Chemical Bonds and Molecules
The ionic (or electrovalent) bond
Cl
(1s)2(2s)2(2p)6(3s)2(3p)5
Na
(1s)2(2s)2(2p)6(3s)1
• Na gives up its (3s) electron, while Cl accepts the electron
to fill up its (3p) shell
• Na  Na+ ; Cl  Cl- ; Attractive potential (NaCl molecule)
The ionic bond
• How do atoms bond together?
– Coulomb force – Electromagnetic / Long Range
Repulsive
component
(nuclei)
Force related to potential energy: F = -dV/dr
Negative slope: dV/dr<0 – repulsive force
Positive slope: dV/dr>0 – attractive force
A,B>0 and n>m to have a potential well
Attractive
component
(electrons)
Covalent bond
Cl
(1s)2(2s)2(2p)6(3s)2(3p)5
Cl2 Molecule
• Atoms not as easily ionized
• Share their outer electrons (ex: diatomic molecules)
Wave Functions Overlap (covalent
+
bond) in the hydrogen ion H2
Two hydrogen ions far apart
Two hydrogen ions closer
Overlap of their wave functions (ψ1+ψ2 or ψ1-ψ2)
Concentration of
negative charge
Electron probability density depends on the
relative sign of the two wave functions.
Coulomb potential
energy of the protons
The Hydrogen Ion (cont.)
Bonding
Antibonding
Total energy of the ion = energy protons + energy electron
(Up + E+) or (Up + E-)
The Hydrogen Molecule
Minimum:
E = -16.3eV
r = 0.106 nm
2
2
E = (-13.6eV)Z /n
with Z=2 and n=1
+
Energy required to break the H2 molecule:
+
+
B = E(H+H ) – E(H2 ) = -13.6eV – (-16.3eV)
= 2.7 eV
No minimum
 No bound state
Hydrogen Bond
+δ H
−δ
O
−δ
O
H
+δ
H
+δ
+δ H
• Binding between molecules due to weak electric
and magnetic forces
• High boiling points in liquid – molecules don’t
easily separate
Other bonds
• Van der Waals bond:
– Found in liquids and solids at low temperatures
– Ex: graphite
• Atoms in a sheet held together by strong covalent
bonds
• Adjacent sheets held together by Van der Waals
bonds
• Metallic bond:
– (Quasi-)free valence electrons shared by a
number of atoms
Bonding
HC
pp covalent bond
CH
H2O
sp bond
Oxygen: 1s22s22p4
Opportunity for 2 covalent bonds with H
sp-hybrid bond
3-D ?
Ammonia NH3
Nitrogen: 1s22s22p3
Opportunity for 3 covalent bonds with H
Benzene
Methane CH4
Molecules
• At the atomic level, electromagnetic radiations
may induce transitions between electronic levels
• At the molecule level, they can induce (through
emission, absorption, scattering…) transitions
between “molecular states”, e.g. collective modes
in the molecule.
– Example:
• Rotational states
• Vibrational states
States in a molecules (I)
• Rotational States in a simple case
– Diatomic molecule: two atoms
connected with a massless and rigid
rod
Moment of inertia
– Angular Momentum (Quantum):
Exercise
• Estimate the value of Erot for the lowest rotational energy
state of N2 (example 10.1 p336)
States in a molecules (II)
• Vibrational states:
– Two atoms oscillating around their equilibrium position
– Two mass connected with a massless spring [model: Harmonic
Oscillator]
with
κ: spring constant
µ: reduced mass  µ=(m1.m2)/(m1+m2)
– Assuming a pure ionic bond, we can estimate κ:
-10
• Application: r~10 m  k~460 N/m
Vibrational modes
Vibration and Rotation
• Total Energy:
• Transitions between states:
– ΔE = Eph  Energy of the photon emitted/absorbed in the
process
– Example: from l+1 to l
– Δl = 1: same ΔEl ; Δn = 1: same ΔEn
BAND SPECTRUM:
ΔEn
Part of the emission
spectrum of N2
Band Spectrum
• Vibrational energies
typically greater than
rotational energies
• Allowed transitions Δl=±1:
– Photon carries away its
intrinsic momentum of one
quantum unit (ħ)
Absorption spectrum
• In the absorption spectrum of HCl, the spacing between
the peaks can be used to compute the rotational inertia I.
The missing peak in the center corresponds to the
forbidden Δℓ = 0 transition.
• The central frequency