Computational Study of Octasilacubane
Structural Properties with Density
Functional Theory Method
Mehdi Nabati & Mehrdad Mahkam
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ISSN 1876-990X
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DOI 10.1007/s12633-014-9276-1
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DOI 10.1007/s12633-014-9276-1
ORIGINAL PAPER
Computational Study of Octasilacubane
Structural Properties with Density Functional
Theory Method
Mehdi Nabati · Mehrdad Mahkam
Received: 25 September 2014 / Accepted: 23 December 2014
© Springer Science+Business Media Dordrecht 2015
Abstract In the present study, the density functional theory
method with various basis sets for optimizing and computing the structural and energetic properties of octasilacubane
were performed at 298.15 K and 1 atmosphere. The data
from the calculations on this compound show us the internal
angles in the structure are 90 degrees. For this reason, the
molecule has serious angular pressure. This angular strain
is tolerated by a higher percentage of p-orbitals of silicon
atoms in the Si-Si σ -bonds formation. According to calculation, σ(Si−Si) bonds in the octasilacubane system are formed
from an sp3.44 d0.02 hybrid. Also, IR and NMR spectra of
the structure were simulated. The electronic chemical potential, the hardness and electrophilicity power of the molecule
were obtained from frontier orbitals energies. The data show
the structure has low electrophilicity. Heats of formation and
detonation parameters were then calculated at studied levels
of B3LYP (Becke, 3 parameter, Lee-Yang-Parr) theory. The
simulation results revealed that this compound because for
its high molecular weight is not a viable candidate of high
energy density materials (HEDMs).
Keywords Cubane · Octasiliacubane · Heat of formation
Detonation properties · Electrophilicity index
1 Introduction
Cubane, pentacyclo[4.2.0.02,5 .02,8 .04,7 ]octane, the important member of the family of 20 possible (CH)8 species,
was originally thought impossible to prepare. In 1964,
Philip Eaton and his coworkers reported the first practical
M. Nabati () · M. Mahkam
Chemistry Department, Faculty of Science,
Azarbaijan Shahid Madani University, Tabriz, Iran
e-mail: [email protected]
synthesis of the cubane carbon skeleton [1]. They also
synthesized the highly nitrated cubanes as high energy compounds in 2000 [2]. Cubane is a highly strained system,
and its nitrogen-rich derivatives are energetic materials. The
density and enthalpy of cubane are 1.29 g/cm3 and 144
kcal/mol, respectively [3]. The cubane based compounds are
more attractive because of their high symmetry and high
strain. Octasilacubane, the cubane system with six fused
four-membered silicon rings, is remarkable for its electronic
properties that are related to its highly strained Si-Si σ bonded framework. So far, this compound has not been
synthesized, but it has been discussed by Shigeru Nagase
in 1989 [4]. Until now, several octasilacubanes have been
reported [5, 6]. The main two derivatives of this compound named octakis(1,1,2-trirnethylpropyl)octasilacubane
and octakis(tertbutyldimethylsilyl)octasilacubane were prepared in 1988 and 1992 [7, 8]. In the present work, we
report the theoretical study of octasilacubane. A particularly important method is to model a molecular system
prior to synthesizing that molecule in the laboratory. This
is a very useful means because synthesizing a compound
could need months of labor and raw materials, and generates
toxic waste. A second use of computational chemistry is in
understanding a problem more completely [9–11]. There are
some properties of a molecule that can be obtained theoretically more easily than by experimental means. The density
functional theory (DFT) methods are theoretical techniques
for the prediction of structural and detonation properties of
various chemical systems [12]. There are many DFT methods that have been used in the last few decades [13]. We
have successfully used B3LYP (Becke, 3 parameter, LeeYang-Parr) method with different basis sets for computing
geometry, natural bond orbital population, surface density,
frontier orbitals energy and heat of formation through an
atomization reaction.
