Thiết kế các vật liệu nano từ các cluster trộn sinmm

SỞ KHOA HỌC VÀ CƠNG NGHỆ TP HỒ CHÍ MINH VIỆN KHOA HỌC VÀ CƠNG NGHỆ TÍNH TỐN BÁO CÁO TỔNG KẾT THIẾT KẾ CÁC VẬT LIỆU NANO TỪ CÁC CLUSTER TRỘN SinMm Đơn vị thực hiện: PTN Khoa học phân tử Chủ nhiệm đề nhiệm vụ: TS Nguyễn Minh Tâm TP HỒ CHÍ MINH, THÁNG 05/2018 SỞ KHOA HỌC VÀ CƠNG NGHỆ TP HỒ CHÍ MINH VIỆN KHOA HỌC VÀ CƠNG NGHỆ TÍNH TỐN BÁO CÁO TỔNG KẾT THIẾT KẾ CÁC VẬT LIỆU NANO TỪ CÁC CLUSTER TRỘN SinMm Viện trưởng: Nguyễn Kỳ Phùng Đơn vị thực hiện: PTN Khoa học phân tử Chủ nhiệm nhiệm vụ: TS Nguyễn Minh Tâm Nguyễn Minh Tâm TP HỒ CHÍ MINH, THÁNG 05/2018 Thiết kế vật liệu Nano từ Cluster trộn SinMm MỤC LỤC Trang MỞ ĐẦU ĐƠN VỊ THỰC HIỆN KẾT QUẢ NGHIÊN CỨU I Báo cáo khoa học II Tài liệu khoa học xuất 30 III Chương trình giáo dục đào tạo 31 IV Hội nghị, hội thảo 32 V File liệu 33 TÀI LIỆU THAM KHẢO 34 CÁC PHỤ LỤC 36 PHỤ LỤC 1: Bài báo “A DFT investigation on geometry and chemical bonding of isoelectronic Si8N6V-, Si8N6Cr, and Si8N6Mn+ clusters” PHỤ LỤC 2: Bài báo “On the role of different types of electron in double ring tubular clusters” PHỤ LỤC 3: Bài báo “B3@Si12+: strong stabilizing effects of a triatomic cyclic boron unit on tubular silicon clusters” Viện Khoa học Cơng nghệ Tính tốn TP Hồ Chí Minh Page Thiết kế vật liệu Nano từ Cluster trộn SinMm MỞ ĐẦU Trong dự án này, đề xuất tiếp tục mở rộng nghiên cứu lý thuyết cluster silicon pha tạp Silicon vật liệu ứng dụng nhiều ngành cơng nghiệp bán dẫn, đặc biệt cho bóng bán dẫn Trong xu hướng thu nhỏ, thiết bị điện tử sớm đạt tới kích thước cluster nguyên tử Do đó, hạt nano dựa silic xem vật liệu hứa hẹn cho hệ thiết bị điện tử xác định chuẩn bị tạp chất thích hợp Thuộc tính cluster chủ yếu xác định chất nguyên tố kích thước chúng Khi đưa vào tạp chất, gọi tượng pha tạp, thuộc tính cụm nguyên tố sửa đổi Điều phụ thuộc vào chất tạp chất Nếu biết rõ cấu trúc tính chất cluster pha tạp phù hợp, đặc tính cluster pha tạp kiểm sốt, thu tính chất thích hợp Tuy nhiên, việc pha tạp thách thức liên tục khoa học cluster, địi hỏi thí nghiệm cẩn thận phân tích lý thuyết thích hợp Trong bối cảnh này, điều quan trọng thiết kế cluster silicon có độ bền nhiệt động lực học cao cách đưa tạp chất nguyên tử kim loại nguyên tố nhóm khác, cách sử dụng phương pháp lý thuyết Từ kết lý thuyết, cluster tiềm đề xuất làm khối xây dựng cho vật liệu nano chức với ứng dụng công nghệ định Viện Khoa học Cơng nghệ Tính tốn TP Hồ Chí Minh Page Thiết kế vật liệu Nano từ Cluster trộn SinMm Trong đề tài này, đề xuất nghiên cứu sâu có hệ thống hiệu ứng số kim loại chuyển tiếp 3d 4d (Nb, Mo, Ta, W, Mn Fe) cho cấu trúc hình học cấu trúc điện tử cluster silicon Các kim loại chuyển tiếp với cấu hình điện tử khác hoạt động khác pha tạp thành cluster Si Ví dụ, đồng với orbital 3d ưa thích để hấp thụ cạnh mặt đồng phân bền cluster silicon tinh khiết Mặt khác, vanadi có orbital nhỏ nửa 3d thay cho vị trí đồng phân bền cluster silicon Các yếu tố kiểm soát hành vi kim loại chuyển tiếp cluster silicon tìm thấy Tuy nhiên, ảnh hưởng tạp chất thứ hai thứ ba vào cụm silicon chưa rõ ràng Khi tìm quy tắc điều chỉnh mơ hình tăng trưởng cluster silicon pha tạp, thiết kế số cluster với tính chất định, từ cụm đến cụm khối xây dựng cho ống nano, dây nano, fullerene… Từ quan điểm bản, kết hóa học lượng tử hợp lý hóa cách sử dụng phương pháp lý thuyết khác mơ hình vỏ electron, phân vùng mật độ electron hàm sóng Một số quy tắc chung liên quan đến quy tắc đếm điện tử, tính thơm xây dựng Sử dụng quy tắc đơn giản giúp hiểu dự đốn tính chất vật liệu Silicon Viện Khoa học Cơng nghệ Tính tốn TP Hồ Chí Minh Page Thiết kế vật liệu Nano từ Cluster trộn SinMm Lời cảm ơn đến ICST Cơng trình hỗ trợ Sở Khoa học Công nghệ Viện Khoa học Cơng nghệ Tính tốn (ICST) Thành phố Hồ Chí Minh, Việt Nam, theo Hợp đồng số 196/2016/ HÐ-SKHCN ngày 20/12/2016 Viện Khoa học Cơng nghệ Tính tốn TP Hồ Chí Minh Page Thiết kế vật liệu Nano từ Cluster trộn SinMm ĐƠN VỊ THỰC HIỆN Phịng thí nghiệm: Khoa học Phân Tử Chủ nhiệm đề tài: Nguyễn Minh Tâm, Tiến sĩ Thành viên đề tài: Phạm Tấn Hùng, Thạc sĩ Phạm Hồ Mỹ Phương, Tiến sĩ Dương Văn Long, Thạc sĩ Nguyễn Minh Thọ, Tiến sĩ Cơ quan phối hợp: Viện Khoa học Cơng nghệ Tính tốn TP Hồ Chí Minh Page Thiết kế vật liệu Nano từ Cluster trộn SinMm KẾT QUẢ NGHIÊN CỨU I BÁO CÁO KHOA HỌC Cluster silicon pha tạp Boron Cả hai ion B3+ B3- xem hợp chất thơm kép bền.[1] Tính tốn DFT khảo sát quang phổ quang điện tử gần anion B3Si4-10khơng tìm thấy cấu trúc endohedral.2 Trong bối cảnh đó, chúng tơi tiến hành tìm kiếm đơn vị tam ngun làm bền ống Si, thấy chuỗi BxSi120/+ với x = 1, kiểu cấu trúc mới, cấu trúc đối xứng cao D3h B3 nằm ngang lăng trụ Si12 (6 x 2), xác định cấu trúc bền cation B3Si12+ Viện Khoa học Cơng nghệ Tính tốn TP Hồ Chí Minh Page Thiết kế vật liệu Nano từ Cluster trộn SinMm Hình Cấu trúc hình học Si12, BSi12+, B2Si12 B3Si12+ clusters (TPSSh/6311+G(d)) Đặc điểm hình học cụm BSi12+, B2Si12 B3Si12+ biểu diễn hình Kết tính toán nguyên tử pha tạp B khơng ảnh hưởng đến hình dạng Si12 Các khung Si cấu trúc BSi12+ thực tế không thay đổi (Hình 1) Kết tính tốn DFT G4 cho thấy xuất hai nguyên tử B dẫn đến đồng phân bền B2Si12 cấu trúc hình ống bị bóp méo (Hình 1) Do đó, nhị nguyên B2 chèn vào bên lăng trụ Si12 đối xứng thấp (6 x 2) Mặc dù xuất đồng phân hình ống B2Si12 nhấn mạnh tác dụng hai tạp chất B Si12, suy biến lượng hai cấu Viện Khoa học Cơng nghệ Tính tốn TP Hồ Chí Minh Page Thiết kế vật liệu Nano từ Cluster trộn SinMm trúc ống lồng bị vỡ hai nguyên tử B không đủ để tăng độ bền nhiệt động lực học ống Si12 Việc xác định cấu trúc B3@Si12+ bền với hình học D3h singlet (Hình 1), vịng B3 gói lăng trụ Si12 (6 x 6) Tính đối xứng cao B3+ trì, độ dài liên kết B-B B3 lên đến 1,75 Å, dài đáng kể so với cluster B3-/0/+ tự (1.55 - 1.57 Å TPSSh / 6-311 + G (d)) Sự tồn cấu trúc D3h B3@Si12+ nhấn mạnh tác dụng đáng kể cấu trúc đơn vị B3 việc làm bền hình dạng ống Si12 mà theo nghiên cứu thực tế trước cho thấy cluster Si12 tinh khiết khơng có hình dạng đặc biệt (Hình 1) a) b) Hình Phân tích ELF giá trị phân nhánh 0.7 a) mặt bên b) mặt đỉnh Sự xuất B3@Si12+ với cấu trúc B3 hoàn toàn bao phủ ống Si12 rõ ràng chứng minh vịng B3 đáp ứng u cầu hình học để tạo thành vịng tam giác motif hình ống