A direct method for the location of the lowest energy point on a potential surface crossing

Coupled Cluster Theory for Nonadiabatic Dynamics: Nuclear Gradients and Nonadiabatic Couplings in Similarity Constrained Coupled Cluster Theory

Coupled cluster theory is one of the most accurate electronic structure methods for predicting ground and excited state chemistry. However, the presence of numerical artifacts at electronic degeneracies, such as complex energies, has made it difficult to apply the method in nonadiabatic dynamics simulations. While it has already been shown that such numerical artifacts can be fully removed by using similarity constrained coupled cluster (SCC) theory [J. Phys. Chem. Lett. 2017, 8(19), 4801-4807], simulating dynamics requires efficient implementations of gradients and nonadiabatic couplings. Here, we present an implementation of nuclear gradients and nonadiabatic derivative couplings at the similarity constrained coupled cluster singles and doubles (SCCSD) level of theory, thereby making possible nonadiabatic dynamics simulations using a coupled cluster theory that provides a correct description of conical intersections between excited states. We present a few numerical examples that show good agreement with literature values and discuss some limitations of the method.

Excited-State Intramolecular Proton Transfer toward Conical Intersections in Indigo, Epindolidione, and Indirubin

Indigo exhibits a high degree of photostability, experimentally supported by observations such as quenching of fluorescence and an exceptionally short excited-state lifetime. Epindolidione, a structural isomer of indigo, is highly fluorescent in contrast to indigo, while indirubin, another structural isomer, exhibits weak fluorescence similar to that of indigo. To elucidate the origin of the difference in photophysical and photochemical behavior, potential energy profiles of the excited-state intramolecular proton transfer in indigo, epindolidione, and indirubin are computationally studied by quantum chemical calculations using the TDDFT and extended MS-CASPT2 (XMS-CASPT2) methods. As a result, it is found that indigo and indirubin exhibit little energy barrier for the single proton transfer (SPT) in the S1(ππ*) state from the diketo to keto-enol form and low energy of the S1/S0 conical intersection (CI) in the latter form with a planar molecular structure. Epindolidione, on the other hand, exhibits much higher barriers for SPT and access to CI. These results suggest that the excited-state SPT and subsequent nonradiative deactivation via CI are more likely to occur in indigo and indirubin than in epindolidione, which is consistent with the experimental observations described above. For indigo and epindolidione, the deactivation channels via the second SPT from the keto-enol to dienol form are also compared.

On the Topological Phase around Conical Intersections with Tamm-Dancoff Linear-Response Time-Dependent Density Functional Theory

Regions of nuclear-configuration space away from the Franck-Condon geometry can prove problematic for some electronic structure methods, given the propensity of such regions to possess conical intersections, i.e., (highly connected) points of degeneracy between potential energy surfaces. With the likelihood (perhaps even inevitability) for nonadiabatic dynamics simulations to explore molecular geometries in close proximity to conical intersections, it is vital that the performance of electronic structure methods is routinely examined in this context. In a recent paper [Taylor, J. T. J. Chem. Phys. 2023, 159, 214115.], the ability of linear-response time-dependent density functional theory within the adiabatic approximation (AA LR-TDDFT) to provide a proper description of conical intersections, in terms of their topology and topography, was investigated, with particular attention paid to conical intersections between two excited electronic states. For the same prototypical molecules, protonated formaldimine and pyrazine, we herein consider whether AA LR-TDDFT can correctly reproduce the topological phase accumulated by the adiabatic electronic wave function upon traversing a closed path around an excited-to-excited state conical intersection despite not using the appropriate quadratic-response nonadiabatic coupling vectors. Equally, we probe the ability of the ground-to-excited state intersection ring exhibited by AA LR-TDDFT in protonated formaldimine to give rise to a similar topological phase in spite of its incorrect dimensionality.

Optimizing Conical Intersections without Explicit Use of Non-Adiabatic Couplings

We present two alternative methods for optimizing minimum energy conical intersection (MECI) molecular geometries without knowledge of the derivative coupling (DC). These methods are based on the utilization of Lagrange multipliers: (i) one method uses an approximate calculation of the DC, while the other (ii) do not require the DC. Both methods use the fact that information on the DC is contained in the Hessian of the squared energy difference. Tests done on a set of small molecular systems, in comparison with other methods, show the ability of the proposed methods to optimize MECIs. Finally, we apply the methods to the furimamide molecule, to optimize and characterize its S1/S2 MECI, and to optimizing the S0/S1 MECI of the silver trimer.

Doping Efects on Ethane/Ethylene Dehydrogenation Catalyzed by Pt2X Nanoclusters

The catalytic dehydrogenation of light alkanes is key to transform low-cost hydrocarbons to high value-added chemicals. Although Pt is extremely efficient at catalyzing this reaction, it suffers from coke formation that deactivates the catalyst. Dopants such as Sn are widely used to increase the stability and lifetime of Pt. In this work, the dehydrogenation reaction of ethane catalyzed by Pt3 and Pt2X (X=Si, Ge, Sn, P and Al) nanocatalysts has been studied computationally by means of density functional calculations. Our results show how the presence of dopants in the nanocluster structure affects its electronic properties and catalytic activity. Exploration of the potential energy surfaces show that non-doped catalyst Pt3 present low selectivity towards ethylene formation, where acetylene resulting from double dehydrogenation reaction will be obtained as a side product (in agreement with the experimental evidence). On the contrary, the inclusion of Si, Ge, Sn, P or Al as dopant agents implies a selectivity enhancement, where acetylene formation is not energetically favoured. These results demonstrate the effectiveness of such dopant elements for the design of Pt-based catalysts on ethane dehydrogenation.

Development of Parallel On-the-Fly Algorithm for Global Exploration of Conical Intersection Seam Space

Conical intersection (CI) seams are configuration spaces of a molecular system where two or more (spin) adiabatic electronic states are degenerate in energy. They play essential roles in photochemistry because nonradiative decays often occur near the minima of the seam, i.e., the minimum energy CIs (MECIs). Thus, it is important to explore the CI seams and discover the MECIs. Although various approaches exist for CI seam exploration, most of them are local in nature, requiring reasonable initial guesses of geometries and nuclear gradients during the search. Global search algorithms, on the other hand, are powerful because they can fully sample the configurational space and locate important MECIs missed by local algorithms. However, global algorithms are often computationally expensive for large systems due to their poor scalability with respect to the number of degrees of freedom. To overcome this challenge, we develop the parallel on-the-fly Crystal algorithm to globally explore the CI seam space, taking advantage of its superior scaling behavior. Specifically, Crystal is coupled with on-the-fly evaluations of the excited and ground state energies using multireference electronic structure methods. Meanwhile, the algorithm is parallelized to further boost its computational efficiency. The effectiveness of this new algorithm is tested for three types of molecular photoswitches of significant importance in material and biomedical sciences: photostatin (PST), stilbene, and butadiene. A rudimentary implementation of the algorithm is applied to PST and stilbene, resulting in the discovery of all previously identified MECIs and several new ones. A refined version of the algorithm, combined with a systematic clustering technique, is applied to butadiene, resulting in the identification of an unprecedented number of energetically accessible MECIs. The results demonstrate that the parallel on-the-fly Crystal algorithm is a powerful tool for automated global CI seam exploration.

