Timeline of Structural Theory
In large part the science of chemistry is concerned with modelling the chemical structure of matter and understanding the nature of the chemical bond. However, the chemical bond sits right on the boundary between the classical and quantum mechanical worlds and academics, professional chemists and teachers liberally pick ideas, concepts and models from both. To understand the nature of chemical bonding it is necessary to see how the various ideas have developed over the past 200 years. This page introduces the main theoretical approaches to understanding chemical structure and reactivity, places them in historical context and considers them with reference to each other.
When chemists think about the structure and behaviour of a substance like ammonia, NH3, they are influenced by experimental (empirical) evidence, physical theory, the history of science, educational dogma and philosophical position.
There are three general approaches to understanding a substance such as ammonia, NH3:
Chemistry sits right on the boundary between the quantum and classical worlds: the chemical bond is a quantum mechanical construct but the behaviour of molecular entities can often and conveniently be described in classical terms. As a result we have two entirely different types of model of chemical structure, bonding and reactivity.
The diagram below shows a timeline of the development of the main theoretical chemical structure and reactivity ideas over the last 200 years:
The red arrows in the diagram are used to represent the act of "conversion from quantum to classical". They are used twice, between the Bohr atom and Lewis theory, and between VB theory and VSEPR theory. On both occasions there is a theoretical leap of faith because the impression is given that Lewis theory and VSEPR theory are based upon quantum theory, when they are not.
1803: John Dalton argued on the 21st of October 1803 to the Manchester Literary and Philosophical Society in Manchester, and I am writing this text on the 200th anniversary and less than a mile away for the atomic theory originally proposed by the Greeks. Dalton defined an atom as the smallest part of a substance that can participate in a chemical reaction. He proposed that elements are composed of identical atoms and that elements combine in definite proportions, stoichiometry. Dalton also produced an early table of atomic weights.
1869: The Mendeleev Tablelle I, the first plausible periodic table, was published. It was constructed using the recently discovered element, stoichiometric and periodicity data because some 35 elements had been discovered since 1800.
The success of this first version can be attributed to the gaps which Mendeleev correctly predicted would contain undiscovered elements, and he predicted their properties.
To the modern eye, the biggest omissions are the the Group 18 rare gases (He, Ne, Ar, K & Xe) and that only a small number of f-block elements are shown.
Of more importance, however, is that the elements are arranged by mass rather than atomic number, a concept had yet to be discovered so Mendeleev can be forgiven.
The 1869 Tabelle I is a quite remarkable construct:
1896: Radioactivity is a window into atomic structure.
In the year 1904, JJ Thomson proposed that the atom had a "plum pudding" structure, with the negative electrons in circular arrays – the plums – embedded in a spherical pudding of positive charge with mass evenly distributed. It was the study of radioactivity, in particular alpha radiation, that enabled Rutherford to develop his experiments to probe atomic structure.
Elements and Atoms: Case Studies in the Development of Chemistry
Carmen Giunta of Le Moyne College Department of Chemistry has collected many of the original papers plus commentary dealing with eighteenth and nineteenth century science in a web book called Elements and Atoms: Case Studies in the Development of Chemistry. This web resource is highly recommended:
Planck's constant is:
1905: Einstein and the Photoelectric Effect It was known from experiment that metals emit electrons when exposed to light (the system has to be in a vacuum), however, it could not be explained why the rate of emission depended upon the wavelength of the light in the way that it did. In 1905, Einstein showed that if light consisted of particle-like quantised photons, where the energy of the photon depended upon its wavelength, the photoelectric effect could be explained. This work led to a revolution in the understanding of both the electron and light. Light could behave as both a wave and a particle, depending upon the experiment. It was for this work that Einstein received the Nobel prize.
1911: Rutherford, already a Nobel prize winner (1908), interpreted the results of the Geiger-Marsden experiment involving a beam of alpha particles fired at a thin foil of gold designed to measure the deflection as the alpha particles interacted with the "plum-pudding" gold atoms.
Rutherford was astonished with the results which showed that most of the alpha particles passed straight through the gold foil unaffected, but a small minority were deflected by large angles. Rutherford commented at the result: "It was almost as incredible as if you fired a fifteen-inch shell at a piece of tissue paper and it came back and hit you".
