Studies of nonadiabatic dynamics in the singlet fission processes of pentacene dimer via tensor network method.

Singlet fission (SF) is a very significant photophysical phenomenon and possesses potential applications. In this work, we try to give a rather detailed theoretical investigation of the SF process in the stacked polyacene dimer by combining the high-level quantum chemistry calculations and the quantum dynamics simulations based on the tensor network method. Starting with the construction of the linear vibronic coupling model, we explore the pure electronic dynamics and the vibronic dynamics in the SF processes. The role of vibrational modes in nonadiabatic dynamics is addressed. The results show that the super-exchange mechanism mediated by the charge-transfer state is found in both pure electronic dynamics and the nonadiabatic dynamics. Particularly the vibrational modes with the frequencies resonance with the adiabatic energy gap play very import roles in the SF dynamics. This work not only provides a deep and detailed understanding of the SF process but also verifies the efficiency of the tensor network method with the train structure that can serve as the reference dynamics method to explore the dynamics behaviors of complex systems.

Nuclear gradient expressions for molecular cavity quantum electrodynamics simulations using mixed quantum-classical methods.

We derive a rigorous nuclear gradient for a molecule-cavity hybrid system using the quantum electrodynamics Hamiltonian. We treat the electronic-photonic degrees of freedom (DOFs) as the quantum subsystem and the nuclei as the classical subsystem. Using the adiabatic basis for the electronic DOF and the Fock basis for the photonic DOF and requiring the total energy conservation of this mixed quantum-classical (MQC) system, we derived the rigorous nuclear gradient for the molecule-cavity hybrid system, which is naturally connected to the approximate gradient under the Jaynes-Cummings approximation. The nuclear gradient expression can be readily used in any MQC simulations and will allow one to perform the non-adiabatic on-the-fly simulation of polariton quantum dynamics. The theoretical developments in this work could significantly benefit the polariton quantum dynamics community with a rigorous nuclear gradient of the molecule-cavity hybrid system and have a broad impact on the future non-adiabatic simulations of polariton quantum dynamics.

Quasi-diabatic propagation scheme for simulating polariton chemistry.

We generalize the quasi-diabatic (QD) propagation scheme to simulate the non-adiabatic polariton dynamics in molecule-cavity hybrid systems. The adiabatic-Fock states, which are the tensor product states of the adiabatic electronic states of the molecule and photon Fock states, are used as the locally well-defined diabatic states for the dynamics propagation. These locally well-defined diabatic states allow using any diabatic quantum dynamics methods for dynamics propagation, and the definition of these states will be updated at every nuclear time step. We use several recently developed non-adiabatic mapping approaches as the diabatic dynamics methods to simulate polariton quantum dynamics in a Shin-Metiu model coupled to an optical cavity. The results obtained from the mapping approaches provide very accurate population dynamics compared to the numerically exact method and outperform the widely used mixed quantum-classical approaches, such as the Ehrenfest dynamics and the fewest switches surface hopping approach. We envision that the generalized QD scheme developed in this work will provide a powerful tool to perform the non-adiabatic polariton simulations by allowing a direct interface between the diabatic dynamics methods and ab initio polariton information.

Investigation of nonadiabatic dynamics in the photolysis of methyl nitrate (CH3ONO2) by on-the-fly surface hopping simulation.

The photolysis mechanism of methyl nitrate (CH3ONO2) was studied using the on-the-fly surface hopping dynamics at the XMS-CASPT2 level. Several critical geometries, including electronic state minima and conical intersections, were obtained, which play essential roles in the nonadiabatic dynamics of CH3ONO2. The ultrafast nonadiabatic decay dynamics to the ground state were simulated, which gives a proper explanation on the broad and structureless absorption spectra of CH3ONO2. The photodissociation channels, including CH3O + NO2, CH3O + NO + O, and others, as well as their branching ratios, were identified. When the dynamics starts from the lowest two electronic states (S1 and S2), the CH3O + NO2 channel is the dominant photolysis pathway, although we observed the minor contributions of other channels. In contrast, when the trajectories start from the third excited state S3, both CH3O + NO2 and CH3O + NO + O channels become important. Here the CH3O-NO2 bond dissociation takes place first, and then for some trajectories, the N-O bond of the NO2 part breaks successively. The quasi-degeneracy of electronic states may exist in the dissociation limits of both CH3O + NO2 and CH3O + NO + O channels. The current work provides valuable information in the understanding of experimental findings of the wavelength-dependent photolysis mechanism of CH3ONO2.

Analysis of bath motion in MM-SQC dynamics via dimensionality reduction approach: Principal component analysis.

