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Related Concept Videos

Fundamental Mathematical Principles in Pharmacokinetics: Rate and Order of Reaction01:15

Fundamental Mathematical Principles in Pharmacokinetics: Rate and Order of Reaction

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In pharmacokinetics, the rates and order of reactions play a crucial role in understanding how the body processes drugs and help us comprehend drug absorption, distribution, metabolism, and elimination. A critical concept in pharmacokinetics is the rate constant, which quantifies the speed of a reaction. It provides valuable information about the kinetics of drug elimination. The rate constant allows us to determine the rate at which drugs are eliminated from the body.
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Chemical reactions often occur in a stepwise fashion involving two or more distinct reactions taking place in a sequence. A balanced equation indicates the reacting species and the product species, but it reveals no details about how the reaction occurs at the molecular level. The reaction mechanism (or reaction path) provides details regarding the precise, step-by-step process by which a reaction occurs. Each of the steps in a reaction mechanism is called an elementary reaction. These...
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Polarimetry finds application in chemical kinetics to measure the concentration and reaction kinetics of optically active substances during a chemical reaction. Optically active substances have the capability of rotating the plane of polarization of linearly polarized light passing through them—a feature called optical rotation. Optical activity is attributed to the molecular structure of substances. Normal monochromatic light is unpolarized and possesses oscillations of the electrical...
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While the differential rate law relates the rate and concentrations of reactants, a second form of rate law called the integrated rate law relates concentrations of reactants and time. Integrated rate laws can be used to determine the amount of reactant or product present after a period of time or to estimate the time required for a reaction to proceed to a certain extent. For example, an integrated rate law helps determine the length of time a radioactive material must be stored for its...
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Relating Reaction Mechanisms
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The rate of reaction is the change in the amount of a reactant or product per unit time. Reaction rates are therefore determined by measuring the time dependence of some property that can be related to reactant or product amounts. Rates of reactions that consume or produce gaseous substances, for example, are conveniently determined by measuring changes in volume or pressure.
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Related Experiment Video

Updated: Jan 8, 2026

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
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A unified framework for semiclassical reaction rate theory.

Joseph E Lawrence1

  • 1Simons Center for Computational Physical Chemistry, New York University, New York, New York 10003, USA and Department of Chemistry, New York University, New York, New York 10003, USA.

The Journal of Chemical Physics
|December 18, 2025
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A new semiclassical theory unifies instanton theory and semiclassical transition state theory (SCTST) for calculating reaction rate constants. This framework offers a generalized approach for microcanonical scattering rates and includes higher-order corrections.

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Area of Science:

  • Chemical Kinetics
  • Quantum Mechanics
  • Theoretical Chemistry

Background:

  • Existing semiclassical methods like instanton theory and SCTST have limitations.
  • A unified theoretical framework is needed for accurate reaction rate calculations.

Purpose of the Study:

  • Develop a general semiclassical theory for reaction rate constants.
  • Encompass and generalize existing semiclassical methods.
  • Explore new avenues for modeling chemical reaction kinetics.

Main Methods:

  • Formalism based on cumulative reaction probability and instanton contributions.
  • Generalization of Gutzwiller's trace formula.
  • Exact WKB/quantum Hamilton-Jacobi theory for one-dimensional systems.
  • Exploration of connections to VPT2 and thermal instanton theory.

Main Results:

  • Unified framework encompassing instanton theory and SCTST.
  • Generalization to microcanonical scattering rates and all orders in ℏ.
  • Explicit expressions for generalized reduced action up to O(ℏ4).
  • Derivation of thermal instanton rate theory and perturbative corrections.
  • First-order corrections for sphaleron rates above crossover temperature.

Conclusions:

  • The developed theory provides a robust framework for semiclassical reaction rate calculations.
  • It unifies and generalizes existing methods, offering improved accuracy.
  • Potential for developing novel semiclassical methods for chemical kinetics modeling.