We have derived here an exact kinetic equation for the time evolution of the probability distribution for a general reaction coordinate space, starting from a multidimensional Liouville equation based on first-principles theory. To make the equation tractable we use two standard approximations, which reduce the exact equation into a Fokker-Planck-type equation with a sink term. As illustrative examples, we consider its application to two important classes of reactions, viz., the electron transfer and diffusion-controlled reactions. The kinetic equations for the reaction coordinates corresponding to these reactions become one dimensional. We also provide a scheme to find the critical value of the reaction coordinate at which the reaction takes place, and also to obtain the initial distribution function in the same space for different experimental situations. In the case of photoinduced electron transfer, we introduce the effect of excitation frequency through the use of suitable initial distribution functions.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.1103/PhysRevE.83.026104 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Asymmetric electronic distribution induced enhancement in photocatalytic CO-to-CH conversion via boron-doped covalent triazine frameworks.
J Colloid Interface Sci
January 2025
Department of Environmental Science and Engineering, Fuzhou University, Minhou, Fujian 350108, China; State Key Laboratory of Photocatalysis on Energy and Environment, College of Chemistry, Fuzhou University, Minhou, Fujian 350108, China. Electronic address:
Covalent triazine frameworks (CTFs) are emerging as promising platform for photocatalysis, yet their highly symmetric structure leads to significant charge recombination. Herein, we employed a facile non-metallic boron (B) modification with precisely controlled doping site to introduce asymmetric local electron distribution in CTFs, achieving a 15-fold activity enhancement for CO-to-CH conversion. Calculations including frontier orbitals, dipole moments and molecular electrostatic potentials firmly demonstrated the formation of localized polarized electron regions in CTF-1 via B doping.
View Article and Find Full Text PDFLignin-coordinated niobium-based catalyst for the efficient conversion of industrial lignin in choline chloride-lactic acid integrated with ethanol deep eutectic solvent.
Int J Biol Macromol
January 2025
Jiangsu Key Laboratory for Biomass-based Energy and Enzyme Technology, Jiangsu Collaborative Innovation Center of Regional Modern Agriculture & Environmental Protection, School of Chemistry and Chemical Engineering, Huaiyin Normal University, Huai'an 223300, China. Electronic address:
Catalytic depolymerization is a favorable option for the valorization of industrial lignin. In this study, a new strategy was demonstrated for the efficient reductive depolymerization of industrial lignin based on a complex solvent of choline chloride-lactic acid (ChCl-LA) DES integrated with ethanol and a C-supported N-doped niobium-based catalyst with industrial lignin as carbon source (NBC@N-LC). It was found that the introduction of ethanol significantly improved the conversion of industrial lignin in ChCl-LA.
View Article and Find Full Text PDFSynthesis of 1,4-Diketones from Esters Enabled by a Tetraborylethane Reagent.
Org Lett
January 2025
State Key Laboratory for Oxo Synthesis and Selective Oxidation, Lanzhou Institute of Chemical Physics, Chinese Academy of Sciences, Lanzhou, Gansu 730000, China.
A modular synthesis method for 1,4-diketones has been developed. Utilizing inexpensive carboxylic acid esters as carbonyl sources and tetraborylethane () as a nucleophilic reagent, a one-pot strategy for constructing two C-C bonds was established. Notably, this reaction proceeds without the involvement of transition metals and exhibits excellent functional group compatibility.
View Article and Find Full Text PDFOperando Characterization of Fe in Doped Ni(Fe)OH Catalysts for Electrochemical Oxygen Evolution.
J Am Chem Soc
January 2025
Department of Physics, Alba Nova Research Center, Stockholm University, Stockholm SE-106 91 Sweden.
Iron-doped nickel oxyhydroxides, Ni(Fe)OH, are among the most promising oxygen evolution reaction (OER) electrocatalysts in alkaline environments. Although iron (Fe) significantly enhances the catalytic activity, there is still no clear consensus on whether Fe directly participates in the reaction or merely acts as a promoter. To elucidate the Fe's role, we performed X-ray spectroscopy studies supported by DFT on Ni(Fe)OH electrocatalysts.
View Article and Find Full Text PDF[Tc]Technetium and Rhenium Dithiocarbazate Complexes: Chemical Synthesis and Biological Assessment.
Pharmaceutics
January 2025
Laboratory of Nuclear Medicine (LIM-43), Hospital das Clinicas HCFMUSP, Faculdade de Medicina, Universidade de Sao Paulo, Sao Paulo 05403-911, SP, Brazil.
Background/objectives: Dithiocarbazates (DTCs) and their metal complexes have been studied regarding their property as anticancer activities. In this work, using S-benzyl-5-hydroxy-3-methyl-5-phenyl-4,5-dihydro-1H-pirazol-1-carbodithionate (Hbdtc), we prepared [ReO(bdtc)(Hbdtc)] and [[Tc]TcO(bdtc)(Hbdtc)] complexes for tumor uptake and animal biodistribution studies.
Methods: Re complex was prepared by a reaction of H2bdtc and (NBu)[ReOCl], the final product was characterized by IR, H NMR, CHN, and MS-ESI.
Want AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!