Coherence in Chemistry: Foundations and Frontiers.

Coherence refers to correlations in waves. Because matter has a wave-particle nature, it is unsurprising that coherence has deep connections with the most contemporary issues in chemistry research (e.g., energy harvesting, femtosecond spectroscopy, molecular qubits and more). But what does the word "coherence" really mean in the context of molecules and other quantum systems? We provide a review of key concepts, definitions, and methodologies, surrounding coherence phenomena in chemistry, and we describe how the terms "coherence" and "quantum coherence" refer to many different phenomena in chemistry. Moreover, we show how these notions are related to the concept of an interference pattern. Coherence phenomena are indeed complex, and ambiguous definitions may spawn confusion. By describing the many definitions and contexts for coherence in the molecular sciences, we aim to enhance understanding and communication in this broad and active area of chemistry.

From antenna to reaction center: Pathways of ultrafast energy and charge transfer in photosystem II.

The photosystem II core complex (PSII-CC) is the smallest subunit of the oxygenic photosynthetic apparatus that contains core antennas and a reaction center, which together allow for rapid energy transfer and charge separation, ultimately leading to efficient solar energy conversion. However, there is a lack of consensus on the interplay between the energy transfer and charge separation dynamics of the core complex. Here, we report the application of two-dimensional electronic-vibrational (2DEV) spectroscopy to the spinach PSII-CC at 77 K. The simultaneous temporal and spectral resolution afforded by 2DEV spectroscopy facilitates the separation and direct assignment of coexisting dynamical processes. Our results show that the dominant dynamics of the PSII-CC are distinct in different excitation energy regions. By separating the excitation regions, we are able to distinguish the intraprotein dynamics and interprotein energy transfer. Additionally, with the improved resolution, we are able to identify the key pigments involved in the pathways, allowing for a direct connection between dynamical and structural information. Specifically, we show that C505 in CP43 and the peripheral chlorophyll ChlzD1 in the reaction center are most likely responsible for energy transfer from CP43 to the reaction center.

Coherent Modulation of Two-Dimensional Moiré States with On-Chip THz Waves.

van der Waals (vdW) structures host a broad range of physical phenomena. New opportunities arise if different functional layers are remotely modulated or coupled in a device structure. Here we demonstrate the in situ coherent modulation of moiré excitons and correlated Mott insulators in transition metal dichalcogenide (TMD) moirés with on-chip terahertz (THz) waves. Using common dual-gated device structures of a TMD moiré bilayer sandwiched between two few-layer graphene (fl-Gr) gates with hexagonal boron nitride (h-BN) spacers, we launch coherent phonon wavepackets at ∼0.4-1 THz from the fl-Gr gates by femtosecond laser excitation. The waves travel through the h-BN spacer, arrive at the TMD bilayer with precise timing, and coherently modulate the moiré excitons or Mott states. These results demonstrate that the fl-Gr gates, often used for electrical control, can serve as on-chip opto-elastic transducers to generate THz waves for coherent control and vibrational entanglement of functional layers in moiré devices.

Two-Dimensional Moiré Polaronic Electron Crystals.

Two-dimensional moiré materials have emerged as the most versatile platform for realizing quantum phases of electrons. Here, we explore the stability origins of correlated states in WSe_{2}/WS_{2} moiré superlattices. We find that ultrafast electronic excitation leads to partial melting of the Mott states on timescales 5 times longer than predictions from the charge hopping integrals and that the melting rates are thermally activated, with activation energies of 18±3 and 13±2 meV for the one- and two-hole Mott states, respectively, suggesting significant electron-phonon coupling. A density functional theory calculation of the one-hole Mott state confirms polaron formation and yields a hole-polaron binding energy of 16 meV. These findings reveal a close interplay of electron-electron and electron-phonon interactions in stabilizing the polaronic Mott insulators at transition metal dichalcogenide moiré interfaces.

Electron-Nuclear Dynamics Accompanying Proton-Coupled Electron Transfer.

Although photoinduced proton-coupled electron transfer (PCET) plays an essential role in photosynthesis, a full understanding of the mechanism is still lacking due to the complex nonequilibrium dynamics arising from the strongly coupled electronic and nuclear degrees of freedom. Here we report the photoinduced PCET dynamics of a biomimetic model system investigated by means of transient IR and two-dimensional electronic-vibrational (2DEV) spectroscopies, IR spectroelectrochemistry (IRSEC), and calculations utilizing long-range-corrected hybrid density functionals. This collective experimental and theoretical effort provides a nuanced picture of the complicated dynamics and synergistic motions involved in photoinduced PCET. In particular, the evolution of the 2DEV line shape, which is highly sensitive to the mixing of vibronic states, is interpreted by accurate computational modeling of the charge separated state and is shown to represent a gradual change in electron density distribution associated with a dihedral twist that occurs on a 120 fs time scale.

