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I quite liked this article, which describes the synthesis of (-)-batrachotoxin as well as a steroisomer, (+)-batrachotoxin. I would like to know what the precise difference is between the two: are they precise mirror images of each other, or is there something more subtle going on? Is there something specific about the (±) notation (as opposed to S and R, for example) with relevance to the difference between the two?

I had a look online but the original paper is thin on structures that I can understand, and just going on google buries me under a slew of (-)-BTX results.

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From a cursory glance, batrachotoxin has 8 stereocenters. No single Cahn-Ingold-Prelog R or S designation is going to be enough. As a result, we simply identify which enantiomer we're talking about by using the standard optical rotation of the substance. The (+) and (-) forms are enantiomers. They rotate plane polarized light in equal and opposite directions and are non-superimposable mirror images of each other.

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Since Pasteur’s famous crystal separation experiment, it has been known that organic compounds can be chiral. Futhermore, it has been known that chiral organic compounds can rotate linearly polarised light beams. Since structure elucidation, especially stereospecific structure elucidation was a very hard task back in the day, it was common to refer to chiral compounds by the direction they rotate polarised light; (+) being dextrorotatory and (–) being levorotatory.

Most early chemical syntheses would be racemic for the simple reason of no chiral substrates being readily available. Racemic compounds were denoted as (±).

The (+) form and the (–) form are always exact enantiomers, i.e. every stereocentre reversed, every chiral axis reversed, every helical chirality reversed. For example, (–)-tartrate is (2S,3S)-tartrate while (+)-tartrate is (2R,3R)-tartrate. (2R,3S)-tartrate or meso-tartrate is a diastereomer of the former two.

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