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

In pharmaceutical chemistry, one of the requirements for method validation is accuracy, the ability of an analytical method to obtain a value of a measurement that is close to the true value. There are several ways of assessing an analytical method for accuracy.

1. Compare the value from your analytical method with an established or reference method.
2. Use your analytical method to obtain a measurement from a sample with a known quantity (i.e. a reference material), and compare the measured value with the true value.
3. If you don’t have a reference material for the second way, you can make your own by spiking a blank matrix with a measured quantity of the analyte.
4. If your matrix may interfere with the analytical signal, then you cannot spike a blank matrix as described in the third way.  Instead, spike your sample with an known quantity of the standard.  I elaborate on this in a separate tutorial on standard addition, a common technique in analytical chemistry for determining the quantity of a substance when matrix interference exists.  Standard addition is an example of the second way of assessing accuracy as I mentioned above.  You can view the original post of this tutorial on the official JMP blog.

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

In analytical chemistry, the quantity of interest is often estimated from a calibration line.  A technique or instrument generates the analytical response for the quantity of interest, so a calibration line is constructed from generating multiple responses from multiple standard samples of known quantities.  Linearity refers to how well a plot of the analytical response versus the quantity of interest follows a straight line.  If this relationship holds, then an analytical response can be generated from a sample containing an unknown quantity, and the calibration line can be used to estimate the unknown quantity with a confidence interval.

Note that this concept of “linear” is different from the “linear” in “linear regression” in statistics.

This is the the second blog post in a series of Chemistry Lessons of the Day on method validation in analytical chemistry.  Read the previous post on specificity, and stay tuned for future posts!

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.

Physical Chemistry Lesson of the Day – What is the Primary Determinant of the Effective Nuclear Charge for Outer Electrons?

Electrons in the inner shells of an atom shield the electrons in the outer shells pretty well from the nuclear charge.  However, electrons in the same shell don’t shield each other very well.  If an electron spends most of its time below another electron, then the first electron can shield the second electron.  However, this is not the case for electrons in the same shell – they repel each other because they are all negatively charged, and they are at roughly the same average distance from the nucleus.

Thus, the difference between

1. the charge of the nucleus
2. and the charge of the core electrons

is the primary contributor to the effective nuclear charge that the outer electrons experience.

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

When developing any method in analytical chemistry, it must meet several criteria to ensure that it accomplishes its intended objective at or above an acceptable standard.  This process is called method validation, and it has the following criteria* in the pharmaceutical industry:

• specificity
• linearity
• accuracy
• precision
• range
• limit of detection
• limit of quantitation
• robustness**

As I will note in future Chemistry Lessons of the Day, these words are used differently between statistics and chemistry.

*These criteria are taken from Page 723 of the 6th edition of “Quantitative Chemical Analysis” by Daniel C. Harris (2003).

**The Food and Drug Administration does not list robustness as a typical characteristic of method validation.  (See Section B on Page 7 of its “Guidance for Industry Analytical Procedures and Methods Validation for Drugs and Biologics“.)  However, it does mention robustness several times as an important characteristic that “should be evaluated” during the “early stages of method development”.  

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 Chemistry Lesson of the Day – The 2 Conformational Isomers of Ethane

The simplest case of conformational isomerism belongs to ethane, C₂H_6.

Newman projections of the 2 conformational isomers of ethane.

Image courtesy of Mr.Holmium via Wikimedia.

In the Newman projections above, you can see that the dihedral angle between any 2 vicinal hydrogens plays a key role in the stability of ethane.  In particular, there are 2 extrema in that plot of the change in Gibbs free energy vs. the dihedral angle:

• The minimum is attained when the dihedral angle is degrees, where is any integer .  In other words, the vicinal hydrogens are as far apart from each other as possible.  This conformation is called the staggered conformation.

• The maximum is attained when the dihedral angle is  degrees, where is any integer .  In other words, the vicinal hydrogens are as close to each other as possible.  This conformation is called the eclipsed conformation.

