Intuitive Probabilistic Derivation of Black-Scholes

In this blog post I start the series every way to derive BSM-OPM. Here I demonstrate the easiest most intuitive way. Since RMarkdown API is depreciated,  I can’t post the RMarkdown notebook directly on wordpress. I kindly ask you to check it out on github. I basically cover Alexei Krouglov’s derivation.

.pdf version:

Intuitive Probabilistic Derivation of Black Scholes – Option Pricing Formula

Originally published: November 20, 2018

(-)-Aflatoxin B1 (Trost 2003)

Trost’s synthesis of Aflatoxin B1, might be a generic synthesis showcasing The Tsuji-Trost Asymmetric Allylic Alkylation (AAA) for a facile prep of the furobenzofuran core. It was a response to the known ways of using enzymatic kinetic resolution to afford their product. This paper goes to showcase Dynamic Kinetic Asymmetric Transformation (DYKAT).

The Synthesis:

The synthesis starts with a Pechmann condensation. The 1967 synthesis also has this step. The coumarin is Iodated to make the handle for the Tsuji-Trost/Heck. The Tsuji-Trost Asymmetric Allylic Alkylaltion sets the stereocenter thus inducing asymmetry for the rest of the synthesis. While not shown in the Chemistry By Design Synthesis, there was supposed to be an intramolecular Heck Coupling. Which completes the prep of the furobenzofuran ring and sets the second stereocenter. The synthesis proceeds to form the cyclopenteneone ring by performing a Friedel-Crafts off aromatic Coumarin scaffold. I questioned here why Trost did a DIBAL-H reduction to afford the vinyl ether instead of maybe a Hydroboration and elimination. This paper talks about accessing different Aflatoxins, which differ based on chirality and substitution on that hemiketal stereocenter. After reduction, the hemiketal is acetylated with acetic anhydride and eliminated to afford (-)-Alfatoxin B1.

Key Knowledge:

The big addition was taking a racemic γ-tert-butoxycarbonyl-2-butenolide and being able to alkylate asymmetrically. Trost talks about how there was previous work on Kinetic Asymmetric Transformation (KAT), where a chiral palladium complex would form different products depending on the chirality of the substrate. Naturally this facilitates separation of the junk product but leaves much to be desired with a cap at 50% yield. Trost shows a DYKAT where the activated palladium interconverts between from the “mis-matched” to “matched” coordination and likely is caught in transition state “valley” until the substrate is in this matched state.

Aflatoxin B1

Taking a look at the arguments presented for the facial interconversion mechanism, I was not impressed that they didn’t get definitive proof for their conjecture. The proposed a Ligand displacement hypothesis, and a furan aromatization. Their proof was that the yield decreased with increased palladium, which meant that the sigma complex was the favored one.

Aflatoxin B1 2

I think a better proof would have been to lock out migration by probing the change in EE with the binding of a Lewis acid. Or attempting to run the reaction in the presence of a Mukiyama silyl enol ether. Other options include, having a chiral alkyl group for the γ-acyloxybutenolide, and seeing how the enantiomeric excess changed. But I think this may not have added much to the already deep knowledge of the Tsuji-Trost reaction umbrella.

Reflections:

Thinking about the disconnects and my lack of instinct when it came to this synthesis, brings to light that I don’t have a flair for syntheses that hinge on transition metal chemistry outside the classic model systems. This synthesis reminds me that you can guess what kind of chemistry to expect, based on the difficult disconnects, the author, and the history of the class of compounds.

Originally published: November 12, 2018

The Quickest High

Looking through my old synthesis diary I played a game where I could make a fast route to THC. I was quickly disappointed when the best I could reasonably do was 9 or 10 steps (6 after revising and reading different syntheses Trost, Evans, Pinnick’s).

  1. Alpha Bromination of Orange Flavor Ether using NBS and UV light
  2. MOM Protection of Olivitol
  3. In-situ Grignard reagent generation + Palladated Olivetol to do a fancy Kumada Coupling.
  4. Total MOM Deprotection
  5. Sodium ethyl sulfate Demethylation
  6. ZnBr/MgSO4 mediated SN

The world record:

Takes simply (+)-p-mentha-2,8-dien-1-ol and olivetol in 1% BF3*(OEt2) and Anhydrous MgSO4 in DCM at 273K.

Simply put, Razdan does a retro-friedel crafts using BF3 etherate as the Lewis Acid, then has acidic conditions to drive the recombination forward. His paper’s goal was to elucidate the mechanism (mind you this was 1974) and had little stereocontrol.

These syntheses show how important starting materials and one’s ability to take advantage of simple reaction kinetics can improve the efficiency of your chemistry. Switching to Organge Flavor Ether from Terpineol saved me a step from my original route. And using olivetol instead of olivtollic acid saved me from doing a Krapcho Decarboxylation. Razdan’s Synthesis was fast because his choice of a relatively obscure monoterpene “(+)-p-mentha-2,8-dien-1-ol”. The terpene had an allyl cation equivalent eager to go through the retro Friedel-Crafts. He shows that all the coupling prep that I did was somewhat unnecessary. So for you next synthesis remember to choose your starting material wisely.

