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Terahertz Circular Dichroism Spectroscopy of Molecular Assemblies and Nanostructures
Chemical, physical, biological and materials engineering disciplines use a variety of chiroptical spectroscopies to probe geometrical and optical asymmetry in molecules and particles. Electronic (ECD) and vibrational (VCD) circular dichroism are the most common of these techniques and collectively enable the studies of electronic and vibronic transitions with energies between 0.1 and 5.0 eV. The vibrational states with characteristic energies in the range of 0.001–0.01 eV carry valuable information about concerted intermolecular motions in molecules and crystals involving multiple atoms. These vibronic transitions located in the terahertz (THz) part of the spectrum become increasingly more important for the chemistry, physics, and biology of complex molecules and materials However, the methodology and hardware of THz circular dichroism (TCD) are much less developed than the chiroptical spectroscopies for ultraviolet, visible, near- and mid infrared photons. In this report we provide theoretical foundations, practical implementations, comparative assessments, and exemplary applications of TCD spectroscopy. We show that the sign, intensity, and position of TCD peaks are highly sensitive to the three-dimensional structure and long-range organization of molecular crystals, which offer unique capabilities to study (bio) molecules, their crystals, and nanoscale assemblies and apply the novel data processing methodologies. TCD also offers a convenient toolbox to identify new physical phenomena, such as chiral phonons and their propagation in nanostructured matter. We also discuss the major challenges, emerging opportunities and promising research directions, including broad investigation of chiral phonons observed in chiral (nano) crystals and emerging machine learning methodologies for TCD in biological and nanoscale structures. Ubiquity of low-frequency vibrations with rotational components in biomolecular structures, combined with sharpness of peaks in TCD spectra, enables a variety of technological translations.
Coupling, lifetimes, and “strong coupling” maps for single molecules at plasmonic interfaces
The interaction between excited states of a molecule and excited states of a metal nanostructure (e.g., plasmons) leads to hybrid states with modified optical properties. When plasmon resonance is swept through molecular transition frequency, an avoided crossing may be observed, which is often regarded as a signature of strong coupling between plasmons and molecules. Such strong coupling is expected to be realized when 2|$\langle$U$\rangle$|/ℏΓ > 1, where $\langle$U$\rangle$ and Γ are the molecule–plasmon coupling and the spectral width of the optical transition, respectively. Because both $\langle$U$\rangle$ and Γ strongly increase with decreasing distance between a molecule and a plasmonic structure, it is not obvious that this condition can be satisfied for any molecule–metal surface distance. Here, in this work, we investigate the behavior of $\langle$U$\rangle$ and Γ for several geometries. Surprisingly, we find that if the only contributions to Γ are lifetime broadenings associated with the radiative and nonradiative relaxation of a single molecular vibronic transition, including effects on molecular radiative and nonradiative lifetimes induced by the metal, the criterion 2|$\langle$U$\rangle$|/ℏΓ > 1 is easily satisfied by many configurations irrespective of the metal–molecule distance. This implies that the Rabi splitting can be observed in such structures if other sources of broadening are suppressed. Additionally, when the molecule–metal surface distance is varied keeping all other molecular and metal parameters constant, this behavior is mitigated due to the spectral shift associated with the same molecule–plasmon interaction, making the observation of Rabi splitting more challenging.
Analysis of vibronic coupling in a 4f molecular magnet with FIRMS
Vibronic coupling, the interaction between molecular vibrations and electronic states, is a fundamental effect that profoundly affects chemical processes. In the case of molecular magnetic materials, vibronic, or spin-phonon, coupling leads to magnetic relaxation, which equates to loss of magnetic memory and loss of phase coherence in molecular magnets and qubits, respectively. The study of vibronic coupling is challenging, and most experimental evidence is indirect. Here we employ far-infrared magnetospectroscopy to directly probe vibronic transitions in [Yb(trensal)] (where H 3 trensal = 2,2,2-tris(salicylideneimino)trimethylamine). We find intense signals near electronic states, which we show arise due to an “envelope effect” in the vibronic coupling Hamiltonian, which we calculate fully ab initio to simulate the spectra. We subsequently show that vibronic coupling is strongest for vibrational modes that simultaneously distort the first coordination sphere and break the C 3 symmetry of the molecule. With this knowledge, vibrational modes could be identified and engineered to shift their energy towards or away from particular electronic states to alter their impact. Hence, these findings provide new insights towards developing general guidelines for the control of vibronic coupling in molecules.
