Structural formula

Last updated
Skeletal structural formula of Vitamin B12. Many organic molecules are too complicated to be specified by a molecular formula. Cobalamin skeletal.svg
Skeletal structural formula of Vitamin B12. Many organic molecules are too complicated to be specified by a molecular formula.

The structural formula of a chemical compound is a graphic representation of the molecular structure (determined by structural chemistry methods), showing how the atoms are possibly arranged in the real three-dimensional space. The chemical bonding within the molecule is also shown, either explicitly or implicitly. Unlike other chemical formula types, [lower-alpha 1] which have a limited number of symbols and are capable of only limited descriptive power, structural formulas provide a more complete geometric representation of the molecular structure. For example, many chemical compounds exist in different isomeric forms, which have different enantiomeric structures but the same molecular formula. There are multiple types of ways to draw these structural formulas such as: Lewis Structures, condensed formulas, skeletal formulas, Newman projections, Cyclohexane conformations, Haworth projections, and Fischer projections. [2]

Contents

Several systematic chemical naming formats, as in chemical databases, are used that are equivalent to, and as powerful as, geometric structures. These chemical nomenclature systems include SMILES, InChI and CML. These systematic chemical names can be converted to structural formulas and vice versa, but chemists nearly always describe a chemical reaction or synthesis using structural formulas rather than chemical names, because the structural formulas allow the chemist to visualize the molecules and the structural changes that occur in them during chemical reactions. ChemSketch and ChemDraw are popular downloads/websites that allow users to draw reactions and structural formulas, typically in the Lewis Structure style.

Structures in structural formulas

Bonds

Bonds are often shown as a line that connects one atom to another. One line indicates a single bond. Two lines indicate a double bond, and three lines indicate a triple bond. In some structures the atoms in between each bond are specified and shown. However, in some structures, the carbon molecules are not written out specifically. Instead, these carbons are indicated by a corner that forms when two lines connect. Additionally, Hydrogen atoms are implied and not usually drawn out. These can be inferred based on how many other atoms the carbon is attached to. For example, if Carbon A is attached to one other Carbon B, Carbon A will have three hydrogens in order to fill its octet. [3]

This shows the bonds in relation to the electrons being shared. Bonds and Electron Sharing.jpg
This shows the bonds in relation to the electrons being shared.
This shows how bonds are depicted to connect to other atoms in the various structural formulas used. Connection of Bonds.jpg
This shows how bonds are depicted to connect to other atoms in the various structural formulas used.

Electrons

Charges on atoms and their formation Ions.svg
Charges on atoms and their formation

Electrons are usually shown as colored in circles. One circle indicates one electron. Two circles indicate a pair of electrons. Typically, a pair of electrons will also indicate a negative charge. By using the colored circles, the number of electrons in the valence shell of each respective atom is indicated providing further descriptive information regarding the reactive capacity of that atom in the molecule. [3]

Charges

Oftentimes, atoms will have a positive or negative charge as their octet may not be complete. If the atom is missing a pair of electrons or has a proton, it will have a positive charge. If the atom has electrons that are not bonded to another atom, there will be a negative charge. In structural formulas, the positive charge is indicated by ⊕ , and the negative charge is indicated by ⊖ . [3]

This image shows the wedges in the structural formula and how they indicate the stereochemistry of the compound. Absolute configuration.svg
This image shows the wedges in the structural formula and how they indicate the stereochemistry of the compound.

Stereochemistry (Skeletal formula)

Skeletal formula of strychnine. A solid wedged bond seen for example at the nitrogen (N) at top indicates a bond pointing above-the-plane, while a dashed wedged bond seen for example at the hydrogen (H) at bottom indicates a below-the-plane bond. Strychnine.svg
Skeletal formula of strychnine. A solid wedged bond seen for example at the nitrogen (N) at top indicates a bond pointing above-the-plane, while a dashed wedged bond seen for example at the hydrogen (H) at bottom indicates a below-the-plane bond.

