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Related Concept Videos

Hybridization of Atomic Orbitals II03:35

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization
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...
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...
Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

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...
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...
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,...

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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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Published on: April 8, 2020

Quartic scaling second-order approximate coupled cluster singles and doubles via tensor hypercontraction: THC-CC2.

Edward G Hohenstein1, Sara I L Kokkila, Robert M Parrish

  • 1Department of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, USA.

The Journal of Chemical Physics
|April 6, 2013
PubMed
Summary

We introduce a new method, tensor hypercontraction coupled cluster singles and doubles (THC-CC2), to speed up electronic structure calculations. This approach significantly reduces computational scaling for larger molecules.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Electronic Structure Theory

Background:

  • Coupled cluster singles and doubles (CC2) is a key method in electronic structure theory.
  • Density fitting approximations have extended CC2 but struggle with O(N^5) scaling.
  • The computational cost limits CC2's application to larger molecular systems.

Purpose of the Study:

  • To develop a more computationally efficient variant of the CC2 method.
  • To reduce the scaling of CC2 calculations from O(N^5) to O(N^4).
  • To enable the study of larger molecules using CC2.

Main Methods:

  • Introduction of the tensor hypercontraction (THC) approximation to CC2 (THC-CC2).
  • Development of an efficient algorithm for evaluating the THC-CC2 correlation energy.
  • Implementation using a grid-based least-squares THC (LS-THC) approximation for density-fitted integrals.

Main Results:

  • THC-CC2 reduces computational scaling to O(N^4) and storage to O(N^2).
  • Demonstration of the method's quartic scaling.
  • The accuracy of THC-CC2 correlation energies is suitable for practical applications.

Conclusions:

  • THC-CC2 offers a significant computational advantage over traditional CC2.
  • The method effectively addresses the scaling limitations of CC2 for larger systems.
  • THC-CC2 is a promising tool for electronic structure calculations in chemistry.