Silaprismanes
What are the silicon polyprismanes?
Silicon polyprismanes or [n,m]silaprismanes can be considered as the layered dehydrogenated molecules of cyclosilanes (silicon rings), where m is the number of vertices of a closed silicon ring, and n is the number of layers. For a large n, polysilaprismanes can be considered as the analogs of silicon singlewalled nanotubes with an extremely small crosssection in the form of a regular polygon. Nevertheless, unlike traditional nanotubes, polysilaprismanes have rectangles on their surfaces instead of hexagons. So, the angles between the covalent SiSi bonds are different from the value of 109.5° usual for the sp^{3}hybridized orbitals like in bulk (diamondtype) silicon. Even though the elementary representatives of polysilaprismanes were synthesized long ago in early 2000, unfortunately, to date, there has not been developed a universal method for obtaining these molecular systems. Some elementary silaprismanes one can see in Figure 1.
This webpage contains the results of computer simulation of silicon polyprismanes obtained in the framework of the scientific project “Computer simulation of functional nanomaterials based on silicon polyprismanes with controlled physicochemical characteristics” that is supported by the Russian Science Foundation (Grant No. 187200183).
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Figure 1 – Atomic structures of the elementary silaprismanes obtained at the DFT/B3LYP/6311G(d,p) level of theory: [2,3]silaprismane Si_{6}H_{6} (a), [2,4]silaprismane Si_{8}H_{8} (b), [2,5]silaprismane Si_{10}H_{10} (c), [2,6]silaprismane Si_{12}H_{12} (d), [2,7]silaprismane Si_{14}H_{14} (e), and [2,8]silaprismane Si_{16}H_{16} (f). 
Thermodynamic and kinetic stability of elementary silicon prismanes
First of all, we determine structural characteristics (bond lengths and valence angles) and binding energies of elementary silicon [2,m]prismanes with m = 3 – 8. The calculation of vibrational spectra confirmed that these molecular structures correspond to the energy minima. The binding energies of elementary silaprismanes were calculated. The binding energy was determined as the difference between the total energy of a silicon prismane and the sum of the energies of the isolated constituent atoms, referred to the number of atoms in the system. Prismanes that possesses higher binding energy is more thermodynamically stable and vice versa. It has been obtained that the most thermodynamically stable of the structures considered is the [2,5]prismane Si_{10}H_{10}. For m > 5, the thermodynamic stability of elementary silicon prismanes slightly monotonously decreases. For every elementary silicon prismane considered, a set of quantum chemical descriptors is defined: HOMO and LUMO energies, ionization potential, electron affinity, chemical potential, electronegativity, chemical hardness and softness, electrophilicity index. The dependencies of some of these descriptors a well as the binding energy on the number of vertices of a closed silicon ring are presented in Figure 2. Basing on the analysis of HOMOLUMO gaps, it was found that elementary silicon prismanes can be conditionally referred to widegap semiconductors or isolators.
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Figure 2 – The dependencies of binding energy (a), HOMOLUMO gap (b), hardness (c) and softness (d), chemical potential (e), and electrophilicity (e) on the number of vertices of a closed silicon ring constructing the prismane cage, obtained at the DFT/B3LYP/6311G(d,p) level of theory 
We also determine the possible decomposition channels of the elementary silicon prismanes. It has been found that the main mechanism of the stability loss is the breaking of the SiSi bond either inside the silicon ring forming the prismane (intraplane bond) or the corresponding bond between the rings (interplane bond). Moreover, it was confirmed that the priority decomposition channel for the systems with even m = 4, 6, 8 is the breaking of one of the interplane bonds, whereas for the silaprismanes with odd m = 3, 5, 7 the priority decomposition channel is the breaking of one of the intraplane Si–Si bonds. The examples of these mechanisms one can see as the animations presented in Figure 3.
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Figure 3 – Animated minimum energy path for the decomposition process of the [2,3]silaprismane (a) and [2,4]silaprismane (b). TS denotes the transition state or saddle point 
The minimum energy barrier preventing the decomposition, as a measure of kinetic stability, nonmonotonously depends on m, but for the prismanes formed by the silicon rings with an odd number of atoms m = 5, 7 it is higher than the corresponding value for the prismanes formed by the silicon rings with an even m number – 4, 6, 8. Using the Arrhenius equation the estimation of the lifetime of elementary prismanes was made at room temperature (300 K) and at the temperature of 800 K (see Table 1).
Table 1. Minimum energy barriers preventing the decomposition of [2,m]silaprismanes (E_{a}), corresponding frequency factors (A), lifetimes estimated using the Arrhenius formula at room temperature (τ_{300}) and 800 K (τ_{800}).
