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The σ-π model differentiates bonds and lone pairs of σ symmetry from those of π symmetry, while the equivalent-orbital model hybridizes them. The σ-π treatment takes into account molecular symmetry and is better suited to interpretation of aromatic molecules ( Hückel's rule ), although computational calculations of certain molecules tend ...
In chemistry, sigma bonds (σ bonds) or sigma overlap are the strongest type of covalent chemical bond. [1] They are formed by head-on overlapping between atomic orbitals along the internuclear axis. Sigma bonding is most simply defined for diatomic molecules using the language and tools of symmetry groups. In this formal approach, a σ-bond is ...
These orbitals and typically given the notation σ (sigma bonding), π (pi bonding), n (occupied nonbonding orbital, "lone pair"), p (unoccupied nonbonding orbital, "empty p orbital"; the symbol n* for unoccupied nonbonding orbital is seldom used), π* (pi antibonding), and σ* (sigma antibonding). (Woodward and Hoffmann use ω for nonbonding ...
Molecules with multiple bonds or multiple lone pairs can have orbitals represented in terms of sigma and pi symmetry or equivalent orbitals. Different valence bond methods use either of the two representations, which have mathematically equivalent total many-electron wave functions and are related by a unitary transformation of the set of ...
Electronic band structure of graphene. Valence and conduction bands meet at the six vertices of the hexagonal Brillouin zone and form linearly dispersing Dirac cones. When atoms are placed onto the graphene hexagonal lattice, the overlap between the p z (π) orbitals and the s or the p x and p y orbitals is zero by symmetry.
An example of such a rearrangement is the shift of substituents on tropilidenes (1,3,5-cycloheptatrienes). When heated, the pi-system goes through an electrocyclic ring closing to form bicycle[4,1,0]heptadiene (norcaradiene). Thereafter follows a [1,5] alkyl shift and an electrocyclic ring opening. norcaradiene rearrangement
The fact that the Pauli matrices, along with the identity matrix I, form an orthogonal basis for the Hilbert space of all 2 × 2 complex matrices , over , means that we can express any 2 × 2 complex matrix M as = + where c is a complex number, and a is a 3-component, complex vector.
At the same time the p z-orbitals approach and together they form a p z-p z pi-bond. Likewise, the other pair of p y-orbitals form a p y-p y pi-bond. The result is formation of one sigma bond and two pi bonds. In the bent bond model, the triple bond can also formed by the overlapping of three sp 3 lobes without the need to invoke a pi-bond. [5]