Physics Area – PhD course in Theory and Numerical Simulation of Condensed Matter Simulating Plasmon Enhancement of Optical Properties in Hybrid Metal-Organic Nanoparticles Candidate: Advisor: Jacopo Marcheselli Marco Garavelli Stefano Corni Co-advisors: Stefano Baroni Academic Year 2018-19 i “ti´ d 0est` i` tout˜ o pro`V Jewn˜ ;” Dam. fr. 1,2 K.-A “To the chemist, colour is a bountiful clue to composition and, if measured care- fully enough, can reveal delicate truths about molecular structure. It takes a particular turn of mind to see chromatic beauty lurking in the molecular structures of alizarin and indigo, to sense the rich hues within the stark, schematic depictions of these dye molecules. The Italian chemist and writer Primo Levi intimates how this relation between colour and constitution broadens the chemist’s sensitivity to colour: Per quella che è stata la mia esperienza, devo dire che la mia chimica, che poi era una chimica "bassa", quasi una cucina, mi ha fornito in primo luogo un vasto as- sortimento di metafore. Mi ritrovo più ricco di altri colleghi scrittori perché per me termini come "chiaro", "scuro", "pesante", "leggero", "azzurro" hanno una gamma di significati più estesa e più concreta. Per me l’azzurro non è soltanto quello del cielo, ho cinque o se azzurri a disposizione.” Philip Ball, Bright Earth: The Invention of Colour iii SISSA Abstract Simulating plasmon enhancement of optical properties in hybrid metal-organic nanoparticles by Jacopo MARCHESELLI Hybrid organic-inorganic Nanoparticles (HNPs) are very interesting and widely stud- ied materials, for their versatile applications in biotechnology and medicine, with high potential in biomedical imaging, gene and drug delivery, and photothermal can- cer therapy, making them one of the most promising materials for early and accurate cancer diagnosis and effective cancer therapy. However, computing their physico- chemical properties in details proves to be a challenge. While the nature of the or- ganic component of the HNPs necessitates a full quantum chemical treatment, the size of the inorganic component renders this treatment computationally too expen- sive to be assessed with an homogeneous technique. For this reason hybrid models have been developed combining a QM level treat- ment and a classical electromagnetism approach, respectively, for molecules and the inorganic nano-structures upon which they are adsorbed [1]. In particular, the inor- ganic component, usually a metal, is considered as a classical continuous body, char- acterized by its own frequency dependent dielectric function, for which the Maxwell equations are solved using the Boundary Element Method (BEM), while excitation energies due to the energy transfer from the molecule to the metal is evaluated ex- ploiting Time Dependent Density Functional Theory (TDDFT). After proving that the polarization charges distribution, used in BEM, well de- scribe the optical properties of bare inorganic Nanoparticles, reproducing experi- mental spectra [2–4] of bare Gold Nanoparticles using BEM tools, we described the interactions of the organic molecular frame with the Nanoparticles. In order to repro- duce the desired spectroscopic properties for the hybrid system we evaluated on one side the effects introduced by the presence of a Nanoparticle over the energies and the excited state dynamics of the isolated organic dyes (radiative and non radiative deactivation constants). On the other side we computed how the organic layer of dye and surfactant around the gold Nanoparticle affects the plasmonic excitation of the metallic subsystem adding this layer to the electrodynamic computations. v Contents Abstract iii 1 Introduction1 2 Theoretical background9 2.1 Density Functional Theory......................9 2.1.1 Hohenberg and Kohn Theorems...............9 2.1.2 Kohn-Sham solution..................... 11 2.1.3 Exchange-Correlation Functionals.............. 13 2.1.4 Time-Dependent Density Functional Theory........ 14 2.2 Modelling the Dielectric Function.................. 15 2.2.1 Drude-Lorentz model..................... 15 2.2.2 When Drude-Lorentz fails: empirical models for the dielec- tric constant.......................... 17 2.3 Electromagnetic scattering by metal particles............ 17 2.3.1 Local Surface Plasmon Resonance.............. 19 2.4 Maxwell-Garnett Effective Model.................. 20 2.5 Polarizable Continuum Model.................... 20 3 Simulation of Gold Nanoclusters via plane-waves DFT 23 3.1 Introduction.............................. 23 3.2 Computational details......................... 24 3.3 Results and discussion........................ 24 3.4 Conclusions.............................. 29 4 Classical Electro-Magnetic simulations of Gold Nanoparticles 31 4.1 Introduction.............................. 