Chirality (chemistry)

Chirality means that a molecule cannot be superposed on its mirror image. A carbon attached to four different groups is a common source of chirality; the definition concerns the whole molecule, rather than requiring this particular structural feature.

The test is spatial: apply a translation and a rotation to the entire molecule until corresponding chemical atoms coincide, keeping their identities and chemical bonds. A mirror operation is a reflection; physically turning a model is a rotation. They are different operations. If no such superposition exists, the two forms are enantiomers; if one succeeds, the molecule is achiral. A different-looking flat drawing alone establishes neither conclusion.

For a simple molecule with exactly one tetrahedral stereocenter and four constitutionally different substituents, the mirror forms cannot superpose. Compare entire attached groups, including paths around a ring, rather than just the first chemical atom. Several tetrahedral stereocenters require a whole-molecule check: a meso compound can be achiral. Conversely, axial chirality needs no tetrahedral stereocenter.^[ref]

Why care about this distinction? Two enantiomers can fit differently into an already chiral molecule, just as two opposite hands fit differently into one glove. Thus a protein's spatial arrangement can distinguish a mirror pair even when an achiral measurement cannot. Polarimetry provides a different kind of test: it measures a sample's net optical rotation, which depends on the populations of its enantiomers.

Enantiomers are a pair of nonsuperposable mirror-image molecules. The D and L configurations of alanine are an example; glycine has no such pair because its amino acid alpha carbon carries two identical hydrogen chemical atoms. ^[ref]

The word names a relation between two stereoisomers. Merely finding two different spatial arrangements does not make them enantiomers: arrangements that are different but not mirror partners are diastereomers.

A racemate contains the same amount of substance of each member of an enantiomer pair. Their equal and opposite contributions cancel in ordinary solution polarimetry under identical conditions. Zero net optical rotation therefore does not establish achirality of the individual molecules.^[ref]

A chiral molecule fails the whole-molecule mirror-superposition test defining chirality.

Achirality means that a molecule is superposable on its mirror image. A reflection plane that leaves the complete labelled spatial structure unchanged establishes achirality. Absence of such a plane alone is not a complete test: other orientation-reversing spatial symmetries can also make a rigid structure achiral.

Take a central chemical atom at the origin and four substituents at the vertices of an ideal regular tetrahedron:These dimensionless coordinates describe shape, not measured bond lengths. For distinct labels A, B, C and D, define a signed determinantIt is six times the oriented volume of the labelled tetrahedron. A translation cancels from the differences. A rotation $Q$ has $\det Q=+1$ and preserves $\Delta$, whereas the mirror matrix $S=\mathrm{diag}(-1,1,1)$ has $\det S=-1$ and changes it to $-16$. Consequently no rotation can place every distinct label on its mirror partner. This argument uses three-dimensional coordinates, not clockwise order on a page.

Now let C and D both be the same substituent H. Swapping these identical groups is allowed. For this model the half-turnabout the axis $(0,1,1)$ maps the reflected A and B to their original positions and exchanges the two H positions. The models superpose. With distinct C and D, the same half-turn fails precisely at those two labels; the determinant argument rules out every other rotation as well. This is the local reason two identical hydrogen chemical atoms prevent glycine's amino acid alpha carbon from being a tetrahedral stereocenter.

For a flexible molecule, also distinguish conformational isomerism from a persistent enantiomer pair. A particular frozen shape may be chiral while ordinary internal motions interconvert mirror shapes. Turning the entire model is always allowed in a spatial comparison; an internal motion must be considered with its actual accessibility and timescale.

A meso compound is an achiral molecule despite having stereocenters. Tartaric acid, $\mathrm{HOOC}-\mathrm{CH}(\mathrm{OH})-\mathrm{CH}(\mathrm{OH})-\mathrm{COOH}$, has two tetrahedral carbon stereocenters. Its $(2R,3R)$ and $(2S,3S)$ forms are enantiomers, but $(2R,3S)$ and $(2S,3R)$ name the same meso form after equivalent ends are identified. A symmetric spatial arrangement has a mirror plane exchanging its two halves. Thus there are three stereoisomers, not four.^[ref]

Opposite R and S configurations alone do not guarantee a meso compound: the rest of the molecule must permit mirror superposition. Likewise, a meso compound is one achiral chemical compound, whereas a racemate is a mixture of two chiral molecule populations. Both can give zero optical rotation for different reasons.

