Vibrational coherences in half-broadband 2D electronic spectroscopy: Spectral filtering to identify excited state displacements.

Vibrational coherences in ultrafast pump-probe (PP) and 2D electronic spectroscopy (2DES) provide insights into the excited state dynamics of molecules. Femtosecond coherence spectra and 2D beat maps yield information about displacements of excited state surfaces for key vibrational modes. Half-broadband 2DES uses a PP configuration with a white light continuum probe to extend the detection range and resolve vibrational coherences in the excited state absorption (ESA). However, the interpretation of these spectra is difficult as they are strongly dependent on the spectrum of the pump laser and the relative displacement of the excited states along the vibrational coordinates. We demonstrate the impact of these convoluting factors for a model based upon cresyl violet. A careful consideration of the position of the pump spectrum can be a powerful tool in resolving the ESA coherences to gain insights into excited state displacements. This paper also highlights the need for caution in considering the spectral window of the pulse when interpreting these spectra.

Role of Quantum Information in HEOM Trajectories.

Open quantum systems often operate in the non-Markovian regime where a finite history of a trajectory is intrinsic to its evolution. The degree of non-Markovianity for a trajectory may be measured in terms of the amount of information flowing from the bath back into the system. In this study, we consider how information flows through the auxiliary density operators (ADOs) in the hierarchical equations of motion. We consider three cases for a range of baths, underdamped, intermediate, and overdamped. By understanding how information flows, we are able to determine the relative importance of different ADOs within the hierarchy. We show that ADOs sharing a common Matsubara axis behave similarly, while ADOs on different Matsubara axes behave differently. Using this knowledge, we are able to truncate hierarchies significantly, thus reducing the computation time, while obtaining qualitatively similar results. This is illustrated by comparing 2D electronic spectra for a molecule with an underdamped vibration subsumed into the bath spectral density.

Two-Dimensional Electronic Spectroscopy Resolves Relative Excited-State Displacements.

Knowledge of relative displacements between potential energy surfaces (PES) is critical in spectroscopy and photochemistry. Information on displacements is encoded in vibrational coherences. Here we apply ultrafast two-dimensional electronic spectroscopy in a pump-probe half-broadband (HB2DES) geometry to probe the ground- and excited-state potential landscapes of cresyl violet. 2D coherence maps reveal that while the coherence amplitude of the dominant 585 cm-1 Raman-active mode is mainly localized in the ground-state bleach and stimulated emission regions, a 338 cm-1 mode is enhanced in excited-state absorption. Modeling these data with a three-level displaced harmonic oscillator model using the hierarchical equation of motion-phase matching approach (HEOM-PMA) shows that the S1 ← S0 PES displacement is greater along the 585 cm-1 coordinate than the 338 cm-1 coordinate, while Sn ← S1 displacements are similar along both coordinates. HB2DES is thus a powerful tool for exploiting nuclear wavepackets to extract quantitative multidimensional, vibrational coordinate information across multiple PESs.

Phonon Signatures in Photon Correlations.

We show that the second-order, two-time correlation functions for phonons and photons emitted from a vibronic molecule in a thermal bath result in bunching and antibunching (a purely quantum effect), respectively. Signatures relating to phonon exchange with the environment are revealed in photon-photon correlations. We demonstrate that cross-correlation functions have a strong dependence on the order of detection giving insight into how phonon dynamics influences the emission of light. This work offers new opportunities to investigate quantum effects in condensed-phase molecular systems.

The influence of a Hamiltonian vibration vs a bath vibration on the 2D electronic spectra of a homodimer.

