Implementation of Harmonic Quantum Transition State Theory for Multidimensional Systems
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Transition State Theory. I
MIT OpenCourseWare http://ocw.mit.edu 5.62 Physical Chemistry II Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 5.62 Spring 2007 Lecture #33 Page 1 Transition State Theory. I. Transition State Theory = Activated Complex Theory = Absolute Rate Theory ‡ k H2 + F "! [H2F] !!" HF + H Assume equilibrium between reactants H2 + F and the transition state. [H F]‡ K‡ = 2 [H2 ][F] Treat the transition state as a molecule with structure that decays unimolecularly with rate constant k. d[HF] ‡ ‡ = k[H2F] = kK [H2 ][F] dt k has units of sec–1 (unimolecular decay). The motion along the reaction coordinate looks ‡ like an antisymmetric vibration of H2F , one-half cycle of this vibration. Therefore k can be approximated by the frequency of the antisymmetric vibration ν[sec–1] k ≈ ν ≡ frequency of antisymmetric vibration (bond formation and cleavage looks like antisymmetric vibration) d[HF] = νK‡ [H2] [F] dt ! ‡* $ d[HF] (q / N) 'E‡ /kT [ ] = ν # *H F &e [H2 ] F dt "#(q 2 N)(q / N)%& ! ‡ $ ‡ ‡* ‡ (q / N) ' q *' q *' g * ‡ K‡ = # trans &) rot ,) vib ,) 0 ,e-E kT H2 qH2 ) q*H2 , gH2 gF "# (qtrans N) %&( rot +( vib +( 0 0 + ‡ Reaction coordinate is antisymmetric vibrational mode of H2F . This vibration is fully excited (high T limit) because it leads to the cleavage of the H–H bond and the formation of the H–F bond. For a fully excited vibration hν kT The vibrational partition function for the antisymmetric mode is revised 4/24/08 3:50 PM 5.62 Spring 2007 Lecture #33 Page 2 1 kT q*asym = ' since e–hν/kT ≈ 1 – hν/kT vib 1! e!h" kT h! Note that this is an incredibly important simplification. -
Transition State Analysis of the Reaction Catalyzed by the Phosphotriesterase from Sphingobium Sp
Article Cite This: Biochemistry 2019, 58, 1246−1259 pubs.acs.org/biochemistry Transition State Analysis of the Reaction Catalyzed by the Phosphotriesterase from Sphingobium sp. TCM1 † † † ‡ ‡ Andrew N. Bigley, Dao Feng Xiang, Tamari Narindoshvili, Charlie W. Burgert, Alvan C. Hengge,*, † and Frank M. Raushel*, † Department of Chemistry, Texas A&M University, College Station, Texas 77843, United States ‡ Department of Chemistry and Biochemistry, Utah State University, Logan, Utah 84322, United States *S Supporting Information ABSTRACT: Organophosphorus flame retardants are stable toxic compounds used in nearly all durable plastic products and are considered major emerging pollutants. The phospho- triesterase from Sphingobium sp. TCM1 (Sb-PTE) is one of the few enzymes known to be able to hydrolyze organo- phosphorus flame retardants such as triphenyl phosphate and tris(2-chloroethyl) phosphate. The effectiveness of Sb-PTE for the hydrolysis of these organophosphates appears to arise from its ability to hydrolyze unactivated alkyl and phenolic esters from the central phosphorus core. How Sb-PTE is able to catalyze the hydrolysis of the unactivated substituents is not known. To interrogate the catalytic hydrolysis mechanism of Sb-PTE, the pH dependence of the reaction and the effects of changing the solvent viscosity were determined. These experiments were complemented by measurement of the primary and ff ff secondary 18-oxygen isotope e ects on substrate hydrolysis and a determination of the e ects of changing the pKa of the leaving group on the magnitude of the rate constants for hydrolysis. Collectively, the results indicated that a single group must be ionized for nucleophilic attack and that a separate general acid is not involved in protonation of the leaving group. -
Lecture Outline a Closer Look at Carbocation Stabilities and SN1/E1 Reaction Rates We Learned That an Important Factor in the SN
