text: The chirality of a molecule is based on the molecular symmetry of its conformations. A conformation of a molecule is chiral if and only if it belongs to the C, D, T, O, I point groups (the chiral point groups). However, whether the molecule itself is considered to be chiral depends on whether its chiral conformations are persistent isomers that could be isolated as separated enantiomers, at least in principle, or the enantiomeric conformers rapidly interconvert at a given temperature and timescale through low-energy conformational changes (rendering the molecule achiral). For example, despite having chiral gauche conformers that belong to the C point group, butane is considered achiral at room temperature because rotation about the central C–C bond rapidly interconverts the enantiomers (3.4 kcal/mol barrier). Similarly, cis-1,2-dichlorocyclohexane consists of chair conformers that are nonidentical mirror images, but the two can interconvert via the cyclohexane chair flip (~10 kcal/mol barrier). As another example, amines with three distinct substituents (RRRN:) are also regarded as achiral molecules because their enantiomeric pyramidal conformers rapidly invert and interconvert through a planar transition state (~6 kcal/mol barrier).
  However, if the temperature in question is low enough, the process that interconverts the enantiomeric chiral conformations becomes slow compared to a given timescale.  The molecule would then be considered to be chiral at that temperature. The relevant timescale is, to some degree, arbitrarily defined: 1000 seconds is sometimes employed, as this is regarded as the lower limit for the amount of time required for chemical or chromatographic separation of enantiomers in a practical sense.  Molecules that are chiral at room temperature due to restricted rotation about a single bond (barrier to rotation ≥ ca. 23 kcal/mol) are said to exhibit atropisomerism.
  A chiral compound can contain no improper axis of rotation (S), which includes planes of symmetry and inversion center. Chiral molecules are always dissymmetric (lacking S) but not always asymmetric (lacking all symmetry elements except the trivial identity). Asymmetric molecules are always chiral.
  The following table shows some examples of chiral and achiral molecules, with the Schoenflies notation of the point group of the molecule. In the achiral molecules, X and Y (with no subscript) represent achiral groups, whereas X and X or Y and Y represent enantiomers. Note that there is no meaning to the orientation of an S axis, which is just an inversion. Any orientation will do, so long as it passes through the center of inversion. Also note that higher symmetries of chiral and achiral molecules also exist, and symmetries that do not include those in the table, such as the chiral C or the achiral S.
  An example of a molecule that does not have a mirror plane or an inversion and yet would be considered achiral is 1,1-difluoro-2,2-dichlorocyclohexane (or 1,1-difluoro-3,3-dichlorocyclohexane). This may exist in many conformers (conformational isomers), but none of them has a mirror plane. In order to have a mirror plane, the cyclohexane ring would have to be flat, widening the bond angles and giving the conformation a very high energy. This compound would not be considered chiral because the chiral conformers interconvert easily.
  An achiral molecule having chiral conformations could theoretically form a mixture of right-handed and left-handed crystals, as often happens with racemic mixtures of chiral molecules (see Chiral resolution#Spontaneous resolution and related specialized techniques), or as when achiral liquid silicon dioxide is cooled to the point of becoming chiral quartz.