Influences of Quantum Mechanically Mixed Electronic and Vibrational Pigment States in 2D Electronic Spectra of Photosynthetic Systems: Strong Electronic Coupling Cases

In 2D electronic spectroscopy studies, long‐lived quantum beats have recently been observed in photosynthetic systems, and several theoretical studies have suggested that the beats are produced by quantum mechanically mixed electronic and vibrational states. Concerning the electronic‐vibrational quantum mixtures, the impact of protein‐induced fluctuations was examined by calculating the 2D electronic spectra of a weakly coupled dimer with the Franck‐Condon active vibrational modes in the resonant condition [Fujihashi et al., J. Chem. Phys.­ 2015 , 142, 212403.]. This analysis demonstrated that quantum mixtures of the vibronic resonance are rather robust under the influence of the fluctuations at cryogenic temperatures, whereas the mixtures are eradicated by the fluctuations at physiological temperatures. However, this conclusion cannot be generalized because the magnitude of the coupling inducing the quantum mixtures is proportional to the inter‐pigment electronic coupling. In this study, we explore the impact of the fluctuations on electronic‐vibrational quantum mixtures in a strongly coupled dimer with an off‐resonant vibrational mode. Toward this end, we calculate energy transfer dynamics and 2D electronic spectra of a model dimer that corresponds to the most strongly coupled bacteriochlorophyll molecules in the Fenna‐Matthews‐Olson complex in a numerically accurate manner. The quantum mixtures are found to be robust under the exposure of protein‐induced fluctuations at cryogenic temperatures, irrespective of the resonance. At 300 K, however, the quantum mixing is disturbed more strongly by the fluctuations, and therefore, the beats in the 2D spectra become obscure even in a strongly coupled dimer with a resonant vibrational mode. Further, the overall behaviors of the energy transfer dynamics are demonstrated to be dominated by the environment and coupling between the 0 0 vibronic transitions as long as the Huang‐Rhys factor of the vibrational mode is small. The electronic‐vibrational quantum mixtures do not necessarily play a significant role in electronic energy transfer dynamics despite contributing to the enhancement of long‐lived quantum beating in the 2D spectra.     

Polarized IR spectra of the hydrogen bond in 2-thiopheneacetic acid and 2-thiopheneacrylic acid crystals: H/D isotopic and temperature effects

Polarized IR spectra of 2-thiopheneacetic acid and of 2-thiopheneacrylic acid crystals were measured at 293 and 77 K in the υ(O-H) and υ(O-D) band frequency ranges. The corresponding spectra of the two individual systems strongly differ, one from the other, by the corresponding band shapes as well as by the temperature effect characterizing the bands. The crystal spectral properties remain in close relation with the electronic structure of the two different molecular systems. We show that a vibronic coupling mechanism involving the hydrogen bond protons and the electrons on the π- electronic systems in the molecules determines the way in which the vibrational exciton coupling between the hydrogen bonds in the carboxylic acid dimers occurs. Strong coupling in 2-thiopheneacrylic acid dimers prefers a "tail-to-head"-type Davydov coupling widespread by the π- electrons. A weak through-space coupling in 2-thiopheneacetic acid dimers, of a van der Waals type, is responsible for a "side-to-side"-type coupling. The relative contribution of each exciton coupling mechanism in the dimer spectra generation is temperature and the molecular electronic structure dependent. This explains the observed difference in the temperature- induced evolution of the compared spectra.     

Spin—orbit and vibronic perturbations on the chiroptical spectra of dissymmetric pseudo-tetragonal metal complexes