Dọc theo đường này, ba kim loại chuyển Viện Khoa học Cơng nghệ Tính tốn TP Hồ Chí Minh Page Thiết kế vật liệu Nano từ Cluster trộn SinMm PHỤ LỤC 2: Bài báo : On the role of different types of electron in double ring tubular clusters Tạp chí : Chem Phys Lett 685, 2017, 377-384 Tác giả : Dương Văn Long, Minh Thọ Nguyễn Viện Khoa học Cơng nghệ Tính tốn TP Hồ Chí Minh Page 37 Chemical Physics Letters 685 (2017) 377–384 Contents lists available at ScienceDirect Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett Research paper On the role of different types of electron in double ring tubular clusters Long Van Duong c, Minh Tho Nguyen a,b,d,⇑ a Computational Chemistry Research Group, Ton Duc Thang University, Ho Chi Minh City, Viet Nam Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Viet Nam c Institute for Computational Science and Technology (ICST), Ho Chi Minh City, Viet Nam d Department of Chemistry, KU Leuven, Celestijnenlaan 200F, B-3001 Leuven, Belgium b a r t i c l e i n f o Article history: Received 14 May 2017 In final form 30 July 2017 Available online 31 July 2017 a b s t r a c t Partial electron localization functions ELF(r_loca), ELF(p) and ELF(r_delo) of boron Bn and silicon MSi12 double ring (DR) clusters were analyzed In a DR, separated basins are localized within peripheral bonds (r), delocalized outside inner bonds (p), or delocalized above and below peripheral bonds (r) MO spectrum of skeleton D6h Si12 DR follows delightfully the hollow cylinder model A mixture of different sets of MOs makes the D6h Si12 structure highly unstable Upon interacting with 3d orbitals of Cr dopant, such a mixed behavior of MO sets is removed and the Cr@Si12 DR becomes a global minimum structure Ó 2017 Elsevier B.V All rights reserved Introduction Although a wavefunction, or an electron density, contains in principle all chemical information about the corresponding molecular system, it does not give a clear picture on the electron distribution Therefore, it is often preferable to partition such a total wavefunction or total electron density into different regions, or basins, that can be viewed as the more conventional chemical bonds, lone pairs For this purpose, quantum chemical techniques including the localization of molecular orbitals (LMO, being a partition of wavefunction) [1] and the electron localization function (ELF, being a partition of electron density) [2] have long been available In the latter approach, an additional topological analysis of the total ELF, which can be partitioned in terms of contributions from r electrons (ELF-r) and p electrons (ELF-p), further helps to define the nature of localized electrons and to quantify them [3,4] In the ELF approach, the partition of electron density is dependent on the bifurcation values of the function [2] The ELF value, g (r), is confined within the [1,0] interval by expression (1): grị ẳ 1ỵ
2 ð1Þ D Dh where D and Dh are the local kinetic energy density due to the Pauli exclusion principle and the Thomas–Fermi kinetic energy density, respectively A topological analysis of the ELF map shows that a ⇑ Corresponding author at: Computational Chemistry Research Group, Ton Duc Thang University, Ho Chi Minh City, Viet Nam E-mail addresses: minh.nguyen@kuleuven.be, nguyenminhtho@tdt.edu.vn (M.T Nguyen) http://dx.doi.org/10.1016/j.cplett.2017.07.079 0009-2614/Ó 2017 Elsevier B.V All rights reserved structure whose ELF isosurface has a high bifurcation value exhibits an aromatic character, whereas a structure possessing a low bifurcation ELF value is not aromatic In polycyclic hydrocarbons, while bifurcation values of ELF-p function are significantly variable, ranging for example from ELF-p = 0.91 in benzene to ELF-p = 0.35 in cyclooctatetraene, bifurcation values of the ELF-r function are close to a value of ELF-r = 0.35 Hence, the ELF-p value has frequently been used to predict the aromatic character of polycyclic hydrocarbons, whereas the ELF-r counterparts are often neglected In these systems, the ELF-r values only point out the existence of center – electron (2c–2e) bonds such as the total number of CAC and CAH bonds equals to that of r valence (localized) molecular orbitals (MOs) The ELF-r partitions [5] or both ELF-r and ELF-p partitions [6] have been applied to interpret the aromatic character of planar boron clusters [7] In these systems, bifurcation values of ELF-r function have been found to be significantly variable, resulting from a mixture of both r localized and r delocalized electrons (or molecular orbitals) It means that either r delocalized or r localized MOs make their own contributions to the electron cloud In other words, the behaviour of localized and delocalized electrons differs much from each other, and need to be investigated separately However, while p electrons are mainly delocalized, a distinction between the sets of r localized and r delocalized electrons in a certain type of molecules is not a simple task We recently studied the electronic structure of multiple ring boron tubes [8,9] which contain each different sets of localized and delocalized electrons using some simple models of electron in cylinders These models allowed us to recover the construction of the valence MOs in this class of tubular molecules Although the different types of electron can here clearly be distinguished, 378 L.V Duong, M.T Nguyen / Chemical Physics Letters 685 (2017) 377–384 their specific role in the stabilization of a tubular cluster was not fully understood yet In attempt to further understand the duties of r MOs in double ring tube, we analyze in the present study the structure which contains both r localized and r delocalized MOs using an ELF analysis The structures considered include a series of small pure boron clusters B2n with different charge states, and CrSi12 which is a representation of series of transition metal doped silicon clusters TM@Si12 We would stress that the different forms of boron nanotubes have been synthetized [10,11], and we hope that the present predictions would stimulate further experimental preparation of this class of boron compounds Computational methods Standard electronic structure computations are carried out using density