrangements of electron in these orbitals (configurations). Different roots of the Schrödinger equation with this multi-reference ansatz form the excited states and the weights of the different configurations can be used to characterise the states. Unfortunately, the results are very sensitive to the selection of the CAS space and to use it correctly requires experience. It also does not include all of the correlation energy, including only the static correlation due to having all of the important electronic configurations in the wavefunction, but not the dynamic correlation due to the mutual repulsion of the electrons. A perturbation treatment similar to MP2, termed CASPT2, is usually performed on top of the CASSCF. There are a number of reasonably reliable black box methods for calculating excited-state energies that include part of the dynamic correlation from the start, such as the equation of motion CCSD (EOM-CCSD) and algebraic diagrammatic construction 2nd order (ADC(2)) methods. These, however, are based on a single HF determinant and may fail to treat some excited states correctly.
DFT methods include electron correlation by ansatz. Rather than solving the Schrödinger equation directly to obtain the wavefunction and energy, these methods focus on calculating the electron density and obtain quantities such as the energy from this. These methods are very efficient and can treat much larger molecules than MO based methods; however, they suffer from the need for a parameterised functional to describe the correlation and the correct one must be chosen by careful benchmarking. Excited-states can be calculated using time-dependent DFT (TDDFT). TDDFT is often considered less able to describe some types of excited-states accurately, such as charge-transfer states. The Coulomb attenuated approximation is one way to analyse and correct for these missing states.9
There are a range of basis sets that are commonly used to describe the atomic orbitals that build up the MOs. In principle, the larger the basis set is, the more accurate the calculation but the larger the cost in terms of time and computer resources needed. Basis sets are categorised by the number of functions used to describe the atomic orbitals, and the degree of flexibility. There are 2 main families: the Pople family with names such as 3-21G, 6-31G*, 6-311+G*, and the Dunning family with names such as cc-pVDZ, cc-pVTZ, aug-cc-pVTZ. For molecules with states dominated by valence excitations, a reasonable basis set would be what is known as a double-zeta basis set, e.g. 6-31G* or cc-pVDZ. If Rydberg states are involved, or the molecule is anionic, diffuse functions are essential, e.g. 6-31+G* or aug-cc-pVDZ. For greater accuracy, but also at much greater cost in time, a triple-zeta basis may be used, e.g. 6-311+G* or (aug-cc-pVTZ) are used.
Numerically exact solutions of the TDSE are obtained by representing the Hamiltonian on a grid of time-independent basis functions. The evolving wavefunction is then described by the time-dependent amplitudes on the grid. Information may be extracted from the wavefunction, such as the time-evolution of state-populations, or coordinate expectation values, that can be related to an experiment. It is also possible to simulate an experiment directly by including light pulses and calculating a spectroscopic signal. The most powerful form of grid-based quantum dynamics is multi-configurational time-dependent Hartree (MCTDH). This uses time-dependent basis functions to describe the evolving wavefunction in a compact form.10
Despite the efficiency of MCTDH, grid-based methods are expensive. A number of methods have been developed using semi-classical approximations allowing the wavefunction to be represented by a ‘swarm’ of trajectories. The simplest one used to study excited state chemistry is trajectory surface hopping (TSH). Changes of electronic state population are modelled by hopping between the surfaces using a probabalistic algorithm. TSH is simple and intuitive, but it fails to describe the coherence of the nuclear wavefunction on passing through a conical intersection and may fail to describe the subsequent dynamics correctly. It is also difficult to obtain more than a qualitative picture of the dynamics. Many different ways to correct for the inherent problems in TSH have been devised and, if used correctly, it is a useful tool.11,12
Other methods are based on expanding the nuclear wavepacket in a basis set of moving Gaussian wavepackets (GWPs). In the multiple-spawning and coherent coupled states algorithms, these GWPs follow classical trajectories but the full result is obtained in the limit of convergence. In the variational multi-configurational Gaussian (vMCG) approach the GWPs follow coupled ‘quantum’ trajectories that leads to better convergence.13
To run quantum dynamics simulations analytical functions are required for the potential energy surfaces. An additional challenge for excited-state chemistry is that it is necessary to go beyond the Born–Oppenheimer approximation and include non-adiabatic couplings between the electronic states.7,8 Calculating global potential surfaces and couplings can be prohibitive for more than a few degrees of freedom, and most simulations to date are on very small systems, i.e. less than 10 atoms, or use reduced dimensionality models. The latter is a good way of evaluating the essential modes for a problem, but may miss details that are important in real molecules.
