Adiabatic density functional

X. Gonze, "Adiabatic Density Functional Perturbation Theory," Phys. Rev. A 52 (1995), 1096-1114. 

Figure 8, Wavepacket dynamics of the butatriene radical cation after its production in the A state, shown as snapshots of the adiabatic density (wavepacket amplitude squared) at various times. The 2D model uses the coordinates in Figure Ic, and includes the coupled A andX states, The PES are plotted in the adiabatic picture (see Fig. lb). The initial structure represents the neutral ground-state vibronic wave function vertically excited onto the diabatic A state of the radical cation,...

To use direct dynamics for the study of non-adiabatic systems it is necessary to be able to efficiently and accurately calculate electronic wave functions for excited states. In recent years, density functional theory (DFT) has been gaining ground over traditional Hartree-Fock based SCF calculations for the treatment of the ground state of large molecules. Recent advances mean that so-called time-dependent DFT methods are now also being applied to excited states. Even so, at present, the best general methods for the treatment of the photochemistry of polyatomic organic molecules are MCSCF methods, of which the CASSCF method is particularly powerful. 

Adamo, C., Barone, V., 1998a, Implementation and Validation of the Lacks-Gordon Exchange Functional in Conventional Density Functional and Adiabatic Connection Methods , J. Comput. Chem., 19, 418. 

Adamo, C., di Matteo, A., Barone, V., 1999, From Classical Density Functionals to Adiabatic Connection Methods. The State of the Art , Adv. Quantum Chem., 36, 45. 

Bauernschmitt, R., Ahlrichs, R., 1996b, Treatment of Electronic Excitations Within the Adiabatic Approximation of Time Dependent Density Functional Theory , Chem. Phys. Lett., 256, 454. 

Density functional theory, direct molecular dynamics, complete active space self-consistent field (CASSCF) technique, non-adiabatic systems, 404-411 Density operator, direct molecular dynamics, adiabatic systems, 375-377 Derivative couplings conical intersections, 569-570 direct molecular dynamics, vibronic coupling, conical intersections, 386-389 Determinantal wave function, electron nuclear dynamics (END), molecular systems, final-state analysis, 342-349 Diabatic representation ... 

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... 

The time-dependent density functional theory [38] for electronic systems is usually implemented at adiabatic local density approximation (ALDA) when density and single-particle potential are supposed to vary slowly both in time and space. Last years, the current-dependent Kohn-Sham functionals with a current density as a basic variable were introduced to treat the collective motion beyond ALDA (see e.g. [13]). These functionals are robust for a time-dependent linear response problem where the ordinary density functionals become strongly nonlocal. The theory is reformulated in terms of a vector potential for exchange and correlations, depending on the induced current density. So, T-odd variables appear in electronic functionals as well. 

Fortunately, the same limiting conditions that validate the friction approximation can also be used with time-dependent density functional theory to give a theoretical description of rjxx. This expression was originally derived to describe vibrational damping of molecules adsorbed on surfaces [71]. It was later shown to also be applicable to any molecular or external coordinate and at any location on the PES, and thus more generally applicable to non-adiabatic dynamics at surfaces [68,72]. The expression is... 

Goscinski, 0. and Mujica, V. (1987) Adiabatic separation, broken symmetries and geometry optimization, in Erdahl, R. and Smith Jr, V. H. (eds) Density matrices and density functionals, Reidel, Dordrecht. 

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