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Numerical Simulation

Our research activities are centered at the crossroad of atomic scale modeling and real-life experiments and between fundamental aspects and potential applications. Our simulations involve scientific computations on high performance workstations (we are currently installing our own computer cluster due to a donation from the ONERA) and on state-of-the-art supercomputers (IDRIS and CERMM). We use an arsenal of computational tools that have their roots in quantum chemistry, classical and quantum mechanics and statistical thermodynamics. We maintain an intensive collaboration with experimentalists (LSPM, Thales, CEA, EADS, GREMI, DCPH and LPICM) because the experimental confirmation is crucial to judge the reliability of our theoretical work. Recently, we are particularly interested in the “chemistry with a hammer” for non-adiabatic reactions and in the dynamics of the growth, crystallization and deposition of hydrogenated silicon nanocrystals in plasma reactors.The main goal of our research projects lies in the creation of a “synergy” between experiments and theory. To this end, we are extensively employing the methods of classical and ab initio molecular dynamics simulations to predict, explain and guide experiments presently on-going in our own institute or elsewhere. Our simulations allow us to “visualize” the motion of atoms and molecules at the atomic scale as chemical reactions occur (“Virtual Microscope”) providing invaluable information about their molecular mechanisms and kinetics. Dynamical studies are essential since they provide a direct link between potential energy surfaces determined by electronic structure calculations and experimental measurements of the chemical dynamics. After a detailed investigation of the creation of mixed van der Waals clusters by the "pick-up" technique (H. Vach, PRB 59, 13413 [1999]; JCP 113, 1097 [2000]) and the scattering of those mixed rare-gas clusters by surfaces (PRB 61, 2310 [2000]), we are now investigating the dynamics of chemical reactions related to processes taking place in the plasma reactor.

Growth, crystallization and deposition of hydrogenated silicon clusters in a plasma reactor


Based on extensive fluid model calculations (K. Hassouni), we define our “realistic” experimental plasma conditions. We can then follow the dynamics of the cluster growth as a result of the consecutive capture of plasma molecules and radials (SiH4, SiH3, SiH2…) by means of quantum molecular dynamics simulations. In those calculations, the electronic Schr
ödinger equation is solved at each time step of the trajectory calculations (i.e. "on the fly"). A representative result of the cluster growth is shown in the image below:

By means of first-principals molecular dynamics simulations under realistic plasma reactor conditions, we showed that the resulting hydrogenated silicon clusters always turn out to be amorphous. Their interaction with atomic hydrogen, however, can readily make them undergo a phase change to crystalline structures (H. Vach, Q. Brulin, Phys. Rev. Lett. 95, 165502 [2005]; highlighted in NATURE MATERIALS 4, 878 DEC [2005]). The outcome of these hydrogen-induced crystallization processes crucially depends on the relative fluxes of atomic and molecular hydrogen present in the plasma reactor. Those conclusions were experimentally confirmed two years after our theoretical prediction.

For the resulting nanocrystals, we can calculate the electronic structure
and the corresponding Raman and absorption spectra by means of ab-initio theoretical spectroscopy in order to allow their experimental identification (here, for a structure without an inner Si atom):

Using model-potential molecular dynamics simulations, we are presently investigating the collision of those hydrogenated silicon structures and their surface deposition:
The goal of above studies is to be better understand the crucial role that nanocrystals play to achieve the outstanding properties of polymorphous silicon materials used in photovoltaic solar cells. At present, we are investigating how the substrate deposition of nanocrystal can be used for high-speed epitaxial growth of crystalline silicon films.

N. Ning and H. Vach
Deposition dynamics of hydrogenated silicon clusters on a crystalline silicon substrate under typical plasma conditions
J. Phys. Chem. A114, 3297-3305 (2010)


Luninescence quenching in germanium nanocrystals: the role of compression, surface reconstruction, optical excitation, and spin-orbit splitting

Germanium nanostructures have been predicted to exhibit very strong HOMO-LUMO transitions, contrary to the respective silicon structures. However, few experiments have found luminescence that can clearly be attributed to the recombination of quantum-confined electron-hole pairs. Investigating its pressure dependence, we show that the HOMO-LUMO transition in bulk-like hydrogenated Ge and Si nanocrystals can be explained in view of the bulk band structures, which leads to strong transitions in Ge, but not in Si. We identify three effects that strongly limit the transition probabilities in Ge nanocrystals, thus explaining the apparent contradiction with experiments: compression, as found in many experiments, surface reconstructions, and the excitation of the electron-hole pair itself. Calculations of spectra using time-dependent density-functional theory confirm the ground-state calculations.