Vibronic coupling in energy transfer dynamics and two-dimensional electronic-vibrational spectra.

We introduce a heterodimer model in which multiple mechanisms of vibronic coupling and their impact on energy transfer can be explicitly studied. We consider vibronic coupling that arises through either Franck-Condon activity in which each site in the heterodimer has a local electron-phonon coupling or Herzberg-Teller activity in which the transition dipole moment coupling the sites has an explicit vibrational mode-dependence. We have computed two-dimensional electronic-vibrational (2DEV) spectra for this model while varying the magnitude of these two effects and find that 2DEV spectra contain static and dynamic signatures of both types of vibronic coupling. Franck-Condon activity emerges through a change in the observed excitonic structure, while Herzberg-Teller activity is evident in the appearance of significant side-band transitions that mimic the lower-energy excitonic structure. A comparison of quantum beating patterns obtained from analysis of the simulated 2DEV spectra shows that this technique can report on the mechanism of energy transfer, elucidating a means of experimentally determining the role of specific vibronic coupling mechanisms in such processes.

Two-dimensional electronic-vibrational spectroscopy: Exploring the interplay of electrons and nuclei in excited state molecular dynamics.

Two-dimensional electronic-vibrational spectroscopy (2DEVS) is an emerging spectroscopic technique which exploits two different frequency ranges for the excitation (visible) and detection (infrared) axes of a 2D spectrum. In contrast to degenerate 2D techniques, such as 2D electronic or 2D infrared spectroscopy, the spectral features of a 2DEV spectrum report cross correlations between fluctuating electronic and vibrational energy gaps rather than autocorrelations as in the degenerate spectroscopies. The center line slope of the spectral features reports on this cross correlation function directly and can reveal specific electronic-vibrational couplings and rapid changes in the electronic structure, for example. The involvement of the two types of transition moments, visible and infrared, makes 2DEVS very sensitive to electronic and vibronic mixing. 2DEV spectra also feature improved spectral resolution, making the method valuable for unraveling the highly congested spectra of molecular complexes. The unique features of 2DEVS are illustrated in this paper with specific examples and their origin described at an intuitive level with references to formal derivations provided. Although early in its development and far from fully explored, 2DEVS has already proven to be a valuable addition to the tool box of ultrafast nonlinear optical spectroscopy and is of promising potential in future efforts to explore the intricate connection between electronic and vibrational nuclear degrees of freedom in energy and charge transport applications.

Two-dimensional electronic vibrational spectroscopy and ultrafast excitonic and vibronic photosynthetic energy transfer.

Two-dimensional electronic-vibrational (2DEV) spectroscopy is a new coherent spectroscopic technique, which shows considerable promise for unravelling complex molecular dynamics. In this Discussion we describe an application to the energy transfer pathway in the major light harvesting protein, LHCII, providing new data on the center line slopes (CLS) of the spectral peaks. The CLS provides information that appears unique to the 2DEV method. We then outline a general approach to calculating 2DEV spectra which is valid for strongly and weakly coupled molecular systems. We conclude with some prospects for the future development of 2DEV spectroscopy and its theoretical analysis.

Two-dimensional electronic-vibrational spectroscopic study of conical intersection dynamics: an experimental and electronic structure study.

The relaxation from the lowest singlet excited state of the triphenylmethane dyes, crystal violet and malachite green, is studied via two-dimensional electronic-vibrational (2DEV) spectroscopy. After excitation of the dyes at their respective absorption maxima, the ensuing excited state dynamics are tracked by monitoring the C[double bond, length as m-dash]C aromatic stretch. With the aid of electronic structure calculations, the observed transitions in the 2DEV spectra are assigned to specific geometries and a detailed story of the evolution of the nuclear wavepacket as it diffuses on the excited state potential energy surface (PES) and ultimately passes through the conical intersection is developed. Notably, it is revealed that the relaxation of the lowest singlet excited state involves intramolecular charge transfer while the nuclear wavepacket is on the excited state PES. Finally, through analyzing the center line slopes of the measured peaks, we show how both solvent motions and changes in the molecular dipole moment affect the correlation between electronic and vibrational degrees of freedom. This work clearly demonstrates the usefulness of 2DEV spectroscopy in following the motion of nuclear wavepackets after photoexcitation and in studying the interactions between the molecular dipole moment and surrounding solvent environment.

Structure and Dynamics of the Methane-Propane van der Waals Complex.

