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The following is a loose tabular outline showing the historical development of molecular orbital theory (and possibly valence bonding theory as well?):

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.
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 (corpuscles), 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.
1899 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.
1925 Wolfgang Pauli Outlined the “exclusion principle” which states that no two identical fermions may occupy the same quantum state simultaneously.
1925 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, regarded as a distribution through space, which may be spherically symmetric or prominent in certain directions, i.e. directed valence bonds, with a certain density of charge at a particular point.
1928 Linus Pauling Outlined the quantum mechanical basis for 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.
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