Vibronic States Research Articles

Problems of Quantum-Classical Modeling Of the Primary Photoreaction in Rhodopsin

A modified model of the primary photoreaction in rhodopsin, cis-trans photoisomerization of the chromophore (retinal), is studied. The quantum subsystem of the model includes three vibronic states: the ground state, the excited state, and the ground state of the primary photoproduct. These states correspond to three point masses in the classical subsystem. The modification consists in the exponential dependence of the electronic-vibrational coupling constant on the displacement of point masses. The properties of the optimal loci of the multiparameter space, which characterized by the best agreement with the experimental data, are studied. A rather small “multidimensional volume” of these loci shown in all ranges of the used values of the model parameters. Several ways to optimize the quantum-classical model of rhodopsin photoisomerization have been proposed.

Photoionization of Oriented HD(1Σ+) Yields Vibrating HD+(2Σ+) with Charge Breathing and Small Charge Transfer.

The eigenfunctions of the Hamiltonian associated with the oriented vibrating HD+(2Σ+) ion are calculated beyond the Born-Oppenheimer approximation in the nuclear frame. This makes it possible to study the fully correlated electron-nuclear dynamics of the HD+(2Σ+) after ionization of the HD(1Σ+) molecule. The dynamics is then characterized by the time-dependent probability densities and flux densities of the individual particles, i.e., deuteron, proton, and electron. The flux densities confirm that, although the electric dipole moment changes over time, there is no charge migration, as might be expected from the separation of energy levels of the vibronic states. Instead, the variations of the electric dipole moment over time are caused by small charge transfer and asymmetric charge vibration. Fourier transforms of the time-dependent probability and flux densities uncover the net asymmetric effective potential acting on the electron.

Electronic Configuration Assignments for UO from Electric Dipole Moment Measurements.

Diatomic UO has more than 48 bound states within 10000 cm-1 of the ground state. This electronic state congestion has been attributed to interleaved states from the electronic configurations U2+(5f37s)O2- and U2+(5f27s2)O2-, respectively. Ligand field theory predicts that each electronic configuration will exhibit states with distinguishable, characteristic vibrational and rotational constants. However, vibronic state mixing modifies the observed vibration-rotation constants, leading to uncertainty in the configurational assignments. The permanent electric dipole moment (μe) of an electronic state should also manifest a value that is characteristic of the parent electronic configuration. μe and other electrostatic and magnetostatic properties should be less influenced by the vibronic state mixing, providing more robust indicators for configurational assignments. In the present study, we have measured the μe values for four electronic states of UO. The results clearly demonstrate that the ground state (X(1)4) and the first electronically excited state ((2)4) are derived from the U2+(5f37s)O2- and U2+(5f27s2)O2- configurations, respectively.

Illuminating Ligand Field Contributions to Molecular Qubit Spin Relaxation via T1 Anisotropy.

Electron spin relaxation in paramagnetic transition metal complexes constitutes a key limitation on the growth of molecular quantum information science. However, there exist very few experimental observables for probing spin relaxation mechanisms, leading to a proliferation of inconsistent theoretical models. Here we demonstrate that spin relaxation anisotropy in pulsed electron paramagnetic resonance is a powerful spectroscopic probe for molecular spin dynamics across a library of highly coherent Cu(II) and V(IV) complexes. Neither the static spin Hamiltonian anisotropy nor contemporary computational models of spin relaxation are able to account for the experimental T1 anisotropy. Through analysis of the spin-orbit coupled wave functions, we derive an analytical theory for the T1 anisotropy that accurately reproduces the average experimental anisotropy of 2.5. Furthermore, compound-by-compound deviations from the average anisotropy provide a promising approach for observing specific ligand field and vibronic excited state coupling effects on spin relaxation. Finally, we present a simple density functional theory workflow for computationally predicting T1 anisotropy. Analysis of spin relaxation anisotropy leads to deeper fundamental understanding of spin-phonon coupling and relaxation mechanisms, promising to complement temperature-dependent relaxation rates as a key metric for understanding molecular spin qubits.

Modulating Singlet Fission by Scanning through Vibronic Resonances in Pentacene-Based Blends

Vibronic coupling has been proposed to play a decisive role in promoting ultrafast singlet fission (SF), the conversion of a singlet exciton into two triplet excitons. Its inherent complexity is challenging to explore, both from a theoretical and an experimental point of view, due to the variety of potentially relevant vibrational modes. Here, we report a study on blends of the prototypical SF chromophore pentacene in which we engineer the polarizability of the molecular environment to scan the energy of the excited singlet state (S1) continuously over a narrow energy range, covering vibrational sublevels of the triplet-pair state (1(TT)). Using femtosecond transient absorption spectroscopy, we probe the dependence of the SF rate on energetic resonance between vibronic states and, by comparison with simulation, identify vibrational modes near 1150 cm-1 as key in facilitating ultrafast SF in pentacene.

