State Potential Energy Surface Research Articles

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.

Multiple retinal isomerizations during the early phase of the bestrhodopsin photoreaction

Bestrhodopsins constitute a class of light-regulated pentameric ion channels that consist of one or two rhodopsins in tandem fused with bestrophin ion channel domains. Here, we report on the isomerization dynamics in the rhodopsin tandem domains of Phaeocystis antarctica bestrhodopsin, which binds all-trans retinal Schiff-base (RSB) absorbing at 661 nm and, upon illumination, converts to the meta-stable P540 state with an unusual 11-cis RSB. The primary photoproduct P682 corresponds to a mixture of highly distorted 11-cis and 13-cis RSB directly formed from the excited state in 1.4 ps. P673 evolves from P682 in 500 ps and contains highly distorted 13-cis RSB, indicating that the 11-cis fraction in P682 converts to 13-cis. Next, P673 establishes an equilibrium with P595 in 1.2 µs, during which RSB converts to 11-cis and then further proceeds to P560 in 48 µs and P540 in 1.0 ms while remaining 11-cis. Hence, extensive isomeric switching occurs on the early ground state potential energy surface (PES) on the hundreds of ps to µs timescale before finally settling on a metastable 11-cis photoproduct. We propose that P682 and P673 are trapped high up on the ground-state PES after passing through either of two closely located conical intersections that result in 11-cis and 13-cis RSB. Co-rotation of C11=C12 and C13=C14 bonds results in a constricted conformational landscape that allows thermal switching between 11-cis and 13-cis species of highly strained RSB chromophores. Protein relaxation may release RSB strain, allowing it to evolve to a stable 11-cis isomeric configuration in microseconds.

Beyond MD17: the reactive xxMD dataset

System specific neural force fields (NFFs) have gained popularity in computational chemistry. One of the most popular datasets as a bencharmk to develop NFF models is the MD17 dataset and its subsequent extension. These datasets comprise geometries from the equilibrium region of the ground electronic state potential energy surface, sampled from direct adiabatic dynamics. However, many chemical reactions involve significant molecular geometrical deformations, for example, bond breaking. Therefore, MD17 is inadequate to represent a chemical reaction. To address this limitation in MD17, we introduce a new dataset, called Extended Excited-state Molecular Dynamics (xxMD) dataset. The xxMD dataset involves geometries sampled from direct nonadiabatic dynamics, and the energies are computed at both multireference wavefunction theory and density functional theory. We show that the xxMD dataset involves diverse geometries which represent chemical reactions. Assessment of NFF models on xxMD dataset reveals significantly higher predictive errors than those reported for MD17 and its variants. This work underscores the challenges faced in crafting a generalizable NFF model with extrapolation capability.

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.

Combined Quantum Mechanical and Quasi-Classical State-to-State Dynamical Study on the Isotopic Effect in H/D + LiH+/LiD+ → H2/HD/D2 + Li+ Reactions.

Coriolis-coupled quantum mechanical (QM-CC) and quasi-classical trajectory (QCT) calculations are carried out to investigate the dynamics of the H(D) + LiH+(v = 0, j = 0) → H2(HD) (v', j') + Li+ reactions on the ground electronic state potential energy surface reported by Martinazzo et al. (Martinazzo et al., J. Chem. Phys. 2003, 119, 11241). The QM-CC and QCT results at the initial state-selected and state-to-state levels are used to investigate the validity and accuracy of the QCT method for these exoergic barrierless reactions. Furthermore, the QCT method is used to understand the isotopic effects on reaction observables like total and state-to-state integral cross section, differential cross section, product energy disposal, and rate constants of H(D) + LiH+(v = 0, j = 0) → H2(HD) (v', j') + Li+ and H(D) + LiD+(v = 0, j = 0) → HD(D2) (v', j') + Li+ reactions. Attempts are also made to understand the impact of the isotopic substitution on the reaction mechanism. It is observed that QM-CC and QCT results closely follow each other at the initial state-selected and state-to-state levels. Noticeable kinematic effects of reagents on the reactivity and mechanism of the reactions are also observed.

A global 2A″ state potential energy surface for the Al (2P) + O2 (Σg−3) → AlO (2Σ+) + O (3P) reaction based on the doubly hybrid functional XYG3

In this paper, a global and full-dimensional potential energy surface at the 2A″ ground state for the Al + O2 → AlO + O reaction was constructed, for the first time, based on extensive electronic structure calculations using the doubly hybrid functional XYG3 and potential energy surface fittings by neural networks. Details of the reaction paths have been analyzed. It was found that both two intermediates, the cyclic-AlO2 and the linear-OAlO, were able to dissociate to the AlO + O products, and the isomerization process between these two intermediates was controlled by conical intersections between two 2A″ states. Ro-vibrational state resolved integral cross sections have also been calculated at collision energies from 1.0 to 10.0 kcal/mol. The results support the harpooning mechanism in this metal-oxidant-involved reaction.

