The author begins this account of the development of bond theory with a description of the development of the "Lewis atom" which was really an account of the early electronic theory of bonding developed by G. N Lewis from a series of observations and studies starting from Helmholtz claim of the constant charge of an atom and the electrical nature of chemical affinity based on Faraday's electrolytic work. A partial source of this charge was determined from the 1897 discovery of the electron by J. J. Thomson in Cavendish Laboratory where he detected a negatively charged particle lighter than a hydrogen atom when carrying out experiments on ‘conduction of electricity through gases at low pressures’. From these results, Thomson developed the “plum pudding model of negatively charged electrons being embedded in a sphere of positive charge”. Chemical bonds were then interpreted as stemming from the transfer of electrons from an outer circle of electrons to the adjacent atom. In 1904, Thomson developed the first electronic theory of valency: “the chemical bond was nothing more or less than simple electrostatic attraction. A bond was formed when two atoms exchanged, or transferred, one or more electrons, the donor thereby becoming positively charged and the receiver, negatively charged”. As early as 1902, Lewis had developed ideas of bonding (e.g. ‘cubic atoms’) based on observations of the stability of the rare gases (noble) being attributed to the presence of 8 electrons in the outermost sphere of Thomson’s plum pudding model. In 1904, R. Abegg, formally recognized a ‘rule of eight’, pointing to a pattern in the formation of compounds whose valencies (I think he meant here the ‘charge’ formed) of the individual atoms add up to 8, e.g. see table in book. In 1910, Falk and Nelson published a paper entitled “The electron conception of valence” supporting Thomson’s electronic theory of valency in which bonds were formed by the transfer of electrons producing positively and negatively charged particles, introducing bonds as arrows representing the direction of electron transfer. “Although their polarity theory did not explain the bonding of nonionizing molecules, much solid-phase chemistry seemed to support it.” Further essays by other physical chemists “firmly established a polar theory of chemical bonding in America”. Polarity theory was useful to inorganic chemistry but did not serve organic chemistry well, arguing against it on the basis of “the phenomenon of tautomerism, the low dielectric constants, and the poor conductivities of organic compounds”. After 1913(?), Thomson switched from his plum pudding model to one of a “planetary-nuclear model of the atom” based on evidence from Rutherford’s studies, concluding that there were two types of bonds (independently of the Americans), polar and nonpolar where the nonpolar bond can be described as “tubes of force anchoring electrons both to the nucleus and to an adjacent atom” with each bond equivalent to two ‘tubes of force’ or two electrons.
In 1916, hitting upon the shared electron pair theory of bonding, Lewis wrote: “It seemed rather that the union of sodium and chlorine and the union of hydrogen and carbon must represent extreme types of a method of combination which ultimately would be found to be common to all kinds of compounds”. The author interprets this as “where electrons were equally shared, the electron exhibited no polar properties, but if one atom took an unfair share, then the charge being unequally distributed polarity would be produced”. Irving Langmuir helped publicize Lewis’ theory of the shared electron pair bond contributing the term “covalent bond’ to replace nonpolar bond and “reconciling’ Lewis’ static electrons with Bohr’s dynamic electrons. In 1923, Lewis published Valence and the Structure of Atoms and Molecules. In it, he wrote to explain the reactivity of elements and compounds using concepts of dynamic electrons and electrical Coulomb forces of attractions and repulsion. He used Bury’s and Bohr’s theory of electrons in shells shielding the nucleus and where the “orbit as whole” and not the position of an electron within the orbit that drives the chemical behavior. In this theory, “two atoms may conform to the rule of eight or the octet rule not only by the transfer of electrons from one atom to another, but also by sharing one or more pairs of electrons. The electrons which are held in common by two atoms may be considered to belong to the outer shell of both atoms”. Complete ionization was then considered a special case of the new theory. In this context, valency was then defined as the ‘number of electron pairs which an atom shares with another atom’.
