Theoretical study on the carbon nanomaterial-supported Pt complex electrocatalysts for efficient and selective chlorine evolution reaction.

Chlorine is an important chemical which has long been produced in chlor-alkali process using dimensionally stable anodes (DSA). However, some serious drawbacks of DSA inspire the development of alternative anodes for chlorine evolution reaction (CER). In this study, we focused on the graphene- and carbon nanotube-supported platinum tetra-phenyl porphyrins as electrocatalysts for CER, which have been theoretically investigated based on density functional theory. Our results reveal that the supported substrates possess potential CER electrocatalytic activity with very low thermodynamic overpotentials (0.012-0.028 V) via Cl* pathway instead of ClO*. The electronic structures analyses showed that electron transfer from the support to the adsorbed chlorine via the Pt center leads to strong Pt-Cl interactions. Furthermore, the supported electrocatalysts exhibited excellent selectivity toward CER because of high overpotentials and reaction barriers of oxygen evolution process. Therefore, our results may pave the way for designing CER electrocatalyst utilizing emerging carbon nanomaterials.

Development and Investigation of a Grasping Analysis System with Two-Axis Force Sensors at Each of the 16 Points on the Object Surface for a Hardware-Based FinRay-Type Soft Gripper.

The FinRay soft gripper achieves passive enveloping grasping through its functional flexible structure, adapting to the contact configuration of the object to be grasped. However, variations in beam position and thickness lead to different behaviors, making it important to research the relationship between structure and force. Conventional research using FEM simulations has tested various virtual FinRay models but replicating phenomena such as buckling and slipping has been challenging. While hardware-based methods that involve installing sensors on the gripper and the object to analyze their states have been attempted, no studies have focused on the tangential contact force related to slipping. Therefore, we developed a 16-way object contact force measurement device incorporating two-axis force sensors into each of the 16 segmented objects and compared the normal and tangential components of the enveloping grasping force of the FinRay soft gripper under two types of contact friction conditions. In the first experiment, the proposed device was compared with a device containing a six-axis force sensor in one segmented object, confirming that the proposed device has no issues with measurement performance. In the second experiment, comparisons of the proposed device were made under various conditions: two contact friction states, three object contact positions, and two object motion states. The results demonstrated that the proposed device could decompose and analyze the grasping force into its normal and tangential components for each segmented object. Moreover, low friction conditions result in a wide contact area with lower tangential frictional force and a uniform normal pushing force, achieving effective enveloping grasping.

Water-Tolerant Superbase Polyoxometalate [H2(Nb6O19)]6- for Homogeneous Catalysis.

Here, doubly protonated Lindqvist-type niobium oxide cluster [H2(Nb6O19)]6-, fabricated by microwave-assisted hydrothermal synthesis, exhibited superbase catalysis for Knoevenagel and crossed aldol condensation reactions accompanied by activating C-H bond with pKa >26 and proton abstraction from a base indicator with pKa=26.5. Surprisingly, [H2(Nb6O19)]6- exhibited water-tolerant superbase properties for Knoevenagel and crossed aldol condensation reactions in the presence of water, although it is well known that the strong basicity of metal oxides and organic superbase is typically lost by the adsorption of water. Density functional theory calculation revealed that the basic surface oxygens that share the corner of NbO6 units in [H2(Nb6O19)]8- maintained the negative charges even after proton adsorption. This proton capacity and the presence of un-protonated basic sites led to the water tolerance of the superbase catalysis.

How does multi-reference computation change the catalysis chemistry? DFT and CASPT2 studies of the Cu-catalysed coupling reactions between aryl iodides and ß-diketones.