functional theory (DFT) with the aid of the Gaussian 09 program [12] Geometry optimizations are performed using the TPSSh functional [13] in conjunction with the 6-311+G(d) basis set Canonical molecular orbitals are constructed using this DFT method The ELF maps, and the partition yielding the contributions of different classes of MOs to the ELF partitions are calculated using the DGrid-4.6 program [14], and their isosurface maps are plotted using the Gopenmol software [15] Let us mention that while the original ELF approach [2] is a partition of the electron density, the partition in term of orbitals is rather an approximation, either by use of HF orbitals or KS orbitals Results and discussion 3.1 The pure boron double ring tubes B2n The double ring (DR) B20 structure has been studied in much detail in previous reports [8,16–20] Similar to B20, the DR B22 and B24 forms were also determined to be the energetically lowest-lying isomers of the respective sizes [18,21] We recently demonstrated that the electronic structure of the series of DR B2n with n = 10–14 can be rationalized using a one electron in a hollow cylinder model (HCM) [8] Accordingly, the shapes of the valence MOs can perfectly be predicted by the HCM The HCM and its electron count can further be applied to the triple ring (TR) tubes such as the cation B+27 [9] and the TR Si15 of the Mn2Si15 cluster [22] Each hollow cylinder contains three sets of orbitals, namely the s-orbitals (s-MOs), radial (r-MOs) and tangential (t-MOs) The energy spectrum of both sets of r-MOs and t-MOs in these small tubes allowed us to establish a specific electron count for tubular clusters The former set of MOs is rather dependent on the elements considered, either electron-deficient elements such as boron or electron-rich elements such as silicon In a N-string tube, the energy levels of the associated wave functions (MOs) are characterized by the quantum numbers such as (1 N) In an electronrich element tube these levels are occupied If the tubular form is made by electron-deficient elements, the (1 N) energy level is unoccupied while the levels (1 N1) is occupied The HCM’s electron count can be summarized as follows: in total for both radial rMOs and tangential t-MOs sets, the number of (4M) and (4M + 2) electrons with M = 0, 1, 2, 3, should be satisfied for double ring forms of electron-rich and electron-deficient elements, respectively Let us now consider the ELF obtained for the sets of s-MOs (denoted as ELF(r-loca)), r-MOs (ELF(p)), and tangential t-MOs (ELF(r-delo)) to further analyze some features of the DR Bq2n including n =  15 The charge q = 2, 0, is generated in such a way that the total number of electrons in both sets of radial rMOs set and tangential t-MOs satisfy the 4M electron count However, because the B2 14 dianion is found to be strongly distorted from DR geometry, it is not considered further Therefore, the DR clusters that satisfy the 4M count include the following structures hav2+ 2 2+ 2 2+ ing different charge states: B2+ 14, B16, B18, B18 , B20, B22, B22 , B24, B26, 2 2+ 2 B26 , B28, B30 and B30 The ELF(r-loca), ELF(p), and ELF(r-delo) basins for the s-MOs, r-MOs, and t-MOs sets of these structures are presented in Figs and S1 of the Supplementary Information (ESI) file The ELF(r-loca) maps show distribution of localized electrons The relevant basins indicate that the s-MOs set mainly include the (2c–2e) MOs with 2n localized basins forming 2n peripheral B-B bonds According to the shape of ELF(p), electrons in r-MOs set are responsible for the connection between two strings, whereas the shape of ELF(r-delo) indicates that electrons in tMOs set tend to enhance the stability of these peripheral B-B bonds (Fig 1) There are two common points for both ELF(p) and ELF(rdelo) basins First, these basins are preferentially distributed outside the structure Second, these basins tend to avoid to be associated with any specific bond, the electrons prefer to be delocalized [23] In a boron DR which satisfies the 4M electron count, the number of electrons in r-MOs is either larger than that in t-MOs by electrons (De = 4) or equal to each other (De = 0) Fig plots the graph of the peripheral B-B bond lengths and the height of DR structure (being the distance between two strings) of the DR boron clusters considered Interestingly, the height of a DR structure with De = is remarkably larger than that with De = On the contrary, the peripheral B-B bond length of a structure having De = is slightly shorter than the counterpart of the structures having De = In attempt to understand further this phenomenon, we now take a closer look at the ELF(p) and the ELF(r-delo) of the DR tubes 2 2+ 2 2+ B2+ 18, B18 , B22 and B22 displayed in Fig The DR B18 was located to be the lowest-lying isomer in a previous computational study [24], while the DR B2 18 is only an energy local minimum Actually, the global minimum of the dianion B2 18 is a quasi-planar structure [25] which is lower in energy than the corresponding DR structure by 59 kcal/mol Such a large relative energy gap between both the DR and global minimum structures in the dianion B2 18 suggests that addition of four extra electrons into the t-MOs set to the DR B2+ 18 brings in a very negative effect for the DR isomer With the same electron number in the r-MOs set (being 10 electrons), the differ2 ence between the ELF(p) bifurcation values of B2+ 18 and B18 are not significant, being 0.714 and 0.748, respectively On the contrary, the ELF(r-delo) bifurcation value of 0.795 identified for 2+ B2 18 is smaller than that of 0.973 found for B18 Upon addition of four extra electrons into the t-MOs set, more r electrons are delocalized over the peripheral B-B bonds As the results, the peripheral B-B bond distances tend to decrease In addition, r delocalized electrons are mainly distributed above and under the DR strings, and they thus push the two strings far away from each other Therefore, addition of electrons into the tMOs set leads to an increase of the DR height The B2 18 has more r delocalized electrons than the B2+ 18 and the r delocalized elec2+ trons of B2 18 have to move in a smaller space than in B18 (smaller peripheral