Microwave transitions in the region 7-26 GHz were measured for the methane-propane van der Waals complex. The nearly free internal rotation of methane within the complex gives rise to three states that do not relax even in a 5 K supersonic expansion. Eighteen lines have been assigned to the lowest state and are well fitted to a semirigid rotor model, with rotational constants A = 7553.8229 (24) MHz, B = 2483.9200 (8) MHz, and C = 2041.8692 (5) MHz, and six distortion constants. The structure has the methane positioned above the plane defined by the propane carbon atoms with a center-of-mass van der Waals bond distance of 3.98 Å. This is significantly larger than the equilibrium value of 3.71 Å found with ab initio calculations done at the CCSD(T)-F12a/aug-cc-pVTZ level of theory. Further calculations encompassing a large range of angular orientations of the methane subunit indicate that angular motion produces a large zero-point contribution to the energy, which not only lowers the effective barrier to internal rotation of the methane but also increases the radial distance between subunits. Therefore, although in the lowest energy structure the methane can get close to the propane by interdigitating the hydrogens atoms, the zero-point energy effectively flattens out the potential so that the hydrogens become less restricting.

A Study of 2-Iodobutane by Rotational Spectroscopy.

Rotational transitions belonging to 2-iodobutane (sec-butyl-iodide, CH3CHICH2CH3) were measured over the frequency range 5.5-16.5 GHz via jet-pulsed Fourier transform microwave spectroscopy. The complete nuclear quadrupole coupling tensor of iodine, χ, was obtained for the gauche (g)-, anti (a)-, and gauche' (g')-conformers as well as the four (13)C isotopologues of the gauche species. Rotational constants, centrifugal distortion constants, quadrupole coupling constants, and nuclear spin-rotation constants were determined for each species. Changes in χ of the iodine nucleus, resulting from conformational and isotopic differences, are discussed. Isotopic substitution of g-2-iodobutane allowed for an rs structure to be determined for the carbon backbone. Additionally, isotopic substitution in conjunction with an ab initio structure allowed for a fit of various r0 structural parameters belonging to g-2-iodobutane.

Microwave Spectra, Structure, and Ring-Puckering Vibration of Octafluorocyclopentene.

The rotational spectra of octafluorocyclopentene (C5F8) has been measured for the first time using pulsed jet Fourier transform microwave spectroscopy in a frequency range of 6 to 16 GHz. As in the molecule cyclopentene, the carbon ring is nonplanar, and inversion through the plane results in an inversion pair of ground state vibrational energy levels with an inversion splitting of 18.4 MHz. This large amplitude motion leads to the vibration-rotation coupling of energy levels. The symmetric double minimum ring-puckering potential function was calculated, resulting in a barrier of 222 cm-1. The rotational constants A0 = 962.9590(1) MHz, B0 = 885.1643(4) MHz, C0 = 616.9523(4) MHz, A1 = 962.9590(1) MHz, B1 = 885.1643(4) MHz, C1 = 616.9528(4) MHz, and two centrifugal distortion constants for each state were determined for the parent species and all 13C isotopologues. A mixed coordinate molecular structure was determined from a least-squares fit of the ground state rotational constants of the parent and each 13C isotopologue combined with the equilibrium bond lengths and angles from quantum chemical calculations.

Bidirectional Energy Flow in the Photosystem II Supercomplex.

The water-splitting capability of Photosystem II (PSII) of plants and green algae requires the system to balance efficient light harvesting along with effective photoprotection against excitation in excess of the photosynthetic capacity, particularly under the naturally fluctuating sunlight intensity. The comparatively flat energy landscape of the multicomponent structure, inferred from the spectra of the individual pigment-protein complexes and the rather narrow and featureless absorption spectrum, is well known. However, how the combination of the required functions emerges from the interactions among the multiple components of the PSII supercomplex (PSII-SC) cannot be inferred from the individual pigment-protein complexes. In this work, we investigate the energy transfer dynamics of the C2S2-type PSII-SC with a combined spectroscopic and modeling approach. Specifically, two-dimensional electronic-vibrational (2DEV) spectroscopy provides enhanced spectral resolution and the ability to map energy evolution in real space, while the quantum dynamical simulation allows complete kinetic modeling of the 210 chromophores. We demonstrate that additional pathways emerge within the supercomplex. In particular, we show that excitation energy can leave the vicinity of the charge separation components, the reaction center (RC), faster than it can transfer to it. This enables activatable quenching centers in the periphery of the PSII-SC to be effective in removing excessive energy in cases of overexcitation. Overall, we provide a quantitative description of how the seemingly contradictory functions of PSII-SC arise from the combination of its individual components. This provides a fundamental understanding that will allow further improvement of artificial solar energy devices and bioengineering processes for increasing crop yield.

The initial charge separation step in oxygenic photosynthesis.