Originally published: November 8, 2018

(+)-Psiguadial B (Reisman 2016)

Today’s synthesis is (+)-Psiguadial B by Sarah Reisman. I urge everyone to check it out, it is a testament to the dedication total synthesis requires. In the paper she details all the failed reaction pathways and the clever model systems that led to development of the final route.

Synthetic pathway high lights:

  1. Enantioselective Wolf Rearrangment/Ketene addition using  aminoquinoline and (+)-cinchonine.
  2. Hoveyda Grubbs II RCM, and then a Crabtree’s tertiary Alcohol directed double olefin reduction.
  3. Copper Cat. Intrmolecular O-arylation.
  4. DDQ Oxidation, and Cl’ Phenylation.

Sticking with the Reisman Group theme of transition metal methodology development, we see that this synthesis is mostly transition metal catalyzed reactions. Their key additions were the Wolf Rearrangment chemistry, where they did a simple solvent substrate screen. Their other great aaddition was the Phenylation step towards the end of the synthesis. They talk about it being unclear whether an neutral Phenyl would be a suitable candidate. They achieved a 4.8:1 dr, which is reasonable given that they only examined 3 oxidants for this reaction.

Looking into other syntheses the fastest one I found was done by Cramer in 2017. He uses Caryophyllene to do most of the heavy lifting, and touts a bio-mimetic approach. The 1 step is a multicomponent reaction that would make a great group meeting problem. Thinking about what the role of total synthesis is in chemistry; As a context to develop new synthetic techniques, I think Reisman had the more valuable synthesis. I think further exploration into the enantioselective Wolff rearrangement has a lot of merit since photochemistry, has historically been difficult to employ asymmetrically.

Originally published September 19, 2018

(+)-Chromazonarol & (+)-Yahazunone (Baran 2012)

Today’s synthesis is a semisynthesis of (+)-Chromazonarol and (+)-Yuhazunone. These preps start a natural sesquiterpene fragrance Sclareolide. I haven’t developed the intuition yet, but clever functional group interconversion and novel synthetic techniques are the drivers behind remarkable semisyntheses.

Baran showcases the prep of a “Borono-Sclareolide” to access a wide range of Meroterpenoids.  A scalable semisynthesis from (+)-Sclareol to get to (+)-8-O-Acetylchromazonarol and (+)-8-O-Acetylyahazunone. A Li, Csuk, and Li collaboration cut’s Baran’s 7 step prep down to 5 (6 if you count) the Acetyl deprotection. Li, Csuk, and Li improve on Baran’s work by having the core finished in 3 steps compared to Baran’s 6 steps. In addition, Li, Csuk, and Li’s synthesis doesn’t hinge on a Alcohol directed hydroboration to set a stereocenter which resolves one of Baran’s issues. Wu also resolves this issue through a palladium cross coupling but given this groups goals of creating a divergent synthesis, they could not afford to save steps by sacrificing the functionality of the 1,4 benzoquinone.

Originally published: September 18, 2018

ent-Clavilactone B (Barret 2007)

Every once in a while I’ll walk through a synthetsis on Chemistry By Design. Usually it’s to find a unique reaction, or to find out how a unique compound was made. Most of the time it will start with me looking at the molecule and seeing the obvious retrosynthetic points, and then walking through the synthesis to see how close I was.

The criteria in which I choose my syntheses is typically:

  1. Does it have fused rings or an interesting macrocyclic structure?
  2. Is the synthesis less than 20 linear steps?
  3.  does it rely on a magic step that was discovered through serendipity?

Toady I will go through ent-Clavilactone.

Retrosynthetic Instinct:

  1. 5-member lactonization
  2. Sharpless asymmetric epoxidation -> asymmetric induction point
  3. Grubbs II RCM.

The True Retro synthesis:

  1. RCM
  2. Oxidative Lactonization
  3. 3-Component Benzyne Coupling
  4. Sharpless Asymmetric Epoxidation -> asymmetric induction point

Evaluating the forward synthesis:

Barret’s Synthesis aims to form a constraint 10 member benzoquinone using RCM.  His goal was motivated to study SAR of tyrosine kinase inhibitors. His synthesis uses straightforward chemistry to get to his epoxide and the neat twist is on the 3-component Benzyne Coupling, and his lactone isomerization. He states that he employs Yamamoto’s bulky alumnium Complex [ I did not do it service in the synthesis] to isomerize his lactone. It shows robustness in being able to handle a crude mixture of diastereomers and yield a single diastereomer as a product in 80% yield. After affording his lactone and setting the stage for an olefin metathesis, he optimizes his Grubbs II RCM. The synthesis finished with CAN oxdiation of 1,4 dimethyoxybenzene installed during the 3-component benzyne coupling.

The aim to use this synthesis as jumping off point to evaluate SAR of Clavilactones leaves much to be desired. When designing a SAR your goal is make a generlized and robust synthetic route. Relying on Asymmetric Epoxidation, to set your stereochemistry, and then have it be part of your most complex moiety, makes it inflexible so heteroatom substitution.

However, he does leave optionality along the saturated chain for different alkyl substitutions as long as they agree with Gilman, Grignard Organo Lithium addition conditions.

I enjoyed this synthesis and I welcome any opinion and discussion!ent-ClavilactoneB