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

Detail study of Hartree Fock and its assumptions

 

Hartree–Fock (HF) Method

Scientists asked:

“How can we simplify the many-electron problem?”

Replace complex interactions with an average field. This is the Hartree–Fock idea.

Main Assumption

Each electron moves in the average field of all other electrons instead of tracking exact electron–electron motion.

Coupled Cluster Theory

 

Coupled Cluster Theory (CC Theory)

Introduction to CC Theory

Coupled Cluster (CC) is one of the most accurate methods for calculating electronic structure.

It systematically includes electron correlation and is widely used in quantum chemistry.

Møller–Plesset Perturbation Theory (MP2)

 Møller–Plesset Perturbation Theory (MP2)

• Hartree–Fock (HF) → ignores electron correlation  
• CI → includes correlation but very expensive

So we need a method that is

Electron Correlation & Configuration Interaction (CI)

 

Electron Correlation & Configuration Interaction (CI)

Do electrons in a molecule really move independently?

Answer: No
They repel each other and try to avoid each other all the time.

What Hartree–Fock (HF) Assumes

In Hartree–Fock (SCF):

• Each electron moves in an average field of others
• Instant repulsion ignored
• Only one Slater determinant is used

Slater Determinant

 

Slater Determinant

The Problem We Need to Solve

Electrons are:

·         Indistinguishable

·         Follow Pauli Exclusion Principle

·         Wavefunction must be antisymmetric

Born–Oppenheimer Approximation

 Born–Oppenheimer Approximation (BOA)

The Born-Oppenheimer Approximation is a fundamental concept in quantum mechanics that simplifies the Schrödinger equation for many-body systems, like molecules, by separating nuclear and electronic motion.