Excited State Potential Surfaces Research Articles

Machine learning accelerated photodynamics simulations

Machine learning (ML) continues to revolutionize computational chemistry for accelerating predictions and simulations by training on experimental or accurate but expensive quantum mechanical (QM) calculations. Photodynamics simulations require hundreds of trajectories coupled with multiconfigurational QM calculations of excited-state potential energies surfaces that contribute to the prohibitive computational cost at long timescales and complex organic molecules. ML accelerates photodynamics simulations by combining nonadiabatic photodynamics simulations with an ML model trained with high-fidelity QM calculations of energies, forces, and non-adiabatic couplings. This approach has provided time-dependent molecular structural information for understanding photochemical reaction mechanisms of organic reactions in vacuum and complex environments (i.e., explicit solvation). This review focuses on the fundamentals of QM calculations and ML techniques. We, then, discuss the strategies to balance adequate training data and the computational cost of generating these training data. Finally, we demonstrate the power of applying these ML-photodynamics simulations to understand the origin of reactivities and selectivities of organic photochemical reactions, such as cis–trans isomerization, [2 + 2]-cycloaddition, 4π-electrostatic ring-closing, and hydrogen roaming mechanism.

Absorption and fluorescence spectra of new pyrrolo[3,4‐b]quinolizines in condensed phases: A joint experimental and computational study

AbstractNewly synthesized pyrrolo[3,4‐b]quinolizines, blue‐green to orange‐red in fluorescent dye in solutions and yellow to red fluorescent dyes in solid states, were experimentally and computationally investigated for the electronic and fluorescence spectra in solution as well as in solid state. The solvent effects on the absorption and emission spectra were theoretically investigated by the snapshots‐averaged spectra obtained by the first principle molecular dynamics combined with polarizable continuum model (PCM). Alternatively, the solute–solvent interaction effect on the spectra was examined by fragment molecular orbital‐time dependent density functional theory (FMO‐TDDFT) which considered the explicit solute–solvent interactions. The results indicate that the quantitative prediction limitations of PCM and that the solvatochromic shifts in dichloromethane and ethanol were correctly reproduced by FMO‐TDDFT. The luminescence quantum yields of the compounds were analyzed on the excited state potential surface via the S0/S1‐conical intersections.

Photophysics of the red-form Kaede chromophore.

The green fluorescent protein (GFP) drove revolutionary progress in bioimaging. Photoconvertible fluorescent proteins (PCFPs) are an important branch of the FP family, of which Kaede is the prototype. Uniquely, PCFPs can be permanently switched from green to red emitting forms on UV irradiation, facilitating applications in site-specific photolabelling and protein tracking. Optimisation and exploitation of FPs requires understanding of the photophysical and photochemical behaviour of the chromophore. Accordingly, the principal GFP chromophore has been the subject of intense experimental and theoretical investigation. In contrast, the photophysics of the red emitting PCFP chromophore are largely unstudied. Here we present a detailed investigation of the excited-state properties of the Kaede chromophore in solution, utilising steady state measurements, ultrafast time-resolved electronic and vibrational spectroscopies, and electronic structure theory. Its excited state dynamics are very different to those of the parent GFP. Most remarkably, the PCFP chromophore has highly complex wavelength-dependent fluorescence decays and a mean lifetime an order of magnitude longer than the GFP chromophore. Transient electronic and vibrational spectroscopies suggest that these dynamics arise from a range of excited-state conformers that are spectrally and kinetically distinct but chemically similar. These conformers are populated directly by excitation of a broad thermal distribution of ground state structures about a single conformer, suggesting an excited-state potential surface with several minima. Temperature-dependence confirms the existence of barriers on the excited-state surface and reveals the radiationless decay mechanism to be internal conversion. These experimental observations are consistent with a model assuming a simple ground state potential energy surface accessing a complex excited state possessing multiple minima.

