Skeletal formula

thumb|right|upright=0.75|class=skin-invert-image|The skeletal formula of the [[antidepressant drug escitalopram, featuring skeletal representations of heteroatoms, a triple bond, phenyl groups and stereochemistry]]

The skeletal formula, line-angle formula, bond-line formula or shorthand formula of an organic compound is a type of minimalist structural formula representing a molecule's atoms, bonds and some details of its geometry. The lines in a skeletal formula represent bonds between carbon atoms, unless labelled with another element. Labels are optional for carbon atoms, and the hydrogen atoms attached to them.

An early form of this representation was first developed by organic chemist August Kekulé, while the modern form is closely related to and influenced by the Lewis structure of molecules and their valence electrons. Hence they are sometimes termed Kekulé structures or Lewis–Kekulé structures. Skeletal formulas 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 mechanisms and electron delocalization can be readily superimposed.

Several other ways of 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 atoms in 3D space, as a perspective drawing. Other types of representation, such as Newman projection, Haworth projection or Fischer projection, 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 encoded in the depiction. While skeletal and conformational structures are also used in organometallic and inorganic chemistry, the conventions employed also differ somewhat.

The skeleton

Terminology

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 "C"), whereas heteroatoms are always explicitly noted as such ("N" for nitrogen, "Cl" for chlorine, 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 collectively called "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.

Basic structure

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, with lone pairs usually being optional . In fact, skeletal formulae can be thought of as abbreviated Lewis structures that observe the following simplifications:

Carbon atoms are represented by the vertices (intersections or termini) of line segments. For clarity, methyl groups are often explicitly written out as Me or CH<sub>3</sub>, while (hetero)cumulene carbons are frequently represented by a heavy center dot.
Hydrogen atoms attached to carbon are implied. An unlabeled vertex is understood to represent a carbon attached to the number of hydrogens required to satisfy the octet rule, while a vertex labeled with a formal charge and/or nonbonding electron(s) is understood to have the number of hydrogen atoms required to give the carbon atom these indicated properties. Optionally, acetylenic and formyl hydrogens can be shown explicitly for the sake of clarity.
Hydrogen atoms attached to a heteroatom are shown explicitly. The heteroatom and hydrogen atoms attached thereto are usually shown as a single group (e.g., OH, NH<sub>2</sub>) without explicitly showing the hydrogen–heteroatom bond. Heteroatoms with simple alkyl or aryl substituents, like methoxy (OMe) or dimethylamino (NMe<sub>2</sub>), are sometimes shown in the same way, by analogy.
Lone pairs on carbene carbons must be indicated explicitly while lone pairs in other cases are optional and are shown only for emphasis. In contrast, formal charges and unpaired electrons on main-group elements are always explicitly shown.

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.

Contemporary graphical conventions

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 (by American Chemical Society, Royal Society of Chemistry, and Gesellschaft Deutscher Chemiker publications, for instance), 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, UK and 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.

Implicit carbon and hydrogen atoms

For example, the skeletal formula of hexane (top) is shown below. The carbon atom labeled C<sub>1</sub> 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 C<sub>3</sub> has two bonds to other carbons and is therefore bonded to two hydrogen atoms as well. A Lewis structure (middle) and ball-and-stick model (bottom) of the actual molecular structure of hexane, as determined by X-ray crystallography, are shown for comparison.

File:Skeletal-formulae-example-1-hexane.svg|The skeletal formula of hexane, with carbons number one and three labelled

File:Hexane displayed.svg|The Lewis structure of hexane, for reference

File:Hexane-from-xtal-1999-at-an-angle-3D-balls.png|The 3d ball representation of hexane, with carbon (black) and hydrogen (white) shown explicitly.

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It does not matter which end of the chain one starts numbering from, as long as consistency is maintained when drawing diagrams. The condensed formula or the IUPAC name will confirm the orientation. Some molecules will become familiar regardless of the orientation.

Explicit heteroatoms and hydrogen atoms

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 (the prefix hetero- comes from Greek ἕτερος héteros, meaning "other").

Any hydrogen atoms bonded to heteroatoms are drawn explicitly. In ethanol, C<sub>2</sub>H<sub>5</sub>OH, 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 skeletal formula (top), its Lewis structure (middle) and its ball-and-stick model (bottom) of the actual 3D structure of the ethanol molecule in the gas phase, as determined by microwave spectroscopy.

File:Ethanol-2D-skeletal.svg|The skeletal structure of ethanol

File:Ethanol-structure.svg|The Lewis structure of ethanol

File:Ethanol-CRC-MW-trans-3D-balls.png|The 3d ball representation of ethanol

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Pseudoelement symbols

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 called pseudoelement symbols or organic elements and are treated like univalent "elements" in skeletal formulae. A list of common pseudoelement symbols:

General symbols

X for any (pseudo)halogen atom (in the related MLXZ notation, X represents a one-electron donor ligand)
L or L<sub>n</sub> for a ligand or ligands (in the related MLXZ notation, L represents a two-electron donor ligand)
M or Met for any metal atom ([M] is used to indicate a ligated metal, ML<sub>n</sub>, when the identities of the ligands are unknown or irrelevant)
E or El for any electrophile (in some contexts, E is also used to indicate any p-block element)
Nu for any nucleophile

Image:Stereochemistry-example-3D-balls.png|<div style="text-align: center;">Ball-and-stick model of <br/> (R)-2-chloro-2-fluoropentane</div>

Image:(R)-2-Chloro-2-fluoropentane.svg|<div style="text-align: center;">Skeletal formula of <br/> (R)-2-chloro-2-fluoropentane</div>

Image:(S)-2-Chloro-2-fluoropentane.svg|<div style="text-align: center;">Skeletal formula of <br/> (S)-2-chloro-2-fluoropentane</div>

Image:Amphetamine-2D-skeletal.svg|<div style="text-align: center;">Skeletal formula of amphetamine, indicating a mixture of two stereoisomers: (R)- and (S)-</div>

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The relevant chemical bonds can be depicted in several ways:

Solid lines represent bonds in the plane of the paper or screen.
Solid wedges represent bonds that point out of the plane of the paper or screen, towards the observer.
Hashed wedges or dashed lines (thick or thin) represent bonds that point into the plane of the paper or screen, away from the observer.
Wavy lines represent either unknown stereochemistry or a mixture of the two possible stereoisomers at that point.
An obsolescent depiction of hydrogen stereochemistry that used to be common in steroid chemistry is the use of a filled circle centered on a vertex (sometimes called H-dot/H-dash/H-circle, respectively) for an upward pointing hydrogen atom and two hash marks next to vertex or a hollow circle for a downward pointing hydrogen atom.

thumb|center|upright=1.8|class=skin-invert-image|A small filled circle represented an upward pointing hydrogen, while two hash marks represented a downward pointing one.

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.

thumb|upright=1.4|center|class=skin-invert-image|Alkene stereochemistry

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; it is no longer considered an acceptable style for general use but may still be required by computer software.