The Valence Stroke and the Valence Sphere One- and Three-Dimensional Models of Localized Molecular Orbitals

This book is about old wine (valence stroke diagrams) in new bottles (valence sphere models).

Strokes and spheres represent localized molecular orbitals, in the sense that, divorced from their diagrams and models they have no significance. The essence of organic stereochemistry lies in locations of substituents off single, double, and triple bonds.

Valence Sphere Models generate those locations almost magically. Illustrated is an observation made many years ago, in the 19th century, by Thomson and Tait, in the preface to their classic Elements of Natural Philosophy. "It is particularly interesting to note how many theorems, even among those not ordinarily attacked without the help of the Differential Calculus [and, today, in valence theory, with quantum mechanics and computers], have here been found to yield easily to geometrical methods of the most elementary character" [emphasis added].

Both representations above — stroke and sphere — place a tetrahedral arrangement of electron pairs about sites of atomic cores (not shown in the valence sphere models), whether the cores are involved in single, double, or triple bonds; or with lone pairs.

One arrangement (the tetrahedral arrangement) fits all (atomic cores that obey the Octet Rule: usually B+3, C+4, N+5, O+6, and F+7). The arrangement may be generated in two ways: occupancy of alternate corners of a cube, with the atomic core in question at the cube's center; and by the centers of four close-packed spheres, with the atomic core in question in the spheres' interstice, called in packing of, e.g., oxide ions about smaller cations in crystalline oxides a "tetrahedral interstice". The most important figure in chemistry, it's been said, is the tetrahedron. And, we would add, the sphere.

The Tetrahedron, the Cube, and the Tetrahedral Angle

A tetrahedron's corners occupy alternate corners of a circumscribed cube.

The tetrahedron's faces face the cube's other corners.

A face lies opposite a tetrahedron's corner.

(Those facts, we shall see, have enormous consequences for reaction mechanisms.)

The symbol "C" stands for the atomic core C+4. In attack by reagents that have protruding electron domains, the C+4 core moves outward, thereby lengthening its bond that lies opposite the attacked face.

Chemistry's most famous bond angle is "the tetrahedral angle": 109.47º

Bond angles HCH, HNH, and HOH of CH4, NH3, and H2O are 109.47º, 107.1º, and 104.5º.

PERSONAL NOTE: The author's interest in molecular structure was initially ignited on reading about those cited bond angles in an article by R. S. Mulliken, in 1952.

The Tetrahedron's Back Story

Chemistry has but one noteworthy theory and but one set of hypothetical ideas, the theory of the combination of atoms into molecules with its fundamental idea of valence. It is a most beautiful theory, surpassed by none other in the intellectual satisfaction it affords. NORMAN CAMPBELL

The tetrahedron's back story in chemistry, presented here for newcomers to chemical thought, illustrates the nature of the evolution of thought in an inductive science. The story begins with two familiar facts and ends with one of the leading inductions in the history of chemistry (along with John Dalton's Atomic Hypothesis and G. N. Lewis's conjecture regarding electron pairs), by van't Hoff, chemistry's first Nobel Laureate, in 1901.

TWO FAMILIAR FACTS. Molecules of water and carbon dioxide have the chemical formulas H2O and CO2.

A FACT ABOUT HYDROGEN ATOMS. No molecules have chemical formulas of the type HXn for n > 1. (HN3 — "hydrazoic acid" — is an exception.)

AN INFERENCE ABOUT HYDROGEN ATOMS. Hydrogen atoms are never attached by chemical bonds to more than one atom. (HN3's order of atomic attachments is HNNN.)

AN INDUCTION REGARDING H2O. H2O's order of atomic attachments is HOH (not HHO).

A LINGUISTIC CONVENTION REGARDING H. Chemists assign hydrogen atoms a "combining capacity" or "valence" of 1. Hydrogen, they say, is monovalent.

A DEDUCTION REGARDING OXYGEN ATOMS. Chemists deduce — from their linguistic convention for hydrogen; from the reason for that convention; and from the formula for water molecules — that oxygen atoms are divalent.

FACTS ABOUT COMPOUNDS OF CARBON AND OXYGEN. COO designates a peroxide, not thermodynamically stable carbon dioxide.

A CONCLUSION REGARDING CARBON DIOXIDE. Both atoms of oxygen of a molecule of carbon dioxide are attached to the carbon atom.

A DEDUCTION REGARDING CARBON ATOMS. Carbon atoms are tetravalent; or quadrivalent.

GRAPHIC EXPRESSIONS OF VALENCE ASSIGNMENTS. Chemists represent valence assignments by "valence strokes": 1 for H, 2 for O, 4 for C.

BOND FORMATION. To generate models of molecules, chemist indicate the "mutual saturation of chemical affinities" by pointing at each other valence strokes of two different moieties. Generated with hydrogen atoms are the figures -

Molecular hydrogen is, indeed, diatomic, molecular formula H2. Illustrated is -

THE RULE OF NO DANGLING VALENCE STROKES. Molecular hydrogen, for instance, is not H—.

Produced by the Rule are correct atomic linkages and molecular formulas for molecules of dihydrogen (H—H), water (H—O—H), and hydrogen peroxide (H—O—O—H). Not accounted for, however, by the drawing —O—, is -

A FACT ABOUT OXYGEN MOLECULES. They're diatomic!

AN INFERENCE REGARDING OXYGEN ATOMS. As for adjacent valence strokes of polyvalent carbon atoms, the pair of directed valence strokes of an oxygen atom are not collinear.

In an oxygen atom's "valence shell", together with its two valence strokes that represent shared electron pairs (discussed later; and illustrated on p1) are two pairs of unshared electrons.

For molecules of dioxygen and water, valence assignments together with "the mutual saturation of chemical affinities" procedure, the Rule regarding dangling affinities, and the angular inference regarding oxygen's affinities yield these valence stroke diagrams:

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H2O is, indeed, a bent molecule (

(OO bonds of O2, whose valence strokes...