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Notes: We investigate ultrafast multi-state nuclear dynamics in a triatomic cluster. In particular, we explore how the intracluster nuclear dynamics of the Ag3−/Ag3/Ag3+ system is reflected in the femtosecond pump-probe negative ion-to neutral-to positive ion (NENEPO) signals. The nuclear dynamics is based on classical trajectories on the ground electronic adiabatic state potential hypersurfaces obtained from accurate ab initio quantum chemistry calculations. The nuclear dynamics of Ag3 initiated from the linear transition state involves distinct sequential processes of configurational relaxation to the triangular configuration, intracluster collisions, and the onset of IVR, resonant, and dissipative IVR, and vibrational equilibration. We determined the timescales for these processes and discussed their dependence on the initial cluster temperature. The Wigner representation of the density matrix was utilized to simulate the NENEPO-zero kinetic energy (NENEPO-ZEKE) signal and the total (integrated over the photoelectron energy) NENEPO signal. We show how geometrical change, completion of IVR and vibrational coherence effects can be identified in the NENEPO signals. A comparison of the calculated NENEPO signals with the available experimental data is presented. © 1998 American Institute of Physics.

Notes: A new 11-electron relativistic effective core potential (11e-RECP) for Ag atom based on correlated level of theory and the associated atomic orbital (AO) basis set have been derived which allows for an accurate determination of excited states. This has been verified by comparing the calculated excited states of the dimer with experimental data. Therefore, we applied the new 11e-RECP in the framework of the linear response equation-of-motion coupled-cluster (EOM-CC) method to determine absorption spectra of small Agn=2−4 and Agn=2−4+ clusters. The correlation treatment of 11 electrons per atom and calculations of transition energies and oscillator strengths in a large energy interval allowed us to investigate the influence of d-electrons on the spectroscopic patterns. We have found that d-electrons play a crucial role for accurate predictions of absorption spectra in spite of the fact that they are not always directly involved in the leading excitations contributing to the intense transitions. The calculated spectroscopic patterns for the stable structures are compared with available experimental data. © 1999 American Institute of Physics.

Notes: The absorption spectra of Ag5–8 have been determined in the framework of the linear response equation-of-motion coupled cluster method and related techniques employing 11-electron relativistic effective core potential. In these treatments electron correlation effects for 11 electrons per atom are included, providing an accurate description of excited states of silver clusters. The calculations of transition energies and oscillator strengths have been carried out in a large energy interval for the stable structures and for the isomeric forms higher in energy. This allowed us to investigate the influence of structural properties on the spectroscopic patterns and to determine the role of d-electrons. Inclusion of d-electrons in the correlation treatment is mandatory to obtain accurate values for transition energies, but the excitations of s-electrons are primarily responsible for the spectroscopic patterns. They are characterized by the interference phenomena known in molecular spectroscopy which lead to a small number of intense and a large number of weak resonances. The calculated absorption spectra for the stable structures provide accurate predictions of the optical response properties in the gas phase and at the zero temperature. Since for neutral silver clusters the experimental data in the gas phase are not yet available, we also calculated spectra for deformed structures which model the influence of the environment such as rare-gas atoms, solid Ar-matrix or He-droplet. Comparison of our results with available experimental data permits us to identify structural properties responsible for the recorded spectral features. © 2001 American Institute of Physics.

Notes: Bimetallic silver–gold clusters offer an excellent opportunity to study changes in metallic versus "ionic" properties involving charge transfer as a function of the size and the composition, particularly when compared to pure silver and gold clusters. We have determined structures, ionization potentials, and vertical detachment energies for neutral and charged bimetallic AgmAun [3≤(m+n)≤5] clusters. Calculated VDE values compare well with available experimental data. In the stable structures of these clusters Au atoms assume positions which favor the charge transfer from Ag atoms. Heteronuclear bonding is usually preferred to homonuclear bonding in clusters with equal numbers of hetero atoms. In fact, stable structures of neutral Ag2Au2, Ag3Au3, and Ag4Au4 clusters are characterized by the maximum number of hetero bonds and peripheral positions of Au atoms. Bimetallic tetramer as well as hexamer are planar and have common structural properties with corresponding one-component systems, while Ag4Au4 and Ag8 have 3D forms in contrast to Au8 which assumes planar structure. At the density functional level of theory we have shown that this is due to participation of d electrons in bonding of pure Aun clusters while s electrons dominate bonding in pure Agm as well as in bimetallic clusters. In fact, Aun clusters remain planar for larger sizes than Agm and AgnAun clusters. Segregation between two components in bimetallic systems is not favorable, as shown in the example of Ag5Au5 cluster. We have found that the structures of bimetallic clusters with 20 atoms Ag10Au10 and Ag12Au8 are characterized by negatively charged Au subunits embedded in Ag environment. In the latter case, the shape of Au8 is related to a pentagonal bipyramid capped by one atom and contains three exposed negatively charged Au atoms. They might be suitable for activating reactions relevant to catalysis. According to our findings the charge transfer in bimetallic clusters is responsible for formation of negatively charged gold subunits which are expected to be reactive, a situation similar to that of gold clusters supported on metal oxides. © 2002 American Institute of Physics.

