Theoretical interpretation of the photoelectron detachment spectra of Na−2–5 and of the absorption spectra of Na3, Na4, and Na8 clusters

Metal cluster plasmons analyzed by energy-resolved photoemission

The optical response of size-selected metal clusters is studied by wavelength-dependent photoemission and energy-resolved photoelectron detection. Relative photodetachment cross sections giving information on the plasmon are determined for the example of closed-shell Ag₉₁^-. Notably, the peak energy of this anion (3.74 eV) is higher than the small particle limit in Mie theory of 3.5 eV. Different methods to extract cross sections from the spectra are applied. In particular, we compare the results obtained by integrating the full electron yields to analyses based on evaluating specified binding energy windows. The approach opens up new possibilities to conduct studies on Landau fragmentation as a result of multielectron excitations.

GW approximation of the many-body problem and changes in the particle number

A stringent test for an exchange-correlation approximation in electronic structure calculations is the equality between the ionization energy of the neutral system and the affinity of the singly positively charged system. All of the commonly used approximations (local, semilocal, hybrid) for the exchange correlation within density functional theory fail badly with this test. They consequently present a localization or delocalization error, resulting in a highest occupied molecular orbital or lowest unoccupied molecular orbital gap over- or underestimation. The GW approximation appears as the best available framework to describe particle number changes. The small remaining error can be further reduced by devising a DeltaSCF-like method within the GW approximation. The proposed approach is necessary as soon as localized states are involved, e.g., in finite systems or defect states in crystals.

Time-dependent density-functional theory in the projector augmented-wave method

We present the implementation of the time-dependent density-functional theory both in linear-response and in time-propagation formalisms using the projector augmented-wave method in real-space grids. The two technically very different methods are compared in the linear-response regime where we found perfect agreement in the calculated photoabsorption spectra. We discuss the strengths and weaknesses of the two methods as well as their convergence properties. We demonstrate different applications of the methods by calculating excitation energies and excited state Born-Oppenheimer potential surfaces for a set of atoms and molecules with the linear-response method and by calculating nonlinear emission spectra using the time-propagation method.

Hydration Process of Na2- in Small Water Clusters: Photoelectron Spectroscopy and Theoretical Study of Na2-(H2O)n

Photoelectron spectroscopy (PES) of Na2- (H2O)n (n < or = 6) was investigated to examine the solvation of sodium aggregates in small water clusters. The PES bands for the transitions from the anion to the neutral ground and first excited states derived from Na2 (1(1)Sigmag+) and Na2 (1(3)Sigmau+) shifted gradually to the blue, and those to the higher-excited states correlated to the 3(2)S + 3(2)P asymptote dropped down rapidly to the red and almost degenerated on the 1(3)Sigmau+-type band at n = 4. Quantum chemical calculations for n up to 3 showed that the spectra can be ascribed to structures where one of the Na atoms is selectively hydrated. From the electron distributions, it is found that the Na- -Na+(H2O)n- -type electronic state grows with increasing cluster size, which can be regarded as a sign of the solvation of Na2- with ionization of the hydrated Na.

Electronic States of Sodium Dimer in Ammonia Clusters: Theoretical Study of Photoelectron Spectra for Na2-(NH3)n (n = 0−6)

The geometries, energetics, and vertical detachment energies of Na2-(NH3)n (n = 0-6) were examined by ab initio molecular orbital methods in connection with their photoelectron spectra. One of the Na atoms is selectively solvated in the most stable structures for each n. The solvated Na is spontaneously ionized and the formation of a solvated electron occurs with increasing n, giving rise to the Na-Na+(NH3)n(e-)-type state. The ground and two lowest-lying excited states derived from the 11Sigma g+, 13Sigma u+, and 13Pi u states of Na2, respectively, are of ion-pair character though the 13Sigma u+-type state has an intermediate nature slowly changing to the radical-pair state with increasing n. On the other hand, the higher states stemming from the 11Sigma u+, 13Sigma g+, and 11Pi u states of Na2 show a developing radical-pair nature as n increases. The size dependences of the photoelectron spectra such as the near parallel shifts of the first and second bands, as well as the rapid red shifts of the higher bands, are studied on the basis of the electronic change of the neutrals by solvation.

