Excited State Potential Energy Surfaces Research Articles

A Comprehensive Multireference Study of Excited-State Ni-Br Bond Homolysis in (dtbbpy)NiII(aryl)(Br).

The mechanism of visible light-driven Ni-C(aryl) bond homolysis in (2,2'-bipyridine)NiII(aryl)(halide) complexes, which play a crucial role in metallaphotoredox catalysis for cross-coupling reactions, has been well studied. Differently, the theoretical understanding of Ni-halide bond homolysis remains limited. In this study, we introduce a novel electronic structural framework to elucidate the mechanisms underlying photoinduced Ni-Br bond rupture in the (dtbbpy)NiII(aryl)(Br) complex. Using multireference ab initio calculations, we characterized the excited state potential energy surfaces corresponding to metal-to-ligand charge transfer (MLCT) and ligand-to-metal charge transfer (LMCT). Our calculations reveal that the Ni-Br dissociation, triggered by an external photocatalyst, begins with the promotion of Ni(II) to a 1MLCT excited state. This state undergoes intersystem crossing with repulsive triplet surfaces corresponding to the 3MLCT and Br-to-Ni 3LMCT states, resulting in Ni-Br bond breaking via the Dexter energy transfer mechanism. In the absence of a photocatalyst, the photoexcited Ni(II) favors Ni-C(aryl) homolysis, whereas the presence of a photocatalyst promotes Ni-Br dissociation. The Ni(III) species, resulting from the oxidation of Ni(II) by the photocatalyst, was found to be unproductive toward Ni-Br or Ni-C(aryl) activation.

Analytic Gradients for Equation-of-Motion Coupled Cluster with Single, Double, and Perturbative Triple Excitations.

Understanding the process of molecular photoexcitation is crucial in various fields, including drug development, materials science, photovoltaics, and more. The electronic vertical excitation energy is a critical property, for example in determining the singlet-triplet gap of chromophores. However, a full understanding of excited-state processes requires additional explorations of the excited-state potential energy surface and electronic properties, which is greatly aided by the availability of analytic energy gradients. Owing to its robust high accuracy over a wide range of chemical problems, equation-of-motion coupled cluster with single and double excitations (EOM-CCSD) is a powerful method for predicting excited-state properties, and the implementation of analytic gradients of many EOM-CCSD variants (excitation energies, ionization potentials, electron attachment energies, etc.) along with numerous successful applications highlights the flexibility of the method. In specific cases where a higher level of accuracy is needed or in more complex electronic structures, the inclusion of triple excitations becomes essential, for example, in the EOM-CCSD* approach of Saeh and Stanton. In this work, we derive and implement for the first time the analytic gradients of EOMEE-CCSD*, which also provides a template for analytic gradients of related excited-state methods with perturbative triple excitations. The capabilities of analytic EOMEE-CCSD* gradients are illustrated by several representative examples.

Photoisomerization of heptamethine cyanine (Cy7) dyes: A theoretical study

In this study, density functional theory (DFT) combined with time-dependent (TD) DFT calculations were employed to investigate the photoisomerization reaction kinetics of two near infrared (NIR) heptamethine cyanine (Cy7-NH3 and Cy7-SO3) dyes in the ground singlet state and the first excited singlet state. We found that the photoisomerization of the ground state all-trans Cy7 molecules results in at least one mono-cis and one all-cis species that demonstrate redshifted emission, in agreement with recently published transient state excitation modulation spectroscopy and fluorescence correlation spectroscopy measurements. The transition states were estimated for a whole photoisomerization pathway for both the ground singlet and first excited singlet state potential energy surfaces. We have found that all-cis isomers of the studied Cy7 dyes can be achieved through a sequential two-step photoisomerization within the excited singlet state potential energy surface, along the double CC bond adjacent to edge group (leading to mono-cis isomer 1) and along the double CC bond adjacent to the central-chain group (leading to mono-cis isomer 2). Computations show that all-trans→ mono-cis isomer 1→all-cis kinetics is limited by the first trans→ mono-cis isomer 1 stage, while the all-trans→ mono-cis isomer 2→all-cis pathway is limited by the second mono-cis isomer 2→all-cis stage. Accounting for the fact that mono-cis isomer 2 demonstrates red-shifted emission compared to the all-trans form and that this mono-cis isomer 2 is reachable through the energetically favorable all-trans→ mono-cis isomer 2 stage, we concluded that the experimentally observed red-shifted emission by Cy7-NH3 and Cy7-SO3 should be assigned to the formation of mono-cis isomer 2 species. If the all-cis isomer is populated through the double-step photoisomerization it can also be considered as a source of red-shifted emission. However, as follows from our simulations, the all-cis isomer is kinetically intricate to achieve compared to the mono-cis isomer 2.