The stability of ethane is dependent on this dihedral angle.

• If the vicinal hydrogens are far part from each other (in a staggered conformation, for example), then there is less torsional strain* between the 2 carbon-hydrogen bonds, resulting in more stability.

• If the vicinal hydrogens are close to each other (in an eclipsed conformation, for example), then there is greater torsional strain* between the 2 carbon-hydrogen bonds resulting in less stability.

*In my undergraduate education, I learned that the greater stability in the staggered conformation is due to less torsional (steric) strain.  However, Vojislava Pophristic & Lionel Goodman (2001) argued that the effect is actually due to the stabilizing effect of hyperconjugation.  Song et al. (2005) and Mo and Yao (2007) rebutted this argument in separate publications.  Read these articles as searched under “ethane hyperconjugation steric strain” on Google Scholar for more information.

References

• Pophristic, V., & Goodman, L. (2001). Hyperconjugation not steric repulsion leads to the staggered structure of ethane. Nature, 411(6837), 565-568.
• Song, L., Lin, Y., Wu, W., Zhang, Q., & Mo, Y. (2005). Steric strain versus hyperconjugative stabilization in ethane congeners. The Journal of Physical Chemistry A, 109(10), 2310-2316.
• Mo, Y., & Gao, J. (2007). Theoretical analysis of the rotational barrier of ethane. Accounts of chemical research, 40(2), 113-119.

Organic and Inorganic Chemistry Lesson of the Day – Conformational Isomers (or Conformers)

Conformational isomerism is a special type of stereoisomerism that arises from the rotation of a single bond.  Specifically, 2 molecules are conformational isomers (or conformers) if they can be interconverted exclusively by the rotation of a single bond.  This type of isomerism differs from configurational stereoisomerism, whose isomers can only be interconverted by breaking certain bonds and reattaching* them to produce different 3-dimensional orientations.  Examples of configurational isomers include enantiomers, diastereomers, cis/trans isomers and meso isomers.

Different conformers are notable for having different stabilities, depending on the electrostatic interactions between the substituents along the single bond of interest.  I will talk about these differences in greater depth in future Chemistry Lessons of the Day.

*Such reattachment of the bonds must not result in different connectivities (or sequence of bonds); otherwise, that would result in structural isomers.

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

• enantiomers
• diastereomers
• meso isomer
• cis/trans isomers

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 – Optical Rotation (a.k.a. Optical Activity)

A substance consisting of a chiral compound can rotate linearly polarized light – this property is known as optical rotation (more commonly called optical activity).  The direction in which the light is rotated is one way to distinguish between a pair of enantiomers, as they rotate linearly polarized light in opposite directions.

Imagine if you are an enantiomer, and linearly polarized light approaches you.

• If the light is rotated clockwise from your perspective, then you are a dextrorotary enantiomer.
• Otherwise, if the light is rotated counterclockwise from your perspective, then you are a levorotary enantiomer.

In a previous Chemistry Lesson of the Day, I introduced the concept of diastereomers, and I used threose as an example.  Let’s use threose to illustrate some notation about optical activity.

(-)-Threose

• Levorotary compounds are denoted by the prefix (-), followed by a hyphen, then followed by the name of the compound.  The above molecule is (-)-threose.
• Dextrorotary compounds are denoted by the prefix (+), followed by a hyphen, then followed by the name of the compound.  The enantiomer of (-)-threose is (+)-threose.

A compound’s optical rotation is determined by a polarimeter.

I strongly discourage the use of the prefixes (d)- and (l-) to distinguish between enantiomers.  Use (+) and (-) instead.

Beware of the difference between designating enantiomers as (+) or (-) and designating stereogenic centres as either (R) or (S).

It is important to note that optical rotation is usually referred to as a bulk property.

Organic and Inorganic Chemistry Lesson of the Day – Cis/Trans Isomers Are Diastereomers

Recall that the definition of diastereomers is simply 2 molecules that are NOT enantiomers.  Diastereomers often have at least 2 stereogenic centres, and my previous lesson showed an example of how such diastereomers can arise.