Photoelectron Spectroscopy on Small Anionic Copper-Carbonyl Clusters

Anion photoelectron spectroscopy in combination with density functional theory (DFT) calculations has been used to study mono- and dinuclear copper-carbonyl clusters Cun(CO)m- (n = 1, 2; m = 2-5). The adiabatic detachment energies of the anions have been measured which correspond to the electron affinities of the respective neutral species. The corresponding values are 0.95 eV for Cu(CO)2, 1.02 eV for Cu(CO)3, 1.04 eV for Cu(CO)4, 1.43 eV for Cu2(CO)4, and 1.19 eV for Cu2(CO)5. All spectra exhibit a pronounced vibrational fine structure on the adiabatic photodetachment peak. The energy splitting is close to the energy of the C-O stretching vibration of the neutral cluster (final state). The DFT calculations clearly indicate that in all clusters the highest occupied molecular orbital (HOMO) is a CO-derived π* orbital. Furthermore the calculations are used to give insight into geometry, frontier orbitals, vibrational frequencies and spin multiplicity of the neutral and anionic clusters.

Geometrical and electronic structures of AumAgn (2⩽m+n⩽8)

The structural and electronic properties of Au(m)Ag(n) binary clusters (2 < or = m + n < or = 8) have been investigated by density functional theory with relativistic effective core potentials. The results indicate that Au atoms tend to occupy the surface of Au(m)Ag(n) clusters (n > or = 2 and m > or = 2). As a result, segregation of small or big bimetallic clusters can be explained according to the atomic mass. The binding energies of the most stable Au(m)Ag(n) clusters increase with increasing m+n. The vertical ionization potentials of the most stable Au(m)Ag(n) clusters show odd-even oscillations with changing m+n. The possible dissociation channels of the clusters considered are also discussed.

Finite lifetime effects on the polarizability within time-dependent density-functional theory

We present an implementation for considering finite lifetime of the electronic excited states into linear-response theory within time-dependent density-functional theory. The lifetime of the excited states is introduced by a common phenomenological damping factor. The real and imaginary frequency-dependent polarizabilities can thus be calculated over a broad range of frequencies. This allows for the study of linear-response properties both in the resonance and nonresonance cases. The method is complementary to the standard approach of calculating the excitation energies from the poles of the polarizability. The real and imaginary polarizabilities can then be calculated in any specific energy range of interest, in contrast to the excitation energies which are usually solved only for the lowest electronic states. We have verified the method by investigating the photoabsorption properties of small alkali clusters. For these systems, we have calculated the real and imaginary polarizabilities in the energy range of 1-4 eV and compared these with excitation energy calculations. The results showed good agreement with both previous theoretical and experimental results.

Simple DFT model of clusters embedded in rare gas matrix: Trapping sites and spectroscopic properties of Na embedded in Ar

We present a theoretical model to study the dynamics of metallic clusters embedded in a rare gas matrix. We describe the active electrons of the embedded cluster using time dependent density functional theory, while the surrounding matrix is described in terms of classical molecular dynamics of polarizable atoms. The coupling between the cluster and the rare gas atoms is deduced from the work of Gross and Spiegelmann [J. Chem. Phys. 108, 4148 (1998)] and reformulated explicitly in a simple and efficient density functional form. The electron rare gas interaction takes the form of an averaged dipole fluctuation term, which retains the van der Waals long range interaction, and a short range repulsive pseudopotential, which accounts for the Pauli repulsion of the electron by the rare gas atom. We applied our model to Na clusters embedded in Ar matrix. For the latter we developed an efficient local pseudopotential, which allows studying systems containing more than 10(3) Ar atoms. We show that large systems are indeed necessary to account properly for long range polarization of the matrix, that competes with the matrix confinement effect. We focus our study on Na(2), Na(4), and Na(8). For each system, we have determined the geometry of the most favorable trapping site by means of damped molecular dynamics. We present the effect of matrix embedding on the optical absorption spectrum. For Na(2), the trapping site can be unambiguously identified by comparison of the absorption spectrum with experiment. For Na(4) the spectrum of the embedded cluster is significantly different from the free cluster spectrum, while for Na(8) differences are less pronounced.