Topological organic chemistry. 12. Whole-molecule Schultz topological indices of alkanes

The formation of carbon-carbon bonds leading to the creation of the carbon chain is the basis of organic chemistry. August Kekulé and Archibald Scott Couper independently developed this idea of carbon chain formation.
Hydrocarbons are the simplest organic compounds composed of carbons and hydrogens. Based on the bond order between carbons, the hydrocarbons are further classified into alkanes, alkenes, and alkynes. 
Alkanes are the simplest hydrocarbons with sp3 hybrid carbon atoms. These sp3...

Organic compounds of the same molecular formula can have different structural formulas called constitutional isomers, and the phenomenon is known as constitutional isomerism. Alkanes with four or more carbons showing multiple structures with the same molecular formula thereby exhibit constitutional isomerism.
The linear isomer of an alkane is prefixed by the term “n”; hence a linear isomer of pentane is known as n-pentane. Based on the type of branching, some of the branched isomers are given...

In the late 19th-century, the number of new chemical compounds discovered increased tremendously. Hence, the necessity arose to develop a naming system for the systematic nomenclature of these newly discovered compounds. IUPAC (International Union for Pure and Applied Chemistry), established in 1919, sets rules for the nomenclature.
The alkane nomenclature considers the length of the carbon chain, the number, and the location of the substituent to arrive at its systematic name. The IUPAC...

In an organic molecule, free rotation about the carbon-carbon single bond results in energetically different conformers of the molecule. Due to this rotation, called the internal rotation, ethane has two major conformations — staggered and eclipsed.
Staggered conformation is a low energy and more stable conformation with the C-H bonds on the front carbon placed at 60°dihedral angles relative to the C-H bonds on the back carbon, leading to a reduced torsional strain. In staggered ethane, the...

Olefins, which are unsaturated hydrocarbons containing one or more carbon–carbon double bonds, are broadly divided into alkenes and cycloalkenes. The general chemical formula of an alkene is CnH2n.
Doubly bonded carbons are sp2 hybridized and have a trigonal planar geometry. The double bond is composed of a σ bond formed by the overlap of hybrid orbitals and a π bond produced by the lateral overlap of unhybridized 2p orbitals on both the carbons. Each carbon atom is bonded to two hydrogen atoms...

The degree of unsaturation (U), or index of hydrogen deficiency (IHD), is defined as the difference in the number of pairs of hydrogen atoms between the compound and the acyclic alkane with the same number of carbon atoms. Each double bond or ring costs two hydrogen atoms compared to a saturated analog and results in one degree of unsaturation.
The degree of unsaturation for hydrocarbons is U = (2C + 2 − H) / 2, where C is the number of carbon atoms and H is the number of hydrogen atoms.
For...