Nonadiabatic Coupling Effects Research Articles

Extended theoretical modeling of reverse intersystem crossing for thermally activated delayed fluorescence materials.

Thermally activated delayed fluorescence (TADF) materials and multi-resonant (MR) variants are promising organic emitters that can achieve an internal electroluminescence quantum efficiency of ~100%. The reverse intersystem crossing (RISC) is key for harnessing triplet energies for fluorescence. Theoretical modeling is thus crucial to estimate its rate constant (kRISC) for material development. Here, we present a comprehensive assessment of the theory for simulating the RISC of MR-TADF molecules within a perturbative excited-state dynamics framework. Our extended rate formula reveals the importance of the concerted effects of nonadiabatic spin-vibronic coupling and vibrationally induced spin-orbital couplings in reliably determining kRISC of MR-TADF molecules. The excited singlet-triplet energy gap is another factor influencing kRISC. We present a scheme for gap estimation using experimental Arrhenius plots of kRISC. Erroneous behavior caused by approximations in Marcus theory is elucidated by testing 121 MR-TADF molecules. Our extended modeling offers in-depth descriptions of kRISC.

Coherent-Phonon-Driven Intervalley Scattering and Rabi Oscillation in Multivalley 2D Materials.

Resolving the complete electron scattering dynamics mediated by coherent phonons is crucial for understanding electron-phonon couplings beyond equilibrium. Here we present a time-resolved theoretical investigation on strongly coupled ultrafast electron and phonon dynamics in monolayer WSe_{2}, with a focus on the intervalley scattering from the optically "bright" K state to "dark" Q state. We find that the strong coherent lattice vibration along the longitudinal acoustic phonon mode [LA(M)] can drastically promote K-to-Q transition on a timescale of ∼400 fs, comparable with previous experimental observation on thermal-phonon-mediated electron dynamics. Further, this coherent-phonon-driven intervalley scattering occurs in an unconventional steplike manner and further induces an electronic Rabi oscillation. By constructing a two-level model and quantitatively comparing with abinitio dynamic simulations, we uncover the critical role of nonadiabatic coupling effects. Finally, a new strategy is proposed to effectively tune the intervalley scattering rates by varying the coherent phonon amplitude, which could be realized via light-induced nonlinear phononics that we hope will spark experimental investigation.

Isomerism effects in relaxation dynamics of Au24(SR)16 thiolate-protected gold nanoclusters

Understanding the excited state behavior of isomeric structures of thiolate-protected gold nanoclusters is still a challenging task. In this paper, based on grand unified model and ring model for describing thiolate-protected gold nanoclusters, we have predicted four isomers of Au24(SR)16 nanoclusters. Density functional theory calculations show that the total energy of one of the predicted isomers is 0.1 eV lower in energy than previously crystallized isomer. The nonradiative relaxation dynamics simulations of Au24(SH)16 isomers are performed to reveal the effects of structural isomerism on relaxation process of the lowest energy states, in which that most of the low-excited states consist of core states. In addition, crystallized isomer possesses the shorter e–h recombination time, whereas the most stable isomer has the longer recombination time, which may be attributed to the synergistic effect of nonadiabatic coupling and decoherence time. Our results could provide practical guidance to predict new gold nanoclusters for future experimental synthesis, and stimulate the exploration of atomic structures of same sized gold nanoclusters for photovoltaic and optoelectronic devices.

Analysis of molecular photomechanical performance using a one-dimensional harmonic model

