Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Crystal Field Theory - Tetrahedral and Square Planar Complexes

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,...

Crystal Field Theory - Octahedral Complexes

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...

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

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...

Coupled Reactions

Coupled Reactions

Cellular processes such as building and breaking down complex molecules occur through stepwise chemical reactions. Some of these chemical reactions are spontaneous and release energy, whereas others require energy to proceed. Cells often couple the energy-releasing reaction with the energy-requiring one to carry out important cell functions.
Energy in adenosine triphosphate or ATP molecules is easily accessible to do work. ATP powers the majority of energy-requiring cellular reactions. Cells...

Spin–Spin Coupling: One-Bond Coupling

Spin–Spin Coupling: One-Bond Coupling

Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...

Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)

Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)

Vicinal or three-bond coupling is commonly observed between protons attached to adjacent carbons. Here, nuclear spin information is primarily transferred via electron spin interactions between adjacent C‑H bond orbitals. This generally favors the antiparallel arrangement of spins, so 3J values are usually positive.
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the involved orbitals. The...

You might also read

Related Articles

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

Sort by

Same author

Single-reference coupled-cluster theory based on the multi-purpose cluster operator.

The Journal of chemical physics·2026

Same author

Observation of Structurally Diverse Complexes OCeNi(CO)<sub>3</sub><sup>-</sup> and CeNi(CO)<sub>3</sub><sup>-</sup> with the Shortest Ce-Ni Bond and Ce≡O Triple Bond.

The journal of physical chemistry letters·2026

Same author

Fermionic mean-field dynamics for spin systems beyond free fermions.

The Journal of chemical physics·2026

Same author

Difunctional Uranium Catalysis for Photoaerobic C-N Bond Cross-Coupling.

The Journal of organic chemistry·2026

Same author

Atom-specific vibrational analysis reveals labile bonds in linear and branched PFOA molecules.

The Journal of chemical physics·2026

Same author

The optoelectronic properties of group IV nanoparticles.

Physical chemistry chemical physics : PCCP·2026

Search research articles

Related Experiment Video

Updated: May 8, 2026

Synthesis of In37P20(O2CR)51 Clusters and Their Conversion to InP Quantum Dots

Synthesis of In₃₇P₂₀(O₂CR)₅₁ Clusters and Their Conversion to InP Quantum Dots

Published on: May 7, 2019

Coupled cluster calculations on TiO2 nanoclusters.

Enrico Berardo¹, Han-Shi Hu, Karol Kowalski

¹Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, United Kingdom.

The Journal of Chemical Physics

|August 17, 2013

Summary

This summary is machine-generated.

Calculating excited states of titanium dioxide clusters using Equation-of-Motion Coupled Cluster (EOM-CC) methods reveals that including triple excitations significantly impacts excitation energies, especially for larger clusters. Active-space methods offer a cost-effective approach to accurate results.

More Related Videos

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

In Situ Synthesis of Gold Nanoparticles without Aggregation in the Interlayer Space of Layered Titanate Transparent Films

In Situ Synthesis of Gold Nanoparticles without Aggregation in the Interlayer Space of Layered Titanate Transparent Films

Published on: January 17, 2017

Related Experiment Videos

Last Updated: May 8, 2026

Synthesis of In37P20(O2CR)51 Clusters and Their Conversion to InP Quantum Dots

Synthesis of In₃₇P₂₀(O₂CR)₅₁ Clusters and Their Conversion to InP Quantum Dots

Published on: May 7, 2019

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

In Situ Synthesis of Gold Nanoparticles without Aggregation in the Interlayer Space of Layered Titanate Transparent Films

In Situ Synthesis of Gold Nanoparticles without Aggregation in the Interlayer Space of Layered Titanate Transparent Films

Published on: January 17, 2017

Area of Science:

Computational Chemistry
Quantum Chemistry
Materials Science

Background:

Titanium dioxide (TiO2) clusters are crucial in photocatalysis and materials science.
Accurate calculation of their electronic excited states is essential for understanding their optical properties.

Purpose of the Study:

To compute benchmark excitation energies for TiO2, Ti2O4, and Ti3O6 clusters.
To investigate the impact of including triple excitations in Equation-of-Motion Coupled Cluster (EOM-CC) calculations.

Main Methods:

Employed various Equation-of-Motion Coupled Cluster (EOM-CC) approaches.
Calculated excitation energies for singlet excited states.
Compared results from different levels of theory, including those with and without triple excitations.

Main Results:

Inclusion of triple excitations caused a rigid shift in excitation energies for TiO2 and Ti2O4.
Excited states crossing was observed for the Ti3O6 trimer upon inclusion of triples.
Perturbative treatment of triples offered no advantage over EOM-CCSD.
Active-space EOM-CCSDt(II/I) methods closely approximated full EOM-CCSDT results at lower computational cost.

Conclusions:

Triple excitations play a significant role in the excited states of titanium dioxide clusters, particularly for larger aggregates.
Active-space coupled cluster methods provide an efficient and accurate alternative for calculating excited states.