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Related Concept Videos

The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra. Schrödinger...
Transition State Theory01:25

Transition State Theory

Transition-state theory, also known as activated-complex theory, provides a molecular-level explanation of reaction rates in both gas-phase and solution-phase reactions. It extends earlier kinetic models by considering the formation of a short-lived, high-energy configuration during a reaction.The progress of a chemical reaction can be represented using a reaction profile, which plots potential energy against the reaction coordinate. As two reactant molecules approach one another, their...
Estimation of the Physical Quantities01:05

Estimation of the Physical Quantities

On many occasions, physicists, other scientists, and engineers need to make estimates of a particular quantity. These are sometimes referred to as guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. The physicist Enrico Fermi was famous for his ability to estimate various kinds of data with surprising precision. Estimating does not mean guessing a number or a formula at random. Instead, estimation means using prior experience and sound...
The Uncertainty Principle04:08

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He mathematically...
Reaction Mechanisms: The Steady-State Approximation01:26

Reaction Mechanisms: The Steady-State Approximation

The steady-state approximation, also referred to as the quasi-steady-state approximation to differentiate it from a true steady state, is a widely used method for simplifying calculations in complex reaction mechanisms. This approach is particularly useful when dealing with multi-step reactions that involve reverse reactions or several steps, which can significantly increase mathematical complexity and make the reactions nearly unsolvable analytically.The steady-state approximation operates on...
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π Electron Effects on Chemical Shift: Overview

An applied magnetic field causes loosely bound π-electrons in organic molecules to circulate, producing a local or induced diamagnetic field over a large spatial volume. As the molecules tumble in solution, the field generated by π-electrons in spherical substituents results in a zero net field. However, the net field generated by π-electrons in non-spherical substituents is not zero. The effect of this induced field depends on the orientation of the molecule with respect to B0, resulting in...

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Related Experiment Video

Updated: Jun 17, 2026

Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method
05:51

Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method

Published on: July 19, 2019

Approximate inclusion of quantum effects in transition path sampling.

Dimitri Antoniou1, Steven D Schwartz

  • 1Department of Biophysics, Albert Einstein College of Medicine, 1300 Morris Park Ave., Bronx, New York 10461, USA.

The Journal of Chemical Physics
|December 17, 2009
PubMed
Summary

We developed a new method combining quantum and classical mechanics for studying chemical reactions. This approach accurately captures quantum effects in complex systems, improving reaction pathway analysis.

Related Experiment Videos

Last Updated: Jun 17, 2026

Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method
05:51

Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method

Published on: July 19, 2019

Area of Science:

  • Chemical Physics
  • Quantum Mechanics
  • Computational Chemistry

Background:

  • Transition path sampling (TPS) is crucial for understanding reaction mechanisms.
  • Accurately incorporating nuclear quantum effects in TPS remains a challenge.
  • Many systems involve both quantum and classical degrees of freedom.

Purpose of the Study:

  • To develop an efficient method for including nuclear quantum effects in TPS.
  • To enable accurate simulations of systems with mixed quantum-classical behavior.

Main Methods:

  • Developed a mixed centroid/classical transition path sampling approach.
  • Utilized the normal mode centroid method for the quantum subsystem.
  • Ensured computational efficiency without sacrificing accuracy.

Main Results:

  • Successfully applied the method to a model system with significant quantum effects.
  • Demonstrated the method's ability to capture essential quantum dynamical features.
  • The normal mode centroid method proved computationally feasible and accurate.

Conclusions:

  • The proposed mixed centroid/classical TPS method is effective for systems with quantum and classical components.
  • This approach enhances the study of reaction dynamics by accurately including nuclear quantum effects.
  • Offers a computationally viable pathway for exploring complex chemical processes.