Many theoretical and experimental studies have been reported about the structure and properties of C20 molecule [1-6]. C20 molecule is potentially the smallest fullerene. The synthesis and characterization of this molecule have been performed in the gas phase . The notable structure of C20 has been the question of numerous theoretical researches [8, 9]. Fullerenes are considered as promising candidates for basic elements in nanoscale devices, and several instances of fullerene-based devices have been already considered both experimentally and theoretically [10, 11]. Modification of C20 is a matter of common attention for experimentalists and theoreticians to seem into the structure as well as electronic properties. The structure and properties of fullerene C20 and its derivatives C20(C2H2)n and C20(C2H4)n (n=1–4) have been explored , and illustrated that the most stable fullerene C20 and its derivatives C20(C2H2)n and C20(C2H4)n (n=1–3) reveal significant aromaticity, while C20(C2H2)4 and C20(C2H4)4 have no spherical aromaticity. Furthermore, heteroatom impacts on structure, stability and aromaticity of XnC20-n fullerenes have been established . The interaction of C20 with N2X2 (X=H, F, Cl, Br, Me) has been investigated theoretically . Also, theoretical study of solvent effect on the interaction of C20 and N2H2 has been reported.
The synthesis and characterization of several homonuclear combinations –Si=Si- have been investigated [15-17]. The large number of reviews published during the past decade reflects the progress in this field [18-20]. Their Lewis acidic character has been supported by the reactions of REER (E= Si, Ge, Sn) with R′NC: (R′ = But, Mesitylene, SiMe3) [21-23]. Also, reactivity of a disilyne RSi≡SiR (R= SiiPr[CH(SiMe3)2]2) toward π-Bonds has been investigated24.
Solvent exhibits significant role in physical and chemical processes. The presence of specific and non-specific interactions between the solvent and the solute molecules is responsible for the change in several properties such as molecular geometry, the electronic structure and dipole moment of the solute [14, 25-34].
Numerous experimental and theoretical investigations have been reported about adsorption of ethylene (C2H4) and acetylene (C2H2) at various surfaces [35-37]. Many investigations have been exploring the more reactivity of the π bond of the disilenes toward many reagents, rather than alkenes and alkynes. This increase reactivity attributed to the relatively small HOMO-LUMO gap and its biradical character . For instance, smooth [2 + 2] cycloadditions of the π bond of disilenes toward alkenes and alkynes to give the disilacyclobutane and disilacyclobutene derivatives, respectively [39, 40]. Furthermore, there are much less reports about the π bond nature of disilynes with a silicon-silicon triple bond, which has two clear π bonds (πin and πout)[15, 41-43], although small number researches have reported about the reactivity of alkyne analogues [22, 44, 45]. An evaluation of the chemical behavior of heavier group 14 element alkyne analogues with that of alkynes has special attention [46-48].
In the basis of the extensive attentions on the nature of alkene analogues of silicon, we are interested in the theoretical study of interaction fullerene C20 with Si2H2 in both gas and solution phases. Experimental study has not reported about the interaction between C20 and Si2H2, yet. Therefore, theoretical study and the effective factors of this interaction are attractive for us. The structure, frontier orbital analysis, selected IR-active vibration, thermochemical parameters and 29Si NMR chemical shift of the C20…Si2H2 have been explored. In addition, the influence of the solvent on the structural properties of C20…Si2H2 molecule will be evaluated.
All calculations were carried out with the Gaussian 09 suite program . The calculations of systems contain C, Si and H described by the standard 6-311++G(d,p) basis set [50-53]. Geometry optimization was performed utilizing with the hybrid functional of Truhlar and Zhao (M06-2X) .
A vibration analysis was performed at each stationary point found, that confirm its identity as an energy minimum.
The interaction energy, I.E, can be evaluated from the difference between energy of the molecule and sum of the energies of the C20 and Si2H2:
I.E = E(C20…Si2H2) – [E (C20)+ E(Si2H2)]
The calculated interaction energies have corrected for basis set superposition errors (BSSE), which were computed for all calculations using the counterpoise correction method of Boys and Bernardi . This error is owing to the different number of basis functions included in the molecule and monomer calculations. Since the molecule employs a basis set larger than the one employed by monomers, in most cases this error models the molecule to be too attractive. As it has been studied before, when BSSE is corrected along the whole surface, important changes in the potential energy surface appear, not only in the energy, but also in the position of the minimum as well as its topology [56, 57].
