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 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.

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.

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

Abstract:

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.

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.

D-threose.svg 2

(-)-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:

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 – 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 – Stereogenic Centre

A stereogenic centre (often called a stereocentre) is an atom that satisfies 2 conditions:

  1. it is bonded to at least 3 substituents.
  2. interchanging any 2 of the substituents would result in a stereoisomer.

If a molecule has only 1 stereogenic centre, then it definitely has a non-superimposable mirror image (i.e. this molecule is chiral and is an enantiomer).  However, depending on its stereochemistry, it is possible for a molecule with 2 or more stereogenic centres to be achiral; such molecules are called meso isomers (or meso compounds), and I will discuss them in a later lesson.

In organic chemistry, the stereogenic centre is usually a carbon atom that is attached to 4 substituents in a tetrahedral geometry.  In inorganic chemistry, the stereogenic centre is usually the metal centre of a coordination complex.

In organic chemistry, stereogenic centres with substituents in a tetrahedral geometry are common.  Inorganic coordination complexes can also have a tetrahedral geometry.  A stereoisomer with n tetrahedral stereogenic centres can have at most 2^n stereoisomers.  The “at most” caveat is important; as mentioned above, it is possible for a molecule with 2 or more stereogenic centres to have a spatial arrangement that results in having a superimposable mirror image; such isomers are meso isomers.   I will discuss meso isomers in more detail in a later 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.

dibromoethylene

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.

cisplatin and transplatin

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.

Inorganic Chemistry Lesson of the Day: 5-Coordinated Complexes

There are 2 common geometries for 5-coordinated complexes:

  • Square pyramid: The metal centre is coordinated to 4 ligands in a plane and a 5th ligand above the plane.
  • Trigonal bipyramid: The metal centre is coordinated to 3 ligands in a plane and 2 lignads above and below the plane.

Inorganic Chemistry Lesson of the Day: 2-Coordinated Complexes

Some coordination complexes have just 2 ligands attached to the metal centre.  These complexes have a linear geometry; this allows the greatest separation of the electron clouds in the metal-ligand bonds, which minimizes electron repulsion.

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