Vibronic Dynamics Research Articles

Vibronic relaxation dynamics of o-dichlorobenzene in its lowest excited singlet state

Vibronic dynamics of o-dichlorobenzene in its lowest excited singlet state, S1, is investigated in real time by using femtosecond pump-probe method, combined with time-of-flight mass spectroscopy and photoelectron velocity mapping technique. Relaxation processes for the excitation in the range of 276–252 nm can be fitted by single exponential decay model, while in the case of wavelength shorter than 252 nm two-exponential decay model must be adopted for simulating transient profiles. Lifetime constants of the vibrationally excited S1 states change from 651 ± 10 ps for 276 nm excitation to 61 ± 1 ps for 242 nm excitation. Both the internal conversion from the S1 to the highly vibrationally excited ground state S0 and the intersystem crossing from the S1 to the triplet state are supposed to play important roles in de-excitation processes. Exponential fitting of the de-excitation rates on the excitation energy implies such de-excitation process starts from the highly vibrationally excited S0 state, which is validated, by probing the relaxation following photoexcitation at 281 nm, below the S1 origin. Time-dependent photoelectron kinetic energy distributions have been obtained experimentally. As the excitation wavelength changes from 276 nm to 242 nm, different cationic vibronic vibrations can be populated, determined by the Franck-Condon factors between the large geometry distorted excited singlet states and final cationic states.

Nodeless vibrational amplitudes and quantum nonadiabatic dynamics in the nested funnel for a pseudo Jahn-Teller molecule or homodimer.

The nonadiabatic states and dynamics are investigated for a linear vibronic coupling Hamiltonian with a static electronic splitting and weak off-diagonal Jahn-Teller coupling through a single vibration with a vibrational-electronic resonance. With a transformation of the electronic basis, this Hamiltonian is also applicable to the anti-correlated vibration in a symmetric homodimer with marginally strong constant off-diagonal coupling, where the non-adiabatic states and dynamics model electronic excitation energy transfer or self-exchange electron transfer. For parameters modeling a free-base naphthalocyanine, the nonadiabatic couplings are deeply quantum mechanical and depend on wavepacket width; scalar couplings are as important as the derivative couplings that are usually interpreted to depend on vibrational velocity in semiclassical curve crossing or surface hopping theories. A colored visualization scheme that fully characterizes the non-adiabatic states using the exact factorization is developed. The nonadiabatic states in this nested funnel have nodeless vibrational factors with strongly avoided zeroes in their vibrational probability densities. Vibronic dynamics are visualized through the vibrational coordinate dependent density of the time-dependent dipole moment in free induction decay. Vibrational motion is amplified by the nonadiabatic couplings, with asymmetric and anisotropic motions that depend upon the excitation polarization in the molecular frame and can be reversed by a change in polarization. This generates a vibrational quantum beat anisotropy in excess of 2/5. The amplitude of vibrational motion can be larger than that on the uncoupled potentials, and the electronic population transfer is maximized within one vibrational period. Most of these dynamics are missed by the adiabatic approximation, and some electronic and vibrational motions are completely suppressed by the Condon approximation of a coordinate-independent transition dipole between adiabatic states. For all initial conditions investigated, the initial nonadiabatic electronic motion is driven towards the lower adiabatic state, and criteria for this directed motion are discussed.

Ultrafast dynamics of multi-exciton state coupled to coherent vibration in zinc chlorin aggregates for artificial photosynthesis.

Ultrafast vibronic dynamics induced by the interaction of the Frenkel exciton with the coherent molecular vibrations in a layer-structured zinc chlorin aggregates prepared for artificial photosynthesis have been studied by 7.1 fs real-time vibrational spectroscopy with multi-spectrum detection. The fast decay of 100 ± 5fs is ascribed to the relaxation from the higher multi-exciton state (MES) to the one-exciton state, and the slow one of 863 ± 70fs is assigned to the relaxation from Q-exciton state to the dark nonfluorescent charge-transfer (CT) state, respectively. In addition, the wavelength dependences of the exciton-vibration coupling strength are found to follow the zeroth derivative of the transient absorption spectra of the exciton. It could be explained in term of the transition dipole moment modulated by dynamic intensity borrowing between the B transition and the Q transition through the vibronic interactions.

