DSpace at VNU: Ab-initio study of intermolecular interaction and structure of liquid cyclopentasilane

Chemical Physics 400 (2012) 59–64

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Chemical Physics
journal homepage: www.elsevier.com/locate/chemphys

Ab-initio study of intermolecular interaction and structure of liquid
cyclopentasilane
Pham Tien Lam a, Ayumu Sugiyama a,b, Takashi Masuda b, Tatsuya Shimoda a,b, Nobuo Otsuka a,
Dam Hieu Chi a,b,c,⇑
a
b
c

Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan
Japan Science and Technology Agency, ERATO, Shimoda Nano-Liquid Process Project, 2-5-3 Asahidai, Nomi, Ishikawa 923-1211, Japan
Faculty of Physics, Hanoi University of Science, 334 Nguyen Trai, Thanh Xuan, Hanoi, Viet Nam

a r t i c l e

i n f o

Article history:
Received 13 May 2011
In final form 15 February 2012
Available online 13 March 2012
Keywords:
DFT
Cyclopentasilanes
Liquid silicon

a b s t r a c t
We report on an ab initio calculation study of intermolecular interactions between cyclopentasilane (CPS)
molecules in liquid CPS. Our calculations show that the SiAH bonds that are oriented toward the center of
the ring of a CPS molecule play a significant role in the interaction between CPS molecules. This interaction results in the formation of special bonds between CPS molecules, which resemble hydrogen bonds.
These hydrogen bonds cause a red shift of IR absorption peaks corresponding to the SiAH stretch vibration. The formation of hydrogen bonds in the liquid phase of CPS was further confirmed by ab-initio
molecular dynamics simulations. The analysis of pair correlation functions has shown a significant contribution of hydrogen bonds to the structure of the CPS liquid system.
Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction
In recent years, liquid processes for fabricating electronic devices have attracted considerable attention. In contrast to conventional processes, liquid processes improve the material utilization
efficiency, simplify the processing method, and involve smaller
and low-cost manufacturing apparatus [22,14,18,17,25,31,7]. Liquid processes enable us to fabricate large-scale electronic circuits
and introduce novel applications that would be difficult to develop
using conventional techniques [23].
The preparation of functional solutions, which are stable solutions containing materials, for a target device is the most important step in the liquid processes. For the fabrication of electronic
devices, cyclopentasilane (Si5H10-CPS) is the most suitable candidate for a source material of functional solutions among various
silicon compounds because it has the ability to undergo ring-opening polymerization and transform into high-purity Si. In addition,
CPS can also act as a solvent of polysilanes. Recently, Shimoda
et al. successfully synthesized liquid silicon from CPS by photopolymerization [23]; the obtained solution of polysilanes can be
transformed into an amorphous Si film via thermal decomposition.
The results of the described above study have raised a realistic
possibility of the large-scale applications of liquid processes to the
fabrication of Si-based electronic devices by using CPS. To this end,
⇑ Corresponding author at: Japan Advanced Institute of Science and Technology,
1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan.
E-mail address: (D.H. Chi).
0301-0104/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved.
/>
however, it is necessary to clarify and control the entire microscopic process of polymerization, because such processes occur

in the liquid state; hence, they involve complex interactions of
the constituent molecules. For this purpose, both a first principles
simulation approach and an experimental approach are required.
In this study, we have investigated the structure of the liquid
CPS. We have focused on interactions between CPS molecules
and the bonding nature in CPS solution. The investigations were
mainly based on ab initio calculations, including density functional
theory (DFT) [11,13] calculations, Hartree–Fock (HF) calculations,
and second order Møller–Plesset (MP2) perturbation theory calculations. Ab-initio molecular dynamics (MD) simulations of liquid
CPS were performed using the Car–Parrinello method [1]. This
study has shown that the SiAH bonds of a CPS molecule that are
oriented toward the centers of the rings of the other CPS molecules
play a significant role in the interaction between the CPS molecules. This interaction results in the formation of special bonds between CPS molecules which resemble hydrogen bonds. Similarly to
hydrogen bonds in the water system, these hydrogen bonds cause
the red shift of IR absorption peaks corresponding to the SiAH
stretch vibration. The formation of hydrogen bonds in liquid CPS
was further confirmed via ab initio molecular dynamics simulations using a system of 27 CPS molecules. The pair correlation radial distribution functions (RDFs) between the centers of mass of
CPS molecules and H atoms, gCenterÀH(r), and those between the
center of mass of CPS molecules and Si atoms, gCenterÀSi(r), were
analyzed. gCenterÀH(r) shows a peak at approximately 2.1 Å, which
is attributed to the hydrogen atoms which are involved in a