Ab initio molecular dynamics study of intersystem crossing dynamics for MH2 (M = Si, Ge, Sn, Pb) on spin-pure and spin-mixed potential energy surfaces.

Recently, surface-hopping ab initio molecular dynamics (SH-AIMD) simulations have come to be used to discuss the mechanisms and dynamics of excited-state chemical reactions, including internal conversion and intersystem crossing. In dynamics simulations involving intersystem crossing, there are two potential energy surfaces (PESs) governing the motion of nuclei: PES in a spin-pure state and PES in a spin-mixed state. The former gives wrong results for molecular systems with large spin-orbit coupling (SOC), while the latter requires a potential gradient that includes a change in SOC at each point, making the computational cost very high. In this study, we systematically investigate the extent to which the magnitude of SOC affects the results of the spin-pure state-based dynamics simulations for the hydride MH2 (M = Si, Ge, Sn, Pb) by performing SH-AIMD simulations based on spin-pure and spin-mixed states. It is clearly shown that spin-mixed state PESs are indispensable for the dynamics simulation of intersystem crossing in systems containing elements Sn and Pb from the fifth period onward. Furthermore, in addition to the widely used Tully's fewest switches (TFS) algorithm, the Zhu-Nakamura (ZN) global switching algorithm, which is computationally less expensive, is applied to SH for comparison. The results from TFS- and ZN-SH-AIMD methods are in qualitative agreement, suggesting that the less expensive ZN-SH-AIMD can be successfully utilized to investigate the dynamics of photochemical reactions based on quantum chemical calculations.

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.

Strongly Bound Polynuclear Anions Comprising Scandium Fluoride Building Blocks.

The stability of polynuclear anions composed of ScF3 building blocks was studied by using ab initio and density functional theory electronic structure methods and flexible basis sets. Thorough exploration of ground state potential energy surfaces of (Sc2F7)-, (Sc3F10)-, and (Sc4F13)- anions which may be viewed as comprising ScF3 fragments and the additional fluorine atom led to determining the isomeric structures thereof. It was found that the most stable isomers which are predicted to dominate at room temperature correspond to the compact structures enabling the formation of a large number of Sc-F-Sc bridging linkages rather than to the chain-like structures. The vertical electron detachment energies of the (ScnF3n+1)- anions were found to be very large (spanning the 10.85-12.29 eV range) and increasing with the increasing number of scandium atoms (n) and thus the ScF3 building blocks involved in the structure. Thermodynamic stability of (ScnF3n+1)- anions (i.e., their susceptibility to fragmentation) was also verified and discussed.

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.

Toward Quantum Chemical Free Energy Simulations of Platinum Nanoparticles on Titania Support.

Platinum nanoparticles (Pt-NPs) supported on titania surfaces are costly but indispensable heterogeneous catalysts because of their highly effective and selective catalytic properties. Therefore, it is vital to understand their physicochemical processes during catalysis to optimize their use and to further develop better catalysts. However, simulating these dynamic processes is challenging due to the need for a reliable quantum chemical method to describe chemical bond breaking and bond formation during the processes but, at the same time, fast enough to sample a large number of configurations required to compute the corresponding free energy surfaces. Density functional theory (DFT) is often used to explore Pt-NPs; nonetheless, it is usually limited to some minimum-energy reaction pathways on static potential energy surfaces because of its high computational cost. We report here a combination of the density functional tight binding (DFTB) method as a fast but reliable approximation to DFT, the steered molecular dynamics (SMD) technique, and the Jarzynski equality to construct free energy surfaces of the temperature-dependent diffusion and growth of platinum particles on a titania surface. In particular, we present the parametrization for Pt-X (X = Pt, Ti, or O) interactions in the framework of the second-order DFTB method, using a previous parametrization for titania as a basis. The optimized parameter set was used to simulate the surface diffusion of a single platinum atom (Pt1) and the growth of Pt6 from Pt5 and Pt1 on the rutile (110) surface at three different temperatures (T = 400, 600, 800 K). The free energy profile was constructed by using over a hundred SMD trajectories for each process. We found that increasing the temperature has a minimal effect on the formation free energy; nevertheless, it significantly reduces the free energy barrier of Pt atom migration on the TiO2 surface and the transition state (TS) of its deposition. In a concluding remark, the methodology opens the pathway to quantum chemical free energy simulations of Pt-NPs' temperature-dependent growth and other transformation processes on the titania support.

