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Related Concept Videos

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.
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...
Chemical Shift: Internal References and Solvent Effects01:17

Chemical Shift: Internal References and Solvent Effects

In an NMR sample, precise measurement of the absolute absorption frequencies of nuclei is difficult. A standard internal reference compound is added, and the frequency difference between the reference signal and sample signals is measured.
The internal reference compound generally used in NMR spectroscopy is tetramethylsilane (TMS). TMS is preferred because it is chemically inert, soluble in NMR solvents, and easily removable. Also, the highly shielded methyl protons in TMS yield an intense...
Reduced Mass Coordinates: Isolated Two-body Problem01:12

Reduced Mass Coordinates: Isolated Two-body Problem

In classical mechanics, the two-body problem is one of the fundamental problems describing the motion of two interacting bodies under gravity or any other central force. When considering the motion of two bodies, one of the most important concepts is the reduced mass coordinates, a quantity that allows the two-body problem to be solved like a single-body problem. In these circumstances, it is assumed that a single body with reduced mass revolves around another body fixed in a position with an...
Molecules with Multiple Chiral Centers02:25

Molecules with Multiple Chiral Centers

Molecules that possess multiple chiral centers can afford a large number of stereoisomers. For instance, while some molecules like 2-butanol have one chiral center, defined as a tetrahedral carbon atom with four different substituents attached, several molecules like butane-2,3-diol have multiple chiral centers. A simple formula to predict the number of stereoisomers possible for a molecule with n chiral centers is 2n. However, there can be a lower number where some of the stereoisomers are...

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Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
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Cholesky decomposition within local multireference singles and doubles configuration interaction.

Tsz S Chwee1, Emily A Carter

  • 1Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA.

The Journal of Chemical Physics
|February 23, 2010
PubMed
Summary

A new computational chemistry method, Cholesky decomposition local multireference singles and doubles configuration interaction (CD-LMRSDCI), significantly speeds up calculations for large molecules. This advance enables the study of complex chemical systems with up to 50 heavy atoms.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Theoretical Chemistry

Background:

  • Traditional multireference singles and doubles configuration interaction (MRSDCI) methods are computationally expensive.
  • Linear scaling methods aim to reduce the computational cost of electronic structure calculations.
  • Previous work introduced a linear scaling MRSDCI (LMRSDCI) method using Cholesky vectors.

Purpose of the Study:

  • To develop a more efficient and cost-effective local multireference singles and doubles configuration interaction (LMRSDCI) method.
  • To reduce the computational cost and storage requirements of LMRSDCI calculations.
  • To enable the application of LMRSDCI to larger molecular systems.

Main Methods:

  • Developed a local multireference singles and doubles configuration interaction method using Cholesky decomposition (CD-LMRSDCI).
  • Replaced nonorthogonal projected atomic orbitals with localized orthogonal virtual orbitals to simplify calculations.
  • Restructured the rate-limiting step to be driven by two-electron integral search, utilizing Cholesky vectors for efficient processing.

Main Results:

  • The CD-LMRSDCI method is an order of magnitude faster than previous LMRSDCI approaches.
  • Storage requirements are significantly reduced, allowing for calculations on molecules with up to 50 heavy atoms.
  • Cholesky vector generation, transformation, and integral assembly are the new rate-limiting steps, though overall efficiency is greatly improved.

Conclusions:

  • The developed CD-LMRSDCI method offers substantial speedups and reduced storage for electronic structure calculations.
  • This method significantly expands the feasibility of accurate quantum chemical studies for larger and more complex molecules.
  • Further optimization of Cholesky vector-related steps could lead to even greater computational efficiency.