(Invited) Why Is Pacman so Hungry? Femtosecond M-Edge XANES Explains the Low Quantum Yield of µ-Oxo Bis(Fe Porphyin) Photocatalysts

Bridged μ-oxo iron bisporphyrins serve as photocatalysts for oxidative organic transformations, but suffer from low quantum efficiency. This low performance has been primarily attributed to the short lifetime of Fe(II)/Fe(IV)=O state formed after LMCT excitation, but a competing proposal claims that the majority photoproduct is a catalytically inactive ligand-centered ion pair. We use femtosecond optical and M2,3-edge XANES spectroscopy to investigate the early photodynamics of the μ-oxo iron bisporphyrin, (TPPFe)2O, providing evidence for the preferential formation of an TPPFe(III)+/TPPFe(III)-O- ion pair state instead of the desired TPPFe(II)/TPPFe(IV)=O. This work provides new guidance for catalyst design, suggesting that the excited-state potential surfaces must be redesigned to promote formation of the catalytically active state.

Barely fluorescent molecules. I. Twin-discharge jet laser-induced fluorescence spectroscopy of HSnCl and DSnCl.

The divalent tin transient molecules HSnCl and DSnCl have been detected for the first time by laser-induced fluorescence (LIF) spectroscopy. HSnCl/DSnCl were produced in a twin-discharge jet using separate precursor streams of SnH4/SnD4 and the discharge products from HCl/DCl, both diluted in high pressure argon. The Ã1A″-X̃1A' spectrum of HSnCl consists of a single vibronic 00 0 band with a very short fluorescence lifetime (∼30ns). In contrast, the LIF spectrum of DSnCl exhibits three bands (00 0,20 1,and20 2), whose fluorescence lifetimes decrease from 393ns (00) to less than 10ns (22). Single vibronic level emission spectra have been recorded, providing information on all three vibrational modes in the ground state. Previous detailed ab initio studies indicate that these molecules dissociate into SnCl + H on the excited state potential surface and this is the cause of the short fluorescence lifetimes and breaking off of the fluorescence. It is fortunate that the HSnCl excited state zero-point level is still fluorescent or it would not be detectable by LIF spectroscopy.

Barely fluorescent molecules. II. Twin-discharge jet laser-induced fluorescence spectroscopy of HSnBr and DSnBr.

HSnBr and DSnBr have been detected for the first time by a combination of laser-induced fluorescence (LIF), fluorescence hole-burning, and wavelength resolved emission spectroscopies. The transient molecules were produced in a twin-discharge jet using separate precursor streams of SnH4/SnD4 and HBr/DBr, both diluted in high pressure argon. The Ã1A″-X̃1A' spectrum of HSnBr only consists of the 00 0 and 20 1 cold bands that show clearly resolved subband structure with fluorescence lifetimes varying from 526 to 162ns. The DSnBr LIF spectrum exhibits four bands (00 0, 20 1, 20 2, and 10 1) whose fluorescence lifetimes decrease from 525ns (00) to 175ns (11). Single vibronic level emission spectra have provided extensive information on the ground state vibrations, including all the anharmonicities and the harmonic frequencies. Fluorescence hole-burning experiments have shown that a few higher HSnBr nonfluorescent levels are very short-lived but still detectable. The ab initio studies of Tarroni and Clouthier [J. Chem. Phys. 156, 064304 (2022)] show that these molecules dissociate into SnBr + H on the excited state potential surface and this is the cause of the short fluorescence lifetimes and breaking off of the LIF spectra. HSnBr is a barely fluorescent molecule in the sense that only vibrational levels less than or equal to 317cm-1 in the excited state emit detectable photons down to the ground state.

Real-time Observation of Structural Dynamics Triggering Excimer Formation in a Perylene Bisimide Folda-dimer by Ultrafast Time-Domain Raman Spectroscopy.

