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. 

Plasmonic red shifts of nanoparticles are commonly used in imaging technologies to probe the character of local environments, and the understanding of their dependence on size, shape, and surrounding media has therefore become an important target for research. The red shift of plasmon resonances changes character at about 8-10 nm of size for spherical gold nanoparticles-above this value, the red shift progresses linearly with particle size, while below this size, the red shift changes nonlinearly and more strongly with size. Using an atomistic discrete interaction model, we have studied the special properties of the nanoparticle surface layers and discovered its importance for ultrafine plasmonic nanoparticles and their red shifts. We find that the physical origin for the specific properties inherent to the surface layer of atoms near the nanoparticle boundary is related to the anisotropy of the local environment of atoms in this layer by other atoms. The anisotropy changes the conditions for light-induced nonlocal interactions of neighboring atoms with each other and with the incident radiation compared to the atoms located in the particle core with isotropic nearest surroundings by other atoms. The local anisotropy of the nanoparticle crystal lattice is a geometric factor that increases toward its boundary and that is the most fundamental factor underlying the physical differences between the nanoparticle surface layer and the core material. It is shown that the inflexion point at 8-10 nm is due to a change in the dominant physical origin of the red shift -from chaotization of atomically light-induced dipoles within the surface layer in the case of ultrafine nanoparticles to retardation effects for large nanoparticles in which the relative volume of the surface layer decreases rapidly to a negligible value with increasing nanoparticle size. The patterns revealed are the basis for predicting the manifestation of surface layer effects in ultrafine plasmonic nanoparticles of different and of different materials.

It is shown that the accepted proof of the anti-symmetrised geminal power (AGP) wave functions lack of size consistency is not general enough to constitute a proof for the size consistency of the AGP wave function. The origin of the size consistency problem for AGP wave function in previous proofs is shown to stem from the perceived notion that the natural orbitals of the AGP always can be localised or guessed a priori. We here show that by applying different constraints on a more general geminal coefficient matrix that the ionised/electron-attached determinants can be eliminated in different ways in a spin-restricted basis, which is not possible in the accepted proof. Furthermore it is shown how different constraints on the coefficients in the geminal coefficient matrix can lead to different ionisation channels upon dissociation. We discuss the consequences of the generation of natural orbitals from the solution of the AGP using a more general coefficient matrix. Finally the modern use of the natural AGP as a reference function for another correlation method is discussed where improvements to the orbitals used in the modern AGP are suggested. 

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.

We will here revisit Nakatsuji's theorem of the necessary and sufficient conditions of the wave function and reinterpret these conditions in the new light of our findings. It will here be shown that the equations for the necessary and sufficient conditions are not independent and that these equations can be reduced to a single equation. This observation reduces the number of conditions for the wave function for the electronic Hamiltonian to (Formula presented.), where (Formula presented.) is the number of basis functions, which coincide with the number of parameters in the two-particle reduced density matrix. Since only the highest order electron interaction term determines the necessary and sufficient conditions Nakatsuji's theorem can in this way be interpreted as a generalized Brillouin theorem. In this way the stationary conditions for the wave function of Hamiltonians with any n-body interaction takes a similar form. It is hoped that this new interpretation of the necessary and sufficient conditions as a generalized Brillouin theorem can give insights into the development of novel and compact representations of the wave function.

We present an analysis of ultrafine metallic nanoparticles (1-15 nm) with respect to electromagnetic field generation by plasmonic excitations. A number of structures with different symmetries and geometries are studied in order to analyze the distributions of plasmonically generated near-electric fields and the concentration of hot and cold spots around the particles. The study is made possible by the recent development of an extended discrete interaction model (Ex-DIM) where the explicit dependency of the plasmonic spectra on the structure and composition of particles in the range of 1-15 nm is accounted for. With the Ex-DIM, the optical response of the internal crystal structure of the nanoscale particles can be visualized, thereby making it possible to predict the dependence of the generated local fields with respect to the position of the particles relative to the external field polarization. The results indicate rather surprising concentrations of the plasmon fields in very confined hot spots also in cases when the particles retain a high symmetry. The consequence of the findings of this study when using small symmetric nanoparticles for near-field imaging is briefly discussed.

X-ray processes involve interactions with high-energy photons. For these short wavelengths, the perturbing field cannot be treated as constant, and there is a need to go beyond the electric-dipole approximation. The exact semi-classical light-matter interaction operator offers several advantages compared to the multipole expansion such as improved stability and ease of implementation. Here, the exact operator is used to model x-ray scattering in metal K pre-edges. This is a relativistic two-photon process where absorption is dominated by electric-dipole forbidden transitions. With the restricted active space state-interaction approach, spectra can be calculated even for the multiconfigurational wavefunctions including second-order perturbation. However, as the operator itself depends on the transition energy, the cost for evaluating integrals for hundreds of thousands unique transitions becomes a bottleneck. Here, this is solved by calculating the integrals in a molecular-orbital basis that only runs over the active space, combined with a grouping scheme where the operator is the same for close-lying transitions. This speeds up the calculations of single-photon processes and is critical for the modeling of two-photon scattering processes. The new scheme is used to model Kα resonant inelastic x-ray scattering of iron-porphyrin complexes with relevance to studies of heme enzymes, for which the total computational time is reduced by several orders of magnitude with an effect on transition intensities of 0.1% or less.

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.

In the H2S molecule, the interplay between different core levels can be investigated in great detail in relation to x-ray spectroscopy, which requires a theory for interpretation. Hence, valence and core excitations into the two antibonding molecular orbitals of the H2S molecule have been calculated within a multi-configurational wave function framework. Scanning along the S-H stretching coordinates, we derive potential energy surfaces and transition dipole moments involving the ground state and core and valence excited states. Both valence excitations and the S1s(-1) and S2p(-1) core excitations show pairs of dissociative and bound electronic states. These pairs of states are nearly degenerate in H2S at the ground state geometry. The close degeneracy together with conical intersections makes H2S an interesting target for x-ray spectroscopy involving ultra-fast dissociation influenced by non-adiabatic transitions and interference. For future investigations with x-ray absorption spectroscopy (XAS) and resonant inelastic x-ray scattering (RIXS), it is valuable to compare H2S with the water molecule, which exhibits state-selective gating to different vibrational modes [R. C. Couto et al., Nat. Commun. 8, 14165 (2017)] in its well-separated O1s(-1) core excited states. The dense manifolds of the S2p(-1) core excited states will complicate the analysis of K-alpha edge RIXS, but dynamical effects could be evaluated through detuning and by comparing with L edge XAS. In L edge RIXS, the dynamical effects will be more pronounced due to the longer lifetime of the S2p(-1) core excited states compared to the S1s(-1) core excited states.

We present the theory and the analytical and numerical solution for the calculation of the oscillator and rotatory strengths of molecular systems using a state-specific formalism. For a start, this is done in the context of the exact semiclassical light–matter interaction in association with electronic wave functions expanded in a Gaussian basis. The reader is guided through the standard approximations of the field, e.g., the use of commutators, truncation of Taylor expansions, and the implications of these are discussed in parallel. Expressions for the isotropically averaged values are derived, recovering the isotropic oscillator strength in terms of the transition electric-dipole moment, and the isotropic rotatory strength in terms of the transition electric-dipole and magnetic-dipole moments. This chapter gives a detailed description of the computation of the integrals over the plane wave in association with Gaussian one-particle basis sets. Finally, a brief description is given of how the computed oscillator and rotatory strengths are related to the quantities commonly used and discussed in experimental studies.