60

P.T. Lam et al. / Chemical Physics 400 (2012) 59–64

hydrogen bond, while gCenterÀSi(r) shows a peak at approximately
3.3 Å of the Si atom in a hydrogen bond. The results indicate a significant contribution of hydrogen bonds to the structure of the CPS
liquid system. Further, we believe that the hydrogen bonds investigated in this study play a key role in the reactions in CPS solution.

2. Calculation method
It is well known that DFT calculations involve low computational costs; however, they fails in describing the intermolecular
interaction that is mainly driven by dispersion forces. The calculation results strongly depend on the employed exchange–correlation functionals employed. Local density approximation (LDA) for
exchange–correlation functionals has been reported to overestimate the intermolecular interaction, whereas generalized gradient
approximation (GGA) functionals underestimate it [16,30,19].
Therefore, in this study, in order to select appropriate calculation
methods for evaluating the interaction between CPS molecules,
the interaction between 2 CPS molecules was evaluated using the
HF method and DFT methods with various functionals, including
the LDA–VWN functional, the GGA–PBE functional, and the hybrid
B3LYP functional. The results were compared with those of the
MP2 method. The calculations were performed using Dmol3 code
[3,4] and Gaussian 03 code [8].
The interaction between CPS molecules was described on the
basis of potential energy surfaces (PES). The PES were calculated
by changing the distance between the centers of mass of the two
CPS molecules. The binding energies between these two CPS molecules were estimated by the depth of the potential well on the
PES. The reference potential energies were chosen as the total energy of the two CPS molecules system with a separation of 10 Å.
Fig. 1 shows typical PES for the interaction between two CPS molecules, calculated using Dmol3 code and Gaussian 03 code. These
PES were calculated for the configuration in which the two CPS
molecules are aligned nearly parallel to each other (configuration
A in the later discussion and Fig. 3). Among molecular orbital
methods, the HF method predicts the repulsive interaction between CPS molecules, whereas the MP2 method predicts the
attraction between CPS molecules, as shown in Fig. 1. It implies
that the correlation effect plays an important role in the interaction
between CPS molecules because the MP2 theory has been reported
to recover 80–90% of the correlation effect [12].
The same tendency is observed for DFT calculations because the
prediction of the interaction between CPS molecules strongly depends on the employed exchange–correlation functionals. The
GGA–PBE functional calculations and the hybrid B3LYP functional

calculations predict a weak interaction between CPS molecules,
whereas the LDA–VWN functional calculations predict an attraction. The VWN-functional with the standard double numerical plus
polarization function (DNP) formulated in Dmol3 code predicts a
binding energy of 0.507 eV and an equilibrium distance between
the CPS molecules of 4.25 Å, while the VWN functional with the
standard 6-311G⁄⁄ basis set formulated in the Gaussian 03 code
predicts the binding energy of 0.579 eV and the equilibrium distance between CPS molecules of 4.20 Å. The MP2 calculation with
the 6-311G⁄⁄ basis set formulated in the Gaussian 03 code predicts
a binding energy of 0.437 eV and an equilibrium distance between
CPS molecules of 4.55 Å. Although the LDA–VWN functional
slightly overestimates the binding energy and underestimates the
equilibrium distance between CPS molecules, it is clearly seen that
the results of the LDA–VWN functional are in reasonable agreement with those of the MP2 theory calculations, as shown in
Fig. 1. Therefore, the LDA–VWN functional can be used to simulate
the interaction between CPS molecules.
The interactions of CPS molecules were investigated using DFT
molecular dynamics (MD) simulations (Born–Oppenheimer MD
simulations). The LDA–VWN functional describes well the interaction between two CPS molecules; hence the simulations were carried out using the LDA–VWN functional with DNP basis set
formulated in the Dmol3 code. The simulations were carried out
within microcanonical ensemble for 10 ps with the time step of
1 fs. Minimum energy structures derived from the simulations
were fully relaxed for reaching more accurate minimum energy
structures. All optimizations were calculated using the LDA–VWN
functional, the GGA–PBE functional, the hybrid B3LYP functional,
and MP2 the method along with standard 6-311G⁄⁄ basis set formulated in Gaussian 03 code.
For ab initio MD simulations of liquid CPS with a supercell containing 27 CPS molecules, we employed the Car–Parrinello method
formulated in CPMD code [1,2]. The fictitious mass of electrons was
500 au which enables us to integrate equations of motion with
time step of 0.121 fs and to maintain the adiabaticity of the simulations. The total length of simulation is 10 ps, and the result of the