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2 Computational Methods
All computational studies were performed with the
Gaussian 03 package [14] using the B3LYP method with
6-31G(d), 6-31G(d,p), 6-311G(d), 6-311G(d,p) 6-31+G(d),
6-31+G(d,p), 6-311+G(d), 6-311+G(d,p), SVP, cc-pVTZ
and CBSB7 basis sets. The designation B3LYP consists of
the Vosko, Wilk, Nusair (VWN3) local correlation functional [15] and the Lee, Yang, Parr (LYP) correlation
correction function [16, 17]. All computational sets were
used as implemented in the Gaussian computational study.
The geometry of octasilacubane was optimized without any
structural or symmetry restrictions. The studied methods
were used to predict the HOF (heat of formation) of the
molecule via the atomization reaction. Vibrational analyses without any symmetry constraints were done for each
set of calculations. Theoretical calculations have been performed in the gas phase [18]. To calculate the densities of
octasilacubane, the molecular volume data was required.
The molecular volume V was defined as inside a contour of
0.001 electrons/bohr3 density. The computational molecular
density ρ (ρ =M/V, where M = molecular weight) was also
calculated.
3 Results and Discussion
3.1 The Geometry of Octasilacubane
As mentioned above, we were successful in computing the
structural properties of the octasilacubane system with DFT
methods at 298.15 K and 1 atmosphere; therefore, we use
the DFT method for computing the octasilacubane system
properties. The geometric structure of the studied molecule
is shown in Fig. 1. As seen from the data obtained from
Fig. 1 The geometric structure of octasilacubane
the calculations in the B3LYP/CBSB7 level, the Si-Si and
Si-H σ -bonds length are 2.401 and 1.487 Aº, respectively.
It is also observed that the Si-Si-Si and Si-Si-H angles are
90.01 and 125.27 degrees respectively. From the experimental data of the octasilacubane derivatives, the Si-Si σ -bonds
length and the Si-Si-Si angles are about 2.38-2.42 Aº and
88.5-92 degrees, respectively [19]. Our calculated geometry
of the structure agrees well with the experimental values.
The main objective is to study the nature of bonding in
the octasilacubane, by using natural bond orbital analysis.
The results from NBO computations can provide the electronic structure details of the compound. The natural bond
orbital calculation was carried out at the B3LYP/CBSB7
level. According to calculation, σ (Si-Si) bonds in the
octasilacubane system are formed from an sp3.44 d0.02
hybrid. Also, the σ (Si-H) bonds are formed from an
sp2.04 d0.01 hybrid on silicon atoms with s orbital on hydrogen atoms. So, the hydrogen atoms of the molecule are
acidic. It eliminates the angular strain in the octasilacubane
structure, the more p orbitals of silicon atoms used for
forming Si-Si bonds. The molecular electrostatic potential
(MEP) is the force acting on a positive test charge (a proton) located at a given point p(x,y,z) in the vicinity of
a molecule through the electrical charge cloud generated
through the molecule’s electrons and nuclei. Despite the
fact that the molecular charge distribution remains unperturbed through the external test charge (no polarization
occurs) the electrostatic potential of a molecule is still a
good guide in assessing the molecules reactivity towards
positively or negatively charged reactants [20]. The MEP
is typically visualized through mapping its values onto the
surface reflecting the molecule’s boundaries [21]. The threedimensional electrostatic potential maps of the structures
are shown in Fig. 2. The red loops and the blue loops
indicate negative and positive charge development for a
particular system respectively.
Fig. 2 The 3-D electrostatic potential map of octasilacubane
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25.5579 (H), 25.5584 (H), 25.5602 (H), 25.5611 (H),
346.1935 (Si), 346.1936 (Si), 346.3317 (Si), 346.3319 (Si),
346.3572 (Si), 346.3573 (Si), 346.4464 (Si), 346.4467 (Si).
3.3 The Frontier Molecular Orbital Energies
Fig. 3 The IR spectra of octasilacubane in the B3LYP/CBSB7 method
3.2 NMR and IR Studies of Octasilacubane
The IR spectrum is one basic property of a compound, and
also an effective measure to identify structures. Here, vibrational frequencies were calculated by using B3LYP/CBSB7
level. Figure 3 provides structures’ IR spectra.