The photochemical reaction of a molecule leads to a change in the position of its nuclei that can be harnessed to perform mechanical work. Photomechanical materials use this effect to act as light-powered actuators. In this paper, a one-dimensional model based on coupled harmonic potential energy surfaces is developed to describe the photomechanical response of a molecule. This model generates predictions that are qualitatively consistent with standard mechanochemistry models for ground state rate reactions. To analyze the photomechanical process, excited state dynamics like photon absorption and relaxation are included. The model allows us to derive analytical expressions for the work output, blocking force, and absorbed photon-to-work efficiency. The effects of nonadiabatic electronic coupling, unequal frequency potentials, and the cycling efficiency are also analyzed. If the starting state is the stable (lower energy) isomer, it is possible to attain photon-to-work efficiencies up to 55.4%. If initial state is higher in energy, for example a metastable isomer, then one-way efficiencies > 100% are possible due to the release of stored potential energy. Photomechanical materials can be competitive with photovoltaic–piezoelectric combinations in terms of efficiency, but current materials will require substantial improvement before they can approach the theoretical limits.Graphical abstract

Nonadiabatic vibronic effects in single-molecule junctions: A theoretical study using the hierarchical equations of motion approach

The interaction between electronic and vibrational degrees of freedom is an important mechanism in nonequilibrium charge transport through molecular nanojunctions. While adiabatic polaron-type coupling has been studied in great detail, new transport phenomena arise for nonadiabatic coupling scenarios corresponding to a breakdown of the Born-Oppenheimer approximation. Employing the numerically exact hierarchical equations of motion approach, we analyze the effect of nonadiabatic electronic-vibrational coupling on electron transport in molecular junctions considering a series of models with increasing complexity. The results reveal a significant influence of nonadiabatic coupling on the transport characteristics and a variety of interesting effects, including negative differential conductance. The underlying mechanisms are analyzed in detail.

UV absorption spectrum and photodissociation dynamics of CH2OO following excitation to the B 1 A′ state

The spectroscopy and dynamics of the smallest Criegee intermediate CHOO following UV excitation to the B state is studied theoretically, based on multireference electronic wave functions and a quantum dynamical approach for the nuclear motion. Two interacting electronic states and two nuclear degrees of freedom are considered in the dynamical treatment. The UV absorption spectrum is found to agree very well with available experimental recordings when accounting for broadening effects due to vibrational and rotational congestion and lifetime effects. Upon higher resolution two different energetic regimes can be approximately distinguished, a higher-energy regime where the spectral envelope is broad and structureless, and dissociation is prompt, and a lower-energy regime featuring narrow resonances which are supported by the shallow well occurring at intermediate O–O distances, and decay by tunnelling to the repulsive outer part of the potential energy surface. The importance of nonadiabatic coupling effects is pointed out and future steps for an improved theoretical treatment are outlined.

QM/MM Nonadiabatic Dynamics: the SHARC/COBRAMM Approach.

We present the SHARC/COBRAMM approach to enable easy and efficient excited-state dynamics simulations at different levels of electronic structure theory in the presence of complex environments using a quantum mechanics/molecular mechanics (QM/MM) setup. SHARC is a trajectory surface-hoping method that can incorporate the simultaneous effects of nonadiabatic and spin-orbit couplings in the excited-state dynamics of molecular systems. COBRAMM allows ground- and excited-state QM/MM calculations using a subtractive scheme, with electrostatic embedding and a hydrogen link-atom approach. The combination of both free and open-source program packages provides a modular and extensive framework to model nonadiabatic processes after light irradiation from the atomistic scale to the nano-scale. As an example, the relaxation of acrolein from S1 to T1 in solution is provided.

Propagative block diagonalization diabatization of DFT/MRCI electronic states.

We present a framework for the calculation of diabatic states using the combined density functional theory and multireference configuration interaction (DFT/MRCI) method. Due to restrictions present in the current formulation of the DFT/MRCI method (a lack of analytical derivative couplings and the inability to use non-canonical Kohn-Sham orbitals), most common diabatization strategies are not applicable. We demonstrate, however, that diabatic wavefunctions and potentials can be reliably calculated at the DFT/MRCI level of theory using a propagative variant of the block diagonalization diabatization method (P-BDD). The proposed procedure is validated via the calculation of diabatic potentials for LiH and the simulation of the vibronic spectrum of pyrazine. In both cases, the combination of the DFT/MRCI and P-BDD methods is found to correctly recover the non-adiabatic coupling effects of the problem.

Non-adiabatic effects in the H3+ spectrum.