For this reason, much of the present development is of direct dynamics methods where the potential surfaces are calculated ‘on-the-fly’ as the simulation progresses.14 Implementations of TSH,15–17 or GWP propagation in the form of coherent coupled states (CCS),18ab initio multi-spawning (AIMS)19 and direct dynamics vMCG (DD-vMCG)13 have all been used, but to date the limitations of the electronic structure methods and the cost of these calculations has limited them to providing predominantly mechanistic information.
The field of quantum dynamics is less mature than quantum chemistry and computer codes are only now starting emerge that can be used by the non-expert. Examples are the Quantics package based on the MCTDH algorithm, codes such as Sharc and Newton-X for surface hopping and AIMS for multiple spawning.
The oscillator strengths are a standard property obtained in an excited-state calculation and provide an idea of which states may be accessed directly in the photoexcitation process. VIEs may be determined by calculating the difference between the energies of the neutral and ion at the optimised geometry of the neutral molecule. In addition, approximate ionisation energies can be obtained using Koopman's theory, and more accurate values from outer valence Green's function (OVGF) or ionisation potential EOM-CCSD (IP-EOM-CCSD) methods. The ionisation probabilities are also important, for example, if more than one ionisation continuum is accessible the signal may come from one channel predominantly; these may be obtained by calculating what is called the Dyson norm, which are related to the overlap of the wavefunctions of the neutral and the ion states. When calculating this norm it is important to go beyond the one-electron Koopman's picture and include correlation into the description of the orbitals of the neutral and ion involved.20 More accurate transition intensities can be obtained using extensive calculations based on, for example, Green's Functions.21
Timescales for different processes can be obtained from quantum dynamics traditional calculations dynamics calculations, whether grid-based or trajectory-based, require a global potential function. These are obtained by a mathematical fit to quantum chemistry calculations over a range of geometries, followed by refining to fit any known experimental data. Direct dynamics misses out this step and uses the quantum chemistry to obtain the potential surfaces as the propagation evolves. These timescales can be compared with those derived from TRPES measurements in order to identify the processes being observed experimentally. Ideally, the actual signal would be calculated. This can be done in a straightforward, but computationally expensive, way using grid-based simulations,22,23 or approximately from trajectory based methods.24
TRPES following photoexcitation to S1 with 3070 cm−1 of excess vibrational energy are presented in Fig. 5(a). The total integrated photoelectron signals as a function of pump–probe delay were fitted to biexponential functions (eqn (1)) and a plot of the ratio of the amplitude of the slow component to the amplitude of the fast component, as a function of probe wavelength was a step function centered at 250 nm (Fig. 5(b)), i.e. when the probe energy increases ≥4.96 eV, the observation window widens to cover more of the excited state potential energy surface. Such a distinct threshold is a signature of a new ionisation pathway opening up and provided the first hint that there must be a change in the electronic character along the adiabatic potential energy surface.