An allene has a $\mathrm{C}=\mathrm{C}=\mathrm{C}$ unit whose terminal substituents lie in perpendicular planes. In $\mathrm{abC}=\mathrm{C}=\mathrm{Ccd}$, with $a\ne b$ and $c\ne d$, the two terminal pairs can define enantiomers without any tetrahedral carbon stereocenter. The groups need be different within each end pair, not all four mutually different. This is axial chirality.^[ref]

chirality produced by distinguishable terminal substituents arranged about the constrained axis of a spiro framework.

Axial stereoisomerism in suitably substituted alkylidenecyclohexanes, where the constrained ring and alkene distinguish two handed arrangements.

Stereoisomerism arising from restricted rotation about a bond. A hindered biaryl can make otherwise similar methylene hydrogens diastereotopic on the NMR timescale.

Optical activity is the ability to rotate the direction of linear polarization of transmitted light. In an achiral solvent, the two members of an enantiomer pair have equal and opposite optical rotations at the same wavelength, temperature and concentration. The measured angle concerns a bulk sample; it is not a geometric rotation of the molecules.^[ref]

The rotating object in this description is the direction along which the electric field oscillates. At each position the transmitted light can still have linear polarization: its electric field moves back and forth along a line, while the orientation of that line changes along the sample. Nothing requires the molecules to turn bodily through the observed angle. This makes polarimetry a bridge from molecular chirality to a visible bulk measurement, and, with a suitable calibration, a way to follow concentration or the balance of enantiomers.

In a transparent, isotropic chemical solution, natural optical rotation can be understood as circular birefringence: the two opposite circular polarizations accumulate different wave phases, and their equal-amplitude sum remains linearly polarized along a rotated direction. Circular dichroism instead means unequal absorption of those components and can produce elliptical polarization. These are related responses, not interchangeable measurements. General birefringence need not produce this simple rotation of linear polarization.^[ref]

Optical rotation is the signed angle measured in polarimetry. Positive rotation is clockwise for an observer facing the incoming light; negative rotation is counterclockwise. State the viewing convention, wavelength, temperature, solvent, concentration and path length when comparing measurements. R and S configuration specifies spatial arrangement, and does not predict the sign of optical rotation.^[ref]

Here the observer stands beyond the sample, on the detector side, looking back toward the source. Measure both the polarimeter analyzer angle $\theta$ and the optical rotation $\alpha$ clockwise from the blank's polarization direction. Looking from the source end reverses the apparent sense. A line has no distinguished arrowhead, so an intensity scan alone determines its orientation only modulo $180^{\circ }$; continuity or additional information must choose the appropriate rotation branch.

For a chemical solution in a validated linear regime,where $l$ is path length in $\mathrm{dm}$ and $c$ is solute mass per final solution volume in $\mathrm{g}\mathrm{m}{\mathrm{L}}^{-1}$. These conventions give specific rotation units $\mathrm{deg}\mathrm{mL}{\mathrm{g}}^{-1}\mathrm{d}{\mathrm{m}}^{-1}$. Specify solvent, temperature $T$ and wavelength $\lambda$: specific rotation is conditional on the sample environment.^[ref]

For an original model, stipulate an unnamed enantiomer pair in the same achiral solvent at $T=20^{\circ }\mathrm{C}$ and wavelength $\lambda =589\mathrm{nm}$. Assign the positive member specific rotation $+40\mathrm{deg}\mathrm{mL}{\mathrm{g}}^{-1}\mathrm{d}{\mathrm{m}}^{-1}$, assumed constant over the modeled concentrations. With $l=1\mathrm{dm}$ and $c=0.200\mathrm{g}\mathrm{m}{\mathrm{L}}^{-1}$,These are chosen model parameters, not measured properties of a named material. Doubling only $l$ or only $c$ doubles $\alpha$ within this stipulated linear model; doubling both multiplies it by four. A real chemical solution must be checked for concentration dependence rather than assuming that $0.200\mathrm{g}\mathrm{m}{\mathrm{L}}^{-1}$ is dilute enough.

For an additive mixture containing only this enantiomer pair as solutes, put $k=[\alpha {]}_{+}$ and write $c_{+},c_{-}$ for their mass concentrations. ThenBecause enantiomers have the same molar mass, their relative mole fractions within the pair also equal their relative mass fractions: $c_{+}=x_{+}c$, $c_{-}=x_{-}c$. Thus $\alpha =klc(x_{+}-x_{-})$, which connects optical rotation to enantiomeric excess.

The enantiomeric excess of an enantiomer pair is the magnitude of the difference between their relative mole fractions, $\mathrm{ee}=|x_{+}-x_{-}|$, often reported as a percentage. Here $x_{+}+x_{-}=1$ counts the pair only, excluding solvent; the signs label optical rotation under the specified conditions, not R and S configuration.