last 5 ps was used for the analysis. The computations were performed only at the C point of the Brillouin zone. We used ultra-soft
pseudo-potentials [29] with a plane wave cutoff of 30 Ry. The LDA
functional with a Pade form for the exchange correlation energy
optimized by S. Goedecker, M. Teter, and J. Hutterin [9] is applied.
This functional was tested by calculations of the interactions between 2 CPS molecules. The results are in a good agreement with
MP2 and LDA–VWN functional calculations. We have used a supercell with a side length of 19.123 Å. Such a supercell size represent
CPS under ambient conditions at density of 0.963 g cmÀ1.

3. Electronic structure of isolated CPS molecule

Fig. 1. Potential energy surfaces of two CPS molecules.

In a recent report we presented the results of ab initio studies of
an isolated a CPS molecule with three stable configurations [5]. We
found that the twist configuration of CPS molecule with the C2
symmetry is the most stable, even though the differences in energy
of the three configurations is quite small, i.e, < 0.1 eV.
As in the case of other silane compounds, the delocalization of
molecular orbitals (MOs) i.e., conjugation of r orbitals, [15,27] is
an important characteristic of CPS. Fig. 2 shows the lowest unoccupied molecular orbital (LUMO) and highest occupied molecular
orbital (HOMO) of CPS molecule. The LUMO appears similar to
the lowest p-bonding orbital of the Si penta-ring, but it shows
nodes at the center of SiAH bonds. This can, therefore, be seen as
an anti-bonding orbital from conjugated p-orbitals of the pentaring and s-orbitals of the hydrogen atoms in a CPS molecule. On
the other hand, the HOMO is an anti-bonding molecular orbital


P.T. Lam et al. / Chemical Physics 400 (2012) 59–64

Fig. 2. The LUMO and the HOMO of a CPS molecule: the red part is the positive part,

and the blue part is the negative part. (For interpretation of the references to colour
in this figure legend, the reader is referred to the web version of this article.)

from a r-orbital of Si atoms with s-orbitals of a specific pair of
hydrogen atoms. The shape of the LUMO strongly suggests a mode
of interaction between MOs of two molecules in the liquid phase as
the mutual delocalization of MOs [6,20], in which the molecules
that constitute the LUMO act as electron acceptors.
4. Intermolecular interaction between CPS molecules
All the typical configurations of a system that consists of two
CPS molecules with minimum energy are searched using first principles molecular dynamic simulations. The obtained configurations
are shown in Fig. 3. These configurations were fully relaxed for
reaching more accurate minimum energy configurations. The binding energies were calculated using Eq. (1)

DE ¼ 2 Á ECPS À E2CPS

ð1Þ

in which ECPS is the total energy of an isolated CPS molecule with
the twist configuration, and E2CPS is the total energy of the system
consists of two CPS molecules. The optimization calculations were
carried out using Gaussian 03 package. The obtained results are
summarized in Table 1.
According to the LDA–VWN and MP2 calculations, configuration
A and configuration B are significantly more stable than the
remaining configurations, as seen in Table 1. The binding energy
and the equilibrium distance between the CPS molecules in configuration A, which are given by LDA–VWN with the 6-311G⁄⁄ basis
set, are approximately 0.481 eV and 4.19 Å, respectively, while
those given by the MP2/6-311G⁄⁄ calculations are 0.440 eV and
4.53 Å, respectively. In comparison with MP2, the GGA–PBE functional and hybrid B3LYP functional calculations show a weak interaction between CPS molecules. This further confirms that GGA

functionals fail to represent weak interactions.

Fig. 3. Typical minimum structures extracted from first principles molecular
dynamics.