The molecular mechanism of a Cu-catalysed coupling reaction was theoretically studied using density functional theory (DFT) and the complete active space self-consistent field method followed by the second-order perturbation theory (CASSCF/CASPT2) to investigate the effects of the strong electron correlation of the Cu centre on the reaction profile. Both DFT and CASSCF/CASPT2 calculations showed that the catalytic cycle proceeds via an oxidative addition (OA) reaction, followed by a reductive elimination (RE) reaction, where OA is the rate-determining step. Although the DFT-calculated activation energies of the OA and RE steps are highly dependent on the choice of functionals, the CASSCF/CASPT2 results are less affected by the choice of DFT-optimised geometries. Therefore, with a careful assessment based on the CASSCF/CASPT2 single-point energy evaluation, an optimal choice of the DFT geometry is of good qualitative use for energetics at the CASPT2 level of theory. Based on the changes in the electron populations of the 3d orbitals during the OA and RE steps, the characteristic features of the DFT-calculated electronic structure were qualitatively consistent with those calculated using the CASSCF method. Further electronic structure analysis by the natural orbital occupancy of the CASSCF wavefunction showed that the ground state is almost single-reference in this system and the strong electron correlation effect of the Cu centre can be dealt with using the MP2 or CCSD method, too. However, the slightly smaller occupation numbers of the 3dπ orbital in the course of reactions suggested that the electron correlation effect of the Cu(III) centre appears through the interaction between the 3dπ orbital and the C-I antibonding σ* orbital in the OA step, and between the 3dπ orbital and the Cu-C antibonding σ* orbital in the RE step.

Analysis of Contact Force and Shape Change on Grasping a Square Object Using an Actual Fin Ray Soft Gripper.

The Fin Ray-type soft gripper (FRSG) is a typical soft gripper structure and applies the deformation characteristics of the Fin Ray structure. This structure functions to stabilize the grasping of an object by passive deformation due to external forces. To analyze the performance of detailed force without compromising the actual FRSG characteristics, it is effective to incorporate multiple force sensors into the grasping object without installing them inside the Fin Ray structure. Since the grasping characteristics of the FRSG are greatly affected by the arrangement of the crossbeams, it is also important to understand the correspondence between the forces and the geometry. In addition, the grasping characteristics of an angular object have not been verified in actual equipment. Therefore, in this study, a contact force measurement device with 16 force sensors built into the grasping object and a structural deformation measurement device using camera images were used to analyze the correspondence between force and structural deformation on an actual FRSG. In the experiment, we analyzed the influence of the crossbeam arrangement on the grasping force and the grasping conditions of the square (0°) and rectangular (45°) shapes, and state that an ideal grasp in a square-shaped (45°) grasp is possible if each crossbeam in the FRSG is arranged at a different angle.

Mechanistic Insights into the Selectivity of Norcarane Oxidation by Oxo-Manganese(V) Porphyrin Complexes.

Oxo-Mn(V) porphyrin complexes perform competitive hydroxylation, desaturation, and radical rearrangement reactions using diagnostic substrate norcarane. Initial C-H cleavage proceeds through the two hydrogen abstraction steps from the two adjacent carbon on the norcarane and then through selective reactions various products are generated. Using density functional theory calculations, we show that the hydroxylation and desaturation reactions are triggered by a rate-determining H-abstraction step, whereas the rate-determining step for the radical rearrangement is located at the rebound step (TS2). We find that the endo-2 reaction is favorable over other reactions, which is consistent with the experimental result. Furthermore, the competitive pathways for norcarane oxidation depend on the non-covalent interaction between norcarane and the porphyrin-ring, and orbital energy gaps between donor and acceptor orbitals because of stable or unstable acceptor orbital. The stereo- and regio-selectivities of norcarane oxidation are hardly sensitive to the zero-point energy and thermal free energy corrections.

Theoretical Study on the Vapochromic Ni(II)-Quinonoid Complex: One-Dimensional Stacking Structure-Based Color Switching.

Vapochromic crystals of Ni(II)-quinonoid complexes were theoretically investigated using density functional theory (DFT) calculations. Kato et al. previously reported that the purple crystals of a four-coordinate Ni(II)-quinonoid complex (1P) exhibited vapochromic characteristics upon exposure to methanol gas, resulting in orange crystals of the six-coordinate methanol-bound complex (1O) [Angew. Chem., Int. Ed.2017, 56, 2345-2349]. However, the authors did not characterize the crystal structure of 1P. In the present study, we computationally predicted the crystal structure of 1P by performing a crystal structure search with classical force-field computations followed by optimization using DFT calculations. The simulated powder X-ray diffraction pattern of the DFT-optimized structure agreed with experimental observations, indicating that our predicted crystal structure is reliable. Investigation of the optimized crystal structure of 1P revealed that its color change arose from changes in its 1D-band structure, which consists of Ni 3d orbitals and quinonoid π-orbitals. Intermolecular interactions were weakened upon the binding of methanol to the Ni(II) center in 1O. Consequently, the intermolecular 3d-π interaction in 1P lowered the band gap and induced the red-shifting of the monomeric four-coordinate Ni(II)-quinonoid complex. Meanwhile, the obtained absorption spectrum of 1O closely corresponded to that of the monomeric six-coordinate Ni(II)-quinonoid complex. Our study provides a new strategy for accurately predicting molecular crystal structures and reveals a new insight into vapochromism based on band structure color switching.

