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Related Concept Videos

¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...
2D NMR: Heteronuclear Single-Quantum Correlation Spectroscopy (HSQC)01:19

2D NMR: Heteronuclear Single-Quantum Correlation Spectroscopy (HSQC)

Heteronuclear single-quantum correlation spectroscopy (HSQC) is a 2D NMR technique that reveals one-bond correlations between hydrogen and a heteronucleus. The HSQC experiment is similar to the heteronuclear correlation experiment (HETCOR) but is more sensitive. In the HSQC spectrum, the proton chemical shift is plotted on the horizontal F2 axis, while the 13C chemical shift is plotted on the vertical F1 axis. The corresponding proton and 13C spectra are also shown. The HSQC contour plot does...
Hybridization of Atomic Orbitals II03:35

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization
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...
2D NMR: Overview of Heteronuclear Correlation Techniques01:18

2D NMR: Overview of Heteronuclear Correlation Techniques

Heteronuclear correlation spectroscopy is an analytical technique that investigates the coupling between different types of nuclei, often a proton and an X-nucleus, such as carbon-13 or nitrogen-15. This method is commonly used in nuclear magnetic resonance (NMR) spectroscopy to gain insights into complex chemical compounds' structural and compositional aspects. A typical heteronuclear correlation spectrum displays X-nucleus chemical shifts on one axis and a proton spectrum on the other axis.
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...

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Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid
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Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid

Published on: January 25, 2020

Localized sample-based quantum diagonalization for strongly correlated chemistry.

Qiaohong Wang1,2, Kevin J Sung3, Ruhee D'Cunha4

  • 1Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL 60637.

Proceedings of the National Academy of Sciences of the United States of America
|July 10, 2026
PubMed
Summary
This summary is machine-generated.

We introduce LASSQD, a hybrid quantum-classical method for calculating transition-metal complex ground states. This approach significantly reduces computational cost while maintaining accuracy, enabling larger system sizes.

Keywords:
quantum chemistryquantum computationstrong correlationtransition-metal complexes

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Compact Quantum Dots for Single-molecule Imaging
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Compact Quantum Dots for Single-molecule Imaging

Published on: October 9, 2012

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Last Updated: Jul 12, 2026

Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid
08:54

Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid

Published on: January 25, 2020

Compact Quantum Dots for Single-molecule Imaging
17:14

Compact Quantum Dots for Single-molecule Imaging

Published on: October 9, 2012

Area of Science:

  • Computational Chemistry
  • Quantum Computing
  • Materials Science

Background:

  • Transition-metal complexes present significant computational challenges for electronic structure calculations.
  • Accurate ground state calculations are crucial for understanding chemical properties and reactivity.
  • Existing quantum and classical methods struggle with the strong correlation inherent in these systems.

Purpose of the Study:

  • To develop a computationally efficient and accurate method for solving the ground states of transition-metal complexes.
  • To integrate quantum sampling with fragment-based multireference theory.
  • To enable the treatment of larger and more complex systems than previously possible.

Main Methods:

  • Development of a hybrid quantum-classical workflow named LASSQD.
  • Combination of sample-based quantum diagonalization (SQD) and localized active space self-consistent field (LASSCF).
  • Utilizing a sparse approximation of the ground-state wavefunction to reduce computational cost.

Main Results:

  • LASSQD achieves accuracy comparable to LASSCF (within 1 kcal/mol) for iron-based complexes.
  • Demonstrated significant reduction in computational cost compared to traditional methods.
  • Successfully computed the spin gap of iron-porphyrin, a system inaccessible to LASSCF.
  • Enabled treatment of larger fragment sizes due to cost reduction.

Conclusions:

  • LASSQD is a scalable and reliable strategy for generating multireference wave functions.
  • Provides a robust starting point for post-SCF correlation methods.
  • Represents a promising pathway toward quantum-enhanced electronic structure calculations.