Construction of Highly Accurate Machine Learning Potential Energy Surfaces for Excited-State Dynamics Simulations Based on Low-Level Data Sets.

Machine learning is capable of effectively predicting the potential energies of molecules in the presence of high-quality data sets. Its application in the construction of ground- and excited-state potential energy surfaces is attractive to accelerate nonadiabatic molecular dynamics simulations of photochemical reactions. Because of the huge computational cost of excited-state electronic structure calculations, the construction of a high-quality data set becomes a bottleneck. In the present work, we first built two data sets. One was obtained from surface hopping dynamics simulations at the semiempirical OM2/MRCI level. Another was extracted from the dynamics trajectories at the CASSCF level, which was reported previously. The ground- and excited-state potential energy surfaces of ethylene-bridged azobenzene at the CASSCF computational level were constructed based on the former low-level data set. Although non-neural network machine learning methods can achieve good or modest performance during the training process, only neural network models provide reliable predictions on the latter external test data set. The BPNN and SchNet combined with the Δ-ML scheme and the force term in the loss functions are recommended for dynamics simulations. Then, we performed excited-state dynamics simulations of the photoisomerization of ethylene-bridged azobenzene on machine learning potential energy surfaces. Compared with the lifetimes of the first excited state (S1) estimated at different computational levels, our results on the E isomer are in good agreement with the high-level estimation. However, the overestimation of the Z isomer is unimproved. It suggests that smaller errors during the training process do not necessarily translate to more accurate predictions on high-level potential energies or better performance on nonadiabatic dynamics simulations, at least in the present case.

Machine Learning Accelerates Precise Excited-State Potential Energy Surface Calculations on a Quantum Computer.

Electronically excited-state problems represent a crucial research field in quantum chemistry, closely related to numerous practical applications in photophysics and photochemistry. The emerging of quantum computing provides a promising computational paradigm to solve the Schrödinger equation for predicting potential energy surfaces (PESs). Here, we present a deep neural network model to predict parameters of the quantum circuits within the framework of variational quantum deflation and subspace search variational quantum eigensolver, which are two popular excited-state algorithms to implement on a quantum computer. The new machine learning-assisted algorithm is employed to study the excited-state PESs of small molecules, achieving highly accurate predictions. We then apply this algorithm to study the excited-state properties of the ArF system, which is essential to a gas laser. Through this study, we believe that with future advancements in hardware capabilities, quantum computing could be harnessed to solve excited-state problems for a broad range of systems.

Uncovering the sensing mechanism of a zinc ion sensor: Fluorescence enhancement induced by the elimination of the TICT state

Precise detection of zinc ion is of fundamental importance in the fields of environment protection and food safety. A comprehensive understanding of the sensing mechanism will help to the design of such sensors. The detailed photophysical process of a zinc ion sensor as well as the sensing mechanism are uncovered with the aid of density functional theory (DFT) and time-dependent density functional theory (TDDFT). Both the ground state and first excited state potential energy surfaces (PES) of the sensor are carefully explored to reveal the photo-physical process of the sensor. Excited state intramolecular proton transfer (ESIPT) is observed on the S1 state PES. Then, the twist motion of C=N double bond is triggered after the ESIPT process, which leads to a twisted intramolecular charge transfer (TICT) state. This TICT state is found to make the sensor non-emissive. With the addition of Zn2+, the TICT state is eliminated which greatly enhances the fluorescence of the sensor and achieves zinc ion detection. The interaction of the sensor with Cd2+ and Hg2+ are also explored, which well explains the good selectivity of the sensor.

