Analytical Chemistry Lesson of the Day – Linearity in Method Validation

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 Lesson 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.

butane conformers

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.

butane 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.

Eric’s Enlightenment for Wednesday, June 3, 2015

  1. Jodi Beggs uses the Rule of 70 to explain why small differences in GDP growth rates have large ramifications.
  2. Rick Wicklin illustrates the importance of choosing bin widths carefully when plotting histograms.
  3. Shana Kelley et al. have developed an electrochemical sensor for detecting selected mutated nucleic acids (i.e. cancer markers in DNA!).  “The sensor comprises gold electrical leads deposited on a silicon wafer, with palladium nano-electrodes.”
  4. Rhett Allain provides a very detailed and analytical critique of Mjölnir (Thor’s hammer) – specifically, its unrealistic centre of mass.  This is an impressive exercise in physics!
  5. Congratulations to the Career Services Centre at Simon Fraser University for winning TalentEgg’s Special Award for Innovation by a Career Centre!  I was fortunate to volunteer there as a career advisor for 5 years, and it was a wonderful place to learn, grow and give back to the community. My career has benefited greatly from that experience, and it is a pleasure to continue my involvement as a guest blogger for its official blog, The Career Services Informer. Way to go, everyone!

Eric’s Enlightenment for Monday, June 1, 2015

  1. A comprehensive graphic of public perceptions about chemistry in the United Kingdom – compiled by the Royal Society of Chemistry.  (Hat Tip: Neil Smithers)
  2. Qing Ke et al. compiled a list of “sleeping beauties” in science – articles that were not appreciated at the time of publication and required much passage in time before becoming popular in the scientific community.  (Unfortunately, that original article is gated by subscription.)  As reported in, “the longest sleeper in the top 15 is a statistics paper from Karl Pearson, entitled, ‘On lines and planes of closest fit to systems of points in space‘.  Published in Philosophical Magazine in 1901, this paper awoke only in 2002.”  Out of those top 15 sleeping beauties, 7 were in chemistry.  A full pre-published version of Ke et al.’s paper can be found on arXiv.
  3. What would the Earth’s stratospheric ozone layer look like if the Montreal Protocol was never enacted to ban halocarbon refrigerants, solvents, and aerosol-can propellants?  Using simulations, Martyn Chipperfield et al. “found that the Antarctic ozone hole would have grown by an additional 40% by 2013.”
  4. Jan Hoffman on new challenges in mental health for university students: “Anxiety has now surpassed depression as the most common mental health diagnosis among college students, though depression, too, is on the rise. More than half of students visiting campus clinics cite anxiety as a health concern, according to a recent study of more than 100,000 students nationwide by the Center for Collegiate Mental Health at Penn State.”

Eric’s Enlightenment for Friday, May 29, 2015

  1. P2N3: An aromatic ion made of just phosphorous and nitrogen.  (Yes, aromaticity can be entirely inorganic!)
  2. Using 3-D printing and plastics to make prosthetics.
  3. David Beckwroth and Scott Sumner talk at length about reforming monetary policy with NGDP targeting in this video interview/seminar.
  4. Anky Lai gives a nice introduction to PROC TABULATE (PDF document) – an alternative to PROC FREQ and PROC MEANS in SAS.  Check out her awesome code samples for generating nicely formatted tables and exporting them conveniently into spreadsheets in Excel!

Eric’s Enlightenment for Tuesday, May 26, 2015

  1. Frances Woolley on the changing dynamics in the relationship between economists and the media in Canada over the past 8 years.
  2. The unintended consequences of labour policies that are meant to be friendly for parents and families – a nice account of many examples by Claire Cain Miller.
  3. FanGraphs explains batting average on balls in play (BABIP) in great detail.
  4. How Neil Bartlett discovered compounds that contain noble gases.  (Yes – they can react!)  He began his research at the University of British Columbia in Vancouver (my hometown).  He also discovered a compound in which oxygen is a positively charged ion.  Very cool stuff!

Eric’s Enlightenment for Friday, May 22, 2015

  1. John Urschel (academically published mathematician and NFL football player) uses logistic regression, expected value and variance to anticipate that the new farther distance for the extra-point conversion will not reduce its use in the NFL.
  2. John Ioannidis is widely known for his 2005 paper “Why most published research findings are false“.  In 2014, he wrote another paper on the same topic called “How to Make More Published Research True“.
  3. Yoshitaka Fujii holds the record for the number of retractions of academic publications for a single author: 183 papers, or “roughly 7 percent of all retracted papers between 1980 and 2011”.
  4. The chemistry of why bread stales, and how to slow retrogradation.

