DFT Functionals

 

DFT Functionals – Concept, Categories, and Detailed Study

Why Functionals Are Used in DFT

In Density Functional Theory, the total electronic energy of a system is written as:

Introduction to Density Functional Theory (DFT)

 Introduction to Density Functional Theory (DFT)

1. Introduction

In computational chemistry, we use quantum mechanics and computer simulations to study molecules and materials. One of the most powerful and widely used methods is Density Functional Theory (DFT).

Vibrational Analysis (IR Spectroscopy from DFT)

 

Vibrational Analysis (IR Spectroscopy from DFT)

 “After optimizing a molecule using DFT, how do we know the structure is correct and stable?”

Then say:

“We verify it using vibrational analysis and compare with IR spectra.”

What is Vibrational Analysis?

Definition:

Vibrational analysis studies how atoms in a molecule move (vibrate) around their equilibrium positions.

Time-Dependent Density Functional Theory

 

Time-Dependent Density Functional Theory (TD-DFT)

“What does DFT calculate — ground state or excited state?”

Answer: Ground state

Then say:

But what happens when a molecule absorbs light?
An electron gets excited.
DFT cannot properly describe this — so we need TD-DFT.

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.

Molecular Modeling Using Molecular Mechanics

 

Molecular Modeling Using Molecular Mechanics

Molecular models can be constructed in two main ways. Either researchers use an existing commercial force-field-based software package, or they build the molecule by assembling structural fragments stored in the molecular modeling program’s database.

 

Introduction to Quantum Mechanics

Quantum mechanics is the branch of chemistry and physics that describes the behavior of matter and energy at the atomic and molecular scale.

Molecular Mechanics (MM) and Force Field Methods

 

Molecular Mechanics (MM) and Force Field Methods

What is Molecular Mechanics?

Molecular Mechanics (MM) is a computational method used to study molecules by applying classical physics laws instead of quantum mechanics.  OR

Molecular mechanics is a computational method that calculates molecular structure and energy using classical mechanics and force field equations without explicitly considering electrons.

Difference Between Classical Physics and Quantum Mechanics

 

Difference Between Classical Physics and Quantum Mechanics

Classical physics explains the motion and energy of large objects such as cars, balls, and planets.

Quantum mechanics explains the behavior of tiny particles like electrons and atoms where classical laws fail.

Why we use computational chemistry over experimental work in this era?

 Why we use computational chemistry over experimental work?

We use computational chemistry to understand, predict, and design chemical systems using computers, often reducing the need for expensive and time-consuming laboratory experiments.

Introduction to computational chemistry, method, tools, and applications

 Computational Chemistry (Introduction)

Computational chemistry is a branch of chemistry that uses computer simulations, mathematical models and theoretical chemistry methods to study the structure, properties, and reactions of molecules. Instead of doing experiments only in laboratories, scientists use computers to predict molecular behavior, energies, and reaction mechanisms.

Or

Computational chemistry applies quantum mechanics, molecular mechanics, and statistical methods using computers to understand the chemical environment.