Restricted TDDFT

Lately, the CP-MD approach has been combined with a mixed QM/MM scheme [10-12] which enables the treatment of chemical reactions in biological systems comprising tens of thousands of atoms [11, 26]. Furthermore, CP-MD and mixed QM/MM CP-MD simulations have also been extended to the treatment of excited states within a restricted open-shell Kohn-Sham approach [16, 17, 27] or within a linear response formulation of TDDFT [16, 18], enabling the study of biological photoreceptors [28] and the in situ design of optimal fluorescence probes with tailored optical properties [32]. Among the latest extensions of this method are also the calculation of NMR chemical shifts [14]. 

To date, most applications of TDDFT have been in the linear response regime. Calculations of the photoresponse from Eqs. (154) and (155) are, by now, a mature subject. The literature on such calculations is enormous and a whole volume [153] has been devoted to the subject. In this section we shall restrict ourselves to the basic ideas rather than describing the applicational details. 

In the first part of this work, a brief overview over several strategies to combine such time domain transport simulations with first principles electronic structure theory is given. For the latter, we restrict ourselves to a discussion of time dependent density functional theory (TDDFT) only. This method is by far the most employed many body approach in this field and provides an excellent ratio of accuracy over computational cost, allowing for the treatment of realistic molecular devices. This digest builds on the earlier excellent survey by Koentopp and co-workers on a similar topic [13]. Admittedly and inevitably, the choice of the covered material is biased by the authors interests and background. 

Most implementations of TDDFT to an open-shell system use an spin-unrestricted approach, because orbital-energy differences concerned with partially occupied orbitals are generally too small in a spin-restricted approach, and the orbital-energy difference in DFT is the leading term in the electron-excitation energy. 

Singlet excited-state geometries of a set of medium-sized molecules, including 1,2,4,5-tetrazine, with different characteristic lowest excitations have been studied with two closely related restricted open-shell Kohn-Sham methods and within linear response to time-dependent DFT (TDDFT). The results are compared to wave function-based methods <2003JMT(630)163>. 

The level of theoretical calculations on conjugated polymers, and other organic semiconductors, has developed rapidly in recent years, such that reliable ab initio,density functional theory (DFT), and time-dependent DFT (TDDFT) are possible. Results of general quantum chemical calculations on these materials have been reviewed, and we will restrict our discussion to a few recent examples. 

For that purpose, electronic spectra are first classified according to the character of the states involved. A very basic distinction relies on the electronic structure of the corresponding initial state from which the transition occurs. This initial state is not necessarily the ground state of the system, shown schematically in Figure 4, which includes the three most common possibilities. For a more detailed discussion of this point in the context of restricted and unrestricted TDDFT approaches, see Ref. 22. 

Figrire 8 An overview of quantum chemical methods for excited states. Bold-italic entries indicate methods that are currently applicable to large molecules. Important abbreviations used Cl (configuration Interaction), TD (time-dependent), CC (coupled-cluster), HF (Hartree-Fock), CAS (complete active space), RAS (restricted active space), MP (Moller-Plesset perturbation theory), S (singles excitation), SD (singles and doubles excitation), MR (multireference). Geometry optimizations of excited states for larger molecules are now possible with CIS, CASSCF, CC2, and TDDFT methods. 

CC2, CCS, etc.) can be devised offering a good balance between cost and accuracy. Other simple (second-order) perturbative approaches that are comparable to CC2 can be found in the ADC(2) [19] or CIS(D) [20] methods. As is the case for TDDFT, these linear response or propagator formulations are not only interesting from a formal perspective (by allowing one to obtain information from the excited states based on ground-state quantities) but also because of their black box nature, that is, one does not need to construct a complicated, multi-reference wavefunction via the definition of orbital active spaces. However, as we shall see, the restriction to closed-shell references somewhat limits their applicability to the actinides. 

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