The complex-formation dynamics of O + H(D)2+ (v = 0,1; j = 0) reactions on 12A'' and 12A′

The reactions O + H(D)2+ are studied based on the ground state potential energy surface (PES) 12A″ and the first excited PES 12A′. Both two potential energy surfaces comprise deep wells during the minimum energy reaction path. The average lifetimes of the complex-formation of the title reactions as a function of translational energy are calculated. The results indicated that the average lifetime of the complex-formation decreases with the increasing of collision energy for the two potential energy surfaces. There are two kinds of reaction mechanisms, one is direct reaction mechanism; another is indirect one. The indirect mechanism is dominated for all the collision energies studied. However, with the increasing of the collision energy, the direct reaction mechanism becomes more and more pronounced. Besides, the influences of reagent vibrational excitation and isotopic effect on the scalar properties and vector properties are studied in detail respectively in this work. The reagent vibrational excitation enhances the number of the direct reactive trajectories remarkably on 12A″, though it has nearly no influence on the average lifetime of the complex formation. In strong contrast, the reagent vibrational excitation suppresses the number of indirect reactive trajectories and reduces the average lifetime of the complex formation on the 12A′. The isotopic substitution has no influence on the scalar properties; however, it affects the vector properties strongly.

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.

Photodegradation of Flutamide and Halogen Derivatives of Nitrobenzotrifluoride: The NO Release Channel.

The photodegradation of the nonsteroidal antiandrogen drug flutamide has been long linked to the photoisomerization involving the nitro group. In this work, the dynamics of NO photoelimination upon photolysis at 266 nm of flutamide, nitrobenzotrifluoride, and its halogen derivatives were investigated. Similar to nitrobenzene and its derivatives, a bimodal translational energy distribution was observed for the NO photofragment indicating the presence of two distinct elimination channels resulting in slow and fast components. The trends in the slow/fast branching ratio show that halogen substitution at the para position increases the triplet state yield due to the internal heavy-atom effect leading to enhancement of the fast component. Furthermore, the topology of the triplet state potential energy surface showed that the minimum energy path favors the oxaziridine ring-type intermediate over the NO2 roaming mechanism in all five molecules investigated. The steric interaction between the NO2 group and the CF3 group, which are placed in the ortho position, lowers the barrier for the formation of the oxaziridine transition state compared to that of nitrobenzene.

Photoproduct formation in coenzyme B12-dependent CarH photoreceptor via a triplet pathway.

CarH is a cobalamin-based photoreceptor which has attracted significant interest due to its complex mechanism involving its organometallic coenzyme-B12 chromophore. While several experimental and computational studies have sought to understand CarH's mechanism of action, there are still many aspects of the mechanism which remain unclear. While light is needed to activate the Co-C5' bond, it is not entirely clear whether reaction pathway involves singlet or triplet diradical states. A recent experimental study implicated triplet pathway and importance of intersystem crossing (ISC) as a viable mechanistic route for photoproduct formation in CarH. Herein, a combined quantum mechanics/molecular mechanics approach (QM/MM) was used to explore the involvement of triplet states in CarH. Two possibilities were explored. The first possibility involved photo-induced homolytic cleavage of the Co-C5' where the radical pair (RP) would deactivate to a triplet state (T0) on the ground state potential energy surface (PES). However, a pathway for the formation of the photoproduct, 4',5'-anhydroadenosine (anhAdo), on the triplet ground state PES was not energetically feasible. The second possibility involved exploring a manifold of low-lying triplet excited states computed using TD-DFT within the QM/MM framework. Viable crossings of triplet excited states with singlet excited states were identified using semiclassical Landau-Zener theory and the effectiveness of spin-orbit coupling by El-Sayed rules. Several candidates along both the Co-NIm potential energy curve (PEC) and Co-C5'/Co-NIm PES were identified, which appear to corroborate experimental findings and implicate the possible role of triplet states in CarH.

Coherent Mixing of Singlet and Triplet States in Acrolein and Ketene: A Computational Strategy for Simulating the Electron-Nuclear Dynamics of Intersystem Crossing.

We present a theoretical study of intersystem crossing (ISC) in acrolein and ketene with the Ehrenfest method that can describe a superposition of singlet and triplet states. Our simulations illustrate a new mechanistic effect of ISC, namely, that a superposition of singlets and triplets yields nonadiabatic dynamics characteristic of that superposition rather than the constituent state potential energy surfaces. This effect is particularly significant in ketene, where mixing of singlet and triplet states along the approach to a singlet/singlet conical intersection occurs, with the spin-orbit coupling (SOC) remaining small throughout. In both cases, the effects require many recrossings of the singlet/triplet state crossing seam, consistent with the textbook treatment of ISC.