Fig. 5 (a) Contour plot of TRPES data following excitation of benzene with a 243 nm pump pulse and a 235 nm probe pulse as a function of pump–probe delay. Reproduced from J. Chem. Phys., 2012, 137, 204310, with the permission of AIP Publishing. (b) Plot of the ratio of the amplitudes of the slow and fast components of the biexponential decay of excited state population observed, following photoexcitation at 243 nm, plotted as a function of probe wavelength. Reproduced from ref. 25 with permission from Elsevier. |
Simulations allowed us to distinguish between resonant and non-resonant (Fig. 3) contributions to the signal.22 Quantum dynamics calculations using potential surfaces calculated at the CASPT2 level with a (6,6) CAS and a Roos ANO basis set truncated to 6-31G* quality showed that the initial dynamics after excitation into S1 is along the ‘prefulvene’ mode that takes benzene to the low lying S1/S0 CI. Importantly, as shown in Fig. 6(a), the S1 and T2 states are nearly degenerate over a wide range of geometries along this coordinate and, despite the very weak spin–orbit coupling, efficient ISC can take place, ending with population being trapped in T1 (Fig. 6(b)).28
Fig. 6 (a) Potential energy surfaces along the prefulvene mode (blue = S0; red = T1; black = T2; green = S1). (b) Excited state singlet (green) and singlet + triplet (red) populations as a function of time after vertical excitation into the S1 state. The blue curve represents the approximate population in the Franck–Condon region. Adapted from ref. 27 with permission from the Royal Society of Chemistry. |
Aniline is a structural motif found in the purine nucleotides, adenine and guanine and in the pyramidine nucleotide, cytosine. Numerous experimental studies of the photochemistry and photophysics of isolated aniline molecules in the gas-phase, using H-atom (Rydberg) photofragment translational spectroscopy,31 femtosecond pump–probe photoionisation spectroscopy32 and femtosecond pump–probe velocity map ion imaging,33 have shed light on the N–H dissociation mechanism and timescales, but the mechanism of electronic relaxation remained a matter of debate until recently. By using a combination of continuous molecular beam TRPES measurements and detailed quantum chemistry investigations of the potential energy landscape and relaxation pathways, we found that following photoexcitation of the 21ππ* state, the dominant non-radiative decay pathway involved an extremely efficient method of transferring population straight back to the ground state.30,34,35
The decay associated spectra derived from the TRPES (using eqn (2)) recorded following photoexcitation at 236 nm (5.25 eV) close to the 21ππ* ← S0 absorption maximum revealed four time constants (Fig. 7). The spectrum associated with the 116 fs timescale was dominated by an intense, positive amplitude feature that corresponded energetically to the 21ππ* photoelectron spectrum. The spectrum associated with the 259 fs timescale had a positive amplitude in the region of the photoelectron spectrum, corresponding to the sharp π3s component of the 11π3s/πσ* state at 1.0 eV, and a negative amplitude corresponding to the photoelectron spectrum of the 11ππ* state, suggesting that population was flowing from the π3s component of the 11π3s/πσ* state to the 11ππ* state. The PAD of the sharp feature at 1.0 eV had β2 = 0.8, consistent with ionisation from the atomic-like 3s character of the π3s component of the 11π3s/πσ* state (Section 2.4). The spectrum of the 81 ps component mirrored the shape of the negative amplitude component of the spectrum associated with the 259 fs decay.
Fig. 7 (a) Contour plot of TRPES data following excitation of aniline with a 236 nm pump pulse and a 300 nm probe pulse as a function of pump–probe delay. (b) Spectral components of the four decays derived using eqn (2). Adapted from ref. 30 with permission from the Royal Society of Chemistry. |
Detailed CASSCF and XMCQDPT2 (a variant of CASPT2) calculations were performed to explore the potential energy landscape and relaxation pathways of photoexcited aniline (Fig. 8).35 The CASSCF calculations employed two different active spaces: an (8,7) CAS that included 3 occupied π orbitals, 3 unoccupied π* orbitals and the occupied N-atom lone pair orbital; a (10,9) CAS that also included the occupied 3s/πσ* orbital. These calculations found a new prefulvene-like minimum energy CI connecting the 11ππ* state with S0 in which the carbon atom carrying the amino group is distorted out-of-plane. They showed us that excitation above the 11π3s/πσ* vertical excitation energy could be followed by relaxation from the 11ππ* state to S0 through this CI. We also found