Oxidation of Flavin by Molecular Oxygen: Computational Insights into a Possible Radical Mechanism

As a highly electrophilic moiety capable of oxidizing a variety of small organic molecules and biomolecules, flavin is an important prosthetic group in many enzymes. Upon oxidation of the substrate, flavin is converted into its reduced (dihydrogenated) form. The catalytic cycle is completed through oxidation back to the oxidized form, thus restoring the enzyme's oxidizing capability. While it has been firmly established that oxidation of the reduced form of flavin is cast by molecular oxygen, yielding oxidized flavin and hydrogen peroxide, the mechanism of this process is still poorly understood. Herein, we investigate the radical mechanism, which is one of the possible reaction mechanisms, by quantum chemical calculations. Because molecular oxygen exists as a triplet in its electronic ground state, whereas the products are singlets, the reaction is accompanied by hopping between electronic surfaces. We find that the rate-limiting factor of flavin oxidation is likely associated with the change in the spin state of the system. By considering several possible reactions involving flavin and its derivatives in the radical form and by examining the corresponding parts of the potential energy surface in various spin states, we estimate the effective barrier of the kinetically and thermodynamically preferred variant of flavin oxidation to be about 15 kcal/mol in the gas phase and about 7 kcal/mol in a polar (aqueous) environment. This is in agreement with kinetic studies of the corresponding monoamine oxidase enzymes, confirming the radical mechanism as a viable option for flavin regeneration in enzymes.

Computational Investigations of the Detailed Mechanism of Reverse Intersystem Crossing in Inverted Singlet-Triplet Gap Molecules

Inverted singlet-triplet gap (INVEST) materials have promising photophysical properties for optoelectronic applications due to an inversion of their lowest singlet (S1) and triplet (T1) excited states. This results in an exothermic reverse intersystem crossing (rISC) process that potentially enhances triplet harvesting, compared to thermally activated delayed fluorescence (TADF) emitters with endothermic rISCs. However, the processes and phenomena that facilitate conversion between excited states for INVEST materials are underexplored. We investigate the complex potential energy surfaces (PESs) of the excited states of three heavily studied azaphenalene INVEST compounds, namely, cyclazine, pentazine, and heptazine using two state-of-the-art computational methodologies, namely, RMS-CASPT2 and SCS-ADC(2) methods. Our findings suggest that ISC and rISC processes take place directly between the S1 and T1 electronic states in all three compounds through a minimum-energy crossing point (MECP) with an activation energy barrier between 0.11 to 0.58 eV above the S1 state for ISC and between 0.06 and 0.36 eV above the T1 state for rISC. We predict that higher-lying triplet states are not populated, since the crossing point structures to these states are not energetically accessible. Furthermore, the conical intersection (CI) between the ground and S1 states is high in energy for all compounds (between 0.4 to 2.0 eV) which makes nonradiative decay back to the ground state a relatively slow process. We demonstrate that the spin-orbit coupling (SOC) driving the S1-T1 conversion is enhanced by vibronic coupling with higher-lying singlet and triplet states possessing vibrational modes of proper symmetry. We also rationalize that the experimentally observed anti-Kasha emission of cyclazine is due to the energetically inaccessible CI between the bright S2 and the dark S1 states, hindering internal conversion. Finally, we show that SCS-ADC(2) is able to qualitatively reproduce excited state features, but consistently overpredict relative energies of excited state structural minima compared to RMS-CASPT2. The identification of these excited state features elaborates design rules for new INVEST emitters with improved emission quantum yields.

A tale of two topological isomers: Uptuning [FeIV(O)(Me4cyclam)]2+ for olefin epoxidation

TMC-anti and TMC-syn, the two topological isomers of [FeIV(O)(TMC)(CH3CN)]2+ (TMC = 1,4,8,11-tetramethyl-1,4,8,11-tetraazacyclotetradecane, or Me4cyclam), differ in the orientations of their FeIV=O units relative to the four methyl groups of the TMC ligand framework. The FeIV=O unit of TMC-anti points away from the four methyl groups, while that of TMC-syn is surrounded by the methyl groups, resulting in differences in their oxidative reactivities. TMC-syn reacts with HAT (hydrogen atom transfer) substrates at 1.3- to 3-fold faster rates than TMC-anti, but the reactivity difference increases dramatically in oxygen-atom transfer reactions. R2S substrates are oxidized into R2S=O products at rates 2-to-3 orders of magnitude faster by TMC-syn than TMC-anti. Even more remarkably, TMC-syn epoxidizes all the olefin substrates in this study, while TMC-anti reacts only with cis-cyclooctene but at a 100-fold slower rate. Comprehensive quantum chemical calculations have uncovered the key factors governing such reactivity differences found between these two topological isomers.

Minimum-Energy Conical Intersections by Compressed Multistate Pair-Density Functional Theory

Compressed multistate pair-density functional theory (CMS-PDFT) is a multistate version of multiconfiguration pair-density functional theory that can capture the correct topology of coupled potential energy surfaces (PESs) around conical intersections. In this work, we develop interstate coupling vectors (ISCs) for CMS-PDFT in the OpenMolcas and PySCF/mrh electronic structure packages. Yet, the main focus of this work is using ISCs to calculate minimum-energy conical intersections (MECIs) by CMS-PDFT. This is performed using the projected constrained optimization method in OpenMolcas, which uses ISCs to restrain the iterations to the conical intersection seam. We optimize the S1/S0 MECIs for ethylene, butadiene, and benzene and show that CMS-PDFT gives smooth PESs in the vicinities of the MECIs. Furthermore, the CMS-PDFT MECIs are in good agreement with the MECI calculated by the more expensive XMS-CASPT2 method.