Insights into the electronic structure and mechanism of norcarane hydroxylation by OxoMn(V) porphyrin complexes: A density functional theory study.

Norcarane hydroxylation by neutral [PorMn(V)O-L] (L═OH- , F- ) and cationic [PorMn(V)O-L]+ (L═H2 O, imidazole) oxoMn(V) porphyrin complex models has been investigated by density functional theory calculations to better understand the reaction mechanism and electronic structure. We found that the energy barriers of norcarane hydroxylation by cationic oxoMn(V) porphyrin complexes are lower than those by neutral oxoMn(V) porphyrin complexes. This indicates that cationic oxoMn(V) porphyrin complexes enhance norcarane hydroxylation compared with neutral oxoMn(V) porphyrin complexes. According to electronic structure analysis, in the C─H activation step, electron transfer occurs through initial interaction between the σCH and rich-oxygen π(Mn═O) orbitals to form real donor orbitals, followed by transfer to the acceptor π*(Mn═O) orbitals. Moreover, single electron shifts from norcarane (CH) to Mn atom during C─H activation. The positive charge of the cationic complex stabilizes the acceptor orbital more than the donor orbital, reducing the energy gap between these orbitals, thus lowering the reaction barrier.

Thermal stability of crown-motif [Au9(PPh3)8]3+ and [MAu8(PPh3)8]2+ (M = Pd, Pt) clusters: Effects of gas composition, single-atom doping, and counter anions.

The thermal behaviors of ligand-protected metal clusters, [Au9(PPh3)8]3+ and [MAu8(PPh3)8]2+ (M = Pd, Pt) with a crown-motif structure, were investigated to determine the effects of the gas composition, single-atom doping, and counter anions on the thermal stability of these clusters. We successfully synthesized crown-motif [PdAu8(PPh3)8][HPMo12O40] (PdAu8-PMo12) and [PtAu8(PPh3)8][HPMo12O40] (PtAu8-PMo12) salts with a cesium-chloride-type structure, which is the same as the [Au9(PPh3)8][PMo12O40] (Au9-PMo12) structure. Thermogravimetry-differential thermal analysis/mass spectrometry analysis revealed that the crown-motif structure of Au9-PMo12 was decomposed at ∼475 K without weight loss to form Au nanoparticles. After structural decomposition, the ligands were desorbed from the sample. The ligand desorption temperature of Au9-PMo12 increased under 20% O2 conditions because of the formation of Au nanoparticles and stronger interaction of the formed O=PPh3 than PPh3. The Pd and Pt single-atom doping improved the thermal stability of the clusters. This improvement was due to the formation of a large bonding index of M-Au and a change in Au-PPh3 bonding energy by heteroatom doping. Moreover, we found that the ligand desorption temperatures were also affected by the type of counter anions, whose charge and size influence the localized Coulomb interaction and cluster packing between the cationic ligand-protected metal clusters and counter anions.

Time-dependent DFT study of the K-edge spectra of vanadium and titanium complexes: effects of chloride ligands on pre-edge features.

X-ray absorption near edge structures (XANES) of vanadium and titanium complexes were investigated with time-dependent density functional theory (TDDFT). In particular, observed characteristic K-edge features in the presence of chloride ligands were assigned. Although TDDFT includes a large systematic error attributed to the 1s core energy levels of transition metals, pre-edge spectral shapes could be reproduced by a simple energy shift in the calculated excitation energies. The doublet peak in the pre-edge region was assigned to dipole-allowed transitions from 1s to 3d + 4p hybridized orbitals, while a characteristic shoulder peak in the chloride complex was assigned to excitations of chloride 4p orbitals. A similar but weak absorption band was computed for the methyl complex as excitation to C-H σ* orbitals. However, because these excitations were highly dependent on the direction of the C-H bonds, the shoulder peak was not experimentally observed because of methyl free rotation. Hence, the intensity of the shoulder peak was proportional to the number of chloride ligands unless other ligands contribute to this energy region and, therefore, could be used to detect the presence or absence of chloride ligands in unknown compounds, such as reaction intermediates.