Ultrafast terahertz Stark spectroscopy reveals the excited-state dipole moments of retinal in bacteriorhodopsin

The photoinduced all-trans to 13-cis isomerization of the retinal Schiff base represents the ultrafast first step in the reaction cycle of bacteriorhodopsin (BR). Extensive experimental and theoretical work has addressed excited-state dynamics and isomerization via a conical intersection with the ground state. In conflicting molecular pictures, the excited state potential energy surface has been modeled as a pure S[Formula: see text] state that intersects with the ground state, or in a 3-state picture involving the S[Formula: see text] and S[Formula: see text] states. Here, the photoexcited system passes two crossing regions to return to the ground state. The electric dipole moment of the Schiff base in the S[Formula: see text] and S[Formula: see text] state differs strongly and, thus, its measurement allows for assessing the character of the excited-state potential. We apply the method of ultrafast terahertz (THz) Stark spectroscopy to measure electric dipole changes of wild-type BR and a BR D85T mutant upon electronic excitation. A fully reversible transient broadening and spectral shift of electronic absorption is induced by a picosecond THz field of several megavolts/cm and mapped by a 120-fs optical probe pulse. For both BR variants, we derive a moderate electric dipole change of 5 [Formula: see text] 1 Debye, which is markedly smaller than predicted for a neat S[Formula: see text]-character of the excited state. In contrast, S[Formula: see text]-admixture and temporal averaging of excited-state dynamics over the probe pulse duration gives a dipole change in line with experiment. Our results support a picture of electronic and nuclear dynamics governed by the interaction of S[Formula: see text] and S[Formula: see text] states in a 3-state model.

Theoretical study of the photoisomerization of 1,2-bispyrazinyl-ethylene and the halogen ion salts of 1-Pyrazinyl-2-(4’-methylpyrazinyl)ethylene

ContextIt has been reported that photoexcitation of azastilbene compounds like E-1,2-bispyrazinyl-ethylene (bpe) can undergo E → Z photoisomerization of its quaternary salts via the excited triplet state. However, experimentally it is possible to get low fluorescence and photoisomerisation quantum yields in a state with higher internal conversion than intersystem crossing. We modelled bpe and its methylated derivative (bpeMe), as well as its quaternary halogen salts (bpeMeX with X = F−, Cl−, Br− and I−) to study levels of fluorescence, phosphorescence and excited state potential energy surfaces (PES). Results support experimental observations of molecules where the anion of a salt is an efficient electron donor, that molecules with weak electron-donating anions like Cl− to give increased fluorescence and photoisomerization, as compared to molecules with stronger electron-donating anions like I−, which are dominated by competing electron transfer. The fluorescence of bpeMeF and bpeMeCl was found to be stronger than bpeMeBr and bpeMeI. A deep well in the triplet excited state of bpeMeI is considered responsible for the decreased photoisomerization, compared to what was experimentally observed for bpeMeCl. Uniquely, the bpeMeI molecule is characterised by near-zero splitting of the s1 and t1 excited states that can enhance charge transfer. The quaternary salt of bpeMe with stronger electron-donating Br− anion was observed to undergo fluorescence and phosphorescence at much lower energy compared to those with weak electron-donating F− and Cl− anions. This research shows how to control the excited state fluorescence, phosphorescence and isomerization of quaternary halogen salts of methyl derivatives of 1,2-bispyrazinyl-ethylene, which aids experimental design where excited state isomerization is considered.MethodsGeometry optimization, molecular electrostatic potential (MESP), and time dependent density functional theory (TDDFT) calculations were conducted utilizing Gaussian 16 with the B3LYP functional and the 6–31 + G(d,p) basis set. The minimum energy path (MEP) for the E to Z isomerization of the molecules was established employing the Nudged-Elastic-Band (NEB) method, implemented in Orca 4.2. Precise energies of the E → Z isomerization reaction path were determined employing CASSCF and a more accurate multireference method, NEVPT2.

Acid Violet 3: A Base-Activated Water-Soluble Photoswitch.