The influence of spin—orbit and vibronic interactions upon the chiroptical properties of nearly degenerate dd transitions in metal complexes of pseudo-tetragonal symmetry is investigated. A model system is considered in which three nearly degenerate dd excited states are coupled via both spinorbit and vibronic interactions. Vibronic interactions among the three nearly degenerate dd electronic states are assumed to arise from a pseudo-Jahn—Teller (PJT) mechanism involving three different vibrational modes (each nontotally symmetric in the point group of the undistorted model system).A vibronic hamiltonian is constructed (for the excited states of the model system) which includes linear coupling terms in each of the three PJT-active vibrational modes as well as a linear coupling term in one totally symmetric mode of the system and a spin—orbit interaction term. Wavefunctions and eigenvalues for the spin—orbit/vibronic perturbed excited states. of the model system are obtained by diagonalizing this hamiltonian in a basis constructed of uncoupled vibrational and electronic (orbital and spin) wavefunctions.Rotatory strengths associated with transitions to vibronic levels of the perturbed system are calculated and “rotatory strength spectra” are computed assuming gaussian shaped vibronic spectral components. Calculations are carried out for a number of vibronic and spin—orbit coupling parameters and for various splitting energies between the interacting electronic states. The calculated results suggest that chiroptical spectra associated with transitions to a set of nearly degenerate dd excited states of a chiral transition metal complex cannot be interpreted directly without some consideration of the effects introduced by spin—orbit and vibronic perturbations. These perturbations can lead to substantial alterations in the sign patterns and intensity distributions of rotatory strength among vibronic levels derived from the interacting electronic states and it is generally not valid to assign specific features in the observed circular dichroism spectra to transitions between states with well-defined electronic (orbital and spin) identities.Our theoretical model is conservative with respect to the total (or net) rotatory strength associated with transitions to levels derived from the three interacting electronic states; the vibronic and spin—orbit coupling operators are operative only within this set of states. That is, the total (or net) rotatory strength associated with these transitions remains invariant to the vibronic and spin—orbit coupling parameters of the model.     

On the limitations of adiabatic population transfer between molecular electronic states induced by intense femtosecond laser pulses

The possibility to perform a stimulated Raman adiabatic passage process in molecules on the ultrafast time scale is investigated theoretically. Motivated by recent experiments, the mid R:B<--mid R:X electronic transitions in molecular iodine are studied as a prototype example with the goal to selectively induce a population transfer employing two intense and time-delayed ultrashort laser pulses and different coupling schemes. For the purpose of interpretation, the coupled multilevel vibronic problem is reduced to a quasi-three-level system by averaging over the vibrational degree of freedom. It is shown that the vibrational dynamics becomes essential at high field intensities. Considering a 2-dimensional parameter space (intensity and delay time of the femtosecond laser pulses), a strong-field control landscape is constructed.     

An unusually large nonadiabatic error in the BNB molecule

The vibronic coupling model of Ko?uppel, Domcke, and Cederbaum in one dimension is introduced as a means to estimate the effects of electronic nonadiabaticity on the vibrational energy levels of molecules that exhibit vibronic coupling. For the BNB molecule, the nonadiabatic contribution to the nominal fundamental vibrational energy of the antisymmetric stretching mode is approximately -80?cm(-1). The surprisingly large effect for this mode, which corresponds to an adiabatic potential that is essentially flat near the minimum due to the vibronic interaction, is contrasted with another model system that also exhibits a flat potential (precisely, a vanishing quadratic force constant) but has a significantly larger gap between interacting electronic states. For the latter case, the nonadiabatic contribution to the level energies is about two orders of magnitude smaller even though the effect on the potential is qualitatively identical. A simple analysis shows that significant nonadiabatic corrections to energy levels should occur only when the affected vibrational frequency is large enough to be of comparable magnitude to the energy gap involved in the coupling. The results provide evidence that nonadiabatic corrections should be given as much weight as issues such as high-level electron correlation, relativistic corrections, etc., in quantum chemical calculations of energy levels for radicals with close-lying and strongly coupled electronic states even in cases where conical intersections are not obviously involved. The same can be said for high-accuracy thermochemical studies, as the zero-point vibrational energy of the BNB example contains a nonadiabatic contribution of approximately -70?cm(-1) (-0.9?kJ mol(-1)).     