We have thus been able to explain the apparent contradiction between the theoretical prediction of strong photoluminescence (PL) in Ge NCs and the fact that it has not been observed experimentally.

Combining electronic structure calculations and molecular dynamics simulations, we are presently exploring how the absorption spectra of hydrogenated silicon clusters change with temperature. Such an investigation is of crucial importance since most theoretical spectroscopic studies are actually performed
at an unrealistic temperature of zero Kelvin.

H.-Ch. Weissker, N. Ning, F. Bechstedt, and H. Vach “Luminescence and absorption in germanium and silicon nanocrystals: The influence of compression, surface reconstruction, optical excitation, and spin-orbit splitting”
Physical Review B 83, 1254131-1254136 (2011).

Spontaneous self-assembly of silica nanocages into inorganic framework materials


The possibility of the formation of different silica nanostructures based on fully coordinated spheroidal nanocages (SiO2)24
is theoretically investigated using a pair-wise potential and the ReaxFFSiO reactive force field. Molecular dynamics simulations at room temperature predict that while these nanocages are thermally stable, they spontaneously undergo dimerization upon contact by forming two siloxane bridges. The corresponding reaction pathways obtained with both methods are quantitatively confirmed by electronic structure calculations performed at the Hartree-Fock and density functional theory levels. The barrierless dimerization of silica nanocages is the first step of subsequent polymerizations into strongly bound inorganic materials. Routes to polymerization and possible applications are discussed.


A common feature of all dimerization processes between silica nanocages is the high reactivity of the double-bridge Si2O2 rhombi. These units are progressively eliminated as the polymerization continues. As a result, only the surface of the growing material remains reactive. As the emerging structure becomes larger, it thus approaches more and more the features of a chemically inert material. Moreover, the addition of each (SiO2)24 nanocage decreases the total binding energy of the polymerizing structure considerably (by about 150 kcal/mol), yielding an ever more stable structure that can, for instance, withstand considerably higher temperatures than the monomer nanocage discussed above. These properties could be suitable for the creation of adhesives and protective coatings. Due to its dielectric character, the polymerized (SiO2)24 units may be useful for manufacturing nanoscale capacitors in miniature electronic devices, which should be operational over a broad temperature range. Due to its high porosity and its high surface area, the material might also be suitable for use in chromatography columns, or as a substrate for heterogeneous catalysis. Finally, due to the periodicity of
the nanocages, the (SiO2)24-based solid might be employed as a storage matrix for small metal clusters and thus find application as a three-dimensional photonic crystal for X-rays. Since the polymerized (SiO2)24 should be chemically inert, such devices could work in a wide range of environments.

N. Ning, F. Calvo, A.C.T. van Duin, D. J. Wales, and H. Vach,
Spontaneous Self-Assembly of Silica Nanocages into Inorganic Framework Materials
Journal of Physical Chemistry C 113, 518-523 (2009)
 

“Chemistry with a hammer”


Some chemical reactions do simply not take place since the involved barrier heights are too high to be overcome under normal reaction conditions. For the “Chemistry with a hammer”, Sylvia Ceyer (MIT) was the first to propose placing such reactants inside a van der Waals cluster and making this cluster violently hit a hard surface. Due to the impact, extreme conditions of pressure and temperature are experienced by the reactants inside the cluster. At the same time, the reactants cannot easily “escape” since they are sterically hindered by the surrounding rare-gas cluster. Consequently, unusual  chemical reactions between the concerned reactants can take place. In our work, we extend this basically “mechanical concept” to a quantum level and we show that common rules of quantum mechanics might break down due to the surface impact of those clusters.
More in detail, combining classical molecular dynamics simulations with high level, multiconfigurational ab initio calculations, we demonstrate that even relatively mild collisions between ground state oxygen molecules can readily lead to the formation of highly reactive singlet oxygen molecules via a novel ‘‘ladder climbing’’ mechanism. We employ our findings to shed some light on two recent experiments that have remained poorly understood until now. The first one concerns the highly efficient cluster-catalyzed etching of silicon surfaces, whereas the second one involves a yet to be explained ‘‘dark channel’’ observed for the ozone photolysis in the stratosphere.