Rutherford proposed a model of the atom had a very small, dense, positively charged nucleus surrounded by electrons.
The HyperPhysics website has a nice diagram comparing the tiny size of the nucleus and the size of a gold atom with the sizes of the Sun and the solar system. This is our version of the diagram, converted to metric units:
The "Rutherford Atom" has developed into a model that is still widely used, although the artists impressions hugely distort the relative sizes of the various atomic components (much to this author's annoyance!):
1913: The Bohr Atom In 1913 Niels Bohr - while working in Rutherford's laboratory - constructed a model of the atom that had small, light, fast, particle-like, negatively charged electrons "orbiting" a small, massive positively charged nucleus... although the reason why the electron did not spiral into the nucleus could not be explained. The electron shells were quantised, and as the electrons moved from shell to shell they emitted or absorbed photons the energy of which was equal to the energy difference between the shells.
The Bohr model is the first plausible model of the atom and it is still widely used in education, particularly in illustrations because it is so easy to draw and understand.
Lewis used the new ideas about atomic structure that were widely discussed in his labs:
Lewis proposed the two electron chemical bond, later named the covalent bond by Langmuir. Linus Pauling supported the Lewis analysis, here.
The Lewis model in its modern form is widely taught in schools and at university level, even though Lewis's electrons are entirely classical:
In essence, Lewis 'octet' theory is electron accountancy with magic numbers:
Some examples of Lewis theory in action:
Lewis theory is good at describing:
Lewis theory is very accommodating and is able to 'add-on' those bits of chemical structure and reactivity that it is not very good at explaining itself. Consider the mechanism of electrophilic aromatic substitution, SEAr:
In Lewis theory, benzene's six π-electrons have exactly the same status as neon's eight electrons. Both are magic numbers associated with stability, but no explanation is given as to why this should be so.
Read more about Lewis structures and the relationship between Lewis theory and other structural theories in an excellent page by physicist John Denker.
1913-25: Spectroscopy & Quantum Numbers Atomic spectra had been taken since the 1850s by scientists like Bunsen and Kirchhoff. In Denmark, Niels Bohr re-studied atomic spectra and - along with Sommerfield, Stoner and Pauli - devised the quantum numbers from empirical (spectroscopic) evidence:
1926: The Schrödinger Wave Equation
Edwin Schrödinger knew of de Broglie's proposal that a electrons exhibited wave-particle duality. With this idea in mind, he devised/constructed a differential equation for a wavelike electron resonating in three dimensions about a point positive charge.
Solutions to the Schrödinger wave equation - resonance modes described by mathematical wavefunctions - assumed discrete, quantised, energies which corresponded to spectral lines of one electron atoms and ions: H, He+, Li2+ etc., and they corresponded exactly with Bohr's quantum numbers. This development lead to quantum mechanics.
Waves and the the mathematical functions that describe them: wavefunctions, are well understood mathematically. For example, they can be added together or subtracted from each other. Consider two sine waves and their superposition, here:
The atomic orbitals derived from the Schrödinger wave equation, being waves, can be added together. The arithmetic can be carried out in various ways.
Atomic Orbitals are constructed from the four quantum numbers. The AOs fill with electrons, lowest energy AO first, the aufbau principle. An orbital can contain a maximum of two electrons, and these must be of opposite spin, the Pauli exclusion principle. One final rule, Madelung's rule points out that the orbitals fill with electrons as n + l, as principle quantum number plus subsidiary quantum number, rather than n.
Orbitals shape and phase. s-Orbitals are radial and they have n-1 (n minus one) nodes, where n is the principal quantum number. Thus, the 1s orbital is devoid of nodes, the 2s orbital has one node, etc. The s-orbital nodes are spherical and they are best viewed in cross section (below). There is a change of phase at the node. Max Born suggested that the squared wavefunction equates electron density, but squaring results in the loss of all phase information.
p-Orbitals have both radial and angular components and have a "figure of 8" shape.
1928: Pauling's Five Rules: Crystal Structure
The crystal structure of an ionic compound can be predicted using a set of empirical rules:
1932: Pauling's Electronegativity Linus Pauling used empirical heat of reaction data to introduce the elemental property of electronegativity which he defined as: "The desire of an atom to attract electrons to itself".
