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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...
Free Energy Changes for Nonstandard States03:25

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The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 1 bar; concentrations other than 1 M) is related to the standard free energy change according to this equation:
Electronic Structure of Atoms02:28

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An atom comprises protons and neutrons, which are contained inside the dense, central core called the nucleus, with electrons present around the nucleus. Taking into account the wave–particle duality of electrons and the uncertainty in position around the nucleus, quantum mechanics provides a more accurate model for the atomic structure. It describes atomic orbitals as the regions around the nucleus where electrons of discrete energy exist, characterized by four quantum numbers:  n, l, ml, and...
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Energy Diagrams, Transition States, and Intermediates02:13

Energy Diagrams, Transition States, and Intermediates

Free-energy diagrams, or reaction coordinate diagrams, are graphs showing the energy changes that occur during a chemical reaction. The reaction coordinate represented on the horizontal axis shows how far the reaction has progressed structurally. Positions along the x-axis close to the reactants have structures resembling the reactants, while positions close to the products resemble the products.  Peaks on the energy diagram represent stable structures with measurable lifetimes, while other...
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Related Experiment Video

Updated: Jun 8, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Quantum Monte Carlo calculations for minimum energy structures.

Lucas K Wagner1, Jeffrey C Grossman

  • 1Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA. lkwagner@mit.edu

Physical Review Letters
|September 28, 2010
PubMed
Summary
This summary is machine-generated.

We developed a new method using quantum Monte Carlo calculations to efficiently find minimum energy structures. This approach averages stochastic energy estimates for precise results in complex systems like H2O-OH-.

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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations
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Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations

Published on: October 12, 2019

Area of Science:

  • Computational Chemistry
  • Materials Science
  • Quantum Mechanics

Background:

  • Finding minimum energy structures is crucial for understanding chemical and physical properties.
  • Accurate energy calculations are computationally expensive, limiting their application to complex systems.
  • Stochastic methods offer a potential route to balance accuracy and computational cost.

Purpose of the Study:

  • To present an efficient computational method for determining minimum energy structures.
  • To leverage energy estimates from quantum Monte Carlo calculations for structural optimization.
  • To demonstrate the impact of quantum Monte Carlo-derived minima on potential energy surface behavior.

Main Methods:

  • A novel stochastic method utilizing energy estimates from quantum Monte Carlo (QMC) calculations.
  • Averaging stochastic energy estimates to achieve precise structural minima.
  • Application of the algorithm to minimize the energy of the H2O-OH- complex.

Main Results:

  • The proposed method efficiently identifies minimum energy structures.
  • Inexpensive calculations with moderate statistical uncertainty yield precise structural information.
  • Minimizing energy using QMC calculations significantly influences the qualitative behavior of the potential energy surface for the H2O-OH- complex.

Conclusions:

  • The developed stochastic method provides an efficient pathway to find minimum energy structures.
  • Quantum Monte Carlo energy estimates are valuable for accurate structural determination.
  • Accurate structural minima are essential for a correct qualitative description of potential energy surfaces.