atomic orbitals

Examples of atomic orbitals 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.
  • It is possible to combine the known orbitals of constituent atoms in a molecule to describe its electron orbitals.
  • 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

• Single Covalent Bonds

  • An atomic orbital is defined as the probability of finding an electron in an area around an atom's nucleus.
  • Covalent bonding occurs when two atomic orbitals come together in close proximity and their electron densities overlap.
  • Regardless of the atomic orbital type, sigma bonds can occur as long as the orbitals directly overlap between the nuclei of the atoms.
  • The shapes of the first five atomic orbitals are shown in order: 1s, 2s, and the three 2p orbitals.
  • These are all possible overlaps between different types of atomic orbitals that result in the formation of a sigma bond between two atoms.

• Atomic and Molecular Orbitals

  • A more detailed model of covalent bonding requires a consideration of valence shell atomic orbitals.
  • Just as the valence electrons of atoms occupy atomic orbitals (AO), the shared electron pairs of covalently bonded atoms may be thought of as occupying molecular orbitals (MO).
  • 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.

• sp2 Hybridization

  • The two carbon atoms form a sigma bond in the molecule by overlapping two sp2 orbitals.
  • Notice again how the three atomic orbitals yield the same number of hybrid orbitals.
  • The p-orbitals that are unused by the carbon atoms in the hybridization overlap to form the C=C.
  • The atomic s- and p-orbitals in boron's outer shell mix to form three equivalent 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.

• Hybridization in Molecules Containing Double and Triple Bonds

  • In chemistry, hybridization is the concept of mixing atomic orbitals to form new hybrid orbitals suitable for describing bonding properties.
  • The hybrids are named for the atomic orbitals involved in the hybridization.
  • In methane (CH4) for example, a set of sp3 orbitals forms by mixing one s- and three p-orbitals on the carbon atom.
  • When the two O-atoms are brought up to opposite sides of the carbon atom in carbon dioxide, one of the p orbitals on each oxygen forms a pi bond with one of the carbon p-orbitals.
  • The sp hybridized orbitals are used to overlap with the 1s hydrogen orbitals and the other carbon atom.

• The Building-Up (Aufbau) Principle

  • The Aufbau principle determines an atom's electron configuration by adding electrons to atomic orbitals following a defined set of rules.
  • The rule is based on the total number of nodes in the atomic orbital, n + ℓ, which is related to the energy.
  • It models atomic orbitals as "boxes" of fixed energy into which at most two electrons can be placed.
  • However, the energy of an electron in an atomic orbital depends on the energies of all the other electrons of the atom.
  • The likely location of an electron around the nucleus of an atom is called an orbital.

• The Phase of Orbitals

  • Two atomic orbitals can overlap in two ways depending on their phase relationship.
  • This molecular orbital is called the bonding orbital and its energy is lower than that of the original atomic orbitals.
  • In this anti-bonding molecular orbital with energy much higher than the original atomic orbitals, any electrons present are located in lobes pointing away from the central internuclear axis.
  • The in-phase combination of the s orbitals from the two hydrogen atoms provides a bonding orbital that is filled, whereas the out-of-phase combination provides an anti-bonding orbital that remains unfilled.
  • If two parallel p-orbitals experience sideways overlap on adjacent atoms in a molecule, then a double or triple bond can develop.

• sp Hybridization

  • Atoms that exhibit sp hybridization have sp orbitals that are linearly oriented; two sp orbitals will be at 180 degrees to each other.
  • When atomic orbitals hybridize, the valence electrons occupy the newly created orbitals.
  • The number of atomic orbitals combined always equals the number of hybrid orbitals formed.
  • The electronic differences in an isolated Be atom and in the bonded Be atom can be illustrated using an orbital energy-level diagram.
  • Hybridization of an s orbital and a p orbital of the same atom produces two sp hybrid orbitals.

• sp3 Hybridization

  • In a tetravalent molecule, four outer atoms are bonded to a central atom.
  • In the ground state of the free carbon atom, there are two unpaired electrons in separate 2p orbitals.
  • The simplest of these is ethane (C2H6), in which an sp3 orbital on each of the two carbon atoms joins (overlaps) to form a carbon-carbon bond; then, the remaining carbon sp3 orbital overlaps with six hydrogen 1s orbitals to form the ethane molecule.
  • If lone electron pairs are present on the central atom, thet can occupy one or more of the sp3 orbitals.
  • In the water molecule, the oxygen atom can form four sp3 orbitals.

• 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.
  • Pi, or $\pi$, bonds occur when there is overlap between unhybridized p orbitals of two adjacent atoms.
  • From the perspective of the carbon atoms, each has three sp2 hybrid orbitals and one unhybridized p orbital.
  • As the carbon atoms approach each other, their orbitals overlap and form a bond.
  • Each carbon has two sp hybrid orbitals, and one of them overlaps with its corresponding one from the other carbon atom to form an sp-sp sigma bond.