Derivatives of methane can be obtained by replacing one or...

Derivatives of methane can be obtained by replacing one or more hydrogen atoms with other atoms, such as F, Cl, or Br. Suppose you had a supply of methane and the necessary chemicals and equipment to make derivatives of methane containing all possible combinations of the elements $\mathrm{H}, \mathrm{F}, \mathrm{Cl}$, and $\mathrm{Br}$. What would be the point groups of the molecules you could make? You should find 35 possible molecules, but they can be arranged into five sets for assignment of point groups.

Key Concepts

C_1

The C? point group is defined by having no symmetry elements aside from the identity operation. In the context of methane derivatives, this occurs when all four substituents are different (or the arrangement of substituents does not allow any symmetry element) leading to completely asymmetric (chiral) molecules. These molecules have no rotational axis, mirror plane, or inversion center.

T_d

The T?d? (tetrahedral) point group is the symmetry group of a perfect tetrahedron. In the context of methane derivatives, this occurs when all four substituents are identical. Molecules in this group have four three?fold axes (C?) and three two?fold axes (C?), along with several mirror planes and improper rotations. Methane (CH?) is the classic example of a T?d? symmetric molecule.

C_{3v}

The C?3v? point group is typical for molecules that have a threefold rotation axis (C?) and three vertical mirror planes. In methane derivatives, this symmetry arises when three of the substituents are identical and the fourth is different (for example, CH?X). The threefold axis retains the symmetry from the three identical groups, while the mirror planes include the unique substituent.

C_{2v}

The C?v point group is characterized by a twofold rotation axis (C?) together with two mutually perpendicular mirror planes that contain this axis. This symmetry is encountered in tetrahedral molecules when there are two sets of identical substituents arranged in a symmetrical fashion (for example, in a molecule with two of one substituent and two of another that are arranged opposite to one another). The presence of the C? axis and mirror planes reduces the symmetry compared to T?d? or C?3v?.

C_s

The C? point group is the simplest case of symmetry beyond no symmetry at all, having only one mirror plane (?). For methane derivatives, C? symmetry appears when the arrangement of substituents permits only a single plane of reflection, with no proper rotation axes other than the identity. Molecules in this group are unsymmetrical in other respects but are not chiral due to that single mirror plane.

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