B-B bond length leading to smaller radius of the DR) It is the reason for why the delocalization level, or otherwise put, the aromatic character of r delocalized electrons of B2 18 , is much decreased It means that addition of extra delocalized electrons has created a reversed effect on the overall stability of the dianion B2 18 , making it much less stable thermodynamically We demonstrated that the dication B2+ 22 DR is the lowest-lying isomer whereas the B2 22 DR is computed to be 21 kcal/mol higher in energy than the quasi-planar global minimum This is due to a strong charge effect [18] As compared to the cases of B2+ 18 and 2 B2 18 , the B22 DR results from four additional electrons to the rMOs set of the B2+ 22 DR The p electrons are again responsible for L.V Duong, M.T Nguyen / Chemical Physics Letters 685 (2017) 377–384 379 B182+ a) ELF( -loca) = 0.803 b) ELF( ) = 0.714 c) ELF( -delo) = 0.973 a) ELF( -loca) = 0.787 b) ELF( ) = 0.748 c) ELF( -delo) = 0.795 a) ELF( -loca) = 0.771 b) ELF( ) = 0.831 c) ELF( -delo) = 0.916 a) ELF( -loca) = 0.801 b) ELF( ) = 0.752 c) ELF( -delo) = 0.916 B182- B222+ B222- 2 2+ 2 Fig Properties of B2+ 18, B18 , B22 and B22 double ring (DR) structures (a) ELF(r-loca), (b) ELF(p), and (c) ELF(r-delo) connection between both strings of the DR Therefore, when receiving more p electrons, the DR height of structure is getting smaller (Fig 2), and the space available for p electrons moving 2+ within the DR B2 22 also becomes smaller than that in the DR B22 2+ 2 dication Interestingly, both DR B22 and DR B22 have similar ELF (r-delo) bifurcation values, while the ELF(p) bifurcation value of 2+ DR B2 22 (ELF(p) = 0.75) is smaller than that of DR B22 (ELF(p) = 0.83) It is obvious that a structure which has more delocalized electrons moving in a smaller space, tends to decrease its aromatic character Let us analyze these DR structures further to clarify this point Each of Bq2n DR structures considered has 2n peripheral B-B bonding and 2n inner B-B bonding connecting two rings together The total number of B-B bonds in this structure amount thus to 4n If the DR structure has Np electrons in r-MOs set, the electron number responsible for one inner B-B bonding is Np/2n If the DR structure has Nr electron in t-MOs set, the electron number which enhances one peripheral B-B bonding is thus Nr/2n The average number of electron per a bond is defined in Eq (2): Ndelo ẳ Np ỵ Nr 4n ð2Þ Table lists the lengths of peripheral B-B bonds, heights of DR structures, electron number in r-MOs set, electron number in tMOs set, electron number responsible for one inner B-B bond, electron number responsible for one inner B-B bonding, and average number of electrons per bond of all Bq2n DR structures considered A common point for these DR’s that are demonstrated to be 2+ 2+ global minima (B2+ 14, B18, B20, B22, B24) is that they have an average number of electron per a bond smaller than 0.5 (for dication structure) or equal to 0.5 (for neutral structure) This raises to a conclusion that the average number of electrons per bond being less than or equal to 0.5 is one necessary condition to make a DR global minimum Such a condition is in fact not sufficient Although the average number of electrons per bond of DR B28 is 0.5, this structure is found to be 4 kcal/mol higher in energy as computed at the CCSD(T) level than the global minimum [26] However, DR B28 structure can be considered as a highly aromatic isomer The ELF (p) and ELF(r-delo) of DR B28 are significantly high (ELF = 0.875 and 0.897, respectively) The average number of electron per bond of DR B16 is also 0.5, but again this structure is not stable as its relative energy is much larger with respect to the corresponding global structure The Np/2n value of B16 (being 0.625) is one of the largest Np/2n values, and the Nr/2n value of the B16 (being 0.375) is one of the smallest Nr/2n value In addition, Fig indicates that B16 has the smallest height of DR structure and largest peripheral B-B bonding length These observations on B16 reinforce the above conclusion that when adding more p electrons, the DR height of struc- 380 L.V Duong, M.T Nguyen / Chemical Physics Letters 685 (2017) 377–384 Np/2n = 0.625 in the B16, and this is the reason for why the DR B2 14 becomes strongly distorted 2 Other DR dianions such as B2 18 and B22 are local minima having low aromatic character because their Ndelo values are larger than 0.5 The decreasing Ndelo value of B2 2n with respect to the increasing cluster size leads to an increasing aromatic character Although the 2 Ndelo values of B2 26 and B30 are larger than 0.5, the ELF(p) and ELF (r_delo) bifurcation values are remarkably increased Therefore, both dianions exhibits high aromatic character However, they are not expected to be the global energy minima because the large size leads to numerous candidates and other factors emerge to be 2+ more predominant The DR B2+ 26 and B30 dications deserve to be considered as candidates for global minima because their Ndelo values are smaller than 0.5 3.2 The role of Cr atom in stabilizing the double ring Si12 structure Fig Peripheral B-B bond lengths and heights of DR structures having De = or De = ture is getting smaller and when removing r electrons, the peripheral B-B bond is getting longer Especially, the large difference between Np/2n and Nr/2n values of B16 makes the effect become more clearly via the extremes of the DR’s height and the peripheral B-B bonding length of B16 The ELF(p) bifurcation value of B16 also falls into the smallest values among the ELF(p) bifurcation values in the DR series It consolidates the conclusion that a structure which has more delocalized electrons moving within a smaller space, tends to decrease its aromatic character In the trend that the electron number in r-MOs set is either greater than, or equal to, the electron number in t-MOs set In DR B2 14 , the electron number in r-MOs amounts to 10 and the electron number in t-MOs to It leads to the value of Np/2n = 0.714 for the structure However, this value is even larger than that of For a comprehensive view on the general pattern of DR structures, a series of DR structures from electron-rich element