Reorganization Energies for Interfacial Proton-Coupled Electron Transfer to a Water Oxidation Catalyst.

The reorganization energy (λ) for interfacial electron transfer (ET) and proton-coupled ET (PCET) from a conductive metal oxide (In2O3:Sn, ITO) to a surface-bound water oxidation catalyst was extracted from kinetic data measured as a function of the thermodynamic driving force. Visible light excitation resulted in rapid excited-state injection (kinj > 108 s-1) to the ITO, which photo-initiated the two interfacial reactions of interest. The rate constants for both reactions increased with the driving force, -ΔG°, to a saturating limit, kmax, with rate constants consistently larger for ET than for PCET. Marcus-Gerischer analysis of the kinetic data provided the reorganization energy for interfacial PCET (0.90 ± 0.02 eV) and ET (0.40 ± 0.02 eV), respectively. The magnitude of kmax for PCET was found to decrease with pH, behavior that was absent for ET. Both the decrease in kmax and the larger reorganization energy for an unwanted competing PCET reaction from the ITO to the oxidized catalyst showcases a significant kinetic advantage for driving solar water oxidation at high pH. Computational analysis revealed a larger inner-sphere reorganization energy contribution for PCET than for ET arising from a more significant change in the Ru-O bond length for the PCET reaction. Extending the Marcus-Gerischer theory to PCET by including the excited electron-proton vibronic states and the proton donor-acceptor motion provided an apparent reorganization energy of 1.01 eV. This study demonstrates that the Marcus-Gerischer theory initially developed for ET can be reliably extended to PCET for quantifying and interpreting reorganization energies observed experimentally.

Excitation energy transfer and vibronic coherence in intact phycobilisomes.

The phycobilisome is an oligomeric chromoprotein complex that serves as the principal mid-visible light-harvesting system in cyanobacteria. Here we report the observation of excitation-energy-transfer pathways involving delocalized optical excitations of the bilin (linear tetrapyrrole) chromophores in intact phycobilisomes isolated from Fremyella diplosiphon. By using broadband multidimensional electronic spectroscopy with 6.7-fs laser pulses, we are able to follow the progress of excitation energy from the phycoerythrin disks at the ends of the phycobilisome's rods to the C-phycocyanin disks along their length in <600 fs. Oscillation maps show that coherent wavepacket motions prominently involving the hydrogen out-of-plane vibrations of the bilins mediate non-adiabatic relaxation of a manifold of vibronic exciton states. However, the charge-transfer character of the bilins in the allophycocyanin-containing segments localizes the excitations in the core of the phycobilisome, yielding a kinetic bottleneck that enables photoregulatory mechanisms to operate efficiently on the >10-ps timescale.

Hyperfine structures and the field effects of the heterohalogen fluorides in the vibronic ground state

The hyperfine structures of heterohalogen fluorides (ClF, BrF, and IF) in their vibronic ground state are calculated by diagonalizing the Hamiltonian matrix including the hyperfine interactions. The Stark and Zeeman effects of the hyperfine structures are studied as well. Perturbations of the Stark and Zeeman sub-levels are observed, and thus, the perturbations selection rules are summarized. The hyperfine-rotation dipole transition moment is calculated and the hyperfine-rotation spectrum is simulated. Compared with other heteronuclear halides, the heterohalogen fluorides exhibit simple hyperfine structure due to the 1/2 nuclear spin and 0 quadrupole of F atom. Therefore, the spectra of the halogen fluorides are relatively simple and easier to be studied experimentally. Our results may provide essential information for further investigations and applications of the heterohalogen fluorides.

H2O-NH4+-Induced Emission Modulation in Sb3+-Doped (NH4)2InCl5·H2O.

