Glossary

A Axis of Symmetry: Any molecule is said to have n-fold axis of symmetry, Cn, if the rotation of the molecule about that axis by 3600/n produces an orientation which is indistinguishable from the initial one. The general symbol of the proper axis of rotation is Cn where the subscript n denotes the order of axis

I Improper Axes of Symmetry: If the rotation of a molecule about an axis through an axis by 3600/n followed by reflection through a plane perpendicular to the axis produces an orientation which is indistinguishable from the initial one ,it is called improper rotation symmetry and the axis is called n-fold axis of improper rotation(Sn). Inversion Operation: If the reflection of all the atoms of a molecule through a point within the molecule produces an orientation which is indistinguishable from the initial one, it is

called inversion operation and that point is called centre of symmetry. M Metal Carbonyl: Metal carbonyls are coordination complexes of transition metals with carbon monoxide ligands. Metal carbonyls are useful in organic synthesis and as catalysts or catalyst precursors in homogeneous catalysis, such as hydroformylation and Reppe chemistry. In the Mond process, nickel carbonyl is used to produce pure nickel. In organometallic chemistry, metal carbonyls serve as precursors for the preparation of other organometalic complexes

P Plane of Symmetry: Reflection symmetry, line symmetry, mirror symmetry, mirror-image symmetry, or bilateral symmetry is symmetry with respect to reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry. The plane of symmetry may be regarded as the hypothetical plane passing through a molecule which bisects the molecule into two equal halves which are just mirror-images of each other. The standard symbol for the plane of symmetry is σ. The same symbol is also used for the reflection operation. There are three types of plane of symmetry:

i) Vertical plane of symmetry (σv): The plane of symmetry which is parallel to the principal axis or which contains the principal axis is called vertical plane of symmetry.

ii) Horizontal plane of symmetry (σh): The plane of symmetry which is perpendicular to the principal axis of symmetry is called horizontal plane of symmetry.

iii) Dihedral plane of symmetry (σd): The plane of symmetry which bisects the angle between two C2 axes of symmetry is called the dihedral plane of symmetry.

S

Symmetry Operation: In the context of molecular symmetry, a symmetry operation is a permutation of atoms such that the molecule or crystal is transformed into a state indistinguishable from the starting state. Two basic facts follow from this definition, which emphasize its usefulness.

1. Physical properties must be invariant with respect to symmetry operations. 2. Symmetry operations can be collected together in groups which are isomorphous to permutation groups.

SymmetryElement: A symmetry element is a point of reference about which symmetry operations can take place. In particular, symmetry elements can be centers of inversion, axes of rotation and mirror planes.

Do You Know?

Beautiful Examples of Symmetry In Nature:

Sun-Moon Symmetry: while the sun’s width is about four hundred times larger than that of the moon, the sun is also about four hundred times further away. The symmetry in this ratio makes the sun and the moon appear almost the same size when seen from Earth, and therefore makes it possible for the moon to block the sun when the two are aligned

Milky Way Glaxy: Having recently discovered a new section on the edges of the Milky Way Galaxy, astronomers now believe that the galaxy is a near-perfect mirror image of itself. Based on this new information, scientists are more confident in their theory that the galaxy has only two major arms: the Perseus and the Scutum- Centaurus. In addition to having mirror symmetry, the Milky Way has another incredible design—similar to nautilus shells and sunflowers—whereby each “arm” of the galaxy represents a logarithmic spiral beginning at the center of the galaxy and expanding outwards

Spider Webs: There are around 5,000 types of orb web spiders, and all create nearly perfect circular webs with almost equidistant radial supports coming out of the middle and a spiral woven to catch prey.

Animals:

Most animals have bilateral symmetry—which means that they can be split into two matching halves, if they are evenly divided down a center line. Even humans possess bilateral symmetry, and some scientists believe that a person’s symmetry is the most important factor in whether we find them physically beautiful or not. In other words, if you have a lopsided face, you’d better hope you have a lot of other redeeming qualities

Sunflowers Sunflowers boast radial symmetry and an interesting type of numerical symmetry known as the Fibonacci sequence. The Fibonacci sequence is 1, 2, 3, 5, 8, 13, 21, 24, 55, 89, 144, and so on (each number is determined by adding the two preceding numbers together). If we took the time to count the number of seed spirals in a sunflower, we’d find that the amount of spirals adds up to a Fibonacci number. In fact, a great many plants (including romanesco broccoli) produce petals, leaves, and seeds in the Fibonacci sequence,which is why it’s so hard to find a four-leaf clover.

Time line:

Year Description Image

1929 Hans Bethe used characters of point group operations in his study of ligand field theory in 1929,

1933 Eugene Wigner used group theory to explain the selection rules of atomic spectroscopy.

1934 Robert Mulliken was the first to publish character tables in English (1933), and E. Bright Wilson used them in 1934 to predict the symmetry of vibrational normal modes

Weblinks :

1. https://www.staff.ncl.ac.uk/j.p.goss/symmetry/Molecules_pov.html

2. www.mathsisfun.com/geometry/symmetry-artist.html

3. www.ics.uci.edu/~eppstein/junkyard/sym.html

4. www.wileyindia.com

5. pubs.acs.org/doi/abs/10.1021/ic50015a049

Suggestive Reading:

Elschenbroich, C. (2006). Organometallics. Weinheim: Wiley-VCH. ISBN 3-527-29390-6.

Symmetry And Group Theory For Chemist (English) 01 Edition

A Simple Approach to Group Theory in Chemistry by swarnalakshmi, T Saroja, R M Ezhilarasi

Chemical Applications of Group Theory : F. Albert Cotton