Harmonic frequencies (cm−1 ), IR intensities (KM/Mole)
380.722 (0.014) stretching Si-Si, 380.982 (0.001) stretching Si-Si, 381.370 (0.005) stretching Si-Si, 385.810 (1.857)
stretching Si-Si, 386.243 (1.869) stretching Si-Si, 386.459
(1.864) stretching Si-Si, 461.887 (0.0002) bending SiH, 462.232 (0.0005) bending Si-H, 463.262 (0.0004)
bending Si-H, 567.326 (0.001) bending Si-H, 567.886
(0.002) bending Si-H, 672.963 (113.617) bending Si-H,
673.268 (113.471) bending Si-H, 673.481 (113.425) bending Si-H, 2178.48 (22.910) stretching Si-H, 2182.842
(0.0002) stretching Si-H, 2183.952 (331.404) stretching SiH, 2184.929 (0.0001) stretching Si-H, 2185.779 (342.908)
stretching Si-H, 2185.831 (0.107) stretching Si-H, 2186.561
(348.695) stretching Si-H.
The NMR analysis is an important property of a compound, and also an effective measure to identify structures.
Here, the nucleus shielding (ppm) for the structure was
calculated by using B3LYP/CBSB7 level.
Table 1 shows the HOMO and LUMO energies (ε) of the
molecule computed at the studied levels of theory. Figure 4
provides the frontier orbitals map. In the density functional
theory (DFT) method, μ (the negative of the electronegativity, χ) is the electronic chemical potential that shows
the electron trend to migrate from the electronic cloud, and
pertains to both electronic affinity and ionization potential
characters. The absolute hardness η is defined as a feature
that derives from the μ. If η >0, the charge transfer process
is energetically favorable [22]. The ionization energy and
electron affinity can be replaced by the frontier molecular
orbitals HOMO and LUMO energies, respectively [23]. The
index ω is defined as the electrophilicity character that measures the energy stabilization when the system obtains an
additional electronic charge from the environment. So, we
can acquire the reactivity indexes such as μ, η and ω from
frontier orbitals energies by the following equations:
μ(eV ) = (εLUMO
+ εHOMO )/2
(1)
η(eV ) = εLUMO − εHOMO
(2)
ω(eV ) = μ2 /2η
(3)
The index ω denotes electrophilicity power 1.62, 2.06,
1.52, 1.72, 1.64, 1.59, 1.22, 1.17 and 1.31 for C2 H2 , C2 HF,
BH3 , HNO3 , CS2 , C4 H4 , Azulene, Anthracene and Perylene respectively [24]. In this study, the index ω value
of the octasilacubane has been calculated by the application of density functional theory using various basis sets
(Table 1). From the data, it is seen that the molecule has low
electrophilicity.
Table 1 The frontier orbitals energy and electrophilicity of octasilacubane at studied methods
Methods
εHOMO (eV)
εLUMO (eV)
µ(eV)
η(eV )
ω(eV)
B3LYP/6-31G(d)
B3LYP/6-31G(d,p)
B3LYP/6-311G(d)
B3LYP/6-311G(d,p)
B3LYP/6-31+G(d)
B3LYP/6-31+G(d,p)
B3LYP/6-311+G(d)
B3LYP/6-311+G(d,p)
B3LYP/SVP
B3LYP/cc-pVTZ
B3LYP/CBSB7
−0.22216
−0.22186
−0.22516
−0.22506
−0.22465
−0.22444
−0.22493
−0.22469
−0.22441
−0.22331
−0.22281
−0.05779
−0.05771
−0.06543
−0.06477
−0.06268
−0.06266
−0.06667
−0.06602
−0.06709
−0.07327
−0.07348
0.139975
0.139785
0.145295
0.144915
0.143665
0.143550
0.145800
0.145355
0.145750
0.148290
0.148145
0.16437
0.16415
0.15973
0.16029
0.16197
0.16178
0.15826
0.15867
0.15732
0.15004
0.14933
0.060
0.060
0.066
0.069
0.064
0.064
0.067
0.067
0.068
0.073
0.073
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explosive performance of materials and can be predicted by
the following empirical Kamlet-Jacob equations [26]:
1/2
(1 + 1.3ρ)
(4)
D = 1.01 NM 1/2 Q1/2
Fig. 4 The frontier orbitals of octasilacubane
3.4 Heats of Formation, Predicted Densities
and Detonation of the Structure
The heats of formation (HOF) value were calculated at
all studied levels of theory and are listed in Table 2. In
this study, the atomization reaction method is employed.
