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

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 study h

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Ab-initio study of intermolecular interaction and structure of liquid

cyclopentasilane

Pham Tien Lama, Ayumu Sugiyamaa,b, Takashi Masudab, Tatsuya Shimodaa,b, Nobuo Otsukaa,

Dam Hieu Chia,b,c,⇑

a

Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan

b Japan Science and Technology Agency, ERATO, Shimoda Nano-Liquid Process Project, 2-5-3 Asahidai, Nomi, Ishikawa 923-1211, Japan

c

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 interac-tion results in the formainterac-tion 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 vibra-tion 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 con-tribution of hydrogen bonds to the structure of the CPS liquid system

1 Introduction

In recent years, liquid processes for fabricating electronic

de-vices have attracted considerable attention In contrast to

conven-tional 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]

Li-quid 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

solu-tions containing materials, for a target device is the most

impor-tant step in the liquid processes For the fabrication of electronic

devices, cyclopentasilane (Si5H10-CPS) is the most suitable

candi-date for a source material of functional solutions among various

silicon compounds because it has the ability to undergo

ring-open-ing 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

photo-polymerization[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,

however, it is necessary to clarify and control the entire micro-scopic 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 calcu-lations 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 mole-cules This interaction results in the formation of special bonds be-tween 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 simula-tions using a system of 27 CPS molecules The pair correlation ra-dial distribution functions (RDFs) between the centers of mass of CPS molecules and H atoms, gCenterH(r), and those between the center of mass of CPS molecules and Si atoms, gCenterSi(r), were analyzed gCenterH(r) shows a peak at approximately 2.1 Å, which

is attributed to the hydrogen atoms which are involved in a

⇑ Corresponding author at: Japan Advanced Institute of Science and Technology,

1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan.

E-mail address: dam@jaist.ac.jp (D.H Chi).

Contents lists available atSciVerse ScienceDirect

Chemical Physics

j o u r n a l h o m e p a g e : w w w e l s e v i e r c o m / l o c a t e / c h e m p h y s

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hydrogen bond, while gCenterSi(r) shows a peak at approximately

3.3 Å of the Si atom in a hydrogen bond The results indicate a

sig-niﬁcant contribution of hydrogen bonds to the structure of the CPS

liquid system Further, we believe that the hydrogen bonds

inves-tigated 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

computa-tional costs; however, they fails in describing the intermolecular

interaction that is mainly driven by dispersion forces The

calcula-tion results strongly depend on the employed

exchange–correla-tion funcexchange–correla-tionals employed Local density approximaexchange–correla-tion (LDA) for

exchange–correlation functionals has been reported to

overesti-mate 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 Dmol3code

[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

mol-ecules were estimated by the depth of the potential well on the

PES The reference potential energies were chosen as the total

en-ergy of the two CPS molecules system with a separation of 10 Å

Fig 1shows typical PES for the interaction between two CPS

mol-ecules, calculated using Dmol3code 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

be-tween 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

de-pends 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 attrac-tion The VWN-functional with the standard double numerical plus polarization function (DNP) formulated in Dmol3code 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 dis-tance 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 agree-ment 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 interac-tion between two CPS molecules; hence the simulainterac-tions were car-ried out using the LDA–VWN functional with DNP basis set formulated in the Dmol3code 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 for-mulated in Gaussian 03 code

For ab initio MD simulations of liquid CPS with a supercell con-taining 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 simu-lations The total length of simulation is 10 ps, and the result of the last 5 ps was used for the analysis The computations were per-formed only at theCpoint 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 be-tween 2 CPS molecules The results are in a good agreement with MP2 and LDA–VWN functional calculations We have used a super-cell with a side length of 19.123 Å Such a supersuper-cell size represent CPS under ambient conditions at density of 0.963 g cm1

3 Electronic structure of isolated CPS molecule

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 ofrorbitals,[15,27]is

an important characteristic of CPS.Fig 2shows the lowest unoccu-pied molecular orbital (LUMO) and highest occuunoccu-pied molecular orbital (HOMO) of CPS molecule The LUMO appears similar to the lowestp-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 conjugatedp-orbitals of the penta-ring and s-orbitals of the hydrogen atoms in a CPS molecule On the other hand, the HOMO is an anti-bonding molecular orbital

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from ar-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

prin-ciples molecular dynamic simulations The obtained conﬁgurations

are shown inFig 3 These conﬁgurations were fully relaxed for

reaching more accurate minimum energy conﬁgurations The

bind-ing energies were calculated usbind-ing Eq.(1)

in which ECPSis the total energy of an isolated CPS molecule with

the twist conﬁguration, and E2CPSis 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 inTable 1

