Elastic Image Pair Method for Finding Transition States on Potential Energy Surfaces Using Only First Derivatives

Theoretical study on hydroformylation catalyzed by cationic cobalt(II) complexes

Hydroformylation is one of the most important homogeneous reactions in industrial production. Herein, a density functional theory (DFT) method was employed to investigate two proposed reaction mechanisms of hydroformylation catalyzed by cationic cobalt(II) complexes, the carbonyl dissociative mechanism and the associative mechanism. The calculated results showed that the heterolytic H2 activation is the rate-determining step for both the dissociative mechanism and the associative mechanism, with energy barriers of 26.8 kcal mol-1 and 40.5 kcal mol-1, respectively. Meanwhile, the regioselectivity, the spin multiplicity of the catalyst and the substituent effects on the reaction were also investigated. The most stable cobalt(II) catalyst has a doublet state and the linear aldehyde is the dominant product. In addition, it was found that the energy barrier of the reaction decreased when the electron density of the Co center of the catalyst was increased by changing the ligand. The catalytic activity of the catalyst was proposed to be the best when the PEt2 group of the ligand is replaced by the P(tBu)2 group. This study might not only provide new insights for hydroformylation catalyzed by cobalt but also facilitate theory-guided design of novel transition metal catalysts for hydroformylation.

Locating Transition States by Variational Reaction Path Optimization with an Energy-Derivative-Free Objective Function

Locating transition states is essential for understanding molecular reactions. We propose a double-ended transition state search method by revisiting a variational reaction path optimization method known as the MaxFlux method. Although its original purpose is to add temperature effects to reaction paths, we conversely let the temperature approach zero to obtain an asymptotically exact minimum energy path and its corresponding transition state in variational formalism with an energy-derivative-free objective function. Using several numerical techniques to directly optimize the objective function, the present method reliably finds transition states with low computational cost. In particular, only three force evaluations per iteration are sufficient. This is confirmed on a variety of molecular reactions where the nudged elastic band method often fails. The present method is implemented in Python using the Atomic Simulation Environment and is available on GitHub.

Cyclopentadienone Diphosphine Ruthenium Complex: A Designed Catalyst for the Hydrogenation of Carbon Dioxide to Methanol

The development of homogeneous metal catalysts for the efficient hydrogenation of carbon dioxide (CO2) into methanol (CH3OH) remains a significant challenge. In this study, a new cyclopentadienone diphosphine ligand (CPDDP ligand) was designed, which could coordinate with ruthenium to form a Ru-CPDDP complex to efficiently catalyze the CO2-to-methanol process using dihydrogen (H2) as the hydrogen resource based on density functional theory (DFT) mechanistic investigation. This process consists of three catalytic cycles, stage I (the hydrogenation of CO2 to HCOOH), stage II (the hydrogenation of HCOOH to HCHO), and stage III (the hydrogenation of HCHO to CH3OH). The calculated free energy barriers for the hydrogen transfer (HT) steps of stage I, stage II, and stage III are 7.5, 14.5, and 3.5 kcal/mol, respectively. The most favorable pathway of the dihydrogen activation (DA) steps of three stages to regenerate catalytic species is proposed to be the formate-assisted DA step with a free energy barrier of 10.4 kcal/mol. The calculated results indicate that the designed Ru-CPDDP and Ru-CPDDPEt complexes could catalyze hydrogenation of CO2 to CH3OH (HCM) under mild conditions and that the transition-metal owning designed CPDDP ligand framework be one kind of promising potential efficient catalysts for HCM.

A general method for locating stationary points on the mixed-spin surface of spin-forbidden reaction with multiple spin states

Some chemical reactions proceed on multiple potential energy surfaces and are often accompanied by a change in spin multiplicity, being called spin-forbidden reactions, where the spin-orbit coupling (SOC) effects play a crucial role. In order to efficiently investigate spin-forbidden reactions with two spin states, Yang et al. [Phys. Chem. Chem. Phys. 20, 4129-4136 (2018)] proposed a two-state spin-mixing (TSSM) model, where the SOC effects between the two spin states are simulated by a geometry-independent constant. Inspired by the TSSM model, we suggest a multiple-state spin-mixing (MSSM) model in this paper for the general case with any number of spin states, and its analytic first and second derivatives have been developed for locating stationary points on the mixed-spin potential energy surface and estimating thermochemical energies. To demonstrate the performance of the MSSM model, some spin-forbidden reactions involving 5d transition elements are calculated using the density functional theory (DFT), and the results are compared with the two-component relativistic ones. It is found that MSSM DFT and two-component DFT calculations may provide very similar stationary-point information on the lowest mixed-spin/spinor energy surface, including structures, vibrational frequencies, and zero-point energies. For the reactions containing saturated 5d elements, the reaction energies by MSSM DFT and two-component DFT agree very well within 3 kcal/mol. As for the two reactions OsO+ + CH4 → OOs(CH2)+ + H2 and W + CH4 → WCH2 + H2 involving unsaturated 5d elements, MSSM DFT may also yield good reaction energies of similar accuracy but with some counterexamples. Nevertheless, the energies may be remarkably improved by a posteriori single point energy calculations using two-component DFT at the MSSM DFT optimized geometries, and the maximum error of about 1 kcal/mol is almost independent of the SOC constant used. The MSSM method as well as the developed computer program provides an effective utility for studying spin-forbidden reactions.