such as carbon, silicon, germanium are also investigated following the same approach However, pure electron-rich element DR’s are not stable as equilibrium structures Instead, electron-rich DR structures are found following a doping by a transition metal such as Ti@Si12, V@Si12, Cr@Si12, Mn@Si12, Fe@Si12 [27–33], [Vx@Si12](x =  3) [34], [Fe@Ge10]3 [35,36], [Co@Ge10]3 [37], Mo@Ge12 [38], [ Pd@Bi10]4+, [Pt@Bi10]4+ [39], As a representative for this group of compounds, we investigate here in some detail the chromium doped silicon cluster Cr@Si12 This cluster has been established to have a  DR shape in which the Cr dopant is located at the center of the tube However, the ideal structure with D6h Cr@Si12 exhibits an imaginary frequency and becomes an energy global minimum with a D3d form [27,29,33] The following study attempts to point out a reason for thermodynamic instability of the pure D6h Si12 DR, how a Cr atom stabilizes the DR The stability of the singly doped cluster Cr@Si12 was previously analyzed using fragment MOs [31] We carry out geometry optimizations in the singlet, triplet, quintet and septet spin states to determine the lowest-lying state for a DR Si12 skeleton The BP86 functional [40,41] which is known to be more suitable for the transition metal doped silicon clusters, is used in conjunction with the aug-cc-pVTZ basis set Results summarized in Table S2 (ESI) indicate that the DR Si12 stationary point, in its Table Peripheral B-B bond length (Å): LB-B(P); height of DR structure (Å): HDR; the electron number of r-MOs set: Np; the electron number of t-MOs set: Nr, the p electron number in a peripheral B-B bond: N2np ; the r electron number in a B-B bond between two rings: N2nr ; and the average of delocalized electron number in a B-B bond of DR structure The considered DR structures are Bq2n with n =  15, q = 2, 0, 2, and the total number Np + Nr satisfies the 4M count a b c d DR structure LB-B(P) (Å) HDR (Å) Np Nr Np 2n Nr 2n Ndelo B2+a 14 B2d 14 B16c B2+a 18 B2c 18 B20a B2+a 22 B2c 22 B24a B2+b 26 B2 26 B28c B2+b 30 B2 30 1.616 – 1.634 1.632 1.625 1.607 1.610 1.632 1.616 1.619 1.617 1.607 1.607 1.622 1.506 – 1.433 1.445 1.499 1.510 1.531 1.459 1.467 1.482 1.512 1.524 1.537 1.478 10 10 10 10 10 10 14 14 14 14 14 14 18 6 6 10 10 10 10 10 10 14 14 14 14 0.429 0.714 0.625 0.556 0.556 0.500 0.455 0.636 0.583 0.538 0.538 0.500 0.467 0.600 0.429 0.429 0.375 0.333 0.556 0.500 0.455 0.455 0.417 0.385 0.538 0.500 0.467 0.467 0.429 0.571 0.500 0.444 0.556 0.500 0.455 0.545 0.500 0.462 0.538 0.500 0.467 0.533 DR structures which have been demonstrated to be global minima DR structures which are expected to be global minima DR structure which have been demonstrated to be local minima The B2 14 dianion is strongly distorted from a DR geometry All data for this DR structure are computed in keeping a DR shape L.V Duong, M.T Nguyen / Chemical Physics Letters 685 (2017) 377–384 triplet state, has negative frequencies, and lies 52 kcal/mol higher in energy than the global isomer [42] It is clearly not an equilibrium structure, but for purpose of comprehension we consider such a DR Si12 as a component of the stable doped Cr@Si12 cluster The latter is resulted from interaction between the triplet DR Si12 and a triplet Cr atom Fig presents an orbital interaction diagram from a set of occupied valence MOs of DR Si12 and orbital contribution from Cr into the resulting Cr@Si12 Energy levels predicted by the hollow cylinder model (HCM) are also given for comparison Let us first analyze the whole valence MOs of DR Si12 to understand the instability of this skeleton These MOs can again be sep- 381 arated into three sets, namely, s-MOs, r-MOs and t-MOs when using the HCM (Fig 1) The HCM has been presented in our previous studies [8,9,22] for antiprismatic nanotube structures The model is derived from the solution of the Schrӧdinger equation in cylindrical coordinates for a particle of mass m moving in a hollow cylinder (Eq (3)): ! @2 @ @2 @2 ỵ ỵ þ wðq; h; zÞ þ jðq; zÞ2 wðq; h; zÞ ¼ @ q2 q @ q q2 @h2 @z2 ð3Þ Energy levels of one electron in a HCM are defined by Eq (4): Fig Shape of the entire set of occupied valence MOs of CrSi12 The whole valence occupied and some unoccupied MOs of the Si12 skeleton are used for fragment analysis Contributions of atomic orbitals of Cr to CrSi12 are also established Shape of MOs of the DR Si12 are shown and compared to the hollow cylinder model spectrum with HCM parameters: e ¼ 0:81 and Lf ¼ 2:71 382 L.V Duong, M.T Nguyen / Chemical Physics Letters 685 (2017) 377–384 s-MOs r-MOs t-MOs a) B20 (D10d) ELF( -loca) = ELF( ) = 0.79 0.779 ELF( -delo) = 0.857 b) Triplet Si12 skeleton (D6h) ELF( -loca) = 0.860 ELF( = 0.819 ELF( = 0.745 ELF( -delo) = 0.686 c) Si12Cr (D6h) ELF( -loca) = 0.772 ELF( -delo) = 0.973 Fig A comparison of typical ELF(r-loca), ELF(p), and ELF(r-delo) for (a) DR B20, (b) D6h triplet DR Si12 skeleton, and (c) D6h Cr@Si12 structure E¼ 2 h 2mR2 kln Rị ỵ kp L ị f ! Lf ẳ 2:71 4ị Each energy level is function of three quantum numbers, including a rational ðk ¼ 1; 2; 3; Þ, a rotational (l ¼ 0; 1; 2; 3; ), and a radial (n ¼ 1; 2; 3; ) quantum number We now assign the rotational quantum numbers by the Greek letters, namely l ¼ r; p; d; /; The MOs of DR Si12 appear to obey the HCM with the parameters of e ¼ 0:81 and The energy spe r ctrum of this HCM shown in Fig compares to MOs computed by DFT The shapes of the D6h Si12 skeleton MOs have a nearly perfect match with those of HCM The correlation between the D6h Si12 MOs and the HCM energy spectrum (with e ¼ 0:81 and Lf ẳ 2:71ị is given in Figs S2 and Table S1 of the ESI file The radius and the height of DR Si12 are computed to be 2.32 Å and 2.36 Å, respectively Then, the active radius (r ¼ e:R) of 1.89 Å, which is drawn from the HCM, is shorter as compared to the value of 2.10 Å of the Si van der Waals radii [43] The height of the hollow cylinder model L (L ¼ L f R) is 6.31 Å Compared to the real height of 2.36 Å of the Si12 DR (being the distance between two rings of the DR), the height of the hollow cylinder in Si12, in which electrons move, is larger, DL = 1.99 (DL ẳ 6:31  2:36ị=2) These values are illustrated together with the geometry