Chirality in skeletal formulas is indicated by the Natta projection method. Stereochemistry is used to show the relative spatial arrangement of atoms in a molecule. Wedges are used to show this, and there are two types: dashed and filled. A filled wedge indicates that the atom is in the front of the molecule; it is pointing above the plane of the paper towards the front. A dashed wedge indicates that the atom is behind the molecule; it is pointing below the plane of the paper. When a straight, un-dashed line is used, the atom is in the plane of the paper. This spatial arrangement provides an idea of the molecule in a 3-dimensional space and there are constraints as to how the spatial arrangements can be arranged. [3]

Unspecified stereochemistry

Fructose, with a bond at the hydroxyl (OH) group upper left of image with unknown or unspecified stereochemistry Skeletal Structure of Cyclic D-Fructose.svg
Fructose, with a bond at the hydroxyl (OH) group upper left of image with unknown or unspecified stereochemistry

Wavy single bonds represent unknown or unspecified stereochemistry or a mixture of isomers. For example, the adjacent diagram shows the fructose molecule with a wavy bond to the HOCH2- group at the left. In this case the two possible ring structures are in chemical equilibrium with each other and also with the open-chain structure. The ring automatically opens and closes, sometimes closing with one stereochemistry and sometimes with the other.

Skeletal formulas 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, but is no longer considered an acceptable style for general use. [4]

Alkene stereochemistry E-Z notation in alkenes.svg
Alkene stereochemistry

Lewis structures

Representation of molecules by the Lewis structure Structuresandmolecules.svg
Representation of molecules by the Lewis structure

Lewis structures (or "Lewis dot structures") are flat graphical formulas that show atom connectivity and lone pair or unpaired electrons, but not three-dimensional structure. This notation is mostly used for small molecules. Each line represents the two electrons of a single bond. Two or three parallel lines between pairs of atoms represent double or triple bonds, respectively. Alternatively, pairs of dots may be used to represent bonding pairs. In addition, all non-bonded electrons (paired or unpaired) and any formal charges on atoms are indicated. Through the use of Lewis structures, the placement of electrons, whether it is in a bond or in lone pairs, will allow for the identification of the formal charges of the atoms in the molecule to understand the stability and determine the most likely molecule (based on molecular geometry difference) that would be formed in a reaction. Lewis structures do give some thought to the geometry of the molecule as oftentimes, the bonds are drawn at certain angles to represent the molecule in real life. Lewis structure is best used to calculate formal charges or how atoms bond to each other as both electrons and bonds are shown. Lewis structures give an idea of the molecular and electronic geometry which varies based on the presence of bonds and lone pairs and through this one could determine the bond angles and hybridization as well.

Condensed formulas

In early organic-chemistry publications, where use of graphics was strongly limited, a typographic system arose to describe organic structures in a line of text. Although this system tends to be problematic in application to cyclic compounds, it remains a convenient way to represent simple structures:

(ethanol)

Parentheses are used to indicate multiple identical groups, indicating attachment to the nearest non-hydrogen atom on the left when appearing within a formula, or to the atom on the right when appearing at the start of a formula:

or (2-propanol)

In all cases, all atoms are shown, including hydrogen atoms. It is also helpful to show the carbonyls where the

is implied through the being placed in the brackets. For example:

(acetone)

Therefore, it is important to look to the left of the atom in the bracket to make sure what atom it is attached to. This is helpful when converting from condensed formula to another form of structural formula such as skeletal formula or Lewis structures. There are different ways to show the various functional groups in the condensed formulas such as aldehyde as , Carboxylic acids as or , Esters as or . However, the use of condensed formulas does not give an immediate idea of the molecular geometry of the compound or the number of bonds between the carbons, it needs to be recognized based on the number of atoms attached to the carbons and if there are any charges on the carbon. [5]

Skeletal formulas

Skeletal formulas are the standard notation for more complex organic molecules. In this type of diagram, first used by the organic chemist Friedrich August Kekulé von Stradonitz, [6] the carbon atoms are implied to be located at the vertices (corners) and ends of line segments rather than being indicated with the atomic symbol C. Hydrogen atoms attached to carbon atoms are not indicated: each carbon atom is understood to be associated with enough hydrogen atoms to give the carbon atom four bonds. The presence of a positive or negative charge at a carbon atom takes the place of one of the implied hydrogen atoms. Hydrogen atoms attached to atoms other than carbon must be written explicitly. An additional feature of skeletal formulas is that by adding certain structures the stereochemistry, that is the three-dimensional structure, of the compound can be determined. Often times, the skeletal formula can indicate stereochemistry through the use of wedges instead of lines. Solid wedges represent bonds pointing above the plane of the paper, whereas dashed wedges represent bonds pointing below the plane.

