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Molecular orbital theory

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In chemistry, molecular orbital theory is a method for determining molecular structure in which electrons are not assigned to individual bonds between atoms, but are treated as moving under the influence of the nuclei in the whole molecule. 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 constituent atomic orbitals χi, according to the following equation:

Ψ j = ∑ c i j X i {\displaystyle \Psi _{j}=\sum c_{ij}\mathrm {X} _{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 linear combination of atomic orbitals approximation and is used in computational chemistry. Molecular orbital theory is closely related to valence bond theory.

History

Molecular orbital theory was developed, in the years after valence bond theory (1927) had been established, primarily through the efforts of Friedrich Hund, Robert Mulliken, John C. Slater, and John Lennard-Jones. By 1933, the molecular orbital theory had become accepted as a valid and useful theory. According to German physicist and physical chemist Erich Hückel, the first quantitative use of molecular orbital theory was the 1929 paper of Lennard-Jones. The first accurate calculation of a molecular orbital wavefunction was that made by Charles Coulson in 1938 on the hydrogen molecule. By 1950, molecular orbitals were completely defined as eigenfunctions (wave functions) of the self-consistent field Hamiltonian and it was at this point that molecular orbital theory became fully rigorous and consistent. The following timeline shows the key steps and contributors in the precursory developments to each of these theories, which are both closely intertwined:

Date Person Contribution
1838 Michael Faraday Discovered “cathode rays” when, during an experiment, he passed current through a rarefied air filled glass tube and noticed a strange light arc starting at the anode (positive electrode) and ending at the cathode (negative electrode).
1852 Edward Frankland Initiated the theory of valency by proposing that each element has a specific “combining power”, e.g. some elements such as nitrogen tend to combine with three other elements (e.g. NO3) while others may tend to combine with five (e.g. PO5), and that each element strives to fulfill it’s combining power (valency) quota so as to satisfy their affinities.
1879 William Crookes Showed that cathode rays (1838), unlike light rays, can be bent in a magnetic field.
1891 Alfred Werner Proposed a theory of affinity and valence in which affinity is an attractive force issuing from the center of the atom which acts uniformly from towards all parts of the spherical surface of the central atom.
1892 Heinrich Hertz Showed that cathode rays (1838) could pass through thin sheets of gold foil and produce appreciable luminosity on glass behind them.
1896 Henri Becquerel Discovered “radioactivity” a process in which, due to nuclear disintegration, certain elements or isotopes spontaneously emit one of three types of energetic entities: alpha particles (positive charge), beta particles (negative charge), and gamma particles (neutral charge).
1897 Joseph Thomson Showed that cathode rays (1838) bend under the influence of both an electric field and a magnetic field and to explain this he suggested that cathode rays are negatively charged subatomic electrical particles or “corpuscles” (electrons), stripped from the atom; and in 1904 proposed the “plum pudding model" in which atoms have a positively charged amorphous mass (pudding) as a body embedded with negatively charged electrons (raisins) scattered throughout in the form of non-random rotating rings.
1900 Max Planck To explain black body radiation (1862), he suggested that electromagnetic energy could only be emitted in quantized form, i.e. the energy could only be a multiple of an elementary unit E = hν, where h is Planck's constant and ν is the frequency of the radiation.
1902 Gilbert Lewis To explain the octet rule (1893), he developed the “cubical atom” theory in which electrons in the form of dots were positioned at the corner of a cube and suggested that single, double, or triple “bonds” result when two atoms are held together by multiple pairs of electrons (one pair for each bond) located between the two atoms (1916).
1904 Richard Abegg Noted the pattern that the numerical difference between the maximum positive valence, such as +6 for H2SO4, and the maximum negative valence, such as -2 for H2S, of an element tends to be eight (Abegg's rule).
1907 Ernest Rutherford To test the plum pudding model (1904), he fired, positively-charged, alpha particles at gold foil and noticed that some bounced back thus showing that atoms have a small-sized positively charged atomic nucleus at its center.
1913 Niels Bohr To explain the Rydberg formula (1988), which correctly modeled the light emission spectra of atomic hydrogen, Bohr hypothesized that negatively charged electrons revolve around a positively charged nucleus at certain fixed “quantum” distances and that each of these “spherical orbits” has a specific energy associated with it such that electron movements between orbits requires “quantum” emissions or absorptions of energy.
1916 Arnold Sommerfeld To account for the Zeeman effect (1896), i.e. that atomic absorption or emission spectral lines change when the light is first shinned through a magnetic field, he suggesting that there might be “elliptical orbits” in atoms in addition to spherical orbits.
1919 Irving Langmuir Building on the work of Lewis (1916), he coined the term "covalence" and postulated that coordinate covalent bonds occur when the electrons of a pair come from the same atom.
1924 Louis De Broglie Postulated that electrons in motion are associated with some kind of waves the lengths of which are given by Planck’s constant h divided by the momentum of the mv = p of the electron: λ = h / mv = h / p.
1925 Friedrich Hund Outlined the “rule of maximum multiplicity” which states that when electrons are added successively to an atom as many levels or orbits are singly occupied as possible before any pairing of electrons with opposite spin occurs and made the distinction that the inner electrons in molecules remained in atomic orbitals and only the valence electrons needed to be in molecular orbitals involving both nuclei.
1925 Wolfgang Pauli Outlined the “exclusion principle” which states that no two identical fermions may occupy the same quantum state simultaneously.
1926 Erwin Schrödinger Used De Broglie’s electron wave postulate (1924) to develop a “wave equation” that represents mathematically the distribution of a charge of an electron distributed through space, being spherically symmetric or prominent in certain directions, i.e. directed valence bonds, which gave the correct values for spectral lines of the hydrogen atom.
1927 Walter Heitler Used Schrödinger’s wave equation (1926) to show how two hydrogen atom wavefunctions join together, with plus, minus, and exchange terms, to form a covalent bond.
1927 Robert Mulliken In 1927 Mulliken worked, in coordination with Hund, to develop a molecular orbital theory where electrons are assigned to states that extend over an entire molecule and in 1932 introduced many new molecular orbital terminologies, such as σ bond, π bond, and δ bond.
1928 Linus Pauling Outlined the nature of the chemical bond in which he used Heitler’s quantum mechanical covalent bond model (1927) to outline the quantum mechanical basis for all types of molecular structure and bonding and suggested that different types of bonds in molecules can become equalized by rapid shifting of electrons, a process called “resonance” (1931), such that resonance hybrids contain contributions from the different possible electronic configurations.
1929 John Lennard-Jones Introduced the linear combination of atomic orbitals approximation for the calculation of molecular orbitals.
1932 Werner Heisenberg Applied perturbation theory to the two-electron problem and showed how resonance arising from electron exchange could explain exchange forces.
1938 Charles Coulson Made the first accurate calculation of a molecular orbital wavefunction with the hydrogen molecule.

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.{{cite book}}: CS1 maint: multiple names: authors list (link)
  3. Coulson, Charles, A. (1952). Valence. Oxford at the Clarendon Press.{{cite book}}: CS1 maint: multiple names: authors list (link)
  4. Lennard-Jones Paper of 1929 - Foundations of Molecular Orbital Theory.
  5. Hückel, E. (1934). Trans. Faraday Soc. 30, 59.
  6. Coulson, C.A. (1938). Proc. Camb. Phil. Soc. 34, 204.
  7. Hall, G.G. Lennard-Jones, Sir John. (1950). Proc. Roy. Soc. A202, 155.

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