Reaction dynamics for the Cl(2P) + XCl → XCl + Cl(2P) (X = H, D, Mu) reaction on a high-fidelity ground state potential energy surface.

In this work, the dynamics of a prototypical heavy-light-heavy abstract reaction, Cl(2P) + HCl → HCl + Cl(2P), is investigated both by constructing a new potential energy surface (PES) and by rate coefficient calculations. Both the permutation invariant polynomial neural network method and the embedded atom neural network (EANN) method, based on abinitio MRCI-F12+Q/AVTZ level points, are used for obtaining globally accurate full-dimensional ground state PES, with the corresponding total root mean square error being only 0.043 and 0.056 kcal/mol, respectively. In addition, this is also the first application of the EANN in a gas-phase bimolecular reaction. The saddle point of this reaction system is confirmed to be nonlinear. In comparison with both the energetics and rate coefficients obtained on both PESs, we find that the EANN is reliable in dynamic calculations. A full-dimensional approximate quantum mechanical method, ring-polymer molecular dynamics with a Cayley propagator, is employed to obtain the thermal rate coefficients and kinetic isotopic effects of the title reaction Cl(2P) + XCl→ XCl + Cl(2P) (H, D, Mu) on both new PESs, and the kinetic isotope effect (KIE) is also obtained. The rate coefficients reproduce the experimental results at high temperatures perfectly but with moderate accuracy at lower temperatures, but the KIE is with high accuracy. The similar kinetic behavior is supported by quantum dynamics using wave packet calculations as well.

Analytical excited state gradients for time-dependent density functional theory plus tight binding (TDDFT + TB).

Understanding photoluminescent mechanisms has become essential for photocatalytic, biological, and electronic applications. Unfortunately, analyzing excited state potential energy surfaces (PESs) in large systems is computationally expensive, and hence limited with electronic structure methods such as time-dependent density functional theory (TDDFT). Inspired by the sTDDFT and sTDA methods, time-dependent density functional theory plus tight binding (TDDFT + TB) has been shown to reproduce linear response TDDFT results much faster than TDDFT, particularly in large nanoparticles. For photochemical processes, however, methods must go beyond the calculation of excitation energies. Herein, this work outlines an analytical approach to obtain the derivative of the vertical excitation energy in TDDFT + TB for more efficient excited state PES exploration. The gradient derivation is based on the Z vector method, which utilizes an auxiliary Lagrangian to characterize the excitation energy. The gradient is obtained when the derivatives of the Fock matrix, the coupling matrix, and the overlap matrix are all plugged into the auxiliary Lagrangian, and the Lagrange multipliers are solved. This article outlines the derivation of the analytical gradient, discusses the implementation in Amsterdam Modeling Suite, and provides proof of concept by analyzing the emission energy and optimized excited state geometry calculated by TDDFT and TDDFT + TB for small organic molecules and noble metal nanoclusters.

Sequential Multistep Excited-State Structural Transformations in N,N'-Diphenyl-dihydrodibenzo[a,c]phenazine Fluorophores.

We demonstrate that a single polycyclic π-scaffold can undergo sequential multistep excited-state structural evolution along the bent, planar, and twisted conformers, which coexist to produce intrinsic multiple fluorescence emissions in room-temperature solution. By installing a methyl or trifluoromethyl group on the ortho-site of N,N'-diphenyl-dihydrodibenzo[a,c]phenazine (DPAC), the enhanced steric effects change the fluorescence emission of DPAC from a dominant red band to well-resolved triple bands. The ultra-broadband triple emissions of ortho-substituted DPACs range from ≈350 to ≈850 nm, which is unprecedented for small fluorophores with molecular weight of <500. Ultrafast spectroscopy and theoretical calculations clearly reveal that the above dramatic changes originate from the influence of steric hindrance on the shape of excited state potential energy surface (S1 PES). Compared to the steep S1 PES of parental DPAC, the introduction of ortho-substituent is shown to make the path of structural evolution in S1 wider and flatter, so the ortho-substituted derivatives exhibit slower structural transformations from bent to planar and then to twisted forms, yielding intrinsic triple emission. The results provide the proof of concept that the bent, planar, and twisted emissive states can coexist in the same S1 PES, which greatly expand the fundamental understanding of the excited-state structural relaxation.