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Related Concept Videos

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...
Frost Circles for Different Conjugated Systems01:18

Frost Circles for Different Conjugated Systems

The inscribed polygon method is consistent with Hückel’s 4n + 2 rule and helps to learn whether the given cyclic compound is aromatic or not. The compound is stable and aromatic if every bonding molecular orbital (MO) is completely filled with a pair of electrons. However, if the non-bonding or antibonding orbitals are filled with electrons, the compound is unstable and not aromatic. Consider the Frost circle diagrams for cycloalkenes containing 4 to 8 carbons.
Structure of Benzene: Molecular Orbital Model01:18

Structure of Benzene: Molecular Orbital Model

According to the molecular orbital (MO) model, benzene has a planar structure with a regular hexagon of six sp2 hybridized carbons. As shown in Figure 1, each carbon is bonded to three other atoms with C–C–C and H–C–C bond angles of 120°. The C–H bond length is 109 pm, and the C–C bond length is 139 pm which is midway between the single bond length of sp3 hybridized carbons (154 pm) and sp2 hybridized carbons (133 pm).
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.
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.
Newman Projections02:06

Newman Projections

Different notations are used to represent the three-dimensional structure of molecules on two-dimensional surfaces. One of the most commonly used representations is the dash-wedge formula. The dashed wedges, solid wedges, and the plane lines indicate the groups situated behind the plane, coming out of the plane, and in the plane, respectively.
The organic molecules rotate across the single bonds leading to numerous temporary three-dimensional structures of varying energy known as conformers.

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Related Experiment Video

Updated: Jul 11, 2026

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules
09:32

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules

Published on: April 12, 2019

RNA structures with pseudo-knots: graph-theoretical, combinatorial, and statistical properties.

C Haslinger1, P F Stadler

  • 1Institut für Theoretische Chemie, Universität Wien, Austria. grisu@tbi.univie.ac.at

Bulletin of Mathematical Biology
|September 22, 2007
PubMed
Summary
This summary is machine-generated.

This study introduces bi-secondary structures, a generalized RNA structure model that includes pseudo-knots. RNA folding patterns remain largely consistent even with pseudo-knots, revealing extensive neutral networks in sequence space.

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Last Updated: Jul 11, 2026

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules
09:32

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Published on: April 12, 2019

Analyzing and Building Nucleic Acid Structures with 3DNA
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Published on: August 15, 2018

Area of Science:

  • Computational biology
  • Bioinformatics
  • Structural biology

Background:

  • Nucleic acid secondary structures are crucial contact structures.
  • Conventional definitions exclude pseudo-knots, found in many functional RNA molecules.

Purpose of the Study:

  • To generalize RNA secondary structures to include pseudo-knots, termed bi-secondary structures.
  • To analyze the complexity and properties of these generalized structures.
  • To investigate the impact of pseudo-knots on RNA folding and sequence-structure relationships.

Main Methods:

  • Developed a graph-theoretical framework for bi-secondary structures.
  • Derived exact upper bounds on the number of bi-secondary structures.
  • Utilized kinetic folding simulations and an extended energy model.

Main Results:

  • Bi-secondary structures are planar trivalent graphs with specific embedding properties.
  • The number of bi-secondary structures grows approximately as 2.35n.
  • Introducing pseudo-knots does not alter global RNA sequence-structure map features.
  • A significant fraction of neutral mutations and interconnected neutral networks were identified.

Conclusions:

  • Bi-secondary structures provide a more comprehensive model for RNA structural diversity.
  • Pseudo-knots do not fundamentally change RNA folding landscapes, supporting evolutionary adaptability.
  • The identified neutral networks suggest robust evolutionary pathways for RNA molecules.