Characterizing Ultrafast Intersystem Crossing Pathways in Molecular Pt Dimers Using Time-Resolved Wide-Angle X-ray Scattering
Vibronic coupling between transition metal charge transfer states is a potential mechanism for enhancing the intersystem crossing (ISC) rate. Vibronic coupling-driven ISC has been observed in Pt(II) dimer complexes, where the trajectory across excited-state pathways is tuned by atomic displacements via Pt–Pt stretching vibrations. Time-resolved wide-angle X-ray scattering (TR-WAXS) was utilized to quantify the Pt–Pt contraction following metal–metal-to-ligand charge transfer (MMLCT) excitation in Pt dimers with different bridging ligands. Both complexes exhibit Pt–Pt bond formation with a decrease in Pt–Pt distance of ∼ 0.25 Å and coherent vibrational wavepackets (CVWPs) encoded in the Pt–Pt contraction of both dimers. However, the complexes exhibit different time-dependent evolution of their CVWPs. Analysis of interference patterns between different CVWPs is used to track the trajectory across the excited-state surfaces. Furthermore, this work demonstrates that the interference between CVWPs in ultrafast TR-WAXS encodes indirect information regarding electronic excited-states to reveal the Pt dimer bridge-dependent ISC mechanism.
Influence of Linker Identity on the Photochemistry of Uranyl-Organic Frameworks
While uranyl-based metal–organic frameworks (MOFs) boast impressive photocatalytic abilities, significant questions remain regarding their excitation pathways and methods to fine-tune their performance due to the lack of information regarding heterogeneous uranyl catalysis. Herein, we investigated how linker identity and photoexcitation impact uranyl photocatalysis when the uranyl coordination environment remains constant. Toward this end, we prepared three uranyl-based MOFs (NU-1301, NU-1307, and ZnTCPP-U2) and then examined the structural and photochemical properties of each through X-ray diffraction, X-ray absorption, and photoluminescence. We then correlated our observations to the photocatalytic performance for fluorination of cyclooctane. The excitation profile from NU-1301 and NU-1307 exhibited spin-forbidden linker transitions and uranyl vibronic progressions, with uranyl excitation and emission being most dominant in NU-1301. Consequently, NU-1301 was a more active photocatalyst than NU-1307. In contrast, the excitation profile from ZnTCPP-U2 contained transitions associated with the porphyrin linker exclusively. Photocatalytic activity from ZnTCPP-U2 significantly underperformed in comparison to that of the other two MOFs. Furthermore, these data suggest that linkers’ photophysical properties can be used to predict the photocatalytic behavior of uranyl-containing MOFs.
Reconsidering spin-phonon relaxation in magnetic molecules
Because of the larger intra-molecular distortion, optical phonons usually have stronger spin-phonon coupling than acoustic phonons in molecular magnets. This property may pose problems to the theory of spin relaxation in ordinary paramagnetic materials, which have served as the basis for the understanding of spin dynamics in molecular magnets for decades. In this review, we explain why the Raman processes driven by optical phonons can play a dominant role at low temperature and provide unconventional dependence between relaxation time and temperature. Especially, we emphasize that the sub-barrier relaxation and anomalously low Raman exponents are two common signatures of the dominance. Here, we also present the algorithm and implementation for calculating spin-phonon relaxation in molecular solids with density functional theory codes.
The interplay of excitonic delocalization and vibrational localization in optical lineshapes: A variational polaron approach
The dynamics of molecular excitonic systems are complicated by a competition between electronic coupling (which drives delocalization) and vibrational-electronic (vibronic) interactions (which tend to encourage electronic localization). A particular challenge of molecular systems is that they typically possess a large number of independent vibrations, with frequencies often spanning the entire spectrum of relevant electronic energy gaps. Recent spectroscopic observations and numerical simulations on a water-soluble chlorophyll-binding protein (WSCP) reveal a transition between two regimes of vibronic behavior, a Redfield-like regime in which low-frequency vibrations respond to a delocalized excitonic state, and a Förster-like regime where high-frequency vibrations act as incoherent excitations on individual pigments. Although numerical simulations can reproduce these effects, there is a need for a simple, systematic theory that accurately describes the smooth transition between these two regimes in experimental spectra. Here we address this challenge by generalizing the variational polaron transform approach of [Bloemsma et al., Chem. Phys. 481, 250 (2016)] to include arbitrary bath densities for systems with or without symmetry. We benchmark this theory against both numerical matrix-diagonalization methods and experimental 77 K fluorescence spectra for two WSCP variants, obtaining quite satisfactory agreement in both cases. Here, we apply this theory to offer an explanation for the large loss in apparent electronic coupling in the WSCP Q57K mutant and to examine the likely impact of the interplay between excitonic delocalization and vibrational localization on vibrational sideband shapes and apparent coupling strengths in high-resolution optical spectra for chlorophyll-protein complexes such as WSCP.