Two other important ideas were covered in Lewis’ Valence book: 1) a broader definition of acids as electron pair acceptors and bases as electron pair donors; and 2) identification of hydrogen coordination between a carbon and oxygen atom by his student Maurice Huggins as a “hydrogen bond”
Lewis' electronic theory of bonding found a receptive audience in America and Britain but was slow to spread in France and Germany due to a number of political, cultural, and social factors. In the meantime, however, the wheels of mathematical physics were actively turning in Germany. One of the significant events related to the electronic theory is the determination of the number of electrons necessary to neutralize what can then be measured by x-ray spectroscopy (by correlation) as the number of positive charges in an atom. In 1912, Max von Laue, an optical physicist, postulated that “if x-rays were shortwave radiation then, assuming that crystals arose from a periodic array of atoms comparable in dimensions to the wavelength of the x-radiation, the waves ought to be diffracted”. Experiments to confirm the diffraction effects were then used by Bragg father and son to develop a mathematical method of crystal structure determination. Harold Moseley used these results to develop the science of x-ray spectroscopy. By measuring the wavelengths of characteristic reflections for each element, Moseley discovered a ‘unique atomic number’ that when arranged in sequence (with a few exceptions) followed the same order of the elements in periodic table according to atomic weight’. Because the atomic number equaled the positive nuclear charge (not sure how this connection was made), the number of electrons in each required for a neutral overall charge can now be determined. This significant finding prompted the author to note that “Rontgen’s discovery therefore, not only revolutionized orthopedic surgery, but helped to transform chemists’ ideas of the structure of materials and stimulated the physicists’ interpretation of the nature of the atom”.
Development of the quantum mechanical theory of electronic structure:
By the end of the 19th century, there was a clear bifurcation in fields of interests of chemists and physicists: chemists dealt with 90 or so elements of matter while physicists dealt with “a more nebulous mathematical world of energy and electromagnetic waves”. The chemists’ material particles were discrete while energy was continuous. In the early 1900’s, Max Planck’s developed his quantum theory based on his blackbody radiation studies that showed that, "at the atomic level, energy could not be emitted or absorbed continuously but only in small discrete steps he called quanta. In this quantum theory, energy radiated from a lamp or heat source only appeared to radiate continuously because it was a smoothed or averaged effect of large numbers of quanta” (which Einstein called photons in 1905). In 1913 Bohr developed his planetary model of the atom skirting the "paradox of classical physics that revolving electrons would lose energy continuously and therefore slowly collapse into the nucleus", by assuming that electrons revolved around the nucleus without radiating continuously. Adopting Planck's quantum theory, he correlated observed lines in a substance's spectrum with the energy of the emitted or absorbed photon as an electron jumped from one orbit to another. Good correlation was found with experimental data for hydrogen but "atoms with more than one electron proved more recalcitrant.” In 1923 Bohr and Bury’s were able to correlate atomic electronic structure theory with spectroscopic data by refining Bohr’s planetary model with the addition of quantum numbers to define the ‘orbits’ and the magnetic and spin properties of electrons within the atom. In this refined theory, electrons were assumed to be arranged into shells corresponding to the principal quantum number n. Subshells were assumed to exist to explain the properties of the transition and rare-earth elements. In 1924 Louis de Broglie’s thesis postulated a dual nature (corpuscular and wave-like) to electrons in analogy to Einstein’s postulate of the dual nature of light. (Davisson and Germer in 1927 found evidence for this upon observing electrons exhibiting diffraction patterns like x-rays by being diffracted by matter.) Building upon deBroglie's thesis, in 1926, Erwin Schrodinger used wave mechanics and formulated a partial differential equation (now known as Schrodinger’s equation) whose solution/s were interpreted as a measure of the density of electron charge at each point and equivalent to a probability density for an electron being found at a particular point in the ‘wave cloud’. (Pauling was to later interpret this electron cloud as the region where bonds were most likely to form.). Heisenberg applied abstract matrix algebra to reformulate Planck’s treatment of discontinuous phenomena and this "‘new quantum mechanics’ fitted the known spectral phenomena even better than Bohr’s and Sommerfeld’s treatment and was soon to be found equivalent formally to the ‘wave mechanics’ treatment of Schrodinger.”
