The processes leading to the widespread presence of crystalline silicates throughout the galaxy¹ and the origin of the observed extended red emission in diffuse galactic background,² currently believed to be due to silicon nanoparticles,³ are still far from being understood. One of the most abundant oxygen-bearing condensable species in molecular astronomical regions is SiO. It has been conjectured that silicate formation probably proceeds via the agglomeration of these molecular species.^4-7 Since the ratio of oxygen to silicon in SiO is 1 while it is 2 for SiO₂, one of the important questions is whether the passage occurs in a single step or through the gradual oxygen enrichment of the agglomerated species. In the later case, what are the intermediate steps and what is the minimum size that marks the beginning of the oxygen enrichment. Since an enrichment of a portion must make the other part oxygen deficient, it is pertinent to ask if the origin of silicon nanoparticles is also rooted in the agglomeration of SiO units. If so, when do the Si-Si bonds first appear as the SiO motifs grow and how do the silicon-rich cores develop that could lead to silicon nanoparticles as the clusters grow? Answers to these questions not only are of general interest in the evolution of planetesimals but are critical to a fundamental understanding of the interstellar extinction.⁸

In this work, we use a synergistic approach combining detailed experimental investigations on the clustering of SiO units in molecular beams and first principles electronic structure studies to elucidate the condensation processes at the nanoscale that can lead to the formation of silicates⁹ on one hand and silicon nanoparticles¹⁰ on the other. We demonstrate that as SiO units assemble to form bigger clusters,^11-13 the chemistry drives the agglomeration toward structures that are silicon rich at the center and oxygen rich (often resembling SiO₂ motifs) at the periphery. Further, there are specific (SiO)_n sizes for which the energy gained in the addition of the subsequent SiO to the existing (SiO)_n structure can break the cluster into an oxygen rich and an oxygen poor fragment. The initial oxygen rich fragments growing out of such processes have an oxygen-to-Si ratio that is marginally higher than 1. However, these fragments, once generated, act as the seed for further enrichment by subsequently combining with selected (SiO)_n clusters to generate fragments that are even richer in oxygen and eventually leading to the SiO₂ formation. It is shown that the smallest oxygen enriching cascade involves Si₅O₆, Si₃O₄, Si₂O₃, as the intermediate products and eventually leads to SiO₂. The studies also demonstrate that the extended red emission generally attributed to silicon nanoparticles and the recently discovered blue luminescence attributed to polyaromatic hydrocarbons¹⁴ could also have contributions from emissions coming from Si_nO_m clusters. Indeed, the calculated gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital ranges from 0.84 to 3.84 eV. It is further interesting to note that the Si core formation begins at a very rudimentary stage, a (SiO)₅ cluster already shows the hallmark of a silicon-silicon bond. Apart from the interest in astrophysics, some of the (SiO)_n nanostructures obtained in our work are quite unique and may find applications in other areas.

The current experimental studies were carried out in a femtosecond laser based time-of-flight mass spectrometer system equipped with a laser vaporization (LaVa) source.^15-17 The silicon oxide clusters were generated employing three different methods to examine the nature of the evolving clusters. Figure 1 shows representative distributions produced through the laser vaporization of SiO solid under an argon environment and photoionized using 1-2 mJ, 800 nm, 50 fs pulses, The product clusters were analyzed using a conventional time-of-flight mass spectrometer. For comparison purposes, other experimental methods were employed including the study of silicon oxide clusters by vaporizing silicon under a helium/oxygen environment and analyzing the resulting clusters as described above and in other cases extracting cluster cations directly from the source that are formed in the plasma-like environment existing in the LaVa source which employs a Nd:YAG laser, operated with approximately 4 mJ/pulse photons at 532 nm. In yet another experiment, the clusters were generated by vaporizing solid SiO₂, whereupon cations were directly extracted. Since we are primarily interested in the formation of SiO₂ from SiO, in this paper we only present results on clusters originating in agglomerations of SiO molecules from vaporized SiO solid, but the main result of the findings was that with all methods, polymers of varying ratios of SiO and SiO₂ were prominent evolving species.

Figure 1 Mass spectra of clusters formed by vaporizing solid SiO and ionizing the resultant clusters.

In addition to pure (SiO)_n⁺ clusters, the data presented in Figure 1, reveal the presence of single oxygen enriched species, namely, Si₂O₃⁺, Si₃O₄⁺, Si₄O₅⁺, Si₅O₆⁺, Si₆O₇⁺, and small amount of Si₇O₈⁺. Also interesting are formation of the oxygen-deficient clusters and in particular the pure silicon clusters, though their origin through SiO photochemistry cannot be discounted. There are variations in the intensity across each series. In the pure (SiO)_n⁺ clusters, there is a precipitous drop in intensity from (SiO)₅⁺ to (SiO)₆⁺. A similar decline in intensity is noticeable from Si₆O₇⁺ to Si₇O₈⁺. In addition there is a large peak at Si⁺. The oxygen-rich species Si₂O₃⁺ and Si₃O₄⁺ were also observed in the beams where clusters were formed through vaporization of silicon under oxygen or formed through the vaporization of solid SiO₂, indicating that they are particularly stable. The most surprising experimental finding is the conspicuous absence of SiO₂⁺ in all the experiments except for very minor intensity of the cations extracted from the silicon vaporized under oxygen. This could be due to a low photoionization cross section at the wavelengths employed in these experiments. Our focus on the other hand is on the origin of the Si_nO_m species and hence this possibility does not bear directly on the results published in this paper. We easily detect species of all other Si to O ratios in the beam.