a minimum energy CI connecting the 11π3s/πσ* and 11ππ* states close to the local minimum on the 11π3s/πσ* potential surface, suggesting that photoexcitation to the 11π3s/πσ* state could be followed by relaxation to the 11ππ* state, supporting our TRPES measurements. We also found evidence for a new pathway from the 21ππ* state to S0 that we proposed to pass through a three-state CI involving the 21ππ*, 11π3s/πσ* and 11ππ* states. Subsequent TRPES measurements comparing the relaxation pathways of aniline and d7-aniline at a range of photoexcitation wavelengths confirmed the existence of a three-state CI.36 We have also developed a model of the coupled excited-state potential surfaces of aniline using EOM-CCSD/aug-cc-pVDZ calculations that reproduced the overlapping bands of the absorption spectrum and highlighted the significance of relaxation pathways due to coupling between bright valence and dark Rydberg states.37 Other detailed TRPES measurements and calculations on aniline and its derivatives by Townsend and coworkers have investigated the nature of the evolution of the electronic character along the mixed Rydberg-valence 11π3s/πσ* surface.38–40
Fig. 8 Schematic diagram illustrating key CASSCF and XMCQDPT2 calculated features on the potential energy landscape and relaxation pathways following photoexcitation to the first few singlet excited states of aniline. Reproduced from ref. 35 with permission from the Royal Society of Chemistry. |
The TRPES recorded following excitation at 200 nm (Fig. 9(a)) and decay associated spectra derived using eqn (2) (Fig. 9(b)), revealed a flow of population from electronic states producing photoelectrons with high eKE to electronic states producing photoelectrons with lower eKEs.45 The electronic states producing photoelectrons with lower eKEs were then observed to decay out of the Franck–Condon window. Static and dynamic calculations were performed at the CASPT2/aug-cc-pVDZ level of theory with extra basis functions added to treat the Rydberg character of the low-lying excited states. An (8,8) CAS was used and the wavefunction state-averaged over seven states.46
Fig. 9 (a) Contour plot of TRPES data following excitation of pyrrole with a 200 nm pump pulse and a 300 nm probe pulse as a function of pump–probe delay. (b) Spectral components of the two decays derived using eqn (2) (red = 27 fs; blue = 34 fs). (c) Diabatic state populations calculated using wavepacket dynamics on a vibronic coupling model of the pyrrole excited-state manifold following excitation to the B2(21ππ*) state. Reproduced from ref. 45 with permission from Elsevier. |
The electronic states involved in the electronic relaxation processes were determined using conservation of energy and calculations of the Dyson norms for ionisation (Section 3.3) that showed B2(21ππ*) and A2(11πσ*) states ionised to the D0 continuum and A1(11ππ*) and B1(21πσ*) states ionises to both the D0 and D1 continua. Thus, following photoexcitation of the B1(21πσ*) state at 217 nm, the two measured time-constants, 13 fs and 29 fs, could be attributed to IC from the initially populated B1(21πσ*) state to the A2(11πσ*) state followed by population flow on the A2(11πσ*) state out of the Franck–Condon region. Following photoexcitation of the B2(21ππ*) state at 200 nm, the two measured time-constants, 27 fs and 34 fs, could be attributed to IC from the initially populated B2(21ππ*) state to the B1(21πσ*) and A2(11πσ*) states.
Detailed quantum dynamics studies then allowed us to propose that following excitation of the B2(21ππ*) state, population was transferred through the A2(1π3pz) state to the B1(21πσ*) state before being transferred to the A2(11πσ*) state (Fig. 9(c)). Another recent study combining TRPES and quantum dynamics also found evidence for the involvement of the A2(1π3pz) state in the electronic relaxation of pyrrole following photoexcitation at 200 nm.47
The TRPES recorded following excitation at 245 nm (Fig. 10(a)) and decay associated spectra derived using eqn (2) (Fig. 10(b)), revealed dynamics occurring on two timescales of 46 fs and 270 fs. The 47 fs timescale had positive amplitudes in the range 0–1.3 eV but negative amplitudes around 1.45 eV, suggesting an evolution along the excited potential energy surface from a region with a photoelectron spectrum with lower eKE to a region with a photoelectron spectrum with higher eKE. The spectrum associated with the 270 fs timescale is centered around 1.45 eV with positive amplitude, suggesting that once populated, the region of the excited potential energy surface with a photoelectron spectrum with higher eKE decays out of the photoionisation window with a slightly longer timescale.