We have studied the solvation effects by using self-consistent reaction field (SCRF) approach, in particular using the polarizable continuum model (PCM) .
The GaussSum 3.0 software package was used to evaluate the detailed analysis of the atomic orbitals contributions to the complex .
Chemical shift values are calculated using the Gauge independent atomic orbital (GIAO) method at the same method and basis sets of optimization .
The bonding interactions between the C20 and Si2H2 fragments have been analyzed by means of the energy decomposition analysis implemented in Multiwfn 3.3.5. package . In this method, the instantaneous interaction energy (Eint) between the two fragments can be divided into three main components:
Epolar is electron density polarization term (also called as induction term)
Epolar = E (SCF last) – E (SCF 1st)
Eels is electrostatic interaction term, and EEx is exchange repulsion term.
RESULTS AND DISCUSSION
The computed interaction energies (I.E) for the C20…Si2H2 molecule (Fig. 1) in the gas phase and various solvents have been gathered in Table 1. The comparison of interaction energy value in gas phase and solution phase show more interaction between C20 and Si2H2 in solution phase. It can be expected that interaction between C20 and Si2H2 increases in the presence of more polar solvents. There is a good linear correlation between interaction energy values and dielectric constants of solvents:
I.E = -0.039 e - 99.34; R² = 0.983
Where, is the dielectric constant of solvent. The interaction energy in gas phase was corrected by the BSSE. The uncorrected and corrected by BSSE of interaction energies is -98.78 kcal/mol and -96.45 kcal/mol, respectively.
The nature of the C…Si chemical bond in the C20…Si2H2 molecule has been investigated using an energy decomposition analysis (EDA). These calculations show that the total interaction energy between C20 and Si2H2 is -98.78 kcal/mol. Also, EDA calculations reveal that the polarization energy (-198.62 kcal/mol) stabilized the C20…Si2H2 adduct, whereas the sum of electrostatic and exchanging energy destabilized the adduct by 99.84 kcal/mol.
The stabilization energies by solvents (solvation energy, Esolv) have been calculated (Table 1). These values are the relative energy of the title compound in a solvent to that in the gas phase. As we can see the solvation energies are dependent on the size of the dielectric constant of solvents, and these values decrease with the increase of dielectric constants of solvents. As a result, the stability of C20…Si2H2 molecule increases in more polar solvents. This is because a dipole in the molecule will induce a dipole in the medium, and the electric field applied to the solute by the solvent (reaction) dipole will in turn interact with the molecular dipole to result in net stabilization. Hence, C20…Si2H2 molecule has more stability in polar solvent rather than in the gas phase. There is a good correlation between dielectric constants and Esolv:
Selected geometrical parameters of C20…Si2H2 molecule are given in Table 2. These values show that Si-C and Si-Si distances increase in solution rather than to that in the gas phase. On the other hand, these values are dependent on the size of the dielectric constant of solvents, and these values increase with the increase of dielectric constants of solvents. There is a good correlation between these parameters and dielectric constants:
Also, the comparison of interaction energy value in gas phase and solution phase and SiC distances show that SiC distance decrease with the decrease of interaction energies. There is a good correlation between interaction energy and SiC distances:
r(SiC)= -379.0 I.E + 626.1; R² = 0.998
The dipole moments of C20…Si2H2 molecule in gas phase and different solvents have been listed in Table 1. As seen in Table 1, these values increase in solution phase. In the solution phase, dipole moments increase with increasing of polarity of the solvents. Also, these values show a good relationship with interaction energy values:
m= -0.868 Esolv + 4.355; R² = 1
Molecular orbital analysis
The energies of the frontier orbitals (HOMO, LUMO) along with the corresponding HOMO–LUMO energy gaps for of C20…Si2H2 molecule in gas phase and different solvents are given in Table 2.