We elucidate the influence of the system-bath boundary placement within an open quantum system, with emphasis on the two-dimensional electronic spectra, through the application of the hierarchical equations of motion formalism for an exciton system. We apply two different models, the Hamiltonian vibration model (HVM) and bath vibration model (BVM), to a monomer and a homodimer. In the HVM, we specifically include the vibronic states in the Hamiltonian capturing vibronic quenching, whereas in the BVM, all vibrational details are contained within the bath and described by an underdamped spectral density. The resultant spectra are analyzed in terms of energetic peak position and thermodynamic broadening precision in order to evaluate the efficacy of the two models. The HVM produces 2D spectra with accurate peak positional information, while the BVM is well suited to modeling dynamic peak broadening. For the monomer, both models produce equivalent spectra in the limit where additional damping associated with the underdamped vibration in the BVM approaches zero. This is supported by analytical results. However, for the homodimer, the BVM spectra are redshifted with respect to the HVM due to an absence of vibronic quenching in the BVM. The computational efficiency of the two models is also discussed in order to inform us of the most appropriate use of each method.

Exploring the Effect of Augmented Reality on Cognitive Load, Attitude, Spatial Ability, and Stereochemical Perception.

Augmented reality (AR) has the capacity to afford a virtual experience that obviates the reliance on using two-dimensional representations of 3D molecules for teaching stereochemistry to undergraduate students. Using a combination of quantitative instruments and qualitative surveys/interviews, this study explored the relationships between students' attitudes, perceived cognitive load, spatial ability, and academic performance when engaging in an asynchronous online stereochemistry activity. Our activity was designed using elements of game-based learning, and integrated AR technologies. The control group was provided with a copy of our activity that used two-dimensional drawings, whereas the AR group completed an activity using the AR technologies. For this cohort of students, results indicated significant improvement in academic performance in both the control and AR groups. The introduction of AR technologies did not result in the AR group outperforming the control group. Participants from both groups displayed significant improvements in spatial ability throughout the research period. Further, a moderate correlation (r s = 0.416) between students' spatial ability and academic performance was found. No significant intergroup differences in the perceived cognitive loads of students were observed. A significant difference was observed on one item of the Intellectual Accessibility subscale of the ASCI (V2), Complicated-Simple. We found no correlation for student attitude or cognitive load with academic performance. The findings of this study provide insights for future AR-related studies to explore the role of spatial ability, student attitude, and cognitive load in learning performance. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s10956-022-09957-0.

Excited State Resonance Raman of Flavin Mononucleotide: Comparison of Theory and Experiment.

Blue light absorbing flavoproteins play important roles in a variety of photobiological processes. Consequently, there have been numerous investigations of their excited state structure and dynamics, in particular by time-resolved vibrational spectroscopy. The isoalloxazine chromophore of the flavoprotein cofactors has been studied in detail by time-resolved Raman, lending it a benchmark status for mode assignments in excited electronic states of large molecules. However, detailed comparisons of calculated and measured spectra have proven challenging, as there are many more modes calculated than are observed, and the role of resonance enhancement is difficult to characterize in excited electronic states. Here we employ a recently developed approach due to Elles and co-workers ( J. Phys. Chem. A 2018, 122, 8308-8319) for the calculation of resonance-enhanced Raman spectra of excited states and apply it to the lowest singlet and triplet excited states of the isoalloxazine chromophore. There is generally good agreement between calculated and observed enhancements, which allows assignment of vibrational bands of the flavoprotein cofactors to be refined. However, some prominently enhanced bands are found to be absent from the calculations, suggesting the need for further development of the theory.

Excited State Vibrations of Isotopically Labeled FMN Free and Bound to a Light-Oxygen-Voltage (LOV) Protein.

Flavoproteins are important blue light sensors in photobiology and play a key role in optogenetics. The characterization of their excited state structure and dynamics is thus an important objective. Here, we present a detailed study of excited state vibrational spectra of flavin mononucleotide (FMN), in solution and bound to the LOV-2 (Light-Oxygen-Voltage) domain of Avena sativa phototropin. Vibrational frequencies are determined for the optically excited singlet state and the reactive triplet state, through resonant ultrafast femtosecond stimulated Raman spectroscopy (FSRS). To assign the observed spectra, vibrational frequencies of the excited states are calculated using density functional theory, and both measurement and theory are applied to four different isotopologues of FMN. Excited state mode assignments are refined in both states, and their sensitivity to deuteration and protein environment are investigated. We show that resonant FSRS provides a useful tool for characterizing photoactive flavoproteins and is able to highlight chromophore localized modes and to record hydrogen/deuterium exchange.