On the use of vibronic coherence to identify reaction coordinates for ultrafast excited-state dynamics of transition metal-based chromophores
In this study, the question of whether one can use information from quantum coherence as a means of identifying vibrational degrees of freedom that are active along an excited-state reaction coordinate is discussed. Specifically, we are exploring the notion of whether quantum oscillations observed in single-wavelength kinetics data exhibiting coherence dephasing times that are intermediate between that expected for either pure electronic or pure vibrational dephasing are vibronic in nature and therefore may be coupled to electronic state-to-state evolution. In the case of a previously published Fe(ιι) polypyridyl complex, coherences observed subsequent to 1 A 1 → 1 MLCT excitation were linked to large-amplitude motion of a portion of the ligand framework; dephasing times on the order of 200–300 fs suggested that these degrees of freedom could be associated with ultrafast (~100 fs) conversion from the initially formed MLCT excited state to lower-energy, metal-centered ligand-field excited state(s) of the compound. Incorporation of an electronically benign but sterically restrictive Cu(ι) ion into the superstructure designed to interfere with this motion yielded a compound exhibiting a ~25-fold increase in the compound’s MLCT lifetime, a result that was interpreted as confirmation of the initial hypothesis. However, new data acquired on a different chemical system – Cr(acac') 3 (where acac' represents various derivatives of acetylacetonate) – yielded results that call into question this same hypothesis. Coherences observed subsequent to 4 A 2 → 4 T 2 ligand-field excitation on a series of molecules implicated similar vibrational degrees of freedom across the series, but exhibited dephasing times ranging from 340 fs to 2.5 ps without any clear correlation to the dynamics of excited-state evolution in the system. Taken together, the results obtained on both of these chemical platforms suggest that while identification of coherences can indeed point to degrees of freedom that should be considered as candidate modes for defining reaction trajectories, our understanding of the factors that determine the interplay across coherences, dephasing times, and electronic and geometric structure is insufficient at the present time to view this parameter as a robust metric for differentiating active versus spectator modes for ultrafast dynamics.
Photoactivation Transition State and Dynamical Response of the Orange Carotenoid Protein
The orange carotenoid protein (OCP) regulates light harvesting in cyanobacteria by acting as a photoreceptor in its resting form, OCP O , and by effecting the quenching of bilin excitons upon binding to the core of the phycobilisome in its photoactivated red form, OCP R . We show herein using fluorescence anisotropy measurements and the action spectra for the rate constants of the two light-driven steps in the mechanism that the photoactivation of the OCP from Synechocystis sp. PCC 6803 is triggered by excited-state motions of the canthaxanthin chromophore that yield a twisted and bent conformation. Well-tempered metadynamics simulations reveal that a bicycle-pedal configuration, due to twisting of the two adjacent C=C bonds at the C13−C14 and C15−C15′ positions in the center of canthaxanthin’s π-conjugated isoprenoid backbone, can be accommodated by the binding site in the OCP, with the energy of a captured photon required to cross the local activation energy barriers from the dark equilibrium structure. The bicycle-pedal configuration breaks the conserved hydrogen-bonding interactions between the carbonyl substituent of the β-ionone end ring of canthaxanthin and the adjacent W288 and Y201 residues in the C-terminal domain. The action spectra are modulated by the vibronic excitation prepared by absorption transitions to the S 2 state, indicating that the photoactivation reactions are triggered by the canthaxanthin chromophore well prior to vibrational equilibration. These findings show that an ultrafast structural response of the OCP protein to the excited-state motions of the canthaxanthin chromophore controls the photoactivation yield and the sensing of blue light.
Spin–vibronic coherence drives singlet–triplet conversion
Design-specific control over the transitions between excited electronic states with different spin multiplicities is of the utmost importance in molecular and materials chemistry. Previous studies have indicated that the combination of spin-orbit and vibronic effects, collectively termed the spin-vibronic effect, can accelerate quantum-mechanically forbidden transitions at non-adiabatic crossings. However, it has been difficult to identify precise experimental manifestations of the spin-vibronic mechanism. Here we present coherence spectroscopy experiments that reveal the interplay between the spin, electronic and vibrational degrees of freedom that drive efficient singlet-triplet conversion in four structurally related dinuclear Pt(II) metal-metal-to-ligand charge-transfer (MMLCT) complexes. Photoexcitation activates the formation of a Pt-Pt bond, launching a stretching vibrational wavepacket. The molecular-structure-dependent decoherence and recoherence dynamics of this wavepacket resolve the spin-vibronic mechanism. Further, we find that vectorial motion along the Pt-Pt stretching coordinates tunes the singlet and intermediate-state energy gap irreversibly towards the conical intersection and subsequently drives formation of the lowest stable triplet state in a ratcheting fashion. This work demonstrates the viability of using vibronic coherences as probes to clarify the interplay among spin, electronic and nuclear dynamics in spin-conversion processes, and this could inspire new modular designs to tailor the properties of excited states.
