Ground State Potential Energy Surface Research Articles

Exploring how molluscan purple has survived throughout the Ages: The excited state dynamics of 6,6′-dibromoindigotin

The color purple has long been used as a symbol of royalty and power in art, fashion, and architecture. This correlation with aristocracy can be traced back to the use of molluscan purple, a rich purple dye that is still presently more expensive than gold, by royalty as early as the 18th century BCE. While the molluscan purple dye is composed of a mixture of various proteins, its color is derived from indigotin, indirubin and their brominated derivatives, including the molecule, 6,6′-dibromoindigotin, an analogue of the indigotin dye which is also widely used in various modern industries. Both dyes can exhibit high stability, in particular against photodamage from UV and Visible radiation. In this study, we present the gas phase absorption spectrum and excited-state lifetimes of 6,6′-dibromoindigotin combined with static calculations of the excited and ground-state potential energy surfaces. The lifetime measurements reveal that molluscan purple has nearly the same relaxation rate as indigotin providing new insights in the possible relaxation mechanisms of the indigotin family of dye molecules.

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.

Unveiling Quantum Interference in the D+ + H2 Nonadiabatic Reaction Dynamics at Low Collision Energies.

Fully converged nonadiabatic dynamics calculations of the D+ + H2 → H+ + HD reaction are performed at low temperatures using the time-dependent wave packet approach based on a set of precise 3 × 3 diabatic potential energy surfaces (PESs) ( Phys. Chem. Chem. Phys., 2021, 23, 7735-7747, DOI: 10.1039/D0CP04100A). The D+ + H2 reaction is mediated by a dense manifold of resonances associated with the deep potential well on the ground-state PES. The calculated results show that the nonadiabatic coupling can affect the resonance positions, deviating from the expectation based solely on adiabatic considerations. Furthermore, significant forward-backward asymmetry in total differential cross sections (DCSs) is revealed, which is markedly influenced by nonadiabatic effects. The nonadiabatic effects not only affect the contribution of partial waves in the reaction but also make the interference patterns in the DCSs change significantly.

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.

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.

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.

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.

Computational Analysis of Chemical Reactions Using a Variational Quantum Eigensolver Algorithm without Specifying Spin Multiplicity.

The analysis of a chemical reaction along the ground-state potential energy surface in conjunction with an unknown spin state is challenging because electronic states must be separately computed several times using different spin multiplicities to find the lowest energy state. However, in principle, the ground state could be obtained with just a single calculation using a quantum computer without specifying the spin multiplicity in advance. In the present work, ground-state potential energy curves for PtCO were calculated as a proof-of-concept using a variational quantum eigensolver (VQE) algorithm. This system exhibits a singlet-triplet crossover as a consequence of the interaction between Pt and CO. VQE calculations using a statevector simulator were found to converge to a singlet state in the bonding region, while a triplet state was obtained at the dissociation limit. Calculations performed using an actual quantum device provided potential energies within ±2 kcal/mol of the simulated energies after error mitigation techniques were adopted. The spin multiplicities in the bonding and dissociation regions could be clearly distinguished even in the case of a small number of shots. The results of this study suggest that quantum computing can be a powerful tool for the analysis of the chemical reactions of systems for which the spin multiplicity of the ground state and variations in this parameter are not known in advance.

Reduction of CO2 with Hydrated Electrons: Ab Initio Computational Studies for Finite-Size Cluster Models.