DFT insight into axial ligand effects on electronic structure and mechanistic reactivity of oxoiron(iv) porphyrin.

A series of DFT studies on the epoxidation reactions of olefins by oxoiron(iv) porphyrin cation radical complexes are performed in this work, to elucidate the axial ligand effects on the electronic features and reaction mechanism in detail. We analyzed the molecular orbitals, spin populations, and Mulliken charges along the intrinsic reaction coordinate route. From the findings, we confirmed that the interaction between the axial ligand and the oxoiron(iv) porphyrin is strong and the initial changes in the electronic structures occur early during the reaction, which further enhances the reactivity toward olefin epoxidation. More importantly, the patterns of the electron transfer from olefin to oxoiron(iv) porphyrin were impacted by the axial ligand. The pattern of successive electron transfer from Fe-O to porphyrin and then from C[double bond, length as m-dash]C to Fe-O for oxoiron(iv) porphyrin in case of fluorine and acetate axial ligands, whereas the pattern of electron transfer occurs from C[double bond, length as m-dash]C to porphyrin for oxoiron(iv) porphyrin in case of chlorine and nitrate axial ligands during the epoxidation reaction of the olefins. We also determined the intersystem crossing between the quartet and sextet spin states occurring at the second transition state (TS2) by the analysis of the two-dimensional potential energy surface.

Extending nudged elastic band method to reaction pathways involving multiple spin states.

There are diverse reactions including spin-state crossing, especially the reactions catalyzed by transition metal compounds. To figure out the mechanisms of such reactions, the discussion of minimum energy intersystem crossing (MEISC) points cannot be avoided. These points may be the bottleneck of the reaction or inversely accelerate the reactions by providing a better pathway. It is of great importance to reveal their role in the reactions by computationally locating the position of the MEISC points together with the reaction pathway. However, providing a proper initial guess for the structure of the MEISC point is not as easy as that of the transition state. In this work, we extended the nudged elastic band (NEB) method for multiple spin systems, which is named the multiple spin-state NEB method, and it is successfully applied to find the MEISC points while optimizing the reaction pathway. For more precisely locating the MEISC point, a revised approach was adopted. Meanwhile, our examples also suggest that special attention should be paid to the criterion to define an image optimized as the MEISC point.

Can large active-space CASSCF calculation make sense to the reaction analysis of iron complex? A benchmark study of methane oxidation reaction by FeO.

A methane oxidation reaction by FeO+ cation was theoretically investigated based on the density functional theory (DFT) and the complete active-space self-consistent field (CASSCF) method as well as the coupled-cluster singles, doubles, and perturbative triples (CCSD(T)) to explore the active-space dependency to computational analyses in such strongly correlated reaction systems. A small active-space CASSCF(5e in 5o) calculation, which only includes five 3d orbitals of the Fe atom in the active-space, showed remarkable difference both in energy and geometry compared to those computed by the DFT and CCSD(T) methods. Interestingly, a large active-space CASSCF(17e in 17o) calculation, which includes almost all the valence orbitals gives a qualitative agreement with either the DFT or the CCSD(T) results in the first half part of the reaction, although it varies from them in the latter half part. Therefore, it is indicated that the active-space dependency is serious in some part of the reaction and the small active-space CASSCF might lead a wrong discussion. We further investigated the optimized geometry of the intermediate complex with the small and the large active-space CASSCF methods as well as the CCSD(T) method, and found that the CASSCF(5e in 5o)-optimized geometry is considerably different from the others. In consequence, a small active-space CASSCF/CASPT2 calculation does not really work for such a strongly correlated reaction system even qualitatively, and a sophisticated assessment using the large active-space CASSCF/CASPT2 method will be indispensable. © 2018 Wiley Periodicals, Inc.

Substitution effects on olefin epoxidation catalyzed by Oxoiron(IV) porphyrin π-cation radical complexes: A dft study.