However, while an enantiomer must have at least 1 stereogenic centre, there is nothing in the definition of a diastereomer that requires it to have any stereogenic centres.  In fact, a diastereomer does not have to be chiral.  A pair of cis/trans isomers are also diastereomers.  Recall the example of trans-1,2-dibromoethylene and cis-1,2-dibromoethylene:

 

Image courtesy of Roland1952 on Wikimedia.

These 2 molecules are stereoisomers – they have the same atoms and sequence/connectivity of bonds, but they differ in their spatial orientations.  They are NOT mirror images of each other, let alone non-superimposable mirror images.  Thus, by definition, they are diastereomers, even though they are not chiral.

Organic and Inorganic Chemistry Lesson of the Day – Meso Isomers

A molecule is a meso isomer if it

• is a member of a set of stereoisomers that includes enantiomers
• has a superimposable mirror image (i.e. it is achiral)

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 tetrahedral stereogenic centres has at most stereoisomers; such a molecule would have less than 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.

Organic and Inorganic Chemistry Lesson of the Day – Diastereomers

I previously introduced the concept of chirality and how it is a property of any molecule with only 1 stereogenic centre.  (A molecule with stereogenic centres may or may not be chiral, depending on its stereochemistry.)  I also defined 2 stereoisomers as enantiomers if they are non-superimposable mirror images of each other.  (Recall that chirality in inorganic chemistry can arise in 2 different ways.)

It is possible for 2 stereoisomers to NOT be enantiomers; in fact, such stereoisomers are called diastereomers.  Yes, I recognize that defining something as the negation of something else is unusual.  If you have learned set theory or probability (as I did in my mathematical statistics classes) then consider the set of all pairs of the stereoisomers of one compound – this is the sample space.  The enantiomers form a set within this sample space, and the diastereomers are the complement of the enantiomers.

It is important to note that, while diastereomers are not mirror images of each other, they are still non-superimposable.  Diastereomers often (but not always) arise from stereoisomers with 2 or more stereogenic centres; here is an example of how they can arise.  (A pair of cis/trans-isomers are also diastereomers, despite not having any stereogenic centres.)

1) Consider a stereoisomer with 2 tetrahedral stereogenic centres and no meso isomers*.  This isomer has stereoisomers, where denotes the number of stereogenic centres.

2) Find one pair of enantiomers based on one of the stereogenic centres.

3) Find the other pair enantiomers based on the other stereogenic centre.

4) Take any one molecule from Step #2 and any one molecule from Step #3.  These cannot be mirror images of each other.  (One molecule cannot have 2 different mirror images of itself.)  These 2 molecules are diastereomers.

Think back to my above description of enantiomers as a proper subset within the sample space of the pairs of one set of stereoisomers.  You can now see why I emphasized that the sample space consists of pairs, since multiple different pairs of stereoisomers can form enantiomers.  In my example above, Steps #2 and #3 produced 2 subsets of enantiomers.  It should be clear by now that enantiomers and diastereomers are defined as pairs.  To further illustrate this point,

a) call the 2 molecules in Step#2 A and B.

b) call the 2 molecules in Step #3 C and D.

A and B are enantiomers.  A and C are diastereomers.  Thus, it is entirely possible for one molecule to be an enantiomer with a second molecule and a diastereomer with a third molecule.

Here is an example of 2 diastereomers.  Notice that they have the same chemical formula but different 3-dimensional orientations – i.e. they are stereoisomers.  These stereoisomers are not mirror images of each other, but they are non-superimposable – i.e. they are diastereomers.

(-)-Threose

(-)-Erythrose

 

 

 

 

 

 

Images courtesy of Popnose, DMacks and Edgar181 on Wikimedia.  For brevity, I direct you to the Wikipedia entry for diastereomers showing these 4 images in one panel.

In a later Chemistry Lesson of the Day on optical rotation (a.k.a. optical activity), I will explain what the (-) symbol means in the names of those 2 diastereomers.

