Lecture 1 Notes: Symmetry Operations
Consider the symmetry properties of an object (e.g. atoms of a molecule, set of
orbitals, vibrations). The collection of objects is commonly referred to as a basis set
classify objects of the basis set into symmetry o
Lecture 6 Notes: Common Approximations
A common approximation employed in the construction of molecular orbitals (MOs)
th
is the linear combination of atomic orbitals (LCAOs). In the LCAO method, the k
molecular orbital, k, is expanded in an atomic orbita
Lecture 5 Notes: Molecule Orientation
The D point groups are distiguished from C point groups by the presence of
rotation axes that are perpindicular to the principal axis of rotation.
Dn: Cnand nC2(h = 2n)
Example: Co(en)3
3+
is in the D3 point group,
Re
Lecture 4 Notes: Molecular Points
The symmetry properties of molecules (i.e. the atoms of a molecule form a basis
set) are described by point groups, since all the symmetry elements in a molecule
will intersect at a common point, which is not shifted by a
Lecture 2 Notes: Inverse Operations
The inverse of A (defined as (A)
1
) is B if A B = E
For each of the five symmetry operations:
(E)
()
(i)
1
1
1
=E
(E)
=
()
=i
(i)
1
1
1
nm
= Cn
2 1
e.g. (C5 )
m 1
= Sn
m 1
= Sn
(Sn )
nm
= = E
i=i i=E
m 1
(Cn )
(Sn )
Lecture 3 Notes: Irreducible Representations
Similarity transformations yield irreducible representations, i, which lead to
the useful tool in group theory the character table. The general strategy for
determining i is as follows: A, B and C are matrix re
Lecture 9 Notes: LCAO Method
The LCAO method for cyclic systems provides a convenient starting point for
the development of the electronic structure of solids.
At very large N, as the circumference of the circle approaches , the cyclic
problem converges t
Lecture 8 Notes: Polynomial Derivation
This lecture will provide a derivation of the LCAO eigenfunctions and eigenvalues of N
total number of orbitals in a cyclic arrangement. The problem is illustrated below:
There are two derivations to this problem.
Po
Lecture 10 Notes: Metal Complexion
Metal complexes are Lewis acid-base adducts formed between metal ions (the acid)
and ligands (the base).
The interaction of the frontier atomic (for single atom ligands) or molecular (for
many atom ligands) orbitals of t
Lecture 7 Notes: Huckel Theory
The energies (eigenvalues) may be determined by using the Hckel approximation.
A1g
1
6
E A
123456
A1g H A1gdA
1g
| H |A
1g
1g
1
1 2 3 4 56
6
H
1
1 2 3 4 5 6
6
1 H11 H12 H13 H14 H15 H16 H21 H22
6
H23 H24 H25 H26
H (