Lead-based metal halide perovskites have received widespread attention for their promising application prospects in the field of lighting and display due to their excellent optical properties. However, the toxicity of lead may hinder their further commercial application. Herein, a zero-dimensional (0D) metal halide (NH4)2InCl5·H2O with an orthorhombic structure and the Pnma space group was produced. With doping with Sb3+, these products exhibit one highly efficient and wide yellow emission band (∼450-850 nm) in their photoluminescence (PL) spectra, which covers almost the entire visible spectral range at room temperature; however, they give two emission bands with long decay lifetimes (microseconds) at low temperature. Temperature-dependent steady-state PL, transient PL spectroscopy, temperature-dependent Raman spectra characterization, and theoretical band structure calculations confirm that the dual-band emission at low temperature originates from the dual vibronic levels of the self-trapped exciton (STE) in the hole-vibration state, whose vibration energy is related to the H2O-NH4+ connection in the valence band. This result proves that the vibronic state in STE formation involves both electrons and holes in the excited states, the opposite of this happens in the electron-vibration band in most perovskite halides. These results provide new insight into the luminescent mechanism of Sb3+ in halide perovskites, especially used for emission color modulation by the temperature-dependent electron- or hole-vibration processes.

Multireference configuration interaction study of the predissociation of C2 via its F1Πu state.

Photodissociation is one of the main destruction pathways for dicarbon (C2) in astronomical environments, such as diffuse interstellar clouds, yet the accuracy of modern astrochemical models is limited by a lack of accurate photodissociation cross sections in the vacuum ultraviolet range. C2 features a strong predissociative F1Πu-X1Σg + electronic transition near 130nm originally measured in 1969; however, no experimental studies of this transition have been carried out since, and theoretical studies of the F1Πu state are limited. In this work, potential energy curves of excited electronic states of C2 are calculated with the aim of describing the predissociative nature of the F1Πu state and providing new ab initio photodissociation cross sections for astrochemical applications. Accurate electronic calculations of 56 singlet, triplet, and quintet states are carried out at the DW-SA-CASSCF/MRCI+Q level of theory with a CAS(8,12) active space and the aug-cc-pV5Z basis set augmented with additional diffuse functions. Photodissociation cross sections arising from the vibronic ground state to the F1Πu state are calculated by a coupled-channel model. The total integrated cross section through the F1Πu v = 0 and v = 1 bands is 1.198 × 10-13 cm2 cm-1, giving rise to a photodissociation rate of 5.02 × 10-10 s-1 under the standard interstellar radiation field, much larger than the rate in the Leiden photodissociation database. In addition, we report a new 21Σu + state that should be detectable via a strong 21Σu +-X1Σg + band around 116nm.

Vibronic Exciton-Phonon States in Stack-Engineered van der Waals Heterojunction Photodiodes.

Stack engineering, an atomic-scale metamaterial strategy, enables the design of optical and electronic properties in van der Waals heterostructure devices. Here we reveal the optoelectronic effects of stacking-induced strong coupling between atomic motion and interlayer excitons in WSe2/MoSe2 heterojunction photodiodes. To do so, we introduce the photocurrent spectroscopy of a stack-engineered photodiode as a sensitive technique for probing interlayer excitons, enabling access to vibronic states typically found only in molecule-like systems. The vibronic states in our stack are manifest as a palisade of pronounced periodic sidebands in the photocurrent spectrum in frequency windows close to the interlayer exciton resonances and can be shifted “on demand” through the application of a perpendicular electric field via a source-drain bias voltage. The observation of multiple well-resolved sidebands as well as their ability to be shifted by applied voltages vividly demonstrates the emergence of interlayer exciton vibronic structure in a stack-engineered optoelectronic device.

Vibrational probes of anharmonic interactions in the molecular ferroelectric 2-methylbenzimidazole

We report experimental and computational characterization of the anharmonic interactions between the constituents of the molecular ferroelectric material 2-methylbenzimi-dazole (MBI). Using experimental Raman spectroscopy measurements across a wide range of temperatures we assess the anharmonic properties of this material’s vibrations we expect to play a major role in proton tautomerism (PT) mechanism that explain ferroelectric switching in MBI. Through an application of the standard theory of anharmonic contributions to the interatomic potential energy of MBI we develop and apply a method to decipher how cubic and quartic anharmonic coupling to low frequency lattice vibrations affect the frequency of an intramolecular ring vibration of the molecular constituents of this material capable of modulating carbon-nitrogen double bonds that alternate in the PT mechanism. In addition, we use the theory of vibrational solitons to show the appearance of satellites peaks red-shifted from the N-H stretching vibration of MBI stem from self-trapped vibron states. We assess the number of these trapped states and the modes along which trapping occurs to show MBI possesses distinct phases in which excitations of the N-H stretching vibration couple to different low frequency lattice vibrational modes. We propose increased N-H stretching vibrational trapping at low temperature helps explain reductions in the temperature-dependent dielectric constant of MBI measured previously. These results highlight the important role vibrational spectroscopy can play in understanding how intermolecular interactions impact the structural dynamics of materials central to sustainable information storage and nonlinear optical technologies