In the present work, the mechanisms of the reduction of the CO2 molecule with hydrated electrons to the hydroxyl-formyl (HOCO) radical were studied with ab initio computational methods. Hydrated hydronium radicals, H3O(H2O)n (n = 0,3,6), are considered as finite-size models of the hydrated electron in liquid water. The investigation of cluster models allows the application of high-accuracy electronic-structure methods, which are not computationally feasible in condensed-phase simulations. Reaction paths and potential-energy (PE) profiles of the proton-coupled electron-transfer reaction from hydrated H3O radicals to the CO2 molecule were explored on the ground-state PE surface. The computationally efficient unrestricted second-order Møller-Plesset method is employed, and its accuracy has been carefully benchmarked in comparison with complete-active-space self-consistent-field and multi-reference second-order perturbation calculations. The results provide insights into the interplay of electron transfer from the diffuse Rydberg-type unpaired electron of H3O to the CO2 molecule, the contraction of the electron cloud by the re-hybridization of the carbon atom of CO2, and proton transfer from the nearest water molecule to the CO2- anion, followed by Grotthus-type proton rearrangements to form stable clusters. Starting from local energy minima of hydrogen-bonded CO2-H3O(H2O)n complexes, the reaction to form HOCO-(H2O)n+1 complexes is exothermic by about 1.3 eV (125 kJ/mol). The reaction is barrier controlled with a barrier of the order of a few tenths of an electron volt, depending on size and conformation of the water cluster. This barrier is at least an order of magnitude lower than the barrier of the reaction of CO2 with any closed-shell partner molecule. The HOCO radicals can recombine by H-atom transfer (disproportionation), resulting in formic acid or a dihydroxycarbene product, as well as by the formation of a C-C bond, resulting in oxalic acid. The strong exothermicity of these radical-radical recombination reactions likely results in the fragmentation of the closed-shell products formic acid and oxalic acid, which explains the strong specificity for CO formation observed in recent experiments of Hamers and co-workers.

SO2 Photodissociation at 193 nm Directly Forms S(3P) + O2(3Σg-): Implications for the Archean Atmosphere on Earth.

It is well-documented that photodissociation of SO2 at λ = 193 nm produces O(3Pj) + SO X(3Σ-). We provide experimental evidence of a new product channel from one-photon absorption producing S(3Pj) + O2 X(3Σg-) in 2-4% yield. We probe the reactant and all products with time-resolved photoelectron photoion coincidence spectroscopy. High-level ab initio calculations suggest that the new product channel can only occur on the ground-state potential energy surface through internal conversion from the excited state, followed by isomerization to a transient SOO intermediate. Classical trajectories on the ground-state potential energy surface with random initial conditions qualitatively reproduce the experimental yields. This unexpected photodissociation pathway may help reconcile discrepancies in sulfur mass-independent fractionation mechanisms in Earth's geologic history, which shape our understanding of the Archean atmosphere and the Great Oxygenation Event in Earth's evolution.

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.

Theoretical studies on the kinetics and dynamics of the BeH+ + H2O reaction: comparison with the experiment.

The reaction of BeH+ with background gaseous H2O may play a role in qubit loss for quantum information processing with Be+ as trapped ions, and yet its reaction mechanism has not been well understood until now. In this work, a globally accurate, full-dimensional ground-state potential energy surface (PES) for the BeH+ + H2O reaction was constructed by fitting a total of 170 438 ab initio energy points at the level of RCCSD(T)-F12/aug-cc-pVTZ using the fundamental invariant-neural network method. The total root-mean-square error of the final PES was 0.178 kcal mol-1. For comparison, quasi-classical trajectory calculations were carried out on the PES at an experimental temperature of 150 K. The obtained thermal rate constant and product branching ratio of the BeD+ + H2O reaction agreed quite well with experimental results. In addition, the vibrational state distributions and energy disposals of the products were calculated and rationalized using the sudden vector projection model.

Strategies to Enhance the Rate of Proton‐Coupled Electron Transfer Reactions in Dye‐Water Oxidation Catalyst Complexes

AbstractA thorough understanding of the proton‐coupled electron transfer (PCET) steps that are involved in photocatalytic water oxidation is of crucial importance in order to increase the efficiency of dye‐sensitized photoelectrochemical cells (DS‐PEC) for solar to fuel conversion. This work provides a computational investigation of the ground and excited state potential energy surfaces of PCET reactions in two supramolecular dye‐catalyst complexes for photocatalytic water splitting. The intrinsic reaction coordinate path is computed for the rate limiting PCET step in the catalytic cycle for both complexes. By using time‐dependent density functional theory calculations, we show that the ground and excited state potential energy surfaces have a (near) degeneracy in the region of the PCET transition state. We discuss two possible strategies that take advantage of this feature to accelerate the PCET reaction: (i) through optimizing the conditions for vibronic coupling by chemical design and synthesis or (ii) through populating the product state with appropriately tuned laser pulses.