61

One can clearly see that the binding energies strongly depend
on the number of SiAH bonds that are oriented toward the centers
of the rings of other CPS molecule. In the case of configuration A,
two SiAH bonds of two CPS molecules are oriented toward the center of the ring of each molecule. In the case of configuration B, only
one SiAH bond of a CPS molecule is oriented toward the ring of the
other CPS molecule. In contrast, no SiAH bond is oriented toward
the ring of another CPS molecule in the case of configurations C
and D; however the SiAH bond is oriented toward the SiASi bond
of the other CPS molecule. From this result, we can suggest that the
SiAH bonds that are oriented toward the center of the ring or the
SiASi bond of the other CPS molecule plays a crucial role in the
interaction between CPS molecules.
In order to gain an insight into the nature of the interaction between CPS molecules and the role of SiAH bonds that are oriented
toward the center of the ring of a CPS molecule in the interaction,
electronic structures of these configurations were analyzed. The
deformation of the electron density distribution of two CPS molecules approaching each other was calculated by using Eq. (2)

Mq ¼ q2CPS À ðqCPS1 þ qCPS2 Þ

ð2Þ

where q2CPS is the electron density of the two interacting CPS molecules; qCPSÀ1 and qCPSÀ2 are electron densities of the two isolated
CPS molecules. The cross sections of the deformation of the electron

density distribution of two mutually interacting CPS molecules in
configurations A, B, C, and D are shown in Fig. 4. A significant deformation of the electron density can be found in the area between CPS
molecules, as compared to the original electron density distribution
of the isolated molecules. For configuration A and configuration B,
we can see the special deformation in electron density in the area
where SiAH bonds is oriented toward the center of the CPS rings.
It is clearly seen that electron density decreases at the center of
the SiAH bonds and increases in the area between the H atom of
the SiAH bonds and the center of the penta-rings. The existence
of such areas implies that a significant bi-directional charge transfer
between two CPS molecules has occured. The shape of the deformation of electron density shown in Fig. 4 suggests that there is charge
transfer from SiAH r-bonding orbitals to the LUMO of CPS molecues. A similar phenomenon has also observed for the well-established case of hydrogen bonds in others systems [20,24]. Further,
from the viewpoint of MO theory, we can explain this result by a
significant overlapping between the electronic states the molecules
or the delocalization of MOs [6,20].
Fig. 5 shows the wavefunctions corresponding to configuration
A. These wavefunctions may be assigned to the bonding state and
anti-bonding states that arise from the overlapping of the molecular orbitals of the two molecules. Fig. 5(a) clearly shows that the
sign of the wavefunction does not change along the line connecting
two molecules, while in Fig. 5(b), the sign of wavefunction changes
along this line. This result confirms the suggestion that the mode of
interaction between orbitals of two CPS molecules is the mutual
delocalization between the HOMO and LUMO. It should be noted
that the such a picture is not observed in the case of two cyclopentane (C5H10) molecules in the similar configurations. No significant
deformation of the electron density distribution is observed in the
region between cyclopentane molecules.
In the cases of configurations C and D the deformation of electron density distribution is much smaller than that in the cases of
configurations A and B. The SiAH bonds that are oriented toward
the center of the rings, therefore, significantly enhance the overlapping of electronic states of CPS molecules in the configurations A
and B. We can hence suggest that the interaction between two

CPS molecules in which the SiAH bond of one molecule is oriented
toward the center of the other CPS molecule constitutes a local
bond and the SiAH bond acts as an electron donor to the other


62

P.T. Lam et al. / Chemical Physics 400 (2012) 59–64

Table 1
The binding energies [DE (eV)] and the equilibrium distances between the centers of mass of the two CPS molecules [De (Å)].
VWN

PBE
⁄⁄

A
B
C
D

DE
De
DE
De
DE
De
DE
De

B3LYP
⁄⁄

MP2
⁄⁄

6-311G

aug-cc-pvdz

6-311G

aug-cc-pvdz

6-311G

aug-cc-pvdz

6-311G⁄⁄

aug-cc-pvdz

0.481
4.19
0.346
4.48
0.208
6.77
0.247
6.11

0.581
4.16
0.356
4.50
0.265
6.78
0.311
6.11

0.043
4.91
0.032
6.28
0.025
7.82
0.032
6.75

0.093
4.92
0.068
6.00
0.049
7.50
0.046
7.12

À0.005
5.31

0.000
10.18
0.001
11.59
0.000
11.92

0.004
5.30
0.005
10.21
0.005
7.913
0.006
8.29

0.440
4.53
0.272
4.88
0.118
7.28
-

0.479
4.42
0.377
5.21
0.234
7.15

-

Table 2
Melting point (MT) and boiling point (BP) data of certain silane compounds [10].
Compound

MP/°C

BP/°C

n-Si5H12
iso-Si5H12
neo-Si5H12
n-Si6H14
neo-Si6H14
n-Si7H16
cyclo-Si5H10
cyclo-Si6H12

À72.8
À109.8
À57.8
À47.7
À47.7
À30.1
À10.5
+16.5

153.2
146.2

130.0
193.6
193.6
226.8
194.3
226.0

Fig. 4. Cross section of the deformation of electron density distribution.

