Adiabatic time dependent density

Durbeej B, Eriksson LA (2006) Protein-bound chromophores astaxanthin and phytochromo-bilin excited state quantum chemical studies. Phys Chem Chem Phys 8 4053 071 Eurche E, Ahlrichs R (2002) Adiabatic time-dependent density functional methods for excited state properties. J Chem Phys 117 7433-7447... 

Furche F, Ahlrichs R (2002) Adiabatic time-dependent density functional methods for excited state properties. J Chem Phys 117 7433-7447... 

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... 

The simplest possible approximation of the time-dependent xc potential is the so-called time-dependent or adiabatic local density approximation (ALDA). It employs the functional form of the static LDA with a time-dependent density ... 

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... 

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. 

In the time-dependent calculations, we adopt the commonly used adiabatic approximation, where the xc potential is calculated with the time-dependent density. The adiabatic approximation had many successful applications to atomic and molecular processes in intense external fields [39,41], For the studies of the diatomic molecules [29,32,42], we utilize the LBa (van Leeuwen-Baerends) xc potential [43] ... 

Adiabatic Approximations. There is a very simple procedure that allows the use of the plethora of existing xc functionals for ground-state DFT in the time-dependent theory. Let us assume that VxcH is an approximation to the ground-state xc density functional. We can write an adiabatic time-dependent xc potential as... 

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. 

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