High-level ab initio study of disulfur monoxide: Ground state potential energy surface and band origins for six isotopic species

In this work, a series of potential energy surfaces (PESs) of S2O was constructed in order to get the most accurate ab initio band origins of this massive molecule. The convergence of the coupled cluster energies with respect to both basis set size [aug-cc-pCVXZ, X = T, Q, 5, and 6] and the order of the excitation [CC(n), n = 2, 3, and 4] was analyzed. For the first time, the band origins of 32S216(18)O were variationally calculated with the error of 0.5 cm−1 using the ab initio PES. The vibrational energies of the most abundant six isotopologues of S2O were predicted.

Multi-state Energy Landscape for Photoreaction of Stilbene and Dimethyl-stilbene.

We have recently developed the reaction space projector (ReSPer) method, which constructs a reduced-dimensionality reaction space uniquely determined from reference reaction paths for a polyatomic molecular system and projects classical trajectories into the same reaction space. In this paper, we extend ReSPer to the analysis of photoreaction dynamics and relaxation processes of stilbene and present the concept of a "multi-state energy landscape," incorporating the ground- and excited-state reaction subspaces. The multi-state energy landscape successfully explains the previously established photoreaction processes of cis-stilbene, such as the cis-trans photoisomerization and photocyclization. In addition, we discuss the difference in the excited-state reaction dynamics between stilbene and 1,1'-dimethyl stilbene based on a common reaction subspace determined from the framework part of reference structures with different number of atoms. This approach allows us to target any molecule with a common framework, greatly expanding the applicability of the ReSPer analysis. The multi-state energy landscape provides fruitful insight into photochemical reactions, exploring the excited- and ground-state potential energy surfaces, as well as comprehensive reaction processes with nonradiative transitions between adiabatic states, within the stage of a reduced-dimensionality reaction space.

Vibrational levels of a generalized Morse potential.

A Generalized Morse Potential (GMP) is an extension of the Morse Potential (MP) with an additional exponential term and an additional parameter that compensate for MP's erroneous behavior in the long range part of the interaction potential. Because of the additional term and parameter, the vibrational levels of the GMP cannot be solved analytically, unlike the case for the MP. We present several numerical approaches for solving the vibrational problem of the GMP based on Galerkin methods, namely, the Laguerre Polynomial Method (LPM), the Symmetrized LPM, and the Polynomial Expansion Method (PEM), and apply them to the vibrational levels of the homonuclear diatomic molecules B2, O2, and F2, for which high level theoretical near full configuration interaction (CI) electronic ground state potential energy surfaces and experimentally measured vibrational levels have been reported. Overall, the LPM produces vibrational states for the GMP that are converged to within spectroscopic accuracy of 0.01 cm-1 in between 1 and 2 orders of magnitude faster and with much fewer basis functions/grid points than the Colbert-Miller Discrete Variable Representation (CN-DVR) method for the three homonuclear diatomic molecules examined in this study. A Python library that fits and solves the GMP and similar potentials can be downloaded from https://gitlab.com/gds001uw/generalized-morse-solver.

Parametrization of the PM7 Semiempirical Quantum Mechanical Method for Silver Nanoclusters.

Semiempirical quantum mechanical methods (SEQMs) are widely used in computational chemistry because of their low computational cost, but their accuracy depends on the quality of the parameters. The neglect of diatomic differential overlap method PM7 is among the few SEQMs that contain parameters for Ag, but the experimental reference data was insufficient to obtain reliable parameters in the original parametrization. In this work, we reparametrize the PM7 parameters for Ag to accurately reproduce the ground-state potential energy surfaces of Ag clusters. Since little experimental data is available, we use reference data obtained from the ab initio method CCSD(T). The resulting parameters significantly reduce the errors in binding energies, energies required to displace clusters along their normal modes, and relative energies of isomers compared to the default PM7 Ag parameters.

