Chemical Physics 400 (2012) 59–64 Contents lists available at SciVerse ScienceDirect 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 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: dam@jaist.ac.jp (D.H Chi) 0301-0104/$ - see front matter Ó 2012 Elsevier B.V All rights reserved http://dx.doi.org/10.1016/j.chemphys.2012.02.010 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 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 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 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 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 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 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 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 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 Electronic structure of isolated CPS molecule Fig 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 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 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 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 These configurations were fully relaxed for reaching more accurate minimum energy configurations The binding energies were calculated using Eq (1) DE ¼ 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 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 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 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 qCPS1 ỵ qCPS2 ị 2ị 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 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 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 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 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 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 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 IR spectra of liquid CPS calculated from molecular dynamic simulations Magenta line corresponds to the IR spectrum of a single CPS molecule Fig Bonding state (HOMO-4, 0.3 eV below HOMO level) (a) and anti-bonding state of (LUMO) (b) of hydrogen bonds of 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 [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 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 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 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 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 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 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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