The system-plus-bath model is an important tool to understand the nonadiabatic dynamics of large molecular systems. Understanding the collective motion of a large number of bath modes is essential for revealing their key roles in the overall dynamics. Here, we applied principal component analysis (PCA) to investigate the bath motion in the basis of a large dataset generated from the symmetrical quasi-classical dynamics method based on the Meyer-Miller mapping Hamiltonian nonadiabatic dynamics for the excited-state energy transfer in the Frenkel-exciton model. The PCA method clearly elucidated that two types of bath modes, which either display strong vibronic coupling or have frequencies close to that of the electronic transition, are important to the nonadiabatic dynamics. These observations were fully consistent with the physical insights. The conclusions were based on the PCA of the trajectory data and did not involve significant pre-defined physical knowledge. The results show that the PCA approach, which is one of the simplest unsupervised machine learning dimensionality reduction methods, is a powerful one for analyzing complicated nonadiabatic dynamics in the condensed phase with many degrees of freedom.

Brightening up Circularly Polarized Luminescence of Monosubstituted Polyacetylene by Conformation Control: Mechanism, Switching, and Sensing.

The first example of luminescent monosubstituted polyacetylenes (mono-PAs) is presented, based on a contracted cis-cisoid polyene backbone. It has an excellent circularly polarized luminescence (CPL) performance with a high dissymmetric factor (up to the order of 10-1 ). The luminescence stems from the helical cis-cisoid PA backbone, which is tightly fixed by the strong intramolecular hydrogen bonds, thereby reversing the energy order of excited states and enabling an emissive energy dissipation. CPL switches are facilely achieved by the solvent and temperature through reversible conformational transition. By taking advantages of fast response and high sensitivity, the thin film of mono-PAs could be used as a CPL-based probe for quantitative detection of trifluoroacetic acid with a wider linear dynamic range than those of photoluminescence and circular dichroism. This work opens a new avenue to develop novel smart CPL materials through modulating conformational transition.

Multi-Resonance Deep-Red Emitters with Shallow Potential-Energy Surfaces to Surpass Energy-Gap Law*.

Efficient organic emitters in the deep-red region are rare due to the "energy gap law". Herein, multiple boron (B)- and nitrogen (N)-atoms embedded polycyclic heteroaromatics featuring hybridized π-bonding/ non-bonding molecular orbitals are constructed, providing a way to overcome the above luminescent boundary. The introduction of B-phenyl-B and N-phenyl-N structures enhances the electronic coupling of those para-positioned atoms, forming restricted π-bonds on the phenyl-core for delocalized excited states and thus a narrow energy gap. The mutually ortho-positioned B- and N-atoms also induce a multi-resonance effect on the peripheral skeleton for the non-bonding orbitals, creating shallow potential energy surfaces to eliminate the high-frequency vibrational quenching. The corresponding deep-red emitters with peaks at 662 and 692 nm exhibit narrow full-width at half-maximums of 38 nm, high radiative decay rates of ca. 108  s-1 , ≈100 % photo-luminescence quantum yields and record-high maximum external quantum efficiencies of ca. 28 % in a normal planar organic light-emitting diode structure, simultaneously.

Online high-pH reversed-phase liquid chromatography × low-pH reversed-phase liquid chromatography tandem electrospray ionization mass spectrometry combined with pulse elution gradient in the first dimension for the analysis of alkaloids in Macleaya cordata (willd.) R. Br.

An online high-pH reversed-phase liquid chromatography× low-pH reversed-phase liquid chromatography tandem electrospray ionization mass spectrometry combined with pulse elution gradient in the first dimension was constructed to separate and identify alkaloids from Macleaya cordata (willd.) R. Br. The modulation was performed by using a dual second dimensional columns interface combined with a make-up dilution pump, which is responsible for dilution and neutralization of the first dimensional effluent, and the dual second dimensional columns integrated the trapping and the separation function to reduce the second dimension system dead volume. Taking advantage of the dissociable characteristics of alkaloids, mobile phases with different pH values were applied in the first dimension (pH 9.0) and the second dimension (pH 2.6) to improve the orthogonality of two-dimension separation. Besides, the pulse elution gradient in first dimension and second dimensional gradient were carefully optimized and much better separation was achieved compared to the separation with the traditional two-dimensional liquid chromatography approach. Finally, mass measurement was performed for alkaloids in M. cordata (willd.) R. Br. by coupling proposed two-dimensional liquid chromatography system with triple quadrupole mass spectrometry, and 39 alkaloids were successfully identified by comparing the obtained result with the former reported results.

