Failure of TDDFT

We will come back to this theoretical considerations when assessing the achievements and failures of TDDFT in different cases. 

In the previous sections we showed the results of several TDDFT calculations, most of them agreeing quite well with experiment. Clearly no physical theory works for all systems and situations, and TDDFT is not an exception. It is the purpose of this section to show some examples where the theory does not work. However, before proceeding with our task, we should specify what we mean by failures of TDDFT . TDDFT is an exact reformulation of the time-dependent many-body Schrodinger equation - it can only fail in situations where quantum-mechanics also fails. The key approximation made in practical applications is the approximation for the xc potential. Errors in the calculations should therefore be imputed to the functional used. As a large majority of TDDFT calculations use the ALDA or the adiabatic GGA, we will be mainly interested in the errors caused by these approximate functionals. Furthermore, and as we already mentioned in the previous section, there... 

The analysis done for naphthalene above can shed some light of the general failure of TDDFT in underestimation of the La transitions in PAHs. Using the self-interaction free LHF potential does not obviate this problem, as is illustrated in Table 9. To the best of our knowledge, the cause of this shortcoming of TDDFT is not well understood. We note, however, that the same incorrect ordering of and occurs in the CIS approximation, which is also self-interaction free. The analysis here shows that this is a failure of approximations for the XC kernel rather than to the ground-state potential. 

The genesis of the failure of TDDFT can be traced to the fact that TDDFT is a linear response theory. When an excitation moves charge from one area in a molecule to another, both ends of that molecule will geometrically relax. While charge transfer between molecules can be well approximated by ground-state density functional calculations of the total energies of the species involved, TDDFT must deduce the correct transitions by... 

In the case of the protonated Schiff base model, the forces computed from the LR-TDDFT Sj PES lead to a single bond rotation instead of double bond isomerization. This failure might be related to the local approximation of the exchange-correlation functional or, as suggested by the significantly different results obtained with P-TDDFT, to a breakdown of the linear response approximation. Further investigations in this respect are needed. P-TDDFT and ROKS correctly... 

Whenever a method is shown to work well, it inevitably gets applied to many scientific investigations, and specific failures then appear. Charge-transfer excitations are of great importance in photochemistry, especially of biological systems, but many workers are now finding abysmal results with TDDFT for... 

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