Lecture 15
Molecular Orbitals for Diatomic Molecules
, Solution will involve molecular orbitals - similar to atomic orbitals -
but centred around all of the nuclei in molecule. Each defined by sets of
quantum numbers, with electron probability density determined by 2,
where = molecular wave function.
Approximate method:
At any moment, electron near one nucleus - approximate behaviour like
electron in atomic orbital for that atom. Over time - electron associated with
other nuclei in molecule. Therefore construct molecular orbitals (m.o.'s) by
forming:
Linear Combination of Atomic
Orbitals
, It is this, LCAO , m ethod w hich w e w ill use to construct
m .o's.
Simplest example - H2: two H atoms HA and HB
Only two a.o.'s (1sA, 1sB) to form linear combinations.
General rule: n a.o.'s n m.o.'s
So we can only construct 2 m.o.'s for H2 - and these are:
b = 1sA + 1sB and a = 1sA - 1sB
i.e. the sum (b) and the difference (a) of the constituent
a.o.'s.
Consider the electron distribution in each of these:
Molecular Orbitals for Diatomic Molecules
, Solution will involve molecular orbitals - similar to atomic orbitals -
but centred around all of the nuclei in molecule. Each defined by sets of
quantum numbers, with electron probability density determined by 2,
where = molecular wave function.
Approximate method:
At any moment, electron near one nucleus - approximate behaviour like
electron in atomic orbital for that atom. Over time - electron associated with
other nuclei in molecule. Therefore construct molecular orbitals (m.o.'s) by
forming:
Linear Combination of Atomic
Orbitals
, It is this, LCAO , m ethod w hich w e w ill use to construct
m .o's.
Simplest example - H2: two H atoms HA and HB
Only two a.o.'s (1sA, 1sB) to form linear combinations.
General rule: n a.o.'s n m.o.'s
So we can only construct 2 m.o.'s for H2 - and these are:
b = 1sA + 1sB and a = 1sA - 1sB
i.e. the sum (b) and the difference (a) of the constituent
a.o.'s.
Consider the electron distribution in each of these:
