Analytical Chemistry Lesson of the Day – Specificity in Method Validation and Quality Assurance

In pharmaceutical chemistry, one of the requirements for method validation is specificity, the ability of an analytical method to distinguish the analyte from other chemicals in the sample.  The specificity of the method may be assessed by deliberately adding impurities into a sample containing the analyte and testing how well the method can identify the analyte.

Statistics is an important tool in analytical chemistry, and, ideally, there is no overlap in the vocabulary that is used between the 2 fields.  Unfortunately, the above definition of specificity is different from that in statistics.  In a previous Machine Learning and Applied Statistics Lesson of the Day, I introduced the concepts of sensitivity and specificity in binary classification.  In the context of assessing the predictive accuracy of a binary classifier, its specificity is the proportion of truly negative cases among the classified negative cases.

Organic Chemistry Lesson of the Day – The 4 Conformational Isomers of Butane

In a previous Chemistry Lesson of the Day, I introduced the simplest case of conformational isomerism – the staggered and eclipsed conformations of ethane.  The next most complicated case of conformational isomerism belongs to butane.  Here are the Newman’s projections of the 4 possibilities.

Modified image courtesy of Avitek from Wikimedia.

The conformational isomers are named with respect to the proximity of the 2 methyl groups.  The dihedral angle between the 2 methyl groups, θ, is below each Newman projection.  From left to right, the conformational isomers are:

• fully eclipsed (θ = 0 degrees)
• gauche (θ = 60 degrees)
• eclipsed (θ = 120 degrees)
• anti (θ = 180 degrees)

Clearly, the fully eclipsed conformation has the most steric strain* between the 2 methyl groups, so its internal energy is highest.

Clearly, the anti conformation has the lowest steric strain between the 2 methyl groups, so its internal energy is lowest.

The gauche conformation has less steric strain than the eclipsed conformation, so its internal energy is the lower of the two conformations.

From lowest to highest internal energy, here is the ranking of the conformation isomers:

1. anti
2. gauche
3. eclipsed
4. fully eclipsed

This can be visualized by the following energy diagram.

Image courtesy of Mr.Holmium from Wikimedia.

*As mentioned in my previous Chemistry Lesson of the Day on the 2 conformational isomers of ethane, there is some controversy about what really causes the internal energy to increase in eclipsed conformations.  Some chemists suggest that hyperconjugation is responsible.

Organic and Inorganic Chemistry Lesson of the Day – Stereoisomers

Two molecules are stereoisomers if they

• have the same molecular formula
• have the same sequence of bonds between each molecule’s constituent atoms
• have different 3-dimensional (spatial or geometric) orientations of the constituent atoms

Examples of stereoisomers include

It is important to emphasize that stereoisomers are defined for 2 or more molecules.  Consider 3 isomers, A, B and C.

• A and B may be stereoisomers.
• A and C may not be stereoisomers.  They may be structural isomers, which have the same atoms but different sequences of bonds.

Organic and Inorganic Chemistry Lesson of the Day – Optical Rotation is a Bulk Property

It is important to note that optical rotation is usually discussed as a bulk property, because it’s usually measured as a bulk property by a polarimeter.  Any individual enantiomeric molecule can almost certainly rotate linearly polarized light.  However, in a bulk sample of a chiral substance, there is usually another molecule that can rotate light in the opposite direction.  This is due to the uniform distribution of the stereochemistry of a random sample of the molecules of one compound.  (In other words, the substance consists of different stereoisomers of one compound, and the proportions of the different stereoisomers are roughly equal.)  Because one molecule’s rotation of the light can be cancelled by another molecule’s optical rotation in the opposite direction, such a random sample of the compound would have no net optical rotation.  This type of cancellation will definitely occur in a racemic mixture.  However, if a substance is enantiomerically pure, then all of the molecules in that substance will rotate linearly polarized light in the same direction – this substance is optically active.

Organic and Inorganic Chemistry Lesson of the Day – The Difference Between (+)/(-) and (R)/(S) in Stereochemical Notation

In a previous Chemistry Lesson of the Day, I introduced the concept of optical rotation (a.k.a. optical activity).  You may also be familiar with the Cahn-Ingold-Prelog priority rules for designating stereogenic centres as either (R) or (S).   There is no direct association between the (+)/(-) designation and the (R)/(S) designation.  In other words, an (R)-enantiomer can be dextrorotary or levorotary – it must be determined on a case-by-case basis.  The same holds true for an (S)-enantiomer.