*I will discuss meso isomers in a separate lesson.

Inorganic Chemistry Lesson of the Day – 2 Different Ways for Chirality to Arise in Coordination Complexes

In a previous Chemistry Lesson of the Day, I introduced chirality and enantiomers in organic chemistry; recall that chirality in organic chemistry often arises from an asymmetric carbon that is attached to 4 different substituents.  Chirality is also observed in coordination complexes in inorganic chemistry.  There are 2 ways for chirality to be observed in coordination complexes:

1.   The metal centre has an asymmetric arrangement of ligands around it.

• This type of chirality can be observed in octahedral complexes and tetrahedral complexes, but not square planar complexes.  (Recall that square planar complexes have a plane formed by the metal and its 4 ligands.  This plane can serve as a plane of reflection, and any mirror image of a square planar complex across this plane is clearly superimposable onto itself, so it cannot have chirality just by having 4 different ligands alone.)

2.   The metal centre has a chiral ligand (i.e. the ligand itself has a non-superimposable mirror image).

• Following the sub-bullet under Point #1, a square planar complex can be chiral if it has a chiral ligand.

 

Organic and Inorganic Chemistry Lesson of the Day – Chirality and Enantiomers

In chemistry, chirality is a property of a molecule such that the molecule has a non-superimposable mirror image.  In other words, a molecule is chiral if, upon reflection by any plane, it cannot be superimposed onto itself.

Chirality is a property of the 3-dimensional orientation of a molecule, and molecules exhibiting chirality are stereoisomers.  Specifically, two molecules are enantiomers of each other if they are non-superimposable mirror images of each other.  In organic chemistry, chirality commonly arises out of an asymmetric carbon atom, which is a carbon that is attached to 4 different substituents.  Chirality in inorganic chemistry is more complicated, and I will discuss this in a later lesson.

It is important to note that enantiomers are defined as pairs.  This will be later emphasized in the lesson on diastereomers.

Organic and Inorganic Chemistry Lesson of the Day – Cis/Trans Isomers

Cis/Trans isomerism is a type of stereoisomerism in which the relative positions of 2 functional groups differ between the isomers.  An isomer is cis if the 2 functional groups of interest are closer to each other, and trans if they are farther from each other.  You may find these definitions to be non-rigorous based on the subjectivity of “closer” and “farther”, but cis/trans isomers have only 2 possible relative positions for these functional groups, so “closer” and “farther” are actually obvious to identify.  It’s easier to illustrate this with some examples.

Let’s start with an organic molecule.

Image courtesy of Roland1952 on Wikimedia.

The molecule on the left is trans-1,2-dibromoethylene, and the molecule on the right is cis-1,2-dibromoethylene.  The 2 functional groups of interest are the 2 bromides, and the isomerism arises from the 2 different ways that these bromides can be positioned relative to each other.  (Notice that the 2 bromides are bonded to different carbon atoms, thus the “1,2-” designation in its name.)  Relative to the other bromide, one bromide can either be on the same of the double bond (“closer”) or on the opposite side of the double bond (“farther”).  To view the isomerism from another perspective, the double bond serves as the plane of separation, and the bromides can be on different sides of that plane (trans) or the same sides of the plane (cis).  Cis/Trans isomerism often arises in organic chemistry because of a bond with restricted rotation, and such restriction is often due to a double bond or a ring structure.  Such a bond often serves as the plane of separation on which the relative positions of the 2 functional groups can be established.

 

Let’s now consider a coordination complex in inorganic chemistry.

Image courtesy of Anypodetos on Wikimedia.

Cisplatin and transplatin are both 4-coordinated complexes with a square planar geometry.  Their ligands are 2 chlorides and 2 ammonias.  When looking at the pictures above, it’s obvious that there are only 2 relative positions for one chloride to take compared to the other chloride – they can be either closer to each other (cis) or farther apart (trans).

Cis/Trans isomerism can also arise in 6-coordinated octahedral complexes in inorganic chemistry.