Lecture outline A closer look at carbocation stabilities and SN1/E1 reaction rates We learned that an important factor in the SN1/E1 reaction pathway is the stability of the carbocation intermediate. The more stable the carbocation, the faster the reaction. But how do we know anything about the stabilities of carbocations? After all, they are very unstable, high-energy species that can't be observed directly under ordinary reaction conditions. In protic solvents, carbocations typically survive only for picoseconds (1 ps - 10–12s). Much of what we know (or assume we know) about carbocation stabilities comes from measurements of the rates of reactions that form them, like the ionization of an alkyl halide in a polar solvent. The key to connecting reaction rates (kinetics) with the stability of high-energy intermediates (thermodynamics) is the Hammond postulate. The Hammond postulate says that if two consecutive structures on a reaction coordinate are similar in energy, they are also similar in structure. For example, in the SN1/E1 reactions, we know that the carbocation intermediate is much higher in energy than the alkyl halide reactant, so the transition state for the ionization step must lie closer in energy to the carbocation than the alkyl halide. The Hammond postulate says that the transition state should therefore resemble the carbocation in structure. So factors that stabilize the carbocation also stabilize the transition state leading to it. Here are two examples of rxn coordinate diagrams for the ionization step that are reasonable and unreasonable according to the Hammond postulate. We use the Hammond postulate frequently in making assumptions about the nature of transition states and how reaction rates should be influenced by structural features in the reactants or products. -
Glossary of Terms Used in Photochemistry, 3Rd Edition (IUPAC
Pure Appl. Chem., Vol. 79, No. 3, pp. 293–465, 2007. doi:10.1351/pac200779030293 © 2007 IUPAC INTERNATIONAL UNION OF PURE AND APPLIED CHEMISTRY ORGANIC AND BIOMOLECULAR CHEMISTRY DIVISION* SUBCOMMITTEE ON PHOTOCHEMISTRY GLOSSARY OF TERMS USED IN PHOTOCHEMISTRY 3rd EDITION (IUPAC Recommendations 2006) Prepared for publication by S. E. BRASLAVSKY‡ Max-Planck-Institut für Bioanorganische Chemie, Postfach 10 13 65, 45413 Mülheim an der Ruhr, Germany *Membership of the Organic and Biomolecular Chemistry Division Committee during the preparation of this re- port (2003–2006) was as follows: President: T. T. Tidwell (1998–2003), M. Isobe (2002–2005); Vice President: D. StC. Black (1996–2003), V. T. Ivanov (1996–2005); Secretary: G. M. Blackburn (2002–2005); Past President: T. Norin (1996–2003), T. T. Tidwell (1998–2005) (initial date indicates first time elected as Division member). The list of the other Division members can be found in <http://www.iupac.org/divisions/III/members.html>. Membership of the Subcommittee on Photochemistry (2003–2005) was as follows: S. E. Braslavsky (Germany, Chairperson), A. U. Acuña (Spain), T. D. Z. Atvars (Brazil), C. Bohne (Canada), R. Bonneau (France), A. M. Braun (Germany), A. Chibisov (Russia), K. Ghiggino (Australia), A. Kutateladze (USA), H. Lemmetyinen (Finland), M. Litter (Argentina), H. Miyasaka (Japan), M. Olivucci (Italy), D. Phillips (UK), R. O. Rahn (USA), E. San Román (Argentina), N. Serpone (Canada), M. Terazima (Japan). Contributors to the 3rd edition were: A. U. Acuña, W. Adam, F. Amat, D. Armesto, T. D. Z. Atvars, A. Bard, E. Bill, L. O. Björn, C. Bohne, J. Bolton, R. Bonneau, H. -
An Improved Potential Energy Surface for the H2cl System and Its Use for Calculations of Rate Coefficients and Kinetic Isotope Effects Thomas C
Chemistry Publications Chemistry 8-1996 An Improved Potential Energy Surface for the H2Cl System and Its Use for Calculations of Rate Coefficients and Kinetic Isotope Effects Thomas C. Allison University of Minnesota - Twin Cities Gillian C. Lynch University of Minnesota - Twin Cities Donald G. Truhlar University of Minnesota - Twin Cities Mark S. Gordon Iowa State University, [email protected] Follow this and additional works at: http://lib.dr.iastate.edu/chem_pubs Part of the Chemistry Commons The ompc lete bibliographic information for this item can be found at http://lib.dr.iastate.edu/ chem_pubs/327. For information on how to cite this item, please visit http://lib.dr.iastate.edu/ howtocite.html. This Article is brought to you for free and open access by the Chemistry at Iowa State University Digital Repository. It has been accepted for inclusion in Chemistry Publications by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. An Improved Potential Energy Surface for the H2Cl System and Its Use for Calculations of Rate Coefficients and Kinetic Isotope Effects Abstract We present a new potential energy surface (called G3) for the chemical reaction Cl + H2 → HCl + H. The new surface is based on a previous potential surface called GQQ, and it incorporates an improved bending potential that is fit ot the results of ab initio electronic structure calculations. Calculations based on variational transition state theory with semiclassical transmission coefficients corresponding to an optimized multidimensional tunneling treatment (VTST/OMT, in particular improved canonical variational theory with least-action ground-state transmission coefficients) are carried out for nine different isotopomeric versions of the abstraction reaction and six different isotopomeric versions of the exchange reaction involving the H, D, and T isotopes of hydrogen, and the new surface is tested by comparing these calculations to available experimental data. -