Perspective drawings

Newman projection and sawhorse projection

The Newman projection and the sawhorse projection are used to depict specific conformers or to distinguish vicinal stereochemistry. In both cases, two specific carbon atoms and their connecting bond are the center of attention. The only difference is a slightly different perspective: the Newman projection looking straight down the bond of interest, the sawhorse projection looking at the same bond but from a somewhat oblique vantage point. In the Newman projection, a circle is used to represent a plane perpendicular to the bond, distinguishing the substituents on the front carbon from the substituents on the back carbon. In the sawhorse projection, the front carbon is usually on the left and is always slightly lower. Sometimes, an arrow is used to indicate the front carbon. The sawhorse projection is very similar to a skeletal formula, and it can even use wedges instead of lines to indicate the stereochemistry of the molecule. The sawhorse projection is set apart from the skeletal formulas because the sawhorse projection is not a very good indicator of molecule geometry and molecular arrangement. Both a Newman and Sawhorse Projection can be used to create a Fischer Projection.

Cyclohexane conformations

Certain conformations of cyclohexane and other small-ring compounds can be shown using a standard convention. For example, the standard chair conformation of cyclohexane involves a perspective view from slightly above the average plane of the carbon atoms and indicates clearly which groups are axial (pointing vertically up or down) and which are equatorial (almost horizontal, slightly slanted up or down). Bonds in front may or may not be highlighted with stronger lines or wedges. The conformations progress as follows: chair to half-chair to twist-boat to boat to twist-boat to half-chair to chair. The cyclohexane conformations may also be used to show the potential energy present at each stage as shown in the diagram. The chair conformations (A) have the lowest energy, whereas the half-chair conformations (D) have the highest energy. There is a peak/local maximum at the boat conformation (C), and there are valleys/local minimums at the twist-boat conformations (B). In addition, cyclohexane conformations can be used to indicate if the molecule has any 1,3 diaxial-interactions which are steric interactions between axial substituents on the 1,3, and 5 carbons. [7]

Chair conformation of beta-D-Glucose Beta-D-Glucose.svg
Chair conformation of beta-D-Glucose
The cyclohexane conformations in relation to the potential energy at each conformation Cyclohexane ring flip and relative conformation energies.svg
The cyclohexane conformations in relation to the potential energy at each conformation

Haworth projection

The Haworth projection is used for cyclic sugars. Axial and equatorial positions are not distinguished; instead, substituents are positioned directly above or below the ring atom to which they are connected. Hydrogen substituents are typically omitted.

However, an important thing to keep in mind while reading an Haworth projection is that the ring structures are not flat. Therefore, Haworth does not provide 3-D shape. Sir Norman Haworth, was a British Chemist, who won a Nobel Prize for his work on Carbohydrates and discovering the structure of Vitamin C. During his discovery, he also deducted different structural formulas which are now referred to as Haworth Projections. In a Haworth Projection a pyranose sugar is depicted as a hexagon and a furanose sugar is depicted as a pentagon. Usually an oxygen is placed at the upper right corner in pyranose and in the upper center in a furanose sugar. The thinner bonds at the top of the ring refer to the bonds as being farther away and the thicker bonds at the bottom of the ring refer to the end of the ring that is closer to the viewer. [8]

Fischer and Haworth projection of Glucopyranose Glucopyranose.jpg
Fischer and Haworth projection of Glucopyranose

Fischer projection

The Fischer projection is mostly used for linear monosaccharides. At any given carbon center, vertical bond lines are equivalent to stereochemical hashed markings, directed away from the observer, while horizontal lines are equivalent to wedges, pointing toward the observer. The projection is unrealistic, as a saccharide would never adopt this multiply eclipsed conformation. Nonetheless, the Fischer projection is a simple way of depicting multiple sequential stereocenters that does not require or imply any knowledge of actual conformation. A Fischer projection will restrict a 3-D molecule to 2-D, and therefore, there are limitations to changing the configuration of the chiral centers. Fischer projections are used to determine the R and S configuration on a chiral carbon and it is done using the Cahn Ingold Prelog rules. It is a convenient way to represent and distinguish between enantiomers and diastereomers. [8]

Limitations

A structural formula is a simplified model that cannot represent certain aspects of chemical structures. For example, formalized bonding may not be applicable to dynamic systems such as delocalized bonds. Aromaticity is such a case and relies on convention to represent the bonding. Different styles of structural formulas may represent aromaticity in different ways, leading to different depictions of the same chemical compound. Another example is formal double bonds where the electron density is spread outside the formal bond, leading to partial double bond character and slow inter-conversion at room temperature. For all dynamic effects, temperature will affect the inter-conversion rates and may change how the structure should be represented. There is no explicit temperature associated with a structural formula, although many assume that it would be standard temperature.

See also

Notes

  1. Structural formula is a type of chemical formula. [1]

Related Research Articles

In chemistry, a chemical formula is a way of presenting information about the chemical proportions of atoms that constitute a particular chemical compound or molecule, using chemical element symbols, numbers, and sometimes also other symbols, such as parentheses, dashes, brackets, commas and plus (+) and minus (−) signs. These are limited to a single typographic line of symbols, which may include subscripts and superscripts. A chemical formula is not a chemical name since it does not contain any words. Although a chemical formula may imply certain simple chemical structures, it is not the same as a full chemical structural formula. Chemical formulae can fully specify the structure of only the simplest of molecules and chemical substances, and are generally more limited in power than chemical names and structural formulae.

Monosaccharides, also called simple sugars, are the simplest forms of sugar and the most basic units (monomers) from which all carbohydrates are built. Simply, this is the structural unit of carbohydrates.

<span class="mw-page-title-main">Stereoisomerism</span> When molecules have the same atoms and bond structure but differ in 3D orientation

In stereochemistry, stereoisomerism, or spatial isomerism, is a form of isomerism in which molecules have the same molecular formula and sequence of bonded atoms (constitution), but differ in the three-dimensional orientations of their atoms in space. This contrasts with structural isomers, which share the same molecular formula, but the bond connections or their order differs. By definition, molecules that are stereoisomers of each other represent the same structural isomer.

<span class="mw-page-title-main">Simplified molecular-input line-entry system</span> Chemical species structure notation

The simplified molecular-input line-entry system (SMILES) is a specification in the form of a line notation for describing the structure of chemical species using short ASCII strings. SMILES strings can be imported by most molecule editors for conversion back into two-dimensional drawings or three-dimensional models of the molecules.

In chemistry, resonance, also called mesomerism, is a way of describing bonding in certain molecules or polyatomic ions by the combination of several contributing structures into a resonance hybrid in valence bond theory. It has particular value for analyzing delocalized electrons where the bonding cannot be expressed by one single Lewis structure. The resonance hybrid is the accurate structure for a molecule or ion; it is an average of the theoretical contributing structures.

<span class="mw-page-title-main">Lewis structure</span> Diagrams for the bonding between atoms of a molecule and lone pairs of electrons

Lewis structures – also called Lewis dot formulas, Lewis dot structures, electron dot structures, or Lewis electron dot structures (LEDs) – are diagrams that show the bonding between atoms of a molecule, as well as the lone pairs of electrons that may exist in the molecule. A Lewis structure can be drawn for any covalently bonded molecule, as well as coordination compounds. The Lewis structure was named after Gilbert N. Lewis, who introduced it in his 1916 article The Atom and the Molecule. Lewis structures extend the concept of the electron dot diagram by adding lines between atoms to represent shared pairs in a chemical bond.

<span class="mw-page-title-main">Fischer projection</span> Method of representing 3D organic molecules as a 2D image

In chemistry, the Fischer projection, devised by Emil Fischer in 1891, is a two-dimensional representation of a three-dimensional organic molecule by projection. Fischer projections were originally proposed for the depiction of carbohydrates and used by chemists, particularly in organic chemistry and biochemistry. The use of Fischer projections in non-carbohydrates is discouraged, as such drawings are ambiguous and easily confused with other types of drawing. The main purpose of Fischer projections is to show the chirality of a molecule and to distinguish between a pair of enantiomers. Some notable uses include drawing sugars and depicting isomers.

