Adiabatic density functional approach

The reason for this difference is very simple. It is that the density functional approach calculates the rate for the adiabatic channel. For AG x> this will proceed via an activated complex with successor-state formal electron density parameter A = 1 for AGq <-x, it will proceed via an activated... 

Fuchs M, Gonze X (2002) Accurate density functionals Approaches using adiabatic-connection fluctuation-dissipation theorem, Phys. Rev. B, 65 235109... 

A large class of time-dependent quantum problems involves strongly interacting coupled fields requiring self-consistent non-perturbative and non-adiabatic approaches. We present here a general framev ork for analyzing these, based on Liouvillean Quantum Field Dynamics. Thus a multifunctional extension of the time-dependent density functional approach to many-body problems is... 

The first equation describes the classical motion of the nuclei (ions) the second equation describes the classical motion of the Kohn-Sham orbital tpi. It is interesting to note that when fi 0, eq. (28) reduces to the Kohn-Sham equation and accordingly the energy density functional reduces to the adiabatic energy. In principle, the smaller the /x, the closer tpi approach the adiabatic states. [68] In fact, in CPMD, /x cannot be set to zero because there would not be dynamical optimization of tp,. Usually, the size of /x is chosen so that the deviation of tpi from the adiabatic states has a negligible effect on the MD simulation, while it still allows as large as possible time-step. 

Figure 27 Excitation energies for the He atom obtained with different approaches. KS marks the orbital eigenvalues for the exact Kohn-Sham potential, ALDA the results with the adiabatic local-density approximation, and for the TDOEP approaches different orbital-dependent functionals have been used. Both the ALDA and the TDOEP results have been obtained using the time-dependent density-functional theory...

Time-dependent density functional theory (TDDET)i" within the linear response formalismi -" ] is nowadays the most widely used approach to the calculation of electronic excitation energies of molecules and solids. Applied within the adiabatic approximation and with the usual local or semilocal density functionals, TDDFT... 

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