-Ken Tanaka, Hiromi Sagae, Kazuki Toyoda, Keiichi Noguchi, and Masao Hirano J. Am. Chem. Soc.

Previous articles have highlighted FlexMol's ability to represent nearly all forms of molecular chirality, including many that are alien to popular cheminformatics tools. FlexMol provides just a few basic elements and rules for their combination, resulting in a system that is both extensible and systematic. For example, similar elements are used to represent the axial chirality of biaryls, the geometrical isomerism of alkenes, and the configuration of square-planar metal complexes. In this article, we'll see how FlexMol can encode an example from the very recent literature: planar-chiral metacyclophanes as described by Tanaka and coworkers.

Configuration or Conformation?

The question we have to answer is what form of stereochemistry needs to be represented - configuration or conformation. We follow the simple rule that isomers interconvertable through bond rotations are treated as conformations and conclude that to represent a metacyclophane, we'll be dealing with conformation. See the original Dietz specification for a more rigorous analysis.

A FlexMol Representation

Let's choose a specific molecule to encode in FlexMol (Y,Z=CH₂) . Using the atom numbering given in the figure above, we can construct the complete FlexMol representation. Rather than reproduce it completely here, I'll just highlight the stereochemically-relevant part:

<!-- snip -->
<conformation>
  <conformationWheel>
    <gammaSequence source="17" target="8">
      <connections>
        <atomPair source="17" target="8"></atomPair>
      </connections>
    </gammaSequence>
    <halfPlane>
      <lower atom="16"></lower>
    </halfPlane>
    <halfPlane>
      <upper atom="9"></upper>
    </halfPlane>
    <halfPlane></halfPlane>
    <halfPlane>
      <upper atom="7"></upper>
    </halfPlane>
  </conformationWheel>
  <conformationWheel>
    <gammaSequence source="11" target="10">
      <connections>
        <atomPair source="11" target="10"></atomPair>
      </connections>
    </gammaSequence>
    <halfPlane>
      <lower atom="12"></lower>
    </halfPlane>
    <halfPlane>
      <upper atom="2"></upper>
    </halfPlane>
    <halfPlane></halfPlane>
    <halfPlane>
      <upper atom="9"></upper>
    </halfPlane>
  </conformationWheel>
</conformation>
<!-- snip -->

This conformation contains two conformationWheels, each corresponding to one of the two bonds about which rotation is restricted. Notice the similarity of this FlexMol code compared to the examples for BINOL, and an N-arylacrylanilide. To better visualize the relationships among atoms, axes, and half-planes, consider the following cartoons:

It should be clear that the enantiomeric representation of our molecule would produce an arrangement of half-planes that was the inverse of those shown here, and distinguishable by manual inspection or software implementation. One such implementation is contained in the open source framework Octet

Conclusions

As the example in this article demonstrates, FlexMol can fully encode the planar-chirality of the new class of axially-chiral metacyclophanes reported in a recent J. Am. Chem. Soc. article. Exactly the same FlexMol elements were used as in previous examples illustrating axial chirality and alkene geometry. Systematic and extensible methods for encoding diverse forms of chirality are not only feasible - one of them already exists.

-Andre Lapierre, Steven Geib, and Dennis Curran, J. Am. Chem. Soc. ASAP

Recently, Heck cyclizations of axially chiral N-arylacrylanilids were reported by Lapierre, Geib, and Curran. Faithfully communicating this kind of chirality in machine-readable form is virtually impossible using today's most popular technologies. A previous article showed how a new XML-based molecular language, FlexMol, could fully represent the axial chirality of BINOL. This article will apply the same principles to an N-arylacrylanilide.

The Complete FlexMol Representation

Given the atom numbering of the above molecule, we can construct a complete FlexMol representation. Rather than reproduce the entire XML document here, I'll just include stereochemically-relevant excerpts.

