Simulation of ultrafast excited-state dynamics and elastic x-ray scattering by quantum wavepacket dynamics

The Quest to Simulate Excited-State Dynamics of Transition Metal Complexes

This Perspective describes current computational efforts in the field of simulating photodynamics of transition metal complexes. We present the typical workflows and feature the strengths and limitations of the different contemporary approaches. From electronic structure methods suitable to describe transition metal complexes to approaches able to simulate their nuclear dynamics under the effect of light, we give particular attention to build a bridge between theory and experiment by critically discussing the different models commonly adopted in the interpretation of spectroscopic experiments and the simulation of particular observables. Thereby, we review all the studies of excited-state dynamics on transition metal complexes, both in gas phase and in solution from reduced to full dimensionality.

Method for Calculating Excited Electronic States Using Density Functionals and Direct Orbital Optimization with Real Space Grid or Plane-Wave Basis Set

A direct orbital optimization method is presented for density functional calculations of excited electronic states using either a real space grid or a plane-wave basis set. The method is variational, provides atomic forces in the excited states, and can be applied to Kohn-Sham (KS) functionals as well as orbital-density-dependent (ODD) functionals including explicit self-interaction correction. The implementation for KS functionals involves two nested loops: (1) An inner loop for finding a stationary point in a subspace spanned by the occupied and a few virtual orbitals corresponding to the excited state; (2) an outer loop for minimizing the energy in a tangential direction in the space of the orbitals. For ODD functionals, a third loop is used to find the unitary transformation that minimizes the energy functional among occupied orbitals only. Combined with the maximum overlap method, the algorithm converges in challenging cases where conventional self-consistent field algorithms tend to fail. The benchmark tests presented include two charge-transfer excitations in nitrobenzene and an excitation of CO to degenerate π* orbitals where the importance of complex orbitals is illustrated. The application of this method to several metal-to-ligand charge-transfer and metal-centered excited states of an Fe^II photosensitizer complex is described, and the results are compared to reported experimental estimates. This method is also used to study the effect of the Perdew-Zunger self-interaction correction on valence and Rydberg excited states of several molecules, both singlet and triplet states, and the performance compared to semilocal and hybrid functionals.

Imaging conical intersection dynamics during azobenzene photoisomerization by ultrafast X-ray diffraction

X-ray diffraction is routinely used for structure determination of stationary molecular samples. Modern X-ray photon sources, e.g., from free-electron lasers, enable us to add temporal resolution to these scattering events, thereby providing a movie of atomic motions. We simulate and decipher the various contributions to the X-ray diffraction pattern for the femtosecond isomerization of azobenzene, a textbook photochemical process. A wealth of information is encoded besides real-time monitoring of the molecular charge density for the cis to trans isomerization. In particular, vibronic coherences emerge at the conical intersection, contributing to the total diffraction signal by mixed elastic and inelastic photon scattering. They cause distinct phase modulations in momentum space, which directly reflect the real-space phase modulation of the electronic transition density during the nonadiabatic passage. To overcome the masking by the intense elastic scattering contributions from the electronic populations in the total diffraction signal, we discuss how this information can be retrieved, e.g., by employing very hard X-rays to record large scattering momentum transfers.

Excited-state dynamics of [Mn(im)(CO)3(phen)]+: PhotoCORM, catalyst, luminescent probe?

Mn(I) α-diimine carbonyl complexes have shown promise in the development of luminescent CO release materials (photoCORMs) for diagnostic and medical applications due to their ability to balance the energy of the low-lying metal-to-ligand charge transfer (MLCT) and metal-centered (MC) states. In this work, the excited state dynamics of [Mn(im)(CO)₃(phen)]⁺ (im = imidazole; phen = 1,10-phenanthroline) is investigated by means of wavepacket propagation on the potential energy surfaces associated with the 11 low-lying S_n singlet excited states within a vibronic coupling model in a (quasi)-diabatic representation including 16 nuclear degrees of freedom. The results show that the early time photophysics (<400 fs) is controlled by the interaction between two MC dissociative states, namely, S₅ and S₁₁, with the lowest S₁-S₃ MLCT bound states. In particular, the presence of S₁/S₅ and S₂/S₁₁ crossings within the diabatic picture along the Mn-CO_axial dissociative coordinate (q_Mn-COaxial) favors a two-stepwise population of the dissociative states, at about 60-70 fs (S₁₁) and 160-180 fs (S₅), which reaches about 10% within 200 fs. The one-dimensional reduced densities associated with the dissociative states along q_Mn-COaxial as a function of time clearly point to concurrent primary processes, namely, CO release vs entrapping into the S₁ and S₂ potential wells of the lowest luminescent MLCT states within 400 fs, characteristics of luminescent photoCORM.

Ultrafast processes: coordination chemistry and quantum theory

Coordination compounds, characterized by fascinating and tunable electronic properties, are capable of binding easily to proteins, polymers, wires and DNA. Upon irradiation, these molecular systems develop functions finding applications in solar cells, photocatalysis, luminescent and conformational probes, electron transfer triggers and diagnostic or therapeutic tools. The control of these functions is activated by the light wavelength, the metal/ligand cooperation and the environment within the first picoseconds (ps). After a brief summary of the theoretical background, this perspective reviews case studies, from 1st row to 3rd row transition metal complexes, that illustrate how spin-orbit, vibronic coupling and quantum effects drive the photophysics of this class of molecules at the early stage of the photoinduced elementary processes within the fs-ps time scale range.