Full-dimensional treatment of short-time vibronic dynamics in a molecular high-order-harmonic-generation process in methane

We present derivation and implementation of the Multi-Configurational Strong-Field Approximation with Gaussian nuclear Wave Packets (MC-SFA-GWP) -- a version of the molecular strong-field approximation which treats all electronic and nuclear degrees of freedom, including their correlations, quantum-mechanically. The technique allows, for the first time, realistic simulation of high-harmonic emission in polyatomic molecules without invoking reduced-dimensionality models for the nuclear motion or the electronic structure. We use MC-SFA-GWP to model isotope effects in high-harmonics generation (HHG) spectroscopy of methane. The HHG emission in this molecule transiently involves strongly vibronically-coupled $^2F_2$ electronic state of the $\rm CH_4^+$ cation. We show that the isotopic HHG ratio in methane contains signatures of: a) field-free vibronic dynamics at the conical intersection (CI); b) resonant features in the recombination cross-sections; c) laser-driven bound-state dynamics; as well as d) the well-known short-time Gaussian decay of the emission. We assign the intrinsic vibronic feature (a) to a relatively long-lived ($\ge4$ fs) vibronic wave packet of the singly-excited $\nu_4$ ($t_2$) and $\nu_2$ ($e$) vibrational modes, strongly coupled to the components of the $^2F_2$ electronic state. We demonstrate that these physical effects differ in their dependence on the wavelength, intensity, and duration of the driving pulse, allowing them to be disentangled. We thus show that HHG spectroscopy provides a versatile tool for exploring both conical intersections and resonant features in photorecombination matrix elements in the regime not easily accessible with other techniques.

Quantifying Early Time Quantum Decoherence Dynamics through Fluctuations

We introduce a general but simple relation between the timescale for quantum coherence loss and the initial fluctuations of operators that couple a quantum system with a surrounding bath. The relation allows the prediction and measurement of early time decoherence dynamics for any open quantum system, through purity, without reconstructing the system's many-body density matrix. It is applied to predict the decoherence time for basic models-the Holstein chain, spin-boson and Caldeira-Legget models-commonly employed to capture electronic, vibrational, and vibronic dynamics in molecules. Such development also offers a practical platform to test the ability of approximate quantum dynamics methods to capture decoherence. In particular, a class of mixed quantum-classical schemes for molecular dynamics where the bath is treated classically, such as Ehrenfest dynamics, are shown to correctly capture short-time decoherence when the initial conditions are sampled from the Wigner distribution. These advances provide a useful platform to develop decoherence times for molecular processes and to test approximate molecular dynamics methods.

Vibrational relaxation beyond the linear damping limit in two-dimensional optical spectra of molecular aggregates.

We present a computational model for the spectra of molecular aggregates with signatures of vibronic progression. Vibronic dynamics is implemented by coupling the dynamics of Frenkel excitons with underdamped vibrations. Vibrational dynamics includes linear damping resulting in the exponential decay and quadratic damping inducing subexponential or power law relaxation and increasing vibrational decoherence as demonstrated on lineshapes of the absorption spectrum. Simulations of the third-order coherent response account for bath reorganization during excitonic transport, which allows us to study the line-shape evolution of cross peaks of 2D spectra.

Vibronic eigenstates and the geometric phase effect in the 2E″ state of NO3.