Intensity (arb)

NVE
400K
500K
CPS

1800

500

1000

1900

1500

2000

2000

2100

2500

Frequency (cm-1)
Fig. 6. IR spectra of liquid CPS calculated from molecular dynamic simulations.
Magenta line corresponds to the IR spectrum of a single CPS molecule.

Fig. 5. Bonding state (HOMO-4, 0.3 eV below HOMO level) (a) and anti-bonding
state of (LUMO) (b) of hydrogen bonds of 2 CPS molecules.

CPS molecule. This interaction is similar to the well-known weak
hydrogen bond with p proton acceptors or electron donnors
(p = benzene ring, C„C triple bond, C@C double bond, Py, Im)
[24]. However, the bond energies of such hydrogen bonds
($65 meV [28]) are much smaller than those of the interactions between CPS molecules ($0.5 eV). The interaction between CPS molecules can therefore be considered as ‘‘hydrogen bond’’ between
SiAH bonds and penta-rings of CPS molecules. It should be noted
that the suggestion about the mode of interaction between orbitals
of two CPS molecules being the mutual delocalization between LUMOs and occupied orbitals is well consistent with the model of a
hydrogen bond in which the penta-ring of CPS the serves as an
electron acceptor. Further, the symmetry of the deformation of
the electron density distribution with the bonding state and the
anti-bonding state suggests that the formation of hydrogen bonds
between the CPS molecules can be attributed to the overlapping
between the r orbital corresponding to the SiAH bond, electron

donor, and the LUMO of the remaining CPS molecule, electron
acceptor. This is similar to the concept of r-conjugation in silane
compounds in which the overlapping of r SiASi orbitals was used
to explain the optical properties and photochemistry of oligomeric

silanes [15,26,21].
The fact that the hydrogen bonds are induced by the SiAH
bonds that are oriented toward the center of the ring of a CPS molecule can be inferred as the reason for the relatively high boiling
points of cyclopentasilane and cyclohexasilane as compared to
those of silanes with the comparable molecular mass. As shown
in Table 2 [10], the melting points of n-Si5 H12 and iso-Si5H12 are
À72.8 °C and À109.8 °C, respectively, while those of CPS and cyclohexasilane are À10.5 °C and +16.5 °C, respectively. A similar tendency is observed for the boiling point data in Table 2. This
implies that the hydrogen bonds formed by the SiAH bonds oriented toward the center of the CPS ring may play a significant role
in the interaction between CPS molecules and also between cyclohexasilane molecules in their liquid and solid states.
It is well known that in the water, the hydrogen bonds strongly
modify the infrared (IR) spectrum of single water molecules; the
hydrogen bonds broaden and red-shift the peaks corresponding
to the OAH stretch vibration of the OAH bond. To confirm this


P.T. Lam et al. / Chemical Physics 400 (2012) 59–64

property, we carried out a frequency analysis of a 2 CPS molecules
system (by analytical methods). Our analysis result shows that the
stretch vibration of the SiAH bonds that get involved into hydrogen bonds significantly shifts in the red direction from that of
the single CPS molecule. This implies that the formation of hydrogen bonds also modifies the stretch vibration of SiAH bonds. This
similarity to the water system provides further evidence of the formation of hydrogen bonds between CPS molecules. The calculation
of IR spectrum from molecular dynamics simulation shows the
same result as shown in Fig. 6.
5. Structural and bonding properties of liquid CPS
We have carried out first principle molecular dynamics simulations of liquid CPS with a system of 27 CPS molecules. The structure of liquid CPS is characterized using pair correlation radial
distribution functions (RDFs) between the center of mass (CM) of
CPS molecules and silicon (gCenterÀSi(r)) and those between the
CM of the CPS molecules and hydrogen gCenterÀH(r). The main purpose of the simulations is to evaluate the hydrogen bond to the
structure of liquid CPS.

