molecular orbital

Examples of molecular orbital in the following topics:

• Linear Combination of Atomic Orbitals (LCAO)

  • An LCAO approximation is a quantum superposition of atomic orbitals, used to calculate molecular orbitals in quantum chemistry.
  • These models provide a simple model of molecule bonding, understood through molecular orbital theory.
  • A linear combination of atomic orbitals, or LCAO, is a quantum superposition of atomic orbitals and a technique for calculating molecular orbitals in quantum chemistry.
  • Essentially, n atomic orbitals combine to form n molecular orbitals.
  • Predict which orbitals can mix to form a molecular orbital based on orbital symmetry, and how many molecular orbitals will be produced from the interaction of one or more atomic orbitals

• Theoretical Models for Pericyclic Reactions

  • A general introduction to molecular orbitals was presented earlier.
  • A molecular orbital diagram of ethene is created by combining the twelve atomic orbitals associated with four hydrogen atoms and two sp2 hybridized carbons to give twelve molecular orbitals.
  • The remaining six molecular orbitals are antibonding, and are empty.
  • As a rule, higher energy molecular orbitals have a larger number of nodal surfaces or nodes.
  • The wave functions that describe molecular orbitals undergo a change in sign at nodal surfaces.

• Atomic and Molecular Orbitals

  • It is convenient to approximate molecular orbitals by combining or mixing two or more atomic orbitals.
  • In general, this mixing of n atomic orbitals always generates n molecular orbitals.
  • The notation used for molecular orbitals parallels that used for atomic orbitals.
  • In the case of bonds between second period elements, p-orbitals or hybrid atomic orbitals having p-orbital character are used to form molecular orbitals.
  • The manner in which atomic orbitals overlap to form molecular orbitals is actually more complex than the localized examples given above.

• The Phase of Orbitals

  • When constructing molecular orbitals, the phase of the two orbitals coming together creates bonding and anti-bonding orbitals.
  • The sign of the phase itself does not have physical meaning except when mixing orbitals to form molecular orbitals.
  • Two same-sign orbitals have a constructive overlap forming a molecular orbital with the bulk of the electron density located between the two nuclei.
  • This molecular orbital is called the bonding orbital and its energy is lower than that of the original atomic orbitals.
  • A bond involving molecular orbitals that are symmetric with respect to rotation around the bond axis is called a sigma bond (σ-bond).

• Bonding and Antibonding Molecular Orbitals

  • In MO theory, molecular orbitals form by the overlap of atomic orbitals.
  • The sign of the phase itself does not have physical meaning except when mixing orbitals to form molecular orbitals.
  • Two same-sign orbitals have a constructive overlap, forming a molecular orbital with the bulk of the electron density located between the two nuclei.
  • A bond involving molecular orbitals that are symmetric with respect to rotation around the bond axis is called a sigma bond (σ-bond).
  • The next step in constructing an MO diagram is filling the newly formed molecular orbitals with electrons.

• Electron Configurations

  • The electron configuration is the distribution of electrons of an atom or molecule in atomic or molecular orbitals.
  • The electron configuration is the distribution of electrons of an atom or molecule in atomic or molecular orbitals.
  • Electron configurations describe electrons as each moving independently in an orbital, in an average field created by all other orbitals.
  • In atoms, electrons fill atomic orbitals according to the Aufbau principle (shown in ), stated as: a maximum of two electrons are put into orbitals in the order of increasing orbital energy—the lowest-energy orbitals are filled before electrons are placed in higher-energy orbitals.
  • The molecular orbitals are labelled according to their symmetry, rather than the atomic orbital labels used for atoms and monoatomic ions: hence, the electron configuration of the diatomic oxygen molecule, O2, is 1σg2 1σu2 2σg2 2σu2 1πu4 3σg2 1πg2.

• Explanation of Valence Bond Theory

  • In chemistry, valence bond (VB) theory is one of two basic theories—along with molecular orbital (MO) theory—that use quantum mechanics to explain chemical bonding.
  • $\pi$ bonds occur when two (unhybridized) p-orbitals overlap.
  • Both types of overlapping orbitals can be related to bond order.
  • VB theory complements molecular orbital (MO) theory, which does not adhere to the VB concept that electron pairs are localized between two specific atoms in a molecule.
  • MO theory states that electrons are distributed in sets of molecular orbitals that can extend over the entire molecule.

• Hybridization in Molecules Containing Double and Triple Bonds

  • Hybridized orbitals are very useful in explaining of the shape of molecular orbitals for molecules, and are an integral part of valence bond theory.
  • In sp2 hybridization, the 2s orbital mixes with only two of the three available 2p orbitals, forming a total of 3 sp2 orbitals with one p-orbital remaining.
  • sp hybridization explains the chemical bonding in compounds with triple bonds, such as alkynes; in this model, the 2s orbital mixes with only one of the three p-orbitals, resulting in two sp orbitals and two remaining p-orbitals.
  • In this model, the 2s orbital mixes with only one of the three p-orbitals, resulting in two sp-orbitals and two remaining unchanged p-orbitals.
  • The sp hybridized orbitals are used to overlap with the 1s hydrogen orbitals and the other carbon atom.

• sp2 Hybridization

  • In order to explain the bonding, the 2s orbital and two of the 2p orbitals (called sp2 hybrids) hybridize; one empty p-orbital remains.
  • The pi bond between the carbon atoms perpendicular to the molecular plane is formed by 2p–2p overlap.
  • This illustration shows how an s-orbital mixes with two p orbitals to form a set of three sp2 hybrid orbitals.
  • These particular orbitals are called sp2 hybrids, meaning that this set of orbitals derives from one s- orbital and two p-orbitals of the free atom.
  • In sp^2 hybridization, the 2s orbital mixes with only two of the three available 2p orbitals, forming a total of three sp^2 orbitals with one p-orbital remaining.

• Double and Triple Covalent Bonds

  • Double and triple bonds can be explained by orbital hybridization, or the 'mixing' of atomic orbitals to form new hybrid orbitals.
  • A combination of s and p orbitals results in the formation of hybrid orbitals.
  • Hybrid orbitals are denoted as spx, where s and p denote the orbitals used for the mixing process, and the value of the superscript x ranges from 1-3, depending on how many p orbitals are required to explain the observed bonding.
  • From the perspective of the carbon atoms, each has three sp2 hybrid orbitals and one unhybridized p orbital.
  • The bond lengths and angles (indicative of the molecular geometry) are indicated.