The effect of non-adiabatic coupling on the computed rovibrational energy levels amounts to about 2 cm-1 for H3+ and must be included in high-accuracy calculations. Different strategies to obtain the corresponding energy shifts are reviewed in the article. A promising way is to introduce effective vibrational reduced masses that depend on the nuclear configuration. A new empirical method that uses the stockholder atoms-in-molecules approach to this effect is presented and applied to H3+. Furthermore, a highly accurate potential energy surface for the D3+ isotopologue, which includes relativistic and leading quantum electrodynamic terms, is constructed and used to analyse the observed rovibrational frequencies for this molecule. Accurate band origins are obtained that improve existing data. This article is part of a discussion meeting issue 'Advances in hydrogen molecular ions: H3+, H5+ and beyond'.

Modeling Electron Injection at Semiconductor–Molecule Interfaces using First-Principles Dynamics Simulation: Effects of Nonadiabatic Coupling, Self-energy, and Surface Models

Excited electron transfer across semiconductor–molecule heterogeneous interfaces is central to various future electronic and optoelectronic devices. At the same time, first-principles modeling of s...

Electronically nonadiabatic wave packet propagation using frozen Gaussian scattering.

We present an approach, which allows to employ the adiabatic wave packet propagation technique and semiclassical theory to treat the nonadiabatic processes by using trajectory hopping. The approach developed generates a bunch of hopping trajectories and gives all additional information to incorporate the effect of nonadiabatic coupling into the wave packet dynamics. This provides an interface between a general adiabatic frozen Gaussian wave packet propagation method and the trajectory surface hopping technique. The basic idea suggested in [A. D. Kondorskiy and H. Nakamura, J. Chem. Phys. 120, 8937 (2004)] is revisited and complemented in the present work by the elaboration of efficient numerical algorithms. We combine our approach with the adiabatic Herman-Kluk frozen Gaussian approximation. The efficiency and accuracy of the resulting method is demonstrated by applying it to popular benchmark model systems including three Tully's models and 24D model of pyrazine. It is shown that photoabsorption spectrum is successfully reproduced by using a few hundreds of trajectories. We employ the compact finite difference Hessian update scheme to consider feasibility of the ab initio "on-the-fly" simulations. It is found that this technique allows us to obtain the reliable final results using several Hessian matrix calculations per trajectory.

Long-range states in excited ultracold 3He*–4He* dimers

Long-range bound states of the excited heteronuclear –He* system that dissociate to either (1s2s S1) + (1s2p Pj) or (1s2p Pj) + (1s2s S1), where , are investigated using both single-channel and multichannel calculations in order to analyse the effects of Coriolis and non-adiabatic couplings. The multichannel calculations predict two groups of resonances above the lowest asymptotic energy. One of these groups dissociates to an atomic pair with the 2p excitation on the fermionic atom and the other dissociates to two asymptotes which correspond to the 2p excitation on either atom. Many of these resonances could be identified with levels in the single-channel calculation although the differences in energies were large. The total parity was found to have a significant influence on the ability to make these identifications. No purely bound states were found, although several resonances with line widths smaller than 1 MHz were obtained.

Ultrashort-laser-pulse-mediated asymmetry in the branching of dissociated fragments of HD+: Effects of a weak third pulse and carrier envelope phase of the dissociating pulse

We have numerically explored the possibility of controlling the branching ratio of the two distinguishable photodissociation products of HD${}^{+}$ (neutral D and neutral H) in an ultrashort laser field. In our multipulse scheme, a bound vibrational wave packet is generated in the ground electronic state of HD${}^{+}$ by vertical ionization from the ground state of HD. The control pulse acts on this wave packet at different time delays after the wave-packet generation is completed. It was found that, for a broad range of delay times between the pump pulse and the control pulse, any possible asymmetry in the branching ratio disappears due to the nonadiabatic coupling effects present in HD${}^{+}$. A third pulse, termed the driving pulse, with a relatively longer duration and a much weaker field strength, is introduced to counterbalance the nonadiabatic effects relevant for this heteronuclear system and to guide the dissociative reaction to a specific product channel. In fact, we have shown that the application of the driving pulse reproduces the branching-ratio pattern obtained on variation in the interpulse delay time between the pump pulse and the control pulse in the absence of the nonadiabatic coupling effects. The role of both the delay time between the pump pulse and the control pulse as well as the carrier envelope phase effects of the optical field of the control laser on the branching ratios in the two reaction channels were studied. The robustness of the driving pulse mediated asymmetry control, and any possible introduction of asymmetry by the driving pulse itself were also investigated.

