Nonadiabatic Excited-State Molecular Dynamics Modeling of Photoinduced Dynamics in Conjugated Molecules

Quantum transition probabilities during a perturbing pulse: Differences between the nonadiabatic results and Fermi's golden rule forms

For a perturbed quantum system initially in the ground state, the coefficient c_k(t) of excited state k in the time-dependent wave function separates into adiabatic and nonadiabatic terms. The adiabatic term a_k(t) accounts for the adjustment of the original ground state to form the new ground state of the instantaneous Hamiltonian H(t), by incorporating excited states of the unperturbed Hamiltonian H₀ without transitions; a_k(t) follows the adiabatic theorem of Born and Fock. The nonadiabatic term b_k(t) describes excitation into another quantum state k; b_k(t) is obtained as an integral containing the time derivative of the perturbation. The true transition probability is given by b_k(t) ², as first stated by Landau and Lifshitz. In this work, we contrast b_k(t) ² and c_k(t) ². The latter is the norm-square of the entire excited-state coefficient which is used for the transition probability within Fermi's golden rule. Calculations are performed for a perturbing pulse consisting of a cosine or sine wave in a Gaussian envelope. When the transition frequency ω_k0 is on resonance with the frequency ω of the cosine wave, b_k(t) ² and c_k(t) ² rise almost monotonically to the same final value; the two are intertwined, but they are out of phase with each other. Off resonance (when ω_k0 ≠ ω), b_k(t) ² and c_k(t) ² differ significantly during the pulse. They oscillate out of phase and reach different maxima but then fall off to equal final values after the pulse has ended, when a_k(t) ≡ 0. If ω_k0 < ω, b_k(t) ² generally exceeds c_k(t) ², while the opposite is true when ω_k0 > ω. While the transition probability is rising, the midpoints between successive maxima and minima fit Gaussian functions of the form a exp[-b(t - d)²]. To our knowledge, this is the first analysis of nonadiabatic transition probabilities during a perturbing pulse.

Charge transfer dynamics at the boron subphthalocyanine chloride/C60 interface: non-adiabatic dynamics study with Libra-X

The Libra-X software for non-adiabatic molecular dynamics is reported. It is used to comprehensively study the charge transfer dynamics at the boron subphtalocyanine chloride (SubPc)/fullerene (C₆₀) interface.

An ab initio multiple cloning approach for the simulation of photoinduced dynamics in conjugated molecules

Multidimensional wave function: a superposition of Gaussian coherent states guided by Ehrenfest trajectories suited to clone and swap their electronic amplitudes.

Energy transfer and spatial scrambling of an exciton in a conjugated dendrimer

Photoexcitation of multichromophoric light harvesting molecules induces a number of intramolecular electronic energy relaxation and redistribution pathways that can ultimately lead to ultrafast exciton self-trapping on a single chromophore unit.

The correspondence between the conformational and chromophoric properties of amorphous conjugated polymers in mesoscale condensed systems

For π-conjugated polymers, the notion of spectroscopic units or "chromophores" provides illuminating insights into the experimentally observed absorption/emission spectra and the mechanisms of energy/charge transfer. To date, however, no statistical analysis has revealed a direct correspondence between chromophoric and conformational properties-with the latter being fundamental to polymer semiconductors. Herein, we propose a "persistence length" calculation to re-evaluate chain conformation over a full conjugation length. The mesoscale condensed systems of MEH-PPV and MEH-PPV/C₆₀ hybrid (system size ∼10 × 10 × 10 nm³) are utilized as two prototypical model systems, along with a full range of segmental lengths (2-20-mer) and five lowest singlet excited states to hint at the generality of the features presented. We demonstrate, for the first time, that two properly re-defined conformational factors that characterize chain folding and planarity, respectively, capture excellently the population distribution of chromophores in both systems investigated. In contrast, the conventional strategy of utilizing two adjacent monomer units to characterize (local) chain conformation results in only an inconspicuous correlation between the two, as previously reported. It is further shown that chain folding-and not chain planarity-is more relevant in capturing the associated oscillator strength for the first excited state, where the transient dipole moments are known to align with the chain conformation, although the corresponding excitation energy and exciton size seem relatively unaffected. The observed effects of C₆₀ on the MEH-PPV adsorption spectra also agree with recent experimental trends. Overall, the present findings are expected to aid future multiscale computer simulations and spectroscopy-data interpretations for polymer semiconductors and their hybrid systems.