of the skeleton Si12 in Fig S3 of the ESI file Such an extended height is closer to the Si van der Waals radii The fact that the active radius r and the extended height DL of the hollow cylinder are close to Si van der Waals radii demonstrates that the HCM is suitable to rationalize the distribution of the whole valence MOs in Si12 DR Nevertheless, this is not a sufficient condition to form a stable DR structure Using the previous approach for Bn DR clusters, we now separate the MOs of Si12 skeleton into three sets, namely, the r-MOs set including MOs assigned by kl2-orbital, the t-MOs set including MOs assigned by 3l1-orbital, and the s-MOs set including MOs assigned by kl1-orbital with k  The partial ELF map is constructed for each set and they are shown in Fig 4b, together with a comparison with those of the DR B20 given in Fig 4a At the first glance, the ELF(r-loca), ELF(p), and ELF(r-delo) maps of Si12 DR show a mixed behavior They exhibit 12 peripheral Si-Si bonds while its s-MOs set includes 32 electrons Therefore, it is not surprising that ELF(r-loca) of Si12 shows not only 12 center – electron (2c–2e) peripheral basins but also small basins outside the inner SiASi bonds In other words, the s-MOs set of Si12 is not only responsible for 12 (2c–2e) peripheral bonds but also involve in enhancement of the inner SiASi bonds that should normally belong to the r-MOs set The main ELF domains for r-MOs set of Si12 are delocalized along the diagonal line and outside of DR It means that r-MOs of Si12 are in part overlapped with the t-MOs set The ELF domains for t-MOs set include 18 basins that are delocalized tangentially along the edges of the hollow cylinder Of these basins, are delocalized outside the edges Accordingly, the t-MOs set of Si12 also joins the r-MOs set In summary, each set from s-MOs, t-MOs and r-MOs sets presents a specific role to stabilize the Si12 DR but they are largely overlapped This phenomenon points out a certain uniformity of the whole set of valence electrons of the Si12 DR skeleton in the HCM, that is resulting from sp3 hybridization of Si atoms It is known that the entire set of valence electrons of the stable DR B20 can also be separated into three distinct sets that obey three L.V Duong, M.T Nguyen / Chemical Physics Letters 685 (2017) 377–384 different HCMs (one HCM for each set of s-MOs, r-MOs and t-MOs, with apart HCM parameters from each set), and follow their own magic numbers On the contrary, the valence electrons of Si12 DR skeleton obey only one HCM, this structure is not an equilibrium structure, due to overlapping interactions between the three MOs sets In order to stabilize the DR, orbitals of the doped metal atom need to destroy the uniformity of valence electrons of the DR skeleton Let us consider the s-MOs set of Cr@Si12 Based on the analysis for planar boron clusters, Arvanitidis et al [7] pointed out an interesting quantum rule governing the maximum node for the angular momentum If the number of atoms in the outer ring is equal to 2m, there is one occupied orbital transforming as cos(mu) If the number is odd, being 2m + 1, there is a pair of cyclic orbitals transforming as cos(mu) and sin(mu) There are some differences from the structure of the double ring electron-rich element The Si12 skeleton includes Si atoms in each ring, but the HOMO–5 and HOMO–4 are two occupied orbitals with nodes for the angular momentum They are not degenerate MOs because the HOMO–5 consists of 3pxy orbitals and HOMO–5 of 3s orbitals Furthermore, the HOMO–2 and HOMO–20 , which correspond to 1c1-orbital in HCM, have the number of node for the angular momentum greater than (being 4), and this fact has been predicted in our previous study by using the cylinder model [44] The ELF(r-loca) displayed in Fig.4b is calculated from s-MOs set The ELF(r-loca) domains of Si12 skeleton includes 12 (2c-2e) localized basins and small basins delocalized outside the edges in DR Si12 Interestingly, we attempt to calculate a partial ELF for the MOs of Si12 skeleton which satisfy the maximum angular node [7] by removing HOMO–2, HOMO–20 , and HOMO–4 This partial ELF map (given in Fig S4 of the Supplementary information file) shows that the small basins delocalized outside the edges in DR Si12 have been removed We would suggest that a future study on other tubular structures of rich-electron element should attempt this type of ELF analysis to confirm our following suggestion: ‘in the s-MOs set, the peripheral localized electrons belong to the MOs which satisfy the rule about the maximum angular node of Arvanitidis et al [7] The MOs which not obey this rule, provide delocalized electrons outside the edge of the tube Fig indicates that the HOMO and HOMO’ are remarkably the sole MOs formed from interactions between the DR skeleton MOs and Cr atomic orbitals The anti-bonds between the HOMO–2, HOMO–20 of Si12 skeleton and the dxy  dx2 y2 orbital of Cr turn the delocalized HOMO–2, HOMO–20 of Si12 skeleton to the localized HOMO, HOMO’ in Cr@Si12 (the HOMO, HOMO’ of Cr@Si12 is higher than the HOMO–2, HOMO–20 of Si12 skeleton by 0.22 eV in energy.) Fig 4c shows a small difference in ELF(r-loca) of both structures Six (6) small basins delocalized outside the edges in DR Si12 now become six small basins localized within the inner Si-Si bonds of Cr@Si12 ELF(r-loca) domains of Cr@Si12 include 12 (2c– 2e) localized basins and small basins localized in the inner SiASi bonds Otherwise, the interaction with the Cr atomic orbitals help transfer s-MOs electrons from delocalized electrons of the Si12 skeleton making localized electrons of the doped Cr@Si12 Finally, s-MOs electrons in the Cr@Si12 behave as localized electrons In the r-MOs set of Cr@Si12, the HOMO–3 and HOMO–30 are formed from LUMO+4 and LUMO+40 (1r2-orbitals) of DR Si12 and AO ðdxy  dx2 y2 Þ of Cr, while HOMO–4 and HOMO–40 are formed from LUMO and LUMO’ (2p2-orbitals) of DR Si12 and orbital ðdyz  dxz Þ of Cr Upon interaction, ELF(p) domains of Cr@Si12 become remarkably similar to ELF(p) of B20 It means that the rMOs set in Cr@Si12 is the main responsible for stabilization of Si- 383 Si bonds between two strings, whereas the basins being responsible for stabilization