Computational Design of an Electro-Organocatalyst for Conversion of CO2 into Formaldehyde

Density functional theory calculations employing a hybrid implicit/explicit solvation method were used to explore a new strategy for electrochemical conversion of CO2 using an electro-organocatalyst. A particular structural motif is identified that consists of an electron-rich vicinal enediamine (>N-C═C-N<) backbone, which is capable of activating CO2 by the formation of a C-C bond while subsequently facilitating the transfer of electrons from a chemically inert cathode to ultimately produce formaldehyde. Unlike transition metal-based electrocatalysts, the electro-organocatalyst is not constrained by scaling relations between the formation energies of activated CO2 and adsorbed CO, nor is it expected to be active for the competing hydrogen evolution reaction. The rate-limiting steps are found to occur during two proton-coupled electron transfer (PCET) sequences and are associated with the transfer of a proton from a proton transfer mediator to a carbon atom on the electro-organocatalyst. The difficulty of this step in the second PCET sequence necessitates an electrode potential of -0.85 V vs RHE to achieve the maximum turnover frequency. In addition, it is postulated that the electro-organocatalyst should also be capable of forming long-chain aldehydes by successively carrying out reductive aldol condensation to grow the alkyl chain one carbon at a time.

Topology of Conical Intersection Seams and the Geometric Phase

In this paper, we demonstrate two topological properties of crossing seams, that is, the sets of points in the N-dimensional space of nuclear coordinates where two electronic eigenstates are degenerate. We shall examine the typical case of states of the same spin with accidental degeneracies, whereby the crossing seam is of dimension N - 2. The first property we demonstrate is that a crossing seam has no boundary, therefore, it must either extend asymptotically to infinite values of one or more coordinates or wrap on itself. The second property is that two (or more) crossing seams can intersect each other but in such a way that neither of them ends at the intersection. When N = 3, the crossing seam is a line in a 3D space; this is so in triatomic molecules but also in reduced dimensionality treatments of larger polyatomics. The above-mentioned rules then mean that the crossing seam is a line of infinite length or a closed loop and can split into three branches but not in two. The example of the first two excited 1A' states of H2Cl+ illustrates these rules and shows their usefulness for computational search and characterization of crossing seams.

Highly efficient implementation of analytic nonadiabatic derivative couplings within the pseudospectral method

A pseudospectral implementation of nonadiabatic derivative couplings in the Tamm-Dancoff approximation is reported, and the accuracy and efficiency of the pseudospectral nonadiabatic derivative couplings are studied. Our results demonstrate that the pseudospectral method provides mean absolute errors of 0.2%-1.9%, while providing a significant speedup. Benchmark calculations on fullerenes (Cn, n up to 100) using B3LYP achieved 10- to 15-fold, 8- to 17-fold, and 43- to 75-fold speedups for 6-31G**, 6-31++G**, and cc-pVTZ basis sets, respectively, when compared to the conventional spectral method.

Photochemical mechanistic study of hexafluorobenzene involving the low-lying states

The photochemical isomerization and nonradiative decay processes of hexafluorobenzene (HFB) were investigated theoretically to gain insights into its photochemical mechanism and the perfluoro effect. A complete mechanistic scheme is presented through the characterization of all the possible minima and transition states of the S0, S1, and S2 states at the CASPT2/6-311G**//CAS(6,7)/6-31G* level. On the S0 potential energy surface, HFB could isomerize to three different products [Dewar-HFB (S0-P1), benzvalene-HFB (S0-P2), and fulvene-HFB (S0-P3)]. Following excitation to the S2 state with the perpendicular π → σ* transition, a chair-type minimum with Cs symmetry was found on the S2 potential energy surface. The adjacent S2/S1 conical intersection was immediately accessible from the S2 minimum. The nature of the S1 state was confirmed to have a π → π* character. Both the S2 and S1 photochemistries of HFB yielded Dewar-HFB via the S1/S0 conical intersection. The regeneration of the S0 state from the S1 and T2 states via intersystem crossing or internal conversion was also revealed.

A Local Diabatisation Method for Two-State Adiabatic Conical Intersections

A methodology to locally characterize conical intersections (CIs) between two adiabatic electronic states for which no nonadiabatic coupling (NAC) vectors are available is presented. Based on the Hessian and gradient at the CI, the branching space coordinates are identified. The potential energy surface around the CI in the branching space is expressed in the diabatic representation, from which the NAC vectors can be calculated in a wave-function-free, energy-based approach. To demonstrate the universality of the developed methodology, the minimum-energy CI (MECI) between the first (S1) and second (S2) singlet excited states of formamide is investigated at the state-averaged complete active space self-consistent field (SA-CASSCF) and extended multistate complete active space second-order perturbation theory (XMS-CASPT2) levels of theory. In addition, the asymmetrical MECI between the ground state (S0) and S1 of cyclopropanone is evaluated using SA-CASSCF, as well as (ME)CIs between the S1 and S2 states of benzene using SA-CASSCF and time-dependent density functional theory (TDDFT). Finally, a CI between the S1 and S2 excited states of thiophene was analyzed using TDDFT.

Benchmarking non-adiabatic quantum dynamics using the molecular Tully models

On-the-fly non-adiabatic dynamics methods are becoming more important as tools to characterise the time evolution of a system after absorbing light. These methods, which calculate quantities such as state energies, gradients and interstate couplings at every time step, circumvent the requirement for pre-computed potential energy surfaces. There are a number of different algorithms used, the most common being Tully Surface Hopping (TSH), but all are approximate solutions to the time-dependent Schrödinger equation and benchmarking is required to understand their accuracy and performance. For this, a common set of systems and observables are required to compare them. In this work, we validate the on-the-fly direct dynamics variational multi-configuration Gaussian (DD-vMCG) method using three molecular systems recently suggested by Ibele and Curchod as molecular versions of the Tully model systems used to test one-dimensional non-adiabatic behaviour [Ibele et al., Phys. Chem. Chem. Phys. 2020, 22, 15183-15196]. Parametrised linear vibronic potential energy surfaces for each of the systems were also tested and compared to on-the-fly results. The molecules, which we term the Ibele-Curchod models, are ethene, DMABN and fulvene and the authors used them to test and compare several versions of the Ab Initio Multiple Spawning (AIMS) method alongside TSH. The three systems present different deactivation pathways after excitation to their ππ* bright states. When comparing DD-vMCG to AIMS and TSH, we obtain crucial differences in some cases, for which an explanation is provided by the classical nature and the chosen initial conditions of the TSH simulations.