The experimental observations raise four startling questions. (1) Why do pure (SiO)_n clusters exhibit a marked drop in intensity at n = 6? (2) What processes lead to the formation of oxygen-enriched species? What is the relative stability of Si_nO_n+1 species and does SiO₂ form in this enrichment cycle? If yes, why is it not seen in the cation experiments and are there alternate ways to detect its presence? (3) Does the clustering of SiO units lead to the formation of silicon nanoparticles? Is the same mechanism responsible for the presence of Si⁺ and small Si_n⁺ clusters? (4) What are the HOMO-LUMO gaps and optical excitation energies in Si_nO_m clusters and do they lie in the regions covering from infrared to blue observed in experiments? Since one starts with SiO molecules, the most likely mechanism of growth is the addition of SiO units. The natural starting point is then investigating the clustering of SiO molecules.

Motivated by the above observations, we undertook theoretical investigations on the clustering of SiO units. The theoretical studies are based on first principles calculations using density functional theory¹⁸ and generalized gradient approximation¹⁹ for exchange and correlation. The total energies, equilibrium geometries of clusters of Si_nO_n (1 n 12), Si_nO_n+1 (1 n 12), and Si_nO_n-1 (1 n 12) clusters and their cations were calculated using a linear combination of atomic orbitals-molecular orbital (LCAO-MO) approach. The atomic orbitals were represented by the double-zeta valence polarization basis set.²⁰ The calculations were carried out using the deMon code²¹ developed by Koester and co-workers. An auxiliary basis set was used for the variational fitting of the Coulomb potential²² and the numerical integration of the exchange-correlation energy and potential were performed on an adaptive grid.²³ The minimum structures were fully optimized in delocalized internal coordinates without constraints using the rational function optimization method and the Broyden, Fletcher, Goldfarb, and Shanno update.²⁴ Several initial configurations were used in order to prevent getting trapped in local minima of the potential energy surface.

Figure 2 shows the ground-state geometries of Si_nO_n clusters. Note that the ground states for Si_nO_n containing 2-4 are all open ring structures. The structure of Si₅O₅ is a double ring sharing a common Si atom. This cluster marks the beginning of the silicon core and the geometries of higher Si_nO_n clusters are all marked by silicon-rich cores of increasing size. In fact, the structure of Si₈O₈ can be looked upon as an interior Si₄ square with edges decorated with SiO₂ molecules. By the time one reaches Si₁₂O₁₂, the Si core has grown to a cube of eight Si atoms. This indicates a natural tendency for Si_nO_n clusters to segregate into Si-rich cores with oxygen-rich and particularly SiO₂ outer shells. It is then feasible that the extended red emission^3,10,25 discovered in 1980 originates in the silicon cores of the Si_nO_n aggregates. Apart from its astrochemical interest, the above findings may enable SiO aggregation on surfaces as a possible approach to forming extended pure silicon nanostructures.^13,26 We would like to add that Zhang et al.¹³ have also reported studies on (SiO)_n clusters where they assumed a tetrahedral-like Si core. Our structures on small sizes (n 6) agree with their findings; however, we find more stable structures at larger sizes.

Figure 2 Calculated ground-state geometries for SinOn. The total atomization energy and selected bond lengths in angstroms are listed. Si atoms are in gray, O atoms are in red.

While the above calculations indicate segregation, they do raise a puzzle. SiO is a very stable molecule with an atomization energy of 8.21 eV while SiO₂ only has an atomization energy of 12.78 eV or an atomization energy of 6.39 eV per SiO bond. Si₂ has binding energy of only 2.45 eV and hence the formation of Si-Si bonds and SiO₂ bonds would both seem to be energetically unfavorable. What then leads to the Si-rich cores and oxygen-rich outer shells? The answer to this riddle lies in the chemistry of atoms. Si atoms are marked by tetrahedral bonding in the bulk while higher coordinations are observed in Si_n clusters. On the other hand, oxygen is divalent. As Figure 2 shows, in all the clusters, the oxygen atoms are generally bonded to two other atoms. As the cluster size grows, a compact structure demands higher coordination in the interior. It then provides a natural selection process for oxygen to be transferred to the outer layers. It is this special chemistry that leads to the observed evolution of the structures. How does the segregation affect the overall stability of the Si_nO_n species? Are there processes that can take advantage of this segregation to isolate the exterior SiO₂?

To understand the evolutions in geometries and to identify any particularly stable species, let us first consider the stability of pure (SiO)_n clusters. To this end we calculated the atomization energy (AE) representing the energy required to break a (SiO)_n cluster into n Si and n O atoms

Figure 3 (A) Mininum fragmentation energy (FE) (eq 1) of SinOn clusters. (B) Ionization potentials of SinOm clusters. (C) HOMO-LUMO gap for SinOm clusters.

The FEs shown in Figure 3 show a dramatic increase from n = 6 to 7. This would make (SiO)₆ as a relatively unstable species. Could this decreased stability lead to fragmentation into subunits with uneven silicon-oxygen composition? An investigation of this possibility requires ground states for oxygen-rich and silicon-rich clusters. To this end, we determined the ground-state geometries of Si_nO_n+1 and Si_nO_n-1 clusters. The key issue is then to identify clusters where the energy gained in combining the two units is sufficient to break it into an oxygen-rich and a oxygen-poor fragment. We thus analyzed the energetics of the reaction

The last mystery is the absence of SiO₂ in Figure 1. The mass spectra shown in Figure 1 are obtained by ionizing the neutral species formed in the beam via a laser whose wavelength is around 800 nm (or 1.55 eV). To examine the feasibility of such a process, one must consider the energy required for ionizing the various species. To this end, we calculated the vertical ionization potential of all the Si_nO_n, Si_nO_n+1, and Si_nO_n-1 species. These are shown in Figure 3b. Note that SiO₂ has the highest ionization potential of 12.19 eV. It would take seven photons to ionize the clusters. Further, the HOMO-LUMO gap in SiO₂ is 3.8 eV, making the absorption cross section really small. The lack of SiO₂ in Figure 1 is then simply related to the inability to ionize the species. On the other hand, SiO₂ has an electron affinity of 1.87 eV, and therefore it should be possible to detect them in experiments on anions. Indeed, the mass spectra of anionic clusters²⁸ generated by vaporizing silicon in a helium atmosphere containing O₂ show the formation of SiO₂^- whereas our experiments detecting cations generated by photoionizing neutral species do not show any significant SiO₂⁺ species!

The final issue relates to the occurrence of extended red emission^3,10,29 and the recently observed blue luminescence.¹⁴ The extended red emission manifests itself through a broad, featureless emission band with peaks occurring in the range 610-820 nm. The blue luminescence corresponds to wavelength in region 357-486 nm. In the past, these have been associated with polycyclic aromatic hydrocarbons (PAHs) notably molecules containing three to four aromatic rings. Our electronic structure calculations indicated that many of the Si_nO_m species have HOMO-LUMO gaps that could lead to emissions in these regions. This is seen in Figure 3c, which shows the HOMO-LUMO gap in Si_nO_n, Si_nO_n+1, and Si_nO_n-1 clusters containing up to 16 Si atoms. Note that the gaps vary from 0.84 to 3.84 eV. It is then interesting to explore if these clusters could also contribute to these emissions. To examine this possibility we performed time-dependent density functional theory (TD-DFT) calculations as implemented in the Gaussian 03 code.³⁰ The B3LYP exchange correlation functional was used because it is known to provide better optical absorption energies. A 6-31+G* basis set using the same generalized gradient as in the previous calculations was employed for structure optimization and TD-DFT calculations. This method has been previously shown to yield accurate results in other silicon systems. Figure 4 shows the results for Si_nO_n, Si_nO_n+1, and Si_nO_n-1 clusters. For the Si_nO_n and Si_nO_n+1 clusters, the wavelengths range from 225 to 850 nm. The inclusion of Si_nO_n-1 clusters extends the range to 1150 nm. These frequencies include the observed ERE and BL. Note that the above calculations examine the absorption spectra. A calculation of the emission spectra requires further relaxations and will form the basis of a future publication.

Figure 4 Optical gaps for the SinOm clusters.

To summarize, the present work answers two main questions that have remained unanswered for a long time. It provides a microscopic mechanism that leads to the formation of oxygen rich with SiO₂ as the terminal member via the clustering of SiO molecules and their collisions. It shows that the clustering of the SiO molecules results in structures marked by pure Si_n cores and that the extended red emission observed in interstellar space could be originating in these cores. Apart from its applications in understanding the interstellar extinction and blue luminescence, the present work provides a workable approach to generate silicon nanostructures by assembling SiO molecules.

Acknowledgment

We gratefully acknowledge the assistance of S. E. Kooi and B. D. Leskiw, in performing the measurements presented in Figure 1, and helpful discussions with them and J. A. Nuth and B. Donn during the course of the study. A.W.C. gratefully acknowledges support from U.S. Air Force Office of Scientific Research Grant F49620-01-1-0328 for the experiments on SiO clusters. A.C.R., P.A.C., J.U.R., and S.N.K. acknowledge financial support from the U.S. Department of Energy Grant DE-FG02-02ER46009 for the theoretical studies. A.A. acknowledges support from NASA's Cosmochemistry and Origins of the Solar System Program.