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Atomic Orbitals and Quantum Numbers

  • Principle Quantum Number, n: Corresponds to the energy level of a given electron in an atom. Basically a measure of size. The smaller the number, the closer the shell is to the nucleus.
  • Azimuthal Quantum number, l: describes the subshells which are within each electron shell. l ranges from 0 to n-1.
  • 0 corresponds to the s subshell which is spherical and symmetric
  • 1 corresponds to the p subshell which is composed of two lobes located symmetrically about the nucleus and contains there is a node (zero probability)
  • 2 corresponds to the d subshell are four symmetrical lobes and have two nodes. Shapes are usually not tested.
  • 3 corresponds to the f subshell
  • Energy increases as l increases
  • Magnetic Quantum Number, ml: describes the orbitals within the subshell. Ranges from –l to +l.
  • Spin Quantum Number, ms: distinguishes the spin on the electrons in each orbital: ± 1/2

Molecular Orbitals

  • When two atomic orbitals combine, they form molecular orbitals.
    • If the signs of the wave function are the same, then a lower energy bonding orbital is produced.
    • If the signs are different, a higher energy antibonding orbital is produced.

Sigma and Pi Bonds (bonding)
  • Sigma Bonds: when a molecular orbital is formed by head-to-head or tail-to-tail overlap
    • All single bonds are sigma and they accommodate two electrons.
  • Pi Bonds: when two p-orbitals line up in parallel (Side-by-side)
    • One Pi bond on top of an existing sigma bond is a double bond
    • A sigma bond and two pi bonds forms a triple bond
    • Double and triple bonds hinder rotation and lock the atoms in position.
    • Cannot exist independently of a sigma bond
  • Double bonds are shorter than single bonds and thus are stronger
  • Pi bonds are weaker than Sigma bonds and will be broken first in order to turn a double bond into a single bond
  • Double bonds make for stiffer molecules


  • Hybrid Orbitals: formed by mixing different types of orbitals

  • Four orbitals point towards different vertices of a tetrahedron, which is why carbons prefer this geometry.
  • Most common type of hybridization for carbon.
  • If asked for how much “s character” a certain hybrid has. Simply look at the name and use it to solve the problem. Sp3 would have 25% s character and 75% p character

  • One s orbital is mixed with two p
  • Hybridization seen in alkenes
  • Third p-orbital is left unhybridized, this orbital participates in pi bonds.
  • Three hybridized sp2 orbitals are 120 degrees apart from each other

  • Hybridization for molecules with triple bonds: two p-orbitals are for pi bonds (unhybridized) while the third p orbital combines with the s orbital to form two sp-orbitals
  • sp hybridized orbitals are oriented 180 degrees apart


  • Resonance delocalization of electron occurs in molecules that have conjugated bonds
  • Conjugation: alternating single and multiple bonds
    • This pattern aligns a number of unhybridized p-orbitals down the backbone of the molecule
    • p electrons can then delocalize through the p-orbital system, which adds stability to the molecule.
  • True electron density will favor the most stable form (lacks formal charges, or form full octets on highly electronegative atoms).
  • The true form of a molecule is a hybrid of the multiple resonance structures.