Achieving Pure Green Electroluminescence with CIEy of 0.69 and EQE of 28.2% from an Aza-Fused Multi-Resonance Emitter.

Pure green emitters are essential for realizing an ultrawide color gamut in next-generation displays. Herein, by fusing the difficult-to-access aza-aromatics onto B (boron)-N (nitrogen) skeleton, a hybridized multi-resonance and charge transfer (HMCT) molecule AZA-BN was successfully synthesized through an effective one-shot multiple cyclization method. AZA-BN shows pure green fluorescence with photoluminance quantum yield of 99.7 %. The corresponding green device exhibits a maximum external quantum efficiency and power efficiency of 28.2 % and 121.7 lm W-1 , respectively, with a full width half maximum (FWHM) of merely 30 nm and Commission Internationale de l'Eclairage (CIE) coordinate y of 0.69, representing the purest green bottom-emitting organic light-emitting diode.

Performance of trajectory surface hopping method in the treatment of ultrafast intersystem crossing dynamics.

We carried out extensive studies to examine the performance of the fewest-switches surface hopping method in the description of the ultrafast intersystem crossing dynamic of various singlet-triplet (S-T) models by comparison with the results of the exact full quantum dynamics. Different implementation details and some derivative approaches were examined. As expected, it is better to perform the trajectory surface hopping calculations in the spin-adiabatic representation or by the local diabatization approach, instead of in the spin-diabatic representation. The surface hopping method provides reasonable results for the short-time dynamics in the S-T model with weak spin-orbital coupling (diabatic coupling), although it does not perform well in the models with strong spin-orbital coupling (diabatic coupling). When the system accesses the S-T potential energy crossing with rather high kinetic energy, the trajectory surface hopping method tends to produce a good description of the nonadiabatic intersystem crossing dynamics. The impact of the decoherence correction on the performance of the trajectory surface hopping is system dependent. It improves the result accuracy in many cases, while its influence may also be minor for other cases.

Ultrafast unidirectional chiral rotation in the Z-E photoisomerization of two azoheteroarene photoswitches.

Unidirectional rotation represents a very important functional feature in photochemistry, such as in the design of light-driven molecular rotary motors. Great attention has recently been devoted to the unidirectional preference of the torsional motion of azobenzene and other molecules. Azoheteroarenes offer functional advantages over their more conventional azobenzene counterparts due to the introduction of heteroaromatic rings. In this paper, the Z-E photoisomerization dynamics of two azoheteroarenes, 1,2-bis(1-methyl-1H-imidazol-2-yl)diazene and 1,2-bis(1H-imidazol-2-yl)diazene, are investigated with trajectory surface-hopping molecular dynamics at the semi-empirical OM2/MRCI level. Starting from the S1 excited state of the M-helical Z-isomer of both azoheteroarenes, more than 99% of the trajectories decay to their ground states through the M-helical conical intersections by twisting about the central N[double bond, length as m-dash]N double bond. This chiral path preference can be well understood by the energy profiles generated by the linear interpolation between the Franck-Condon geometry of the M-helical Z-isomer and the relevant S1/S0 conical intersections. The Z-E photoisomerization mechanisms of these two azoheteroarenes display a higher preference for unidirectional rotary dynamics under a chiral path than their counterpart azobenzene.

Analysis of trajectory similarity and configuration similarity in on-the-fly surface-hopping simulation on multi-channel nonadiabatic photoisomerization dynamics.

We propose an "automatic" approach to analyze the results of the on-the-fly trajectory surface hopping simulation on the multi-channel nonadiabatic photoisomerization dynamics by considering the trajectory similarity and the configuration similarity. We choose a representative system phytochromobilin (P Φ B) chromophore model to illustrate the analysis protocol. After a large number of trajectories are obtained, it is possible to define the similarity of different trajectories by the Fréchet distance and to employ the trajectory clustering analysis to divide all trajectories into several clusters. Each cluster in principle represents a photoinduced isomerization reaction channel. This idea provides an effective approach to understand the branching ratio of the multi-channel photoisomerization dynamics. For each cluster, the dimensionality reduction is employed to understand the configuration similarity in the trajectory propagation, which provides the understanding of the major geometry evolution features in each reaction channel. The results show that this analysis protocol not only assigns all trajectories into different photoisomerization reaction channels but also extracts the major molecular motion without the requirement of the pre-known knowledge of the active photoisomerization site. As a side product of this analysis tool, it is also easy to find the so-called "typical" or "representative" trajectory for each reaction channel.