Fig. 10 (a) Contour plot of TRPES data following excitation of pyrrole dimers with a 245 nm pump pulse and a 300 nm probe pulse as a function of pump–probe delay. (b) Spectral components of the decays derived using eqn (2) (blue = 46 fs; green = 270 fs). (c) Adiabatic potential energy curves for the S0 (black), S1 (blue) and S2 (red) states calculated at the DFT/MRCI/aug-cc-pVDZ level along the N–H dissociation coordinate of monomer A. This figure is taken from ref. 50. |
The dimer is held together by an NH⋯π bond. CASPT2 calculations with an (8,8) CAS showed that the S1 and S2 states have 3s character at the Franck–Condon point. The S1(πB3sA) state has charge-transfer character, with the dominant configuration corresponding to excitation from a π orbital localised on monomer B to the 3s orbital localised on the N-atom of monomer A (Fig. 10(c)). In contrast, the S2(πA3sA) state is dominated by a configuration corresponding to excitation from a π orbital localised on monomer A to the 3s orbital localised on the same monomer, reminiscent of the A2(π3s) state of the pyrrole monomer. EOM-IP-CCSD/aug-cc-pVDZ photoionisation cross-section calculations revealed that the S1 state ionises preferentially to the D0 state but the S2 state ionises preferentially to the higher lying D2 state. From the calculated VEEs, IEs and photoionisation cross-sections, we were able to deduce that following photoexcitation of the S2 state at 245 nm, population was flowing to the S1 charge-transfer state on a timescale of 46 fs and that this charge transfer state then decayed on a slightly longer timescale of 270 fs. Calculated potential energy surfaces of the S0, S1 and S2 states along the N–H dissociation coordinate r of monomer A are presented in Fig. 10(c) and show that the transfer in population from the S2 state to the S1 state is likely to occur at the avoided crossing along the N–H bond stretch. Similar time-signatures were subsequently observed in a pump–probe ionisation study of size-selected pyrrole dimers.51
By using a combination of ESI (Section 2.2), TRPES measurements and quantum chemistry calculations we were able to unravel the excited state dynamics of p-HBDI−in vacuo.52 The decay associated spectra derived from the TRPES using eqn (2) (Fig. 11) revealed a flow of population from electronic states producing photoelectrons with high eKE to electronic states producing photoelectrons with lower eKEs on a timescale of 330 fs. The electronic states producing photoelectrons with lower eKEs were then observed to decay out of the Franck–Condon window on a timescale of 1.4 ps.
Fig. 11 (a) TRPES following excitation of pHBDI− with a 500 nm pump pulse and an 800 nm probe pulse as a function of pump–probe delay. (b) Spectral components of the two decays derived using eqn (2) (green = 330 fs; blue = 1.4 ps; sum = blue). (c) Schematic potential energy curves of S1 and D0 along the minimum energy path from the Franck–Condon (FC) region to the fluorescent state (FS) and twisted intermediate (TI) together with CASPT2 calculated energies in eV. Adapted from ref. 52 with permission from the Royal Society of Chemistry. |
CASSCF calculations of the energies of key geometries on the excited S1 potential energy surface of the anion and the D0 potential energy surface of the corresponding neutral radical were performed using a (12,11) CAS and a 6-31G* basis set and these were improved using the CASPT2 method with an ANO-pVDZ basis set. These calculations (Fig. 11(c)) allowed us to assign the 330 fs timescale to rotation about the bridging C–C bond to form a twisted intermediate and the 1.4 ps timescale to dynamics away from the twisted intermediate towards a CI with the ground state. Remarkably, these results were very similar to measurements of timescales for the non-radiative decay of p-HBDI− in solution,53 pointing to a large influence of the protein environment on the excited S1 potential energy surface. Subsequent TRPES measurements by Verlet and coworkers found a faster timescale of 40 fs following excitation at higher photon energies.54 Recent time-resolved action spectroscopy measurements and XMCQDPT2 calculations by Andersen and Bochenkova and coworkers have shown that when the anions are cooled to 100 K, population is trapped on the S1 potential energy surface for 1.2 ns, which is long enough for fluorescence to compete with IC.55
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