Hi Bensafi Toufik

Limitations of TD-DFT and Solutions:

Regards!

Prem

Dear Bensafi,

Time-dependent DFT has several limitations:

1. Approximate exchange-correlation functionals

The accuracy of TD-DFT depends on the exchange-correlation (XC) functional used. Standard functionals like the generalized gradient approximation and hybrid functionals struggle with charge-transfer excitations, Rydberg states, and double excitations.

Solution is using long-range corrected functionals or range-separated hybrid functionals can improve the description of charge-transfer excitations. Double hybrid functionals or correlated wave-function methods (like ADC, EOM-CCSD) may be used when higher accuracy is needed.

2. Underestimation of excitation energies for Rydberg states

Local/semi-local functionals tend to underestimate excitation energies for Rydberg states because they do not properly account for the correct asymptotic behavior of the XC potential.

Adding asymptotic corrections such as using the correct asymptotic potential (tuned range-separated functionals), can mitigate this problem.

3. Failure in describing double and multi-excitations

TD-DFT is based on the linear response formalism, which assumes single excitations dominate. It fails to capture states with strong double-excitation character!

Going beyond linear response TD-DFT, such as using time-dependent density matrix functional theory or many-body perturbation theory, can also better describe these cases.

4. Limited accuracy for strongly correlated systems

TD-DFT performs poorly in systems where strong electron correlation is important, such as in transition metal complexes or strongly correlated materials.

Multireference methods like CASSCF (Complete Active Space Self-Consistent Field) or TD-DMRG can be used instead.

5. Adiabatic approximation in the exchange-correlation kernel

Most TD-DFT calculations use the adiabatic approximation, meaning the XC kernel is time-independent. This limits the ability to describe memory effects and leads to errors in capturing certain nonadiabatic effects.

Using orbital-dependent kernels, such as exact exchange, or even incorporating nonadiabatic corrections can improve results.

6. Computational cost for large ssystems

While TD-DFT is computationally efficient compared to wavefunction-based methods, it still scales poorly for large molecular systems.

Techniques like linear-scaling TD-DFT, real-time TD-DFT, or ML-based approximations can help make calculations more efficient.

Hope it helps.