Main page QUANTUM CHEMISTRY PRIMER:  A BRIEF SUMMARY
 
Part I:   What are orbitals? Part II: Valence Bond Theory   Part III: Molecular Orbital Theory 
Atomic orbitals Hybridized orbitals Molecular orbitals 
Graphical representations of orbitals Electronic structure Energy ordering of MOs
How are bonds made? σ and π bonds Lobe size
Why are bonds made? Resonance HOMO & LUMO 
   

ABOUT ORBITALS AND BONDING

  1. Orbitals are volumes of space where electrons are allowed to spend their time.  These volumes are described by mathematical functions (wavefunctions) that have algebraic signs (plus or minus - do not confuse it with charge!).
  2. The wavefunctions themselves do not have physical equivalent, but the values of their squares correspond to the probability of finding an electron in given volumes of  space (called electron density).
  3. Orbitals (but not their graphical representations, see below) are constructed in such a way that the probability of finding one electron within their volume is unity (100%).
  4. An orbital may not accommodate more than two electrons.  These electrons must have opposite spins.
  5. Each orbital has energy associated with it; i.e. electrons within that orbital have the specified energy.
  6. The graphical representations of orbitals usually are drawn to show "spaces" corresponding to 90% probability of finding an electron within the enclosed volume. These 3D shapes are called teasingly for descriptive purposes: blobs, cages, boxes, etc.)  All the points on the drawn surfaces have identical (and usually quite low) electron density. They represent sort of "borders" or "skins" for spaces in which electrons are allowed.
  7. Atomic orbitals (s and p for us) are centered on atoms.  They serve as "building blocks" for orbitals found in molecules.
  8. The molecules are constructed from atoms, and the "new" volumes for electrons in the resulting molecules are constructed from the atomic orbitals of atoms participating in bonding. Two basic set of rules used are known as the Valence Bond (VB) Theory and the Molecular Orbital (MO) Theory.  The theories use different language, but are equivalent.
  9. In VB, atomic orbitals on a given atom are premixed (hybridized) and then used to form bonds, pairwise between atoms one bond at a time.
  10. In MO, atomic orbitals of all atoms are mixed to form molecular orbitals that span many atoms (or even the whole molecule).
  11. The driving force for bonding is to achieve a particularly stable electronic configuration  (see noble gases) when the atoms have two (for H), or eight electrons (for C, O, N, F) in their valence shells.  That configuration can be achieved by totally giving up electrons to the bonding partner (or taking them away).  In such a case we deal with ionic bonds that are rather uncommon in organic chemistry.  In most cases the octet configuration (or doublet for H) is achieved by sharing of electrons.  This kind of bonding is called covalent.
  12.  The sharing (bonding) is accomplished via superposition (overlap) of atomic or hybrid orbitals to form bonds (VB) or molecular orbitals (MO).  The overlap is accomplished in an "additive" manner (bonding) or in a "destructive" (subtractive) manner (antibonding).
  13. In the "additive" interaction of (for example) two atomic orbitals the new orbital volume encloses both atoms.  The electrons in that volume (valence orbital or molecular orbital) interact with both nuclei (the electrons are shared).  The new orbital is of lower energy than the atomic orbitals used to generate it.  To preserve the number of orbitals, the "additive" mode is accompanied by the "destructive" ("subtractive") mode where the new orbital volumes do not encompass both nuclei.  The electrons in such an orbital cannot be shared, i.e. the orbital has a node (or more precisely: a nodal plane) between the nuclei.  This (antibonding) orbital is of higher energy than the atomic orbitals from which it was generated. To the first approximation, the lowering of energy of the bonding orbital as compared to the constituent atomic orbitals is the same as the corresponding rise in energy of the antibonding orbital.
  14. The interaction of two orbitals (atomic, hybridized or molecular) is stronger (more energy lowering, see the point above) if the orbitals are closer in energy, and if the overlap between them (interpenetration of their spaces) is larger.

 
Important concepts: atomic orbitals, hybrid orbitals, molecular orbitals, overlap, bonding  orbitals, antibonding orbitals, nodes, orbital energies.
 