Relation between Vibrational Dephasing Time and Energy Gap Fluctuations

Dephasing processes are present in basically all applications in which quantum mechanics plays a role. These applications certainly include excitation energy and charge transfer in biological systems. In a previous study, we have analyzed the vibrational dephasing time as a function of energy gap fluctuation for a large set of molecular simulations. In that investigation, individual molecular subunits were the focus of the calculations. The set of studied molecules included bacteriochlorophylls in Fenna-Matthews-Olson and light-harvesting system 2 complexes as well as bilins in PE545 aggregates. The present work extends this study to entire complexes, including the respective intermolecular couplings. Again, it can be concluded that a universal and inverse proportionality exists between dephasing time and variance of the excitonic energy gap fluctuations, whereas the respective proportionality constants can be rationalized using the energy gap autocorrelation functions. Furthermore, these findings can be extended to the gaps between higher-lying neighboring excitonic states.

Electronic Delocalization, Vibrational Dynamics, and Energy Transfer in Organic Chromophores

The efficiency of materials developed for solar energy and technological applications depends on the interplay between molecular architecture and light-induced electronic energy redistribution. The spatial localization of electronic excitations is very sensitive to molecular distortions. Vibrational nuclear motions can couple to electronic dynamics driving changes in localization. The electronic energy transfer among multiple chromophores arises from several distinct mechanisms that can give rise to experimentally measured signals. Atomistic simulations of coupled electron-vibrational dynamics can help uncover the nuclear motions directing energy flow. Through careful analysis of excited state wave function evolution and a useful fragmenting of multichromophore systems, through-bond transport and exciton hopping (through-space) mechanisms can be distinguished. Such insights are crucial in the interpretation of fluorescence anisotropy measurements and can aid materials design. This Perspective highlights the interconnected vibrational and electronic motions at the foundation of nonadiabatic dynamics where nuclear motions, including torsional rotations and bond vibrations, drive electronic transitions.

Charge Transport in Molecular Materials: An Assessment of Computational Methods

The booming field of molecular electronics has fostered a surge of computational research on electronic properties of organic molecular solids. In particular, with respect to a microscopic understanding of transport and loss mechanisms, theoretical studies assume an ever-increasing role. Owing to the tremendous diversity of organic molecular materials, a great number of computational methods have been put forward to suit every possible charge transport regime, material, and need for accuracy. With this review article we aim at providing a compendium of the available methods, their theoretical foundations, and their ranges of validity. We illustrate these through applications found in the literature. The focus is on methods available for organic molecular crystals, but mention is made wherever techniques are suitable for use in other related materials such as disordered or polymeric systems.

Ultrafast Non-Förster Intramolecular Donor-Acceptor Excitation Energy Transfer

Ultrafast intramolecular electronic energy transfer in a conjugated donor-acceptor system is simulated using nonadiabatic excited-state molecular dynamics. After initial site-selective photoexcitation of the donor, transition density localization is monitored throughout the S₂ → S₁ internal conversion process, revealing an efficient unidirectional donor → acceptor energy-transfer process. Detailed analysis of the excited-state trajectories uncovers several salient features of the energy-transfer dynamics. While a weak temperature dependence is observed during the entire electronic energy relaxation, an ultrafast initially temperature-independent process allows the molecular system to approach the S₂-S₁ potential energy crossing seam within the first ten femtoseconds. Efficient energy transfer occurs in the absence of spectral overlap between the donor and acceptor units and is assisted by a transient delocalization phenomenon of the excited-state wave function acquiring Frenkel-exciton character at the moment of quantum transition.

The role of tachysterol in vitamin D photosynthesis – a non-adiabatic molecular dynamics study

To investigate the role of tachysterol in the regulation of vitamin D photosynthesis, we studied its absorption properties and photodynamics by ab initio methods and non-adiabatic molecular dynamics.

Phonon bottleneck and long-lived excited states in π-conjugated pyrene hoop

The phonon bottleneck in the nonradiative relaxation of a pyrene-based nanohoop slows down electronic relaxation and allows multi-channel relaxation.

Photoinduced dynamics in cycloparaphenylenes: planarization, electron–phonon coupling, localization and intra-ring migration of the electronic excitation

Cycloparaphenylenes represent the smallest possible fragments of armchair carbon nanotubes.

