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Download Computing the Optical Properties of Large Systems by Tim Joachim Zuehlsdorff PDF

By Tim Joachim Zuehlsdorff

This paintings addresses the computation of excited-state houses of structures containing hundreds of thousands of atoms. to accomplish this, the writer combines the linear reaction formula of time-dependent density useful thought (TDDFT) with linear-scaling concepts recognized from ground-state density-functional concept. This extends the diversity of TDDFT, which by itself can't take on the various huge and fascinating platforms in fabrics technological know-how and computational biology. The strengths of the process built during this paintings are tested on a few difficulties concerning large-scale platforms, together with exciton coupling within the Fenna-Matthews-Olson advanced and the research of low-lying excitations in doped p-terphenyl natural crystals.

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Extra info for Computing the Optical Properties of Large Systems

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4 Fast-Fourier Transforms and Ewald Summation In Sect. 1 it is pointed out that to obtain the DFT eigenstates of an infinite, periodic system, it is sufficient to solve for the functions |u ik in a single primitive real space unit cell for some discrete mesh of points k confined to the first Brillouin zone in reciprocal space. The periodicity of the Kohn–Sham potential allows for the use of a number of special techniques to speed up calculations. For every density ρ(r) constructed in the self-consistent solution to the Kohn–Sham equations, a new Kohn– Sham potential has to be constructed.

39) with the primitive reciprocal lattice vectors defined as bi · a j = 2πδi j . 41) G = m 1 b1 + m 2 b2 + m 3 b3 for m 1 , m 2 , m 3 ∈ Z. Note that from Bloch’s theorem it follows that ψik (r) = ψi[k+G] (r) and thus it m is sufficient to limit the range of allowed k-vectors to − 21 ≤ N jj ≤ 21 in order to obtain the full solution of the system. The reciprocal space to which k is limited by introducing this range to the allowed values of m j is known as the first Brillouin zone and it contains all information of the entire system.

Thus in an insulator, the Kohn–Sham single particle density matrix decays exponentially with distance and the rate of the exponential decay A is a function of the band gap [49]. Since the density matrix is represented by localised functions, it follows that in the case of insulators L{v} and P{v} are sparse for sufficiently large system sizes. In the limit of large enough systems, the resulting matrices of all matrix products required in the energy minimisation become sparse and all matrix operations can be performed in O(N ) effort.

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