Quantum Chemistry
The Wave-Mechanical Model
Quantum Numbers Hund’s Rule of Maximum Multiplicity
1) Principle Quantum Number (𝑛): When there is more than one orbital at a
Possible values: 1, 2, 3, 4…(positive integers) particular energy level, only one electron will
Meaning: fill each orbital until each has one electron.
● Average distance of the orbital from After this, pairing will occur with the addition
the nucleus of one electron to each orbital.
● Energy level/shell.
2) Angular Momentum Quantum Number (𝑙): Electron Configuration
Possible values: 0, 1, 2, 3, 4…(n-1) Shows how electrons are distributed inside
Meaning: the subshells and among the orbitals.
● The shape of the orbital.
● l = 1 ➡ s orbital (spherical) Examples:
l = 2 ➡ p orbital (dumbbell-shaped) 2 2 2
l = 3 ➡ d orbital (cloverleaf) ● Carbon (electron # = 6): 1𝑠 2𝑠 2𝑝
l = 4 ➡ f orbital (complex shape) ● Sodium (electron # = 11): [Ne]3𝑠
1
(noble gas shortened)
3) Magnetic Quantum Number (𝑚𝑙):
Possible values: − 𝑙... 0... + 𝑙 Subshell Capacity
Meaning:
● s: 2 electrons (1 orbital)
● Spatial orientation of the shape of the
orbital (𝑙) in 3D space. ● p: 6 electrons (3 orbitals)
● d: 10 electrons (5 orbitals)
4) Spin Quantum Number (𝑚𝑠): ● f: 14 electrons (7 orbitals)
1 1
Possible values: + or −
2 2 Possible Quantum Numbers in Subshells
Meaning: ● s: 𝑙 = 0, 𝑚𝑙 = 0
● The direction of electron spin (+ up or
- down) ● p: 𝑙 = 1, 𝑚𝑙 =− 1, 0, 1
● Each orbital holds a maximum of 2
● d: 𝑙 = 2, 𝑚𝑙 =− 2, − 1, 0, 1, 2
electrons with opposite spins.
● f: 𝑙 = 3, 𝑚𝑙 =− 3, − 2, − 1, 0, 1, 2, 3
Pauli Exclusion Principle
No two electrons in the same atom can have
the same set of four quantum numbers.
Aufbau Principle
When filling the orbitals of multielectronic
atoms, ground-state configurations are
realized when the lowest energy orbital
available is filled.
Order of filling: 1s ➡ 2s ➡ 2p ➡ 3s ➡ 3p ➡
4s ➡ 3d ➡ 4p ➡ 5s ➡ 4d ➡ 5p ➡ 6s ➡ 4f
➡ 5d ➡ 6p ➡ 7s ➡ 5f ➡ 6d ➡ 7p ➡…
, Electrostatic Repulsion (VSEPR With Lone Pairs:
Theory)
VSEPR – Valence Shell Electron Repulsion 1) 3 electron pairs, 1 lone pair – Bent/Angular
Example: 𝑆𝑂2
States that: Electron pairs around a central
atom arrange themselves in such a way to
minimize repulsion. 2) 4 electron pairs, 1 lone pair – Trigonal
Used to: Predict the arrangement of electron Pyramidal
pairs around a central atom. Example: 𝑁𝐻3
Shapes Based on Electron Pairs: 3) 4 electron pairs, 2 lone pairs –
No lone pairs: Bent/Angular
Example: 𝐻20
1) 2 electron pairs – Linear
Example: 𝐵𝑒𝐹2
4) 5 electron pairs, 1 lone pair – See-saw
Example: 𝑆𝐹4
2) 3 electron pairs – Trigonal Planar
Example: 𝐵𝐹3
5) 5 electron pairs, 2 lone pairs – T-shaped
Example: 𝐶𝑙𝐹3
3) 4 electron pairs – Tetrahedral
Example: 𝐶𝐻4
6) 5 electron pairs, 3 lonely pairs – Linear
Example: 𝑋𝑒𝐹2
4) 5 electron pairs – Trigonal Bypiramid
Example: 𝑃𝐶𝑙5 7) 6 electron pairs, 1 lone pair – Square
Pyramidal
Example: 𝐵𝑟𝐹5
5) 6 electron pairs – Octahedral
Example: 𝑆𝐹6 8) 6 electron pairs, 2 lone pairs – Square
Planar
Example: 𝑋𝑒𝐹4
The Wave-Mechanical Model
Quantum Numbers Hund’s Rule of Maximum Multiplicity
1) Principle Quantum Number (𝑛): When there is more than one orbital at a
Possible values: 1, 2, 3, 4…(positive integers) particular energy level, only one electron will
Meaning: fill each orbital until each has one electron.
