The skeletal formula, also called line-angle formula or shorthand formula, of an organic compound is a type of molecular structural formula that serves as a shorthand representation of a molecule's bonding and some details of its molecular geometry. A skeletal formula shows the skeletal structure or skeleton of a molecule, which is composed of the skeletal atoms that make up the molecule. It is represented in two dimensions, as on a piece of paper. It employs certain conventions to represent carbon and hydrogen atoms, which are the most common in organic chemistry.
An early form of this representation was first developed by the organic chemist Friedrich August Kekulé von Stradonitz, while the modern form is closely related to and influenced by the Lewis (dot) structure of molecules and their valence electrons. For this reason, they are sometimes termed Kekulé structures or Lewis-Kekulé structures. Skeletal formulae have become ubiquitous in organic chemistry, partly because they are relatively quick and simple to draw, and also because the curved arrow notation used for discussions of reaction mechanism and/or delocalization can be readily superimposed.
Several other methods for depicting chemical structures are also commonly used in organic chemistry (though less frequently than skeletal formulae). For example, conformational structures look similar to skeletal formulae and are used to depict the approximate positions of the atoms of a molecule in three-dimensional space, as a perspective drawing. Other types of representations, e.g., Newman projections, Haworth projections and Fischer projections, also look somewhat similar to skeletal formulae. However, there are slight differences in the conventions used, and the reader needs to be aware of them in order to understand the structural details that are encoded in these depictions. While skeletal and conformational structures are also used in organometallic and inorganic chemistry, the conventions employed also differ somewhat.
The skeletal structure of an organic compound is the series of atoms bonded together that form the essential structure of the compound. The skeleton can consist of chains, branches and/or rings of bonded atoms. Skeletal atoms other than carbon or hydrogen are called heteroatoms.
The skeleton has hydrogen and/or various substituents bonded to its atoms. Hydrogen is the most common non-carbon atom that is bonded to carbon and, for simplicity, is not explicitly drawn. In addition, carbon atoms are not generally labelled as such directly (i.e. with a "C"), whereas heteroatoms are always explicitly noted as such (i.e. using "N" for nitrogen, "O" for oxygen, etc.)
Heteroatoms and other groups of atoms that give rise to relatively high rates of chemical reactivity, or introduce specific and interesting characteristics in the spectra of compounds are called functional groups, as they give the molecule a function. Heteroatoms and functional groups are known collectively as "substituents", as they are considered to be a substitute for the hydrogen atom that would be present in the parent hydrocarbon of the organic compound in question.
As in Lewis structures, covalent bonds are indicated by line segments, with a doubled or tripled line segment indicating double or triple bonding, respectively. Likewise, skeletal formulae indicate formal charges associated with each atom (although lone pairs are usually optional, see below). In fact, skeletal formulae can be thought of as abbreviated Lewis structures that observe the following simplifications:
In the standard depiction of a molecule, the canonical form (resonance structure) with the greatest contribution is drawn. However, the skeletal formula is understood to represent the "real molecule" – that is, the weighted average of all contributing canonical forms. Thus, in cases where two or more canonical forms contribute with equal weight (e.g., in benzene, or a carboxylate anion) and one of the canonical forms is selected arbitrarily, the skeletal formula is understood to depict the true structure, containing equivalent bonds of fractional order, even though the delocalized bonds are depicted as nonequivalent single and double bonds.
Since skeletal structures were introduced in the latter half of the 19th century, their appearance has undergone considerable evolution. The graphical conventions in use today date to the 1980s. Thanks to the adoption of the ChemDraw software package as a de facto industry standard[how?] (by American Chemical Society, Royal Society of Chemistry, and Gesellschaft Deutscher Chemiker publications, for instance),[original research?] these conventions have been nearly universal in the chemical literature since the late 1990s. A few minor conventional variations, especially with respect to the use of stereobonds, continue to exist as a result of differing US and UK and Continental European practice, or as a matter of personal preference. As another minor variation between authors, formal charges can be shown with the plus or minus sign in a circle or without the circle. The set of conventions that are followed by most authors is given below, along with illustrative examples.
(1) Bonds between sp2 and/or sp3 hybridized carbon or heteroatoms are conventionally represented using 120° angles whenever possible, with the longest chain of atoms following a zigzag pattern unless interrupted by a cis double bond. Unless all four substituents are explicit, this is true even when stereochemistry is being depicted using wedged or dashed bonds (see below).
(2) If all four substituents to a tetrahedral carbon are explicitly shown, bonds to the two in-plane substituents still meet at 120°; the other two substituents, however, are usually shown with wedged and dashed bonds (to depict stereochemistry) and subtend a smaller angle of 60-90°.
(3) The linear geometry at sp hybridized atoms is normally depicted by line segments meeting at 180°.
