Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene π orbitals.
¹H NMR: Pople Notation01:09

¹H NMR: Pople Notation

The Pople nomenclature system classifies spin systems based on the difference between their chemical shifts. Coupled spins are denoted by capital letters with subscripts indicating the number of equivalent nuclei. When the coupled nuclei have well-separated chemical shifts, they are assigned letters that are far apart in the alphabet, such as A and X. When the difference in chemical shifts is small, coupled nuclei are named using adjacent letters of the alphabet (AB, MN, or XY).
A proton...
MO Theory and Covalent Bonding02:40

MO Theory and Covalent Bonding

The molecular orbital theory describes the distribution of electrons in molecules in a manner similar to the distribution of electrons in atomic orbitals. The region of space in which a valence electron in a molecule is likely to be found is called a molecular orbital. Mathematically, the linear combination of atomic orbitals (LCAO) generates molecular orbitals. Combinations of in-phase atomic orbital wave functions result in regions with a high probability of electron density, while...
Crystal Field Theory - Octahedral Complexes02:58

Crystal Field Theory - Octahedral Complexes

Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

Crystal Field Theory - Tetrahedral and Square Planar Complexes

Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
¹H NMR: Complex Splitting01:13

¹H NMR: Complex Splitting

A proton M that is coupled to a proton X results in doublet signals for M. However, NMR-active nuclei can be simultaneously coupled to more than one nonequivalent nucleus. When M is coupled to a second proton A, such as in styrene oxide, each peak in the doublet is split into another doublet.
Splitting diagrams or splitting tree diagrams are routinely used to depict such complex couplings. While drawing splitting diagrams, the splitting with the larger coupling constant is usually applied first.

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Fragment, Entangle, and Consolidate: Strong Correlation through Bifold Quantum Circuits.

Journal of chemical theory and computation·2026
Same author

A platinum butterfly effect: small changes turn an anticancer drug into a non-toxic metalloantibiotic with in vivo efficacy.

npj antimicrobials and resistance·2026
Same author

Resource Estimation for VQE on Small Molecules: Impact of Fermion Mappings and Hamiltonian Reductions.

Journal of computational chemistry·2026
Same author

Determination of molecular excited states <i>via</i> symmetry guided subspace search variational quantum eigensolver.

Physical chemistry chemical physics : PCCP·2026
Same author

Operator commutativity screening and progressive operator block reordering toward many-body inspired quantum state preparation.

The Journal of chemical physics·2026
Same author

Discovery of quaternary ammonium compounds with broad antibacterial activity and efficacy in S. aureus infection model.

European journal of medicinal chemistry·2026

Related Experiment Video

Updated: May 20, 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

Unitary group adapted state-specific multi-reference coupled cluster theory: formulation and pilot numerical

Rahul Maitra1, Debalina Sinha, Debashis Mukherjee

  • 1Raman Center for Atomic, Molecular and Optical Sciences, Indian Association for the Cultivation of Science, Kolkata 700 032, India.

The Journal of Chemical Physics
|July 19, 2012
PubMed
Summary

We developed a new spin-free multi-reference coupled cluster theory (UGA-SSMRCC) for accurate electron correlation descriptions. This method simplifies calculations and provides results closer to full configuration interaction, outperforming previous spin-orbital approaches.

More Related Videos

Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates
06:35

Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates

Published on: February 15, 2016

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

Related Experiment Videos

Last Updated: May 20, 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

Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates
06:35

Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates

Published on: February 15, 2016

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 Chemistry
  • Theoretical Chemistry

Background:

  • Accurate description of electron correlation is crucial in quantum chemistry.
  • Existing multi-reference coupled cluster (MRCC) methods can be computationally demanding and suffer from spin contamination.
  • Spin-free formulations offer potential advantages in simplifying calculations and improving accuracy.

Purpose of the Study:

  • To formulate and implement a novel spin-free state-specific multi-reference coupled cluster (SSMRCC) theory using the unitary group adapted (UGA) approach.
  • To provide a more computationally tractable and accurate alternative to existing MRCC methods.
  • To demonstrate the efficacy of the new UGA-SSMRCC formulation through numerical examples.

Main Methods:

  • Developed a spin-free SSMRCC theory based on the unitary group adapted (UGA) approach.
  • Utilized a multi-exponential cluster expansion of the wave-operator Ω with spin-free unitary generators.
  • Employed a normal-ordered exponential parametrization for the cluster expansion, leading to a terminating series and straightforward equation generation via Wick algebra.
  • Ensured size-extensivity and avoided intruder states through exploitation of redundancies in cluster operators.

Main Results:

  • The proposed UGA-SSMRCC theory offers a simpler and more accessible spin-free MRCC formulation compared to existing methods like the Datta-Mukherjee Ansatz.
  • Numerical results demonstrate that UGA-SSMRCC provides accurate descriptions of electron correlation.
  • For non-singlet systems, UGA-SSMRCC results show less spin contamination and are often closer to full configuration interaction (FCI) energies than spin-orbital based SSMRCC results, particularly compared to M(s)=0 calculations.

Conclusions:

  • The UGA-SSMRCC theory is an effective and computationally advantageous method for describing electron correlation in multi-reference systems.
  • This formulation simplifies spin-free MRCC calculations while maintaining high accuracy.
  • UGA-SSMRCC presents a promising advancement for theoretical chemistry, offering improved results over spin-orbital based methods, especially for non-singlet states.