(R)/(S) can be used to distinguish between enantiomers in one exception: If the stereoisomer has only 1 stereogenic centre, then this designation can also serve as a way to distinguish between 2 enantiomers.

Furthermore, note that the designation of optical rotation applies to a molecule, whereas the R/S designation applies to a particular stereogenic centre within a molecule.  Thus, a molecule with 2 stereogenic centres may have one (R) stereogenic centre and one (S) stereogenic centre.  However, a chiral compound consisting purely of one enantiomer can rotate linearly polarized light in only one direction, and that direction must be determined on a case-by-case basis by a polarimeter.

Organic and Inorganic Chemistry Lesson of the Day – DO NOT USE THE PREFIXES (d-) and (l-) TO CLASSIFY ENANTIOMERS

In a recent Chemistry Lesson of the Day, I introduced the concept of optical rotation, and I mentioned the use of (+) and (-) to denote dextrorotary and levorotary compounds, respectively.

Some people use d- and l- instead of (+) and (-), respectively.  I strongly discourage this, because there is an old system of classifying stereogenic centres that uses the prefixes D- and L-, and the obvious similarity between the prefixes of the 2 systems causes much confusion.

This old system classifies stereogenic centres based on the similarities of their configurations to the 2 enantiomers of glyceraldehyde.  It is confusing, non-intuitive, and outdated, so I will not discuss its rationale or details on my blog.  (If you are interested, here is a good explanation from the University of Maine’s chemistry department.)

Also, note that D- and L- classify stereogenic centres, whereas d- and l- classify enantiomers – this just adds more confusion.

In short,

• DO NOT use d- and l- to classify enantiomers; use (+) and (-) instead.
• DO NOT use D- and L- to classify stereogenic centres; use the Cahn-Ingold-Prelog priority rules (R/S) instead.

Organic and Inorganic Chemistry Lesson of the Day – Meso Isomers

A molecule is a meso isomer if it

Meso isomers have an internal plane of symmetry, which arises from 2 identically substituted but oppositely oriented stereogenic centres.  (By “oppositely oriented”, I mean the stereochemical orientation as defined by the Cahn-Ingold-Prelog priority system.  For example, in a meso isomer with 2 tetrahedral stereogenic centres, one stereogenic centre needs to be “R”, and the other stereogenic centre needs to be “S”. )  This symmetry results in the superimposability of a meso isomer’s mirror image.

By definition, a meso isomer and an enantiomer from the same stereoisomer are a pair of diastereomers.

Having at least 2 stereogenic centres is a necessary but not sufficient condition for a molecule to have meso isomers.  Recall that a molecule with $n$ tetrahedral stereogenic centres has at most $2^n$ stereoisomers; such a molecule would have less than $2^n$ stereoisomers if it has meso isomers.

Meso isomers are also called meso compounds.

Here is an example of a meso isomer; notice the internal plane of symmetry – the horizontal line that divides the 2 stereogenic carbons:

(2R,3S)-tartaric acid

Image courtesy of Project Osprey from Wikimedia (with a slight modification).

Organic and Inorganic Chemistry Lesson of the Day – Racemic Mixtures

A racemic mixture is a mixture that contains equal amounts of both enantiomers of a chiral molecule.  (By amount, I mean the usual unit of quantity in chemistry – the mole.  Of course, since enantiomers are isomers, their molar masses are equal, so a racemic mixture would contain equal masses of both enantiomers, too.)

In synthesizing enantiomers, if a set of reactants combine to form a racemic mixture, then the reactants are called non-stereoselective or non-stereospecific.

in 1895, Otto Wallach proposed that a racemic crystal is more dense than a crystal with purely one of the enantiomers; this is known as Wallach’s rule.  Brock et al. (1991) substantiated this with crystallograhpic data.

Reference:

Brock, C. P., Schweizer, W. B., & Dunitz, J. D. (1991). On the validity of Wallach’s rule: on the density and stability of racemic crystals compared with their chiral counterparts. Journal of the American Chemical Society, 113(26), 9811-9820.