Fast construction of the Kohn–Sham response function for molecules

Abstract

The use of the LCAO (Linear Combination of Atomic Orbitals) method for excited states involves products of orbitals that are known to be linearly dependent. We identify a basis in the space of orbital products that is local for orbitals of finite support and with a residual error that vanishes exponentially with its dimension. As an application of our previously reported technique we compute the Kohn-Sham density response function χ0 for a molecule consisting of N atoms in N 2 Nω operations, with Nω the number of frequency points. We test our construction of χ0 by computing molecular spectra directly from the equations of Petersilka-Gossmann-Gross in N 2 Nω operations rather than from Casida's equations which takes N 3 operations. We consider the good agreement with previously calculated molecular spectra as a validation of our construction of χ0. Ongoing work indicates that our method is well suited for the computation of the GW self-energy Σ = iGW and we expect it to be useful in the analysis of exitonic effects in molecules.

Optical response of silver clusters and their hollow shells from linear-response TDDFT

“…The method that we are utilizing in this work is an efficient iterative way of solving linear response equations in which we exploit the locality of the operators and use an LCAO expansion of the Kohn-Sham (KS) eigenstates [42,43]. Although the method has a relatively high asymptotic scaling of the computational complexity O(N 3 ), it has been demonstrated to be a useful alternative to other methods [26,53].…”

“…The dominant products described above have been used in TDDFT, Hedin's GW approximation and for solving a Bethe-Salpeter equation [42,43,67,68]. However, the construction of dominant products, although mathematically rigorous and sparsity-preserving, has the important disadvantage of generating a large number of functions.…”

“…In this work, we apply linear-response TDDFT using a linear combination of atomic orbitals (LCAO) as a basis set to describe the electronic states of the clusters. Our method [42,43] has been recently enhanced in several respects. Besides the generality of the geometries and chemical species characteristic of ab-initio methods (in the present case our linearresponse solver is coupled to the SIESTA method [44,45]), the main advantage of the method is its computational efficiency that stems from the use of an iterative scheme to compute the optical response, as well as an efficient basis to express the products of atomic orbitals.…”

Plasmonic Response of Metallic Nanojunctions Driven by Single Atom Motion: Quantum Transport Revealed in Optics

“…[85] In order to address the complex correlation of electronics and optics in sub-nanometric junctions where the atoms in the system are allowed to adapt to the mechanical boundary conditions, we performed atomistic quantum mechanical calculations of the electronic structure, the optical response, and the structural evolution of a plasmonic cavity. In our calculations we employed an efficient implementation [86][87][88] of linear response Time-Dependent Density Functional Theory (TDDFT) in conjunction with the SIESTA Density Functional Theory (DFT) package. [89,90] The plasmonic cavity in our simulation is formed by two large sodium clusters, containing 380 atoms each of them, in close proximity.…”

Atomistic Near-Field Nanoplasmonics: Reaching Atomic-Scale Resolution in Nanooptics

“…In all these applications, the optical response that determines the properties of plasmonic surface modes is typically determined in the framework of classical electrodynamics, by solving Maxwell's equations for a particular material, shape, size and environment. In this way, for instance, plasmonic modes of spherical nanoparticles, 18,19 nanoshells, 20 nanorings, 21 nanorods, [22][23][24][25] nanostars, 26,27 dimers, 3,28,29 or particle oligomers 30,31 have been routinely estimated during the last years. The mode volumes typically reached in these structures are in the range of some tens of nanometers, and the actual degree of their field confinement is determined by the morphology of the nanostructure (curvature, thickness, interaction between different particles,...), 5,[32][33][34] The effective squeezing of electromagnetic energy into these nanometric dimensions has triggered out referring to plasmonic nanostructures as optical nanoantennas.…”