Molecular orbital theory



In atoms, but are treated as moving under the influence of the nuclei in the whole molecule.[1] In this theory, each molecule has a set of molecular orbitals, in which it is assumed that the molecular orbital wave function ψf may be written as a simple weighted sum of the n constituent atomic orbitals χi, according to the following equation:[2]

\psi_j = \sum_{i=1}^{n} c_{ij} \chi_i

The cij coefficients may be determined numerically by substitution of this equation into the Schrödinger equation and application of the variational principle. This method is called the valence bond theory in the 1930s, before it was realized that the two methods are closely related and that when extended they become equivalent.

History

Main article: History of quantum mechanics

Molecular orbital theory was developed, in the years after valence bond theory (1927) had been established, primarily through the efforts of Friedrich Hund, ab initio quantum chemistry methods. Parallel to this rigorous development, molecular orbital theory was applied in an approximate manner using some empirically derived parameters in methods now known as semi-empirical quantum chemistry methods.[10]

Overview

Molecular orbital (MO) theory uses a linear combination of atomic orbitals) associated almost entirely with one nucleus or the other, and thus they spend equal time between nuclei or not. These electrons neither contribute nor detract from bond strength.

Molecular orbitals are further divided according to the types of atomic orbitals combining to form a bond. These orbitals are results of electron-energy levels.

MO theory provides a global, delocalized perspective on chemical bonding. For example, in the MO theory for hypervalent molecules, it is no longer necessary to invoke a major role for d-orbitals. In MO theory, any electron in a molecule may be found anywhere in the molecule, since quantum conditions allow electrons to travel under the influence of an arbitrarily large number of nuclei, so long as permitted by certain quantum rules. Although in MO theory some molecular orbitals may hold electrons which are more localized between specific pairs of molecular atoms, other orbitals may hold electrons which are spread more uniformly over the molecule. Thus, overall, bonding (and electrons) are far more delocalized (spread out) in MO theory, than is implied in VB theory. This makes MO theory more useful for the description of extended systems.

An example is that in the MO picture of benzene, composed of a hexagonal ring of 6 carbon atoms. In this molecule, 24 of the 30 total valence bonding electrons are located in 12 σ (sigma) bonding orbitals which are mostly located between pairs of atoms (C-C or C-H), similar to the valence bond picture. However, in benzene the remaining 6 bonding electrons are located in 3 π (pi) molecular bonding orbitals that are delocalized around the ring. Two are in a MO which has equal contributions from all 6 atoms. The other two have a vertical nodes at right angles to each other. As in the VB theory, all of these 6 delocalized pi electrons reside in a larger space which exists above and below the ring plane. All carbon-carbon bonds in benzene are chemically equivalent. In MO theory this is a direct consequence of the fact that the 3 molecular pi orbitals form a combination which evenly spreads the extra 6 electrons over 6 carbon atoms.[11]

In molecules such as methane, the 8 valence electrons are in 4 MOs that are spread out over all 5 atoms. However, it is possible to transform this picture, without altering the total wavefunction and energy, to one with 8 electrons in 4 localized orbitals that are similar to the normal bonding picture of four two-electron covalent bonds. This is what has been done above for the σ (sigma) bonds of benzene, but it is not possible for the π (pi) orbitals. The delocalised picture is more appropriate for ionisation and spectroscopic properties. Upon ionization, a single electron is taken from the whole molecule. The resulting ion does not have one bond different from the other three Similarly for electronic excitations, the electron that is excited is found over the whole molecule and not in one bond.

As in benzene, in substances such as metal.

See also

References

  1. ^ Daintith, J. (2004). Oxford Dictionary of Chemistry. New York: Oxford University Press. ISBN 0-19-860918-3. 
  2. ^ Licker, Mark, J. (2004). McGraw-Hill Concise Encyclopedia of Chemistry. New York: McGraw-Hill. ISBN 0-07-143953-6. 
  3. ^ Coulson, Charles, A. (1952). Valence. Oxford at the Clarendon Press. 
  4. ^ a b Spectroscopy, Molecular Orbitals, and Chemical Bonding - Robert Mulliken's 1966 Nobel Lecture
  5. ^ Lennard-Jones Paper of 1929 - Foundations of Molecular Orbital Theory.
  6. ^ Hückel, E. (1934). Trans. Faraday Soc. 30, 59.
  7. ^ Coulson, C.A. (1938). Proc. Camb. Phil. Soc. 34, 204.
  8. ^ Hall, G.G. Lennard-Jones, Sir John. (1950). Proc. Roy. Soc. A202, 155.
  9. ^ Frank Jensen, Introduction to Computational Chemistry, John Wiley and Sons, 1999, pg 65 - 69, ISBN 0 471 98055
  10. ^ Frank Jensen, Introduction to Computational Chemistry, John Wiley and Sons, 1999, pg 81 - 92, ISBN 0 471 98055
  11. ^ Introduction to Molecular Orbital Theory - Imperial College London
 
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