Notes: We investigate the ultrafast multistate nuclear dynamics involving adiabatic electronic excited states of nonstoichiometric halide deficient clusters (NanFn−1) characterized by strong ionic bonding and one excess electron, which is localized either in the halide vacancy or on the alkali atom attached to the ionic subunit depending on the cluster size. For this purpose we developed an ab initio adiabatic nuclear dynamics approach in electronic excited and ground states "on the fly" at low computational demand by introducing the "frozen ionic bonds" approximation, which yields an accurate description of excited states considering the excitation of the one excess electron in the effective field of the other n−1 valence electrons involved in the ionic bonding. We combined this multistate dynamics approach with the Wigner–Moyal representation of the vibronic density matrix forming the ab initio Wigner distribution approach to adiabatic dynamics. This method allows the simulation of femtosecond NeExPo-pump–probe and NeExNe-pump–dump signals based on an analytic formulation which utilizes temperature-dependent ground-state initial conditions (Ne), an ensemble of trajectories carried out on the electronic excited state (Ex) for the investigation of the dynamics of the system, and either the cationic (Po) or the ground state (Ne) for the probing step. The choice of the systems has been made in order to determine the time scales of processes involving (i) metallic bond breaking such as during the dynamics in the first excited state of Na2F, and (ii) fast geometric relaxation leaving the bonding frame intact as during the dynamics in the first excited state of Na4F3. The bond-breaking process via a conical intersection involving nonadiabatic dynamics will be presented in the accompanying paper [Hartmann et al., J. Chem. Phys. 114, 2123 (2001)]. The dynamics in the first excited state of Na2F from triangular-to linear-to triangular structure gives rise to fast geometric relaxation due to Na–Na bond breaking at the time scale of ∼90 fs but no signature of internal vibrational energy redistribution (IVR) is present in NeExNe-pump–dump signals since the broken metallic bond prevents the coupling between stretching and bending modes. Instead, anharmonicities of the bending periodic motion have been identified. In contrast, in the case of Na4F3, which is the smallest finite system for a surface F-center prototype of bulk color centers, after the geometric relaxation in the excited state of ∼100 fs leading to the deformed cuboidal type of structure without breaking of bonds, different types of IVR have been identified in NeExNe signals by tuning the dump laser: one-mode selective energy leaving IVR, resonant, and restricted energy arriving IVR corresponding to the selection of different parts of the phase space. Dissipative IVR could not be identified in NeExNe signals of Na4F3 at low initial temperature on the time scale up to 2 ps in spite of 15 degrees of freedom. Due to similar structural and electronic properties such as F centers in bulk, these findings can serve as guidance for establishing the time scales for geometric relaxation and IVR in excited states of larger systems. © 2001 American Institute of Physics.