Extremely narrow peaks in predissociation of sodium dimer due to rovibronic coupling

In sodium dimer the 2 (3)Pi(g), 3 (3)Pi(g), and 4 (3)Sigma(g) (+) electronic states are coupled; the coupling of the two (3)Pi(g) states is due to vibrational motion while the nonadiabatic interaction between the (3)Sigma(g) (+) and the (3)Pi(g) states-in particular, the 3 (3)Pi(g) state-is mediated by rotational interaction. The resulting vibronic problem is studied in some detail. The bound vibrational states of the 3 (3)Pi(g) and 4 (3)Pi(g) (+) states lie in the dissociation continuum of the 2 (3)Pi(g) state and become resonances due to the prevailing nonadiabatic coupling. The resonances are calculated using the complex scaling method and the available ab initio adiabatic potential energy curves. It is demonstrated that the resonances associated with rotational nonadiabatic coupling are narrower by several orders of magnitude than those that emerge from the vibrational nonadiabatic coupling. The predissociation cross section is computed and compared with experiment.     

Vibronic energies and spectra of molecular dimers

We consider three distinct methods of calculating the vibronic levels and absorption spectra of molecular dimers coupled by dipole-dipole interactions. The first method is direct diagonalization of the vibronic Hamiltonian in a basis of monomer eigenstates. The second method is to use creation and annihilation operators leading in harmonic approximation to the Jaynes-Cummings Hamiltonian. The adiabatic approximation to this problem provides insight into spectral behavior in the weak and strong coupling limits. The third method, which serves as a check on the accuracy of the previous methods, is a numerically exact solution of the time-dependent Schrodinger equation. Using these methods, dimer spectra are calculated for three separate dye molecules and show good agreement with measured spectra.     

The vibrational structures of furan, pyrrole, and thiophene cations studied by zero kinetic energy photoelectron spectroscopy

The vibrational structures of the electronic ground states ((approximately)X (2)A(2)) of furan, pyrrole, and thiophene cations have been studied by zero kinetic energy (ZEKE) photoelectron spectroscopic method. In addition to the strong excitations of the symmetric a(1) vibrational modes, other three symmetric vibrational modes (a(2), b(1), and b(2)) have been observed unambiguously. These results which cannot be explained by the Franck-Condon principle illustrate that the vibronic coupling and the Coriolis coupling may play important roles in understanding the vibrational structures of the five-membered heterocycle cations. The vibrationally resolved ZEKE spectra are assigned with the assistance of the density function theory calculations, and the fundamental frequencies for many vibrational modes have been determined for the first time. The first adiabatic ionization energies for furan, pyrrole, and thiophene were determined as 8.8863, 8.2099, and 8.8742 eV, respectively, with uncertainties of 0.0002 eV.     

A simple rule for prediction of intensities of vibrational overtone spectra

The intensities of vibrational overtone absorption transitions are described in terms of vibronic coupling of the ground molecular state to excited electronic configurations. Model calculations indicate an important role of nuclear geometry of excited electronic states relative to the ground state in determination of molecular overtone spectra. A simple rule for qualitative predictions of the overtone spectra for diatomic molecules or local bond modes of polyatomic molecules is proposed.     

Calculation of vibronic couplings for phenoxyl/phenol and benzyl/toluene self-exchange reactions: implications for proton-coupled electron transfer mechanisms

The vibronic couplings for the phenoxyl/phenol and the benzyl/toluene self-exchange reactions are calculated with a semiclassical approach, in which all electrons and the transferring hydrogen nucleus are treated quantum mechanically. In this formulation, the vibronic coupling is the Hamiltonian matrix element between the reactant and product mixed electronic-proton vibrational wavefunctions. The magnitude of the vibronic coupling and its dependence on the proton donor-acceptor distance can significantly impact the rates and kinetic isotope effects, as well as the temperature dependences, of proton-coupled electron transfer reactions. Both of these self-exchange reactions are vibronically nonadiabatic with respect to a solvent environment at room temperature, but the proton tunneling is electronically nonadiabatic for the phenoxyl/phenol reaction and electronically adiabatic for the benzyl/toluene reaction. For the phenoxyl/phenol system, the electrons are unable to rearrange fast enough to follow the proton motion on the electronically adiabatic ground state, and the excited electronic state is involved in the reaction. For the benzyl/toluene system, the electrons can respond virtually instantaneously to the proton motion, and the proton moves on the electronically adiabatic ground state. For both systems, the vibronic coupling decreases exponentially with the proton donor-acceptor distance for the range of distances studied. When the transferring hydrogen is replaced with deuterium, the magnitude of the vibronic coupling decreases and the exponential decay with distance becomes faster. Previous studies designated the phenoxyl/phenol reaction as proton-coupled electron transfer and the benzyl/toluene reaction as hydrogen atom transfer. In addition to providing insights into the fundamental physical differences between these two types of reactions, the present analysis provides a new diagnostic for differentiating between the conventionally defined hydrogen atom transfer and proton-coupled electron transfer reactions.     