Spring 2013 Lecture 13-14
CHM333 LECTURE 13 – 14: 2/13 – 15/13 SPRING 2013 Professor Christine Hrycyna INTRODUCTION TO ENZYMES • Enzymes are usually proteins (some RNA) • In general, names end with suffix “ase” • Enzymes are catalysts – increase the rate of a reaction – not consumed by the reaction – act repeatedly to increase the rate of reactions – Enzymes are often very “specific” – promote only 1 particular reaction – Reactants also called “substrates” of enzyme catalyst rate enhancement non-enzymatic (Pd) 102-104 fold enzymatic up to 1020 fold • How much is 1020 fold? catalyst time for reaction yes 1 second no 3 x 1012 years • 3 x 1012 years is 500 times the age of the earth! Carbonic Anhydrase Tissues ! + CO2 +H2O HCO3− +H "Lungs and Kidney 107 rate enhancement Facilitates the transfer of carbon dioxide from tissues to blood and from blood to alveolar air Many enzyme names end in –ase 89 CHM333 LECTURE 13 – 14: 2/13 – 15/13 SPRING 2013 Professor Christine Hrycyna Why Enzymes? • Accelerate and control the rates of vitally important biochemical reactions • Greater reaction specificity • Milder reaction conditions • Capacity for regulation • Enzymes are the agents of metabolic function. • Metabolites have many potential pathways • Enzymes make the desired one most favorable • Enzymes are necessary for life to exist – otherwise reactions would occur too slowly for a metabolizing organis • Enzymes DO NOT change the equilibrium constant of a reaction (accelerates the rates of the forward and reverse reactions equally) • Enzymes DO NOT alter the standard free energy change, (ΔG°) of a reaction 1. ΔG° = amount of energy consumed or liberated in the reaction 2. -
Reactions of Alkenes and Alkynes
05 Reactions of Alkenes and Alkynes Polyethylene is the most widely used plastic, making up items such as packing foam, plastic bottles, and plastic utensils (top: © Jon Larson/iStockphoto; middle: GNL Media/Digital Vision/Getty Images, Inc.; bottom: © Lakhesis/iStockphoto). Inset: A model of ethylene. KEY QUESTIONS 5.1 What Are the Characteristic Reactions of Alkenes? 5.8 How Can Alkynes Be Reduced to Alkenes and 5.2 What Is a Reaction Mechanism? Alkanes? 5.3 What Are the Mechanisms of Electrophilic Additions HOW TO to Alkenes? 5.1 How to Draw Mechanisms 5.4 What Are Carbocation Rearrangements? 5.5 What Is Hydroboration–Oxidation of an Alkene? CHEMICAL CONNECTIONS 5.6 How Can an Alkene Be Reduced to an Alkane? 5A Catalytic Cracking and the Importance of Alkenes 5.7 How Can an Acetylide Anion Be Used to Create a New Carbon–Carbon Bond? IN THIS CHAPTER, we begin our systematic study of organic reactions and their mecha- nisms. Reaction mechanisms are step-by-step descriptions of how reactions proceed and are one of the most important unifying concepts in organic chemistry. We use the reactions of alkenes as the vehicle to introduce this concept. 129 130 CHAPTER 5 Reactions of Alkenes and Alkynes 5.1 What Are the Characteristic Reactions of Alkenes? The most characteristic reaction of alkenes is addition to the carbon–carbon double bond in such a way that the pi bond is broken and, in its place, sigma bonds are formed to two new atoms or groups of atoms. Several examples of reactions at the carbon–carbon double bond are shown in Table 5.1, along with the descriptive name(s) associated with each. -
Computational Analysis of the Mechanism of Chemical Reactions
