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Theoretical background
Published in Guo-ping Zhang, Georg Lefkidis, Mitsuko Murakami, Wolfgang Hübner, Tomas F. George, Introduction to Ultrafast Phenomena from Femtosecond Magnetism to high-harmonic Generation, 2020
Guo-ping Zhang, Georg Lefkidis, Mitsuko Murakami, Wolfgang Hübner, Tomas F. George
To solve the Kohn-Sham equation (Eq. 3.11), one can use a real grid mesh or basis function. For atoms and molecules, Gaussian functions are often used (see below). In solids a planewave basis is used, together with a pseudopotential for ion cores.e The hybrid basis functions are also used. Augmented planewave basis functions are an example. One uses dual basis functions, one for the core electrons in atomic sphere, called Muffin-tin sphere, and the other the planewave basis for the interstitial regions between atoms. Both basis functions are matched at the sphere boundary in both the value and the slope of the basis. Matching allows the spherical basis to get the crystal momentum index. For time-dependent problems, it is customary to employ the time-dependent density functional theory. The detailed accounts of time-dependent DFT will be given in the next section.
Exact Solutions in the Density Functional Theory (DFT) and Time-Dependent DFT of Mesoscopic Systems
Published in Klaus D. Sattler, st Century Nanoscience – A Handbook, 2019
Density functional theory (DFT) and its time-dependent counterpart TDDFT are formally rigorous approaches to theoretically study the ground-states and the electronic excitations, respectively, of atomic, molecular, and condensed matter systems, including the mesoscopic ones. Practically, the usefulness of DFT and TDDFT is determined by the accuracy and the computational efficiency of the available approximations to the corresponding exchange-correlation (xc) functionals. In the three-dimensional, as well as in the purely low-dimensional, cases, the local-density approximation (LDA) to the xc functional of the corresponding dimensionality is traditionally and predominantly used. However, LDA, as well as its extensions of generalized gradient approximation (GGA) and meta-GGA, encounter severe difficulties when applied to the systems of intermediate dimensionality, i.e., mesoscopic systems. In this chapter, we review the recent progress in the use of the static and dynamic exact exchange (EXX) functional, which we show to be well fit to capture the characteristic features of mesoscopic systems. On this way, we find exact analytical solutions to the exchange-only DFT and TDDFT problems for specific systems of reduced-dimensionality: those of the quasi-2(1)D electron gas with one filled subband. These solutions provide us with important insights into the role of the interparticle interactions, allowing, in particular, to identify and separate the collective and the single-electron regimes in the quantum dynamics of the systems under study.
ab initio Transport Calculations for Single Molecules
Published in Sergey Edward Lyshevski, Nano and Molecular Electronics Handbook, 2018
TDDFT is a machinery for propagating a density in time, not a many-body wavefunction. Hence, as a prerequisite for applying the method an initial density (t = 0) is required. It needs to be represented as a single Slater determinant |0〉 constructed from a (complete) set of effective single particle states ϕm. This is always possible, if at t < 0 the system is in its ground state, then the KS-orbitals of ground state DFT are obvious candidates for 0m. In this case, one has for the density matrix at t = t′ = 0 () n(x,x′)=∑mocc.ϕm*(x)ϕm(x′)
Assessment of time-dependent density functional theory with the restricted excitation space approximation for excited state calculations of large systems
Published in Molecular Physics, 2018
Magnus W. D. Hanson-Heine, Michael W. George, Nicholas A. Besley
Kohn–Sham density functional theory (DFT) [1] has emerged as an extremely popular and successful approach for modelling molecular systems and solids. Within the framework of DFT, electronically excited states are usually studied though linear response time-dependent density-functional theory (TDDFT) [2]. In many studies, for example in biological chemistry or organic photovoltaics, there is a requirement to study the excited states of large molecular-based systems. For the study of excited states, it is often important to have an ab initio based approach since it is more difficult to parameterise reliable empirical methods for excited states. The application of TDDFT to study large systems is challenging owing to the computational cost, both in terms of the time for the calculations and memory required. Efficient schemes for solving the Casida equations for TDDFT and determining the excitation energies and associated oscillator strengths have been developed [3,4]. However, to study large system comprising of hundreds of atoms often requires further approximations to be made. The density functional tight binding (DFTB) method is a semi-empirical form of DFT which can be several orders of magnitude faster than DFT, and a linear response form of DFTB has been reported [5]. Another approach to extend TDDFT to study very large systems is the simplified TDDFT method of Grimme [6]. The approach exploits a Löwdin monopole based approximation to the two electron integrals and single excitation space selection and can be applied to systems of 500–1000 atoms. Other time-dependent semi-empirical approaches have been developed [7–9]. The low lying excited states of large systems have been studied with pseudo spectral TDDFT [10,11] which leads to a significant speedup in the calculations.
The elusive diiodosulphanes and diiodoselenanes
Published in Molecular Physics, 2022
The electronic spectroscopy of these compounds has been studied using TDDFT. For diiodosulphanes, the electronic spectra are known, and these calculations have allowed the assignation of the most intense electronic transitions. There is a large number of intense transitions, most of them are p(I) or π* → σ*(I–S) or σ*(S–S). The calculations have allowed the prediction of the most intense transitions for diiodoselenanes, which are not yet known. The transition near 400 nm which is considered as an indirect evidence of the existence of diiodoselenanes has been predicted to be due to Se2I2.
Mn(III) and Cu(II) complexes of 1-((3-(dimethylamino)propylimino)methyl) naphthalen-2-ol): Synthesis, characterization, catecholase and phenoxazinone synthase activity and DFT-TDDFT study
Published in Journal of Coordination Chemistry, 2018
Swaraj Sengupta, Binitendra Naath Mongal, Suman Das, Tarun K. Panda, Tarun K. Mandal, Michel Fleck, Shyamal K. Chattopadhyay, Subhendu Naskar
The calculations were performed by density functional theory (DFT) implemented in GAUSSIAN09 [27]. The ligand and the complexes were optimized using B3LYP hybrid functional and 6-31 g(d) basis set for hydrogen, carbon, oxygen and nitrogen and LANL2DZ basis set for metals. The electronic spectra were simulated by Time-Dependent Density Functional Theory (TD-DFT). Computational studies were carried out in DMSO solvent using Polarizable Continuum Model (PCM) implemented in Gaussian 09.