Theskeletal formula,line-angle formula,bond-line formula orshorthand formula of anorganic compound is a type of minimaliststructural formula representing amolecule'satoms,bonds and some details of itsgeometry. The lines in a skeletal formula represent bonds between carbon atoms, unless labelled with another element.[1] Labels are optional forcarbon atoms, and thehydrogen atoms attached to them.
An early form of this representation was first developed by organic chemistAugust Kekulé, while the modern form is closely related to and influenced by theLewis structure of molecules and their valence electrons. Hence they are sometimes termedKekulé structures[a] orLewis–Kekulé structures. Skeletal formulas have become ubiquitous inorganic chemistry, partly because they are relatively quick and simple to draw, and also because thecurved arrow notation used for discussions of reaction mechanisms andelectron 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 asNewman projection,Haworth projection orFischer 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 inorganometallic andinorganic 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 calledheteroatoms.[2]
The skeleton has hydrogen and/or varioussubstituents 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" fornitrogen, "Cl" forchlorine, 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 calledfunctional 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 parenthydrocarbon of the organic compound.
As in Lewis structures, covalent bonds are indicated by line segments, with a doubled or tripled line segment indicatingdouble ortriple bonding, respectively. Likewise, skeletal formulae indicateformal charges associated with each atom, with lone pairs usually being optional(seebelow). 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 CH3, while (hetero)cumulene carbons are frequently represented by a heavycenter 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 theoctet 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, NH2) without explicitly showing the hydrogen–heteroatom bond. Heteroatoms with simple alkyl or aryl substituents, like methoxy (OMe) or dimethylamino (NMe2), are sometimes shown in the same way, by analogy.
Lone pairs oncarbene 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, thecanonical 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 theChemDraw software package as ade facto industry standard (byAmerican Chemical Society,Royal Society of Chemistry, andGesellschaft 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.[3] 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.
Bonds between sp2 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 acis double bond. Unless all four substituents are explicit, this is true even when stereochemistry is being depicted using wedged or dashed bonds (see below).[b]
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°.
The linear geometry at sp hybridized atoms is normally depicted by line segments meeting at 180°. Where this involves two double bonds meeting (anallene orcumulene), the bonds are separated by a dot.
Carbo- and heterocycles (3- to 8-membered) are generally represented as regular polygons; larger ring sizes tend to be represented by concave polygons.[c]
Atoms in a group are ordered so that the bond emanates from the atom that is directly attached to the skeleton. For example, thenitro group NO2 is denoted—NO2 orO2N—, depending on the placement of the bond. In contrast, the isomericnitrite group is denoted—ONO orONO—.[d]
For example, the skeletal formula ofhexane (top) is shown below. 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. ALewis structure (middle) andball-and-stick model (bottom) of the actual molecular structure of hexane, as determined byX-ray crystallography, are shown for comparison.
The skeletal formula of hexane, with carbons number one and three labelledThe Lewis structure of hexane, for referenceThe 3d ball representation of hexane, with carbon (black) and hydrogen (white) shown explicitly.
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.
All atoms that are not carbon or hydrogen are signified by theirchemical symbol, for instance Cl forchlorine, O foroxygen, Na forsodium, and so forth. In the context of organic chemistry, these atoms are commonly known asheteroatoms (theprefixhetero- comes from Greekἕτερος héteros, meaning "other").
Any hydrogen atoms bonded to heteroatomsare drawn explicitly. Inethanol, 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 thehydroxyl 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 inreaction mechanisms.
Shown below for comparison are a skeletal formula (top), itsLewis structure (middle) and its ball-and-stick model (bottom) of the actual3D structure of the ethanol molecule in the gas phase, as determined bymicrowave spectroscopy.
There are also symbols that appear to bechemical 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.[4] A list of common pseudoelement symbols:
Z for conjugating electron-withdrawing groups (in the related MLXZ notation, Z represents a zero-electron donor ligand;in unrelated usage, Z is also an abbreviation for the carboxybenzyl group.)
Pr,n-Pr,ornPr for the(normal) propyl group (Pr is also the symbol for the elementpraseodymium.[5] However, since the propyl group is monovalent, while praseodymium is nearly always trivalent, ambiguity rarely, if ever, arises in practice.)
Pn for thepentyl group (or Am for the synonymousamyl group,although Am is also the symbol foramericium.)
Npor Neo for theneopentyl group (Warning: Organometallic chemists often use Np for the relatedneophyl group, PhMe2C–. Np is also the symbol for the elementneptunium.)
Ar for anyaromatic substituent(Ar is also the symbol for the elementargon. However, argon is inert under all usual conditions encountered in organic chemistry, so the use of Ar to represent an aryl substituent never causes confusion.)
Isor Tipp for the 2,4,6-triisopropylphenyl group (the former symbol is derived from the synonymisityl)
An for theanisyl group, usually thepara isomer (An is also the symbol for a genericactinoid element. However, since the anisyl group is monovalent, while the actinides are usually divalent, trivalent, or even higher valency, ambiguity rarely, if ever, arises in practice.)