On the description of conical intersections between excited electronic states with LR-TDDFT and ADC(2)

Conical intersections constitute the conceptual bedrock of our working understanding of ultrafast, nonadiabatic processes within photochemistry (and photophysics). Accurate calculation of potential energy surfaces within the vicinity of conical intersections, however, still poses a serious challenge to many popular electronic structure methods. Multiple works have reported on the deficiency of methods like linear-response time-dependent density functional theory within the adiabatic approximation (AA LR-TDDFT) or algebraic diagrammatic construction to second-order [ADC(2)]-approaches often used in excited-state molecular dynamics simulations-to describe conical intersections between the ground and excited electronic states. In the present study, we focus our attention on conical intersections between excited electronic states and probe the ability of AA LR-TDDFT and ADC(2) to describe their topology and topography, using protonated formaldimine and pyrazine as two exemplar molecules. We also take the opportunity to revisit the performance of these methods in describing conical intersections involving the ground electronic state in protonated formaldimine-highlighting in particular how the intersection ring exhibited by AA LR-TDDFT can be perceived either as a (near-to-linear) seam of intersection or two interpenetrating cones, depending on the magnitude of molecular distortions within the branching space.

Galván I, Rivalta I, Aquilante F, Garavelli M, Lindh R, Segarra-Martí J. Characterizing Conical Intersections in DNA/RNA Nucleobases with Multiconfigurational Wave Functions of Varying Active Space Size

We characterize the photochemically relevant conical intersections between the lowest-lying accessible electronic excited states of the different DNA/RNA nucleobases using Cholesky decomposition-based complete active space self-consistent field (CASSCF) algorithms. We benchmark two different basis set contractions and several active spaces for each nucleobase and conical intersection type, measuring for the first time how active space size affects conical intersection topographies in these systems and the potential implications these may have toward their description of photoinduced phenomena. Our results show that conical intersection topographies are highly sensitive to the electron correlation included in the model: by changing the amount (and type) of correlated orbitals, conical intersection topographies vastly change, and the changes observed do not follow any converging pattern toward the topographies obtained with the largest and most correlated active spaces. Comparison across systems shows analogous topographies for almost all intersections mediating population transfer to the dark 1nO/Nπ* states, while no similarities are observed for the "ethylene-like" conical intersection ascribed to mediate the ultrafast decay component to the ground state in all DNA/RNA nucleobases. Basis set size seems to have a minor effect, appearing to be relevant only for purine-based derivatives. We rule out structural changes as a key factor in classifying the different conical intersections, which display almost identical geometries across active space and basis set change, and we highlight instead the importance of correctly describing the electronic states involved at these crossing points. Our work shows that careful active space selection is essential to accurately describe conical intersection topographies and therefore to adequately account for their active role in molecular photochemistry.

Analytic Non-adiabatic Couplings for Selected Configuration Interaction via Approximate Degenerate Coupled Perturbed Hartree-Fock

We use degenerate perturbation theory and assume that for degenerate pairs of orbitals, the coupled perturbed Hartree-Fock coefficients are symmetric in the degenerate basis to show [Formula: see text] is the only modification needed in the original molecular orbital basis. This enables us to develop efficient and accurate analytic nonadiabatic couplings between electronic states for selected configuration interactions (CIs). Even when the states belong to different irreducible representations, degenerate orbital pairs cannot be excluded by symmetry. For various excited states of carbon monoxide and trigonal planar ammonia, we benchmark the method against the full CI and find it to be accurate. We create a semi-numerical approach and use it to show that the analytic approach is correct even when a high-symmetry structure is distorted to break symmetry so that near degeneracies in orbitals occur. For a range of geometries of trigonal planar ammonia, we find that the analytic non-adiabatic couplings for selected CI can achieve sufficient accuracy using a small fraction of the full CI space.

The carbonyl-lock mechanism underlying non-aromatic fluorescence in biological matter

Challenging the basis of our chemical intuition, recent experimental evidence reveals the presence of a new type of intrinsic fluorescence in biomolecules that exists even in the absence of aromatic or electronically conjugated chemical compounds. The origin of this phenomenon has remained elusive so far. In the present study, we identify a mechanism underlying this new type of fluorescence in different biological aggregates. By employing non-adiabatic ab initio molecular dynamics simulations combined with a data-driven approach, we characterize the typical ultrafast non-radiative relaxation pathways active in non-fluorescent peptides. We show that the key vibrational mode for the non-radiative decay towards the ground state is the carbonyl elongation. Non-aromatic fluorescence appears to emerge from blocking this mode with strong local interactions such as hydrogen bonds. While we cannot rule out the existence of alternative non-aromatic fluorescence mechanisms in other systems, we demonstrate that this carbonyl-lock mechanism for trapping the excited state leads to the fluorescence yield increase observed experimentally, and set the stage for design principles to realize novel non-invasive biocompatible probes with applications in bioimaging, sensing, and biophotonics.

Photoisomerisation of Exo-Imine Complexes and the Role of MECP in the Reverse Thermal Equilibrium: An Experimental and DFT Computational Investigation

Complexes [MCl2 Cp*]2 (M=Ir, Rh), [RuCl2 (p-cymene)]2 and [Ir(C^N)2 Cl]2 (HC^N=a, phenylpyridine ; b, phenylpyrazole,) react with imine ligands derived from ο-aminophenol to yield complexes with an exocyclic C=N bond which has a cis or trans configuration. The trans isomer is favoured except for sterically crowded complexes Cp*M (M=Ir, Rh) when the imine has a mesityl substituent, for which the cis isomer is favoured. The complexes undergo photoisomerisation in visible light but revert back to the original isomer over time or when heated. The rate of the thermal reverse isomerisation depends on the imine substituent and the metal fragment. DFT calculations correctly reproduce the favoured isomer and suggest that the reverse isomerisation occurs by a rehybridisation at the N atom as found in organic imines. In addition, a triplet state, thermally accessible by a Minimum Energy Crossing Point (MECP) provides a low energy pathway for reverse isomerisation in the case of the half-sandwich complexes.

An energy decomposition and extrapolation scheme for evaluating electron transfer rate constants: a case study on electron self-exchange reactions of transition metal complexes

A simple approach to the analysis of electron transfer (ET) reactions based on energy decomposition and extrapolation schemes is proposed. The present energy decomposition and extrapolation-based electron localization (EDEEL) method represents the diabatic energies for the initial and final states using the adiabatic energies of the donor and acceptor species and their complex. A scheme for the efficient estimation of ET rate constants is also proposed. EDEEL is semi-quantitative by directly evaluating the seam-of-crossing region of two diabatic potentials. In a numerical test, EDEEL successfully provided ET rate constants for electron self-exchange reactions of thirteen transition metal complexes with reasonable accuracy. In addition, its energy decomposition and extrapolation schemes provide all the energy values required for activation-strain model (ASM) analysis. The ASM analysis using EDEEL provided rational interpretations of the variation of the ET rate constants as a function of the transition metal complexes. These results suggest that EDEEL is useful for efficiently evaluating ET rate constants and obtaining a rational understanding of their magnitudes.