of peripheral SiASi bonds are now removed The shape of ELF(r-delo) of Cr@Si12 is changed significantly with respect to that of DR Si12 Although the dz2 (Cr) AO contributes just 8% to HOMO–8 (being the ground MO of t-MOs set), it involves in basins delocalized outside the edges of ELF(r-delo) of DR Si12 and this dramatically decreases the ELF counterpart of Cr@Si12 The large increase in the ELF(r-delo) value in going from DR Si12 skeleton to D6h Cr@Si12 reveals a remarkable electron transfer from the inner Si-Si bonds in the former structure to the outside of the latter The remaining basins now prefer to be delocalized outside the structure, and are mainly responsible for formation of SiASi peripheral bonds We now give a short analysis for the cluster [Co@Ge10]3 [37] in order to show the reproducibility of our separated ELF approach Fig S5 of the ESI file shows a comparison of the typical ELF(rloca), ELF(p), and ELF(r-delo) for the singlet DR Ge2 10 skeleton and the [Co@Ge10]3 structure Firstly, we consider the formation of [Co@Ge10]3 by interaction between a singlet DR Ge2 10 and the Co- anion With an odd number of atoms in each ring (being 5), all MOs of s-MOs of Ge2 10 skeleton satisfy the rule about the maximum angular node of Arvanitidis et al [7], with the highest angular node belonging to two pairs of degenerate MOs, namely 1d1orbitals (HOMO–4 and HOMO–40 ) and 2d1-orbitals (HOMO and HOMO’) As a result, the ELF(r-loca) map for the Ge2 10 skeleton shows only the peripheral localized basins, and there is no significant difference from the ELF(r-loca) map for [Co@Ge10]3 For ELF (p) domains, there are a slightly increasing delocalized basins outside the edge part The largest difference comes from the ELF(rdelo) The delocalized basins outside the edge of Ge2 10 skeleton dominate the ELF(r-delo) map, but they are mostly transferred to above and below the [Co@Ge10]3 structure Due to the difference in charges of two structures, the related bifurcation values have been not evaluated In general, thanks to interaction between MOs of DR Si12 skeleton and d orbitals of Cr, electrons in the r-MOs and t-MOs set of Cr@Si12 no longer exhibit an overlapping behavior Instead, each set bears its own responsibility Concluding remarks In the present theoretical study, we analyzed the electron distribution in two series of double ring (DR) tubular clusters, including the pure boron clusters, and the doped Cr@Si12 From the contributions of different combinations of typical molecular orbitals into the partial electron localization functions (ELF), some interesting results emerge as follows: (i) An ELF analysis of the r electrons needs to be separated into the r localized and r delocalized electrons In the basins of the ELF(r-delo) which shows the delocalized character, the electrons not stick in any bond but prefer moving around and within the bonds (ii) In the DR boron B2n series, the valence electrons are separated into three sets: the r localized electrons in peripheral bonds form the structural framework; the p-electrons are mainly delocalized inside the skeleton and enhance the inner bonds, and the delocalized r-electrons moving above and below the skeleton reinforce the peripheral bonds These separated duties constitute a standard for a stabilization of a DR structure (iii) Although the whole set of valence electrons in the D6h Si12 DR obey the hollow cylinder model, the mixed behavior and overlapping of the three sets of MOs causes its instabil- 384 L.V Duong, M.T Nguyen / Chemical Physics Letters 685 (2017) 377–384 ity Interactions between MOs of D6h Si12 DR skeleton and AOs of Cr break out such a mixture and thereby stabilize the doped DR structure (iv) Analysis of the partial ELF maps pointed out that a pure boron double ring loses its aromatic character if the number of delocalized electrons per bond becomes greater than 0.5 Therefore, addition or removal of electrons to a boron DR could make it less or more stable From this analysis, it can 2+ be predicted that the B2+ 26 and B30 are stable double ring structures Acknowledgments We sincerely thank the Department of Science and Technology of Ho Chi Minh City and Institute for Computational Science and Technology at Ho Chi Minh City (ICST), Vietnam, for support under the Grant 196/2016/HÐ-SKHCN Appendix A Supplementary material Figures display the ELF maps, shapes and energies of MOs, and Tables list calculated MO energies from DFT and cylinder model, and Cartesian coordinates of the structures considered Data associated with this article can be found in the online version, at DOI: xxxxx Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.cplett.2017.07 079 References [1] R Daudel, G Leroy, D Peeters, M Sana, Quantum Chemistry, Wiley, 1984 [2] B Silvi, A Savin, Nature 371 (1994) 683 [3] J.C Santos, W Tiznado, R Contreras, P Fuentealba, J Chem Phys 120 (2004) 1670 [4] T.B Tai, V.T.T Huong, M.T Nguyen, Top Heterocycl Chem 38 (2014) 161 [5] L Rincon, R Almeida, J.E Alvarellos, D Garcia-Aldea, A Hasmy, C Gonzalez, Dalton Trans (2009) 3328 [6] T.B Tai, D.J Grant, M.T Nguyen, D.A Dixon, J Phys Chem A 114 (2010) 994 [7] A.G Arvanitidis, T.B Tai, M.T Nguyen, A Ceulemans, Phys Chem Chem Phys 16 (2014) 18311 [8] H.T Pham, L.V Duong, M.T Nguyen, J Phys Chem C 118 (2014) 24181 [9] L.V Duong, H.T Pham, N.M Tam, M.T Nguyen, Phys Chem Chem Phys 16 (2014) 19470 [10] D Ciuparu, R.F Klie, Y Zhu, L Pfefferle, J Phys Chem B 108 (2004) 3967 [11] J Liu, Z Iqbal, Mat Res Soc Proc (2010) 42 [12] M.J Frisch, G.W Trucks, H.B Schlegel, G.E Scuseria, M.A Robb, J.R Cheeseman, G Scalmani, V Barone, B Mennucci, G.A Petersson, et al., Gaussian 09, Wallingford, CT, USA, 2009 [13] J.P Perdew, J Tao, V.N Staroverov, G.E Scuseria, J Chem Phys 120 (2004) 6898 [14] D.M Kohout, version 4.6, Radebeul, 2011 [15] L Laaksonen, J Mol Graph 10 (1992) 33 [16] D.E Bean, P.W Fowler, J Phys Chem C 113 (2009) 15569 [17] B Kiran, S Bulusu, H.J Zhai, S Yoo, X.C Zeng, L.S Wang, Proc Natl Acad Sci U S A 102 (2005) 961 [18] H.T Pham, L.V Duong, B.Q Pham, M.T Nguyen, Chem Phys Lett 577 (2013) 32 [19] M.P Johansson, J Phys Chem C 113 (2009) 524 [20] W An, S Bulusu, Y Gao, X.C Zeng, J Chem Phys 124 (2006) 154310 [21] S