Eric’s Enlightenment for Thursday, May 21, 2015 – A Special Edition on the Mental Health of Chemistry Graduate Students

Today, combining

  • my passion for chemistry,
  • my experienced knowledge of university culture in North America,
  • and my deep concern for mental health issues,

The Chemical Statistician will feature a collection of writing about the struggles that graduate students in chemistry face during their studies, and how those struggles affect their mental health.  This is a special edition of Eric’s Enlightenment.

  1. Chemjobber began a dialogue with Vinylogous about mental health and graduate studies in chemistry in 2013.  It started with this blog post as Part 1, containing reflections of Chemjobber’s own experience and thoughts on general issues on this subject.
  2. In Part 2 of their dialogue, Vinylogous responds to Chemjobber with a very detailed post on his conjectures of why graduate studies in chemistry is so hard on a student’s mental health.
  3. In Part 3 of their dialogue, Chemjobber responds to some of Vinylogous’ main points and addresses possible solutions to mental health challenges for chemistry graduate students.  He/She also begins to answer the question “Is a graduate degree in chemistry worth the sacrifice?”.
  4. In Part 4 of their dialogue, Vinylogous examines some alternative issues in this subject, including possible benefits of chemistry graduate studies for mental health, how some research supervisors aggravate mental health problems, and differences between sub-fields of chemistry.
  5. Finally, in Part 5, Chemjobber concludes this discussion by trying to answer some of the key questions that this dialogue generated and summarizes some of the key points that they learned.
  6. I am surprised that I never learned about this sad story during my studies as a chemistry student: Jason Altom was an accomplished and well-liked doctoral student in chemistry at Harvard University, yet he committed suicide at age 26, citing excessive pressure from abusive research advisers, including his supervisor, Nobel Laureate Elias Corey.  Notably, his suicide notes contained policy recommendations on how academic departments can better protect their students.

The dialogue between Chemjobber and Vinylogous was very productive, with many other chemistry bloggers adding valuable perspectives in their own blog posts.  I highly encourage you to read those articles, too.

I also highly recommend you to read the comments in all 5 blog posts – they add great diversity to the perspectives and experiences about this complicated topic.

Here are some key quotations that I gathered from these articles:

Chemjobber – in Part 1 of the dialogue with Vinylogous.

After weeks and weeks of long hours and frustration in the lab in either my 2nd or 3rd year of graduate school, I remember walking into my apartment bathroom, smashing the mirror with my fist and sitting on the edge of the bathtub. I seem to recall yelling at the top of my lungs “What am I going to do!?!?” about whatever reaction sequence of my total synthesis that simply was not going anywhere.

I can easily say that was one of the darkest periods of my time in graduate school. I am not sure if I was depressed — I’m a synthetic chemist, not a clinical psychologist. Close to ten years later, it’s mostly an unpleasant memory, with little recall of the details that set me off. But I can remember sitting on that bathtub edge, the deep despair of a project that wasn’t going well and the feeling that my entire life was an utter failure. Now, of course, I don’t feel that way at all. I can leave my work at work (mostly, anyway), and my self-worth is not entirely reliant on the yield of my last reaction. But there was a lot of pain in between then and now.

Vinylogous – in Part 2 of the dialogue with Chemjobber.

At one point during my previous degree, when I was doing research, taking classes, and teaching, my advisor told me frankly that my productivity needed to increase. It needed to double. At that point I already felt that I was at my absolutely limit in what I could accomplish in a week. At that point, I had nowhere near enough data for a paper and barely enough for a mediocre conference poster. Weekends had been given up, as had hobbies. When I mentioned to my advisor the many demands on my time, his response was short: “Sometimes you need to prioritize what’s important to you.” (The subtext: stop caring about class and teaching and hobbies). It was an existential moment. I managed somehow to increase my productivity and my efficiency, and within a year or so I had three first-author manuscripts. I defended my M.S. and graduated, moving to another (higher tier) school for a Ph.D. But I left with a pre-conditioned bitterness towards graduate work.

Eric’s Enlightenment for Tuesday, May 5, 2015

  1. The inherent flaws of defining and estimating job vacancy rates – a commentary by Philip Cross, a former chief economic analyst at Statistics Canada.
  2. Adding to my previous entry about CRISPR, here is Douglas Mortlock’s in-depth discussion of the problems in Jiang et al.’s study.  Note that his entire blog is devoted to CRISPR.
  3. Robin Hanson’s proposal to evaluate teachers and students using linear regression while controlling for related variables.
  4. A video on the health benefits of avocados from a chemical perspective – including the best way to cut an avocado and how to slow the browning of a guacamole dip.

