Ultrafast Raman observation of the perpendicular intermediate phantom state of stilbene photoisomerization.

Trans-cis photoisomerization is generally described by a model in which the reaction proceeds via a common intermediate having a perpendicular conformation around the rotating bond, irrespective of from which isomer the reaction starts. Nevertheless, such an intermediate has yet to be identified unambiguously, and it is often called the 'phantom' state. Here we present the structural identification of the common, perpendicular intermediate of stilbene photoisomerization using ultrafast Raman spectroscopy. Our results reveal ultrafast birth and decay of an identical, short-lived transient that exhibits a vibrational signature characteristic of the perpendicular state upon photoexcitation of the trans and cis forms. In combination with ab initio molecular dynamics simulations, it is shown that the photoexcited trans and cis forms are funnelled off to the ground state through the same, perpendicular intermediate.

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

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

Total and orbital density-based analyses of molecules revealing long-range interaction regions.

Total and orbital electron densities of molecules are explored for the effect of the long-range correction (LC) for density functional theory (DFT) exchange functionals by comparing to the effect of the ab initio coupled cluster singles and doubles (CCSD) method. Calculating the LC effect on the total electron densities shows that the LC stabilizes the electrons around the long-range interaction regions of kinetic energy density, which are assumed to be electrons other than free electrons and self-interacting electrons, while the CCSD method stabilizes the electrons in the long-range interaction regions in the vertical molecular planes. As a more precise test, the LC effect on orbital densities are compared to the CCSD effect on Dyson orbital densities. Surprisingly, these effects are similar for the unoccupied orbitals, indicating that the LC covers the effects required to reproduce the CCSD Dyson unoccupied orbitals. For exploring the discrepancies between these effects on the occupied orbitals, the photoionization cross sections are calculated as a direct test for the shapes of the HOMOs to investigate the differences between these effects on the occupied orbitals. Consequently, the LC clearly produces the canonical HOMOs close to the CCSD Dyson and experimental ones, except for the HOMO of benzene molecule that mixes with the HOMO - 1 for the CCSD Dyson orbitals. This indicates that the orbital analyses using the photoionization cross sections are available as a direct test for the quality of DFT functionals.

Reactive orbital energy theory serving a theoretical foundation for the electronic theory of organic chemistry.

It is established that the reactive orbital energy theory (ROET) theoretically reproduces the rule-based electronic theory diagrams of organic chemistry by a comparative study on the charge transfer natures of typical organic carbon-carbon and carbon-heteroatom bond formation reactions: aldol, Mannich, α-aminooxylation, and isogyric reactions. The ROET, which is an expansion of the reaction electronic theories (e.g., the frontier orbital theory) in terms of orbital energies, elucidates the reactive orbitals driving reactions and the charge transferability indices of the reactions. Performing the ROET analyses of these reactions shows that the charge transfer directions given in the rule-based diagrams of the electronic theory are reproduced even for the functional groups of charge transfer destinations in all but only two processes for 38 reaction processes. The ROET analyses also make clear the detailed orbital-based pictures of these bond formation reactions: that is, the use of the out-of-plane antibonding π orbitals in acidic conditions (enol-mode) and in-plane antibonding π orbitals in basic conditions (enolate-mode), which explain the experimentally assumed mechanisms such as the π-bond formations in acidic conditions and σ-bond formations at α-carbons in basic conditions. Furthermore, the ROET analyses explicate that the methyl group initially accepts electrons and then donates them to the bond formations in the target reactions. It is, consequently, suggested that the ROET serves a theoretical foundation for the electronic theory of organic chemistry.

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.

Dynamically Hidden Reaction Paths in the Reaction of CF3 + + CO.

Reaction paths on a potential energy surface are widely used in quantum chemical studies of chemical reactions. The recently developed global reaction route mapping (GRRM) strategy automatically constructs a reaction route map, which provides a complete picture of the reaction. Here, we thoroughly investigate the correspondence between the reaction route map and the actual chemical reaction dynamics for the CF3 + + CO reaction studied by guided ion beam tandem mass spectrometry (GIBMS). In our experiments, FCO+, CF2 +, and CF+ product ions were observed, whereas if the collision partner is N2, only CF2 + is observed. Interestingly, for reaction with CO, GRRM-predicted reaction paths leading to the CF+ + F2CO product channel are found at a barrier height of about 2.5 eV, whereas the experimentally obtained threshold for CF+ formation was 7.48 ± 0.15 eV. In other words, the ion was not obviously observed in the GIBMS experiment, unless a much higher collision energy than the requisite energy threshold was provided. On-the-fly molecular dynamics simulations revealed a mechanism that hides these reaction paths, in which a non-statistical energy distribution at the first collisionally reached transition state prevents the reaction from proceeding along some reaction paths. Our results highlight the existence of dynamically hidden reaction paths that may be inaccessible in experiments at specific energies and hence the importance of reaction dynamics in controlling the destinations of chemical reactions.

