Lecture 2 Notes: Inverse Functions
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 8 Notes: Market Impact
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.
Polynomial
Lecture 3 Notes: Triangular 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 rep
Lecture 1 Notes: Symmetric 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
Lecture 6 Notes: Multiplication Result Theory
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
Lecture 10 Notes: Donor Ligands
Before tackling the business of the complex, the nature of the ligand frontier orbitals
must be considered. There are three general classes of ligands, as defined by their
frontier orbitals: -donor ligands, -donor ligands a
Lecture 9 Notes: Market Fluctuations
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
Lecture 5 Notes: Distinguished Characteristics
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
Lecture 4 Notes: Point Groups
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 any o