Sodium trimers

Higgins J, Ernst W E, Caiiegari C, Reho J, Lehmann K K, Scoies G and Gutowski M 1996 Spin poiarized aikaii ciusters observation of quartet states of the sodium trimer Phys. Rev. Lett. 77 4532... 

Gomez Llorente, J.M. and Taylor, H.S. (1989). Spectra in the chaotic region A classical analysis for the sodium trimer, J. Chem. Phys. 91, 953-961. 

Na2 (2) the possibility of controlled "hot band" formation through disruption of the free jet expansion allowing the mapping of vlbronic structure in the ground electronic state of sodium trimer, and (3) the observation of very efficient energy transfer between sodium dimer and polyatomic sodium. The current studies are discussed in the light of recent experimental and theoretical characterization of Nas. Preliminary studies of the reaction Nas + Cl - NaCl + Na2 are discussed as they pertain. to the dissociation energy of Naa. 

In the course of similar experiments in which the liquid nitrogen baffle above is removed, an intriguing phenomena has been observed. We have been able to induce sodium D-line fluorescence upon single photon pumping at energies far lower than that required to simultaneously dissociate dimeric sodium and produce emission from excited atoms. The atomic fluorescence and its characterization will be the subject of our following discussion. Briefly, we have observed and characterized laser induced atomic fluorescence upon photodissocia-tlon of sodium trimers formed under a variety of conditions. 

Laser Induced Atomic Fluorescence and Sodium Trimer Fluctuation Bands... 

Peak Separations Sodium Trimer Photodissociation Spectrum... 

The intensities of the 83/2 and Pi/2 fluctuation bands in Figure 8 are in the ratio 2 to 1, virtually a statistical distribution however, the relative Intensity distributions for the Pi/2 and Pa/2 fluctuation bands differ notably. Much more pronounced differences are observed for the "hot bands" depicted in Figures 6 and 7 where the P3/2/ Pi/2 ratio varies with exciting frequency and in many instances approaches 8/1. This difference in intensity ratio must reflect very different geometries for the lower discrete states from which pumping occurs in bound-free transition. Again such a result would appear to correlate well with the theoretical analysis of the sodium trimer surface. Martin and Davidson predict that a linear symmetric conformation lies only 1050 cm above the ground... 

In order to augment the upper bound for the Naa dissociation energy obtained in the studies outlined above, we have undertaken an experiment involving sodium trimer oxidation. The experiment involves the study of the reaction... 

Martin and Davidson ( 3) have examined the structure of the sodium trimer at the SCF-CI level and find results that are very similar to those which have been obtained for Lis. Nas has an optimum C2V geometry with 82 symmetry, a Ai configuration corresponding to a saddle point lying only 0.6 kcal/mol higher in energy. The linear form lies only 3 kcal/mol above the minimum 82 geometry. The Nas molecule is bound with respect to the dissociation limit Na2 + Na by 8.5 kcal/mol. 

As mentioned in Section 33.2, the many-body expansion cannot be expected to work for metals. One reason is that most atoms forming metals have open-shell ground states of symmetry other than S, therefore it is difficult to determine quantum states of the subsystems needed in the definition of the expansion, cf. Section 33.10. The second reason is that the complete delocalization of the conduction electrons results in the electronic structure of a metal that is very far from that of monomers. The first problem does not occur for alkaline-earth metals or for high-spin alkali-metal clusters, and the many-body expansion can be defined for such clusters. However, this expansion appears to be very slowly convergent [106-108]. For some specific information about the spin-polarized sodium trimer, see Section 33.10.2. 

The nonadditive effects are much more important if more than one monomer is in an open-shell state. For example, it has been found both experimentally [107] and theoretically [108,167] that the three-body force plays a critical role in stabilizing the sodium trimer in the spin-polarized " A2 state. Similar, although gradually less and less pronounced stabilization effect has been predicted [108] for heavier high-spin aUcali-metal trimers, whereas for the hthium trimer the three-body effect has been found to be really dramatic— the complete potential is at least four times more attractive than... 

Willner, K., Theoretical study of weakly bound vibrational states of the sodium trimer Numerical methods prospects for the formation of Na in an ultracold gas, Thbse de doctoral (PhD thesis) and Doktor der Naturwissenschaften dr. rer. nat., Universite Paris-Sud XI and Universitat Hannover, Qrsay (France) and Hannover (Germany), 2005. 