Computational Analysis of the Mechanism of Chemical Reactions in Terms of Reaction Phases: Hidden Intermediates and Hidden Transition States ELFI KRAKA* AND DIETER CREMER Department of Chemistry, Southern Methodist University, 3215 Daniel Avenue, Dallas, Texas 75275-0314 RECEIVED ON JANUARY 9, 2009 CON SPECTUS omputational approaches to understanding chemical reac- Ction mechanisms generally begin by establishing the rel- ative energies of the starting materials, transition state, and products, that is, the stationary points on the potential energy surface of the reaction complex. Examining the intervening spe- cies via the intrinsic reaction coordinate (IRC) offers further insight into the fate of the reactants by delineating, step-by- step, the energetics involved along the reaction path between the stationary states. For a detailed analysis of the mechanism and dynamics of a chemical reaction, the reaction path Hamiltonian (RPH) and the united reaction valley approach (URVA) are an effi- cient combination. The chemical conversion of the reaction complex is reflected by the changes in the reaction path direction t(s) and reaction path curvature k(s), both expressed as a function of the path length s. This information can be used to partition the reaction path, and by this the reaction mech- anism, of a chemical reaction into reaction phases describing chemically relevant changes of the reaction complex: (i) a contact phase characterized by van der Waals interactions, (ii) a preparation phase, in which the reactants prepare for the chemical processes, (iii) one or more transition state phases, in which the chemical processes of bond cleavage and bond formation take place, (iv) a product adjustment phase, and (v) a separation phase. -
How Do Methyl Groups Enhance the Triplet Chemiexcitation Yield of Dioxetane?
How Do Methyl Groups Enhance the Triplet Chemiexcitation Yield of Dioxetane? Morgane Vacher,∗,y Pooria Farahani,z Alessio Valentini,{ Luis Manuel Frutos,x Hans O. Karlsson,y Ignacio Fdez. Galván,y and Roland Lindh∗,y yDepartment of Chemistry – Ångström, The Theoretical Chemistry Programme, Uppsala University, Box 538, 751 21 Uppsala, Sweden zInstituto de Química, Departamento de Química Fundamental, Universidade de São Paulo, C.P. 05508-000, São Paulo, Brazil {Département de Chimie, Université de Liège, Allée du 6 Août, 11, 4000 Liège, Belgium xDepartamento de Química Física, Universidad de Alcalá, E-28871 Alcalá de Henares, Madrid, Spain E-mail: [email protected]; [email protected] arXiv:1708.04114v1 [physics.chem-ph] 10 Aug 2017 1 Abstract Chemiluminescence is the emission of light as a result of a non-adiabatic chemical reaction. The present work is concerned with understanding the yield of chemilumines- cence, in particular how it dramatically increases upon methylation of 1,2-dioxetane. Both ground-state and non-adiabatic dynamics (including singlet excited states) of the decomposition reaction of various methyl-substituted dioxetanes have been simulated. Methyl-substitution leads to a significant increase in the dissociation time scale. The rotation around the O-C-C-O dihedral angle is slowed down and thus, the molecular system stays longer in the “entropic trap” region. A simple kinetic model is proposed to explain how this leads to a higher chemiluminescence yield. These results have im- portant implications for the design of efficient chemiluminescent systems in medical, environmental and industrial applications. Graphical TOC Entry 2 Rationalising the yields of chemical reactions in terms of simple and accessible concepts is one of the aims of theoretical chemistry. -
Angwcheminted, 2000, 39, 2587-2631.Pdf
REVIEWS Femtochemistry: Atomic-Scale Dynamics of the Chemical Bond Using Ultrafast Lasers (Nobel Lecture)** Ahmed H. Zewail* Over many millennia, humankind has biological changes. For molecular dy- condensed phases, as well as in bio- thought to explore phenomena on an namics, achieving this atomic-scale res- logical systems such as proteins and ever shorter time scale. In this race olution using ultrafast lasers as strobes DNA structures. It also offers new against time, femtosecond resolution is a triumph, just as X-ray and electron possibilities for the control of reactivity (1fs 10À15 s) is the ultimate achieve- diffraction, and, more recently, STM and for structural femtochemistry and ment for studies of the fundamental and NMR spectroscopy, provided that femtobiology. This anthology gives an dynamics of the chemical bond. Ob- resolution for static molecular struc- overview of the development of the servation of the very act that brings tures. On the femtosecond time scale, field from a personal perspective, en- about chemistryÐthe making and matter wave packets (particle-type) compassing our research at Caltech breaking of bonds on their actual time can be created and their coherent and focusing on the evolution of tech- and length scalesÐis the wellspring of evolution as a single-molecule trajec- niques, concepts, and new discoveries. the field of femtochemistry, which is tory can be observed. The field began the study of molecular motions in the with simple systems of a few atoms and Keywords: femtobiology ´ femto- hitherto unobserved ephemeral transi- has reached the realm of the very chemistry ´ Nobel lecture ´ physical tion states of physical, chemical, and complex in isolated, mesoscopic, and chemistry ´ transition states 1. -