Interference of Interchromophoric Energy-Transfer Pathways in π-Conjugated Macrocycles

The interchromophoric energy-transfer pathways between weakly coupled units in a π-conjugated phenylene-ethynylene macrocycle and its half-ring analogue have been investigated using the nonadiabatic excited-state molecular dynamics approach. To track the flow of electronic transition density between macrocycle units, we formulate a transition density flux analysis adapted from the statistical minimum flow method previously developed to investigate vibrational energy flow. Following photoexcitation, transition density is primarily delocalized on two chromophore units and the system undergoes ultrafast energy transfer, creating a localized excited state on a single unit. In the macrocycle, distinct chromophore units donate transition density to a single acceptor unit but do not interchange transition density among each other. We find that energy transfer in the macrocycle is slower than in the corresponding half ring because of the presence of multiple interfering energy-transfer pathways. Simulation results are validated by modeling the fluorescence anisotropy decay.

An Efficient, Augmented Surface Hopping Algorithm That Includes Decoherence for Use in Large-Scale Simulations

We propose and implement a highly efficient augmented surface hopping algorithm that (i) can be used for large simulations (with many nuclei and many electronic states) and (ii) includes the effects of decoherence without parametrization. Our protocol is based on three key modifications of the surface hopping methodology: (a) a novel separation of classical and quantum degrees of freedom that treats avoided and trivial crossings efficiently, (b) a multidimensional approximation of the time derivative matrix that avoids explicit construction of the derivative coupling at most time steps, and (c) an efficient approximation for the augmented fewest-switches surface hopping decoherence rate. We will show that this protocol can be several orders of magnitude more efficient than the traditional protocol for large multidimensional problems. Furthermore, the marginal cost for including decoherence effects is now negligible.

Carbon nanorings with inserted acenes: breaking symmetry in excited state dynamics

Conjugated cycloparaphenylene rings have unique electronic properties being the smallest segments of carbon nanotubes. Their conjugated backbones support delocalized electronic excitations, which dynamics is strongly influenced by cyclic geometry. Here we present a comparative theoretical study of the electronic and vibrational energy relaxation and redistribution in photoexcited cycloparaphenylene carbon nanorings with inserted naphthalene, anthracene, and tetracene units using non-adiabatic excited-state molecular dynamics simulations. Calculated excited state structures reflect modifications of optical selection rules and appearance of low-energy electronic states localized on the acenes due to gradual departure from a perfect circular symmetry. After photoexcitation, an ultrafast electronic energy relaxation to the lowest excited state is observed on the time scale of hundreds of femtoseconds in all molecules studied. Concomitantly, the efficiency of the exciton trapping in the acene raises when moving from naphthalene to anthracene and to tetracene, being negligible in naphthalene, and ~60% and 70% in anthracene and tetracene within the first 500 fs after photoexcitation. Observed photoinduced dynamics is further analyzed in details using induced molecular distortions, delocatization properties of participating electronic states and non-adiabatic coupling strengths. Our results provide a number of insights into design of cyclic molecular systems for electronic and light-harvesting applications.

Excitons in poly(para phenylene vinylene): a quantum-chemical perspective based on high-level ab initio calculations

Exciton analyses of high-level quantum-chemical computations for poly(paraphenylene vinylene) reveal the nature of the excitonic bands in PPV oligomers.

Ultrafast electronic energy relaxation in a conjugated dendrimer leading to inter-branch energy redistribution

Dendrimers are arrays of coupled chromophores, where the energy of each unit depends on its structure and conformation.

Non-adiabatic excited state molecular dynamics of phenylene ethynylene dendrimer using a multiconfigurational Ehrenfest approach

Photoinduced dynamics of electronic and vibrational unidirectional energy transfer between meta-linked building blocks in a phenylene ethynylene dendrimer is simulated using a multiconfigurational Ehrenfest in time-dependent diabatic basis (MCE-TDDB) method.

Non-radiative relaxation of photoexcited chlorophylls: theoretical and experimental study

Nonradiative relaxation of high-energy excited states to the lowest excited state in chlorophylls marks the first step in the process of photosynthesis. We perform ultrafast transient absorption spectroscopy measurements, that reveal this internal conversion dynamics to be slightly slower in chlorophyll B than in chlorophyll A. Modeling this process with non-adiabatic excited state molecular dynamics simulations uncovers a critical role played by the different side groups in the two molecules in governing the intramolecular redistribution of excited state wavefunction, leading, in turn, to different time-scales. Even given smaller electron-vibrational couplings compared to common organic conjugated chromophores, these molecules are able to efficiently dissipate about 1 eV of electronic energy into heat on the timescale of around 200 fs. This is achieved via selective participation of specific atomic groups and complex global migration of the wavefunction from the outer to inner ring, which may have important implications for biological light-harvesting function.