The heats of formation of octasilacubane are computed
following the heat of the formation definition [25]. For
octasilacubane, it is 8Si(g) + 4H2(g) → Si8 H8(g) . Therefore,
the HOF for octasilacubane is {[(Eoctasilacubane – 8 ESi – 4
EH2 ) ×627.51 ×4.184] + 8 ×368.2}. Because the computed
total energies are for chemical systems in the gas phase, the
experimental value of 368.2 kJ/mol for the silicon HOF was
used. Density (ρ), detonation velocity (D), and detonation
pressure (P) are the important parameters to evaluate the
P = 1.558ρ 2 NM 1/2 Q1/2
(5)
N = nH /2MW
(6)
M=2
(7)
Q = 0.239Hf /MW
(8)
Where D: detonation velocity in km/s, P: detonation pressure in GPa, ρ: density of a compound in g/cm3 , N: moles
of gaseous detonation products per gram of explosive (in
mol/g), M: average molecular weight of gaseous products
(in g/mol), Q: chemical energy of detonation in kJ/g. Table 2
shows the predicted V, ρ, Q, D and P values of the structures. As seen from the table, the D and P values are very
low. Due to its molecular weight (231.88 amu), this compound is unlikely to be a useful high energy density material
(HEDM) candidate.
4 Conclusions
In this study, a full geometrical optimization of octasilacubane was performed using density functional theory
(DFT, B3LYP) at the levels of 6-31G(d), 6-31G(d,p),
Table 2 Total energy, HOF, predicted density and detonation properties of octasilacubane at studied methods
Methods
Energy (a.u.)
HOF (kJ/mol)
Q (kJ/g)
V* (cm3 /mol)
ρ(g/cm3 )
D (km/s)
P (GPa)
B3LYP/6-31G(d)
−2320.6704
227.775
234.771
162.716
1.425
1.761
1.183
B3LYP/6-31G(d,p)
−2320.6799
234.625
241.831
132.120
1.755
2.041
1.821
B3LYP/6-311G(d)
−2320.8427
252.809
260.574
173.973
1.333
1.732
1.090
B3LYP/6-311G(d,p)
−2320.8562
247.511
255.113
170.690
1.358
1.743
1.120
B3LYP/6-31+G(d)
−2320.6748
239.732
247.095
170.853
1.357
1.729
1.100
B3LYP/6-31+G(d,p)
−2320.6845
246.185
253.746
160.843
1.442
1.810
1.259
B3LYP/6-311+G(d)
−2320.8447
254.917
262.747
134.583
1.723
2.058
1.829
B3LYP/6-311+G(d,p)
−2320.8582
249.590
257.256
134.583
1.723
2.047
1.810
B3LYP/SVP
−2320.0738
138.815
143.079
176.462
1.314
1.478
0.785
B3LYP/cc-pVTZ
−2320.8959
200.680
206.844
111.286
2.084
2.219
2.374
B3LYP/CBSB7
−2320.8725
211.247
217.735
140.378
1.652
1.907
1.531
* Average
valu from 100 single-point volume calculations at studied levels
Q: Heat of explosion, V: Volume of explosion, D: Velocity of detonation, P: Pressure of explosion
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6-311G(d), 6-311G(d,p) 6-31+G(d), 6-31+G(d,p), 6311+G(d), 6-311+G(d,p), SVP, cc-pVTZ and CBSB7. The
octasilacubane structure has more angular strain, and for
this reason more P orbitals of silicon atoms used for forming
Si-Si bonds. The detonation performance data are calculated
according to the HOFs calculated by studied levels of theory
and the values show a very low detonation velocity and pressure. Therefore, it is not a viable candidate for high energy
density materials (HEDMs).
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