The influence of vibronic interactions on the chiroptical spectra of dissymmetric pseudo tetragonal metal complexes

The influence of vibronic interactions on the chiroptical spectra associated with a threesome of nearly degenerate electronic excited states in a dissymmetric molecular system is examined on a formal theoretical model. The model considers two vibrational modes to be effective in promoting pseudo Jahn-Teller (PJT) type interactions between the three closely spaced electronic excited states. Formal expressions are developed for the rotatory strengths of individual vibronic levels derived from the coupled electronic states. Two mode (vibrational)-three state (electronic) vibronic Hamiltonians are constructed (basis set size, 63–108, depending upon interaction parameters used) and diagonalized for a large number of different parameter sets representative of various vibronic coupling strengths, electronic energy level spacings, oscillator (vibrational mode) frequencies, and electronic rotatory strengths. Diagonalization of these vibronic Hamiltonians yields vibronic wave functions and energies which are then used to calculate rotatory strength spectra for the model system. The calculated results demonstrate the profound influence which vibronic interactions of the PJT type may have on the sign patterns and intensity distributions within the rotatory strength spectrum associated with a set of nearly degenerate electronic states. The implication of these results for the interpretation of circular dichroism spectra of chiral transition metal complexes with pseudo tetragonal symmetry are discussed.     

Analysis of the vibronic fine structure in circularly polarized emission spectra from chiral molecular aggregates

Using a Frenkel-exciton model, the degree of circular polarization of the luminescence (g(lum)) from one-dimensional, helical aggregates of chromophoric molecules is investigated theoretically. The coupling between the electronic excitation and a local, intramolecular vibrational mode is taken into account. Analytical expressions for the fluorescence band shape and g(lum) are presented for the case of strong and weak electronic coupling between the chromophoric units. Results are compared to those from numerical calculations obtained using the three particle approximation. g(lum) for the 0-0 vibronic band is found to be independent of the relative strength of electronic coupling between chromophores and excitation-vibration coupling. It depends solely on the number of coherently coupled molecules. In contrast, for the higher vibronic transitions[g(lum)] decreases with decreasing strength of the electronic coupling. In the limit of strong electronic coupling, [g(lum)] is almost constant throughout the series of vibronic transitions but for weak coupling [g(lum)] becomes vanishingly small for all vibronic transitions except for the 0-0 transition. The results are interpreted in terms of dynamic localization of the excitation during the zero point vibrational motion in the excited state of the aggregate. It is concluded that circular polarization measurements provide an independent way to determine the coherence size and bandwidth of the lowest exciton state for chiral aggregates.     

A theoretical study of the chiroptical properties of molecules with isotopically engendered chirality

There has been a considerable interest in the chiroptical properties of molecules whose chirality is exclusively due to an isotopic substitution and numerous examples for the electronic circular dichroism (CD) spectra of isotopically chiral systems have been reported in literature. Four different explanations have been proposed for the mechanism as to how the isotopic substitution induces a chiral perturbation of the otherwise achiral electronic wave function; however, up to now no conclusive answer has been given about the dominating effect responsible for the experimental observations. In this study we will present, for the first time, fully quantum-mechanical calculations of the CD spectra of three different molecular systems with isotopically engendered chirality. As examples, we consider the spectra of organic molecules with ketone and alpha-diketone carbonyl and diene chromophores. The effect of vibronic couplings for the reorientation of the electric and magnetic transition dipole moments is taken into account within the Herzberg-Teller approximation. The ground and excited state geometries and vibrational normal modes are obtained with (time-dependent) density functional theory [(TD)DFT], while the vibronic coupling effects are calculated at the TDDFT and density functional theory/multireference configuration interaction (DFT/MRCI) levels of theory. Generally, the band shapes of the experimental CD spectra are reproduced very well, and also the absolute CD intensities from the simulations are of the right order of magnitude. The sign and the intensity of the CD band are determined by a delicate balance of the contributions of a large number of individual vibronic transitions, and it is found that the vibrational normal modes with a large displacement are dominant. The separation of the calculated CD spectrum into the different contributions due to the overlap of the in-plane and out-of-plane components (regarding the symmetry plane of the unsubstituted molecule) of the electric and magnetic transition dipole moments yields information about the influence of the vibronic coupling effects for the reorientation of the corresponding transition dipole moments. In conclusion, the calculations clearly show that vibronic effects are responsible or at least dominant for the chiroptical properties of isotopically chiral organic molecules.     