Photosystem II is crucial for life on Earth as it provides oxygen as a result of photoinduced electron transfer and water splitting reactions. The excited state dynamics of the photosystem II-reaction center (PSII-RC) has been a matter of vivid debate because the absorption spectra of the embedded chromophores significantly overlap and hence it is extremely difficult to distinguish transients. Here, we report the two-dimensional electronic-vibrational spectroscopic study of the PSII-RC. The simultaneous resolution along both the visible excitation and infrared detection axis is crucial in allowing for the character of the excitonic states and interplay between them to be clearly distinguished. In particular, this work demonstrates that the mixed exciton-charge transfer state, previously proposed to be responsible for the far-red light operation of photosynthesis, is characterized by the ChlD1+Phe radical pair and can be directly prepared upon photoexcitation. Further, we find that the initial electron acceptor in the PSII-RC is Phe, rather than PD1, regardless of excitation wavelength.

Concerted Electron-Nuclear Motion in Proton-Coupled Electron Transfer-Driven Grotthuss-Type Proton Translocation.

Photoinduced proton-coupled electron transfer and long-range two-proton transport via a Grotthuss-type mechanism are investigated in a biomimetic construct. The ultrafast, nonequilibrium dynamics are assessed via two-dimensional electronic vibrational spectroscopy, in concert with electrochemical and computational techniques. A low-frequency mode is identified experimentally and found to promote double proton and electron transfer, supported by recent theoretical simulations of a similar but abbreviated (non-photoactive) system. Excitation frequency peak evolution and center line slope dynamics show direct evidence of strongly coupled nuclear and electronic degrees of freedom, from which we can conclude that the double proton and electron transfer processes are concerted (up to an uncertainty of 24 fs). The nonequilibrium pathway from the photoexcited Franck-Condon region to the E2PT state is characterized by an ∼110 fs time scale. This study and the tools presented herein constitute a new window into hot charge transfer processes involving an electron and multiple protons.

The role of mixed vibronic Qy-Qx states in green light absorption of light-harvesting complex II.

The importance of green light for driving natural photosynthesis has long been underappreciated, however, under the presence of strong illumination, green light actually drives photosynthesis more efficiently than red light. This green light is absorbed by mixed vibronic Qy-Qx states, arising from chlorophyll (Chl)-Chl interactions, although almost nothing is known about these states. Here, we employ polarization-dependent two-dimensional electronic-vibrational spectroscopy to study the origin and dynamics of the mixed vibronic Qy-Qx states of light-harvesting complex II. We show the states in this region dominantly arise from Chl b and demonstrate how it is possible to distinguish between the degree of vibronic Qy versus Qx character. We find that the dynamics for states of predominately Chl b Qy versus Chl b Qx character are markedly different, as excitation persists for significantly longer in the Qx states and there is an oscillatory component to the Qx dynamics, which is discussed. Our findings demonstrate the central role of electronic-nuclear mixing in efficient light-harvesting and the different functionalities of Chl a and Chl b.

Vibronic mixing enables ultrafast energy flow in light-harvesting complex II.

Since the discovery of quantum beats in the two-dimensional electronic spectra of photosynthetic pigment-protein complexes over a decade ago, the origin and mechanistic function of these beats in photosynthetic light-harvesting has been extensively debated. The current consensus is that these long-lived oscillatory features likely result from electronic-vibrational mixing, however, it remains uncertain if such mixing significantly influences energy transport. Here, we examine the interplay between the electronic and nuclear degrees of freedom (DoF) during the excitation energy transfer (EET) dynamics of light-harvesting complex II (LHCII) with two-dimensional electronic-vibrational spectroscopy. Particularly, we show the involvement of the nuclear DoF during EET through the participation of higher-lying vibronic chlorophyll states and assign observed oscillatory features to specific EET pathways, demonstrating a significant step in mapping evolution from energy to physical space. These frequencies correspond to known vibrational modes of chlorophyll, suggesting that electronic-vibrational mixing facilitates rapid EET over moderately size energy gaps.

Solvent Mediated Excited State Proton Transfer in Indigo Carmine.

Excited state proton transfer (ESPT) is thought to be responsible for the photostability of biological molecules, including DNA and proteins, and natural dyes such as indigo. However, the mechanistic role of the solvent interaction in driving ESPT is not well understood. Here, the electronic excited state deactivation dynamics of indigo carmine (InC) is mapped by visible pump-infrared probe and two-dimensional electronic-vibrational (2DEV) spectroscopy and complemented by electronic structure calculations. The observed dynamics reveal notable differences between InC in a protic solvent, D2O, and an aprotic solvent, deuterated dimethyl sulfoxide (dDMSO). Notably, an acceleration in the excited state decay is observed in D2O (<10 ps) compared to dDMSO (130 ps). Our data reveals clear evidence for ESPT in D2O accompanied by a significant change in dipole moment, which is found not to occur in dDMSO. We conclude that the ability of protic solvents to form intermolecular H-bonds with InC enables ESPT, which facilitates a rapid nonradiative S1 → S0 transition via the monoenol intermediate.