Molecular Symmetry and Group Theory: Part 2 Summary

Vocabulary flashcards derived from lecture notes on Molecular Symmetry and Group Theory, focusing on point group classification and symmetry elements.

Point Group

The complete set of symmetry operations exhibited by an isolated molecule that leave at least one common point in the molecule unchanged.

Schönflies Notation

The standard system used by chemists to label point groups, such as $C_{2v}$, $D_{3h}$, and $O_h$.

Group Order ($h$)

The total number of unique symmetry operations within a point group.

Principal Axis ($C_n$)

The highest-order rotation axis in a molecule, used as the first step in identifying point groups.

D (Dihedral) Group

A point group classification used when there are $n$ $C_2$ axes perpendicular to the principal axis.

C (Cyclic) Group

A point group classification used when there are no $C_2$ axes perpendicular to the principal axis.

$$\sigma_h$$

A horizontal mirror plane that is perpendicular to the principal axis of a molecule.

$\sigma_v$ or $\sigma_d$

Mirror planes categorized as vertical or dihedral that contain the principal axis.

$$C_1$$

A non-rotational point group with no symmetry elements; example: $SOFCl$.

$$C_s$$

A non-rotational point group with only a mirror plane ($\sigma$); example: $NOCl$.

$$C_i$$

A non-rotational point group with only an inversion center ($i$).

$$C_{nv}$$

A point group characterized by a $C_n$ axis and $n$ vertical mirror planes; examples include $H_2O$ ($C_{2v}$) and $NH_3$ ($C_{3v}$).

$$C_{nh}$$

A point group characterized by a $C_n$ axis and a horizontal mirror plane; example: 1,5-diazanaphthalene ($C_{2h}$).

$$D_{nh}$$

A point group with a $C_n$ axis, $n$ perpendicular $C_2$ axes, and a horizontal mirror plane; examples include Benzene ($D_{6h}$), $BF_3$ ($D_{3h}$), and $CO_2$ ($D_{\infty h}$).

$$D_{nd}$$

A point group with a $C_n$ axis, $n$ perpendicular $C_2$ axes, and $n$ dihedral mirror planes, but no horizontal mirror plane ($\sigma_h$); example: Staggered Ethane ($D_{3d}$).

Cubic Groups

High-symmetry point groups with multiple high-order axes, including Tetrahedral ($T_d$), Octahedral ($O_h$), and Icosahedral ($I_h$).

$$C_{\infty v}$$

A linear point group with no inversion center where the ends of the molecule are different; examples include $HCl$ and $HCN$.

$$D_{\infty h}$$

A linear point group with an inversion center and identical ends, featuring an infinite number of perpendicular $C_2$ axes; examples include $CO_2$ and $N_2$.

Ammonia Inversion

A dynamic process where $NH_3$ flips through its planar transition state, causing its symmetry to increase from $C_{3v}$ to $D_{3h}$.

Descent in Symmetry

The reduction of a point group and group order ($h$) that occurs when atoms are replaced, such as the conversion of $PF_5$ ($D_{3h}$) to $PF_4Cl$ ($C_{2v}$).