Reconstruction of the vibronic-state density matrix based on pump-probe state-resolved energy spectra

We propose a scheme based on perturbation theory to reconstruct a molecular density matrix (DM) using the pump-probe state-resolved energy spectra. By applying the scheme to an ${\mathrm{O}}_{2}^{+}$ system produced via strong-field ionization, we demonstrate that the reconstruction scheme can retrieve the populations and coherences of vibrational-electronic (vibronic) states while maintaining good robustness. We further extend the strong-field transient ionization model to include the rotational degree of freedom. The evolution of the vibronic-state DM can be recovered, benefiting from the population stabilities between adjacent fractional revivals. The retrieved signals quantitatively capture the distinguishing decay features of the vibronic coherences. Our strategy paves the way toward understanding elaborate vibronic-state DMs in molecular systems.

Magnetic field tuning of crystal field levels and vibronic states in the spin ice compound Ho2Ti2O7 observed with far infrared reflectometry

Low temperature optical spectroscopy in applied magnetic fields provides clear evidence of magnetoelastic coupling in the spin ice material Ho$_2$Ti$_2$O$_7$. In far-IR reflectometry measurements, we observe field dependent features around 30, 61, 72 and 78~meV, energies corresponding to crystal electronic field (CEF) doublets. The calculations of the crystal-field Hamiltonian model confirm that the observed features in IR spectra are consistent with magnetic-dipole-allowed excitations from the ground state to higher $^5$I$_8$ CEF levels. We present the CEF parameters that best describe our field-dependent IR reflectivity measurements. Additionally, we identify a weak field-dependent shoulder near one of the CEF doublets. This indicates that this level is split even in zero-field, which we associate with a vibronic bound state. Modeling of the observed splitting shows that the phonon resides at slightly lower energy compared to the CEF level that it couples to, which is in contrast with previously published inelastic neutron measurements. The magnetic field dependence of the vibronic state shows a gradual decoupling of the phonon with the CEF level as it shifts. This approach should work in pyrochlores and other systems that have magnetic dipole transitions in the IR spectroscopic range, which can elucidate the presence and the ability to tune the nature of vibronic states in a wide variety of materials.

Two-dimensional vibronic spectroscopy with semiclassical thermofield dynamics.

Thermofield dynamics is an exactly correct formulation of quantum mechanics at finite temperature in which a wavefunction is governed by an effective temperature-dependent quantum Hamiltonian. The optimized mean trajectory (OMT) approximation allows the calculation of spectroscopic response functions from trajectories produced by the classical limit of a mapping Hamiltonian that includes physical nuclear degrees of freedom and other effective degrees of freedom representing discrete vibronic states. Here, we develop a thermofield OMT (TF-OMT) approach in which the OMT procedure is applied to a temperature-dependent classical Hamiltonian determined from the thermofield-transformed quantum mapping Hamiltonian. Initial conditions for bath nuclear degrees of freedom are sampled from a zero-temperature distribution. Calculations of two-dimensional electronic spectra and two-dimensional vibrational-electronic spectra are performed for models that include excitonically coupled electronic states. The TF-OMT calculations agree very closely with the corresponding OMT results, which, in turn, represent well benchmark calculations with the hierarchical equations of motion method.

Analytical gradients for nuclear–electronic orbital multistate density functional theory: Geometry optimizations and reaction paths

Hydrogen tunneling plays a critical role in many biologically and chemically important processes. The nuclear-electronic orbital multistate density functional theory (NEO-MSDFT) method was developed to describe hydrogen transfer systems. In this approach, the transferring proton is treated quantum mechanically on the same level as the electrons within multicomponent DFT, and a nonorthogonal configuration interaction scheme is used to produce delocalized vibronic states from localized vibronic states. The NEO-MSDFT method has been shown to provide accurate hydrogen tunneling splittings for fixed molecular systems. Herein, the NEO-MSDFT analytical gradients for both ground and excited vibronic states are derived and implemented. The analytical gradients and semi-numerical Hessians are used to optimize and characterize equilibrium and transition state geometries and to generate minimum energy paths (MEPs), for proton transfer in the deprotonated acetylene dimer and malonaldehyde. The barriers along the resulting MEPs are lower when the transferring proton is quantized because the NEO-MSDFT method inherently includes the zero-point energy of the transferring proton. Analysis of the proton densities along the MEPs illustrates that the proton density can exhibit symmetric or asymmetric bilobal character associated with symmetric or slightly asymmetric double-well potential energy surfaces and hydrogen tunneling. Analysis of the contributions to the intrinsic reaction coordinate reveals that changes in the C-O bond lengths drive proton transfer in malonaldehyde. This work provides the foundation for future reaction path studies and direct nonadiabatic dynamics simulations of a wide range of hydrogen transfer reactions.