Elusive Active Intermediates and Reaction Mechanisms of ortho-/ipso-Hydroxylation of Benzoic Acid by Hydrogen Peroxide Mediated by Bioinspired Iron(II) Catalysts

Aromatic hydroxylation of benzoic acids (BzOH) to salicylates and phenolates is fundamentally interesting in industrial chemistry. However, key mechanistic uncertainties and dichotomies remain after decades of effort. Herein, the elusive mechanism of the competitive ortho-/ipso-hydroxylation of BzOH by H2O2 mediated by a nonheme iron(II) catalyst was comprehensively investigated using density functional theory calculations. Results revealed that the long-postulated FeV(O)(anti-BzO) oxidant is an FeIV(O)(anti-BzO•) species 2 (anti- and syn- are defined by the orientation of the carboxyl oxygen of BzO to the oxo), which rules out the noted two-oxidant mechanism proposed previously. We propose a new mechanism in which, following the formation of an FeV(O)(syn-BzO) species (3) and its electromer FeIV(O)(syn-BzO•) (3'), 3/3' either converts to salicylate and phenolate via intramolecular self-hydroxylation (route A) or acts as an oxidant to oxygenate another BzOH to generate the same products (route B). In route A, the rotation of the BzO group along the C-O bond forms 2, in which the BzO group is orientated by π-π stacking interactions. An electrophilic ipso-addition forms a phenolate by concomitant decarboxylation or an ortho-attack forms a cationic complex, which readily undergoes an NIH shift and a BzOH-assisted proton shift to form a salicylate. In route B, 3 oxidizes an additional BzOH molecule directed by hydrogen bonding and π-π stacking interactions. In both routes, selectivity is determined by the chemical property of the BzO ring. These mechanistic findings provide a clear mechanistic scenario and enrich the knowledge of hydroxylation of aromatic acids.

Tracking the Early Stage of Triplet-Induced Photodamage in a DNA Dimer and Oligomer Containing 5-Methylcytosine

Methylation at the C5 position of cytosine, a naturally occurring epigenetic modification on DNA, shows a high correlation with mutational hotspots in disease such as skin cancer. Due to its essential biological relevance, numerous studies were devoted to confirming that the methylated sites favor the formation of the cyclobutane pyrimidine dimer (CPD), a well-known UV-induced lesion. However, photophysical and photochemical properties of dinucleotides and polynucleotides containing 5-methylcytosine (5mC) remain elusive. Herein, a charge transfer (CT) triplet state, generated via intersystem crossing (ISC) from a CT singlet state that enhanced after methylation on cytosine, is directly observed by using femtosecond transient absorption (TA) and time-resolved mid-infrared (TRIR) spectroscopy together with quantum chemical calculations for the first time in the T5mC dimer. Such an ISC process is quenched due to limitations of the ground-state geometries in 5mC-containing single-strand oligomer d(T5mC)9. This mechanistic information is important for understanding the early stage of triplet state-induced CPD formation in 5mC containing DNA.

Role of Ultrafast Internal Conversion and Intersystem Crossing in the Nonadiabatic Relaxation Dynamics of ortho-Nitrobenzaldehyde

ortho-Nitrobenzaldehyde (oNBA) is a well-known photoactivated acid and a prototypical photolabile nitro-aromatic compound. Despite extensive investigations, the ultrafast relaxation dynamics of oNBA is still not properly understood, especially concerning the role of the triplet states. In this work, we provide an in-depth picture of this dynamics by combining single- and multireference electronic structure methods with potential energy surface exploration and nonadiabatic dynamics simulations using the Surface Hopping including ARbitary Couplings (SHARC) approach. Our results reveal that the initial decay from the bright ππ* state to the S₁ minimum is barrierless. It involves three changes in electronic structure from ππ* (ring) to nπ* (nitro group), to nπ* (aldehyde group), and then to another nπ* (nitro group). The decay of the ππ* takes 60-80 fs and can be tracked with time-resolved luminescence spectroscopy, where we predict for the first time a short-lived coherence of the luminescence energy with a 25 fs period. Intersystem crossing can occur already during the S₄ → S₁ deactivation cascade but also from S₁, with a time constant of about 2.4 ps and such that first a triplet ππ* state localized on the nitro group is populated. The triplet population first evolves into an nπ* and then quickly undergoes hydrogen transfer to form a biradical intermediate, from where the ketene is eventually produced. The majority of the excited population decays from S₁ through two conical intersections of equal utilization, a previously unreported one involving a scissoring motion of the nitro group that leads back to the oNBA ground state and the one involving hydrogen transfer that leads to the ketene intermediate.

Smooth Things Come in Threes: A Diabatic Surrogate Model for Conical Intersection Optimization

The optimization of conical intersection structures is complicated by the nondifferentiability of the adiabatic potential energy surfaces. In this work, we build a pseudodiabatic surrogate model, based on Gaussian process regression, formed by three smooth and differentiable surfaces that can adequately reproduce the adiabatic surfaces. Using this model with the restricted variance optimization method results in a notable decrease of the overall computational effort required to obtain minimum energy crossing points.

Brønsted Acids Promote Olefin Oxidations by Bioinspired Nonheme CoIII(PhIO)(OH) Complexes: A Role for Low-Barrier Hydrogen Bonds

Introduction of Brønsted acids into biomimetic nonheme reactions promotes the oxidative ability of metal-oxygen complexes significantly. However, the molecular machinery of the promoted effects is missing. Herein, a comprehensive investigation of styrene oxidation by a cobalt(III)-iodosylbenzene complex, [(TQA)Co^III(OIPh)(OH)]²⁺ (1, TQA = tris(2-quinolylmethyl)amine), in the presence and absence of triflic acid (HOTf) was performed using density functional theory calculations. Results revealed for the first time that there is a low-barrier hydrogen bond (LBHB) between HOTf and the hydroxyl ligand of 1, which forms two valence-resonance structures [(TQA)Co^III(OIPh)(HO^---HOTf)]²⁺ (1_LBHB) and [(TQA)Co^III(OIPh)(H₂O--OTf^-)]²⁺ (1'_LBHB). Due to the oxo-wall, these complexes (1_LBHB and 1'_LBHB) cannot convert to high-valent cobalt-oxyl species. Instead, styrene oxidation by these oxidants (1_LBHB and 1'_LBHB) shows novel spin-state selectivity, i.e., on the ground closed-shell singlet state, styrene is oxidized to an epoxide, whereas on the excited triplet and quintet states, an aldehyde product, phenylacetaldehyde, is formed. The preferred pathway is styrene oxidation by 1'_LBHB, which is initiated by a rate-limiting bond-formation-coupled electron transfer process with an energy barrier of 12.2 kcal mol^-1. The nascent PhIO-styrene-radical-cation intermediate undergoes an intramolecular rearrangement to produce an aldehyde. The halogen bond between the OH^-/H₂O ligand and the iodine of PhIO modulates the activity of the cobalt-iodosylarene complexes 1_LBHB and 1'_LBHB. These new mechanistic findings enrich our knowledge of nonheme chemistry and hypervalent iodine chemistry and will play a positive role in the rational design of new catalysts.