Eric’s Enlightenment for Friday, May 1, 2015

  1. PROC GLIMMIX Contrasted with Other SAS Statistical Procedures for Regression (including GENMOD, MIXED, NLMIXED, LOGISTIC and CATMOD).
  2. Lee-Ping Wang et al. recently developed the nanoreactor, “a computer model that can not only determine all the possible products of the Urey-Miller experiment, but also detail all the possible chemical reactions that lead to their formation”.  What an exciting development!  It “incorporates physics and machine learning to discover all the possible ways that your chemicals might react, and that might include reactions or mechanisms we’ve never seen before”.  Here is the original paper.
  3. A Quora thread on the best examples of the Law of Unintended Consequences
  4. In a 2-minute video, Alex Tabarrok argues why software patents should be eliminated.

Eric’s Enlightenment for Thursday, April 30, 2015

  1. Simon Jackman from Stanford University provides some simple examples of obtaining the posterior distribution using conjugate priors.  If you are new to Bayesian statistics and need to develop the intuition for the basic ideas, then work through the math in these examples with pen and paper.
  2. Did you know that there are plastics that conduct electricity?  In fact, Alan J. Heeger, Alan G. MacDiarmid and Hideki Shirakawa won the 2000 Nobel Prize in Chemistry for the work on this fascinating subject.
  3. Jared Niemi provides a nice video introduction of mixed-effects models.  I highly encourage you to work through the math with pen and paper.
  4. Alberto Cairo adds a healthy dose of caution about the recent advent of data-driven journalism.  He emphasizes problems like confusing correlation with causation, ecological fallacies, and drawing conclusions based on small sample sizes or unrepresentative samples.

Eric’s Enlightenment for Wednesday, April 29, 2015

  1. Anscombe’s quartet is a collection of 4 data sets that have almost identical summary statistics but appear very differently when plotted.  They illustrate the importance of visualizing your data first before plugging them into a statistical model.
  2. A potential geochemical explanation for the existence of Blood Falls, an outflow of saltwater tainted with iron (III) oxide at the snout of the Taylor Glacier in Antarctica.  Here is the original Nature paper by Jill Mikucki et al.
  3. Jonathan Rothwell and Siddharth Kulkarni from the Brookings Institution use a value-added approach to rank 2-year and 4-year post-secondary institutions in the USA.  Some of the top-ranked universities by this measure are lesser known schools like Colgate University, Rose-Hulman Institute of Technology, and Carleton College.  I would love to see something similar for Canada!
  4. Heather Krause from Datassist provides tips on how to avoid (accidentally) lying with your data.  Do read the linked sources of further information!

Eric’s Enlightenment for Tuesday, April 21, 2015

  1. The standard Gibbs free energy of the conversion of water from a liquid to a gas is positive.  Why does it still evaporate at room temperature?  Very good answer on Chemistry Stack Exchange.
  2. The Difference Between Clustered, Longitudinal, and Repeated Measures Data.  Good blog post by Karen Grace-Martin.
  3. 25 easy and inexpensive ways to clean household appliances using simple (and non-toxic) household products.
  4. A nice person named Alex kindly transcribed the notes for all of Andrew Ng’s video lectures in his course on machine learning at Coursera.

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

The simplest case of conformational isomerism belongs to ethane, C2H6.

ethane conformers

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 180 \times (2n + 1) \div 3 degrees, where n is any integer (n = 0, \pm 1, \pm 2, \pm 3, ...).  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 180 \times (2n) \div 3 degrees, where n is any integer (n = 0, \pm 1, \pm 2, \pm 3, ...).  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.


  • 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.

Café Scientifique – Materials Science Seminar by Neil Branda on Wednesday, November 19, 2014

If you will attend the following seminar, please do come and say “Hello”!  The event is free, but registration is required!  For more information, visit the SFU Café Scientifique’s web site!

SFU Café Scientifique

Time: 7:00 -8:30 pm

Date: Wednesday, November 19, 2014

Place: Boston Pizza, 1045 Columbia Street, New Westminster, BC

Title: It’s a Materials World – From Sticks and Stones to Nanotechnology, how materials have changed our world

Speaker: Neil Branda – Professor of Chemistry at Simon Fraser University, Executive Director of 4D LABS, and Chief Technology Officer of SWITCH Materials


Since the beginning, understanding how materials can be used for specific tasks has resulted in some of the biggest changes to civilizations. Modern society is becoming more and more dependent on the development and use of advanced materials. From the basics to the controversial, how materials have affected they way we live and play will be discussed.

Biography of Speaker:

Dr. Neil Branda is a professor of Chemistry and a Canada Research Chair at Simon Fraser University, the Executive Director of 4D LABS, a research centre for advanced materials and nano-scale devices, CTO of SWITCH Materials Inc., a company he founded to commercialize his molecular switching technology and Founder and Director of the NanoCommunity Canada Research Network, a community of nanotechnology researchers committed to sharing knowledge and working collaboratively to advance applications in medical diagnostics, therapeutics, renewable energy and advanced materials.


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.

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