Adiabatic time dependent density functional theory

Casida ME. Propagator corrections to adiabatic time-dependent density-functional theory hnear response theory. J Chem Phys. 2005 122 054111. 

Gritsenko OV, Baerends EJ. Double excitation effect in non-adiabatic time-dependent density functional theory with an analytic construction of the exchange-correlation kernel in the common energy denominator approximation. Phys Chem Chem Phys. 2009 11 4640-4646. KUmmel S, Kronik L. Orbital-dependent density functionals Theory and apphcations. Rev Mod Phys. 2008 80 3-60. 

Bast R, Jensen HJA, Saue T. Relativistic adiabatic time-dependent density functional theory using hybrid functionals and noncollinear spin magnetization. Int J Quantum Chem. 2009 109 2091-2112. 

For the Pbj and SnJ cages, the calculated electronic absorption spectra at the adiabatic time-dependent density functional theory (TDDFT) level are similar. The absorptions are mainly in the ultraviolet with a strong absorption at about 220-230 mn and a weak absorption between 290-480 nm. The modifications in the absorption spectra induced by the encapsulation of Pu + ion are mainly the introduction of an absorption in the red (700-750 nm) with a blueshift from Snn to Pbi2. The major MOs involved in this excitation are ti [6p(Pu)/5p(Sn) or 6p(Pb)] to h [(6d(Pu)/5p(Sn) or 6p(Pb)]. 

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

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... 

Bauernschmitt R, Ahlrichs R (1996) Treatment of electronic excitations within the adiabatic approximation of time dependent density functional theory. Chem Phys Lett 256 454 64 Stratmann RE, Scuseria GE (1998) An efficient implementation of time-dependent density-functional theory for the calculation of excitation energies of large molecules. J Chem Phys 109 8218-8224... 

Time-Dependent Density Functional Theory (TD-DFT) simulations in adiabatic approximation, carried out on a prototype terthiophene oxidized in the inner position (Raganato et al., 2004), indicated that the oxidation of the thiophene ring leads to the formation of new interactions in the LUMO orbital. The kinetic energy of the electrons in this orbital is lowered, while the energy of the electrons in the HOMO orbital is almost unchanged. As a consequence, the electron affinity of the whole molecule is increased. 

R. Ahlrichs, M. Bar, M. Haser, H. Horn, C. Koknel, Electronic structure calculations on workstation computers The program system Turbomole, Chem. Phys. Lett. 162 (1989) 165 M. Haser, R. Ahlrichs, Improvements on the direct SCF method, J. Comput. Chem. 10 (1989) 104 O. Treutler, R. Ahlrichs, J. Chem. Phys. 102 (1995) 346 R. Bauernschmitt, R. Ahlrichs, Treatment of Electronic Excitations within the Adiabatic Approximation of Time Dependent Density Functional Theory, Chem. Phys. Lett. 256 (1996) 454 S. Grimme, F. Furche, R. Ahlrichs, An improved method for density functional calculations of the frequency-dependent optical rotation, Chem. Phys. Lett. 361 (2002) 321 F. Furche,... 

Bauernschmitt R, Ahlrichs R. Treatment of electronic excitations within the adiabatic approximation of time dependent density functional theory. Chem Phys Lett 1996 256 454-464. 

Bokhan, D., Bartlett, R. J. (2006). Adiabatic ab initio time-dependent density-functional theory employing optimized-efifective-potential many-body perturbation theory potentials. Phys. Rev. A 73,022502. 

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... 

More recently, theoretical studies using on-the-fly trajectory surface hopping (TSH) simulations based on time-dependent density functional theory (TDDFT) electronic structure calculations [39, 41] suggested an important participation of the dark Au(nn ) and B2g(mr ) states in the non-adiabatic relaxation dynamics after excitation to the bright state. 

Electronic Excitations within the Adiabatic Approximation of Time Dependent Density Functional Theory. 

On top of this effective ground-state description a time-dependent extension has been proposed by Niehaus and co-workers, which is usually referred to as a time-dependent density-functional response theory tight-binding (TD-DFRT-TB) scheme. It corresponds to the formulation of Casida s linear-response theory that has been discussed before. The coupling matrix giving the response of the potential with respect to a change in the electron density has to be built as stated in eqn (19), and we use again the adiabatic approximation. 

The third approach is that used by Salahub and co-workers. They initially used DFT RPA but recendy have reported an implementation of time-dependent density functional response theory (TD DFRT). Their Kohn-Sham linear response function involves a coupling matrix, K, which in the RPA case contains only the response to coulomb terms, but in their present implementation contains exchange and correlation response terms. Their K is time independent as they work within the adiabatic approximation. They calculate the frequency dependent polarizability from a sum-over-states (SOS) formula, and hence have to calculate the excitation spectrum. 

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. 

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