Extension of natural reaction orbital approach to multiconfigurational wavefunctions.

Recently, we proposed a new orbital analysis method, natural reaction orbital (NRO), which automatically extracts orbital pairs that characterize electron transfer in reaction processes by singular value decomposition of the first-order orbital response matrix to the nuclear coordinate displacements [Ebisawa et al., Phys. Chem. Chem. Phys. 24, 3532 (2022)]. NRO analysis along the intrinsic reaction coordinate (IRC) for several typical chemical reactions demonstrated that electron transfer occurs mainly in the vicinity of transition states and in regions where the energy profile along the IRC shows shoulder features, allowing the reaction mechanism to be explained in terms of electron motion. However, its application has been limited to single configuration theories such as Hartree-Fock theory and density functional theory. In this work, the concept of NRO is extended to multiconfigurational wavefunctions and formulated as the multiconfiguration NRO (MC-NRO). The MC-NRO method is applicable to various types of electronic structure theories, including multiconfigurational theory and linear response theory, and is expected to be a practical tool for extracting the essential qualitative features of a broad range of chemical reactions, including covalent bond dissociation and chemical reactions in electronically excited states. In this paper, we calculate the IRC for five basic chemical reaction processes at the level of the complete active space self-consistent field theory and discuss the phenomenon of electron transfer by performing MC-NRO analysis along each IRC. Finally, issues and future prospects of the MC-NRO method are discussed.

Reaction Space Projector (ReSPer) for Visualizing Dynamic Reaction Routes Based on Reduced-Dimension Space.

To analyze chemical reaction dynamics based on a reaction path network, we have developed the "Reaction Space Projector" (ReSPer) method with the aid of the dimensionality reduction method. This program has two functions: the construction of a reduced-dimensionality reaction space from a molecular structure dataset, and the projection of dynamic trajectories into the low-dimensional reaction space. In this paper, we apply ReSPer to isomerization and bifurcation reactions of the Au5 cluster and succeed in analyzing dynamic reaction routes involved in multiple elementary reaction processes, constructing complicated networks (called "closed islands") of nuclear permutation-inversion (NPI) isomerization reactions, and elucidating dynamic behaviors in bifurcation reactions with reference to bundles of trajectories. Interestingly, in the second application, we find a correspondence between the contribution ratios in the ability to visualize and the symmetry of the morphology of closed islands. In addition, the third application suggests the existence of boundaries that determine the selectivity in bifurcation reactions, which was discussed in the phase space. The ReSPer program is a versatile and robust tool to clarify dynamic reaction mechanisms based on the reduced-dimensionality reaction space without prior knowledge of target reactions.

Natural reaction orbitals for characterizing electron transfer responsive to nuclear coordinate displacement.

The natural reaction orbital (NRO) is proposed as a new concept for analyzing chemical reactions from the viewpoint of the electronic theory. The pair of the occupied and virtual NROs that characterize electron transfer responsive to nuclear coordinate displacement along the reaction path is automatically extracted from the solution of the coupled-perturbed self-consistent-field (CPSCF) equation for the perturbation of the nuclear displacement. The NRO-based reaction analysis method is applied to several reactions. As a result, it is found that the sum of squares of the singular values, derived from the solution of the CPSCF equation, gives sharp peaks around the transition state structures and at the shoulders of the potential energy curve. The peaks around the transition states suggest a new physical meaning of transition state from the viewpoint of the electronic theory. Furthermore, the double peaks reveal the asynchronous processes of reactions, which are not always shown in potential energy analyses. Since the NRO-based reaction analysis method is universal and robust for describing reaction mechanisms from an electronic theory viewpoint, it is expected to lead to universal reaction analyses based on the electronic theory.

One-to-One Correspondence between Reaction Pathways and Reactive Orbitals.

The one-to-one correspondence between reaction pathways in the potential energy theory and reactive orbitals in the electronic theory for reactions is presented. In this study, the reactive orbital energy method is applied to the intrinsic reaction coordinates of the global reaction route map generated by an automated reaction path search method. The reactive orbital energy method specifies the pairs of occupied and unoccupied reactive orbitals driving chemical reactions and determines whether the reactions are electron transfer-driven or dynamics-driven. Surprisingly, it is found that the reactive orbital pairs are determined one by one for the electron transfer-driven reaction pathways from an identical molecule. The reactive orbital energy method is also found to provide the sophisticated interpretations of reactions for the electronic motions. This one-to-one correspondence is expected to trigger the unification of the potential energy theory and the electronic theory for reactions that have been independently developed.