31 4.2 Computational details......................... 34 4.2.1 Codes............................. 34 4.2.2 Sources of data........................ 34 4.2.3 GNBs’ modelling....................... 35 4.3 Results and discussion........................ 37 4.3.1 Assessment of GNBs’ model shapes............. 37 4.3.2 Assessing base size and truncation effects.......... 40 4.3.3 Base size limits for quasi-static computations........ 43 4.4 Conclusions.............................. 50 5 A Database of the near field enhancement over organic dyes 51 5.1 Introduction.............................. 51 5.2 Computational Details........................ 52 vi 5.2.1 Main Parameters....................... 52 5.2.2 Numerical Setup....................... 54 5.3 Results for NP 623.......................... 57 5.3.1 Emission........................... 57 Dye perpendicular to the surface............... 57 Dye parallel to the surface.................. 58 5.3.2 Quantifying the enhancement performance......... 58 5.3.3 Stokes shift effects...................... 69 5.3.4 Absorption.......................... 75 5.4 Results for NP 775.......................... 80 5.4.1 Emission........................... 80 5.4.2 Quantifying the enhancement performance......... 81 5.4.3 Stokes shift effects...................... 88 5.4.4 Absorption.......................... 92 5.5 Comparison of the nanoparticle effect................ 92 5.6 Conclusions.............................. 97 6 Future perspectives: the hybrid system as a whole 99 References 103 vii List of Figures 1.1 Hybrid nanoparcticles.........................1 1.2 Substituent effects...........................2 1.3 Enhanced absorption of the hybrid systems.............3 1.4 Charge transfer in hybrid organic-inorganic molecules........4 1.5 CT and ET mechanisms for plasmon enhanced reactions......4 1.6 Photoluminescence enhancement...................5 1.7 Solar cell performance improvement.................5 1.8 A collection of Gold nanoparticles in various shapes and sizes...6 2.1 PCM.................................. 21 3.1 Schematic representation of the Gold nanoclusters.......... 25 3.2 Binding energies........................... 26 3.3 Binding energies vs literature..................... 27 3.4 Second order binding energy difference (D2E)............ 27 3.5 HOMO-LUMO gaps......................... 28 3.6 Cluster spectra............................ 28 4.1 NP shapes............................... 35 4.2 Geometry parameters......................... 36 4.3 LSPR vs Aspect Ratio........................ 38 4.4 NP’s absorption spectra........................ 39 4.5 Summary of the experimental and computed LSPR peaks...... 41 4.6 Experimental vs simulated absorption maxima............ 42 4.7 Geometrical uncertainties....................... 43 4.8 Transversal LSPR........................... 44 4.9 Maxima distribution.......................... 45 4.10 Transversal LSPR........................... 45 4.11 Polarized absorptions......................... 46 4.12 LSPR vs Aspect ratio with with TDPLAS ............... 46 4.13 SCUFFEM vs TDPLAS ......................... 48 4.14 Size effects.............................. 48 4.15 Quasi-static size error......................... 49 5.1 Positions considered......................... 55 5.2 Computed spectra of the two NPs studied.............. 56 5.3 NP 623, F, perpendicular, tip, distances............... 59 5.4 NP 623, F, perpendicular, positions, 10 Bohr............ 59 5.5 NP 623, F, perpendicular, positions, 100 Bohr............ 60 5.6 NP 623, F, tip, orientations, 100 Bohr................ 60 5.7 NP 623, Gr, perpendicular, tip, distances............... 61 viii 5.8 NP 623, Gr, perpendicular, positions, 10 Bohr............ 61 5.9 NP 623, Gr, perpendicular, positions, 100 Bohr........... 62 5.10 NP 623, Gr, perpendicular, tip, distances............... 62 5.11 NP 623, Gnr, perpendicular, positions, 10 Bohr............ 63 5.12 NP 623, Gnr, perpendicular, positions, 100 Bohr........... 63 5.13 NP 623, t, perpendicular, tip, distances............... 64 5.14 NP 623, F, parallel, tip, distances.................. 64 5.15 NP 623, F, parallel, positions, 10 Bohr................ 65 5.16 NP 623, F, parallel, positions, 100 Bohr............... 65 5.17 NP 623, Gr, parallel, tip, distances.................. 66 5.18 NP 623, Gr, parallel, positions, 10 Bohr............... 66 5.19 NP 623, Gr, parallel, positions, 100 Bohr............... 67 5.20 NP 623, Gnr, parallel, tip, distances.................. 67 5.21 NP 623, Gnr, parallel, positions, 10 Bohr............... 68 5.22 NP 623, Gnr, parallel, positions, 100 Bohr.............. 68 5.23 NP 623, M, perpendicular, positions, 100 Bohr........... 69 5.24 NP 623, M, perpendicular, positions, 10 Bohr...........