FIG.: (O2)2 potential energy surfaces (PES) as a function of the experimentally available intermolecular distance R(O2-O2) with both oxygen molecules kept at their equilibrium internuclear distance in an H configuration.
FIG.: CASPT2 potential energy surfaces for the oxygen dimer (O2)2 in its H configuration and at its equilibrium intermolecular distance as a function of the internuclear O-O distance in one O2 molecule with the other molecule always kept at its equilibrium internuclear distance; the bold line only serves to highlight the proposed ladder climbing scheme

We have shown that even relatively mild molecular collisions can lead to a breakdown of the Born- Oppenheimer approximation. As a result, the experimentally observed etching of silicon surfaces by molecular oxygen clusters becomes possible due to a non-adiabatic extension of the chemistry with a hammer dynamics which allows violation of quantum mechanical selection rules. Consequently, lower energy barrier reaction pathways can be followed that would otherwise be forbidden. Moreover, our proposed non-adiabatic ladder climbing mechanism may help elucidate a long-lasting  controversy concerning a relaxation effect occurring during ozone photolysis in the stratosphere.
The electronic “ladder climbing” process can not only be achieved by molecular vibrations, but also by molecular rotations. More precisely, complete active space self-consistent field augmented with triplezeta polarizable basis set quantum chemistry calculations of a compressed (O2)2 dimers in various configurations reveal the emergence of possible pathways for the generation of electronically excited singlet O2 molecules upon cluster compression and rotational excitation. This unusual excitation
mechanism becomes possible due to electronic curve crossings in the potential energy surfaces (PES) and due to an important spin–orbit coupling. Extrapolation of the model (O2)2 results to larger clusters suggests a dramatic increase in the population of electronically excited O2 products. This increase may account for the experimentally observed cluster-catalyzed oxidation of silicon surfaces, via singlet oxygen generation induced by cluster impact, followed by surface reactions of highly reactive singlet O2 molecules. Extensive molecular dynamics simulations of (O2)n clusters colliding onto a hot surface indeed reveal that cluster compression is sufficient under typical experimental conditions for nonadiabatic transitions to occur. This work highlights the importance of non-adiabatic effects in the “chemistry with a hammer."

H. Vach, N. Nguyen, Q. Timerghazin, G.H. Peslherbe,
“Nonadiabatic ladder climbing during molecular collisions”
Phys. Rev. Lett. 97, 143402 (2006)

T.-N. V. Nguyen, Q. K. Timerghazin, H. Vach, and G. H. Peslherbe
“Mechanically-Induced Generation of Highly Reactive Excited-State Oxygen Molecules in Cluster-Surface Scattering”
J. Chem. Phys. 134, 64305-64317 (2011).
 
 

Aromatic Silicon Nanoclusters

We report a new nano-crystalline form of silicon that gives birth to pure hydrogenated silicon nanoclusters that absorb light in the ultraviolet, visible and infrared spectral region despite their small size of only 1nm and without the need for expensive or toxic metal atoms. Based on first-principles calculations, we demonstrate that those pure, but over-coordinated silicon nanocrystals are more stable than any other known silicon clusters due to electron delocalization and that they form spontaneously via self assembly (see above).