In the model above, $x_{+}=0.75$ and $x_{-}=0.25$ give $\mathrm{ee}=0.50=50\%$. Keep the same total pair concentration $c=0.200\mathrm{g}\mathrm{m}{\mathrm{L}}^{-1}$, path length, solvent, temperature and wavelength. The two contributions areThe $+8^{\circ }$ pure-member reference therefore gives $\alpha /{\alpha }_{\mathrm{pure},+}=+0.50$. This ratio measures signed population imbalance only for a pure pair with additive linear responses under matching conditions. Adding unrelated solutes, changing total concentration, or changing chemical equilibrium can invalidate that inference. For $x_{+}=x_{-}=0.50$, the racemate gives zero net optical rotation by cancellation; each molecule remains chiral. A zero reading alone proves neither a racemate nor molecular achirality.

Polarimetry measures optical rotation with a polarimeter. The vertical Vernier Go Direct instrument uses a $589\mathrm{nm}$ light-emitting diode source, fixed polarizer, sample cell, motor-driven polarimeter analyzer, photodetector and optical rotary encoder. Calibrate using the same solvent at $10\mathrm{cm}$ fill height; rinse with sample, fill to $10.0\mathrm{cm}$, and read the meniscus to $0.1\mathrm{cm}$. The readout plots illumination against analyzer angle; a maximum near zero or a cosine-squared fit locates $\alpha$.^[ref]

An actual teaching experiment in the Truman State University-hosted Optical Activity Laboratory handout, revised July 2013, uses sucrose chemical solutions. Weigh the sucrose, dissolve completely without heating, and measure final solution volume for concentration. Use one polarimeter throughout; measure the water blank's extinction reading, then each sample's extinction reading and actual liquid path length near $10\mathrm{cm}$. Subtract the blank and plot corrected optical rotation against concentration. The attached apparatus description specifies a vertical light path, an incandescent or tungsten source with yellow filter, sheet polarizers and a rotating eyepiece polarimeter analyzer. Its coarse demonstration permits temperature control to the nearest $5^{\circ }\mathrm{C}$, path length to the nearest millimeter and approximately $1^{\circ }$ angular precision. These are design tolerances, not measured results.^[ref]

For a quantitative comparison, equilibrate blank, reference and sample at the same recorded temperature; use a thermostatted cell when needed. This is a recommended control, not a claim that the teaching instruments provide a thermostat. A yellow filter also passes a band of wavelengths, so its result need not match a narrow-source reference exactly. The laboratory's concentration series tests the linear model rather than establishing it in advance; a second series varying only path length tests the other factor.

For our original ideal model, Malus's law giveswhere $I_0$ is light intensity immediately before the ideal polarimeter analyzer, after sample transmission. It is not the intensity of the original unpolarized source. The angle difference is evaluated in consistent units; the plotted degree values are converted to radians before computing the cosine. Assume transmitted light retains linear polarization, with negligible scattering and no polarization-dependent absorption. The pure positive model, $75:25$ mixture and racemate shift the maxima to $8^{\circ }$, $4^{\circ }$ and $0^{\circ }$, respectively. Minima shift by the same amount, to $98^{\circ }$, $94^{\circ }$ and $90^{\circ }$. Thus an extinction measurement and a maximum measurement recover the same shift after their respective blanks are subtracted.

Repeat blanks and use a reference to check drift and scale. Bubbles, particles, stressed windows and sample absorption can spoil the ideal curve. Vernier specifies $\pm 1^{\circ }$ accuracy; the manual's $\pm 0.1^{\circ }$ fit reproducibility does not establish that accuracy. It warns against interpreting its illumination readout quantitatively and requires a transparent homogeneous sample.^[ref] Neither a zero reading nor a matching specific rotation uniquely identifies a molecule.

A polarimeter uses polarizers to compare the direction of linear polarization before and after light passes through a sample; polarimetry explains the apparatus, readout and controls.

An angular polarimeter associated with Jean-Baptiste Biot, measuring the rotation produced by a sugar solution of known optical path length. The original form used a black-glass polarizing mirror and a calcite analyser; it should not be conflated with a later quartz-wedge compensating instrument.^[ref]

A polarimeter analyzer is the rotatable final polarizer. Comparing its transmission maximum or extinction minimum with the corresponding blank reading measures the sample's optical rotation.

Circular dichroism is unequal absorption of opposite circular polarizations. It can produce elliptical polarization; it is the absorptive response related to optical rotation, rather than the same measured quantity.