The 2E″ state of NO3, a prototype for the Jahn-Teller effect, has been an enigma and a challenge for a long time for both experiment and theory. We present a detailed theoretical study of the vibronic quantum dynamics in this electronic state, uncovering the effects of tunnelling, geometric phase, and symmetry. To this end, 45 vibronic levels of NO3 in the 2E″ state are determined accurately and analyzed thoroughly. The computation is based on a high quality diabatic potential representation of the two-sheeted surface of the 2E″ state developed by us [W. Eisfeld et al., J. Chem. Phys. 140, 224109 (2014)] and on the multi-configuration time dependent Hartree approach. The vibrational eigenstates of the NO3- anion are determined and analyzed as well to gain a deeper understanding of the symmetry properties of such D3h symmetric systems. To this end, 61 eigenstates of the NO3- anion ground state are computed using the single sheeted potential surface of the 1A1 state published in the same reference quoted above. The assignments of both the vibrational and vibronic levels are discussed. A simple model is proposed to rationalize the computed NO3 spectrum strongly influenced by the Jahn-Teller couplings, the associated geometric phase effect, and the tunnelling. Comparison with the available spectroscopic data is also presented.

Excited state dynamics of acrylonitrile: Substituent effects at conical intersections interrogated via time-resolved photoelectron spectroscopy and ab initio simulation

We report a joint experimental and theoretical study on the photoinitiated ultrafast dynamics of acrylonitrile (AN) and two methylated analogs: crotonitrile (CrN) and methacrylonitrile (MeAN). Time-resolved photoelectron spectroscopy (TRPES) and ab initio simulation are employed to discern the conical intersection mediated vibronic dynamics leading to relaxation to the ground electronic state. Each molecule is pumped with a femtosecond pulse at 200 nm and the ensuing wavepackets are probed by means of one and two photon ionization at 267 nm. The predominant vibrational motions involved in the de-excitation process, determined by ab initio trajectory simulations, are an initial twisting about the C=C axis followed by pyramidalization at a carbon atom. The decay of the time-resolved photoelectron signal for each molecule is characterized by exponential decay lifetimes for the passage back to the ground state of 60 ± 10, 86 ± 11, and 97 ± 9 fs for AN, CrN, and MeAN, respectively. As these results show, the excited state dynamics are sensitive to the choice of methylation site and the explanation for the observed trend may be found in the trajectory simulations. Specifically, since the pyramidalization motion leading to the conical intersection with the ground state is accompanied by the development of a partial negative charge at the central atom of the pyramidal group, the electron donation of the cyano group ensures that this occurs exclusively at the medial carbon atom. In this way, the donated electron density from the cyano group “directs” the wavepacket to a particular region of the intersection seam. The excellent agreement between the experimental and simulated TRPES spectra, the latter determined by employing trajectory simulations, demonstrates that this mechanistic picture is consistent with the spectroscopic results.

Photophysics and photostability of pyrimidine molecule and its radical cation: a theoretical study

ABSTRACTMultistate and multimode vibronic dynamics on first five coupled (S1–S2–S3–S4–S5) electronic states of pyrimidine molecule and first four ( – – –) electronic states of pyrimidine radical cation are investigated with the help of ab initio electronic structure calculations of potential energy surfaces (PESs) and first principle quantum dynamical methods. Excited electronic PESs are generated at the MRCI and Equation of Motion Couple Cluster Single and Double (EOM-CCSD) level of theory. Several low-lying conical intersections among various electronic states are found and their impact on the nuclear dynamics is discussed. The simulation of nuclear motion on the underlying coupled electronic states of pyrimidine molecule and its radical cation is examined by both time-independent and time-dependent quantum mechanical methods. In the latter case, a wave packet propagation-based method within multi-configurational time-dependent Hartree algorithm is employed. The theoretical results are verified with the experimental photoelectron spectroscopy, vacuum ultraviolet spectroscopy and resolved (<10 meV) vibrational energy level spectrum of pyrimidine molecule which has good impact on astrobiology.

A Unified Picture of S* in Carotenoids.