Ac for theacetyl group(Ac is also the symbol for the elementactinium. However, actinium is almost never encountered in organic chemistry, so the use of Ac to represent the acetyl group never causes confusion);
Sulfonate esters are oftenleaving groups in nucleophilic substitution reactions.See the articles onsulfonyl andsulfonate groups for further information.
Bs for thebrosyl (p-bromobenzenesulfonyl) group; OBs is the brosylate group
Ms for themesyl (methanesulfonyl) group; OMs is themesylate group
Ns for thenosyl (p-nitrobenzenesulfonyl) group(Ns was the chemical symbol for nielsbohrium, but that was renamedbohrium, Bh); ONs is the nosylate group
Tf for thetriflyl (trifluoromethanesulfonyl) group; OTf is thetriflate group
Nf for thenonaflyl (nonafluorobutanesulfonyl) group,CF 3(CF 2) 3SO 2; ONf is thenonaflate group
Ts fortosyl (p-toluenesulfonyl) group(Ts is also the symbol for the elementtennessine. However, tennessine is too unstable to ever be encountered in organic chemistry, so the use of Ts to represent tosyl never causes confusion); OTs is thetosylate group
Aprotecting 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 ofbond order exist. In these cases, a combination of solid and dashed lines indicate the integer and non-integer parts of the bond order, respectively.
Examples of multiple bonds in skeletal formulae[e]
In recent years,benzene is generally depicted as a hexagon with alternating single and double bonds, much like the structureKekulé originally proposed 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 (the one explicitly shown and the one with the opposite pattern of formal single and double bonds), in which all carbon–carbon bonds are of equivalent length and have a bond order of exactly 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 alternate representation that emphasizes this delocalization uses a circle, drawn inside the hexagon of single bonds, to represent the delocalizedpi orbital. This style, based on one proposed byJohannes 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.[f]
Skeletal formula ofamphetamine, indicating a mixture of two stereoisomers:(R)- and(S)-
The relevant chemical bonds can be depicted in several ways:
Solid lines representbonds 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.[g]
Wavy lines represent either unknown stereochemistry or a mixture of the two possible stereoisomers at that point.
An obsolescent[h] depiction of hydrogen stereochemistry that used to be common insteroid 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. 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 toRichard Kuhn who in 1932 used solid thick lines and dotted lines in a publication. The modernsolid and hashed wedges were introduced in the 1940s byGiulio Natta to represent the structure of highpolymers, and extensively popularised in the 1959 textbookOrganic Chemistry byDonald J. Cram andGeorge S. Hammond.[7]
Skeletal formulae can depictcis andtrans 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.[6]
Dashed lines (green) to show hydrogen bonding inacetic acid.
Hydrogen bonds are generally denoted by dotted or dashed lines. In other contexts, dashed lines may also represent partially formed or broken bonds in atransition state.
^This term is ambiguous, because "Kekulé structure" also refers to Kekulé's famous proposal of a hexagon of alternating single and double bonds for the structure of benzene.
^To prevent a 'kink' from emerging and causing a structure to take up too much vertical space on a page, the IUPAC (Brecher, 2008, p. 352) makes an exception for long chaincis-olefins (such asoleic acid), allowing thecis double bond within them to be depicted with 150° angles, so that the zigzags on either side of the double bond can propagate horizontally.
^Smaller rings may also be drawn as concave to show stereochemistry (such as theconformations of cyclohexane) or polycyclic molecules that cannot be drawn 'flat' without significant distortion (such astropane andadamantane).
^In cases where the atom has bonds coming from both the left and right (such as a secondaryamine NH in the middle of a chain), some authors allow the group's formula to be stacked vertically whereas others draw an explicit vertical bond within the group.
^In this gallery, 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.
^For instance, the acclaimed 1959 textbook by Morrison and Boyd (6th edition, 1992) uses the Thiele notation as its standard depiction of the aryl ring, while the 2001 textbook by Clayden, Greeves, Warren, and Wothers (2nd edition, 2012) uses the Kekulé notation throughout and warns students to avoid using the Thiele notation when writing mechanisms (p. 144, 2nd ed.).
^American and European chemists use slightly different conventions for a hashed bond. Whereas most American chemists draw hashed bonds with short hash marks close to the stereocenter and long hash marks further away (in analogy to wedged bonds), most European chemists start with long hash marks close to the stereocenter that gradually become shorter moving away (in analogy to perspective drawing). In the past, theIUPAC has suggested the use of a hashed bond with hash marks of equal length throughout as a compromise but now prefers the American-style hashed bonds (Brecher, 2006, p. 1905).Some chemists use a thick bond and dotted bond (or hashed bond with equal length hashes) to depictrelative stereochemistry and a wedged bond and hashed bond with unequal hashes to depictabsolutestereochemistry; most others do not make this distinction.
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