<span class="mw-page-title-main">Haworth projection</span> Method for writing structural formulas of monosaccharide molecules

In chemistry, a Haworth projection is a common way of writing a structural formula to represent the cyclic structure of monosaccharides with a simple three-dimensional perspective. Haworth projection approximate the shapes of the actual molecules better for furanoses—which are in reality nearly planar—than for pyranoses which exist in solution in the chair conformation. Organic chemistry and especially biochemistry are the areas of chemistry that use the Haworth projection the most.

<span class="mw-page-title-main">Skeletal formula</span> Representation method in chemistry

The skeletal formula, 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.

<span class="mw-page-title-main">Cyclohexane conformation</span> Structures of cyclohexane

Cyclohexane conformations are any of several three-dimensional shapes adopted by molecules of cyclohexane. Because many compounds feature structurally similar six-membered rings, the structure and dynamics of cyclohexane are important prototypes of a wide range of compounds.

<span class="mw-page-title-main">Conformational isomerism</span> Different molecular structures formed only by rotation about single bonds

In chemistry, conformational isomerism is a form of stereoisomerism in which the isomers can be interconverted just by rotations about formally single bonds. While any two arrangements of atoms in a molecule that differ by rotation about single bonds can be referred to as different conformations, conformations that correspond to local minima on the potential energy surface are specifically called conformational isomers or conformers. Conformations that correspond to local maxima on the energy surface are the transition states between the local-minimum conformational isomers. Rotations about single bonds involve overcoming a rotational energy barrier to interconvert one conformer to another. If the energy barrier is low, there is free rotation and a sample of the compound exists as a rapidly equilibrating mixture of multiple conformers; if the energy barrier is high enough then there is restricted rotation, a molecule may exist for a relatively long time period as a stable rotational isomer or rotamer. When the time scale for interconversion is long enough for isolation of individual rotamers, the isomers are termed atropisomers. The ring-flip of substituted cyclohexanes constitutes another common form of conformational isomerism.

<span class="mw-page-title-main">Newman projection</span> Method of representing the conformation of a single molecular bond

A Newman projection is a drawing that helps visualize the 3-dimensional structure of a molecule. This projection most commonly sights down a carbon-carbon bond, making it a very useful way to visualize the stereochemistry of alkanes. A Newman projection visualizes the conformation of a chemical bond from front to back, with the front atom represented by the intersection of three lines and the back atom as a circle. The front atom is called proximal, while the back atom is called distal. This type of representation clearly illustrates the specific dihedral angle between the proximal and distal atoms.

<span class="mw-page-title-main">Eclipsed conformation</span> Molecular form in which substituents on two adjacent atoms are closest together

In chemistry an eclipsed conformation is a conformation in which two substituents X and Y on adjacent atoms A, B are in closest proximity, implying that the torsion angle X–A–B–Y is 0°. Such a conformation can exist in any open chain, single chemical bond connecting two sp3-hybridised atoms, and it is normally a conformational energy maximum. This maximum is often explained by steric hindrance, but its origins sometimes actually lie in hyperconjugation.

<span class="mw-page-title-main">Ring strain</span> Instability in molecules with bonds at unnatural angles

In organic chemistry, ring strain is a type of instability that exists when bonds in a molecule form angles that are abnormal. Strain is most commonly discussed for small rings such as cyclopropanes and cyclobutanes, whose internal angles are substantially smaller than the idealized value of approximately 109°. Because of their high strain, the heat of combustion for these small rings is elevated.

In chemistry, the Natta projection is a way to depict molecules with complete stereochemistry in two dimensions in a skeletal formula. In a hydrocarbon molecule with all carbon atoms making up the backbone in a tetrahedral molecular geometry, the zigzag backbone is in the paper plane with the substituents either sticking out of the paper toward the viewer or away from the viewer. The Natta projection is useful for representing the tacticity of a polymer.

In organic chemistry, a ring flip is the interconversion of cyclic conformers that have equivalent ring shapes that results in the exchange of nonequivalent substituent positions. The overall process generally takes place over several steps, involving coupled rotations about several of the molecule's single bonds, in conjunction with minor deformations of bond angles. Most commonly, the term is used to refer to the interconversion of the two chair conformers of cyclohexane derivatives, which is specifically referred to as a chair flip, although other cycloalkanes and inorganic rings undergo similar processes.