8 Finding Transition States and Barrier Heights: First Order Saddle Points
8 Finding Transition States and Barrier Heights: First Order Saddle Points So far, you have already considered several systems that did not reside in a minimum of the potential energy surface. Both the bond breaking in the dissociation of H2 as well as the internal rotation of butane were examples of off-equilibrium processes, where the system moves from one equilibrium conformer, i.e. from one minimum, to another. It is intuitively clear that the likelihood of two equilibrium conformers to be transformed into each other by moving along some random path is negligible, and different methods have been established tofind reasonable paths for such transitions. A frequently used approach is transition state theory, which is concerned withfinding a realistic path be- tween potential energy minima. In this set of exercises, you will search for the transition state for a the cyclisation of a deprotonated chloropropanol to propylene oxide, and you willfind the minimum energy path that connects reactants to products via this transition state. 8.1 Synthesis of Propylene Oxide Corrosive propylene oxide (cf.figure 1) is the simplest chiral epoxide and of great indus- trial importance. The historically most important synthesis is based on hydrochlorination and ring closure of the resulting chloropropanols in a basic environment: The resulting epoxide is most often directly used as a racemate. a) What kind of reaction mechanism would you expect? Would you expect the stere- ochemistry at the chiral carbon to be preserved? Identify the chirality centre in the chloropropanoate and the product epoxide. b) Suggest possible transition state structues. Figure 1: Propylene oxide is a toxic, cancerogenic liquid that is produced on large indus- trial scale. -
Theoretical Calculations in Reaction Mechanism Studies
Sumitomo Chemical Co., Ltd. Theoretical Calculations in Organic Synthesis Research Laboratory Reaction Mechanism Studies Akio TANAKA Kensuke MAEKAWA Kimichi SUZUKI In recent decades, quantum chemistry calculations have been used for various chemical fields such as reaction pathway analysis and spectroscopic assignments due to the theoretical developments, especially accuracy improvement of functionals in density functional theory (DFT), and high-speed parallel computers. However, the functionals in DFT should be appropriately employed for a target system or phenomenon because its reproducibility depends on the functionals used. Therefore comparison among obtained results with available experimental data or high-level computations is necessary to avoid misleading. In this review, we report the DFT-based mechanistic studies and spectroscopic analyses on reaction intermediates of catalytic reactions. This paper is translated from R&D Report, “SUMITOMO KAGAKU”, vol. 2013. Introduction reactants, reagents, and catalysts. A wide variety of per- formances of transition-metal catalysts are considerably The homogeneous catalysts with transition-metal dependent on the electronic states belonging to d-orbital complex are widely used for olefin polymerization, and electrons having different oxidative or spin states for manufacturing of fine chemicals, medical and agri- designed by coordinated ligands. To explore high-per- cultural chemicals, and electronic materials. With the formance catalysts, analytical investigation based on use of the catalysts, many types of compounds have electronic states is necessary, and theoretical calcula- been synthesized to bring new functional materials into tions are indispensable for determining the electronic the market. In addition, organometallic catalytic reac- states. tions occur in living organisms to play an important role for sustaining life.