As mentioned earlier, the sodium trimer represents a well-known example for the E e JT effect in the groimd as well as in several excited electronic... 

In the second part of this chapter (Sect. 3.2), different wave packet propagation phenomena in excited alkali trimers are discussed. The time-resolved pseudorotation of the sodium trimer is presented in Sect. 3.2.2. Last but not least, applying laser pulses of the same wavelength but of different pulse width enables a mode-selective preparation of the trimer, hence controlling its dynamics (Sect. 3.2.4). Wave packet propagation on a repulsive PES (Sect. 3.2.5), studied on the potassium trimer, leads to the phenomena of ultrafast photodissociation, which then is the topic of the subsequent chapter. 

In Sects. 3.2.1-3.2.4 a detailed analysis of the sodium trimer excited to its electronic B state is presented. A short review of Naa, with special interest in the spectroscopy of its electronic B state, is given in Sect. 3.2.1. Employing laser pulses of moderate intensities with durations of either 1.4 ps or llOfs to excite the Naa B state, different vibrational modes of the excited trimer are detected selectively in the real-time spectra. While the picosecond laser... 

The point symmetry group of the neutral sodium trimer is Dah- In this symmetry group two of the three vibrational degrees of freedom (see Fig. 3.38), the symmetric bend Qx and the asymmetric stretch Qy, are energetically degenerate. The third normal coordinate is the totally symmetric stretch Qs-... 

Real-Time Pseudorotation of the Sodium Trimer. A typical real-time spectrum obtained with picosecond excitation is shown in Fig. 3.41. The excitation wavelength is 620 nm, which corresponds to an intense resonant peak in the TPI spectrum. A clear beat strucure, symmetrical about the zero of time, is observed. The period amounts to 3 ps. The oscillation is damped with a time constant of about 3.5 ps. A constant offset is present, due to TPI... 

The first theoretical calculations to describe these real-time spectra were based on a simple two-dimensional model of the vibrating/pseudorotating sodium trimer [380]. Ab initio energy surfaces served as guidance for constructing model surfaces. The molecular dynamics of the Naa B system were simulated by the representative time-dependent wave packet Its norm... 

Real-Time Observation of the Sodium Trimer s Breathing Mode. 

In the case of the sodium trimer the Hamilton matrix of the corresponding Schrodinger equation takes a 3 x 3 form. The diagonal elements Ha,... 

In the case of the sodium trimer (see Sect. 3.2.4) the relevant excitation regions in the B state have been determined as between T.Oao and 7.2ao in the Qs coordinate the centers of the excitation regions in the pseudorotation coordinates lie at < = 60°, 180°, 300° and q = 0.56ao. These regions have a diameter of 0.24ao. 

Most of the pump control experiments carried out so far have used diatomic molecules, because in such simple systems, with only one vibrational degree of freedom, the dynamics can be controlled relatively easily. In larger molecular systems with three or more vibrational degrees of freedom, the situation becomes much more complicated and it is an interesting question whether the concept of controlled molecular dynamics can still be realized. Here, it is shown that different vibrational modes of the sodium trimer can be selectively excited during an electronic excitation with ultrashort laser pulses. For this reason, it should in future be possible to control subsequent reactions. The relevant control parameter in these investigations is the duration of the pump pulse. 

As performed for the sodium trimer, configuration interaction ab initio calculations of the PES, combined with time-dependent quantum dynamical simulations, are essential for further comparisons and for a detailed picture of the dynamics. 

The sodium trimer excited to the electronic C state can be regarded as a fascinating model system, which manifests ultrafast predissociation dynamics. While stationary and nanosecond-pump probe spectroscopy gave the first hints that this excited state photodissociates rather fast, real-time TPI spectroscopy opens a window to directly observe these ultrafast processes. But let us first start with a short review of the spectroscopy of this excited electronic state. 

Radiative decay will reduce the real-time signal because the energy of the probe pulse will be not sufficient to ionize these trimers directly. In the case of fragmentation the excited sodium trimer will break into, for example, an excited dimer (Na2) and a monomer (Na), reducing the generated population as well. Therefore, the decreasing real-time signal can be described by the decay function... 

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