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Related Concept Videos

Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must have a...
Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
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...
Quantum Numbers02:43

Quantum Numbers

It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.
Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)

Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
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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Related Experiment Video

Updated: May 23, 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

Spin-adapted density matrix renormalization group algorithms for quantum chemistry.

Sandeep Sharma1, Garnet Kin-Lic Chan

  • 1Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA.

The Journal of Chemical Physics
|April 3, 2012
PubMed
Summary
This summary is machine-generated.

We adapted the spin-adapted density matrix renormalization group (DMRG) algorithm for quantum chemistry, improving efficiency for complex transition metal systems. This method accurately targets closely spaced spin states and enhances computational performance.

Related Experiment Videos

Last Updated: May 23, 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

Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Condensed Matter Theory

Background:

  • The density matrix renormalization group (DMRG) is a powerful algorithm for strongly correlated systems.
  • Extending DMRG to quantum chemical Hamiltonians, especially for transition metals, presents significant computational challenges.
  • Accurate treatment of spin states is crucial for understanding the electronic structure of transition metal compounds.

Purpose of the Study:

  • To adapt the spin-adapted DMRG algorithm for quantum chemical calculations.
  • To improve the efficiency and accuracy of DMRG for complex transition metal systems.
  • To enable the accurate calculation of low and high spin states in these systems.

Main Methods:

  • Extension of the spin-adapted DMRG algorithm using a quasi-density matrix and the Wigner-Eckart theorem.
  • Implementation of a singlet-embedding strategy to target high spin states.
  • Development of an efficient algorithm for calculating reduced density matrices.

Main Results:

  • Demonstrated accurate targeting of microHartree scale spin-ladder spacings in Fe(2)S(2).
  • Calculated particle and spin correlation functions for [Fe(2)S(2)(SCH(3))(4)](2-) to analyze electronic structure.
  • Achieved up to an order of magnitude increase in computational efficiency for Cr(2) using spin-adaptation and singlet embedding.

Conclusions:

  • The spin-adapted DMRG algorithm is a valuable tool for quantum chemical calculations on transition metal systems.
  • The implemented methods enhance computational efficiency and accuracy for complex spin states.
  • This approach extends the applicability of DMRG to challenging problems in materials science and chemistry.