Polariton mediated resonance energy transfer in a fluid.

The focus of this work is on a microscopic quantum electrodynamical understanding of cumulative quantum effects in resonance energy transfer occurring in an isotropic and disordered medium. In particular, we consider quantum coherence, defined in terms of interferences between Feynman pathways, and analyze pure-amplitude and phase cross terms that appear in the Fermi golden rule rate equation that results from squaring the matrix element for mediated energy transfer. It is shown that pure-amplitude terms dominate in the near-zone when chromophores are close in proximity to one another (within a few nanometers), and phase cross terms dominate toward the far-zone when phase differences between different Feynman pathways begin to emerge. This can be understood in terms of physical attributes of the mediating photon, whose character becomes more real at long distances, coinciding with vanishing longitudinal components of the field, as transverse components begin to dominate.

Quantifying non-Markovianity in underdamped versus overdamped environments and its effect on spectral lineshape.

Non-Markovian effects in open quantum systems are central to understanding spectral lineshape. Here, we quantify the non-Markovianity associated with both overdamped and underdamped vibrations in terms of information flow between the bath and the system and compare this with the broadening and ellipticity of two-dimensional spectra. Using the Breuer Laine Piilo (BLP) measure, we link the well-known stochastic models for spectral lineshape with modern quantum information theory. Specifically, we study the effect of non-Markovianity in a system in contact with underdamped vibrations and examine the differences observed on increasing the damping to the overdamped limit. The open quantum system dynamics are evolved using the hierarchical equations of motion, efficiently terminated with a Markovian cutoff, where separate hierarchies are derived for the underdamped and overdamped environments. It is shown that the BLP measure is quantitatively correlated with the ellipticity of two-dimensional spectra and memory effects are more pronounced in underdamped environments, due to the long-lived feedback of information between the system and its bath, compared to overdamped environments. Environmental signatures in spectral lineshapes emerge as a result of information flow from the bath back into the system.

A Quantum Electrodynamics Description of Quantum Coherence and Damping in Condensed-Phase Energy Transfer.

Quantum coherence in condensed-phase electronic resonance energy transfer (RET) is described within the context of quantum electrodynamics (QED) theory. Mediating dressed virtual photons (polaritons) are explicitly incorporated into the treatment, and coherence is understood within the context of interfering Feynman pathways connecting the initial and final states for the RET process. The model investigated is that of an oriented three-body donor, acceptor, and mediator RET system embedded within a dispersive and absorbing polarizable medium. We show how quantum coherence can significantly enhance the rate of RET and give a rigorous picture for subsequent decoherence that is driven by both phase and amplitude damping. Energy-conserving phase damping occurs as a result of geometric and dispersive effects and is associated with destructive interference between Feynman pathways. Dissipative amplitude damping, on the other hand, is attributed to vibronic relaxation and absorptivity of the medium and can be understood as virtual photons (polaritons) leaking into the environment. This model offers insights into the emergence of coherence and subsequent decoherence for energy transfer in photosynthetic systems.

Electronic Energy Transfer in a Subphthalocyanine-Zn Porphyrin Dimer Studied by Linear and Nonlinear Ultrafast Spectroscopy.

The efficient harvesting and transport of visible light by electronic energy transfer (EET) are critical to solar energy conversion in both nature and molecular electronics. In this work, we study EET in a synthetic dyad comprising a visible absorbing subphthalocyanine (SubPc) donor and a Zn tetraphenyl porphyrin (ZnTPP) acceptor. Energy transfer is probed by steady-state spectroscopy, ultrafast transient absorption, and two-dimensional electronic spectroscopy. Steady-state and time-resolved experiments point to only weak electronic coupling between the components of the dimer. The weak coupling supports energy transfer from the SubPc to the zinc porphyrin in 7 ps, which itself subsequently undergoes intersystem crossing to populate the triplet state. The rate of the forward energy transfer is discussed in terms of the structure of the dimer, which is calculated by density functional theory. There is evidence of back energy transfer from the ZnTPP on the hundreds of picoseconds time scale. Sub-picosecond spectral diffusion was also observed and characterized, but it does not influence the picosecond energy transfer.