Silaprismane  E_{a}, eV  A, s^{1}  τ_{300}, s  τ_{800}, s 
[2,3]silaprismane  0.79  3.75·10^{13}  4.62·10^{1}  2.46·10^{9} 
[2,4]silaprismane  1.46  5.26·10^{13}  7.20·10^{10}  3.13·10^{5} 
[2,5]silaprismane  2.36  1.08·10^{14}  4.67·10^{25}  7.18·10^{0} 
[2,6]silaprismane  1.52  7.42·10^{14}  4.63·10^{10}  5.08·10^{6} 
[2,7]silaprismane  2.57  9,99·10^{13}  1.26·10^{29}  1.46·10^{2} 
[2,8]silaprismane  1.26  1.72·10^{14}  8.35·10^{6}  4.99·10^{7} 
It was obtained that the elementary silicon prismanes possess high kinetic stability: the estimation of their lifetimes at room temperature gives the macroscopic (“infinite”) values, and their lifetimes at 800 K are greater than microseconds. The decomposition products of elementary silicon prismanes are the nanostructures containing various irregular multimembered silicon rings that are formed due to the breaking of the corresponding Si–Si bonds. According to the data obtained, it was concluded that the preferable candidates for the construction of extended systems in the form of silicon polyprismanes are the [2,m]silaprismanes with m = 5 – 7.
The doping effect
It has been found that the substitution of hydrogen atoms in silicon elementary prismanes by the functional groups NO2 and NH2 (and in some cases, CH3) distorts the silicon frame of prismane, and the stability of such compounds depends on the conformer type, in other words, on the relative orientation of the attached radicals. Some substituted elementary prismanes are shown in Figure 4. The calculation of the vibrational spectra of these systems is shown that they cannot be referred to the local energy minima since they are the highorder saddle points.
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Figure 4 – Atomic structures of some doped silaprismanes obtained at the DFT/B3LYP/6311G(d,p) level of theory: Si_{6}(NH_{2})_{6} (a), Si_{8}(NO_{2})_{8} (b), Si_{10}(CH_{3})_{10} (c), Si_{12}F_{12} (d), Si_{14}(NH_{2})_{14} (e), Si_{16}(NO_{2})_{16} (f). 
The use for passivation of the fluorine atoms instead of hydrogens conserves the structure of silaprismanes. In this case, the decay channels have the universal character and coincide with the decay channels of the unsubstituted silaprismanes. Consequently, the search for the transition states was carried out similarly as for the elementary unsubstituted silaprismanes. The geometry of the corresponding transition configurations of unsubstituted prismanes was used as the initial approximation. It was obtained that the minimum energy barrier preventing the decomposition, as a measure of the kinetic stability of doped silaprismanes, is significantly lower than the corresponding values for the unsubstituted systems. Thus, it is confirmed that the doping reduces the kinetic stability of silicon prismanes.
Can sp^{3}silicon be the metal?
Yes, it can!
On the example of the extended silicon polyprismanes, the metallic nature of the sp^{3}hybridized silicon allotropes was discovered for the first time. From the analysis of the band structure and the density of electronic states, and the behavior of the transmission function near the Fermi level, it was found that the [n,5], [n,6], [n,7], and [n,8]silaprismanes belong to the class of metals and are conductors. Moreover, an increase in the thermodynamic stability of silicon [n,5], [n,6], [n,7], and [n,8]prismanes with their effective length growth was confirmed. See the video below for the details.
Application prospectives of silaprismanes
For a long time to the present days, diamondtype silicon is the basis of modern consumer and special purpose electronics. However, the active development of nanotechnologies makes it possible to think about the use of silicon in new forms, for example, in the form of polyprismanes, which can qualitatively improve the component base of modern electronic devices. The extraordinary electronic properties of silicon polyprismanes together with their structural and mechanical characteristics make them potentially suitable in the various fields of nextgen technologies. Building the next generation of technological processes is impossible without the use of an improved material base. For example, the miniaturization of electronics inevitably leads to the using of appropriate semiconductor or metallic nanomaterials, which will provide in the future a significant increase in the speed of computing systems. Extended molecules of silicon polyprismanes may be the ultrathin functional nanowires with controlled electronic characteristics and can be used in elements of computational logic. According to our studies, they are potentially good conductors. Encapsulation the metastable nanostructures (for example, nitrogen chains) inside the higher silicon polyprismanes can stabilize the latter, which will make it possible to obtain an effective highenergy material.
Furthermore, high electrophilicity of polyprismanes indicates the possibility of including the charged ions inside their structure that might be useful in biological and medical applications as drug delivery systems. Also, silicon polyprismanes can be used for storing and transporting hydrogen instead of carbon nanomaterials traditionally offered in the literature for these purposes. Their conductive properties will allow one to use the polysilaprismanes as the elements of measuring equipment, for example, tips of a scanning tunneling microscope. Also, the absence of free covalent bonds makes them insensitive to environmental pollutants (free radicals), which reduces the reactivity of the silicon needle, allowing one to achieve the atomic resolutions in the microscope.
Videomaterials
Publications
For detailed information, see the following publications:
1. Gimaldinova M.A., Katin K.P., Salem M.A., Maslov M.M. Energy and electronic characteristics of silicon polyprismanes: density functional theory study // Letters on Materials. 2018. V. 8. P. 454457. DOI: 10.22226/2410353520184454457
2. Katin K.P., Grishakov K.S., Gimaldinova M.A., Maslov M.M. Silicon rebirth: Metallic prismane allotropes of silicon for the nextgen technologies // arXiv:1902.09494 (https://arxiv.org/abs/1902.09494)
Acknowledgments
The presented study was performed with the financial support of the Russian Science Foundation (Grant No. 187200183). We are grateful to DSEPYRI for the organizational support and computational resources provision.