Mg+(2S) and Mg+(2P) in reaction with H2([formula omitted]): A description of the energy surfaces explaining the mechanisms

The lowest two potential energy surfaces which involve Mg+(2P) and Mg+(2S) atoms interacting with H2 molecules are computed to describe both the intermediate complex [MgH2+] formed during their reactive approaches and the asymptotic outcomes of MgH+ + H or of Mg+ + H2. The calculations clearly reveal the presence of an avoided crossing between the two surfaces near the T-geometry of the complexes and the existence on the upper surface of regions where the ionic atomic states of magnesium are “coordinated” with either H2(1Σg+) or H2(3Σu+) states. The implications of these structural results with respect to the existing experiments in cold ion traps are discussed and shown to provide already a qualitative explanation for the final formation of MgH+/MgD+ ions in the trap. In fact, a simplified treatment of the nonadiabatic coupling effects in the region of closest approach between the two Born–Oppenheimer surfaces is given via Landau–Zener curve crossing models and are found to already yield a realistic picture of the behavior seen by the experiments.

Photodissociation and Radiative Association of HeH+ in the Metastable Triplet State

We investigate the photodissociation of HeH(+) in the metastable triplet state as well as its formation through the inverse process, radiative association. In models of astrophysical plasmas, HeH(+) is assumed to be present only in the ground state, and the influence of the triplet state has not been explored. It may be formed by radiative association during collisions between a proton and metastable helium, which are present in significant concentrations in nebulae. The triplet state can also be formed by association of He(+) and H, although this process is less likely to occur. We compute the cross sections and rate coefficients corresponding to the photodissociation of the triplet state by UV photons from a central star using a wave packet method. We show that the photodissociation cross sections depend strongly on the initial vibrational state and that the effects of excited electronic states and nonadiabatic couplings cannot be neglected. We then calculate the cross section and rate coefficient for the radiative association of HeH(+) in the metastable triplet state.

Quantum dynamical study of low-energy photoelectron bands of 2-phenylethyl-N,N-dimethylamine#

The first three photoelectron bands of 2-phenylethyl-N,N-dimethylamine (PENNA) are investigated theoretically, paying particular attention to the vibrational structure and to possible nonadiabatic coupling effects. A substantial vibronic interaction is established between the first and second excited cationic states (corresponding to the second and third photoelectron bands). Their coupling to the cationic ground state is found to be rather weak. This is tentatively attributed to the well-known fact that the latter carries a hole at the amine site, while the former two have the electron removed from benzene-type orbitals. The interaction between the two excited cationic states is characterized by a ‘hidden’ or local symmetry at the phenyl moiety. Preliminary dynamic calculations with two interacting electronic states and four vibrational modes are reported. The computed spectra are compared to experimental results of Weinkauf et al.

A full-dimensional coupled-surface study of the photodissociation dynamics of ammonia using the multiconfiguration time-dependent Hartree method