Acidic azo dyes are widely used for their vibrant colors. However, if their photophysics were better understood and controllable, they could be integrated into many more applications such as photosensing, photomedicine, and nonlinear optics. Here, the proton-controlled photophysics of a widely used acid, hydrazo dye, acid violet 3 (AV3) is explored. Density functional theory is used to predict the ground- and excited-state potential energy surfaces, and the proposed photoisomerization mechanism is confirmed with spectroscopic experiments. The ground-state and first two excited-state surfaces of the three readily accessible protonation states, AV3-H, AV3, and AV3+H, are investigated along both the dihedral rotation and inversion coordinates. The deprotonated AV3-H undergoes photoisomerization with blue light (λex = 453 nm) through a dihedral rotation mechanism. Upon the formation of the cis-isomer, the reversion of AV3-H is predicted to occur through a mixed rotational and inversion mechanism. In contrast, AV3 and its protonated form, AV3+H, do not undergo photoisomerization because there is no driving force for either the rotation or inversion of the azo bond in the excited state. In addition, when the azo bond is acidic, the ground-state dihedral rotation reversion mechanism barrier is lower. The mechanistic insights gained here through the combination of theory and experiment provide a roadmap to control the reactivity of AV3 across 11 orders of magnitude of proton concentration, making them interesting candidates for a range of pharmaceuticals.

Quantum dynamics study of C—H stretching vibrational excitation in the F+CHD<sub>3</sub> → HF+CD<sub>3</sub> reaction

In recent decades, significant progress has been made in the precise theoretical investigation of gas-phase chemical reactions. Presently, a major challenge in the field of quantum dynamics is to develop the precise methodologies for studying chemical reactions involving more than four atoms. As a typical multi-atomic reaction system, the F+CH<sub>4</sub> reaction and its isotopic substitution reactions have attracted widespread attention from both experimental and theoretical perspectives in recent years. Experimental studies on the reaction of F+CHD<sub>3</sub> have revealed that the stretching vibration excitation of the C—H bond inhibits the bond dissociation, favoring the formation of DF+CHD<sub>2</sub> product channels. In this study, we use a seven-dimensional quantum time-dependent wave packet method to investigate the dynamics of the F+CHD<sub>3</sub> reaction in both the reactant vibrational ground state and the first stretching excited state of the C—H bond. In this work, the reaction probabilities under different vibrational conditions are analyzed, showing that when the collision energy is below 0.06 eV, the reaction probability curves exhibit numerous fast-oscillating peaks, supporting the experimentally suggested phenomena of dynamic resonance. In a collision energy range from 0.06 eV to 0.3 eV, the reaction probability for the HF product channel in the vibrational excited state is lower than that in the ground state, which is consistent with experimental observation. Through the analysis of the time-independent wave functions of product channels under low-energy collision conditions, it is found that for reactions involving vibrational ground states, the HF products in the product asymptotic region and the reaction transition state region are in the <i>v'</i> = 2 excited state and <i>v'</i> = 3 excited state of stretching vibration, respectively, which are consistent with previous experimental observations and six-dimensional quantum wave packet simulations. For reactions involving the first excited state of C—H stretching vibration, the HF products in the product asymptotic region and the reaction transition state region are both in the <i>v'</i> = 3 excited state of stretching vibration, which are consistent with the results obtained based on energy analysis. Simulation results indicate that in the case of low-energy collisions, the time-independent wave function for the C—H stretching vibrational excited state tends to be closer to the D atom side in the transition state region. This phenomenon is attributed to the more significant energy advantage of the vibrational excited state potential energy surface in the large collision angle region, explaining the inhibitory effect of stretching vibration excitation on the HF product channel. This study offers important theoretical support for explaining experimental results and contributes to a more in-depth understanding of the influence of vibrational mode excitations on the dynamical processes in poly-atomic reactions.

Ultrafast dynamics in spatially confined photoisomerization: accelerated simulations through machine learning models.