Stereochemistry: Chiral Axis

The chiral axis is directed from Atom 11 to Atom 7. Half planes are arranged in clockwise fashion about this axis. To better visualize the placement of atoms into half planes, consider the following diagram:

This leads to the following FlexMol representation:

<!-- snip -->
<conformationWheel>
  <gammaSequence source="11" target="7">
    <connections>
      <atomPair source="11" target="7"></atomPair>
    </connections>
  </gammaSequence>
  <halfPlane>
    <lower atom="10"></lower>
  </halfPlane>
  <halfPlane>
    <upper atom="5"></upper>
  </halfPlane>
  <halfPlane>
    <lower atom="12"></lower>
  </halfPlane>
  <halfPlane>
    <upper atom="8"></upper>
  </halfPlane>
</conformationWheel>
<!-- snip -->

Stereochemistry: Olefin Geometry

Assignment of olefin geometry in FlexMol was introduced in a previous article. A simple disubstituted olefin was used as an example. Exactly the same principles apply in encoding the trisubstituted olefin geometry of our molecule of interest:

<!-- snip -->
<conformationWheel>
  <gammaSequence source="3" target="2">
    <connections>
      <atomPair source="3" target="2"></atomPair>
    </connections>
  </gammaSequence>
  <halfPlane>
    <lower atom="4"></lower>
    <upper atom="1"></upper>
  </halfPlane>
  <halfPlane>
    <lower atom="5"></lower>
  </halfPlane>
</conformationWheel>
<!-- snip -->

Conclusions

Axial chirality can be fully represented using FlexMol's simple system of axes and half planes. This system can be applied in novel situations, increasing FlexMol's potential as a self-describing molecular language.

A recent article introduced FlexMol as a molecular language with the unique capability of encoding axial chirality. A previous article showed how E/Z geometrical isomerism is encoded with FlexMol. Using the popular chiral reagent and ligand 1,1'-bi-2-naphthol (BINOL) as an example, this tutorial will illustrate in detail how axial chirality is encoded in FlexMol.

Configuration or Conformation?

In contrast to configurational stereoisomers, conformational stereoisomers can be interconverted through bond rotations. So we'll need to use a conformationWheel to represent stereochemistry in BINOL - just as we did with 2-butene. For more rigorous definitions of these concepts, see the original specification by Dietz.

(R)-BINOL

A FlexMol representation and associated atom numbering scheme (R)-BINOL are show below:

<!-- (R)-BINOL -->
<?xml version="1.0" standalone="yes"?>

<molecule>
  <constitution>
    <atoms>
      <atom id="C0" symbol="C" hydrogens="0" ionization="4"></atom>
      <atom id="C1" symbol="C" hydrogens="0" ionization="4"></atom>
      <atom id="C2" symbol="C" hydrogens="1" ionization="4"></atom>
      <atom id="C3" symbol="C" hydrogens="1" ionization="4"></atom>
      <atom id="C4" symbol="C" hydrogens="1" ionization="4"></atom>
      <atom id="C5" symbol="C" hydrogens="1" ionization="4"></atom>
      <atom id="C6" symbol="C" hydrogens="1" ionization="4"></atom>
      <atom id="C7" symbol="C" hydrogens="1" ionization="4"></atom>
      <atom id="C8" symbol="C" hydrogens="0" ionization="4"></atom>
      <atom id="C9" symbol="C" hydrogens="0" ionization="4"></atom>
      <atom id="C10" symbol="C" hydrogens="0" ionization="4"></atom>
      <atom id="C11" symbol="C" hydrogens="0" ionization="4"></atom>
      <atom id="C12" symbol="C" hydrogens="1" ionization="4"></atom>
      <atom id="C13" symbol="C" hydrogens="1" ionization="4"></atom>
      <atom id="C14" symbol="C" hydrogens="1" ionization="4"></atom>
      <atom id="C15" symbol="C" hydrogens="1" ionization="4"></atom>
      <atom id="C16" symbol="C" hydrogens="1" ionization="4"></atom>
      <atom id="C17" symbol="C" hydrogens="1" ionization="4"></atom>
      <atom id="C18" symbol="C" hydrogens="0" ionization="4"></atom>
      <atom id="C19" symbol="C" hydrogens="0" ionization="4"></atom>
      <atom id="O20" symbol="O" hydrogens="1" ionization="2"></atom>
      <atom id="O22" symbol="O" hydrogens="1" ionization="2"></atom>
    </atoms>
    <bonding>
      <bond source="C0" target="C1" bondingElectrons="2"></bond>
      <bond source="C1" target="C2" bondingElectrons="2"></bond>
      <bond source="C2" target="C3" bondingElectrons="2"></bond>
      <bond source="C3" target="C4" bondingElectrons="2"></bond>
      <bond source="C4" target="C5" bondingElectrons="2"></bond>
      <bond source="C0" target="C5" bondingElectrons="2"></bond>
      <bond source="C0" target="C6" bondingElectrons="2"></bond>
      <bond source="C6" target="C7" bondingElectrons="2"></bond>
      <bond source="C7" target="C8" bondingElectrons="2"></bond>
      <bond source="C8" target="C9" bondingElectrons="2"></bond>
      <bond source="C9" target="C1" bondingElectrons="2"></bond>
      <bondingSystem bondingElectrons="10">
        <connections>
          <atomPair source="C0" target="C1"></atomPair>
          <atomPair source="C1" target="C2"></atomPair>
          <atomPair source="C2" target="C3"></atomPair>
          <atomPair source="C3" target="C4"></atomPair>
          <atomPair source="C4" target="C5"></atomPair>
          <atomPair source="C0" target="C5"></atomPair>
          <atomPair source="C0" target="C6"></atomPair>
          <atomPair source="C6" target="C7"></atomPair>
          <atomPair source="C7" target="C8"></atomPair>
          <atomPair source="C8" target="C9"></atomPair>
          <atomPair source="C9" target="C1"></atomPair>
        </connections>
      </bondingSystem>
      <bond source="C10" target="C11" bondingElectrons="2"></bond>
      <bond source="C11" target="C12" bondingElectrons="2"></bond>
      <bond source="C12" target="C13" bondingElectrons="2"></bond>
      <bond source="C13" target="C14" bondingElectrons="2"></bond>
      <bond source="C14" target="C15" bondingElectrons="2"></bond>
      <bond source="C10" target="C15" bondingElectrons="2"></bond>
      <bond source="C10" target="C16" bondingElectrons="2"></bond>
      <bond source="C16" target="C17" bondingElectrons="2"></bond>
      <bond source="C17" target="C18" bondingElectrons="2"></bond>
      <bond source="C18" target="C19" bondingElectrons="2"></bond>
      <bond source="C19" target="C11" bondingElectrons="2"></bond>
      <bondingSystem bondingElectrons="10">
        <connections>
          <atomPair source="C10" target="C11"></atomPair>
          <atomPair source="C11" target="C12"></atomPair>
          <atomPair source="C12" target="C13"></atomPair>
          <atomPair source="C13" target="C14"></atomPair>
          <atomPair source="C14" target="C15"></atomPair>
          <atomPair source="C10" target="C15"></atomPair>
          <atomPair source="C10" target="C16"></atomPair>
          <atomPair source="C16" target="C17"></atomPair>
          <atomPair source="C17" target="C18"></atomPair>
          <atomPair source="C18" target="C19"></atomPair>
          <atomPair source="C19" target="C11"></atomPair>
        </connections>
      </bondingSystem>
      <bond source="C9" target="C19" bondingElectrons="2"></bond>
      <bond source="C8" target="O20" bondingElectron="2"></bond>
      <bond source="C18" target="O21" bondingElectron="2"></bond>
    </bonding>
  </constitution>
  <conformation>
    <conformationWheel>
      <gammaSequence source="C19" target="C9">
        <connections>
          <atomPair source="C9" target="C19"></atomPair>
        </connections>
      </gammaSequence>
      <halfPlane>
        <lower atom="C11"></lower>
      </halfPlane>
      <halfPlane>
        <upper atom="C1"></upper>
      </halfPlane>
      <halfPlane>
        <lower atom="C18"></lower>
      </halfPlane>
      <halfPlane>
        <upper atom="C8"></upper>
      </halfPlane>
    </conformationWheel>
  </conformation>
</molecule>

We've elected to represent BINOL's two pi-systems as ten-atom, ten-electron bondingSystems. We could have just as easily represented each naphthalene ring using alternating single/double bonds containing two and four electrons, respectively. For an explanation of multi-atom pi-system bonding in FlexMol, see this article.

The stereochemically-relevant part of this document is contained within the conformation element. A gammaSequence, or conformational axis, is defined along with four non-empty halfPlanes. Notice how the basic structure of this conformation element closely resembles the one for 2-butene.

To better visualize the the conformation element of (R)-BINOL, consider the following diagram:

The conformationWheel defines a conformational axis vector from atom C19 to atom C9. Arranged about this axis in a clockwise fashion are four non-empty halfPlanes. Picking an arbitrary halfPlane to start with, atom C11 is positioned first in the lower half. This is then followed by the next halfPlane, which contains atom C1 in its upper half. The next halfPlane contains atom C18 in the lower half. Finally, atom C8 is located in the last halfPlane's upper half.

This procedure completely specifies the axial chirality of (R)-BINOL. Notice how no arbitrary stereodescriptors or chiral templates were used. Of course, we could derive the Cahn-Ingold-Prelog stereodescriptor of (R), given the right software.

Many representations of the same chiral axis are possible, just as each connection table can be represented in many different ways. For example, we could have started the conformation element with the halfPlane containing atom C1. In this case, the ordering of atoms would be C1, C18, C8, C11. Similarly, the orientation of our chiral axis could have been defined from atom C9 to atom C19. In this case the ordering of halfPlanes would be reversed, and the upper/lower designations would be inverted.

(S)-BINOL

How is (S)-BINOL encoded in FlexMol? As you might expect, completely analogously to the (R) enantiomer:

<!-- snip -->
<conformation>
  <conformationWheel>
    <gammaSequence source="C19" target="C9">
      <connections>
        <atomPair source="C9" target="C19"></atomPair>
      </connections>
    </gammaSequence>
    <halfPlane>
      <lower atom="C11"></lower>
    </halfPlane>
    <halfPlane>
      <upper atom="C8"></upper>
    </halfPlane>
    <halfPlane>
      <lower atom="C18"></lower>
    </halfPlane>
    <halfPlane>
      <upper atom="C1"></upper>
    </halfPlane>
  </conformationWheel>
</conformation>
<!-- snip -->

As with (R)-BINOL, we can create a diagram representing the conformationWheel of (S)-BINOL:

Conclusions

As you can see, FlexMol completely encodes axial chirality using just a few basic XML elements, rather than chiral templates or stereodescriptors. These were, in fact, the same elements used to encode alkene geometrical isomerism. This modular approach to stereoisomerism results in an extensible system. Future articles will discuss other forms of stereoisomerism that can be represented in FlexMol, including the all-important tetrahedral stereogenic center.

The fundamental idea behind our representation of stereochemistry is to really describe the relative spatial arrangements of the atoms of a chemical structure. For a given constitution, we obtain a unique and unambiguous stereochemical representation. No limitation to predefined types or steregenic units exits; any conceivable relative spatial arrangement of atoms may be uniformly represented by one universally applicable formalism. ...

-Andreas Dietz, J. Chem. Inf. Comput. Sci. 1995, 35, 787-802

A recent article introduced FlexMol, a molecular language designed to encode the multi-atom bonding arrangements present in molecules being increasingly made and used by today's chemists. But FlexMol was designed with much more than bonding in mind. Of all of the difficult areas in molecular representation, perhaps none are more daunting than stereochemistry. This article will introduce the basic ideas behind FlexMol's stereochemistry capabilities using the geometrical isomers of 2-butene as an example.

The Difference Between Configuration and Conformation

FlexMol distinguishes between two complementary stereochemical concepts - conformation and configuration. The difference between the two lies in whether isomers can be interconverted through bond rotations. To paraphrase Dietz:

• Conformation. Two molecules with identical atom connectivities and bonding differ with respect to their conformation if if they possess different relative spatial arrangements of atoms that can be interconverted by rotations about bonds.

• Configuration. Two molecules with identical atom connectivities and bonding differ with respect to their configuration if they possess different relative spatial arrangements of atoms that can not be interconverted by rotations about bonds.

Notice that these definitions say nothing about whether a bond rotation is likely to occur; they simply refer to the possibility of isomer interconversion through bond rotation. Clearly, double bond geometrical isomerism arises from restricted bond rotation. So we'll be relying on FlexMol's support for conformational stereochemistry.

Encoding Cis/Trans Isomerism: 2-Butene

Consider the two isomers of 2-butene. The cis isomer can be encoded in FlexMol as follows:

<!-- cis-2-butane -->
<?xml version="1.0" standalone="yes"?>

<molecule>
  <constitution>
    <atoms>
      <atom id="C0" symbol="C" hydrogens="3" ionization="4"></atom>
      <atom id="C1" symbol="C" hydrogens="1" ionization="4"></atom>
      <atom id="C2" symbol="C" hydrogens="1" ionization="4"></atom>
      <atom id="C3" symbol="C" hydrogens="3" ionization="4"></atom>
    </atoms>
    <bonding>
      <bond source="C0" target="C1" bondingElectrons="2"></bond>
      <bond source="C1" target="C2" bondingElectrons="4"></bond>
      <bond source="C2" target="C3" bondingElectrons="2"></bond>
      <bond source="C3" target="C4" bondingElectrons="2"></bond>
    </bonding>
  </constitution>
  <conformation>
    <conformationWheel>
      <gammaSequence source="C1" target="C2">
        <connections>
          <atomPair source="C1" target="C2"></atomPair>
        </connections>
      </gammaSequence>
      <halfPlane></halfPlane>
      <halfPlane>
        <lower atom="C0"></lower>
        <upper atom="C3"></upper>
      </halfPlane>
    </conformationWheel>
  </conformation>
</molecule>

In contrast to previous FlexMol examples, this representation contains a conformation element, which in turn contains a conformationWeel subelement. The conformationWheel is composed of a gammaSequence and two halfPlanes. The relationship among these elements can be seen in the diagram below.

Stereochemical representation in FlexMol boils down to placing atoms into a set of half-planes intersecting a given axis (Dietz refers to this arrangement as a "pencil of planes"). In the case of cis-2-butene, this axis, or gamma sequence, is the atom pair between atoms C1 and C2. A gamma sequence can consist of two or more atoms, a very useful feature for representing allene stereochemistry, for example. Half planes are specified in clockwise order about this axis. Because half planes always occur in pairs separated by 180 degrees about their common axis, the number of half planes will always be even. Each conformational half plane is further subdivided into two regions labeled appropriately enough "upper" and "lower".

A conformation wheel will always have an equivalent, but opposite representation. For example, cis-2-butene could also be represented with an axis of opposite orientation (C2->C1), opposite ordering of half planes (in this case the same ordering because there are only two half planes), and inverted upper/lower designations. FlexMol only requires that one of these two equivalent arrangements be specified.

In a similar fashion, we can generate a FlexMol representation for trans-2-butene:

<!-- trans-2-butane -->
<?xml version="1.0" standalone="yes"?>

<molecule>
  <constitution>
    <atoms>
      <atom id="C0" symbol="C" hydrogens="3" ionization="4"></atom>
      <atom id="C1" symbol="C" hydrogens="1" ionization="4"></atom>
      <atom id="C2" symbol="C" hydrogens="1" ionization="4"></atom>
      <atom id="C3" symbol="C" hydrogens="3" ionization="4"></atom>
    </atoms>
    <bonding>
      <bond source="C0" target="C1" bondingElectrons="2"></bond>
      <bond source="C1" target="C2" bondingElectrons="4"></bond>
      <bond source="C2" target="C3" bondingElectrons="2"></bond>
      <bond source="C3" target="C4" bondingElectrons="2"></bond>
    </bonding>
  </constitution>
  <conformation>
    <conformationWheel>
      <gammaSequence source="C1" target="C2">
        <connections>
          <atomPair source="C1" target="C2"></atomPair>
        </connections>
      </gammaSequence>
      <halfPlane>
        <upper atom="C3"></upper>
      </halfPlane>
      <halfPlane>
        <lower atom="C0"></lower>
      </halfPlane>
    </conformationWheel>
  </conformation>
</molecule>

This representation contains a conformationWheel with two filled half planes containing the atoms C3 and C0, respectively. The arrangement among the conformational elements can be better seen in the following diagram:

So What?

There are many ways to represent alkene geometrical isomerism, most of which are far simpler than the one outlined here. So what does this additional complexity buy us? In FlexMol, we can use exactly the same formalisms we used for 2-butene isomers to represent the stereochemistries of molecules that simply can not be represented in other systems. Two specific examples include the axial chirality of allenes and biaryls. If you'd like some hints on how to accomplish this, see the allene and binaphthyl FlexMol examples contained in the flexmol directory of the Octet source distribution.

Notice how FlexMol does away with the need to define conformation in terms of sterochemical descriptors, which are quite limited. Instead, FlexMol provides a small set of modular concepts that, when used together, actually describe the underlying conformational features of a molecule. Of course, (E) and (Z) descriptors (and a host of others as well) can be derived from a FlexMol representation given the right software.

Conclusions

We've covered the essentials for conformational representation in FlexMol, and we've seen how to differentiate double bond geometrical isomers. The same principles described here are also used in encoding stereochemical configuration, which will be the subject of a future tutorial.