● Average distance of the orbital from After this, pairing will occur with the addition
the nucleus of one electron to each orbital.
● Energy level/shell.
2) Angular Momentum Quantum Number (𝑙): Electron Configuration
Possible values: 0, 1, 2, 3, 4…(n-1) Shows how electrons are distributed inside
Meaning: the subshells and among the orbitals.
● The shape of the orbital.
● l = 1 ➡ s orbital (spherical) Examples:
l = 2 ➡ p orbital (dumbbell-shaped) 2 2 2
l = 3 ➡ d orbital (cloverleaf) ● Carbon (electron # = 6): 1𝑠 2𝑠 2𝑝
l = 4 ➡ f orbital (complex shape) ● Sodium (electron # = 11): [Ne]3𝑠
1
(noble gas shortened)
3) Magnetic Quantum Number (𝑚𝑙):
Possible values: − 𝑙... 0... + 𝑙 Subshell Capacity
Meaning:
● s: 2 electrons (1 orbital)
● Spatial orientation of the shape of the
orbital (𝑙) in 3D space. ● p: 6 electrons (3 orbitals)
● d: 10 electrons (5 orbitals)
4) Spin Quantum Number (𝑚𝑠): ● f: 14 electrons (7 orbitals)
1 1
Possible values: + or −
2 2 Possible Quantum Numbers in Subshells
Meaning: ● s: 𝑙 = 0, 𝑚𝑙 = 0
● The direction of electron spin (+ up or
- down) ● p: 𝑙 = 1, 𝑚𝑙 =− 1, 0, 1
● Each orbital holds a maximum of 2
● d: 𝑙 = 2, 𝑚𝑙 =− 2, − 1, 0, 1, 2
electrons with opposite spins.
● f: 𝑙 = 3, 𝑚𝑙 =− 3, − 2, − 1, 0, 1, 2, 3
Pauli Exclusion Principle
No two electrons in the same atom can have
the same set of four quantum numbers.
Aufbau Principle
When filling the orbitals of multielectronic
atoms, ground-state configurations are
realized when the lowest energy orbital
available is filled.
Order of filling: 1s ➡ 2s ➡ 2p ➡ 3s ➡ 3p ➡
4s ➡ 3d ➡ 4p ➡ 5s ➡ 4d ➡ 5p ➡ 6s ➡ 4f
➡ 5d ➡ 6p ➡ 7s ➡ 5f ➡ 6d ➡ 7p ➡…
, Electrostatic Repulsion (VSEPR With Lone Pairs:
Theory)
VSEPR – Valence Shell Electron Repulsion 1) 3 electron pairs, 1 lone pair – Bent/Angular
Example: 𝑆𝑂2
States that: Electron pairs around a central
atom arrange themselves in such a way to
minimize repulsion. 2) 4 electron pairs, 1 lone pair – Trigonal
Used to: Predict the arrangement of electron Pyramidal
pairs around a central atom. Example: 𝑁𝐻3
Shapes Based on Electron Pairs: 3) 4 electron pairs, 2 lone pairs –
No lone pairs: Bent/Angular
Example: 𝐻20
1) 2 electron pairs – Linear
Example: 𝐵𝑒𝐹2
4) 5 electron pairs, 1 lone pair – See-saw
Example: 𝑆𝐹4
2) 3 electron pairs – Trigonal Planar
Example: 𝐵𝐹3
5) 5 electron pairs, 2 lone pairs – T-shaped
Example: 𝐶𝑙𝐹3
3) 4 electron pairs – Tetrahedral
Example: 𝐶𝐻4
6) 5 electron pairs, 3 lonely pairs – Linear
Example: 𝑋𝑒𝐹2
4) 5 electron pairs – Trigonal Bypiramid
Example: 𝑃𝐶𝑙5 7) 6 electron pairs, 1 lone pair – Square
Pyramidal
Example: 𝐵𝑟𝐹5
5) 6 electron pairs – Octahedral
Example: 𝑆𝐹6 8) 6 electron pairs, 2 lone pairs – Square
Planar
Example: 𝑋𝑒𝐹4
