Introduction

A-Values are numerical values used in the determination of the most stable orientation of atoms in a molecule (Conformational Analysis), as well as a general representation of steric bulk. A-values are derived from energy measurements of a monosubstituted cyclohexane ring. ^[1] Substituents on a cyclohexane ring prefer to reside in the equatorial position to the axial. The difference in free energy (ΔG) between the higher energy conformation (axial substitution) and the lower energy conformation (equatorial substitution) is the A-value for that particular substituent.

Utility

A-values help predict the conformation of cyclohexane rings. The most stable conformation will be the one which has the substituent or substituents equatorial. When multiple substituents are taken into consideration, the conformation where the substituent with the largest A-value is equatorial is favored.

The utility of A-values can be generalized for use outside of cyclohexane conformations. A-values can help predict the steric effect of a substituent. In general, the larger a substituent’s A-value, the larger the steric effect of that substituent. Methyl has an A-value of 1.74 while tert-butyl has an A-value of ~5. Because the A-value of tert-butyl is higher, tert-butyl has a larger steric effect than methyl. This difference in steric effects can be used to help predict reactivity in chemical reactions.

Other Considerations

It is important to note that A-values do not predict the physical size of a molecule, only the steric effect. For example, the t-butyl group (A-value 4.9) has a larger A-value than the trimethylsilyl group (A-value 2.5), yet the t-butyl group actually occupies less space. This difference can be attributed to the longer length of the carbon-silica bond as compared to the carbon-carbon bond of the t-butyl group. The longer bond allows for less interactions with neighboring substituents, which effectively makes the trimethylsilyl group less sterically hindering, thus, lowering it’s A-value.^[2] This can also be seen when comparing the halogens. Bromine, iodine, and chlorine all have similar A-values even though their atomic radii differ.^[3] A-values then, predict the apparent size of a molecule, and the relative apparent sizes determine the differences in steric effects between compounds. Thus, A-values are useful tools in determining compound reactivity in chemical reactions.

References

^ Muller, P (1994). "Glossary of terms used in physical organic chemistry (IUPAC Recommendations 1994)". PAC. 66: 1077–1184. doi:10.1351/pac199466051077.
^ Hoffman, Robert V. (2004). Organic Chemistry (second ed.). New Jersey: John Wiley and Sons, Inc. p. 167. {{cite book}}: Unknown parameter |trans_title= ignored (|trans-title= suggested) (help)
^ Anslyn, Eric V.; Dougherty, Dennis A. (2006). Modern Physical Organic Chemistry. Sausalito, CA: University Science Books. pp. 104–105.

[PACGlossary-1] Muller, P (1994). "Glossary of terms used in physical organic chemistry (IUPAC Recommendations 1994)". PAC. 66: 1077–1184. doi:10.1351/pac199466051077.

[Hoffmanbook-2] Hoffman, Robert V. (2004). Organic Chemistry (second ed.). New Jersey: John Wiley and Sons, Inc. p. 167. {{cite book}}: Unknown parameter |trans_title= ignored (|trans-title= suggested) (help)

[AnslynDougherty-3] Anslyn, Eric V.; Dougherty, Dennis A. (2006). Modern Physical Organic Chemistry. Sausalito, CA: University Science Books. pp. 104–105.

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