Anomalous emission of an ESIPT-capable zinc(II) complex: An interplay of TADF, TICT and anti-Kasha behaviour

In contrast to the vast majority of organic ESIPT-emitters (ESIPT – excited state intramolecular proton transfer), a pyrimidine-based ESIPT-type ligand HL can bind metal ions without its deprotonation due to the spatial separation of metal-binding and ESIPT cores. The photophysical and photochemical properties of HL and the corresponding ESIPT-capable zinc(II) complex [Zn(HL)Cl2] were theoretically investigated using single-reference (DFT) and multi-reference (CASSCF, NEVPT2) quantum chemical methods. The ESIPT process in both compounds is barrierless and thermodynamically favorable in the S1 and S2 states. HL and [Zn(HL)Cl2] demonstrate abnormal anti-Kasha fluorescence (S2 → S0) and anti-Kasha phosphorescence (T2 → S0) associated with relatively low S2 → S1 and T2 → S1 internal conversion rates. Energetically achievable S1/S0 and T1/S0 intersections are responsible for the fast non-radiative decay of the S1 and T1 states. Quasi-intersections of the S2 and T2 state potential energy surfaces facilitate thermally activated delayed fluorescence (TADF, T2 → S2 → S0) for both compounds. The molecules of [Zn(HL)Cl2] can be trapped and photoexcited from the local minimum of the S0 state in the tautomeric keto form, which results in an anomalously small apparent Stokes shift of 90 nm. The absence of such minimum on the ground state potential energy surface of HL leads to a considerably larger Stokes shift of 165 nm.

Vibrational treatment of hydroxylamine in valence coordinates.

A valence coordinate H2NOH ground state potential energy surface accurate for all levels up to 6000 cm-1 relative to trans zero point energy has been generated at the coupled-cluster single double triple-F12/aug-cc-pVTZ level encompassing the trans and cis as well as the N-H2 permutational conformers. All cis and trans fundamentals and a complete set of eigenfunctions up to about 3100 cm-1 have been calculated and assigned using the improved relaxation method of the Heidelberg multi-configuration time-dependent Hartree package and an exact expression for the kinetic energy in valence coordinates generated by the TANA program. The average and maximal error to all observed transitions is about 6.3 and 14.6 cm-1, respectively. Local cis eigenfunctions exist with up to two quanta in the isomerization mode ν9. Although no significant inversion splittings have been found up to the considered 3100 cm-1, they are expected within the fundamental energy range in view of the calculated 4261 cm-1 H2 permutation/inversion barrier height. The cis-NH2 symmetric stretch fundamental shows a Fermi resonance with a splitting of about 10 cm-1.

Theoretical investigations on photodissociation dynamics of deuterated alkyl halides CD3CH2F

The product branching ratio between different products in multichannel reactions is as important as the over-all rate of reaction, both in terms of practical applications (e.g. models of combustion or atmosphere chemistry) in understanding the fundamental mechanisms of such chemical reactions. A global ground state potential energy surface for the dissociation reaction of deuterated alkyl halide CD3CH2F was computed at the CCSD(T)/CBS//B3LYP/aug-cc-pVDZ level of theory for all species. The decomposition of CD3CH2F is controversial concerning C−F bond dissociation reaction and molecular (HF, DF, H2, D2, HD) elimination reaction. Rice-Ramsperger-Kassel-Marcus (RRKM) calculations were applied to compute the rate constants for individual reaction steps and the relative product branching ratios for the dissociation products were calculated using the steady-state approach. At the different energies studied, the RRKM method predicts that the main channel for DF or HF elimination from 1,2-elimination of CD3CH2F is through a four-center transition state, whereas D2 or H2 elimination from 1,1-elimination of CD3CH2F occurs through a direct three-center elimination. At 266, 248, and 193 nm photodissociation, the main product CD2CH2+DF branching ratios are computed to be 96.57%, 91.47%, and 48.52%, respectively; however, at 157 nm photodissociation, the product branching ratio is computed to be 16.11%. Based on these transition state structures and energies, the following photodissociation mechanisms are suggested: at 266, 248, 193 nm, CD3CH2F→absorption of a photon→TS5→the formation of the major product CD2CH2+DF; at 157 nm, CD3CH2F→absorption of a photon→D/F interchange of TS1→CDH2CDF→H/F interchange of TS2→CHD2CHDF→the formation of the major product CHD2+CHDF.