Using operators to expand the block matrices forming the Hessian of a molecular potential

Martin Carlsen1

  • 1Department of Applied Mathematics and Computer Science, Technical University of Denmark, Building 303B, DK-2800, Kongens Lyngby, Denmark.

Related Concept Videos

Molecular Orbital Theory I02:35

Molecular Orbital Theory I

Overview of Molecular Orbital Theory
39.7K
Molecular Orbital Theory II03:51

Molecular Orbital Theory II

Molecular Orbital Energy Diagrams
21.7K
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...
1.7K
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...
11.3K
π Molecular Orbitals of 1,3-Butadiene01:24

π Molecular Orbitals of 1,3-Butadiene

Conjugated dienes have lower heats of hydrogenation than cumulated and isolated dienes, making them more stable. The enhanced stabilization of conjugated systems can be understood from their π molecular orbitals.
The simplest conjugated diene is 1,3-butadiene: a four-carbon system where each carbon is sp2-hybridized and has an unhybridized p orbital that contains an unpaired electron. According to molecular orbital theory, atomic orbitals combine to form molecular orbitals such that the...
8.6K
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...
51.7K