Optimal Energy Transfer in Light-Harvesting Systems

Photosynthesis is one of the most essential biological processes in which specialized pigment-protein complexes absorb solar photons, and with a remarkably high efficiency, guide the photo-induced excitation energy toward the reaction center to subsequently trigger its conversion to chemical energy. In this work, we review the principles of optimal energy transfer in various natural and artificial light harvesting systems. We begin by presenting the guiding principles for optimizing the energy transfer efficiency in systems connected to dissipative environments, with particular attention paid to the potential role of quantum coherence in light harvesting systems. We will comment briefly on photo-protective mechanisms in natural systems that ensure optimal functionality under varying ambient conditions. For completeness, we will also present an overview of the charge separation and electron transfer pathways in reaction centers. Finally, recent theoretical and experimental progress on excitation energy transfer, charge separation, and charge transport in artificial light harvesting systems is delineated, with organic solar cells taken as prime examples.

Can Disorder Enhance Incoherent Exciton Diffusion?

Recent experiments aimed at probing the dynamics of excitons have revealed that semiconducting films composed of disordered molecular subunits, unlike expectations for their perfectly ordered counterparts, can exhibit a time-dependent diffusivity in which the effective early time diffusion constant is larger than that of the steady state. This observation has led to speculation about what role, if any, microscopic disorder may play in enhancing exciton transport properties. In this article, we present the results of a model study aimed at addressing this point. Specifically, we introduce a general model, based upon Förster theory, for incoherent exciton diffusion in a material composed of independent molecular subunits with static energetic disorder. Energetic disorder leads to heterogeneity in molecule-to-molecule transition rates, which we demonstrate has two important consequences related to exciton transport. First, the distribution of local site-specific hopping rates is broadened in a manner that results in a decrease in average exciton diffusivity relative to that in a perfectly ordered film. Second, since excitons prefer to make transitions that are downhill in energy, the steady state distribution of exciton energies is biased toward low-energy molecular subunits, those that exhibit reduced diffusivity relative to a perfectly ordered film. These effects combine to reduce the net diffusivity in a manner that is time dependent and grows more pronounced as disorder is increased. Notably, however, we demonstrate that the presence of energetic disorder can give rise to a population of molecular subunits with exciton transfer rates exceeding those of subunits in an energetically uniform material. Such enhancements may play an important role in processes that are sensitive to molecular-scale fluctuations in exciton density field.

Steady-state and femtosecond transient absorption spectroscopy of new two-photon absorbing fluorene-containing quinolizinium cation membrane probes

The synthesis, linear photophysical characterization, and nonlinear optical properties of two new symmetrical fluorene-containing quinolizinium derivatives, 2,8-bis((E)-2-(7-(diphenylamino)-9,9-dihexyl-9H-fluoren-2-yl)vinyl)quinolizinium hexafluorophosphate (1) and 2,8-bis((E)-2-(7-((7-(diphenylamino)-9,9-dihexyl-9H-fluoren-2-yl)ethynyl)-9,9-dihexyl-9H-fluoren-2yl)vinyl)quinolizinium hexafluorophosphate (2), are reported. The nature of the dual-band steady-state fluorescence emission of 1 and 2 was determined, and violation of Kasha's rule along with a strong dependence on solvent polarity were shown. A relatively complex structure of two-photon absorption (2PA) spectra of 1 and 2, with maximum cross sections of ∼400-600 GM, was determined using the open aperture Z-scan method. Different types of fast relaxation processes with characteristic times of 0.3-0.5 ps and 1.5-2 ps were observed in the excited states of the new compounds via femtosecond transient absorption pump-probe spectroscopy. To better understand the photophysical behavior of 1 and 2, a quantum-mechanical study was undertaken using TD-DFT and ZINDO/S methods. Simulated linear absorption spectra were found to be in good agreement with experimental data, while 2PA cross sections were overestimated. Although the new dyes were highly fluorescent in nonpolar solvents, they were essentially nonfluorescent in polar media. Significantly, the quinolizinium dyes exhibited fluorescence turn-on behavior upon binding to bovine serum album (BSA) protein, exhibiting over 4-fold fluorescence enhancement, which was a finding that was leveraged to demonstrate cell membrane fluorescence imaging of HeLa cells.