The effects of peripheral fluorine atoms on epoxidation reactions of ethylene by oxoiron(IV) porphyrin cation radical complex in the quartet and sextet spin multiplicities are systematically investigated using the DFT method. The overall reaction routes are determined using a model system of ethylene and Fe(IV)OCl-porphyrin with substituted fluorine atoms. By obtaining the energy diagrams and electron- and spin-density difference contour maps of the transition states and intermediate compounds, we confirm that the electron-withdrawing by peripheral fluorine atoms enhances the reactivity as the number of fluorine atoms increases, as is observed experimentally. The intersystem crossing between the quartet and sextet spin multiplicities is discussed by means of the intrinsic reaction coordinate method. We conclude that the rate-determining step is located at the first transition state (TS1) for the activation of CC and FeO bonds, and the ground electronic state changes from quartet to sextet around the TS1. © 2019 Wiley Periodicals, Inc.

Theoretical Study on the Rhodium-Catalyzed Hydrosilylation of C═C and C═O Double Bonds with Tertiary Silane.

Reaction mechanisms of hydrosilylation of ketone and alkene with tertiary silane using the Wilkinson-type catalyst were theoretically investigated on the basis of density functional calculations using ωB97XD functional. Previously proposed three mechanisms, the Chalk-Harrod (CH) mechanism, the modified Chalk-Harrod (mCH) mechanism, and the outer-sphere mechanism were examined. Besides, we also found two mechanisms, the alternative CH (aCH) mechanism and the double hydride (DH) mechanism. In the aCH mechanism, a four-coordinate rhodium hydride complex formed through the elimination of R3Si-Cl is a catalytically active species. In the DH mechanism, the active species is a six-coordinate complex with two Rh-H bonds. For the C═O double bond hydrosilylation, the rate-determining steps of the aCH and DH mechanisms are both acetone insertion into the Rh-H bond, and the order of the activation barrier is DH < aCH ≈ CH < mCH. For the C═C double bond hydrosilylation, except for the mCH pathway whose rate-determining step is the hydrosilane addition reaction, the rate-determining steps of the CH, aCH, and DH pathways are Si-C reductive elimination reactions. The order of the energy barrier is DH ≈ mCH < aCH ≈ CH. In the outer-sphere mechanism, no stable intermediate or transition state was found. Consequently, we concluded that the DH mechanism is adopted as the mechanism for the Rh-catalyzed hydrosilylation of the carbonyl group while the mCH or DH mechanism is adopted as the mechanism for alkenes under conditions where their active intermediates are formed. The present result revises a hypothesis that the hydrosilylation of the carbonyl group is in general accomplished by the mCH mechanism. The active species in the DH mechanism has one more extra Rh-H bond compared to that of the other pathways, and its interaction with a silyl group, trans-influence, and small steric effect are the origin of the highly efficient catalytic activity, which was not reported before.

How to understand very weak Cr-Cr double bonds and negative spin populations in trinuclear Cr complexes: theoretical insight.

Trinuclear Cr(ii) complex [Cr3(dpa)4Cl2] 1 (Hdpa = dipyridylamine) has two Cr-Cr double bonds linked with each other. DMRG-CASPT2 calculations reproduced its symmetrical structure. The Cr-Cr effective bond order (EBO) was evaluated to be only 0.59 based on the density matrix based on localized orbitals from DMRG-CASSCF orbitals. The CASCI calculations showed a significantly large α-spin population on the terminal Cr atoms as expected but a significantly large ß-spin population on the central Cr atom against expectations. The very small EBO and the presence of a large ß-spin population are not consistent with the simple understanding that 1 has two Cr-Cr double bonds and a quintet ground state, which requests correct understanding of 1 from the viewpoint of chemical bond theory. Comparison of 1 with the allene molecule and allyl radical disclosed that the linked Cr-Cr bonds of 1 resembled the C-C bond of the allyl radical but completely differed from the linked C-C double bonds of allene despite the similar molecular structure. Its N3 analogue [Cr3(dpa)4(N3)2] 2 has non-symmetrical structure with shorter Cr1-Cr2 and longer Cr2-Cr3 bonds unlike 1, indicating that 2 is a valence tautomer of 1. DMRG-CASPT2 could reproduce its non-symmetrical structure but DFT/B3PW91 could not. In 2, the EBO is 0.95 for the shorter Cr1-Cr2 bond and 0.47 for the longer Cr2-Cr3 one. The terminal Cr3 has a very large α spin population, and the other terminal Cr1 has a somewhat large α spin population, but the central Cr2 has a considerably large ß spin population. These results indicate that the Cr1-Cr2 bond conjugates with the Cr2-Cr3 bond, which is inconsistent with the simple understanding that 2 has a quadruple bond between Cr1 and Cr2 and no bond between Cr2 and Cr3. The symmetrical structure has a stronger Cr-X coordinate bond (X = Cl or N3) but less stable Cr3 core than does the non-symmetrical one. The relative stabilities of the symmetrical and the non-symmetrical structures are determined by the balance between stabilization energies from the Cr3 core and the Cr-X coordinate bond. All these findings show that electronic structures and Cr-Cr bonds of 1 and 2 are interesting from the viewpoint of molecular science.

