orbital

Examples of orbital in the following topics:

• 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.
  • In this case, carbon will sp2 hybridize; in sp2 hybridization, the 2s orbital mixes with only two of the three available 2p orbitals, forming a total of three sp hybrid orbitals with one p-orbital remaining.
  • 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.

• The Phase of Orbitals

  • When constructing molecular orbitals, the phase of the two orbitals coming together creates bonding and anti-bonding orbitals.
  • One orbital, based on in-phase mixing of the orbitals, will be lower in energy and termed bonding.
  • Another orbital, based on out-of-phase mixing of the orbitals, will be higher in energy and termed anti-bonding.
  • This molecular orbital is called the bonding orbital and its energy is lower than that of the original atomic orbitals.
  • P-orbital overlap is less than head-on overlap between two s orbitals in a σ-bond due to orbital orientation.

• Atomic and Molecular 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.
  • For example, the sigma molecular orbital that serves to bond two fluorine atoms together is generated by the overlap of p-orbitals (part A below), and two sp3 hybrid orbitals of carbon may combine to give a similar sigma orbital.
  • A mixing of the 2s-orbital with two of the 2p orbitals gives three sp2 hybrid orbitals, leaving one of the p-orbitals unused.

• sp Hybridization

  • In sp hybridization, the s orbital overlaps with only one p orbital.
  • When atomic orbitals hybridize, the valence electrons occupy the newly created orbitals.
  • The p orbital is one orbital that can hold up to two electrons.
  • Hybridization of an s orbital and a p orbital of the same atom produces two sp hybrid orbitals.
  • The left orbital energy-level diagram shows both electrons of Be in the 2s orbital.

• sp3 Hybridization

  • sp3 hybrid orbitals form when a single s and three p orbitals hybridize.
  • The single 2s orbital is spherical, different from the dumbbell-shaped 2p orbitals.
  • In hybridization, carbon's 2s and three 2p orbitals combine into four identical orbitals, now called sp3 hybrids.
  • 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.
  • In the water molecule, the oxygen atom can form four sp3 orbitals.

• 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

• Hybridization in Molecules Containing Double and Triple Bonds

  • In methane (CH4) for example, a set of sp3 orbitals forms by mixing one s- and three p-orbitals on the carbon atom.
  • 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.

• 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.
  • This MO is called the bonding orbital, and its energy is lower than that of the original atomic orbitals.
  • For a corresponding σ-bonding orbital, such an orbital would be symmetrical, but are differentiated from it by an asterisk, as in σ*.

• Hund's Rule

  • Electrons will fill the lowest energy orbitals first and then move up to higher energy orbitals only after the lower energy orbitals are full.
  • Every orbital in a sublevel is singly occupied before any orbital is doubly occupied.
  • Electrons tend to minimize repulsion by occupying their own orbital, rather than sharing an orbital with another electron.
  • Since electrons always occupy an empty orbital before they fill up, it would be incorrect to draw the two 2p electrons in the same orbital, leaving open orbitals unfilled.
  • The orbital diagram is drawn as follows: the first 2 electrons will pair up in the 1s orbital; the next 2 electrons will pair up in the 2s orbital.

• Crystal Field Theory

  • The d orbitals can also be divided into two smaller sets.
  • These three orbitals form the t2g set.
  • Conversely, the eg orbitals are higher in energy.
  • This gives an overview of the d orbitals.
  • The central model shows the combined d-orbitals on one set of axes.