Inclusion of solvation effects leads also to changes on the molecular orbital energies (Table 2). In solution, HOMO and LUMO are destabilized, with respect to the corresponding values in a vacuum. A good relationship exists between frontier orbitals energies and polarity of solvents:
E(HOMO) = -5 ×10-5 e - 0.248; R² = 0.988
E(LUMO) = 5×10-5 e - 0.088; R² = 0.972
Also, HOMO-LUMO gap of C20…Si2H2 molecule in solution phase is more than that of gas phase. A good relationship exists between HOMO-LUMO gap and polarity of solvents:
Gap = 0.002e + 4.352; R² = 0.981
The variations in this property may be illustrated by considering the fact that neutral or charged species enhance their effective radii in solution phase. This signifies that the electrostatic potential q/r will forever diminish from gas phase to solution phase. As a result, solvated species will reduce their effective hardness and subsequently, and become softer in the solution phase 62.
The frontier orbitals distribution of C20…Si2H2 molecule is plotted in Fig. 1. Fig. 1 presents the HOMO and LUMO are distributed mainly on C20. Percentage composition in terms of the defined groups of frontier orbitals illustrates the largest contributions of HOMO and LUMO arise from cage (97.0% and 89.0%, respectively).
Absolute free energy and enthalpy values of studding C20…Si2H2 molecule are reported in Table 3. The solvation free energy and enthalpy values are computed via the following equation:
DXsolvation =Xsolv-Xgas; X=G, H
Table 3 reports that the amount of DGsolv and DHsolv of C20…Si2H2 molecule decrease with heightening the dielectric constant. There is a good relationship between DGsolv and DHsolv with dielectric constant values:
DGsolv = -0.109 e - 1.795; R² = 0.979
DHsolv = -0.108 e- 1.805; R² = 0.979
There is a good relationship between DGsolv and dipole moment values:
m = -1.17 DGsolv + 5.117; R² = 1
Consequently, more polar solvents, the increase in dipole moment of C20…Si2H2 molecule influences its interaction with the solvent.
Table 4 reports the wavenumbers of IR-active, symmetric and asymmetric stretching vibrations of Si-H groups of C20…Si2H2 molecules in gas and solution phases. It can be seen that these values are greater in solution phase rather than gas phase. On the other hand, u(SiH) values have increased with increasing of dielectric constant of solvents.
The first theoretical treatment of the solvent-induced stretching frequency shifts was given by Kirkwood–Bauer–Magat equation (KBM) and is shown through the following equation:
Where ugas is the vibrational frequency of a solute in the gas phase, usolution is the frequency of a solute in the solvent, e is the dielectric constant of the solvent and C is a constant depending on the dimensions and electrical properties of the vibrating solute dipole.
It can be observed that solvent-induced stretching vibrational frequency shifts on the base of KBM equation, have a good linear relationship:
For symmetric stretching of Si-H bonds:
and for, asymmetric stretching of Si-H bonds:
KBM equation only takes into account the solvent dielectric constants. The frequency shifts depend on the solvent dielectric constant.
29Si NMR spectra
29Si NMR spectral data of C20…Si2H2 are gathered in Table 4. In the C20…Si2H2 molecule, chemical shift of Si in gas phase is equal to 157.64 ppm. In various solvents, the chemical shift value of Si is decreased. These values are increased by increasing the solvent polarity.
The dependency of values of chemical shifts on dielectric constant of solvents has been investigated, and there are good relationships between these shifts values and dielectric constant:
d(29Si) = 0.011 e + 150.7; R² = 0.998
Dependency of the chemical shift values of Si atom in the C20…Si2H2 versus (e - 1)/(2e + 1) of KBM equation exhibits a linear relationship between these chemical shift values and KBM parameters. These equations are as follows:
d(29Si) = -0.005(e-1)/(2e+1) + 0.045; R² = 0.976
Theoretical investigation of the interaction of C20 and Si2H2 molecules at the M06-2X/6-311++G(d,p) level of theory in gas solution phases shows that the interaction energy values increase from vacuum to different solvents and interaction between C20 and Si2H2 increases with increasing of dielectric constant of solvents. Solvation energy values indicate the increasing of stability of title complex in more polar solvents. The energy decomposition analysis (EDA) explored the significant interaction between C20 and Si2H2 in C20 … Si2H2 molecule (I.E=-98.78 kcal/mol). On the other hand, the polarization energy stabilized adduct, although the sum of electrostatic and exchanging energy destabilized the C20 … Si2H2 molecule. Also, our calculations showed the good relationship between chemical shift values of 29Si NMR, IR-active symmetric and asymmetric stretching vibrations of Si-H groups and KBM solvent parameters.
CONFLICT OF INTEREST
The authors declare that there is no conflict of interests regarding the publication of this manuscript.