Full-dimensional quantum mechanical computations are carried out to investigate the photodissociation dynamics of à state NH(3) and ND(3) using the multiconfiguration time-dependent Hartree (MCTDH) method with recently developed coupled ab initio potential energy surfaces (PESs) [Z. H. Li, R. Valero, and D. G. Truhlar, Theor. Chim. Acc. 118, 9 (2007)]. To use the MCTDH method efficiently the PESs are represented as based on the high-dimensional model representation. The à ← X̃ absorption spectra for both isotopomers were calculated for the zeroth vibrational state of the ground electronic state. With a view to treating larger systems, Jacobi coordinates are used. Computations on the coupled PES are carried out for two-, three-, five-, and six-dimensional model systems to understand the validity of reduced-dimensional calculations. In addition to the fully coupled calculations, the effect of nonadiabatic coupling on absorption spectra is shown by propagating the initial wavepacket only in the à electronic state. The calculated absorption spectra are shown to be in good agreement with available theoretical and experimental observations. Comparisons with calculations using Radau and valence coordinates show the effect of including the symmetry of the system explicitly. Finally, branching ratios for loss of a hydrogen atom via the two available channels are calculated. These predict that the nonadiabatic product increases with the dimension of the calculations and confirm the importance of the full-dimensional calculations.

Photoassociation spectroscopy of ultracold metastable 3He dimers

The bound states of the fermionic (3)He(2 (3)S(1)) + (3)He(2 (3)P(j)) system, where j = 0, 1, 2, are investigated using the recently available ab initio short-range (1,3,5)Σ(+)(g,u) and (1,3,5)Π(g,u) potentials computed by Deguilhem et al. (J. Phys. B: At., Mol. Opt. Phys., 2009, 42, 015102). Single-channel and multichannel calculations have been undertaken in order to investigate the effects of Coriolis and non-adiabatic couplings. The possible experimental observability of the theoretical levels is assessed using criteria based upon the short-range character of each level and their coupling to metastable ground states. Purely long-range levels have been identified and 30 short-range levels near five asymptotes are suggested for experimental investigation.

Effects of non-adiabatic and Coriolis couplings on the bound states of He(2 3S)+He(2 3P)

The effects of non-adiabatic and Coriolis couplings on the bound states of the He(2 3S1) + He(2 3Pj) system, where j = 0, 1, 2, are investigated using the recently available ab initio short-range 1, 3, 5Σ+g, u and 1, 3, 5Πg, u potentials computed by Deguilhem et al (2009 J. Phys. B: At. Mol. Opt. Phys. 42 015102). Three sets of calculations have been undertaken: single-channel, multichannel without Coriolis couplings and full multichannel with Coriolis couplings. We find that non-adiabatic effects are negligible for 0−u, 0±g, 1u, 2g, 2u, 3g Hund case (c) sets of levels in the j = 2 asymptote but can be up to 15% for some of the 0+u and 1g sets of levels where near degeneracies are present in the single-channel diagonalized potentials. Coriolis couplings are most significant for weakly bound levels, ranging from 1% to 5% for total angular momenta J = 1, 2 and up to 10% for J = 3. Levels near the j = 1 and j = 0 asymptotes agree closely with previous multichannel calculations based upon long-range potentials constructed from retarded resonance dipole and dispersion interactions. Assignment of theoretical levels to experimental observations using criteria based upon the short-range character of each level and their coupling to metastable ground states produces well-matched assignments for the majority of observations. After a 1% increase in the slope of the 5Σ+g, u and 5Πg, u input potentials near the classical turning point is applied, improved matching of previous assignments is obtained and further assignments can be made, reproducing very closely the number of experimental observations.

Quantum nonadiabatic dynamics of hydrogen exchange reactions

In continuation of our earlier effort to understand the nonadiabatic coupling effects in the prototypical H + H 2 exchange reaction [Jayachander Rao et al. Chem. Phys. 333 (2007) 135], we present here further quantum dynamical investigations on its isotopic variants. The present work also corrects a technical scaling error occurred in our previous studies on the H + HD reaction. Initial state-selected total reaction cross sections and Boltzmann averaged thermal rate constants are calculated with the aid of a time-dependent wave packet approach employing the double many body expansion potential energy surfaces of the system. The theoretical results are compared with the experimental and other theoretical data whenever available. The results re-establish our earlier conclusion, on a more general perspective, that the electronic nonadiabatic effects are negligible on the important quantum dynamical observables of these reactive systems reported here.