The behavior of hydroxide and hydronium ions at the hexadecane-water interface studied with second harmonic generation and zeta potential measurements.

By probing the electric potential at the hexadecane-water interface with second harmonic generation and the zeta potential at the surface of a hexadecane droplet in its emulsion, we show that hydronium ions don't have a specific affinity to the oil-water interface although hydroxide ions do. The observed apparent affinity of the hydronium ions to the hexadecane-water interface is more likely a result of the electro-static attraction effect. The adsorption free energy of the hydroxide ions at the oil-water interface was estimated to be -8.3 kcal mol-1. This study provides more experimental evidence for understanding the behavior of hydronium and hydoxide ions at the oil-water interface.

Nonadiabatic dynamics simulation of keto isocytosine: a comparison of dynamical performance of different electronic-structure methods.

The nonadiabatic dynamics of keto isocytosine in the gas phase has been investigated using the on-the-fly trajectory surface hopping method based on two electronic-structure methods: SA-CASSCF and ADC(2). The results estimate an excited-state lifetime of around 1000 fs at the SA-CASSCF level, while a much shorter lifetime of 250-350 fs is obtained at the ADC(2) level. Although three conical intersections (CIs) (Ethyl. I, Ethyl. II and C[double bond, length as m-dash]O stretching) are relevant to the nonadiabatic decay of keto isocytosine, their contributions to the nonadiabatic decay are highly dependent on the electronic-structure methods employed in the dynamics simulation. The Ethyl. II CI is the main channel in the dynamics simulations at the SA-CASSCF level, while the C[double bond, length as m-dash]O stretching CI becomes dominant at the ADC(2) levels. Other high-level electronic-structure methods (MR-CISD and MS-CASPT2) are involved to benchmark our dynamics results. Through the analysis of the reaction pathways from the ground state minimum to the relevant CIs, we expect that the excited-state dynamical features obtained at the MR-CISD and MS-CASPT2 levels should be very similar to those at the SA-CASSCF level. The comparison of results obtained using different excited-state electronic-structure methods could provide guidance for further studies of similar systems.

"Watching" the Dark State in Ultrafast Nonadiabatic Photoisomerization Process of a Light-Driven Molecular Rotary Motor.

Photoisomerization dynamics of a light-driven molecular rotary motor, 9-(2-methyl-2,3-dihydro-1H-cyclopenta[a]naphthalen-1-ylidene)-9H-fluorene, is investigated with trajectory surface-hopping dynamics at the semiempirical OM2/MRCI level. The rapid population decay of the S1 excited state for the M isomer is observed, with two different decay time scales (500 fs and 1.0 ps). By weighting the contributions of fast and slow decay trajectories, the averaged lifetime of the S1 excited state is about 710 fs. The calculated quantum yield of the M-to-P photoisomerization of this molecular rotary motor is about 59.9%. After the S0 → S1 excitation, the dynamical process of electronic decay is followed by twisting about the central C═C double bond and the motion of pyramidalization at the carbon atom of the stator-axle linkage. Although two S0/S1 minimum-energy conical intersections are obtained at the OM2/MRCI level, only one conical intersection is found to be responsible for the nonadiabatic dynamics. The existence of "dark state" in the molecular rotary motor is confirmed through the simulated time-resolved fluorescence emission spectrum. Both quenching and red shift of fluorescence emission spectrum observed by Conyard et al. [ Conyard, J.; Addison, K.; Heisler, I. A.; Cnossen, A.; Browne, W. R.; Feringa, B. L.; Meech, S. R. Nat. Chem. 2012 , 4 , 547 - 551 ; Conyard, J.; Conssen, A.; Browne, W. R.; Feringa, B. L.; Meech, S. R. J. Am. Chem. Soc. 2014 , 136 , 9692 - 9700 ] are well understood. We find that this "dark state" in the molecular rotary motor is not a new electronic state, but the "dark region" with low oscillator strength on the initial S1 state.

Theoretical analysis of excited states and energy transfer mechanism in conjugated dendrimers.

The excited states of the phenylene ethynylene dendrimer are investigated comprehensively by various electronic-structure methods. Several computational methods, including SCS-ADC(2), TDHF, TDDFT with different functionals (B3LYP, BH&HLYP, CAM-B3LYP), and DFT/MRCI, are applied in systematic calculations. The theoretical approach based on the one-electron transition density matrix is used to understand the electronic characters of excited states, particularly the contributions of local excitations and charge-transfer excitations within all interacting conjugated branches. Furthermore, the potential energy curves of low-lying electronic states as the functions of ethynylene bonds are constructed at different theoretical levels. This work provides us theoretical insights on the intramolecular excited-state energy transfer mechanism of the dendrimers at the state-of-the-art electronic-structure theories.

