a ketone. Another example is the pair ethanol H3C–CH2–OH (an alcohol) and dimethyl ether H3C–O–CH2H (an ether). In contrast, 1-propanol and 2-propanol are structural isomers, but not functional isomers, since they have the same significant functional group (the hydroxyl –OH) and are both alcohols. Besides the different chemistry, functional isomers typically have very different infrared spectra. The infrared spectrum is largely determined by the vibration modes of the molecule, and functional groups like hydroxyl and esters have very different vibration modes. Thus 1-propanol and 2-propanol have relatively similar infrared spectra because of the hydroxyl group, which are fairly different from that of methyl ethyl ether. Structural isotopomers In chemistry, one usually ignores distinctions between isotopes of the same element. However, in some situations (for instance in Raman, NMR, or microwave spectroscopy) one may treat different isotopes of the same element as different elements. In the second case, two molecules with the same number of atoms of each isotope but distinct bonding schemes are said to be structural isotopomers. Thus, for example, ethene would have no structural isomers under the first interpretation; but replacing two of the hydrogen atoms (1H) by deuterium atoms (2H) may yield any of two structural isotopomers (1,1-dideuteroethene and 1,2-dideuteroethene), if both carbon atoms are the same isotope. If, in addition, the two carbons are different isotopes (say, 12C and 13C), there would be three distinct structural isotopomers, since 1-13C-1,1-dideuteroethene would be different from 1-13C-2,2-dideuteroethene.) And, in both cases, the 1,2-dideutero structural isotopomer would occur as two stereo isotopoomers, cis and trans. Structural equivalence and symmetry Structural equivalence Two molecules (including polyatomic ions) A and B have the same structure if each atom of A can be paired with an atom of B of the same element, in a one-to-one way, so that for every bond in A there is a bond in B, of the same type, between corresponding atoms; and vice versa. This requirement applies also complex bonds that involve three or more atoms, such as the delocalized bonding in the benzene molecule and other aromatic compounds. Depending on the context, one may require that each atom be paired with an atom of the same isotope, not just of the same element. Two molecules then can be said to be structural isomers (or, if isotopes matter, structural isotopomers) if they have the same molecular formula but do not have the same structure. Structural symmetry and