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Related Concept Videos

Molecular Orbital Theory I02:35

Molecular Orbital Theory I

Overview of Molecular Orbital Theory
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...
Hybridization of Atomic Orbitals II03:35

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization
Electronic Structure of Atoms02:28

Electronic Structure of Atoms


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...
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...
Molecular Orbital Theory II03:51

Molecular Orbital Theory II

Molecular Orbital Energy Diagrams

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Related Experiment Video

Updated: Jun 3, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

Large-scale semidefinite programming for many-electron quantum mechanics.

David A Mazziotti1

  • 1Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA. damazz@uchicago.edu

Physical Review Letters
|March 17, 2011
PubMed
Summary
This summary is machine-generated.

Researchers developed a faster semidefinite programming (SDP) method for calculating two-electron reduced density matrices (2-RDMs) in quantum systems. This advance significantly speeds up computations for strongly correlated electrons, enabling larger-scale applications.

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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

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Last Updated: Jun 3, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
05:39

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Mathematical Optimization

Background:

  • Accurately calculating the energy of many-electron quantum systems is crucial for understanding chemical and physical phenomena.
  • Existing methods often struggle with strongly correlated systems, requiring approximations or extensive computational resources.

Purpose of the Study:

  • To develop a more efficient semidefinite programming (SDP) method for computing the two-electron reduced density matrix (2-RDM).
  • To improve the speed of calculations for strongly correlated quantum systems.

Main Methods:

  • Developed a novel SDP approach for calculating 2-RDMs.
  • Applied the method to model the dissociation of N(2) and the metal-to-insulator transition in H(50).

Main Results:

  • The new SDP method is 10-20 times faster than previous approaches for strongly correlated 2-RDMs.
  • Successfully applied to complex systems like H(50) with a large SDP problem size (9.4×10^6 variables).

Conclusions:

  • The enhanced SDP method offers a significant computational speedup for 2-RDM calculations.
  • This breakthrough expands the feasibility of large-scale applications in quantum chemistry, quantum information, and other scientific fields.