In π-conjugated chain molecules such as carotenoids, coupling between electronic and vibrational degrees of freedom is of central importance. It governs both dynamic and static properties, such as the time scales of excited state relaxation as well as absorption spectra. In this work, we treat vibronic dynamics in carotenoids on four electronic states (|S0⟩, |S1⟩, |S2⟩, and |Sn⟩) in a physically rigorous framework. This model explains all features previously associated with the intensely debated S* state. Besides successfully fitting transient absorption data of a zeaxanthin homologue, this model also accounts for previous results from global target analysis and chain length-dependent studies. Additionally, we are able to incorporate findings from pump-deplete-probe experiments, which were incompatible to any pre-existing model. Thus, we present the first comprehensive and unified interpretation of S*-related features, explaining them by vibronic transitions on either S1, S0, or both, depending on the chain length of the investigated carotenoid.

In Process Citation

In continuation to our earlier work [Sarkar et al., Mol. Phys. 2015, 113, 3073–3084], we present here the vibronic structure and nonradiative decay dynamics of energetically low-lying electronic states of CH2F2+. Interesting comparison is made with the results obtained for the deuterated isotopomer CD2F2+. The results are compared with both broad band as well as high-resolution experimental spectroscopy data available in the literature. The progression of vibrational modes in the spectra is identified, assigned and discussed in relation to the assignments available in the literature. Both time-independent and time-dependent quantum mechanical methods are used to carry out nuclear dynamics calculations. The underlying potential energy surfaces and their coupling surfaces are constructed by rigorous ab initio quantum chemistry calculations.

Molecular Packing Determines Charge Separation in a Liquid Crystalline Bisthiophene-Perylene Diimide Donor-Acceptor Material.

Combined electronic structure and quantum dynamical calculations are employed to investigate charge separation in a novel class of covalently bound bisthiophene-perylene diimide type donor-acceptor (DA) co-oligomer aggregates. In an earlier spectroscopic study of this DA system in a smectic liquid crystalline (LC) film, efficient and ultrafast (subpicosecond) initial charge separation was found to be followed by rapid recombination. By comparison, the same DA system in solution exhibits ultrafast resonant energy transfer followed by slower (picosecond scale) charge separation. The present first-principles study explains these contrasting observations, highlighting the role of an efficient intermolecular charge-transfer pathway that results from the molecular packing in the LC phase. Despite the efficiency of this primary charge-transfer step, long-range charge separation is impeded by a comparatively high Coulomb barrier in conjunction with small electron- and hole-transfer integrals. Quantum dynamical calculations are carried out for a fragment-based model Hamiltonian, parametrized by ab initio second-order Algebraic Diagrammatic Construction (ADC(2)) and Time-Dependent Density Functional Theory (TDDFT) electronic structure calculations. Simulations of coherent vibronic quantum dynamics for up to 156 electronic states and 48 modes are performed using the Multi-Layer Multi-Configuration Time-Dependent Hartree (ML-MCTDH) method. Excellent agreement with experimentally determined charge separation time scales is obtained, and the spatially coherent nature of the dynamics is analyzed.

Quantum Nuclear Dynamics Pumped and Probed by Ultrafast Polarization Controlled Steering of a Coherent Electronic State in LiH.

The quantum wave packet dynamics following a coherent electronic excitation of LiH by an ultrashort, polarized, strong one-cycle infrared optical pulse is computed on several electronic states using a grid method. The coupling to the strong field of the pump and the probe pulses is included in the Hamiltonian used to solve the time-dependent Schrodinger equation. The polarization of the pump pulse allows us to control the localization in time and in space of the nonequilibrium coherent electronic motion and the subsequent nuclear dynamics. We show that transient absorption, resulting from the interaction of the total molecular dipole with the electric fields of the pump and the probe, is a very versatile probe of the different time scales of the vibronic dynamics. It allows probing both the ultrashort, femtosecond time scale of the electronic coherences as well as the longer dozens of femtoseconds time scales of the nuclear motion on the excited electronic states. The ultrafast beatings of the electronic coherences in space and in time are shown to be modulated by the different periods of the nuclear motion.

