1. Chemical Bonding
Hydrogen atom based atomic orbitals a.k.a. hydrogen atom
wavefunctions: 1s, 2s, 2p, 3s, 3p, 3d, …….
1s = 1/()1/2(1/a0)3/2 exp[-r/a0], a0=Bohr Radius = Angstroms
Electron z 
(x,y,z) r y
Nucleus 
r2=x2+y2+z2 x

2. Orbitals, Wavefunctions and Probabilities
The orbital or wavefunction is just a mathematical function
that can have a magnitude and sign (e.g or -0.2) at a
given point r in space.
Probability of finding a 1s electron at a particular point in
space is often not as interesting as finding the electron
in a thin shell between r and r+dr.

3. Orbitals, Wavefunctions and Probabilities
Probability of finding a 1s electron in thin shell
between r and r+dr:
Prob(r,r+dr) ~ 1s 1s [r2]dr
Volume of shell of thickness dr: r 
dV = (4/3) [(r)3+3r2dr+ 3r(dr)2+(dr)3 - r3]
r+dr
dV≈(4)[r2dr]
[r>>>dr  3r2dr>>> 3r(dr)2+(dr)3 ]

4.   Bonding in Diatomic Molecules such as H2 Bonding Axis z1 z2   r1y1 y2   x1 x2
H Nucleus A
H Nucleus B
1s(A) = 1/()1/2(1/a0)3/2 exp[-r1/a0], 1s orbital for atom A
Note the two orbitals are centered at different points in space.

5. 1s = C1[1s(A) + 1s(B)], Sigma 1s Bonding Molecular
orbital. C1 is a constant.
Note that probabilities for finding electron at some position in
space scale like [1s]2 and [1s*]2:
[1s*]2 = {C2[1s(A) - 1s(B)]}2 =
(C2)2{[1s(A)]2 + [1s(B)]2 - 2[1s(A)][1s(B)]}
“Non-interacting” part is result for large
separation between nucleus A and B
[1s]2 = {C1[1s(A) + 1s(B)]}2 =
(C1)2{[1s(A)]2 + [1s(B)]2 + 2[1s(A)][1s(B)]}

6. Notational Detail Oxtoby uses two different notations for orbitals
in the 4th and 5th editions of the class text:
1s in the 4th edition becomes g1s in the 5th edition
1s* in the 4th edition becomes u1s* in the 5th edition
The addition of g and u provides some extra identification
of the orbitals and is the one encountered in the professional
literature.
g and u are from the German “gerade” and “ungerade”

7. H 1s(A) - -1s(B) 1s(A) 1s(B) Wave Functions Electron Densities A B2 +
Wave Functions
Electron Densities A B
1s(A) 1s
[ s * ] 2
[y - y ] 1s 2 s *
= C A B + B
ANTIBONDING - A
Pushes e- away from
region between
nuclei A and B
-1s(B)
- 2[1s(A)][1s(B)] 1s
[y + y ] 1 s
= C A B
+ 2[1s(A)][1s(B)] 1s
[ s ] 2
BONDING + +
Pushes e- between
nuclei A and B A B A B 1s y 2
(n.i.) ~
[(y ) + (y ) ] A B
1s(A)
1s(B) + +
NON-INTERACTING A B A B

8. *1s 1s Potential Energy of H H R H V(R) Separated H, H+ R ∆Ed=2 +
H R H
V(R)
Separated H, H+
*1s
H + H+ R
∆Ed=
255 kJ mol-1
1s
Single electron
holds H2+ together
1.07 Å

9. H2 s1s < 1s < s1s* E s1s CORRELATION DIAGRAM Energy Ordering:
(H Atom A)
(H Atom B)
Atomic Orbital
Atomic Orbital
s1s
H2 Molecular Orbitals

10. He2 s1s CORRELATION DIAGRAM Z for He =2 s1s* E Atomic Orbital
(He Atom A)
(He Atom B)
Atomic Orbital
Atomic Orbital
s1s
He2 Molecular Orbitals

11. Bonding for Second Row Diatomics Involves the n=2 Atomic Shell
Lithium atomic configuration is 1s22s1
(Only the 2s electron is a valence electron.)
Li2 dimer has the configuration:
[(1s)2(1s*)2] (2s)2
= [KK](2s)2
CORRELATION DIAGRAM
For Li2 (2s)2, Bond order =
(1/2)(2-0) = 1
Li2
s2s* E 2s 2s
(Li Atom A)
(Li Atom B)
Atomic Orbital
Atomic Orbital
s2s
Li2 Molecular Orbitals

12. Bonding for Second Row Diatomics: the Role of 2p Orbitals
Once the 2s, 2s* molecular orbitals formed from the
2s atomic orbitals on each atom are filled (4 electrons, Be2),
we must consider the role of the 2p electrons (B2 is first diatomic using 2p electrons).
There are 3 different sets of p orbitals (2px, 2py, and 2pz), all
mutually perpendicular. If we choose the molecular diatomic
axis to be the z axis (this is arbitrary), we have a picture like this:

13.   Nucleus A Nucleus B x1 y1 x2 y2 z1 z2 Bonding Axis 2pz obital on
atom 1 and atom 2
2pz orbitals
point at
each other. - + - +
2px
orbitals
are
parallel
to each
other.
2px orbital on
atom 1 and atom 2 
Nucleus A
Nucleus B x1 y1 x2 y2 z1 z2
Bonding
Axis + + - -