This study sheds light on the exploration of photoresponsive host-guest systems, highlighting the intricate interplay between confined spaces and photosensitive guest molecules. Conducting nonadiabatic molecular dynamics (NAMD) simulations based on electronic structure calculations for such large systems remains a formidable challenge. By leveraging machine learning (ML) as an accelerator for NAMD simulations, we analytically constructed excited-state potential energy surfaces along relevant collective variables to investigate photoisomerization processes efficiently. Combining the quantum mechanics/molecular mechanics (QM/MM) methodology with ML-based NAMD simulations, we elucidated the reaction pathways and identified the key degrees of freedom as reaction coordinates leading to conical intersections. A machine learning-based nonadiabatic dynamics model has been developed to compare the excited-state dynamics of the guest molecule, benzopyran, in both the gas phase and its behavior within the confined space of cucurbit[5]uril. This comparative analysis was designed to determine the influence of the environment on the photoisomerization rate of the guest molecule. The results underscore the effectiveness of ML models in simulating trajectory evolution in a cost-effective manner. This research offers a practical approach to accelerate NAMD simulations in large-scale systems of photochemical reactions, with potential applications in other host-guest complex systems.

Excited-state normal-mode analysis: The case of porphyrins.

We systematically applied excited-state normal mode analysis to investigate and compare the relaxation and internal conversion dynamics of a free-base porphyrin (BP) with those of a novel functional porphyrin (FP) derivative. We discuss the strengths and limitations of this method and employ it to predict very different dynamical behaviors of the two compounds and to clarify the role of high reorganization energy modes in driving the system toward critical regions of the potential energy landscape. We identify the modes of vibrations along which the energy gap between two excited-state potential energy surfaces within the Q band manifold may vanish and find that the excess energy to reach this "touching" region is significantly reduced in the case of FP (0.16eV) as compared to the one calculated for BP (0.92eV). Our findings establish a link between the chemical functionalization and the electronic and vibrational structure that can be exploited to control the internal conversion pathways in a systematic way.

Assessment of the Electron Correlation Treatment on the Quantum-Classical Dynamics of Retinal Protonated Schiff Base Models: XMS-CASPT2, RMS-CASPT2, and REKS Methods.

We compare the performance of three different multiconfigurational wave function-based electronic structure methods and two implementations of the spin-restricted ensemble-referenced Kohn-Sham (REKS) method. The study is characterized by three features: (i) it uses a small set of quantum-classical trajectories rather than potential energy surface mapping, (ii) it focuses, exclusively, on the photoisomerization of retinal protonated Schiff base models, and (iii) it probes the effect of both methyl substitution and the increase in length of the conjugate π-system. For each tested method, the corresponding analytical gradients are used to drive the quantum-classical (Tully's FSSH method) trajectory propagation, including the recent multistate XMS-CASPT2 and RMS-CASPT2 gradients. It is shown that while CASSCF, XMS-CASPT2, and RMS-CASPT2 yield consistent photoisomerization dynamics descriptions, REKS produces, in some of these systems, qualitatively different behavior that is attributed to a flatter and topographically different excited state potential energy surface. The origin of this behavior can be traced back to the effect of the employed density functional approximation. The above studies are further expanded by benchmarking, at the CASSCF and REKS levels, the electronic structure methods using a QM/MM model of the visual pigment rhodopsin.

Fantastical excited state optimized structures and where to find them.

The quantum chemistry community has developed analytic forces for approximate electronic excited states to enable walking on excited state potential energy surfaces (PES). One can thereby computationally characterize excited state minima and saddle points. Always implicit in using this machinery is the fact that an excited state PES only exists within the realm of the Born-Oppenheimer approximation, where the nuclear and electronic degrees of freedom separate. This work demonstrates through abinitio calculations and simple nonadiabatic dynamics that some excited state minimum structures are fantastical: they appear to exist as stable configurations only as a consequence of the PES construct, rather than being physically observable. Each fantastical structure exhibits an unphysically high predicted harmonic frequency and associated force constant. This fact can serve as a valuable diagnostic of when an optimized excited state structure is non-observable. The origin of this phenomenon can be attributed to the coupling between different electronic states. As PESs approach one another, the upper surface can form a minimum that is very close to a near-touching point. The force constant, evaluated at this minimum, relates to the strength of the electronic coupling rather than to any characteristic excited state vibration. Nonadiabatic dynamics results using a Landau-Zener model illustrate that fantastical excited state structures have extremely short lifetimes on the order of a few femtoseconds. Their appearance in a calculation signals the presence of a nearby conical intersection through which the system will rapidly cross to a lower surface.

Computational chemistry‐assisted design of hydrazine‐based fluorescent molecular rotor for viscosity sensors

AbstractDeep understanding of the fluorescence quenching mechanisms of probes plays a crucial role in developing their practical applications. The fluorescence quenching mechanism of hydrazine‐based fluorescence probes needs to be clarified up to the present. Herein, we designed and synthesized a new hydrazine‐based fluorescence probe (HA‐Na) based on the naphthalimide skeleton. We clarified the molecular origin of the non‐fluorescence of this probe with the aid of computational chemistry and spectroscopic analysis. We showed that the significant rotation of the hydrazine group in the excited state potential energy surface, which caused the complete charge separation, was responsible for the fluorescence quenching of the probe in an organic solvent. Once the rotation was prevented in an aggregative state or high‐viscosity solution, the fluorescence of the probe recovered. In other words, the fluorescence quenching mechanism of hydrazine‐based fluorescence probes was attributed to the formation of a twisted intramolecular charge transfer (TICT) state. More importantly, we demonstrated that this fluorescence molecular rotor could be used to monitor the autophagy process in living cells by detecting lysosomal viscosity changes during starvation. Altogether, this work provides an essential theoretical basis for the developing potential hydrazine‐based fluorescence molecular rotors.

The Best Models of Bodipy's Electronic Excited State: Comparing Predictions from Various DFT Functionals with Measurements from Femtosecond Stimulated Raman Spectroscopy.

Density functional theory (DFT) and time-dependent DFT (TD-DFT) are pivotal approaches for modeling electronically excited states of molecules. However, choosing a DFT exchange-correlation functional (XCF) among the myriad of alternatives is an overwhelming task that can affect the interpretation of results and lead to erroneous conclusions. The performance of these XCFs to describe the excited-state properties is often addressed by comparing them with high-level wave function methods or experimentally available vertical excitation energies; however, this is a limited analysis that relies on evaluation of a single point in the excited-state potential energy surface (PES). Different strategies have been proposed but are limited by the difficulty of experimentally accessing the electronic excited-state properties. In this work, we have tested the performance of 12 different XCFs and TD-DFT to describe the excited-state potential energy surface of Bodipy (2,6-diethyl-1,3,5,7-tetramethyl-8-phenyldipyrromethene difluoroborate). We compare those results with resonance Raman spectra collected by using femtosecond stimulated Raman spectroscopy (FSRS). By simultaneously fitting the absorption spectrum, fluorescence spectrum, and all of the resonance Raman excitation profiles within the independent mode displaced harmonic oscillator (IMDHO) formalism, we can describe the PES at the Franck-Condon (FC) region and determine the solvent and intramolecular reorganization energy after relaxation. This allows a direct comparison of the TD-DFT output with experimental observables. Our analysis reveals that using vertical absorption energies might not be a good criterion to determine the best XCF for a given molecular system and that FSRS opens up a new way to benchmark the excited-state performance of XCFs of fluorescent dyes.

Ultrafast Photocontrolled Rotation in a Molecular Motor Investigated by Machine Learning-Based Nonadiabatic Dynamics Simulations.

The thermal helix inversion (THI) of the overcrowded alkene-based molecular motors determines the speed of the unidirectional rotation due to the high reaction barrier in the ground state, in comparison with the ultrafast photoreaction process. Recently, a phosphine-based motor has achieved all-photochemical rotation experimentally, promising to be controlled without a thermal step. However, the mechanism of this photochemical reaction has not yet been fully revealed. The comprehensive computational studies on photoisomerization still resort to nonadiabatic molecular dynamics (NAMD) simulations based on electronic structure calculations, which remains a high computational cost for large systems such as molecular motors. Machine learning (ML) has become an accelerating tool in NAMD simulations recently, where excited-state potential energy surfaces (PESs) are constructed analytically with high accuracy, providing an efficient approach for simulations in photochemistry. Herein the reaction pathway is explored by a spin-flip time-dependent density functional theory (SF-TDDFT) approach in combination with ML-based NAMD simulations. According to our computational simulations, we notice that one of the key factors of fulfilling all-photochemical rotation in the phosphine-based motor is that the excitation energies of four isomers are similar. Additionally, a shortcut photoinduced transformation between unstable isomers replaces the THI step, which shares the conical intersection (CI) with photoisomerization. In this study, we provide a practical approach to speed up the NAMD simulations in photochemical reactions for a large system that could be extended to other complex systems.

