Inorganic Chemistry

• Cₙ Rotation: n-fold rotation
• σ Reflection
  • σₕ Horizontal Reflection: reflection with respect to the plane perpendicular to the principal axis.
  • σᵥ Vertical Reflection: reflection with respect to the plane parallel to the principal axis.
• i Inversion
• S₂ₙ Improper Rotation: Rotation about an axis and reflection along the axis.
  • From German Spiegel 'mirror'

• \( C_1 \) Only identity
• \( C_i \) Identity and inversion
• \( C_s \) Identity and improper rotation
• \( C_{\infty v} \) Linear along an axis and vertical reflections
• \( D_{\infty h} \) Linear along an axis and horizontal reflections
• \( C_{n} \) (Cyclic) Only rotations along a single axis are possible
• \( C_{nv} \) (Pyramidal) Rotations and vertical reflections
• \( C_{nh} \) (Reflection) Rotations and horizontal reflection
• \( D_n \) (Dihedral) Rotations and 2n C₂ rotations perpendicular to principal axis.
• \( D_{nh} \) (Prismatic) Dihedral and horizontal reflection
• \( D_{nd} \) (Antiprismatic) Dihedral and dihedral (vertical) reflections
• \( S_n \) Dihedral and improper rotations
• \( T, T_h, T_d \) (Tetrahedral)
• \( O, O_h \) (Octahedral)
• \( I, I_h \) (Icosahedral)

• n Rotation: n-fold rotation
• m Reflection
  • n/m the mirror plane is perpendicular to the n-fold rotation axis,
• n̄ Rotoinversion: rotation by 2π/n and inversion
  • \(\bar{1}\) is the pure inversion

The symmetries in primary, secondary, tertiary directions are listed in order. The secondary directions are the all equivalent directions perpendicular to the primary direction, and tertiary directions are all equivalent directions between secondary directions. Note that the tertiary directions only occur when the rotational symmetry around the primary direction is even.

When the rotational symmetry is more than 10-fold, paranthesis is used to make it clear that it is not rotational symmetries along two directions.

Translation from Schönflies notation

• \( n \): \( C_n \)
• \( nm, nmm \): \( C_{nv} \). one \( m \) if \( n \) is odd, two \( m \) if \( n \) is even.
• \( \tfrac{n}{m} \): \( C_{nh} \)
• \( n2, n22 \): \( D_n \)
• \( \bar{n}\tfrac{2}{m} \): \( D_{nd} \)
• \( \tfrac{n}{m}\tfrac{2}{m}\tfrac{2}{m} \): \( D_{nh} \)

Chemical Formula

1. For ionic compound, write cation first
2. Write central (metal) atom first
3. Write anionic ligands in alphabetical order (of the name, not formula)
4. Write neutral ligands in alphabetical order
5. Surround with square bracket and add ionic charge to that

e.g. \(\ce{[CoCl2(NH3)4]+}\)

Nomenclature

1. Read cation first
2. Read ligand first and then metal
3. Read ligands in alphabetical order
4. The suffix of metal changes to -ate when the overall charge is negative.
5. Add oxidation state of the metal at the end

e.g.

Some of metals have special name for its anion form:

• Fe: ferrrate
• Ag: argentate
• Sb: Stibate
• Pb: plumbate
• Sn: stannate
• Au: aurate

Transition metal does not have predetermined oxidation number, so notating it is important.

We use abbreviation for complicated ligands

• Halogen often ends in -o.

Formula	Abbreviation	Structure
I	iodo
Br	bromo
\(\ce{N^3-}\)	nitrido
\(\ce{N3-}\)	axido
\(\ce{O^2-\)	oxido
\(\ce{H2O}\)	aqua
\(\ce{SCN-}\)	thiocyano, thiocyanato (bind to N)
\(\ce{NCS-}\)	isocyano (bind to S)

Stereoisomers Stereochemical description can be done with prefixes:

• trans- and cis-
• fac- (facial) and mer- (meridional)

They are diastereomers.

Structural Isomers (or Constitutional Isomers) The covalently bonded atoms can be swapped with the ionically bonded atoms, or other covalently bonded atoms in another complex.

• Hydrate: Hydrate (H2O)-ion swap
• Ionization: Anion-cation swap
• Coordination: Ligand-ligand swap in multi-complex
• Linkage: Ligand orientation difference for bidentate or more

Absolute Configuration