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Related Concept Videos

¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

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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...
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¹H NMR: Complex Splitting01:13

¹H NMR: Complex Splitting

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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...
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Hybridization of Atomic Orbitals II03:35

Hybridization of Atomic Orbitals II

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sp3d and sp3d 2 Hybridization
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Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule01:10

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In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the...
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Hybridization of Atomic Orbitals I03:24

Hybridization of Atomic Orbitals I

47.1K
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...
47.1K
¹H NMR: Pople Notation01:09

¹H NMR: Pople Notation

1.8K
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...
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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Hilbert space multireference coupled cluster tailored by matrix product states.

Ondřej Demel1, Jan Brandejs1,2, Jakub Lang1,3

  • 1J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic.

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A new multireference tailored coupled cluster (TCC) method overcomes bias in strongly correlated molecular systems. This approach treats multiple electronic configurations equally, improving accuracy for challenging quantum chemistry calculations.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Strongly Correlated Systems

Background:

  • Density matrix renormalization group (DMRG) is a leading method for strongly correlated molecules.
  • Standard tailored coupled cluster (TCC) methods exhibit bias in degenerate electronic cases.
  • Dynamic correlation is crucial but challenging to compute accurately in these systems.

Purpose of the Study:

  • Develop a Hilbert-space multireference tailored coupled cluster (MRCC) method.
  • Overcome the reference determinant bias of single-reference TCC.
  • Accurately treat systems with multiple important electronic determinants.

Main Methods:

  • Implemented and compared three Hilbert-space MRCC variants: state universal, Brillouin-Wigner, and Mukherjee's state specific.
  • Applied methods to cyclobutadiene and tetramethyleneethane diradicals.
  • Investigated sensitivity to highest occupied-lowest unoccupied molecular orbital (HOMO-LUMO) orbital rotations.

Main Results:

  • The developed Hilbert-space MRCC method successfully treats multiple determinants on an equal footing.
  • Performance comparison of the three MRCC variants was achieved.
  • Results highlight the importance of addressing orbital rotation sensitivity in Hilbert-space MRCC.

Conclusions:

  • Hilbert-space MRCC offers a robust solution for biased TCC in degenerate cases.
  • Accurate computation of dynamic correlation in strongly correlated systems is advanced.
  • The new method provides a more reliable tool for quantum chemical studies of complex molecules.