Medium dependent optical response in ultra-fine plasmonic nanoparticles.

We study the influence of media on the interaction of ultra-fine plasmonic nanoparticles (≤ 8 nm) with radiation. The important role of the surface layer of the nanoparticles, with properties that differ from the ones in the inner part, is established. Using an atomistic representation of the nanoparticle material and its interaction with light, we find a highly inhomogeneous distribution of the electric field inside and around the particles. It is predicted that with an increase in the refractive index of the ambient medium, the extension of the surface layer of atoms increases, something that also is accompanied by an enhanced red shift of the plasmon resonance band compared to large particles in which the influence of this layer and its relative volume is reduced. It is shown that the physical origin for the formation of a surface layer of atoms near the nanoparticle boundary is related to the anisotropy of the local environment of atoms in this layer which changes the conditions for the interaction of neighboring atoms with each other and with the incident radiation. It is shown that a growth of the refractive index of the ambient medium results in an increase in the local field in the dielectric cavity in which a plasmonic nanoparticle is embedded and which is accompanied by a growth of the amplitude of the plasmon resonance. We predict that in the ultra-fine regime the refractive index sensitivity shows a decreasing trend with respect to size which is opposite to that for larger particles. With the applied atomistic model this work demonstrates close relations between field distributions and properties of ultra-fine nanoparticles.

Thermal degradation of optical resonances in plasmonic nanoparticles.

The dependence of plasmon resonance excitations in ultrafine (3-7 nm) gold nanoparticles on heating and melting is investigated. An integrated approach is adopted, where molecular dynamics simulations of the spatial and temporal development of the atoms constituting the nanoparticles generate trajectories out of which system conformations are sampled and extracted for calculations of plasmonic excitation cross sections which then are averaged over the sample configurations for the final result. The calculations of the plasmonic excitations, which take into account the temperature- and size-dependent relaxation of the plasmons, are carried out with a newly developed Extended Discrete Interaction Model (Ex-DIM) and complemented by multilayered Mie theory. The integrated approach clearly demonstrates the conditions for suppression of the plasmons starting at temperatures well below the melting point. We have found a strong inhomogeneous dependence of the atom mobility in the particle crystal lattice increasing from the center to its surface upon the temperature growth. The plasmon resonance suppression is associated with an increase of the mobility and in the amplitude of phonon vibrations of the lattice atoms accompanied by electron-phonon scattering. This leads to an increase in the relaxation constant impeding the plasmon excitation as the major source of the suppression, while the direct contribution from the increase in the lattice constant and its chaotization at melting is found to be minor. Experimental verification of the suppression of surface plasmon resonance is demonstrated for gold nanoparticles on a quartz substrate heated up to the melting temperature and above.

Atomistic description of plasmonic generation in alloys and core shell nanoparticles.

Using the extended discrete interaction model we investigate the tunabilty of surface plasmon resonances in alloys and core-shell nanoparticles made from silver and gold in the small (1-15 nm) nanoscale regime where classical models based on the bulk dielectric constant may not apply. We show that the surface plasmon resonance of these alloys and core-shell particles to a large extent follow Vegard's law irrespective of the geometry of the nanoparticle. The evolution of the polarizability with size demonstrates a highly non-linear behaviour of the polarizability with the ratio of the constituents and geometry in alloys and core-shell nanoparticles, with the exception of the longitudinal surface plasmon resonance in nanorods and, partly, nanodisc alloys. We here show that the non-linear behaviour can be explained in terms of the difference in polarizability of the mixing constituents and local effects causing a quenching of the dipoles for geometries with a low aspect ratio. A thorough statistical investigation reveals that there is only a small dependence of the surface plasmon resonance on atomic arrangement and exact distribution in a nanoparticle and that the standard deviation decreases rapidly with the size of the nanoparticles. The physical ground for the random distribution algorithm for alloys in discrete interaction models is explained in detail and verified by a statistical analysis. For nanoparticles below 4 nm a sampling strategy is recommended.

Plasmonic nano-shells: atomistic discrete interaction versus classic electrodynamics models.

Using the extended discrete interaction model and Mie theory, we investigate the tunability of the optical polarizability of small metallic nano-shells. We show that the spectral positions of symmetric and antisymmetric dipolar plasmon resonances vary with the ratio of particle radius to hole radius in a manner similar to one predicted for uniform metallic nano-shells using a semiclassical approach of two coupled harmonic oscillators. We show that, according to the extended discrete interaction model, the dipolar plasmon resonances are also present for nano-shells in the 2-13 nm size region and show the same functional dependence seen for larger nano-shells. Using previously fitted data from experiment, we can predict the size-dependence of the plasma frequency for nano-shells in the 1-15 nm size region. We find that Mie theory, which utilizes the electron mean free path correction for the permittivity, is not able to reproduce the same functional form of the dipolar modes for the nano-shells of the same sizes.

Molecular and Electronic Structure of Re2Br4(PMe3)4.

The dinuclear rhenium(II) complex Re2Br4(PMe3)4 was prepared from the reduction of [Re2Br8](2-) with (n-Bu4N)BH4 in the presence of PMe3 in propanol. The complex was characterized by single-crystal X-ray diffraction (SCXRD) and UV-visible spectroscopy. It crystallizes in the monoclinic C2/c space group and is isostructural with its molybdenum and technetium analogues. The Re-Re distance (2.2521(3) Å) is slightly longer than the one in Re2Cl4(PMe3)4 (2.247(1) Å). The molecular and electronic structure of Re2X4(PMe3)4 (X = Cl, Br) were studied by multiconfigurational quantum chemical methods. The computed ground-state geometry is in excellent agreement with the experimental structure determined by SCXRD. The calculated total bond order (2.75) is consistent with the presence of an electron-rich triple bond and is similar to the one found for Re2Cl4(PMe3)4. The electronic absorption spectrum of Re2Br4(PMe3)4 was recorded in benzene and shows a series of low-intensity bands in the range 10 000-26 000 cm(-1). The absorption bands were assigned based on calculations of the excitation energies with the multireference wave functions followed by second-order perturbation theory using the CASSCF/CASPT2 method. Calculations predict that the lowest energy band corresponds to the δ* → σ* transition, while the next higher energy bands were attributed to the δ* → π*, δ → σ*, and δ → π* transitions.

Two- and four-component relativistic generalized-active-space coupled cluster method: implementation and application to BiH.

A string-based coupled-cluster method of general excitation rank and with optimal scaling which accounts for special relativity within the four-component framework is presented. The method opens the way for the treatment of multi-reference problems through an active-space inspired single-reference based state-selective expansion of the model space. The evaluation of the coupled-cluster vector function is implemented by considering contractions of elementary second-quantized operators without setting up the amplitude equations explicitly. The capabilities of the new method are demonstrated in application to the electronic ground state of the bismuth monohydride molecule. In these calculations simulated multi-reference expansions with both doubles and triples excitations into the external space as well as the regular coupled-cluster hierarchy up to full quadruples excitations are compared. The importance of atomic outer core-correlation for obtaining accurate results is shown. Comparison to the non-relativistic framework is performed throughout to illustrate the additional work of the transition to the four-component relativistic framework both in implementation and application. Furthermore, an evaluation of the highest order scaling for general-order expansions is presented.