Two-dimensional femtosecond optical spectroscopy of trapping dynamics in a charge-transfer process

We study charge-transfer dynamics monitored by two-dimensional (2D) optical spectroscopy. The often used model consisting of two coupled diabatic electronic states in a single reaction coordinate is used to demonstrate the relation between the vibronic dynamics and the 2D-spectra. Within the employed wave-function approach, dissipation is included via a quantum-jump algorithm with explicit treatment of dephasing. States with long lifetimes which decay slowly due to the interaction with the environment are identified. Using filtered Fourier transforms, energy and time resolved information about the dissipative system dynamics can be obtained.

Photophysics of barrelene: The Jahn-Teller and pseudo-Jahn-Teller effects

The static and dynamic aspects of Jahn-Teller(JT) and pseudo-Jahn-Teller(PJT) interactions between ground (X˜2A2′) and first three excited electronic states (A˜2E′, B˜2E″ and C˜2A′1 ) of bicyclo- [2,2,2]-octa-2,5,7-triene (barrelene) radical cation (Bl+) are theoretically investigated here. This belongs to the (E + E) ⊗ e and (E + A) ⊗ e JT-PJT class of compounds as described by the symmetry of the electronic states and the molecular point group. The complex vibronic dynamics on the coupled electronic states of the cation is simulated by both time-independent and time-dependent wave packet propagation method using multi configuration time-dependent Hartree scheme. The JT effects in the A˜ and B˜ electronic states and the PJT coupling between the B˜ and C˜ electronic states of Bl+ are found very strong. The final theoretical results are compared with the experimental results.

Two-pulse control over double ionization pathways in CO2.

We visualize and control molecular dynamics taking place on intermediately populated states during different sequential double ionization pathways of CO2 using a sequence of two delayed laser pulses which exhibit different peak intensities. Measured yields of CO2 (2+) and of fragment pairs CO(+)/O(+) as a function of delay between the two pulses are weakly modulated by various vibronic dynamics taking place in CO2 (+). By Fourier analysis of the modulations we identify the dynamics and show that they can be assigned to merely two double ionization pathways. We demonstrate that by reversing the sequence of the two pulses it becomes possible to control the pathway which is taken across CO2 (+) towards the final state in CO2 (2+). A comparison between the yields of CO2 (2+) and CO(+)/O(+) reveals that the modulating vibronic dynamics oscillate out-of-phase with each other, thus opening up opportunities for strong-field fragmentation control on extended time scales.

Revealing the radiative and non-radiative relaxation rates of the fluorescent dye Atto488 in a λ/2 Fabry-Pérot-resonator by spectral and time resolved measurements.

Using a Fabry-Pérot-microresonator with controllable cavity lengths in the λ/2-regime, we show the controlled modification of the vibronic relaxation dynamics of a fluorescent dye molecule in the spectral and time domain. By altering the photonic mode density around the fluorophores we are able to shape the fluorescence spectrum and enhance specifically the probability of the radiative transitions from the electronic excited state to distinct vibronic excited states of the electronic ground state. Analysis and correlation of the spectral and time resolved measurements by a theoretical model and a global fitting procedure allows us to reveal quantitatively the spectrally distributed radiative and non-radiative relaxation dynamics of the respective dye molecule under ambient conditions at the ensemble level.

Ultrafast dynamics of electronically excited diborane radical cation

Full-dimensional quantum mechanical study is carried out to investigate the vibronic structure and internal conversion dynamics of the energetically low-lying electronic excited states of \( {\text{B}}_{{\text{2}}} {\text{H}}_{6}^{{ \cdot + }} \). A model diabatic electronic Hamiltonian, within the quadratic vibronic coupling approach comprising of five energetically low-lying electronic states, is developed, and the parameters of the Hamiltonian are estimated by performing extensive ab initio electronic structure calculations using the equation-of-motion coupled-cluster singles and doubles method. The nuclear dynamics on the constructed diabatic electronic states is studied by employing both time-independent and time-dependent quantum mechanical methods. Theoretically calculated vibronic structure of the electronic states is found to be in excellent accord with the available experimental results. Extremely strong vibronic interactions among the electronic states result highly overlapping and diffuse vibronic bands and complicate the assignment of vibronic progression. Examination of non-radiative internal conversion dynamics revealed very short lifetime (\(<\)60 fs) of the excited electronic states of \( {\text{B}}_{{\text{2}}} {\text{H}}_{6}^{{ \cdot + }} \).