Exact non-adiabatic coupling vectors for the time-dependent density functional based tight-binding method

We report on non-adiabatic coupling vectors between electronic excited states for the time-dependent-density functional theory based tight-binding (TD-DFTB) method. The implementation includes orbital relaxation effects that have been previously neglected and covers also the case of range-separated exchange-correlation functionals. Benchmark calculations with respect to first principles TD-DFT highlight the large dependence of non-adiabatic couplings on the functional. Closer investigations of the topology around a conical intersection between excited states show that TD-DFTB delivers near-exact values of the Berry phase, which paves the way for consistent non-adiabatic molecular dynamics simulations for large systems.

Perturbing π-clouds with Substituents to Study the Effects on Reaction Dynamics of gauche-1,3-Butadiene to Bicyclobutane Electrocyclization

The conical intersection (CI) governs the ultra-fast relaxation of excited states in a radiationless manner and are observed mainly in photochemical processes. In the current work, we investigated the effects of substituents on the reaction dynamics for the conversion of gauche-1,3-butadiene to bicyclobutane via photochemical electrocyclization. We incorporated both electron withdrawing (-F) and donating (-CH₃ ) groups in the conjugated system. In our study, we optimized the minimum energy conical intersection (MECI) geometries using the multi-configurational state-averaged CASSCF approach, whereas, to study the ground state reaction pathways for the substituted derivatives, dispersion corrected, B3LYP-D3 functional was used. The non-adiabatic surface hopping molecular dynamics simulations were performed to observe the behaviour of electronic states involved throughout the photoconversion process. The results obtained from the multi-reference second-order perturbation correction of energy at the XMS-CASPT2 level of theory, topography analysis, and non-adiabatic dynamics suggest that the -CH₃ substituted derivatives can undergo faster thermal conversion to the product in the ground state with a smaller activation energy barrier compared to -F substituted derivative. Our study also reveals that the GBUT to BIBUT conversion follows both conrotatory and disrotatory pathways, whereas, on substitution with -F or -CH₃ , the conversion proceeds via the conrotatory pathway.

Extending multi-layer energy-based fragment method for excited-state calculations of large covalently bonded fragment systems

Recently, we developed a low-scaling Multi-Layer Energy-Based Fragment (MLEBF) method for accurate excited-state calculations and nonadiabatic dynamics simulations of nonbonded fragment systems. In this work, we extend the MLEBF method to treat covalently bonded fragment ones. The main idea is cutting a target system into many fragments according to chemical properties. Fragments with dangling bonds are first saturated by chemical groups; then, saturated fragments, together with the original fragments without dangling bonds, are grouped into different layers. The accurate total energy expression is formulated with the many-body energy expansion theory, in combination with the inclusion-exclusion principle that is used to delete the contribution of chemical groups introduced to saturate dangling bonds. Specifically, in a two-layer MLEBF model, the photochemically active and inert layers are calculated with high-level and efficient electronic structure methods, respectively. Intralayer and interlayer energies can be truncated at the two- or three-body interaction level. Subsequently, through several systems, including neutral and charged covalently bonded fragment systems, we demonstrate that MLEBF can provide accurate ground- and excited-state energies and gradients. Finally, we realize the structure, conical intersection, and path optimizations by combining our MLEBF program with commercial and free packages, e.g., ASE and SciPy. These developments make MLEBF a practical and reliable tool for studying complex photochemical and photophysical processes of large nonbonded and bonded fragment systems.

Modus Operandi of a Pedalo-Type Molecular Switch: Insight from Dynamics and Theoretical Spectroscopy

Molecular switches which can be triggered by light to interconvert between two or more well-defined conformation differing in their chemical or physical properties are fundamental for the development of materials with on-demand functionalities. Recently, a novel molecular switch based on a the azodicarboxamide core has been reported. It exhibits a volume-conserving conformational change upon excitation, making it a promising candidate for embedding in confined environments. In order to rationally implement and efficiently utilize the azodicarboxamide molecular switch, detailed insight into the coordinates governing the excited-state dynamics is needed. Here, we report a detailed comparative picture of the molecular motion at the atomic level in the presence and absence of explicit solvent. Our hybrid quantum mechanics/molecular mechanics (QM/MM) excited state simulations reveal that, although the energy landscape is slightly modulated by the solvation, the light-induced motion is dominated by a bending-assisted pedalo-type motion independent of the solvation. To support the predicted mechanism, we simulate time-resolved IR spectroscopy from first principles, thereby resolving fingerprints of the light-induced switching process. Our calculated time-resolved data are in good agreement with previously reported measured spectra.

Machine learning of double-valued nonadiabatic coupling vectors around conical intersections

In recent years, machine learning has had an enormous success in fitting ab initio potential-energy surfaces to enable efficient simulations of molecules in their ground electronic state. In order to extend this approach to excited-state dynamics, one must not only learn the potentials but also nonadiabatic coupling vectors (NACs). There is a particular difficulty in learning NACs in systems that exhibit conical intersections, as due to the geometric-phase effect, the NACs may be double-valued and are, thus, not suitable as training data for standard machine-learning techniques. In this work, we introduce a set of auxiliary single-valued functions from which the NACs can be reconstructed, thus enabling a reliable machine-learning approach.

Oxidation and Reduction Pathways in the Knowles Hydroamination via a Photoredox-Catalyzed Radical Reaction

Systematic reaction path exploration revealed the entire mechanism of Knowles's light-promoted catalytic intramolecular hydroamination. Bond formation/cleavage competes with single electron transfer (SET) between the catalyst and substrate. These processes are described by adiabatic processes through transition states in an electronic state and non-radiative transitions through the seam of crossings (SX) between different electronic states. This study determined the energetically favorable SET path by introducing a practical computational model representing SET as non-adiabatic transitions via SXs between substrate's potential energy surfaces for different charge states adjusted based on the catalyst's redox potential. Calculations showed that the reduction and proton shuttle process proceeded concertedly. Also, the relative importance of SET paths (giving the product and leading back to the reactant) varies depending on the catalyst's redox potential, affecting the yield.