We compared the computed RDFs of the liquid system with the
geometrical structure of a single CPS molecule. Fig. 7(a) and (b)
show the obtained pair correlation RDFs gCenterÀH(r) and gCenterÀSi(r),
respectively, of the liquid system.
The gCenterÀH(r) function of a simulation for a pseudo-liquid
structure at 50 K exhibits a pronounced peak located at approximately 2.1 Å, which does not correspond to any structure of a single CPS molecule. This peak can be attributed to the hydrogen

(a) 6.00

CPS

5.00

63

atoms that are involved in the hydrogen bonds (SiAH bonds of
which are oriented toward the center of the ring of the CPS molecule), as discussed earlier. At 300 K, this peak becomes a shoulder
of a high peak located at 3.0 Å. These results suggest that the thermal motion of molecules at high temperatures weaken the hydrogen bonds. A detailed analysis shows that the ratio between the
number of H atoms involved in the hydrogen bonds and the number of CPS molecules is nearly 1:1. This is a clear evidence of the
formation of the hydrogen bond in the liquid phase of CPS.
Since the structure of CPS molecules is not ideally planar, the
hydrogen atoms are at different distances from the center of mass
of a molecule, ranging from 2.6 Å to 3.3 Å. The peaks appearing in
the range of 2.6–3.4 Å, therefore, arise from these hydrogen atoms.
Our analysis confirms that each CPS molecule has 10 hydrogen
atoms within this range. A broad peak is observed around 5.0 Å
at 300 K. At 50 K, this peak decomposes into three peaks located
at 4.4 Å, 5.3 Å, and 5.8 Å. For a single CPS molecule, no peaks exist
in this range. These peaks, hence, correspond to the distances from
the center of mass of one CPS molecule to hydrogen atoms of its

neighboring CPS molecule in the configurations A and B, as shown
in Fig. 3.
An analysis of gCenterÀSi(r) of the liquid system was carried out in
the same manner. gCenterÀSi(r) exhibits a sharp peak at approximately 2.1 Å, which corresponds to the distance from the center
of mass of a CPS molecule to its Si atoms. We can also observe
broad peaks in the range of 3.5–5.5 Å. These peaks can be assigned
to the contribution of the Si atoms of a neighboring CPS molecules
that are involved in the hydrogen bonds (SiAH bonds of which are
oriented to the center of the ring of the CPS molecule) in configurations A and B. The results of the simulations for the liquid system, therefore, have a good correspondence with those for two
CPS molecules, previously presented. The most important finding
in the simulations is the significant role of hydrogen bonds in the
structure of the liquid system.

gCenter-H(r)

4.00

6. Conclusion

3.00
2.00
1.00
0.00
0.00

2.00

4.00

(b) 50.00

6.00

8.00

10.00

CPS

3.00

40.00

gCenter-Si(r)

1.50
30.00
0.00
3.00

4.50

6.00

20.00

10.00

0.00
0.00

Ab-initio calculations were carried out to investigate the interactions between CPS molecules, and the structure of liquid CPS.
The simulations were carried out by using DFT methods, HF methods, and MP2 methods formulated in the Dmol3 code and the G03
package. We found that the SiAH bonds that are oriented toward
the center of the ring of a CPS molecule play a significant role in
the interaction between CPS molecules as these bonds enhance
the overlapping of the electronic states of the CPS molecules. This
interaction results in the formation of special bonds between CPS
molecules which resemble hydrogen bonds. These hydrogen bonds
cause the red shift of IR absorption peaks corresponding to the
SiAH stretch vibration. The pair correlation radial distribution
function gCenterÀH(r) shows a peak at approximately 2.0 Å, which
is attributed to the hydrogen atom involved in the hydrogen bond,
while gCenterÀSi(r) shows a peak at approximately 3.3 Å of the Si
atom in a hydrogen bond. The results show that hydrogen bonds
have a significant contribution to the structure of the CPS liquid
system. The hydrogen bonds found in this study are considered
to play a key role in the reactions in CPS solution.
References

2.00

4.00

6.00

8.00

10.00

Fig. 7. Pair correlation radial distribution functions: Center of mass of CPS
molecules and hydrogen (a), center of mass of CPS molecules and silicon (b). Red
lines corresponds to the pair correlation radial distribution functions of a single CPS
molecule. (For interpretation of the references to colour in this figure legend, the
reader is referred to the web version of this article.)

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