(4) Carbo- and heterocycles (3- to 8-membered) are generally represented as regular polygons; larger ring sizes tend to be represented by concave polygons.
(5) Atoms in a group are ordered so that the bond emanates from the atom that is directly attached to the skeleton. For example, the nitro group (NO2), is denoted --NO2 or O2N--, depending on the placement of the bond. In contrast, the isomeric nitrite group is denoted ONO, with the bond appearing on either side.
For example, in the image below, the skeletal formula of hexane is shown. The carbon atom labeled C1 appears to have only one bond, so there must also be three hydrogens bonded to it, in order to make its total number of bonds four. The carbon atom labelled C3 has two bonds to other carbons and is therefore bonded to two hydrogen atoms as well. A ball-and-stick model of the actual molecular structure of hexane, as determined by X-ray crystallography, is shown for comparison, in which carbon atoms are depicted as black balls and hydrogen atoms as white ones.
NOTE: It doesn't matter which end of the chain you start numbering from, as long as you're consistent when drawing diagrams. The condensed formula or the IUPAC name will confirm the orientation. Some molecules will become familiar regardless of the orientation.
All atoms that are not carbon or hydrogen are signified by their chemical symbol, for instance Cl for chlorine, O for oxygen, Na for sodium, and so forth. In the context of organic chemistry, these atoms are commonly known as heteroatoms (where the prefix hetero- comes from the Greek word [héteros], meaning "other").
Any hydrogen atoms bonded to heteroatoms are drawn explicitly. In ethanol, C2H5OH, for instance, the hydrogen atom bonded to oxygen is denoted by the symbol H, whereas the hydrogen atoms which are bonded to carbon atoms are not shown directly.
Lines representing heteroatom-hydrogen bonds are usually omitted for clarity and compactness, so a functional group like the hydroxyl group is most often written -OH instead of -O-H. These bonds are sometimes drawn out in full in order to accentuate their presence when they participate in reaction mechanisms.
Shown below for comparison are a ball-and-stick model (top) of the actual three-dimensional structure of the ethanol molecule in the gas phase, as determined by microwave spectroscopy, its Lewis structure (centre) and its skeletal formula (bottom).
There are also symbols that appear to be chemical element symbols, but represent certain very common substituents or indicate an unspecified member of a group of elements. These are known as pseudoelement symbols or organic elements and are treated like univalent "elements" in skeletal formulae. A list of pseudoelement symbols in common use is shown below:
A protecting group or protective group is introduced into a molecule by chemical modification of a functional group to obtain chemoselectivity in a subsequent chemical reaction, facilitating multistep organic synthesis.
Two atoms can be bonded by sharing more than one pair of electrons. The common bonds to carbon are single, double and triple bonds. Single bonds are most common and are represented by a single, solid line between two atoms in a skeletal formula. Double bonds are denoted by two parallel lines, and triple bonds are shown by three parallel lines.
In more advanced theories of bonding, non-integer values of bond order exist. In these cases, a combination of solid and dashed lines indicate the integer and non-integer parts of the bond order, respectively.
Note: in the gallery above, double bonds have been shown in red and triple bonds in blue. This was added for clarity - multiple bonds are not normally coloured in skeletal formulae.
In recent years, benzene is generally depicted as a hexagon with alternating single and double bonds, much like the structure originally proposed by Kekulé in 1872. As mentioned above, the alternating single and double bonds of "1,3,5-cyclohexatriene" are understood to be a drawing of one of the two equivalent canonical forms of benzene, in which all carbon-carbon bonds are of equivalent length and have a bond order of 1.5. For aryl rings in general, the two analogous canonical forms are almost always the primary contributors to the structure, but they are nonequivalent, so one structure may make a slightly greater contribution than the other, and bond orders may differ somewhat from 1.5.
An alternative representation that emphasizes this delocalization uses a circle, drawn inside the regular hexagon of single bonds. This style, based on one proposed by Johannes Thiele, used to be very common in introductory organic chemistry textbooks and is still frequently used in informal settings. However, because this depiction does not keep track of electron pairs and is unable to show the precise movement of electrons, it has largely been superseded by the Kekuléan depiction in pedagogical and formal academic contexts.
The relevant chemical bonds can be depicted in several ways:
An early use of this notation can be traced back to Richard Kuhn who in 1932 used solid thick lines and dotted lines in a publication. The modern solid and hashed wedges were introduced in the 1940s by Giulio Natta to represent the structure of high polymers, and extensively popularised in the 1959 textbook Organic Chemistry by Donald J. Cram and George S. Hammond.
Skeletal formulae can depict cis and trans isomers of alkenes. Wavy single bonds are the standard way to represent unknown or unspecified stereochemistry or a mixture of isomers (as with tetrahedral stereocenters). A crossed double-bond has been used sometimes; is no longer considered an acceptable style for general use, but may still be required by computer software.