Excited-state dynamics of deuterated indigo

Indigo, a rich blue dye, is an incredibly photostable molecule that has survived in ancient art for centuries. It is also unique in that it can undergo both an excited-state hydrogen and proton transfer on the picosecond timescale followed by a ground-state back transfer. Previously, we performed gas phase excited-state lifetime studies on indigo to study these processes in a solvent-free environment, combined with excited-state calculations. We found two decay pathways, a fast sub-nanosecond decay and a slow decay on the order of 10 ns. Calculations of the excited-state potential energy surface found that both hydrogen and proton transfer are nearly isoenergetic separated by a 0.1 eV barrier. To further elucidate these dynamics, we now report a study with deuterated indigo, using resonance-enhanced multi-photon ionization and pump-probe spectroscopy with mass spectrometric isotopomer selection. From new calculations of the excited-state potential energy surface, we find sequential double-proton or hydrogen transfer, whereby the trajectory to the second transfer passes a second barrier and then encounters a conical intersection that leads back to the ground state. We find that deuteration only increases the excited-state lifetimes of the fast decay channel, suggesting tunneling through the first barrier, while the slower channel is not affected and may involve a different intermediate state.Graphical abstract

(Invited) Theoretical Study on the Environmental Effects on Photoexcited Properties of Donor-Acceptor-Linked Molecules

Photoinduced charge separation process plays important roles in various fields such as natural and artificial photosynthesis, solar cell, and light-emitting diode. Toward an understanding of the molecular mechanism of photoinduced charge separation, we have been studying the excited and charge-separated states of donor-acceptor-linked molecules with theoretical methods such as QM/MM method and molecular dynamics (MD) simulation. In particular, we have focused on the environmental effects on photoexcited properties. In this presentation, we will present recent progress of our research. For example, we will talk about theoretical analysis of acceptor-donor-acceptor type non-fullerene acceptor called TACIC. The excited state of TACIC is known to have a longer lifetime in the film state than in solution. This is in contrast to a similar acceptor-donor-acceptor type non-fullerene acceptor molecule, ITIC, which has a shorter lifetime in the film state than in solution. However, the molecular mechanism is unknown. We analyzed the structures and excited states of the TACIC and ITIC by using quantum chemical calculations and MD simulation. First, it is found that the excited-state potential energy surface of TACIC monomer is similar to that of ITIC monomer, which is consistent with the experimental result that both have similar lifetimes in solution. Next, the packing structure of TACIC in the film state is much different from that of ITIC. Analysis of the excited states of dimer obtained from the film state structure demonstrated that the transition dipole of TACIC dimer is much smaller than that of ITIC dimer. These results could be related to the difference in lifetime of the excited state between TACIC and ITIC in the film state. Further analysis is currently in progress. We will also talk about the photoexcited properties of porphyrin-fullerene linked molecules.

Machine Learning Seams of Conical Intersection: A Characteristic Polynomial Approach.

The machine learning of potential energy surfaces (PESs) has undergone rapid progress in recent years. The vast majority of this work, however, has been focused on the learning of ground state PESs. To reliably extend machine learning protocols to excited state PESs, the occurrence of seams of conical intersections between adiabatic electronic states must be correctly accounted for. This introduces a serious problem, for at such points, the adiabatic potentials are not differentiable to any order, complicating the application of standard machine learning methods. We show that this issue may be overcome by instead learning the coordinate-dependent coefficients of the characteristic polynomial of a simple decomposition of the potential matrix. We demonstrate that, through this approach, quantitatively accurate machine learning models of seams of conical intersection may be constructed.