Visualization of reaction route map and dynamical trajectory in reduced dimension.

In the quantum chemical approach, chemical reaction mechanisms are investigated based on a potential energy surface (PES). Automated reaction path search methods enable us to construct a global reaction route map containing multiple reaction paths corresponding to a series of elementary reaction processes. The on-the-fly molecular dynamics (MD) method provides a classical trajectory exploring the full-dimensional PES based on electronic structure calculations. We have developed two reaction analysis methods, the on-the-fly trajectory mapping method and the reaction space projector (ReSPer) method, by introducing a structural similarity to a pair of geometric structures and revealed dynamic aspects affecting chemical reaction mechanisms. In this review, we will present the details of these analysis methods and discuss the dynamics effects of reaction path curvature and reaction path bifurcation with applications to the CH3OH + OH- collision reaction and the Au5 cluster branching and isomerization reactions.

Real-Time Probing of an Atmospheric Photochemical Reaction by Ultrashort Extreme Ultraviolet Pulses: Nitrous Acid Release from o-Nitrophenol.

Photolysis of o-nitrophenol, contained in brown carbon, is considered to be a major process for the generation of nitrous acid (HONO) in the atmosphere. In this Letter, we used time-resolved photoelectron spectroscopy with 29.5 eV probe pulses and ab initio calculations to disentangle all reaction steps from the excitation to the dissociation of HONO. After excitation, intersystem crossing to the triplet manifold follows ultrafast excited-state intramolecular hydrogen transfer, where the molecules deplanarizes and finally splits off HONO after 0.5-1 ps.

Geometric analysis of anharmonic downward distortion following paths.

A mathematical aspect of the anharmonic downward distortion following (ADDF) path is discussed. The ADDF method is utilized as an automated reaction path search method, which can explore transition state geometries on a potential energy surface from a potential minimum. We show that the maximum number of the ADD stationary paths intersecting the potential minimum is 2f + 1 - 2, where f denotes the degree of freedom of the system. We also show that the bifurcation of the ADD stationary path is essential to detect all the transition states connected from a given minimum. The ADDF computation is demonstrated for a H2 O molecule in which pitchfork bifurcation is observed.

Visualization of the Dynamics Effect: Projection of on-the-Fly Trajectories to the Subspace Spanned by the Static Reaction Path Network.

Following our recent work to reduce a dimension of a set of reference structures along the intrinsic reaction coordinate (IRC) by a classical multidimensional scaling (CMDS) approach (J. Chem. Theory Comput. 2018, 14, 4263-4270), we propose the method to project on-the-fly trajectories into a reduced-dimension subspace determined by the IRC network, using the out-of-sample extension of CMDS. The method was applied to the SN2 reaction, OH- + CH3F, in which trajectories show a bifurcating nature around the highly curved region of the IRC path, and to the structural transformation of Au5 cluster in which the global reaction path network consists of five equilibrium structures and 14 IRCs. It was demonstrated that the present analysis can visualize the dynamics effect by showing a dynamic reaction route on the basis of the static reaction paths.

Visualization of the Intrinsic Reaction Coordinate and Global Reaction Route Map by Classical Multidimensional Scaling.

A classical multidimensional scaling (CMDS) method is employed to visualize an intrinsic reaction coordinate (IRC) and a global reaction route map consisting of the equilibrium minima and transition state structures connected by the IRC network. As demonstrations, the method was applied to the IRCs of the intramolecular proton transfer in malonaldehyde and the SN2 reaction of OH- + CH3F → CH3OH + F-, which are both well described by two principal coordinates. Next, the method was applied to the global reaction route map of the Au5 cluster; the resulting map shows appropriate positions of five minima and 14 transition states in a reduced 2- or 3-dimensional coordinate space successfully.

Analyses of trajectory on-the-fly based on the global reaction route map.

A methodology to analyze a trajectory on-the-fly (TOF) based on a global reaction route map consisting of intrinsic reaction coordinate (IRC) pathways is proposed. By using the distance functions in the configurational space, the location of each point on the trajectories is detected, providing a dynamical picture that the molecular system goes over several minima and transition states in the reaction path network. In its application to structural transformations of an Au5 cluster, a variety of reaction routes are obtained, and the hopping from one IRC to another IRC (IRC-jump) is analyzed. The branching of trajectories over many minima on the potential energy surface via valley-ridge transition points is also discussed.