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Related Concept Videos

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...
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...
Double Resonance Techniques: Overview01:12

Double Resonance Techniques: Overview

Double resonance techniques in Nuclear Magnetic Resonance (NMR) spectroscopy involve the simultaneous application of two different frequencies or radiofrequency pulses to manipulate and observe two distinct nuclear spins. One important application of double resonance is spin decoupling, which selectively suppresses coupling with one type of nucleus while observing the NMR signal from another nucleus, simplifying the spectrum and enhancing resolution.
Spin decoupling is usually achieved by...
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...
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

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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...

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Updated: Jul 1, 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-Classical Hybrid Algorithm for Excited States Based on Divide-and-Conquer Unitary Coupled-Cluster

Takeshi Yoshikawa1,2, Tomoya Takanashi3, Hiromi Nakai2,3

  • 1Faculty of Pharmaceutical Sciences, Toho University, 2-2-1 Miyama, Funabashi-shi, Chiba 274-8510, Japan.

The Journal of Physical Chemistry. A
|June 30, 2026
PubMed
Summary
This summary is machine-generated.

A new quantum linear-response method (DC-qUCCSD-LR) enables scalable excited-state simulations. This approach accurately calculates excitation energies for molecules like hydrogen chains, reducing quantum resource needs.

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Last Updated: Jul 1, 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

Area of Science:

  • Quantum chemistry
  • Computational physics
  • Spectroscopy

Background:

  • Excited-state simulations are crucial for understanding molecular properties.
  • Current quantum methods face scalability challenges.
  • Dynamical polarizability is key for extracting excitation information.

Purpose of the Study:

  • Introduce a scalable quantum linear-response framework.
  • Develop a divide-and-conquer approach for excited-state calculations.
  • Accurately compute excitation energies and oscillator strengths.

Main Methods:

  • Developed a divide-and-conquer (DC) quantum linear-response (qLR) framework.
  • Utilized the variational unitary coupled-cluster ansatz with single and double excitations (qUCCSD).
  • Extracted excitation energies from poles of frequency-dependent dynamical polarizability.

Main Results:

  • DC-qUCCSD-LR accurately reproduces FCI excitation energies for linear hydrogen chains (nH2).
  • Achieved favorable scaling: O(n^1.5) for gate counts and O(n^2.2) for measurements.
  • Demonstrated reduced quantum resource requirements compared to traditional methods.

Conclusions:

  • The polarizability-based qUCC-LR framework is accurate and scalable.
  • The DC extension enhances computational efficiency for excited-state simulations.
  • This method provides a robust foundation for future quantum simulations of molecular excitations.