Silicon nanocrystals (SiNC) have been attracting interest in many fields of nanoscience and nanotechnology for a long time - not only because of the high abundance and non-toxicity of silicon, but also because of their quantum confinement that makes it possible to tune their absorption and emission spectra by simply changing their size. So far, however, the spectral absorption tuning of pure SiNC is limited to the ultraviolet frequency range. To extend the response to the visible and infrared region, metal atoms are often incorporated in the nanocrystals. Unluckily, those metals are often expensive or toxic. Taking advantage of the sometimes surprising nature of chemical bonds in nanoscale objects, we present here a fundamentally novel approach that is based on structure-induced electron-deficiency to cause strong electron delocalization. Based on first-principles calculations, we demonstrate that the resulting pure silicon nanocrystals are unusually stable and do not only absorb light in the ultraviolet, but also in the visible and infrared spectral region without the need for any metal atoms.
Figure 1: Density of states (DOS) analyses of (a) the empty Si18H12 and (b) the filled Si19H12 finite nanotubes. Note the dopant-like behavior of the additional over-coordinated central Si atom causing the appearance of the supplementary peak inside the forbidden gap of the empty nanotube.

The additional peak that appears in the forbidden gap of the empty Si18H12 nanotube due to the insertion of the center Si atom corresponds to the highest-occupied molecular orbital (HOMO) of the Si19H12 nanocrystal which we present in Figure 2.

Figure 2: Different views of the isovalue contour plots of the highest-occupied molecular orbital (HOMO) representing the electron density obtained at the B3LYP/6-311++G** level with an isovalue of 0.02 e/Å -3 for the filled Si19H12 nanocrystal: (a) side, (b) vertical cut through side, (c) top and (d) bottom view. Note the involvement of the center silicon atom for the electron distribution of the HOMO. 

In the same way, we show in Figure 3 how the optical absorption spectrum that is limited to the ultraviolet for the empty structure extends through the visible until the infrared region due to the insertion of the center silicon atom. Needless to say that such an extension of spectral response might readily lead to the environmentally friendly replacement of other expensive or toxic nanocrystals by the presently proposed ones. This replacement might lead to immediate applications in the most various fields of research reaching from potential cancer treatment where the use of gold and silver nanoparticles has been proposed since the resulting laser light absorption at about 800nm (compare Fig. 3) yields optimal efficiency to photovoltaic devices where PbS, PbSe, CdS and CdSe based quantum dots are presently employed to extend energy conversion from the ultraviolet to the infrared region. The proposed over-coordinated SiNC might also be considered for being added to the conventional SiNC employed in recent solar cell and light-emitting diode devices that ingeniously combine the  properties of semiconductor nanocrystals with conjugated polymers (Nano Lett. 2011, 11, 1952–1956).

 
Figure 3: Absorption spectra of Si18H12 and Si19H12; i.e. a comparison between an empty and a filled finite hydrogenated silicon nanotube. Due to the presence of the inner silicon atom, the latter nanocrystal does not only absorb light in the ultraviolet region, but also in the visible and in the infrared.

The proposed nanocrystals are predicted to remain thermally stable at temperatures exceeding 1200K. This high stability makes their experimental synthesis very likely and facilitates their applications. In addition, their properties perfectly comply with those expected for aromatic substances: first, all three hexagons are perfectly planar; second, all silicon-silicon bonds within each of the three hexagons are equivalent in length; third, the introduction of the center silicon atom increases the stability by more than the cohesive energy of bulk silicon which cannot be understood on the basis of regular covalent silicon bonds and which makes them more stable than the experimentally known Si29H24 nanocrystal; fourthly, there are six p-electrons being delocalized and finally, both its magnetic susceptibility exaltation and its magnetic shielding exceed the ones of benzene.