Molecular Photochemistry: Recent Developments in Theory

Photochemistry is a fascinating branch of chemistry that is concerned with molecules and light. However, the importance of simulating light-induced processes is reflected also in fields as diverse as biology, material science, and medicine. This Minireview highlights recent progress achieved in theoretical chemistry to calculate electronically excited states of molecules and simulate their photoinduced dynamics, with the aim of reaching experimental accuracy. We focus on emergent methods and give selected examples that illustrate the progress in recent years towards predicting complex electronic structures with strong correlation, calculations on large molecules, describing multichromophoric systems, and simulating non-adiabatic molecular dynamics over long time scales, for molecules in the gas phase or in complex biological environments.

Intersystem Crossing and Triplet Dynamics in an Iron(II) N-Heterocyclic Carbene Photosensitizer

The electronic excited states of the iron(II) complex [Fe^II(tpy)(pyz-NHC)]²⁺ [tpy = 2,2′:6′,2″-terpyridine; pyz-NHC = 1,1′-bis(2,6-diisopropylphenyl)pyrazinyldiimidazolium-2,2′-diylidene] and their relaxation pathways have been theoretically investigated. To this purpose, trajectory surface-hopping simulations within a linear vibronic coupling model including a 244-dimensional potential energy surface (PES) with 20 singlet and 20 triplet coupled states have been used. The simulations show that, after excitation to the lowest-energy absorption band of predominant metal-to-ligand charge-transfer character involving the tpy ligand, almost 80% of the population undergoes intersystem crossing to the triplet manifold in about 50 fs, while the remaining 20% decays through internal conversion to the electronic ground state in about 300 fs. The population transferred to the triplet states is found to deactivate into two different regions of the PESs, one where the static dipole moment is small and shows increased metal-centered character and another with a large static dipole moment, where the electron density is transferred from the tpy to pyz-NHC ligand. Coherent oscillations of 400 fs are observed between these two sets of triplet populations, until the mixture equilibrates to a ratio of 60:40. Finally, the importance of selecting suitable normal modes is highlighted—a choice that can be far from straightforward in transition-metal complexes with hundreds of degrees of freedom.

Trajectory surface-hopping simulations with a linear vibronic coupling model reveal the competition of major intersystem crossing versus minor internal conversion dynamics in an iron(II) N-heterocyclic carbene dye. The triplet population bifurcates into two regions of the potential energy surfaces, characterized by small and large static dipole moments due to different electronic character and showing coherent oscillations of 400 fs until both triplet populations coexist in a mixture of 60:40.

Photophysics and Photochemistry of Iron Carbene Complexes for Solar Energy Conversion and Photocatalysis

Earth-abundant first row transition metal complexes are important for the development of large-scale photocatalytic and solar energy conversion applications. Coordination compounds based on iron are especially interesting, as iron is the most common transition metal element in the Earth’s crust. Unfortunately, iron-polypyridyl and related traditional iron-based complexes generally suffer from poor excited state properties, including short excited-state lifetimes, that make them unsuitable for most light-driven applications. Iron carbene complexes have emerged in the last decade as a new class of coordination compounds with significantly improved photophysical and photochemical properties, that make them attractive candidates for a range of light-driven applications. Specific aspects of the photophysics and photochemistry of these iron carbenes discussed here include long-lived excited state lifetimes of charge transfer excited states, capabilities to act as photosensitizers in solar energy conversion applications like dye-sensitized solar cells, as well as recent demonstrations of promising progress towards driving photoredox and photocatalytic processes. Complementary advances towards photofunctional systems with both Fe(II) complexes featuring metal-to-ligand charge transfer excited states, and Fe(III) complexes displaying ligand-to-metal charge transfer excited states are discussed. Finally, we outline emerging opportunities to utilize the improved photochemical properties of iron carbenes and related complexes for photovoltaic, photoelectrochemical and photocatalytic applications.

Vibrational wavepacket dynamics in Fe carbene photosensitizer determined with femtosecond X-ray emission and scattering

The non-equilibrium dynamics of electrons and nuclei govern the function of photoactive materials. Disentangling these dynamics remains a critical goal for understanding photoactive materials. Here we investigate the photoinduced dynamics of the [Fe(bmip)2]2+ photosensitizer, where bmip = 2,6-bis(3-methyl-imidazole-1-ylidine)-pyridine, with simultaneous femtosecond-resolution Fe Kα and Kβ X-ray emission spectroscopy (XES) and X-ray solution scattering (XSS). This measurement shows temporal oscillations in the XES and XSS difference signals with the same 278 fs period oscillation. These oscillations originate from an Fe-ligand stretching vibrational wavepacket on a triplet metal-centered (3MC) excited state surface. This 3MC state is populated with a 110 fs time constant by 40% of the excited molecules while the rest relax to a 3MLCT excited state. The sensitivity of the Kα XES to molecular structure results from a 0.7% average Fe-ligand bond length shift between the 1 s and 2p core-ionized states surfaces.