Excited and ground state vibrational dynamics revealed by two-dimensional electronic spectroscopy

Broadband two-dimensional electronic spectroscopy (2DES) can assist in understanding complex electronic and vibrational signatures. In this paper, we use 2DES to examine the electronic structure and dynamics of a long chain cyanine dye (1,1-diethyl-4,4-dicarbocyanine iodide, or DDCI-4), a system with a vibrational progression. Using broadband pulses that span the resonant electronic transition, we measure two-dimensional spectra that show a characteristic six peak pattern from coherently excited ground and excited state vibrational modes. We model these features using a spectral density formalism and the vibronic features are assigned to Feynman pathways. We also examine the dynamics of a particular set of peaks demonstrating anticorrelated peak motion, a signature of oscillatory wavepacket dynamics on the ground and excited states. These dynamics, in concert with the general structure of vibronic two-dimensional spectra, can be used to distinguish between pure electronic and vibrational quantum coherences.     

Multimode Jahn-Teller and pseudo-Jahn-Teller interactions in the cyclopropane radical cation: complex vibronic spectra and nonradiative decay dynamics

The complex vibronic spectra and the nonradiative decay dynamics of the cyclopropane radical cation (CP+) are simulated theoretically with the aid of a time-dependent wave packet propagation approach using the multireference time-dependent Hartree scheme. The theoretical results are compared with the experimental photoelectron spectrum of cyclopropane. The ground and first excited electronic states of CP+ are of X2E' and A2E' type, respectively. Each of these degenerate electronic states undergoes Jahn-Teller (JT) splitting when the radical cation is distorted along the degenerate vibrational modes of e' symmetry. The JT split components of these two electronic states can also undergo pseudo-Jahn-Teller (PJT)-type crossings via the vibrational modes of e', a1' and a2' symmetries. These lead to the possibility of multiple multidimensional conical intersections and highly nonadiabatic nuclear motions in these coupled manifolds of electronic states. In a previous publication [J. Phys. Chem. A 2004, 108, 2256], we investigated the JT interactions alone in the X2E' ground electronic manifold of CP+. In the present work, the JT interactions in the A2E' electronic manifold are treated, and our previous work is extended by considering the coupling between the X2E' and A2E' electronic states of CP+. The nuclear dynamics in this coupled manifold of two JT split doubly degenerate electronic states is simulated by considering fourteen active and most relevant vibrational degrees of freedom. The vibronic level spectra and the ultrafast nonradiative decay of the excited cationic states are examined and are related to the highly complex entanglement of electronic and nuclear degrees of freedom in this prototypical molecular system.     

Nonadiabatic scattering of NO off Au3 clusters: A simple and robust diabatic state manifold generation method for multiconfigurational wavefunctions