H. Vach
“Ultrastable Silicon Nanocrystals due to Electron Delocalization”
Nano Lett. 11, 5477-5481 (2011).



Electron-deficiency Aromaticity


Using a variety of theoretical methods, such as fluid model computations, molecular dynamics simulations and ab initio calculations, we showed that it is possible to obtain aromatic behavior with simple, but extremely stable hydrogenated silicon molecules, without the need of multiple bonds - and therefore without the incorporation of bulky molecules of substitution. In this sense, we are following a completely new approach that seems to be in opposition to present strategies for achieving silicon aromaticity.
Due to its aromatic character, the discovery of benzene has certainly revolutionized the whole development of organic chemistry - both for the fundamental understanding of life at the biochemical level as for the manufacturing of industrial and pharmaceutical products. Therefore, scientists have been searching for a similar, but silicon-based molecule for more than a century to imitate the aromaticity of benzene since silicon is in the same chemical group as carbon. To pursue this goal, researchers have thus explored the formation of multiple bonds between silicon atoms. So far, however, the formation of those multiple bonds has only been possible if the hydrogen atoms were replaced by large and complex stabilization substitutes. Unfortunately, the resulting molecules become so cumbersome that it appears impossible to use them as "building blocks" for the construction of a new set of molecules that is as rich and various as the counterpart in organic chemistry.
As an alternative approach, we have therefore exploited the natural tendency of silicon to overcoordination for the construction of molecules with electron-deficient hexagonal ring geometries. More specifically, we added a central atom in silicon molecules composed of atoms having already four neighbors each.
Figure 1: Although the addition of a silicon atom in the center of one hexagon gives rise to an unstable molecule (a), we find a quasi-stable structure at low temperatures when the atom is inserted between two hexagons (b) and an extremely stable nanostructure (even at temperatures exceeding 1200K) when three hexagons are used (c).

The resulting structures are more stable than any other known silicon nanocrystals and exhibit strongly aromatic properties because of extensive electron delocalization.

Figure 2: Cyclic electron delocalization between the three hexagons and the central atom is at the origin of the high stability of the proposed nanostructure; the indicated stabilization energies are given in kcal / mol.

Since aromaticity is related to induced ring currents, magnetic properties are particularly important for its detection and evaluation. Among several indexes, nucleus-independent chemical shifts (NICS) have become the most widely used aromaticity probe due to its simplicity and efficiency. In Figure 3, we display the NICS values for the proposed Si19H12 cluster evaluated in two perpendicular directions. Since σ contributions usually fall off faster than π ones normal to a ring, we show in Figure 3(a) a scan of NICS values determined along the longitudinal direction in the center of the nanoparticle. As can be seen, the shielding never drops below the maximum values of benzene over the entire length inside of the finite nanotube. Even outside of the nanotube, the shielding diminishes surprisingly slowly leading to NICS(1) values of -7.1 ppm and -9.4 ppm at a distance of 1Å below (see Figure 3b) and above (see Figure 3d) the external hexagons of the finite nanotube, respectively. In the orthogonal direction, each of the three hexagons exhibits a magnetic shielding that also largely exceeds the one of benzene which is coherent with the extremely high stabilization energy of about 5.1 eV. As for benzene, the shielding has a local minimum in the center of both external hexagons which can be understood by the fact that the principal delocalization routes pass trough the twelve bonds connecting the external hexagons to the central one.
 
Figure 3: Chemical shifts determined in two perpendicular directions. This quantity is regularly employed to evaluate the degree of aromaticity. The corresponding maximum value for benzene is only about -10 ppm. Therefore, the nanocrystal proposed here appears to be more aromatic than the best known aromatic representative in organic chemistry.

As shown above, the resulting optical and electronic characteristics are comparable to those currently
obtained only by nanostructures containing expensive or toxic metal atoms.

Figure 4: Adding a central silicon atom increases the stability by 5.1eV although this value should only be around 3.8eV for clusters of this size and 4.6eV for crystalline bulk silicon. This stability is the result of the highly aromatic character induced by the central atom. Besides, the non-toxicity of the proposed nanocrystal, it exhibits outstanding optical properties in a very wide range of wavelengths: Until now, the incorporation of metal atoms, such as cadmium and lead, was necessary in order to make such a small nanostructure absorb light in the visible and infrared.

In summary, we propose for the first time the concept of electron delocalization in electron-deficient hydrogenated silicon nanocrystals leading to aromatic-like behavior. This novel phenomenon seems to be inherently connected to the unique intermediate position that nanoscale objects take between structures of molecular and microscopic dimensions. Because of the absence of formal multiple bonds, we define “electron-deficiency aromaticity” as a chemical property in which the addition of one atom to an already saturated ring structure causes an increase of stability that exceeds the corresponding cohesive energy as a result of the induced electron delocalization.

H. Vach
Electron-Deficiency Aromaticity in Silicon Nanoclusters
J. Chem. Theory Comput. 8, 2088-2094 (2012).

See also :
http://www.polytechnique.edu/accueil/actualites/nanocristaux-de-silicium-aromatiques-270384.kjsp

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