The Pauling Bond
Pauling’s first substantial involvement in developing a bond theory could be found in his doctoral dissertation (on x-ray crystallography study of crystal structures) where he noted that the atomic radii of atoms were “squashed” in the direction in which they formed covalent bonds, a finding that would prove useful in studying the nature of the chemical bond between atoms. In 1927, Heitler and London produced the first ever quantum mechanical treatment of a chemical system, calculating the energy of the hydrogen molecule where the two electrons are held together by two protons. As a result of this, they were able to come up with a ‘fairly’ simple expression for the hydrogen wave function that could be fitted into the Schrödinger equation, “the solution to which gave a binding energy impressively close to that obtained from spectroscopic studies”. Pauling developed his valence bond model for chemical bonding based on his analysis of the Heitler-London treatment of the hydrogen molecule which they extended to the H2+ molecular ion. According to J. H. Sturdivant, Pauling did this “to make the results of quantum mechanics accessible and familiar to chemists untrained in the new theoretical physics, and to fuse the results into the foundations of chemical theory”. Chemical bonding was then explained qualitatively using quantum mechanical results as an overlapping of orbitals (probability density regions defined by solutions to SE) occupied by shared electrons of opposite spins (now taught as Pauling’s spin pairing theory). Friedrich Hund formulated a ‘rule of maximum multiplicity’ (now taught as Hund’s rule) which stated that successive electrons occupy separate orbitals before pairing up with opposite spins (1926). In a 1931 publication in JACS, to explain the observed tetrahedral geometry of tetravalent carbon, Pauling developed the concept of hybridization of s and p orbitals showing lowered energy overall for stable bond formation and resulting in a tetrahedral geometry of the resulting orbitals. The author noted other contributions by Pauling (detailed in his Nature of Chemical Bond book): determination of the ‘electronegativities of compounds’ as the “difference between their energies if all the bonds were covalent and all were ionic”; correlation of diamagnetic and paramagnetic properties to the presence of opposed spins in the paired bonding electrons and the presence of unpaired electrons, respectively; determination of bond angles, ion radii using crystallography; thermodynamic calculation of the energy of crystals; interpretation of the structure of benzene and its reactions. During his prolific career, Pauling found himself working on biochemical research: he determined that the bond between oxygen and hemoglobin is covalent giving arterial blood diamagnetic properties whereas venous blood has paramagnetic properties. Between 1946-1949, he discovered that the disease anemia was due to a deformation of the hemoglobin. In 1936, he developed a theory (along with Alfred Mirsky) that proteins are coiled chains of polypeptide units held together by hydrogen bonds and came up with the stable alpha helix structure for some proteins.
Molecular Orbital Theory
Developed by Spectroscopists Hund and Robert S. Mulliken in 1927-28, the Hund-Mulliken interpretation attributed the more complex spectra of molecules to various rotational, vibrational, and oscillatory motions of nuclei and of electrons around the nuclei. In this treatment of diatomic molecules, the electronic structure of the hydrogen molecule was thought of as being that of a helium atom that has separated rather than two atoms of hydrogen to take into account the more complex interaction between a 2-proton center and each electron. This approach then describes the H-H bond as a ‘molecular orbital’ emerging from the 2 1s electrons. The author summarized the three consequences of this model: it ‘codified and clarified’ spectroscopy; led to the concept of electron promotion (and concept of excited states) and correlated orbitals of diatomic molecules with those of a ‘united atom’ and those of a ‘separated atom’; and became an alternative to the valence bond theory of Pauling. In the 1940’s-1950’s, MO theory began to gain more ground as a better model for dealing with polyatomic molecules. Part of the reason for the increasing relevance of the MO theory was its ‘simplicity’ relative to Pauling’s resonance concept (“by picturing the VB treatment as equivalent to saying that mathematically the bonds between two atoms have to be built up from the polar and covalent forms”) which was not well-received in some circles. He defended it by saying that “his approach was an honest extension of structural theory in which, in any case all formulae were idealizations”. In 1967, Pauling conceded and devoted a substantial section of his introduction to modern structural chemistry text to MO theory but still noted the need to use the simpler VB method for introductory teaching. The author ended this chapter with the following final comment on the competition between MO and VB models: “Paradowski goes to the heart of the matter in his comment on the rivalry between VB and MO 15 : In physics it is possible to develop a simple and detailed model to explain certain classes of phenomena, but chemistry is too complex to be fully explained by such simple theories. To explain chemical phenomena at the present time [1972], one needs several good models. But these ‘good’ models are more flagrantly models, i.e. they explain only a selection of data, and hence the need for several models. Depending upon the symbolic apparatus used, different truths emerge. Twenty years on, this assessment remains true. Theoretical chemistry is still a quirky empirical science based upon a Schrödinger equation that can hardly ever be solved.”
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