VALENCE BOND THEORY
  1. Bonds are made by overlap (electron sharing) of atomic (s, p) or hybridized (sp, sp2, sp3, spx) orbitals.  Formation of a bonding orbital (σ or π) is accompanied by the formation of the corresponding antibonding orbital (σ* or π*).
  2. Electrons are assigned (pairwise) to specific (localized) bonds.
  3. The electronic structure and geometry is arrived at (qualitatively) by finding the best compromise between the maximum overlap (electron-nucleus attraction) and repulsion (electron-electron and nucleus-nucleus).
  4. σ bonds are formed between a pair of atoms within the molecule and are characterized by the increased electron density on the imaginary line connecting the nuclei. The corresponding σ* also form, but are (usually) unoccupied by any electrons. 
  5. π bonds may cover more than two nuclei (see resonance) and are characterized by the increased electron density above and below the imaginary line connecting the nuclei (but not on the line itself).  The corresponding π* orbitals also form but (usually) remain unoccupied.
  6. The electrons are not always shared equally.  More electronegative atoms attract electrons more, and the electron density increases around the more electronegative atom at the expense of the less electronegative atom.  In the extreme, ionic bonds form (see bond dipoles and molecular dipole moments).
  7. Skeletal structures used in chemistry (Lewis structures) correspond to the valence bond model.
  8. Resonance structures are used to represent molecules that are not adequately described by a  single structure, usually because the electrons are shared by more than two nuclei (resonance = conjugation).

 
Important concepts: hybridization, hybrid orbitals, overlap, σ(σ*) and π (π*) bonds, resonance, resonance structures.
 

MOLECULAR ORBITAL THEORY

  1. Molecular orbitals (MO) are made of atomic orbitals.  All atoms in the molecule provide their atomic orbitals for construction of MO, but not all atomic orbitals must participate in all  MO.  The number of MO is equal to the number of atomic orbitals used to generate them.
  2. The MO are delocalized over many atoms.  In general, they do not directly correspond to specific bonds (the exceptions include simple diatomic molecules or some isolated π bonds, such as one in ethylene).
  3. The σ (or σ*) type MO are usually separated from π (or π*) type MO orbitals.  (One exception  that will be discussed by us is called hyperconjugation).
  4. The MO are filled by all available electrons (two per orbital) starting from the lowest energy MO orbital.
  5. The usual energy order of MO is as follows: σ-type orbitals (the lowest energy), π-type orbitals, n-type orbitals (nonbonding, such as lone pairs), π*-type orbitals and σ*-type orbitals (the highest in energy).  The exceptions are known (for example CO molecule). 
  6. In general for each type (σ or π) the energy of the MO increases with the increasing number of nodes (in the bonding sense).
  7. The electronegativity of atoms is reflected in the size of their lobes within the MO. Usually, in bonding orbitals there is more participation (the lobes are larger) by the more electronegative atoms.  In the corresponding antibonding orbitals the lobe sizes are reversed.
  8. All the electrons in all MO determine the structure of the molecule, but the Highest (in  energy) Occupied MO (HOMO) and the Lowest (in energy) Unoccupied MO (LUMO) are the most important from the point of view of reactivity.
  9. Usually, the HOMO corresponds to a filled π-type orbital or a lone pair (nonbonding  electrons), and the LUMO corresponds to an empty π*-type orbital or (if there is no π system) to an empty σ* orbital.
  10. The chemical reactions between molecules are largely governed by HOMO-LUMO interactions (the highest-energy electrons (HOMO) of one molecule "looking for" the lowest-energy unfilled space (LUMO) in the other molecule).  The electron-rich component's (see: Brønsted base, Lewis base, nucleophile, electron donor) HOMO will interact strongly with the electron-deficient component's (see: Brønsted acid, Lewis acid, electrophile, electron acceptor) LUMO.  The difference in energy between these orbitals and the overlap between them (orbital lobe size) will partially determine the facility of the reaction and the site of attack (bond formation).

 
Important concepts: bonding, nonbonding (lone pair) and antibonding MO; electron delocalization, σ (σ*) and π type MO, energies and shapes of MO, HOMO, LUMO.
 
Quantum Chemistry Primer Last updated 06/07/07 Copyright 1997-2008
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