Carbon-based bonding radii

Lewis cubical atom model. Molecular orbital calculations on the one-electron molecule and the two-electron molecule H2 

The modern theory of chemical bonding begins with the article The Atom and the Molecule published by the American chemist G. N. Lewis in 1916 [1], In this article, which is still well worth reading, Lewis for the first time associates a single chemical bond with one pair of electrons held in common by the two atoms After a brief review of Lewis model we turn to a quantum-mechanical description of the simplest of all molecules, viz. the hydrogen molecule ion H J. Since this molecule contains only one electron, the Schrodinger equation can be solved exactly once the distance between the nuclei has been fixed. We shall not write down these solutions since they require the use of a rather exotic coordinate system. Instead we shall show how approximate wavefunctions can be written as linear combinations of atomic orbitals of the two atoms. Finally we shall discuss so-called molecular orbital calculations on the simplest two-electron atom, viz. the hydrogen molecule. 

---

Revised Values of Double-Bond Covalent Radii.—This investigation has led to the value 1.34 A. for the carbon-carbon double-bond distance, 0.04 A. less than the value provided by the table of covalent radii.111 4 Five years ago, when this table was extended to multiple bonds, there were few reliable experimental data on which the selected values for double-bond and triple-bond radii could be based. The single-bond radii were obtained -from the study of a large number of interatomic distances found experimentally by crystal-structure and spectroscopic methods. The spectroscopic value of the triple-bond radius of nitrogen (in N2) was found to bear the ratio 0.79 to the single-bond radius, and this ratio was as-... 

The Wiener index [86] can be expressed in terms of the distance matrix [87] and equals the half-sum of all distance matrix entries. Randi(5 [88] and Kier and Hall indices of order 0-3 [89] are calculated from coordination numbers of atoms or from values of atomic connectivity. The Kier shape index (order 1-3) [90] depends on the number of skeletal atoms, molecular branching, and the ratio of the atomic radius and the radius of the carbon atom in the sp hybridization state. The Kier flexibility index [90] is derived from the Kier shape index. The Balaban index depends on the row sums of the entries of the distance matrix and the cyclomatic number [92,93]. The information content index and its derivatives (order 0-2) are based on the Shannon information theory [95]. Modifications of the information content index are structural information content, complementary information content, and bond information content [96],... 

---