In π‐conjugated organic photovoltaic materials, an excimer state has been generally regarded as a trap state which hinders efficient excitation energy transport. But despite wide investigations of the excimer for overcoming the undesirable energy loss, the understanding of the relationship between the structure of the excimer in stacked organic compounds and its properties remains elusive. Here, we present the landscape of structural dynamics from the excimer formation to its relaxation in a co‐facially stacked archetypical perylene bisimide folda‐dimer using ultrafast time‐domain Raman spectroscopy. We directly captured vibrational snapshots illustrating the ultrafast structural evolution triggering the excimer formation along the interchromophore coordinate on the complex excited‐state potential surfaces and following evolution into a relaxed excimer state. Not only does this work showcase the ultrafast structural dynamics necessary for the excimer formation and control of excimer characteristics but also provides important criteria for designing the π‐conjugated organic molecules.

Nonadiabatic dynamics with spin-flip vs linear-response time-dependent density functional theory: A case study for the protonated Schiffbase C5H6NH2.

Nonadiabatic trajectory surface hopping simulations are reported for trans-C5H6NH2 +, a model of the rhodopsinchromophore, using the augmented fewest-switches algorithm. Electronic structure calculations were performed using time-dependent density functional theory (TDDFT) in both its conventional linear-response (LR) and its spin-flip (SF) formulations. In the SF-TDDFT case, spin contamination in the low-lying singlet states is removed by projecting out the lowest triplet component during iterative solution of the TDDFT eigenvalue problem. The results show that SF-TDDFT qualitatively describes the photoisomerization of trans-C5H6NH2 +, with favorable comparison to previous studies using multireference electronic structure methods. In contrast, conventional LR-TDDFT affords qualitatively different photodynamics due to an incorrect excited-state potential surface near the Franck-Condon region. In addition, the photochemistry (involving pre-twisting of the central double bond) appears to be different for SF- and LR-TDDFT, which may be a consequence of different conical intersection topographies afforded by these two methods. The present results contrast with previous surface-hopping studies suggesting that the LR-TDDFT method's incorrect topology around S1/S0 conical intersections is immaterial to the photodynamics.

A classical ride through a conical intersection

Regarding the correlated electron-nuclear motion in a model system, we investigate the dynamics in the vicinity of a conical intersection (CoIn) between two excited state potential surfaces. It is documented that an ensemble of classical trajectories which move in the complete electronic-nuclear phase space tracks the quantum wave-packet motion through the CoIn which is accompanied by a non-adiabatic population transfer. On the contrary, for an adiabatic circular motion around the position of the CoIn, the quantum mechanical and classical densities deviate substantially. In the latter case, the Born-Oppenheimer classical nuclear motion on a single potential surface is able to track the quantum dynamics.

Excited-State Planarization in Donor-Bridge Dye Sensitizers: Phenylene versus Thiophene Bridges.

Donor-π-acceptor complexes for solar energy conversion are commonly composed of a chomophore donor and a semiconductor nanoparticle acceptor separated by a π bridge. The electronic coupling between the donor and acceptor is known to be large when the π systems of the donor and bridge are coplanar. However, the accessibility of highly coplanar geometries in the excited state is not well understood. In this work, we clarify the relationship between the bridge structure and excited-state donor-bridge coplanarization by comparing rhodamine sensitizers with either phenylene (O-Ph) or thiophene (O-Th) bridge units. Using a variety of optical spectroscopic and computational techniques, we model the S1 excited-state potential surfaces of O-Ph and O-Th along the dihedral coordinate of donor-bridge coplanarization, τ. We find that O-Th accesses a nearly coplanar (τ = 8°) global minimum geometry in S1 where significant intramolecular charge transfer (ICT) character is developed. The S1 coplanar geometry is populated in <10 ps and is stable for ca. 1 ns. Importantly, O-Ph is sterically hindered from rotation along τ and therefore remains at its initial S1 equilibrium geometry far from coplanarity (τ = 56°). Our results demonstrate that donor-bridge dye sensitizers utilizing thiophene bridges should facilitate strong donor-acceptor coupling by an ultrafast and stabilizing coplanarization mechanism in S1. The coplanarization will result in strong donor-acceptor coupling, potentially increasing the electron transfer efficiency. These findings provide further explanation for the success of thiophene as a bridge unit and can be used to guide the informed design of new molecular sensitizers.