Analytical gradients and derivative couplings for the TDDFT-1D method

We derive and implement analytic gradients and derivative couplings for time-dependent density functional theory plus one double (TDDFT-1D) which is a semiempirical configuration interaction method whereby the Hamiltonian is diagonalized in a basis of all singly excited configurations and one doubly excited configuration as constructed from a set of reference Kohn-Sham orbitals. We validate the implementation by comparing against finite difference values. Furthermore, we show that our implementation can locate both optimized geometries and minimum-energy crossing points along conical seams of S₁/S₀ surfaces for a set of test cases.

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.

Theoretical Exploration of Energy Transfer and Single Electron Transfer Mechanisms to Understand the Generation of Triplet Nitrene and the C(sp3)-H Amidation with Photocatalysts

Mechanistic explorations and kinetic evaluations were performed based on electronic structure calculations at the CASPT2//CASSCF level of theory, the Fermi's golden rule combined with the Dexter model, and the Marcus theory to unveil the key factors regulating the processes of photocatalytic C(sp³)-H amidation starting from the newly emerged nitrene precursor of hydroxamates. The highly reactive nitrene was found to be generated efficiently via a triplet-triplet energy transfer process and to be benefited from the advantages of hydroxamates with long-range charge-transfer (CT) excitation from the N-centered lone pair to the 3,5-bis(trifluoromethyl)benzoyl group. The properties of the metal-to-ligand charge-transfer (MLCT) state of photocatalysts, the functionalization of chemical moieties for substrates involved in the charge-transfer (CT) excitation, such as the electron-withdrawing trifluoromethyl group, and the energetic levels of singlet and triplet reaction pathways may regulate the reaction yield of C(sp³)-H amidation. Kinetic evaluations show that the triplet-triplet energy transfer is the main driving force of the reaction rather than the single electron transfer process. The effects of electronic coupling, molecular rigidity, and excitation energies on the energy transfer efficiency were further discussed. Finally, we investigated the inverted behavior of single-electron transfer, which is correlated unfavorably to the catalytic efficiency and amidation reaction. All theoretical explorations allow us to better understand the generation of nitrene with visible-light photocatalysts, to expand highly efficient substrate sources, and to broaden our scope of available photosensitizers for various cross-coupling reactions and the construction of N-heterocycles.

Fast Screening of Minimum Energy Crossing Points with Semiempirical Tight-Binding Methods

The investigation of photochemical processes is a highly active field in computational chemistry. One research direction is the automated exploration and identification of minimum energy conical intersection (MECI) geometries. However, due to the immense technical effort required to calculate nonadiabatic potential energy landscapes, the routine application of such computational protocols is severely limited. In this study, we will discuss the prospect of combining adiabatic potential energy surfaces from semiempirical quantum mechanical calculations with specialized confinement potential and metadynamics simulations to identify S₀/T₁ minimum energy crossing point (MECP) geometries. It is shown that MECPs calculated at the GFN2-xTB level can provide suitable approximations to high-level S₀/S₁ab initio conical intersection geometries at a fraction of the computational cost. Reference MECIs of benzene are studied to illustrate the basic concept. An example application of the presented protocol is demonstrated for a set of photoswitch molecules.

Accurate Non-Adiabatic Couplings from Optimally-Tuned Range-Separated Hybrid Functionals

Precise theoretical calculations of non-adiabatic couplings, which describe the interaction between two Born-Oppenheimer surfaces, are important for the modeling of radiationless decay mechanisms in photochemical processes. Here, we demonstrate that accurate non-adiabatic couplings can be calculated in the framework of linear-response time-dependent density functional theory by using non-empirical, optimally-tuned range-separated hybrid (OT-RSH) functionals. We focus on molecular radicals, in which ultrafast non-radiative decay plays a crucial role, to find that the OT-RSH functional compares well to wave-function based reference data and competes with the accuracy of semi-empirical CAM-B3LYP calculations. Our findings show that the OT-RSH approach provides very accurate non-adiabatic couplings and, therefore, provides a computationally efficient alternative to wave-function based techniques.

Ultrafast Intersystem Crossing Dynamics of 6-Selenoguanine in Water

Rationalizing the photochemistry of nucleobases where an oxygen is replaced by a heavier atom is essential for applications that exploit near-unity triplet quantum yields. Herein, we report on the ultrafast excited-state deactivation mechanism of 6-selenoguanine (6SeGua) in water by combining nonadiabatic trajectory surface-hopping dynamics with an electrostatic embedding quantum mechanics/molecular mechanics (QM/MM) scheme. We find that the predominant relaxation mechanism after irradiation starts on the bright singlet S₂ state that converts internally to the dark S₁ state, from which the population is transferred to the triplet T₂ state via intersystem crossing and finally to the lowest T₁ state. This S₂ → S₁ → T₂ → T₁ deactivation pathway is similar to that observed for the lighter 6-thioguanine (6tGua) analogue, but counterintuitively, the T₁ lifetime of the heavier 6SeGua is shorter than that of 6tGua. This fact is explained by the smaller activation barrier to reach the T₁/S₀ crossing point and the larger spin-orbit couplings of 6SeGua compared to 6tGua. From the dynamical simulations, we also calculate transient absorption spectra (TAS), which provide two time constants (τ₁ = 131 fs and τ₂ = 191 fs) that are in excellent agreement with the experimentally reported value (τ_exp = 130 ± 50 fs) (Farrel et al. J. Am. Chem. Soc. 2018, 140, 11214). Intersystem crossing itself is calculated to occur with a time scale of 452 ± 38 fs, highlighting that the TAS is the result of a complex average of signals coming from different nonradiative processes and not intersystem crossing alone.

InteraChem: Exploring Excited States in Virtual Reality with Ab Initio Interactive Molecular Dynamics

InteraChem is an ab initio interactive molecular dynamics (AI-IMD) visualizer that leverages recent advances in virtual reality hardware and software, as well as the graphical processing unit (GPU)-accelerated TeraChem electronic structure package, in order to render quantum chemistry in real time. We introduce the exploration of electronically excited states via AI-IMD using the floating occupation molecular orbital-complete active space configuration interaction method. The optimization tools in InteraChem enable identification of excited state minima as well as minimum energy conical intersections for further characterization of excited state chemistry in small- to medium-sized systems. We demonstrate that finite-temperature Hartree-Fock theory is an efficient method to perform ground state AI-IMD. InteraChem allows users to track electronic properties such as molecular orbitals and bond order in real time, resulting in an interactive visualization tool that aids in the interpretation of excited state chemistry data and makes quantum chemistry more accessible for both research and educational purposes.