The presence of nonadiabatic effects during the interaction of small molecules with metals has been observed experimentally for the last decades. Specially remarkable are the effects found for NO/Au, where experiments have suggested the presence of very strong vibronic coupling during the molecular scattering. However, the accurate inclusion of the nonadiabatic effects in periodic boundary conditions (PBC) theoretical methods remain an unapproachable challenge. Here, aiming to give some theoretical insight to the strong vibronic coupling, we have adopted a pragmatic point of view, taking use of an auxiliary simplified system, NO/Au₃. We show the importance of nonadiabatic coupling, during the scattering of NO from a Au₃ cluster, using a diabatic representation of 12 electronic states of the system, including a few charge-transfer states. Our diabatic representation is obtained by rotating the orbital and configuration interaction (CI) vectors of a restricted active space (RAS) wavefunction. We present a strategy for extracting the best effective manifold of states relevant to the system, below some prescribed energy, directly from the RAS CI vectors. This scheme is able to disentangle a large dense manifold of adiabatic states with strong coupling and crossings. This approach is also shown to work for multireference configuration interaction (MRCI). By performing quantum propagations, we observed an increase in vibrational redistribution with increasing initial vibrational or translational energies. We suggest that these nonadiabatic effects should also be present at smaller energies in larger clusters. © 2018 Wiley Periodicals, Inc.     

Ab initio simulation of the vibrationally resolved photoelectron spectrum of Si3-

Electron photodetachment spectra provide a wealth of information about the electronic and vibrational level structures of neutral molecules that form stable anions. Experiments carried out for the smallest polyatomic silicon cluster anion (Si3-+hupsilon-->Si3*+e-) show vibrational progressions in six observed electronic bands (X-E) of the neutral species. The authors have performed ab initio calculations using the MRCI+D/aug-cc-pVQZ level for the corresponding electronic states followed by variational calculations of the vibronic levels associated with these adiabatic potential energy surfaces. In contrast to previous approaches, the authors treat the nonadiabatic dynamics on the potential energy surfaces, which allows for a vastly improved reproduction of the experimental level structure and a corrected assignment for band A.     

A multimode analysis of the gas-phase photoelectron spectra in oligoacenes

We present a multimode vibrational analysis of the gas-phase ultraviolet photoelectron spectra of the first ionization in anthracene, tetracene, and pentacene, using electron-vibration constants computed at the density functional theory level. The first ionization of each molecule exhibits a high-frequency vibronic structure; it is shown that this regularly spaced feature is actually the consequence of the collective action of several vibrational modes rather than the result of the interaction with a single mode. We interpret this feature in terms of the missing mode effect. We also discuss the vibronic coupling constants and relaxation energies obtained from the fit of the photoelectron spectra with the linear vibronic model.     

Photoinduced Rydberg ionization spectroscopy of the B state of benzonitrile cation

Photoinduced Rydberg ionization (PIRI) spectra of the second excited electronic state of benzonitrile cation were recorded via the origin and 6a1 and 6b1 vibrational levels of the cation ground electronic state. This B<--X transition was verified to be a forbidden 2B2<--2B1 transition with an origin at 17,225 cm-1 above the ground ionic state. By the use of vibronic coupling calculations, as well as symmetry analysis and comparison of the PIRI spectra via different ground vibrational levels, a nearly complete assignment of the vibrational structure was made, and the vibrational frequencies of the B 2B2 state of benzonitrile cation were obtained based on the assignments. Comparisons of the experimental spectra with simulations from the vibronic structure calculations are also used to validate the theoretical procedures used in the simulations.     

The Jahn-Teller and Barnett effects

In the usual formulation of the Jahn-Teller effect a simplification is made in going from the adiabatic to the crude adiabatic approximation in which the electronic parts of the vibronic wavefunction are assumed independent of the nuclear coordinates. This then neglects momentum coupling in the vibronic coupling matrix. The momentum coupling has been termed the molecular Barnett effect when the active vibration transforms as the irreducible representation of a rotation in the molecular point group. Experimental evidence for the molecular Barnett effect has recently been found. In this paper the various point groups in which momentum and Barnett coupling can occur are investigated. A vibration capable of momentum coupling is contained in the asymmetric direct product of the degenerate electronic state and, as with the Jahn-Teller effect, is possible in the orbitally degenerate electronic states of molecules of all non-linear point groups. A static distortion along such a coordinate will lift the electronic degeneracy. Unlike the Jahn-Teller effect, however, in some point groups a minimum complexity of the molecule is required before such coupling can occur. In particular it will be absent in the degenerate electronic states of such simple molecules of the form X₃(D_3h); XY₃(C_3v, D_3h); XY₄(T_d); and XY₆(O_h).