High-frequency limit of spectroscopy.

We consider an arbitrary quantum mechanical system, initially in its ground-state, exposed to a time-dependent electromagnetic pulse with a carrier frequency ω0 and a slowly varying envelope of finite duration. By working out a solution to the time-dependent Schrödinger equation in the high-ω0 limit, we find that, to the leading order in ω0 -1, a perfect self-cancellation of the system's linear response occurs as the pulse switches off. Surprisingly, the system's observables are, nonetheless, describable in terms of a combination of its linear density response function and nonlinear functions of the electric field. An analysis of a jellium slab and jellium sphere models reveals a very high surface sensitivity of the considered setup, producing a richer excitation spectrum than accessible within the conventional linear response regime. On this basis, we propose a new spectroscopic technique, which we provisionally name the Nonlinear High-Frequency Pulsed Spectroscopy (NLHFPS). Combining the advantages of the extraordinary surface sensitivity, the absence of constraints by the traditional dipole selection rules, and the clarity of theoretical interpretation utilizing the linear response time-dependent density functional theory, NLHFPS has a potential to evolve into a powerful characterization method for nanoscience and nanotechnology.

Breakdown of the ionization potential theorem of density functional theory in mesoscopic systems.

The ionization potential (IP)-theorem of Kohn-Sham (KS) density functional theory (DFT) states that the energy of the highest occupied molecular orbital (HOMO) ϵHOMO equals the negative of the first IP, thus ascribing a physical meaning to one of the eigenvalues of the KS Hamiltonian. We scrutinize the fact that the validity of the IP-theorem relies critically on the electron density n(r), far from the system, to be determined by HOMO only, behaving as n(r)∼r→∞e-2-2ϵHOMOr. While this behavior always holds for finite systems, it does not hold for mesoscopic ones, such as quasi-two-dimensional (Q2D) electron gas or Q2D crystals. We show that this leads to the violation of the IP-theorem for the latter class of systems. This finding has a strong bearing on the role of the KS valence band with respect to the work-function problem in the mesoscopic case. Based on our results, we introduce a concept of the IP band structure as an observable alternative to its unphysical KS counterpart. A practical method of the determination of the IP band structure in terms of DFT quantities is provided.

Many-Body Quantum Dynamics by the Reduced Density Matrix Based on Time-Dependent Density-Functional Theory.

We evaluate the density matrix of an arbitrary quantum mechanical system in terms of the quantities pertinent to the solution of the time-dependent density functional theory (TDDFT) problem. Our theory utilizes the adiabatic connection perturbation method of Görling and Levy, from which the expansion of the many-body density matrix in powers of the coupling constant λ naturally arises. We then find the reduced density matrix ρ_{λ}(r,r^{'},t), which, by construction, has the λ independent diagonal elements ρ_{λ}(r,r,t)=n(r,t), n(r,t) being the particle density. The off-diagonal elements of ρ_{λ}(r,r^{'},t) contribute importantly to the processes unaccessible via the density, directly or by the use of the known TDDFT functionals. Of those, we consider the momentum-resolved photoemission, doing this to the first order in λ, i.e., on the level of the exact exchange theory. In illustrative calculations of photoemission from the quasi-2D electron gas and isolated atoms, we find quantitatively strong and conceptually far-reaching differences with the independent-particle Fermi's golden rule formula.

Theoretical approach to embed nanocrystallites into a bulk crystalline matrix and the embedding influence on the electronic band structure and optical properties of the resulting heterostructures.

We develop an approach and present results of the combined molecular dynamics and density functional theory calculations of the structural and optical properties of the nanometer-sized crystallites embedded in a bulk crystalline matrix. The method is designed and implemented for both compatible and incompatible lattices of the nanocrystallite (NC) and the host matrix, when determining the NC optimal orientation relative to the matrix constitutes a challenging problem. We suggest and substantiate an expression for the cost function of the search algorithm, which is the energy per supercell generalized for varying number of atoms in the latter. The epitaxial relationships at the Si/NC interfaces and the optical properties are obtained and found to be in a reasonable agreement with experimental data. Dielectric functions show significant sensitivity to the NC's orientation relative to the matrix at energies below 0.5 eV.

Quasi-Low-Dimensional Electron Gas with One Populated Band as a Testing Ground for Time-Dependent Density-Functional Theory of Mesoscopic Systems.

We find an exact analytical solution to the exchange-only time-dependent density-functional theory (TDDFT) problem for a significant class of quasi-low-dimensional (QLD) materials: QLD electron gas with only one band filled in the direction perpendicular to the layer or wire. The theory yields the TD exchange potential as an explicit nonlocal operator of the TD spin density. The dressed interband (image states) excitation spectra of quasi-two-dimensional electron gas are obtained, while the comparison with the Kohn-Sham transitions provides insights into the qualitative and quantitative role of the many-body interactions. Important cancellations between the Hartree f_{H} and the exchange f_{x} kernels of TDDFT are found in the low-density regime, elucidating the interrelations between the Kohn-Sham and the many-body dynamics in mesoscopic systems.