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.

What is TD-DFT?

Definition:

Time-Dependent Density Functional Theory (TD-DFT) is a computational method used to study excited states and electronic transitions.

Simple Explanation:

TD-DFT helps us understand how electrons behave when they absorb energy and move to higher energy levels.

It Explains

“An electron moves from a lower energy orbital to a higher energy orbital.”

Represent:

HOMO → LUMO

Simple Idea:

Ground state → electron is stable
Excited state → electron jumps to higher level

Daily Life Analogy

Like a student sitting calmly (ground state), then suddenly jumping on stage when excited.

What Does TD-DFT Calculate?

TD-DFT provides:

Excitation energy

Absorption wavelength (λ_max)

UV-Visible spectrum

Electronic transitions

Important Energy Relation

E = h ν = hc / λ

Explanation:

(E) = excitation energy

(ν) = frequency

(λ) = wavelength

Key Concept:

Smaller energy gap → larger wavelength
Larger energy gap → smaller wavelength

HOMO–LUMO Gap

Explain clearly:

HOMO = Highest Occupied Molecular Orbital

LUMO = Lowest Unoccupied Molecular Orbital

The energy difference between HOMO and LUMO determines how easily excitation occurs.

It means

Small gap → easy excitation

Large gap → difficult excitation

Types of Electronic Transitions

1. π → π*

Common in organic molecules

Strong absorption

2. n → π*

Involves lone pair electrons

Weaker absorption

Different orbitals give different types of transitions.

TD-DFT Output

When you perform a TD-DFT calculation, you obtain:

Excitation energy

Wavelength (nm)

Oscillator strength (f)

Oscillator Strength:

It represents the intensity of absorption

High f → strong absorption

Low f → weak absorption

Why is TD-DFT Important?

Used to simulate UV-Vis spectra

Helps understand color of compounds

Important in:

·         Organic solar cells

·         Dyes

·         Photochemistry

If a molecule absorbs visible light → it appears colored.

Limitations

Sometimes inaccurate for charge-transfer systems

Results depend on chosen functional

Not perfect for all excited states

Comparison

Method	Purpose
DFT	Ground state
TD-DFT	Excited state

 

DFT describes molecules at rest
TD-DFT describes molecules under light

 “What happens if the HOMO-LUMO gap is small?”

Easy excitation and larger wavelength