<span class="mw-page-title-main">Anomeric effect</span> Tendency of some substituents on a cyclohexane ring to prefer axial orientation

In organic chemistry, the anomeric effect or Edward-Lemieux effect is a stereoelectronic effect that describes the tendency of heteroatomic substituents adjacent to a heteroatom within a cyclohexane ring to prefer the axial orientation instead of the less-hindered equatorial orientation that would be expected from steric considerations. This effect was originally observed in pyranose rings by J. T. Edward in 1955 when studying carbohydrate chemistry.

<span class="mw-page-title-main">Cyclic compound</span> Molecule with a ring of bonded atoms

A cyclic compound is a term for a compound in the field of chemistry in which one or more series of atoms in the compound is connected to form a ring. Rings may vary in size from three to many atoms, and include examples where all the atoms are carbon, none of the atoms are carbon, or where both carbon and non-carbon atoms are present. Depending on the ring size, the bond order of the individual links between ring atoms, and their arrangements within the rings, carbocyclic and heterocyclic compounds may be aromatic or non-aromatic; in the latter case, they may vary from being fully saturated to having varying numbers of multiple bonds between the ring atoms. Because of the tremendous diversity allowed, in combination, by the valences of common atoms and their ability to form rings, the number of possible cyclic structures, even of small size numbers in the many billions.

A-values are numerical values used in the determination of the most stable orientation of atoms in a molecule, as well as a general representation of steric bulk. A-values are derived from energy measurements of the different cyclohexane conformations of a monosubstituted cyclohexane chemical. Substituents on a cyclohexane ring prefer to reside in the equatorial position to the axial. The difference in Gibbs free energy (ΔG) between the higher energy conformation and the lower energy conformation is the A-value for that particular substituent.

<span class="mw-page-title-main">Isomer</span> Chemical compounds with the same molecular formula but different atomic arrangements

In chemistry, isomers are molecules or polyatomic ions with identical molecular formula – that is, same number of atoms of each element – but distinct arrangements of atoms in space. Diamond and graphite are a familiar example; they are isomers of carbon. Isomerism refers to the existence or possibility of isomers.

References

  1. Denise DeCooman (2022-04-08). "What are Chemical Formulas and How are They Used?". Study.com. sec. Chemical Formula Examples. Archived from the original on 2022-06-23.
  2. Goodwin, W. M. (2007-04-13). "Structural formulas and explanation in organic chemistry". Foundations of Chemistry. 10 (2): 117–127. doi:10.1007/s10698-007-9033-2. ISSN   1386-4238. S2CID   93952251.
  3. 1 2 3 4 Brown, William Henry; Brent L. Iverson; Eric V. Anslyn; Christopher S. Foote (2018). Organic chemistry (Eighth ed.). Boston. ISBN   978-1-305-58035-0. OCLC   974377227.{{cite book}}: CS1 maint: location missing publisher (link)
  4. J. Brecher (2006). "Graphical representation of stereochemical configuration (IUPAC Recommendations 2006)" (PDF). Pure Appl. Chem. 78 (10): 1897–1970. doi:10.1351/pac200678101897. S2CID   97528124.
  5. Liu, Xin (2021-12-09). "2.1 Structures of Alkenes".{{cite journal}}: Cite journal requires |journal= (help)
  6. "Friedrich August Kekule von Stradonitz –inventor of benzene structure - World Of Chemicals". www.worldofchemicals.com. Retrieved 2022-04-04.
  7. Brown, William Henry (2018). Organic chemistry. Brent L. Iverson, Eric V. Anslyn, Christopher S. Foote (Eighth ed.). Boston, MA. ISBN   978-1-305-58035-0. OCLC   974377227.{{cite book}}: CS1 maint: location missing publisher (link)
  8. 1 2 Zhang, Qing-zhi; Zhang, Shen-song (June 1999). "A New Method To Convert the Fischer Projection of a Monosaccharide to the Haworth Projection". Journal of Chemical Education. 76 (6): 799. doi:10.1021/ed076p799. ISSN   0021-9584.