One- to Two-Exciton Transitions in Perylene Bisimide Dimer Revealed by Two-Dimensional Electronic Spectroscopy.

The excited-state energy levels of molecular dimers and aggregates play a critical role in their photophysical behavior and an understanding of the photodynamics in such structures is important for developing applications such as photovoltaics and optoelectronic devices. Here, exciton transitions in two different covalently bound PBI dimers are studied by two-dimensional electronic spectroscopy (2DES), a powerful spectroscopic method, providing the most complete picture of vibronic transitions in molecular systems. The data are accurately reproduced using the equation of motion-phase matching approach. The unambiguous presence of one-exciton to two-exciton transitions are captured in our results and described in terms of a molecular exciton energy level scheme based on the Kasha model. Furthermore, the results are supported by comparative measurements with the PBI monomer and another dimer in which the interchromophore distance is increased.

Asymmetric Oxidation of Enol Derivatives to α-Alkoxy Carbonyls Using Iminium Salt Catalysts: A Synthetic and Computational Study.

We report herein the first examples of asymmetric oxidation of enol ether and ester substrates using iminium salt organocatalysis, affording moderate to excellent enantioselectivities of up to 98% ee for tetralone-derived substrates in the α-hydroxyketone products. A comprehensive density functional theory study was undertaken to interpret the competing diastereoisomeric transition states in this example in order to identify the origins of enantioselectivity. The calculations, performed at the B3LYP/6-31G(D) level of theory, gave good agreement with the experimental results, in terms of the magnitude of the effects under the specified reaction conditions, and in terms of the preferential formation of the ( R)-enantiomer. Just one of the 30 characterized transition states dominates the enantioselectivity, which is attributed to the adoption of an orientation relative to stereochemical features of the chiral controlling element that combines a CH-π interaction between a CH2 group in the substrate and one of the aromatic rings of the biaryl section of the chiral auxiliary with a good alignment of the acetoxy group with the other biaryl ring, and places the smallest substituent on the alkene (a hydrogen atom) in the most sterically hindered position.

Novel binaphthyl and biphenyl α- and ß-amino acids and esters: organocatalysis of asymmetric Diels-Alder reactions. A combined synthetic and computational study.

Asymmetric catalysis of the Diels-Alder reaction between cyclopentadiene and cinnamaldehydes has been studied using as catalysts a range of novel α- and ß-aminoacids and aminoesters with binaphthyl and biphenyl backbones, providing enantioselectivities of up to 62% ee. B3LYP/6-31G* calculations, including free energy corrections, have been carried out on a binaphthyl catalyst example to identify transition state structures and to aid in the identification of major enantiomers. The calculated product ratios agree well with the experimental data; the transition states identified involve preferential approach of cyclopentene along a trajectory adjacent to the acid/ester group. The four lowest energy transition states display a stabilizing dipolar interaction between the carbonyl group oxygen atom and a terminal proton of the diene unit.

Spectral Filtering as a Tool for Two-Dimensional Spectroscopy: A Theoretical Model.

Two-dimensional optical spectroscopy is a powerful technique for the probing of coherent quantum superpositions. Recently, the finite width of the laser spectrum has been employed to selectively tune experiments for the study of particular coherences. This involves the exclusion of certain transition frequencies, which results in the elimination of specific Liouville pathways. The rigorous analysis of such experiments requires the use of ever more sophisticated theoretical models for the optical spectroscopy of electronic and vibronic systems. Here we develop a nonimpulsive and non-Markovian model, which combines an explicit definition of the laser spectrum, via the equation of motion-phase matching approach (EOM-PMA), with the hierarchical equations of motion (HEOM). This theoretical framework is capable of simulating the 2D spectroscopy of vibronic systems with low frequency modes, coupled to environments of intermediate and slower time scales. In order to demonstrate the spectral filtering of vibronic coherences, we examine the elimination of lower energy peaks from the 2D spectra of a zinc porphyrin monomer upon blue-shifting the laser spectrum. The filtering of Liouville pathways is revealed through the disappearance of peaks from the amplitude spectra for a coupled vibrational mode.

