Basis Sets

 

Basis Sets in Quantum Chemistry

HF, MP2, and CC  are methods used for how to calculate energy

Now the question is

With what mathematical tools do we represent orbitals? That tool is called Basis Sets

So, basis set is Mathematical functions used to describe atomic orbitals

Basis set is a tool to build wavefunction

Example

Drawing a circle using:

• rough hand → poor drawing ❌
• compass → accurate drawing ✔

Basis set = tool for drawing orbitals

  Small basis set → rough result

  Large basis set → accurate result

Why Basis Sets are Important

Even best method (CC) is not perfect, it will give wrong result if basis set is poor

To gain Accuracy = Method + Basis Set must require

Types of Basis Sets

1.       Minimal Basis Set

2.       Split-Valence Basis Set

3.       Polarization Functions

4.       Diffuse Functions 

Minimal Basis Set

This basis set includes STO-3G

“G” stands for Gaussian functions A mathematical functions used to approximate real orbitals

Meaning of STO-3G

STO-3G = Slater-Type Orbital – 3 Gaussian functions

• Real orbital shape. The problem is difficult to calculate mathematically.
• So we approximate STO using Gaussian functions  Because Gaussian is easy for computers
• 3G means: We are using 3 Gaussian functions to represent ONE orbital
• Only used for basic description

Term	Meaning
STO	Real orbital shape
G	Gaussian function
3G	3 Gaussians used

Use:

✔ Fast
❌ Not accurate

Split-Valence Basis Set

✔ Idea:

Valence orbitals → split into multiple functions

Core electrons simple
Valence electrons are study in detailed because bonding happens in valence electrons

Better flexibility

Notation of Split-Valence Basis Set

Numbers + G

Examples

• 3-21G
• 6-31G
• 6-311G

3→ core orbital (3 Gaussians)

2,1 → valence split into two (Valence = 2 functions)

6→ core orbital (6 Gaussians)

3,1 → valence split into two (Valence = 2 functions)

3,1,1 → valence split into three (Valence = 3 functions (more flexible))

6-311G is more accurate than 6-31G

Polarization Functions (Shape Change)

Simple Concept

Normally:

• Orbitals = simple shape

With (d,p)

• Orbitals = flexible, can bend/change

Analogy:

Balloon:

• Normal → round
• After Press → shape change

Example:

6-31G(d)

d orbital add → flexibility increase

Where used:

✔ Chemical reactions
✔ Bonding

Notation:

Numbers + G + (letters)

(d) , (p)

d: Added to heavy atoms (C, O, N)

p: Added to hydrogen

6-31G (d, p) or 6-311G(d, p)

6→ core orbital (6 Gaussians)

3,1 → valence split into two

3,1,1 → valence split into three

d → polarization on heavy atoms

p → polarization on hydrogen

 

6-31G(d,p)

• Geometry optimization
• Medium accuracy

6-311G(d,p)

• More accurate energies
• Research-level work

Basis Set	Meaning	Accuracy
6-31G (d,p)	Double split + polarization	Medium
6-311G (d,p)	Triple split + polarization	Higher

4. Diffuse Functions (Electron Spread)

✔ Idea:

Electron closer to nucleus → dense

Electron far to nucleus → spread

Meaning:

“+” = diffuse added to Heavy atoms

“++” = diffuse added to Heavy atoms as well as Hydrogen

 Example:

• 6-31+G(d,p)
• 6-31++G(d,p)

✔ Where important:

1. Anions (NEGATIVE IONS)

Example:
Cl⁻, OH⁻

Electron is loosely held → far from nucleus

✔ 2. Excited States

Electron jumps to higher orbital
Becomes more spread

✔ 3. Weak Interactions

Hydrogen bonding
van der Waals