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Related Concept Videos

Hybridization of Atomic Orbitals I03:24

Hybridization of Atomic Orbitals I

The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...
Hybridization of Atomic Orbitals II03:35

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization
Valence Bond Theory and Hybridized Orbitals02:38

Valence Bond Theory and Hybridized Orbitals

According to valence bond theory, a covalent bond results when: (1) an orbital on one atom overlaps an orbital on a second atom, and (2) the single electrons in each orbital combine to form an electron pair. The strength of a covalent bond depends on the extent of overlap of the orbitals involved. Maximum overlap is possible when the orbitals overlap on a direct line between the two nuclei.
A σ bond (single bond in a Lewis structure) is a covalent bond in which the electron density is...
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The VSEPR theory can be used to determine the electron pair geometries and molecular structures as follows:
Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation04:01

Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation

Thus far, the ideal gas law, PV = nRT, has been applied to a variety of different types of problems, ranging from reaction stoichiometry and empirical and molecular formula problems to determining the density and molar mass of a gas. However, the behavior of a gas is often non-ideal, meaning that the observed relationships between its pressure, volume, and temperature are not accurately described by the gas laws.

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Related Experiment Video

Updated: Jul 4, 2026

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package
06:37

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

Published on: September 17, 2021

Ab initio molecular dynamics using hybrid density functionals.

Manuel Guidon1, Florian Schiffmann, Jürg Hutter

  • 1Physical Chemistry Institute, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland.

The Journal of Chemical Physics
|June 10, 2008
PubMed
Summary
This summary is machine-generated.

This study presents an efficient implementation for ab initio molecular dynamics simulations using hybrid density functionals. The new method enables large-scale condensed-phase simulations, overcoming previous computational cost limitations.

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Last Updated: Jul 4, 2026

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package
06:37

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Published on: September 17, 2021

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Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
10:52

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

Published on: April 12, 2019

Area of Science:

  • Computational Chemistry
  • Materials Science
  • Quantum Mechanics

Background:

  • Ab initio molecular dynamics (AIMD) simulations with hybrid density functionals are computationally expensive.
  • This high cost has limited their application to small systems.

Purpose of the Study:

  • To present a robust and efficient implementation of Hartree-Fock exchange for AIMD simulations.
  • To enable AIMD simulations of medium-sized condensed-phase systems using hybrid functionals.

Main Methods:

  • Developed and implemented Hartree-Fock exchange for AIMD within the CP2K/Quickstep program.
  • Utilized prescreening techniques for linear scaling of integral evaluation and storage.
  • Employed integral compression for in-core calculations on large systems.
  • Implemented a massively parallel approach with dynamic load balancing.
  • Applied a time-reversible multiple time step scheme for hybrid and local functionals.

Main Results:

  • Demonstrated robustness and efficiency of the new implementation.
  • Achieved linear scaling for integral evaluation and storage.
  • Enabled in-core calculations for systems with thousands of basis functions.
  • Showcased scalability up to hundreds of CPUs.
  • Successfully performed AIMD simulations of liquid water for tens of picoseconds.

Conclusions:

  • The developed implementation significantly reduces the computational cost of AIMD with hybrid functionals.
  • This advancement allows for AIMD simulations of condensed-phase systems with thousands of basis functions.
  • The method opens new possibilities for studying complex systems at the quantum mechanical level.