Excited-State Dynamics of 2-(2'-Hydroxyphenyl)benzothiazole: Ultrafast Proton Transfer and Internal Conversion.

One of the most widely studied model systems for excited-state proton transfer (ESPT) is the 2-(2'-hydroxyphenyl)benzothiazole (HBT) molecule. This compound undergoes ultrafast ESPT followed by internal conversion to return to the ground state. In the present work, we simulate the nonadiabatic photochemistry of HBT using ab initio multiple spawning (AIMS) nuclear dynamics and a complete active space configuration interaction (CASCI) method in conjunction with wave function-in-DFT embedding to obtain ground- and excited-state potential surfaces on-the-fly. Our simulation predicts ultrafast ESPT with a time constant of 48-54 fs and an excited-state lifetime of 1.7-1.8 ps. Following proton transfer, HBT becomes trapped in a metastable keto structure on the S1 state. Eventually, the molecule begins to twist and proceeds toward a seam of intersection with the ground state where internal conversion is highly efficient.

From roaming atoms to hopping surfaces: mapping out global reaction routes in photochemistry.

The photodissociation of small molecules occurs upon irradiation by ultraviolet or visible light, and it is a very important chemical process in Earth's atmosphere, in the atmospheres of other planets, and in interstellar media. Photodissociation is an important method used to thoroughly investigate the fundamental issues of chemical reactivity. Photodissociation involves molecules and reaction fragments moving over ground- and excited-state potential surfaces (PESs). Molecules can move on a single PES (adiabatic pathway) or can cross over from one PES to another (nonadiabatic pathways). For a full theoretical understanding of a photodissociation mechanism, all of the important nonadiabatic and adiabatic pathways must be determined. This is not an easy task. We have developed an efficient computational method, called the global reaction route mapping (GRRM) strategy, that allows a theoretical exploration of ground- and excited-state PESs and their crossing seams in an automatic manner. In this Perspective, we summarize our approaches and present examples of their application together with newly determined chemical insights. These include the complex photodissociation mechanism of the formaldehyde molecule, the exclusive excited-state roaming dynamics of the nitrate radical, and all product channels and conformational memory in the photodissociation of the formic acid molecule. Finally, perspectives for the theoretical design of photofunctional molecules are discussed.

Valence-bond non-equilibrium solvation model for a twisting monomethine cyanine.

We propose and analyze a two-state valence-bond model of non-equilibrium solvation effects on the excited-state twisting reaction of monomethine cyanines. Suppression of this reaction is thought responsible for environment-dependent fluorescence yield enhancement in these dyes. Fluorescence is quenched because twisting is accompanied via the formation of dark twisted intramolecular charge-transfer (TICT) states. For monomethine cyanines, where the ground state is a superposition of structures with different bond and charge localizations, there are two possible twisting pathways with different charge localizations in the excited state. For parameters corresponding to symmetric monomethines, the model predicts two low-energy twisting channels on the excited-state surface, which leads to a manifold of TICT states. For typical monomethines, twisting on the excited state surface will occur with a small barrier or no barrier. Changes in the solvation configuration can differentially stabilize TICT states in channels corresponding to different bonds, and that the position of a conical intersection between adiabatic states moves in response to solvation to stabilize either one channel or the other. There is a conical intersection seam that grows along the bottom of the excited-state potential with increasing solvent polarity. For monomethine cyanines with modest-sized terminal groups in moderately polar solution, the bottom of the excited-state potential surface is completely spanned by a conical intersection seam.