Ab-initio simulation of spin-vibronic spectra of methoxy radical
Despite the fact that experimental and theoretical work on the spectrum of methoxy has stretched from the microwave to the ultraviolet and proceeded for nearly 50 years, parts of the spectrum have remained a challenge to simulate theoretically and make reliable line-by-line assignments. The spectral complexity arises because the radical has a non-zero electron spin and significant vibronic coupling between the two elec- tronic components of the ground state due to the presence of a conical intersection. This work describes a completely ab initio effort to understand and assign the spin- vibronic levels of the X 2E state from 0 to above 3000 cm−1, a region that includes the fundamental transitions of the C-H symmetric and asymmetric stretches that have not previously been identified uniquely. A potential energy surface for methoxy was calculated at the EOM-CCSDT/ANO1 level of theory. Subsequently this potential energy surface was fit to a quartic power series expansion of all nine vibrational nor- mal coordinates (as determined at the minimum of the conical intersection) by the use of a machine-learning-based algorithm. After the addition of spin-orbit coupling, the spin-vibronic problem was solved using both the Krylov-Schur and Lanczos algorithms with the SOCJT3 software to converge eigenvalues up to 3500 cm−1 and their eigen- vectors. The latter were used, in conjunction with the calculated dipole moment and its derivatives (calculated using finite differences at EOM-CCSDT/ANO1 level), to determine spectral intensities for the spin-vibronic spectra. The calculated transition frequencies and intensities were used to simulate and assign the observed transitions of the spin-vibronic spectra of the radical. The credibility of the assignments and their significance is discussed in detail.
Hidden vibronic and excitonic structure and vibronic coherence transfer in the bacterial reaction center
We report two-dimensional electronic spectroscopy (2DES) experiments on the bacterial reaction center (BRC) from purple bacteria, revealing hidden vibronic and excitonic structure. Through analysis of the coherent dynamics of the BRC, we identify multiple quasi-resonances between pigment vibrations and excitonic energy gaps, and vibronic coherence transfer processes that are typically neglected in standard models of photosynthetic energy transfer and charge separation. We support our assignment with control experiments on bacteriochlorophyll and simulations of the coherent dynamics using a reduced excitonic model of the BRC. We find that specific vibronic coherence processes can readily reveal weak exciton transitions. While the functional relevance of such processes is unclear, they provide a spectroscopic tool that uses vibrations as a window for observing excited state structure and dynamics elsewhere in the BRC via vibronic coupling. Vibronic coherence transfer reveals the upper exciton of the “special pair” that was weakly visible in previous 2DES experiments.
Signatures of Antisymmetric Vibrations in the Ultrafast Dynamics of Quadrupolar Dyes
Antisymmetric molecular vibrations are central to ultrafast, nonadiabatic photophysical and photochemical processes such as conical intersection dynamics, Herzberg–Teller couplings and, potentially, singlet fission. Direct spectroscopic identification of such vibrations is, however, challenging, since they are typically Raman inactive and affect optical transitions only weakly. Here, we report experimental signatures of vibronic couplings to a high-frequency antisymmetric vibration in the excited state dynamics of a quasi-quadrupolar molecule by ultrafast two-dimensional electronic spectroscopy (2DES). The early time, sub-50 fs 2DES maps reveal an asymmetric peak pattern with characteristic low-energy cross-peaks. We show that these peaks arise from stimulated emission transitions from an anharmonic, double-minimum excited state potential energy surface formed by vibronic coupling to a high-frequency antisymmetric mode. Simulations based on a phenomenological essential state model support the results. Our findings offer a new approach for identifying antisymmetric vibrations in ultrafast 2DES and track excited state wavepacket motion before relaxation washes out the spectra.