Instanton theory for Fermi's golden rule and beyond

Instanton theory provides a semiclassical approximation for computing quantum tunnelling effects in complex molecular systems. It is typically applied to proton-transfer reactions for which the Born-Oppenheimer approximation is valid. However, many processes in physics, chemistry and biology, such as electron transfers, are non-adiabatic and are correctly described instead using Fermi's golden rule. In this work, we discuss how instanton theory can be generalized to treat these reactions in the golden-rule limit. We then extend the theory to treat fourth-order processes such as bridge-mediated electron transfer and apply the method to simulate an electron moving through a model system of three coupled quantum dots. By comparison with benchmark quantum calculations, we demonstrate that the instanton results are much more reliable than alternative approximations based on superexchange-mediated effective coupling or a classical sequential mechanism. This article is part of the theme issue 'Chemistry without the Born-Oppenheimer approximation'.

Theory of electronic resonances: fundamental aspects and recent advances

Electronic resonances are states that are unstable towards loss of electrons. They play critical roles in high-energy environments across chemistry, physics, and biology but are also relevant to processes under ambient conditions that involve unbound electrons. This feature article focuses on complex-variable techniques such as complex scaling and complex absorbing potentials that afford a treatment of electronic resonances in terms of discrete square-integrable eigenstates of non-Hermitian Hamiltonians with complex energy. Fundamental aspects of these techniques as well as their integration into molecular electronic-structure theory are discussed and an overview of some recent developments is given: analytic gradient theory for electronic resonances, the application of rank-reduction techniques and quantum embedding to them, as well as approaches for evaluating partial decay widths.

Computational development of a phase-sensitive membrane raft probe

Derivatives of the widely used 1,6-diphenyl-1,3,5-hexatriene molecular probe have been considered using a multiscale approach involving spin-flip time-dependent density functional theory, classical molecular dynamics and hybrid quantum mechanics/molecular mechanics. We identify a potential probe of membrane phase (i.e. to preferentially detect liquid-ordered regions of lipid bilayers), which exhibits restricted access to a conical intersection in the liquid-ordered phase but is freely accessible in less ordered molecular environments. The characteristics of this probe also mark it as a candidate for an aggregation induced emission fluorophore.

A Conical Intersection Influences the Ground State Rearrangement of Fulvene to Benzene

The rearrangement of fulvene to benzene is believed to play an important role in the formation of soot during hydrocarbon combustion. Previous work has identified two possible mechanisms for the rearrangement─a unimolecular path and a hydrogen-atom-assisted, bimolecular path. Computational results to date have suggested that the unimolecular mechanism faces a barrier of about 74 kcal/mol, which makes it unable to compete with the bimolecular mechanism under typical combustion conditions. This computed barrier is about 10 kcal/mol higher than the experimental value, which is an unusually large discrepancy for modern electronic structure theory. In the present work, we have reinvestigated the unimolecular mechanism computationally, and we have found a second transition state that is approximately 10 kcal/mol lower in energy than the previously identified one and, therefore, in excellent agreement with the experimental value. The existence of two transition states for the same rearrangement arises because there is a conical intersection between the two lowest singlet states which occurs in the vicinity of the reaction coordinates. The two possible paths around the cone on the lower adiabatic surface give rise to the two distinct saddle points. The lower barrier for the unimolecular mechanism now makes it competitive with the bimolecular one, according to our calculations. In support of this conclusion, we have reanalyzed some previous experimental results on anisole pyrolysis, which leads to benzene as a significant product and have shown that the unimolecular and bimolecular mechanisms for fulvene → benzene must be occurring competitively in that system. Finally, we have identified that similar conical intersections arise during the isomerizations of benzofulvene and isobenzofulvene to naphthalene.

Analytical Gradient Theory for Spin-Free State-Averaged Second-Order Driven Similarity Renormalization Group Perturbation Theory (SA-DSRG-MRPT2) and Its Applications for Conical Intersection Optimizations

Second-order multireference-driven similarity renormalization group perturbation theory (DSRG-MRPT2) provides an efficient means of correcting the dynamical correlation with the multiconfiguration reference function. The state-averaged DSRG-MRPT2 (SA-DSRG-MRPT2) method is the simplest means of treating the excited states with DSRG-MRPT2. In this method, the Hamiltonian dressed with dynamical correlation is diagonalized in the CASCI state subspace (SA-DSRG-MRPT2c) or the configuration subspace (SA-DSRG-MRPT2). This work develops analytical gradient theory for spin-free SA-DSRG-MRPT2(c) with the density-fitting approximation. We check the accuracy of the analytical gradients against the numerical gradients. We present applications for optimizing minimum energy conical intersections (MECI) of ethylene and retinal model chromophores (PSB3 and RPSB6). We investigate the dependence of the optimized geometries and energies on the flow parameters and reference relaxations. The smoothness of the SA-DSRG-MRPT2(c) potential energy surfaces near the reference (complete active space self-consistent field) MECI is comparable to the XMCQDPT2 one. These results render SA-DSRG-MRPT2(c) theory a promising approach for studies of conical intersections.

Diradical Generation via Relayed Proton-Coupled Electron Transfer

Diradical generation followed by radical-radical cross-coupling is a powerful synthetic tool, but its detailed mechanism has yet to be established. Herein, we proposed and confirmed a new model named relayed proton-coupled electron transfer (relayed-PCET) for diradical generation, which could open a door for new radical-radical cross-coupling reactions. Quantum mechanics calculations were performed on a selected carbene-mediated diradical cross-coupling reaction model and a designed model, and the exact electronic structural changes during the radical processes have been observed for the first time.

A catalyzed E/Z isomerization mechanism of stilbene using para-benzoquinone as a triplet sensitizer

Sensitizer molecules affect not only the quantum yield but also the selectivity of photochemical reactions. For an appropriate design of sensitized photochemical processes, we need to elucidate the reaction mechanism in detail. Here we investigated the mechanism of photoisomerization of stilbene via the triplet state with a para-benzoquinone sensitizer using density functional theory. In general, the isomerization of stilbene via the triplet state exhibits (Z)-selectivity (cis-selectivity); however, the para-benzoquinone sensitizer changes it to (E)-selectivity (trans-selectivity). The calculations showed that stilbene and para-benzoquinone form stable exciplexes having a preoxetane structure. The E/Z isomerization occurred via this exciplex, in which para-benzoquinone acted as a photocatalyst rather than a sensitizer only providing excitation energy. The spin-density distribution of the exciplex differed from the isolated stilbene in the triplet state. Therefore, the stilbene moiety could take (E)-conformation in the exciplex. The intermolecular charge-transfer drove the exciplex formation. This specific reaction mechanism originated from the electron-accepting ability of para-benzoquinone in the triplet state.