Excited-state wavepacket and potential reconstruction by coherent anti-Stokes Raman scattering

Among the major challenges in the chemical sciences is controlling chemical reactions and deciphering their mechanisms. Since much of chemistry occurs in excited electronic states, in the last three decades scientists have employed a wide variety of experimental techniques and theoretical methods to recover excited-state potential energy surfaces and the wavepackets that evolve on them. These methods have been partially successful but generally do not provide a complete reconstruction of either the excited state wavepacket or potential. We have recently proposed a methodology for reconstructing excited-state molecular wavepackets and the corresponding potential energy surface [Avisar and Tannor, Phys. Rev. Lett., 2011, 106, 170405]. In our approach, the wavepacket is represented as a superposition of the set of vibrational eigenfunctions of the molecular ground-state Hamiltonian. We assume that the multidimensional ground-state potential surface is known, and therefore these vibrational eigenfunctions are known as well. The time-dependent coefficients of the basis functions are obtained by experimental measurement of the resonant coherent anti-Stokes Raman scattering (CARS) signal. Our reconstruction strategy has several significant advantages: (1) the methodology requires no a priori knowledge of any excited-state potential. (2) It applies to dissociative as well as to bound excited-state potentials. (3) It is general for polyatomics. (4) The excited-state potential surface is reconstructed simultaneously with the wavepacket. Apart from making a general contribution to the field of excited-state spectroscopy, our method provides the information on the excited-state wavepacket and potential necessary to design laser pulse sequences to control photochemical reactions.

Computing UV/vis spectra from the adiabatic and vertical Franck-Condon schemes with the use of Cartesian and internal coordinates

We address the effects of using Cartesian or internal coordinates in the adiabatic Franck-Condon (AFC) and vertical Franck-Condon (VFC) approaches to electronic spectra. The adopted VFC approach is a simplified variant of the original approach [A. Hazra, H. H. Chang, and M. Nooijen, J. Chem. Phys. 151, 2125 (2004)], as we omit any contribution from normal modes with imaginary frequency. For our test molecules ranging from ethylene to flavin compounds, VFC offers several advantages over AFC, especially by preserving the properties of the FC region and by avoiding complications arising from the crossing of excited-state potential surfaces or from the failure of the harmonic approximation. The spectral quality for our target molecules is insensitive to the chosen approach. We also explore the effects of Duschinsky rotation and relate the need for internal coordinates to the absence of symmetry elements. When using Duschinsky rotation and treating larger systems without planar symmetry, internal coordinates are found to outperform Cartesian coordinates in the AFC spectral calculations.

Volume Increment Effect on the Photoisomerization of Hemicyanine Dyes in Oligo(ethylene glycol)s

We studied the excited-state dynamics of three hemicyanine dyes that undergo internal twisting from the localized excited state to the twisted intramolecular charge-transfer state. The dyes differ in the length of the alkyl chain in the aniline moiety and, thus, the volume of the motional moiety increases without having much of an effect on the excited-state potential surface. By employing oligo(ethylene glycol)s as a new homologous series of solvents that covers a high viscosity region, we showed that the excited-state lifetime of the hemicyanines gradually increases at any given viscosity when the size of the substituent increases. We describe our results for the solution-phase photoisomerization processes in terms of the breakdown of Stokes' law, multidimensionality, and the Hubbard relation.

Origin of the size-dependent fluorescence blueshift in [n]cycloparaphenylenes

Quantum chemical electronic structure calculations were employed to investigate the nature of the low-lying excited states of [n]cycloparaphenylenes ([n]CPPs) and the role of static and dynamic geometrical distortions in the bright states. The lowest-energy bright states involve single-electron excitations from S0 ground state to S2 and S3 states, which are at the Franck–Condon geometry the two components of a twofold degenerate 1E state. They couple to a twofold degenerate e vibration which induces Jahn–Teller (JT) deformation of the CPP geometry from circular to oval shape. Non-radiative decay from the S2/S3 states to the ground S0 and first excited, dark S1 states is suppressed due to symmetry rules. The emission spectral features in CPPs with large number of phenylene units n can therefore largely be attributed to the E⊗e JT system associated with S2 and S3. However, absorption and emission energies computed at the respective S0 and S2/S3 minimum energy geometries are found to be nearly identical, independent of the molecular size n in the CPP molecules. In contrast, molecular dynamics simulations performed on the excited state potential surfaces are able to explain the experimentally observed fluorescence blueshift of the strongest emission peaks with increasing molecular size. This unusual feature turns out to be a consequence of large vibrational amplitudes in small [n]CPPs, causing greater Stokes shifts, while large [n]CPPs are more rigid and therefore feature smaller Stokes shifts (“dynamic blueshift”). For the same reasons, symmetry rules are violated to a greater extent in small [n]CPPs, and it is expected that in their case a “static blueshift” due to emission from S1 contributes in the fluorescence spectra.

