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Energy path

Indirect Energy path Direct Energy path... [Pg.320]

Figure B2.5.22. Potential V along the minimum energy path for the stereonuitation of hydrogen peroxide. Adapted from [103]. Figure B2.5.22. Potential V along the minimum energy path for the stereonuitation of hydrogen peroxide. Adapted from [103].
Muller K and Brown L D 1979 Location of saddle points and minimum energy paths by a constrained simplex optimization procedure Theor. Chim. Acta 53 75... [Pg.2358]

Techniques have been developed within the CASSCF method to characterize the critical points on the excited-state PES. Analytic first and second derivatives mean that minima and saddle points can be located using traditional energy optimization procedures. More importantly, intersections can also be located using constrained minimization [42,43]. Of particular interest for the mechanism of a reaction is the minimum energy path (MEP), defined as the line followed by a classical particle with zero kinetic energy [44-46]. Such paths can be calculated using intrinsic reaction coordinate (IRC) techniques... [Pg.253]

The lowest-energy path from one minimum to another passes through a saddle point. [Pg.298]

Chemical processes, such as bond stretching or reactions, can be divided into adiabatic and diabatic processes. Adiabatic processes are those in which the system does not change state throughout the process. Diabatic, or nonadiabatic, processes are those in which a change in the electronic state is part of the process. Diabatic processes usually follow the lowest energy path, changing state as necessary. [Pg.7]

In order to define how the nuclei move as a reaction progresses from reactants to transition structure to products, one must choose a definition of how a reaction occurs. There are two such definitions in common use. One definition is the minimum energy path (MEP), which defines a reaction coordinate in which the absolute minimum amount of energy is necessary to reach each point on the coordinate. A second definition is a dynamical description of how molecules undergo intramolecular vibrational redistribution until the vibrational motion occurs in a direction that leads to a reaction. The MEP definition is an intuitive description of the reaction steps. The dynamical description more closely describes the true behavior molecules as seen with femtosecond spectroscopy. [Pg.159]

FIGURE 18.1 Illustration of how the steepest descent algorithm follows a path that oscillates around the minimum energy path. [Pg.160]

In the chapter on reaction rates, it was pointed out that the perfect description of a reaction would be a statistical average of all possible paths rather than just the minimum energy path. Furthermore, femtosecond spectroscopy experiments show that molecules vibrate in many dilferent directions until an energetically accessible reaction path is found. In order to examine these ideas computationally, the entire potential energy surface (PES) or an approximation to it must be computed. A PES is either a table of data or an analytic function, which gives the energy for any location of the nuclei comprising a chemical system. [Pg.173]

MEP (IRC, intrinsic reaction coordinate, minimum-energy path) the lowest-energy route from reactants to products in a chemical process MIM (molecules-in-molecules) a semiempirical method used for representing potential energy surfaces... [Pg.365]

Prompt instrumentation is usually intended to measure quantities while uniaxial strain conditions still prevail, i.e., before the arrival of any lateral edge effects. The quantities of interest are nearly always the shock velocity or stress wave velocity, the material (particle) velocity behind the shock or throughout the wave, and the pressure behind the shock or throughout the wave. Knowledge of any two of these quantities allows one to calculate the pressure-volume-energy path followed by the specimen material during the experimental event, i.e., it provides basic information about the material s equation of state (EOS). Time-resolved temperature measurements can further define the equation-of-state characteristics. [Pg.54]

Computations have shown that in the quantum region it is possible to have various most probable transition paths (ranging from the classical minimum energy path (MEP) to the straight-line one-dimensional tunneling of early models), depending on the PES geometry. [Pg.7]

A postulated reaction mechanism is a description of all contributing elementary reactions (we will call this the kinetic scheme), as well as a description of structures (electronic and chemical) and stereochemistry of the transition state for each elementary reaction. (Note that it is common to mean by the term transition state both the region at the maximum in the energy path and the actual chemical species that exists at this point in the reaction.)... [Pg.4]

Ki ausc, F. Ilaites, E. Ilowarth, R. and Koomey, J. (1993). Cutting Carbon Emissions—Burden or Benefit The Economics of Energy-Tax and Non-Price Policies. El Cerrito, CA International Project for Sustainable Energy Paths. [Pg.1171]


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Adiabatic potential curve minimum energy paths

Cartesian coordinates, reaction paths potential energy surfaces

Chemical reactivities minimum energy path

Electron kinetic energy through mean free path

Electronic structure minimum energy path calculations

Energy Reaction Path (MERP)

Energy transfer path independence

Energy transfer paths

Energy-conserving path-branching with the force averaging

Free Energies from Transition Path Sampling Simulations

Intrinsic reaction path energy profile

Minimal energy path

Minimum Energy Path Semiclassical

Minimum Energy Paths (MEPS)

Minimum Energy Paths Optimization

Minimum energy path

Minimum energy path , direct molecular

Minimum energy path , intramolecular

Minimum energy path avoidance

Minimum energy path background

Minimum energy path chain reactions

Minimum energy path chemical reactions

Minimum energy path dimers

Minimum energy path reaction rate theory

Minimum energy path single-product channels

Minimum energy path spectroscopy

Minimum energy path system

Minimum energy path transition state theory

Minimum energy path, MEP

Minimum energy paths , potential

Minimum energy paths , potential calculation techniques

Minimum energy paths , potential surfaces

Minimum energy reaction path

Minimum free energy paths

Minimum-energy path coordinate)

Path free energy

Path free energy fluctuations

Path integral free-energy perturbation and

Path integral free-energy perturbation and umbrella sampling

Path of minimum energy

Paths for Evaluating Energy Levels

Pathway minimal energy reaction path

Policy aspects supporting the efficiency path to a sustainable energy system

Potential Energy Surface Molecular Structure, Transition States, and Reaction Paths

Potential energy surface multiple reaction paths

Potential energy surface path avoidance

Potential energy surface reaction path

Potential energy surface transition path sampling

Potential energy surfaces reaction paths, calculation

Potential energy surfaces steepest descent paths

Potential energy surfaces surface atom reaction paths

Rare Event Kinetics and Free Energies in Path Space

Reaction Path Energy Profiles

Reaction coordinate minimum energy path

Reaction path zero-point energy

Reaction paths, potential energy surfaces bifurcations

Reaction paths, potential energy surfaces dynamics

Reaction paths, potential energy surfaces examples

Reaction paths, potential energy surfaces limitations

Reaction paths, potential energy surfaces principles

Reaction paths, potential energy surfaces solution reactions

Reactions energy paths

Steepest descent reaction paths, potential energy surfaces

Subject minimum energy path

The Minimum Energy Path

Thermalization path length energy dependence

Trajectory calculations, reaction path potential energy surfaces

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