According to the LDA–VWN and MP2 calculations, conﬁguration

A and conﬁguration B are signiﬁcantly more stable than the

remaining conﬁgurations, as seen inTable 1 The binding energy

and the equilibrium distance between the CPS molecules in

conﬁg-uration 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

func-tional and hybrid B3LYP funcfunc-tional calculations show a weak

inter-action between CPS molecules This further conﬁrms that GGA

functionals fail to represent weak interactions

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 cen-ter 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 be-tween 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 mole-cules approaching each other was calculated by using Eq.(2)

whereq2CPSis the electron density of the two interacting CPS mol-ecules;qCPS1andqCPS2are 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 inFig 4 A signiﬁcant defor-mation 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 deforma-tion of electron density shown inFig 4suggests that there is charge transfer from SiAHr-bonding orbitals to the LUMO of CPS mole-cues A similar phenomenon has also observed for the well-estab-lished 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]

A These wavefunctions may be assigned to the bonding state and anti-bonding states that arise from the overlapping of the molecu-lar 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 inFig 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 cyclopen-tane (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 elec-tron 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 overlap-ping 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

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.)

Fig 3 Typical minimum structures extracted from ﬁrst principles molecular

dynamics.

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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

be-tween CPS molecules (0.5 eV) The interaction bebe-tween CPS

mol-ecules 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

LU-MOs 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 ther orbital corresponding to the SiAH bond, electron

donor, and the LUMO of the remaining CPS molecule, electron acceptor This is similar to the concept ofr-conjugation in silane compounds in which the overlapping ofrSiASi 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 mol-ecule 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

inTable 2 [10], the melting points of n-Si5H12and iso-Si5H12are

72.8 °C and 109.8 °C, respectively, while those of CPS and cyclo-hexasilane are 10.5 °C and +16.5 °C, respectively A similar ten-dency is observed for the boiling point data in Table 2 This implies that the hydrogen bonds formed by the SiAH bonds ori-ented toward the center of the CPS ring may play a signiﬁcant role

in the interaction between CPS molecules and also between cyclo-hexasilane 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

Table 1

The binding energies [DE (eV)] and the equilibrium distances between the centers of mass of the two CPS molecules [D e (Å)].

6-311G ⁄⁄

aug-cc-pvdz 6-311G ⁄⁄

aug-cc-pvdz

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

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.

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

Frequency (cm -1 )

NVE 400K 500K CPS

1800 1900 2000 2100

Fig 6 IR spectra of liquid CPS calculated from molecular dynamic simulations Magenta line corresponds to the IR spectrum of a single CPS molecule.

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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

hydro-gen bonds signiﬁcantly shifts in the red direction from that of

the single CPS molecule This implies that the formation of

hydro-gen bonds also modiﬁes the stretch vibration of SiAH bonds This

similarity to the water system provides further evidence of the

for-mation of hydrogen bonds between CPS molecules The calculation

of IR spectrum from molecular dynamics simulation shows the

same result as shown inFig 6

5 Structural and bonding properties of liquid CPS

We have carried out ﬁrst principle molecular dynamics

simula-tions of liquid CPS with a system of 27 CPS molecules The

struc-ture of liquid CPS is characterized using pair correlation radial

distribution functions (RDFs) between the center of mass (CM) of

CPS molecules and silicon (gCenterSi(r)) and those between the

CM of the CPS molecules and hydrogen gCenterH(r) The main

pur-pose 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 gCenterH(r) and gCenterSi(r),

respectively, of the liquid system

The gCenterH(r) function of a simulation for a pseudo-liquid

structure at 50 K exhibits a pronounced peak located at

approxi-mately 2.1 Å, which does not correspond to any structure of a

sin-gle CPS molecule This peak can be attributed to the hydrogen

atoms that are involved in the hydrogen bonds (SiAH bonds of which are oriented toward the center of the ring of the CPS mole-cule), 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 ther-mal motion of molecules at high temperatures weaken the hydro-gen bonds A detailed analysis shows that the ratio between the number of H atoms involved in the hydrogen bonds and the num-ber 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

inFig 3

An analysis of gCenterSi(r) of the liquid system was carried out in the same manner gCenterSi(r) exhibits a sharp peak at approxi-mately 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 conﬁgu-rations A and B The results of the simulations for the liquid sys-tem, 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

6 Conclusion Ab-initio calculations were carried out to investigate the inter-actions between CPS molecules, and the structure of liquid CPS The simulations were carried out by using DFT methods, HF meth-ods, and MP2 methods formulated in the Dmol3code 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 gCenterH(r) shows a peak at approximately 2.0 Å, which

is attributed to the hydrogen atom involved in the hydrogen bond, while gCenterSi(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

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