Two-dimensional Fourier transform electronic spectroscopy at a conical intersection

We report measurement and modeling of two-dimensional (2D) electronic spectra of a silicon naphthalocyanine (SiNc) in benzonitrile, a system for which the polarization anisotropy reveals passage through a square-symmetric Jahn-Teller conical intersection in ∼100 fs [D. A. Farrow, W. Qian, E. R. Smith, A. A. Ferro, and D. M. Jonas, J. Chem. Phys. 128, 144510 (2008)]. The measured 2D Fourier transform (FT) spectra indicate loss of electronic coherence on a similar timescale. The 2D spectra arising from femtosecond vibronic dynamics through the conical funnel are modeled by full non-adiabatic treatment of the coupled electronic and vibrational dynamics for a pair of un-damped Jahn-Teller active vibrations responsible for both electronic decoherence and population transfer. Additional damped Jahn-Teller active modes that can cause only decoherence or population transfer are treated with analytical response functions that can be incorporated into the numerical non-adiabatic calculation by exploiting symmetry assignment of degenerate vibronic eigenstates to one of two electronic states. Franck-Condon active totally symmetric modes are incorporated analytically. The calculations reveal that these conical intersection dynamics alone are incapable of destroying the coherence of the initially prepared wavepacket on the experimentally observed timescale and predict an unobserved recurrence in the photon echo slice at ∼200 fs. Agreement with the experimental two-dimensional electronic spectra necessitates a role for totally symmetric vibrational dynamics in causing the echo slice to decay on a ∼100 fs timescale. This extended model also reproduces the ∼100 fs ultrafast electronic anisotropy decay in SiNc when an "asymmetric solvation mode" with a small stabilization energy of ∼2 cm(-1) is included. Although calculations show that inhomogeneities in the energy gap between excited states can broaden the anti-diagonal 2D lineshape, the anti-diagonal width is dominated by totally symmetric vibrational motions in SiNc. For this shallow conical intersection, the non-adiabatic dynamics destroy electronic coherence more slowly than they destroy electronic alignment.

Nonadiabatically Coupled π-Electron Rotation and Molecular Vibration in Aromatic Molecules Excited by Polarized UV/Vis Laser Pulses

We review our theoretical studies on laser-driven ultrafast π-electron rotation (ring current) and vibronically coupled molecular vibrations in aromatic molecules with quasi-degenerate excited states. The main focus of discussion is on the role of laser polarization in controlling the coherent vibronic dynamics. We first present general formulations of the coherent electronic wave packet and expectation value of electronic angular momentum for arbitrary laser polarization within a frozen-nuclei model. We show that the relative quantum phase of the superposed quasi-degenerate states, which determines the oscillating behavior of angular momentum, can be manipulated by the ellipticity and orientation of the incident laser. The controllability of π-electron rotation is demonstrated by electronic wave packet simulations for a model molecule. The results of nuclear wave packet simulations on effective potential energy surfaces of the molecule have revealed that the angular momentum is gradually reduced by nonadiabatic transitions. The amplitude of induced molecular vibration depends significantly on the direction of linear polarization vectors but is insensitive to the helicity of circular polarization. The characteristic feature in vibrational amplitudes is attributed to the interference between nuclear wave packets that acquire different quantum phases in nonadiabatic transition. This feature offers a new strategy for laser control of molecular vibrations through the wave packet interference in nonadiabatic transition.