Specific Spatial Localization of Actin and DNA in a Water/Water Microdroplet: Self-Emergence of a Cell-Like Structure.

The effect of binary hydrophilic polymers on a pair of representative bio-macromolecules in a living cell has been examined. The results showed that these bio-macromolecules exhibited specific localization in cell-sized droplets that were spontaneously formed through water/water microphase segregation under crowding conditions with coexisting polymers. In these experiments, a simple binary polymer system with poly(ethylene glycol) (PEG) and dextran (DEX) was used. Under the conditions of microphase segregation, DNA was entrapped within cell-sized droplets rich in DEX. Similarly, F-actin, linearly polymerized actin, was entrapped specifically within microdroplets rich in DEX, whereas G-actin, a monomeric actin, was distributed evenly inside and outside these droplets. This study has been extended to a system with both F-actin and DNA, and it was found that DNA molecules were localized separately from aligned F-actin proteins to create microdomains inside microdroplets, reflecting the self-emergence of a cellular morphology similar to a stage of cell division.

Spin-Blocking Effect in CO and H2 Binding Reactions to Molybdenocene and Tungstenocene: A Theoretical Study on the Reaction Mechanism via the Minimum Energy Intersystem Crossing Point.

Potential energy profiles and electronic structural interpretation of the CO and H2 binding reactions to molybdenocene and tungstenocene complexes [MCp2] (M = Mo and W, Cp = cycropentadienyl) were studied using density functional theory calculations and ab initio multiconfigurational electronic structure calculations. Experimentally observed slow H2 binding was reasonably explained in terms of the spin-blocking effect. Electronic structural analysis at the minimum-energy intersystem crossing point (MEISCP) revealed that the singly occupied molecular orbital's π-bonding/σ-antibonding character in the M-CO/H2 moiety determines the energy levels of the MEISCP. Analysis of the reaction coordinate showed that the singlet-triplet gap significantly depends on the Cp-M-Cp angle. Therefore, not only the metal-ligand distance but also the Cp-M-Cp angle is an important reaction coordinate to reach the MEISCP, the transition state of H2 binding. The role of spin-orbit coupling is also discussed.

Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms.

Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In this work, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms.

Energy dissipative photoprotective mechanism of carotenoid spheroidene from the photoreaction center of purple bacteria Rhodobacter sphaeroides.

Carotenoid spheroidene (SPO) functions for photoprotection in the photosynthetic reaction centers (RCs) and effectively dissipates its triplet excitation energy. Sensitized cis-to-trans isomerization was proposed as a possible mechanism for a singlet-triplet energy crossing for the 15,15'-cis-SPO; however, it has been questioned recently. To understand the dissipative photoprotective mechanism of this important SPO and to overcome the existing controversies on this issue, we carried out a theoretical investigation using density functional theory on the possible triplet energy relaxation mechanism through the cis-to-trans isomerization. Together with the earlier experimental observations, the possible mechanism was discussed for the triplet energy relaxation of the 15,15'-cis-SPO. The result shows that complete cis-to-trans isomerization is not necessary. Twisting the C15-C15' bond leads to singlet-triplet energy crossing at ϕ(14,15,15',14') = 77° with an energy 32.5 kJ mol(-1) (7.7 kcal mol(-1)) higher than that of the T1 15,15'-cis minimum. Further exploration of the minimum-energy intersystem crossing (MEISC) point shows that triplet relaxation could occur at a less distorted structure (ϕ = 58.4°) with the energy height of 26.5 KJ mol(-1) (6.3 kcal mol(-1)). Another important reaction coordinate to reach the MEISC point is the bond-length alternation. The model truncation effect, solvent effect, and spin-orbit coupling were also investigated. The singlet-triplet crossing was also investigated for the 13,14-cis stereoisomer and locked-13,14-cis-SPO. We also discussed the origin of the natural selection of the cis over trans isomer in the RC.