Electronegative elements, such as fluorine, "want" electrons so they can form negative ions while electropositive elements, such as cesium, like to lose electrons and form positive ions.
The great befit of electronegativity is that the numbers can be used to quantify this effect and predict bond dipole moment (polarity) and degree of ionic character. For example: fluorine (3.98) is electronegative and cesium (0.79) electropositive. CsF is strongly polarised Cs+ F and is 89% ionic.
1930: Valence Bond Theory Once atomic orbitals were understood in terms of both Bohr's quantum numbers and the Schrödinger wave equation, the quest was on to understand bonding in molecules. Linus Pauling's approach was to take the atomic orbitals and mix (hybridize) them together. For example, the 2s orbital can mix with the three 2p orbitals to give four "hybrid" sp3 orbitals which are arranged tetrahedrally about the central atom.
Thus, hybridization can rather easily explain the tetrahedral geometry of methane. Valence bond theory can also explain why the carbons in ethene (ethylene) are triangular planar by invoking sp2 hybridization and why ethyne (acetylene) is linear: sp hybridization.
VB theory also introduces the concept of "resonance", an idea dependent upon electronegativity. For example, chlorine is more electronegative than hydrogen and the compound hydrogen chloride, HCl, is polarised H+Cl. VB theory suggests the various possible forms are in resonance.
VB theory is widely employed in education because it produces easily understandable structures. However, the mathematics of orbital manipulation is easier if non-hybridized orbitals are employed. For this reason VB theory has become a theoretical "dead end" compared with MO theory... or has it? Look here.
Molecular Orbital Theory assumes that molecules are multi-nucleated atoms: the molecular orbitals, MOs, are assumed to encompass the two nuclei. Electrons are added to the MOs using the same rules that are used to add electrons to atomic orbitals: the aufbau principle and the Pauli exclusion principle. MOs have a similar geometry to atomic orbitals, but are more involved. The MO approach is most obviously seen and understood with diatomic molecules, H2, N2, etc.
The MO approach to diatomic hydrogen places the two nuclei (protons) close to each other. An electron is added to the lowest energy MO, the sigma bonding MO. The second electron also goes into the sigma MO. The third electron goes into the next MO which has a node between the two nuclei (a region of zero of electron density) and is called the "sigma star" antibonding MO.
However, the all encompassing MO approach is difficult to apply to molecules with many atoms. The 'trick' is to use the Linear Combination of Atomic Orbital (LCAO) simplification in which atomic orbitals are added together to form molecular orbitals. Hydrogen is constructed by adding two 1s orbitals into a 1 sigma MO.
The interaction of atomic and molecular orbitals can be represented in MO Energy diagrams:
There are various possible AO to MO interactions:
The LCAO approach has been highly developed in software. The AOs are described in terms of "basis functions", such as finite elements, Gaussian type orbitals (GTOs) or Slater type orbitals (STOs). (For historical reasons basis functions are called basis AOs. Such ab initio (or "from the start") software is able to calculate molecular geometry and energy to high precision. Commercial software is available.
1937/9: Hellmann-Feynman Theorem Wikipedia
The Hellmann-Feynman theorem states that once the spatial distribution of electrons has been determined by solving the Schrödinger equation, all the forces in the system can be calculated using classical electrostatics.
Thus classically, the equilibrium configuration of a molecule like H2, (HH, bond length 74 pm) has the resultant force acting on each nucleus vanishing. The electrostatic (++) repulsion between the two positive nuclei is exactly balanced by their attraction to the electrons between them.
The Hellmann-Feynman theorem was discovered independent by Hans Hellmann (1937) and Richard Feynman (1939).
1943: Valence Shell Electron Pair Repulsion (VSEPR) states that electron pairs (both bonded covalent electron pairs and nonbonded "lone-pairs" of electrons) repel each other. Methane, CH4, has four bonded electron pairs and these repel each other to give the four hydrogens tetrahedral geometry about the central carbon. Likewise, ammonia has three bonded electron pairs and one lone pair which mutually repel each other so that ammonia is trigonal pyramidal.
1960s: Frontier Molecular Orbital Theory was developed in the 1960s by Kenichi Fukui who recognised that chemical reactivity can often be explained in terms of interacting Highest Occupied MOs (HOMOs), Lowest Unoccupied MOs (LUMOs) and Singly Occupied MOs (SOMOs).