Notes: We present a theoretical study of a femtosecond photo isomerization process due to a nonadiabatic radiationless decay from the first excited state through a conical intersection occurring in one of the nonstoichiometric halide-deficient clusters with one excess electron (Na3F2). This is an extension of the adiabatic dynamics study presented in the accompanying paper [J. Chem. Phys. 114, 2106 (2001)] for other members of the NanFn−1 series characterized by a strong ionic bonding for which the "frozen ionic bonds" approximation has been justified, allowing consideration of the optical response of the single excess electron in the effective field of the other electrons. In this contribution we outline the extension of the ab initio Wigner-distribution approach to nonadiabatic molecular dynamics which combines the Wigner–Moyal representation of the vibronic density matrix with the ab initio multistate molecular dynamics in the ground- and excited electronic states including the nonadiabatic coupling computed "on the fly" in connection with the fewest-switches hopping algorithm. This scheme allows accounting for temperature-dependent initial conditions, for the propagation in the excited state and in the ground state after the passage through the conical intersection, and for probing in the cationic ground state as well as for deriving analytic expressions for the pump–probe signals which utilize an ensemble of classical trajectories obtained at low computational demand. Our approach permits investigation of the photo isomerization through the conical intersection due to the long amplitude motion in the Na3F2 system in full complexity, taking into account all degrees of freedom. After breaking of one metallic and of one ionic bond the conical intersection occurs at the linear geometry and involves states of different symmetry which differ in the translocation of the one excess electron or positive charge localized at the Na atom from one end to the other of the system and separates two isomers with Cs and C2v structures. From the analysis of the nonadiabatic dynamics, the time scales for the metallic bond breaking of ∼90 fs and for the ionic bond breaking of ∼220 fs, for the passage through the conical intersection after ∼0.4 ps and for the internal vibrational energy redistribution (IVR) of more than 0.9 ps for the individual isomers, have been determined. The simulated fs pump–probe signals confirm the above results and provide the information about the experimental conditions such as laser frequencies and pulse duration under which bond breaking of different type as well as the population of each of the two isomers after the passage through the conical intersection can be identified. In this contribution we show that the mechanism of the photo isomerization at a conical intersection due to a long amplitude motion can occur in atomic clusters and is not necessarily limited to organic photochemistry. © 2001 American Institute of Physics.

Notes: The quenching reaction Na(2P)+N2(1Σ+g,v,J)→Na(2S) +N2(1Σ+g,v',J') has been studied. Scattering calculations have been performed using the surface hopping trajectory method for the two energetically lowest potential energy surfaces of NaN2. The latter have been determined in an ab initio MRD-CI treatment. They exhibit a (avoided) crossing where quenching is likely to occur. Model potentials, which are constructed along the lines given by the ab initio surfaces, are used to investigate the influence of the shape of the potential on the scattering process. Cross sections and final translational energy distributions are compared with experimental data. Alignment and orientation as expressed by the collision induced density matrix have also been considered. Theoretical and experimental results show good agreement. The detailed analysis of the scattering calculations have provided with a better understanding of the quenching process.

Notes: Electronic and geometric structure of mixed neutral BeLik and cationic BeLi+k clusters (k=1–9) has been investigated employing ab initio configuration interaction quantum chemical methods. The values of atomization energies per atom for BeLik with k〈7 and for BeLi+k with k〈8 increase strongly with the cluster size. The binding energy per atom remains nearly unchanged for neutral BeLik with k=7–9 and cationic BeLi+k clusters with k=8 and 9. The quantities which measure cluster stability towards fragmentation processes predict high stabilities for BeLi6 and BeLi+7. The geometries of cluster, their stabilities as well as other properties can be easily interpreted as simple consequences of the nodal properties of the cluster MOs. The connection between the results obtained from this work and from the superatom model has been pointed out. The specific nature of the chemical bonding in mixed clusters obtained from quantum chemical investigations has been analyzed.

Notes: The configuration-interaction (CI) study of excited states of alkali metal clusters accounts for spectroscopical patterns obtained from (i) the photoelectron detachment spectra of their anions and from (ii) the photodepletion spectra of the neutral species, reproduces observed excitation energies, intensities for allowed transitions, and permits an assignment of cluster structures. For Na−2–4 the linear anionic geometries are responsible for the photoelectron detachment spectra. In the case of Na−5, both planar and linear anionic isomers seem to contribute to the recorded spectrum. The calculation of optically allowed states for Na3(C2v) and Na4(D2h) structures and oscillator strengths yield rich spectra which have been fully assigned to the observed ones. In the case of Na8, the Td and the related D2d forms give rise to an intense transition located at ∼495 nm and the weak fine structure shifted to the red in full agreement with the measured spectrum. A molecular versus collective excitation interpretation of absorption spectra is discussed.

Notes: The favorable geometries of small sodium clusters Na+n (n=3–9) are determined with the analytical gradient method in the framework of the ab initio SCF approximation. The transition from the planar towards three-dimensional cluster geometries is understood in terms of some basic quantum theoretical concepts. The binding energies per atom for Na+n clusters calculated with the MRD CI procedure increase, in general, as a function of n. Nevertheless, the atomization energy per atom as well as the ionization potential as functions of the nuclearity n exhibit well developed oscillations for even–odd n. Consequently, the fragmentation energy for the channel Na+n→Na+n−1+Na shows strong oscillations as well. This explains large abundances of cationic clusters with odd nuclearity found in some detection devices. The possible consequences for the fragmentation process of Na+n is discussed. It is found that the process Na+n→Na+n−2+Na2 is favorable for Na+5, Na+7, and Na+9.