Infrared spectroscopy reveals multi-step multi-timescale photoactivation in the photoconvertible protein archetype dronpa.

Photochromic fluorescent proteins play key roles in super-resolution microscopy and optogenetics. The light-driven structural changes that modulate the fluorescence involve both trans-to-cis isomerization and proton transfer. The mechanism, timescale and relative contribution of chromophore and protein dynamics are currently not well understood. Here, the mechanism of off-to-on-state switching in dronpa is studied using femtosecond-to-millisecond time-resolved infrared spectroscopy and isotope labelling. Chromophore and protein dynamics are shown to occur on multiple timescales, from picoseconds to hundreds of microseconds. Following excitation of the trans chromophore, a ground-state primary product is formed within picoseconds. Surprisingly, the characteristic vibrational spectrum of the neutral cis isomer appears only after several tens of nanoseconds. Further fluctuations in protein structure around the neutral cis chromophore are required to form a new intermediate, which promotes the final proton-transfer reaction. These data illustrate the interplay between chromophore dynamics and the protein environment underlying fluorescent protein photochromism.

Interpreting angular momentum transfer between electromagnetic multipoles using vector spherical harmonics.

The transfer of angular momentum between a quadrupole emitter and a dipole acceptor is investigated theoretically. Vector spherical harmonics are used to describe the angular part of the field of the mediating photon. Analytical results are presented for predicting angular momentum transfer between the emitter and absorber within a quantum electrodynamical framework. We interpret the allowability of such a process, which appears to violate conservation of angular momentum, in terms of the breakdown of the isotropy of space at the point of photon absorption (detection). That is, collapse of the wavefunction results in loss of all angular momentum information. This is consistent with Noether's Theorem and demystifies some common misconceptions about the nature of the photon. The results have implications for interpreting the detection of photons from multipole sources and offers insight into limits on information that can be extracted from quantum measurements in photonic systems.

Perspective: Quantum Hamiltonians for optical interactions.

The multipolar Hamiltonian of quantum electrodynamics is extensively employed in chemical and optical physics to treat rigorously the interaction of electromagnetic fields with matter. It is also widely used to evaluate intermolecular interactions. The multipolar version of the Hamiltonian is commonly obtained by carrying out a unitary transformation of the Coulomb gauge Hamiltonian that goes by the name of Power-Zienau-Woolley (PZW). Not only does the formulation provide excellent agreement with experiment, and versatility in its predictive ability, but also superior physical insight. Recently, the foundations and validity of the PZW Hamiltonian have been questioned, raising a concern over issues of gauge transformation and invariance, and whether observable quantities obtained from unitarily equivalent Hamiltonians are identical. Here, an in-depth analysis of theoretical foundations clarifies the issues and enables misconceptions to be identified. Claims of non-physicality are refuted: the PZW transformation and ensuing Hamiltonian are shown to rest on solid physical principles and secure theoretical ground.

Fixing the Conformation of Calix[4]arenes: When Are Three Carbons Not Enough?

Calix[4]arenes are unique macrocycles that through judicious functionalisation at the lower rim can be either fixed in one of four conformations or remain conformationally flexible. Introduction of propynyl or propenyl groups unexpectedly provides a new possibility; a unidirectional conformational switch, with the 1,3-alternate and 1,2-alternate conformers switching to the partial cone conformation, whilst the cone conformation is unchanged, under standard experimental conditions. Using 1 H NMR kinetic studies, rates of switching have been shown to be dependent on the starting conformation, upper-rim substituent, where reduction in bulk enables faster switching, solvent and temperature with 1,2-alternate conformations switching fastest. Ab initio calculations (DFT) confirmed the relative stabilities of the conformations and point towards the partial cone conformer being the most stable of the four. The potential impact on synthesis through the "click" reaction has been investigated and found not to be significant.