The FMO approach was developed by Woodward & Hoffmann in the late nineteen sixties who used it to explain an apparently diverse set of reactions involving π-systems, including Diels-Alder cycloaddition, here. Hoffmann used the approach to explore transition metal complexes.
1941: van Arkel-Ketelaar Triangle recognises three extreme types of bonding: metallic, ionic and covalent and that many bond types are intermediate between the extreme types. This behaviour can be rationalised in terms of electronegativity.
Read in detail about the van Arkel-Ketelaar Triangle in detail elsewhere in this web book.
1993 & 2008: Tetrahedron of Structure, Bonding & Material Type Michael Laing expanded the van Arkel-Ketelaar triangle into a tetrahedron by separating covalent bonding into two types: molecular and network covalent, although Laing uses the terms "van der Waals" and "covalent":
Molecular covalent materials consist of small molecules with strong intramolecular covalent bonds but weak van der Waals intermolecular attraction. Methane and ammonia are molecular materials.
Network covalent materials have strong covalent bonds which extend throughout the material, examples include: diamond, silica and phenolic resins.
Mark R Leach has recently, 2008, quantified the tetrahedron of structure, bonding & material type with respect to valency and electronegativity:
Read in detail about the Tetrahedra of Structure, Bonding & Material Type in detail elsewhere in this web book.
Mechanics and Molecular Dynamics
The techniques allows small molecules such as butane and cyclohexane to be energy minimised into their most stable conformation:
Larger molecules, including DNA and proteins can be modelled using MM software. Below is a representation of bacteriorhodopsin:
In recent years, molecular mechanics has been extended into molecular dynamics to model large dynamic structures, such as proteins, with move over a given time scale. Have a look here (MM) and here (MD).
Modern Geometry Optimisation Software uses a variety of techniques: molecular mechanics, semi-empirical, ab initio (from the beginning) and density functional. The quantum chemistry software completely hides the mathematics of the geometry optimisation process. A molecule is constructed (drawn) with a mouse and the energy minimised using any desired level of theory.
All computational methods uses a broadly similar strategy. Atoms are placed in virtual space in an approximate geometry with respect to bond lengths and angles. A calculation is performed to determine the energy of the system. The software then alters the geometry, and the energy is recalculated. The software loops, until it finds the arrangement of nuclei which gives the system the lowest energy, and this corresponds to the optimum molecular geometry.
The time taken to minimise depends upon the method used, the size of the molecule, the degree of precision required and well as the processor speed and available memory.
It is possible to mix-and-match. An entire protein may be modelled using MM/MD methodology, with the central active site plus substrate optimised using ab initio techniques. Software is available from a number of vendors: WaveFunction, HyperChem (download a fully functional but time limited demo version) and Gaussian.
The Electron Corral
The Bifurcation of Theories & Models
Lewis and colleagues actively debated the new ideas about atomic structure, the Rutherford & Bohr atoms, and postulated how they might give rise to models of chemical structure, bonding & reactivity. Taken directly from the Bohr atom, the Lewis model uses electrons that are "countable dots of negative charge".
Lewis's first ideas about chemical bonding were published in 1916, and later in a more advanced form in 1923. These early ideas have been extensively developed and are now taught to chemistry students the world over.
More advanced models of chemical structure, bonding & reactivity are based upon the Schrödinger equation in which the electron is treated a resonant standing wave.
Although largely outside the scope of this web book, the theoretical dichotomy also occurs in semiconductor physics where electrical behaviour is either modelled in terms of band theory, a natural development of MO theory or in terms of localised electrons & electron holes within the valance band, a development of the VSEPR model.
Summing Up: Mixing & Matching Models & Theories
Chemical theories are either based on:
Quantum chemistry texts can blur the distinction between quantum mechanics and classical mechanics and by grouping together LCAO MO calculations along with VSEPR, MM and MD techniques.
Pick n Mix When - as chemists - we consider a substance like ammonia, we employ a variety of models and ideas, fore example:
Can Orbitals be Observed?
One rather important question remains: Do atomic and molecular orbitals exist? Are they real?
The answer is: No. In principle orbitals cannot be observed.
© Mark R. Leach 1999-
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