Ab Initio Molecular Cavity Quantum Electrodynamics Simulations Using Machine Learning Models.

We present a mixed quantum-classical simulation of polariton dynamics for molecule-cavity hybrid systems. In particular, we treat the coupled electronic-photonic degrees of freedom (DOFs) as the quantum subsystem and the nuclear DOFs as the classical subsystem and use the trajectory surface hopping approach to simulate non-adiabatic dynamics among the polariton states due to the coupled motion of nuclei. We use the accurate nuclear gradient expression derived from the Pauli-Fierz quantum electrodynamics Hamiltonian without making further approximations. The energies, gradients, and derivative couplings of the molecular systems are obtained from the on-the-fly simulations at the level of complete active space self-consistent field (CASSCF), which are used to compute the polariton energies and nuclear gradients. The derivatives of dipoles are also necessary ingredients in the polariton nuclear gradient expression but are often not readily available in electronic structure methods. To address this challenge, we use a machine learning model with the Kernel ridge regression method to construct the dipoles and further obtain their derivatives, at the same level as the CASSCF theory. The cavity loss process is modeled with the Lindblad jump superoperator on the reduced density of the electronic-photonic quantum subsystem. We investigate the azomethane molecule and its photoinduced isomerization dynamics inside the cavity. Our results show the accuracy of the machine-learned dipoles and their usage in simulating polariton dynamics. Our polariton dynamics results also demonstrate the isomerization reaction of azomethane can be effectively tuned by coupling to an optical cavity and by changing the light-matter coupling strength and the cavity loss rate.

Resonance Enhancement of Vibrational Polariton Chemistry Obtained from the Mixed Quantum-Classical Dynamics Simulations.

We applied a variety of mixed quantum-classical (MQC) approaches to simulate the VSC-influenced reaction rate constant. All of these MQC simulations treat the key vibrational levels associated with the reaction coordinate in the quantum subsystem (as quantum states), whereas all other degrees of freedom (DOFs) are treated inside the classical subsystem. We find that, as long as we have the quantum state descriptions for the vibrational DOFs, one can correctly describe the VSC resonance condition when the cavity frequency matches the bond vibrational frequency. This correct resonance behavior can be obtained regardless of the detailed MQC methods that one uses. The results suggest that the MQC approaches can generate semiquantitative agreement with the exact results for rate constant changes when changing the cavity frequency, the light-matter coupling strength, or the cavity lifetime. The finding of this work suggests that one can use computationally economic MQC approaches to explore the collective coupling scenario when many molecules are collectively coupled to many cavity modes in the future.

Influence of Mode-Specific Excitation on the Nonadiabatic Dynamics of Methyl Nitrate (CH3ONO2).

The impact of mode-specific vibrational excitations on initial-preparation conditions was studied by examining the excited-state population decay rates in the nonadiabatic dynamics of methyl nitrate (CH3ONO2). In particular, exciting a few specific modes by adding a single quantum of energy clearly decelerated the nonadiabatic dynamics population decay rates. The underlying reason for this slower population decay was explained by analyzing the profiles of the excited-state potential energy surfaces in the Franck-Condon regions and the topology of the S1/S0 conical intersection. This study not only provides physical insights into the key mechanisms controlling nonadiabatic dynamics but also shows the possibility of controlling nonadiabatic dynamics via mode-specific vibrational excitations.

Ultrafast Internal Conversion Dynamics through the on-the-Fly Simulation of Transient Absorption Pump-Probe Spectra with Different Electronic Structure Methods.

An on-the-fly surface-hopping simulation protocol is developed for the evaluation of transient absorption (TA) pump-probe (PP) signals of molecular systems exhibiting internal conversion to the electronic ground state. We study the nonadiabatic dynamics of azomethane and the associating TA PP spectra at three levels of the electronic-structure theory, OM2/MRCI, SA-CASSCF, and XMS-CASPT2. The impact of these methods on the population dynamics and time-resolved TA PP signals is substantially different. This difference is attributed to the strong non-Condon effects that must be taken into account for the proper understanding and interpretation of time-resolved TA PP signals of nonadiabatic polyatomic systems. This shows that the combination of the dynamical and spectral simulations definitely provides more accurate and detailed information on the microscopic mechanisms of photophysical and photochemical processes. Hence the simulation of time-resolved spectroscopic signals provides another important dimension to examine the accuracy of quantum chemistry methods.