Theoretical Modeling of Electrochemical Proton-Coupled Electron Transfer.

Proton-coupled electron transfer (PCET) plays an essential role in a wide range of electrocatalytic processes. A vast array of theoretical and computational methods have been developed to study electrochemical PCET. These methods can be used to calculate redox potentials and pKa values for molecular electrocatalysts, proton-coupled redox potentials and bond dissociation free energies for PCET at metal and semiconductor interfaces, and reorganization energies associated with electrochemical PCET. Periodic density functional theory can also be used to compute PCET activation energies and perform molecular dynamics simulations of electrochemical interfaces. Various approaches for maintaining a constant electrode potential in electronic structure calculations and modeling complex interactions in the electric double layer (EDL) have been developed. Theoretical formulations for both homogeneous and heterogeneous electrochemical PCET spanning the adiabatic, nonadiabatic, and solvent-controlled regimes have been developed and provide analytical expressions for the rate constants and current densities as functions of applied potential. The quantum mechanical treatment of the proton and inclusion of excited vibronic states have been shown to be critical for describing experimental data, such as Tafel slopes and potential-dependent kinetic isotope effects. The calculated rate constants can be used as input to microkinetic models and voltammogram simulations to elucidate complex electrocatalytic processes.

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.

Characterization of the electronic ground state of Mg[formula omitted] by PFI-ZEKE photoelectron spectroscopy

The X+2Σu+ ground electronic state of the Mg2+ ion has been studied by pulsed-field-ionization zero-kinetic-energy (PFI-ZEKE) photoelectron spectroscopy. Rotationally cold Mg2 molecules produced in a laser-ablation supersonic-expansion source were ionized by resonant two-photon absorption from the X1Σg+(v′′=0) ground vibronic state. The photoelectron spectra of the v+=3−14 vibrational levels of the X+ state were recorded with rotational resolution and their analysis led to the determination of accurate term values and rotational constants for these levels. Improved values of the adiabatic ionization energy of 24Mg2 (51503.9(4) cm−1) and of the ground-state dissociation energy of 24Mg2+ (10572.3(6) cm−1) were determined from experimental data.

Vibronic States and Edge-On Oriented π-Stacking in Poly(3-alkylthiophene) Thin Films

The influence of alkyl side-chain length [CnH2n+1 (A), where n = 6 (hexyl), 8 (octyl), 12 (dodecyl)] and thermal annealing (TA) and the definite roles of these in the quantity and quality of π-stacked crystallinity and edge-on orientated (EO) ordering of spin-coated poly(3-alkylthiophene) [P3AT] thin films, which are of massive significance in their optoelectronic properties, were investigated using complementary optical absorption spectroscopy and X-ray reflectivity (XR) techniques. The energy-band diagram, corresponding to the vibronic levels, obtained from the optical absorption spectrum provides information about the percentage, planarity, local order, and average conjugation length of the crystalline aggregates, while the electron density profile obtained from the XR provides unique information about the EO ordering and its variation along the depth. A prominent EO ordering near the substrate with a gradually decreased ordering toward the top surface is observed in each film. An as-cast P3HT film of shorter side-chain (having a natural nucleation tendency and rigidity) shows a slightly higher crystallinity and weaker excitonic coupling, while as-cast P3DDT film (having longer side-chain flexibility) shows a slightly better EO ordering. After the TA, the planarity of the unfolded backbone improves in each film; however, the effect is maximum in the P3DDT film. The EO ordering also improves throughout the film (by a thermal energy-induced reorientation of crystallites) but more toward the top surface (by increasing the decay length), preserving the exponential decay nature. The P3HT film (with the better initial crystallinity and planarity) shows an appreciable improvement, while the P3DDT film (where the crystallinity increases and crystallites have a better reorientational ability) shows the maximum improvement in the EO ordering. The improvement of the crystallinity (in quantity and quality) and the EO ordering of P3AT in thin films (as active layers), especially near the film–substrate interfaces, are of immense importance for their better in-plane charge carrier mobility in a thin-film transistor.