The Third Dimension of a More O'Ferrall-Jencks Diagram for Hydrogen Atom Transfer in the Isoelectronic Hydrogen Exchange Reactions of (PhX)(2)H(•) with X = O, NH, and CH(2).

A critical element in theoretical characterization of the mechanism of proton-coupled electron transfer (PCET) reactions, including hydrogen atom transfer (HAT), is the formulation of the electron and proton localized diabatic states, based on which a More O'Ferrall-Jencks diagram can be represented to determine the step-wise and concerted nature of the reaction. Although the More O'Ferrall-Jencks diabatic states have often been used empirically to develop theoretical models for PCET reactions, the potential energy surfaces for these states have never been determined directly based on first principles calculations using electronic structure theory. The difficulty is due to a lack of practical method to constrain electron and proton localized diabatic states in wave function or density functional theory calculations. Employing a multistate density functional theory (MSDFT), in which the electron and proton localized diabatic configurations are constructed through block-localization of Kohn-Sham orbitals, we show that distinction between concerted proton-electron transfer (CPET) and HAT, which are not distinguishable experimentally from phenomenological kinetic data, can be made by examining the third dimension of a More O'Ferrall-Jencks diagram that includes both the ground and excited state potential surfaces. In addition, we formulate a pair of effective two-state valence bond models to represent the CPET and HAT mechanisms. We found that the lower energy of the CPET and HAT effective diabatic states at the intersection point can be used as an energetic criterion to distinguish the two mechanisms. In the isoelectronic series of hydrogen exchange reaction in (PhX)(2)H(•), where X = O, NH, and CH(2), there is a continuous transition from a CPET mechanism for the phenoxy radical-phenol pair to a HAT process for benzyl radical and toluene, while the reaction between PhNH(2) and PhNH(•) has a mechanism intermediate of CPET and HAT. The electronically nonadiabatic nature of the CPET mechanism in the phenol system can be attributed to the overlap interactions between the ground and excited state surfaces, resulting in roughly orthogonal minimum energy paths on the adiabatic ground and excited state potential energy surfaces. On the other hand, the minimum energy path on the adiabatic ground state for the HAT mechanism coincides with that on the excited state, producing a large electronic coupling that separates the two surfaces by more than 120 kcal/mol.

Modeling the electron-impact dissociation of methane

The product yield of the electron-impact dissociation of methane has been studied with a combination of three theoretical methods: R-matrix theory to determine the electronically inelastic collisional excitation cross sections, high-level electronic structure methods to determine excited states energies and derivative couplings, and trajectory surface hopping (TSH) calculations to determine branching in the dissociation of the methane excited states to give CH(3), CH(2), and CH. The calculations involve the lowest 24 excited-state potential surfaces of methane, up to the ionization energy. According to the R-matrix calculations, electron impact preferentially produces triplet excited states, especially for electron kinetic energies close to the dissociation threshold. The potential surfaces of excited states are characterized by numerous avoided and real crossings such that the TSH calculations show rapid cascading down to the lowest excited singlet or triplet states, and then slower the dissociation of these lowest states. Product branching for electron-impact dissociation was therefore estimated by combining the electron-impact excitation cross sections with TSH product branching ratios that were obtained from the lowest singlet and triplet states, with the singlet dissociation giving a comparable formation of CH(2) and CH(3) while triplet dissociation gives CH(3) exclusively. The overall branching in electron-impact dissociation is dominated by CH(3) over CH(2). A small branching yield for CH is also predicted.

Howard E. Zimmerman (1926-2012)

Howard E. Zimmerman (1926-2012)