Vibronic Coupling and Exciton Chirality: Electronic and Structural Rearrangement between Helical to Zero Momentum Molecular Exciton States
Helical porphyrin aggregates are attractive macromolecular nanostructures for biomimetic light-harvesting and energy transfer in solar energy technology due to their large light absorbing cross sections and promising energy conservation benefits from chiral-induced spin selectivity. However, with these soft materials, it is imperative that we understand how the nuclear degrees of freedom impact the excitonic energy landscape and dynamics, particularly pertaining to how it influences the chiral angular momentum of the excitons. To this end, we have measured time-resolved depolarization ratios using femtosecond stimulated Raman spectroscopy to uncover the vibronic coupling guided by molecular vibrations between excitons of different angular momentum in helical tetra(sulfonatophenyl)porphyrin aggregates. We find that while transient absorption anisotropy reveals rapid (1 ps lifetime) exciton rotation from helical to achiral states in the Q-band, time-resolved vibrational depolarization ratios evolve on remarkably faster time scales (<500 fs lifetime) for the totally symmetric 1530 cm –1 vibration and the nontotally symmetric 1540 cm –1 vibration. The time-resolved depolarization ratios of the 1540 cm –1 vibration, in particular, show strong evidence of vibronic coupling and nonadiabatic exciton behavior that mediates the nonradiative transition between chiral and achiral excitons. Furthermore, our study shows that for rational design of helical molecular aggregates for exciton transport, the vibronic coupling between excitons of different angular momenta driven by molecular vibrations must be considered especially in the case where chiral-induced spin selectivity is desired.
Interference between Franck–Condon and Herzberg–Teller Terms in the Condensed-Phase Molecular Spectra of Metal-Based Tetrapyrrole Derivatives
The commonly used Franck-Condon (FC) approximation is inadequate for explaining the electronic spectra of compounds that possess vibrations with substantial Herzberg-Teller (HT) couplings. Metal-based tetrapyrrole derivatives, which are ubiquitous natural pigments, often exhibit prominent HT activity. In this paper, we compare the condensed phase spectra of zinc-tetraphenylporphyrin (ZnTPP) and zinc-phthalocyanine (ZnPc), which exhibit vastly different spectral features in spite of sharing a common tetrapyrrole backbone. The absorption and emission spectra of ZnTPP are characterized by a lack of mirror symmetry and nontrivial temperature dependence. In contrast, mirror symmetry is restored, and the nontrivial temperature-dependent features disappear in ZnPc. We attribute these differences to FC-HT interference, which is less pronounced in ZnPc because of a larger FC component in the dipole moment that leads to FC-dominated transitions. A single minimalistic FC-HT vibronic model reproduces all the experimental spectral features of these molecules. These observations suggest that FC-HT interference is highly susceptible to chemical modification.
Excited states of lutetium oxide and its singly charged cation
Vibronic spectra of lutetium oxide (LuO) seeded in supersonic molecule beams are investigated with mass-analyzed threshold ionization (MATI) spectroscopy and second-order multiconfigurational quasi-degenerate perturbation (MCQDPT2) theory. Six states of LuO and four states of LuO + are located by the MCQDPT2 calculations, and an a 3 Π(LuO + ) ← C 2 Σ + (LuΟ) transition is observed by the MATI measurement. Finally, the vibronic spectra show abnormal vibrational intervals for both the neural and cation excited states, and the abnormality is attributed to vibrational perturbations induced by interactions with neighboring states.
Charge Delocalization and Vibronic Couplings in Quadrupolar Squaraine Dyes
Squaraines are prototypical quadrupolar charge-transfer chromophores that have recently attracted much attention as building blocks for solution-processed photovoltaics, fluorescent probes with large two-photon absorption cross sections, and aggregates with large circular dichroism. Their optical properties are often rationalized in terms of phenomenological essential state models, considering the coupling of two zwitterionic excited states to a neutral ground state. As a result, optical transitions to the lowest S 1 excited state are one-photon allowed, whereas the next higher S 2 state can only be accessed by two-photon transitions. A further implication of these models is a substantial reduction of vibronic coupling to the ubiquitous high-frequency vinyl-stretching modes of organic materials. Here, in this study, we combine time-resolved vibrational spectroscopy, two-dimensional electronic spectroscopy, and quantum-chemical simulations to test and rationalize these predictions for nonaggregated molecules. We find small Huang–Rhys factors below 0.01 for the high-frequency, 1500 cm –1 modes in particular, as well as a noticeable reduction for those of lower frequency modes in general for the electronic S 0 → S 1 transition. The two-photon allowed state S 2 is well separated energetically from S 1 and has weak vibronic signatures as well. Thus, the resulting pronounced concentration of the oscillator strength in a narrow region relevant to the lowest electronic transition makes squaraines and their aggregates exceptionally interesting for strong and ultrastrong coupling of excitons to localized light modes in external resonators with chiral properties that can largely be controlled by the molecular architecture.