Chacko, D.G Kanhere, I Boustani, Phys Rev B 68 (2003) [22] H.T Pham, T.T Phan, N.M Tam, L.V Duong, M.P Pham-Ho, M.T Nguyen, Phys Chem Chem Phys 17 (2015) 17566 [23] L.V Duong, M.T Nguyen, Phys Chem Chem Phys 19 (2017) 14913 [24] Y Yuan, L Cheng, J Chem Phys 137 (2012) 044308 [25] D Moreno, S Pan, L.L Zeonjuk, R Islas, E Osorio, G Martinez-Guajardo, P.K Chattaraj, T Heine, G Merino, Chem Commun 50 (2014) 8140 [26] J Zhao, X Huang, R Shi, H Liu, Y Su, R.B King, Nanoscale (2015) 15086 [27] S.N Khanna, B.K Rao, P Jena, Phys Rev Lett 89 (2002) 016803 [28] P Sen, L Mitas, Phys Rev B 68 (2003) [29] J Ulises Reveles, S.N Khanna, Phys Rev B 72 (2005) [30] L Guo, G Zhao, Y Gu, X Liu, Z Zeng, Phys Rev B 77 (2008) [31] M.B Abreu, A.C Reber, S.N Khanna, J Phys Chem Lett (2014) 3492 [32] J.M Goicoechea, J.E McGrady, Dalton Trans 44 (2015) 6755 [33] N.D Phi, N.T Trung, E Janssens, V.T Ngan, Chem Phys Lett 643 (2016) 103 [34] X Huang, H.G Xu, S Lu, Y Su, R.B King, J Zhao, W Zheng, Nanoscale (2014) 14617 [35] T Kramer, J.C Duckworth, M.D Ingram, B Zhou, J.E McGrady, J.M Goicoechea, Dalton Trans 42 (2013) 12120 [36] B Zhou, M.S Denning, D.L Kays, J.M Goicoechea, J Am Chem Soc 131 (2009) 2802 [37] J.Q Wang, S Stegmaier, T.F Fassler, Angew Chem Int Ed 48 (2009) 1998 [38] R Trivedi, K Dhaka, D Bandyopadhyay, RSC Adv (2014) 64825 [39] R.B King, I Silaghi-Dumitrescu, M.M Uta, Inorg Chem 48 (2009) 8508 [40] A.D Becke, Phys Rev A 38 (1988) 3098 [41] J.P Perdew, Phys Rev B 33 (1986) 8822 [42] N.M Tam, M.T Nguyen, Chem Phys Lett 584 (2013) 147 [43] M Mantina, A.C Chamberlin, R Valero, C.J Cramer, D.G Truhlar, J Phys Chem A 113 (2009) 5806 [44] L.V Duong, M.T Nguyen, Phys Chem Chem Phys 18 (2016) 22732 Thiết kế vật liệu Nano từ Cluster trộn SinMm PHỤ LỤC 3: Bài báo : B3@Si12+: strong stabilizing effects of a triatomic cyclic boron unit on tubular silicon clusters Tạp chí : Phys Chem Chem Phys 20, 2018, 7588-7592 Tác giả : Phạm Tấn Hùng, Đặng Thị Tuyết Mai, Dương Văn Long, Nguyễn Minh Tâm, Minh Thọ Nguyễn Viện Khoa học Cơng nghệ Tính tốn TP Hồ Chí Minh Page 38 PCCP PAPER Cite this: Phys Chem Chem Phys., 2018, 20, 7588 B3@Si12+: strong stabilizing effects of a triatomic cyclic boron unit on tubular silicon clusters† Hung Tan Pham,d Thi Tuyet Mai Dang,c Long Van Duong,d Nguyen Minh Tamab and Minh Tho Nguyen *abc Remarkably strong effects of the aromatic B3 cycle in stabilizing tubular silicon clusters were observed for the first time The doped cluster B3@Si12+ presents a novel structural motif for silicon clusters in Received 17th January 2018, Accepted 19th February 2018 which a B3 cycle is encapsulated into a (6  2) Si12 prism giving rise to a high symmetry stable tubular DOI: 10.1039/c8cp00380g only retains a delocalized bonding pattern within the Si12 prism but also enables a two-fold aromaticity structure (D3h) A large amount of electron density is transferred to the boron cycle, and the B3d unit not for the resulting silicon double ring This double ring can be used as a building block to make longer rsc.li/pccp nanotubes Silicon is well known as an essential element in the optical and electronic industries Therefore, silicon-based clusters have been extensively studied by both theories and experiments in a search for alternative opto-electronic materials.1–12 Bare silicon clusters are not stable in a high symmetry form and easily collapse due to the existence of dangling bonds at the clusters’ surface Due to this intrinsic phenomenon, bare silicon clusters cannot be used as building blocks in the assembly of nanomaterials Previous investigations clearly showed that silicon based clusters having high symmetry can be made upon doping by transition metal elements.13–20 Many endohedrally encapsulated silicon clusters in which the metal dopant is covered by a silicon host have been prepared For example, Sc, Ti and V atoms can form stable M@Si16 cages and more importantly they can be assembled in [M@Si16]n heterooligomers.13,14 A metal–silicon tube was synthesized on the basis of Be@Si12.15 As for an embryo structure to build up tube-like materials, Mn2@Si15 presents a particular unit in which the Mn2 dimer stabilizes the smallest (3  5) Si triple ring.16 V@Si12 hexagonal prisms can connect together yielding a honeycomb-like magnetic sheet.17 Also with V-dopants, a hexagonal prism structure was found upon doping of two or three V atoms into a Si12 host in which the dopants form a a Computational Chemistry Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam E-mail: nguyenminhtho@tdt.edu.vn, nguyenminhtam@tdt.edu.vn b Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Vietnam c Department of Chemistry, KU Leuven, Celestijnenlaan 200F, B-3001 Leuven, Belgium E-mail: minh.nguyen@kuleuven.be d Institute for Computational Science and Technology (ICST), Ho Chi Minh City, Vietnam † Electronic supplementary information (ESI) available See DOI: 10.1039/ c8cp00380g 7588 | Phys Chem Chem Phys., 2018, 20, 7588 7592 vertical V axis inside a (6  2) Si12 tube.18 The tubular form involving both prism and anti-prism Si12 enclosing two Mo, Ta, Nb, or W atoms was also stable.19 However a vertical arrangement is not convenient, as a linear metal trimer does not correspond to the most stable form The geometry and chemical bonding of silicon clusters doped by various elements have carefully been discussed in recent work.21,22 This brief summary indicates that the cluster containing 12 Si atoms presents a particular structural motif in which a tubular shape can be generated following doping by metal dopants.20 It is known that the pure stable Si12 cluster is a low symmetry cage (Fig 1).12 This raises a legitimate question as to whether a triatomic dopant can be encapsulated by a tubular Si12 host? Actually, both B3+ and B3 ions are characterized as doubly aromatic stable compounds.23 Recent DFT calculations and photoelectron spectroscopy investigations on the B3Si4–10 anions found no endohedral structure.24 In this context, we set out to search for triatomic units that can stabilize Si tubes, and find that in the series of BxSi120/+ clusters with x = 1, and 3, a novel structural motif where a high symmetry D3h B3 cycle is horizontally placed in a (6  2) Si12 prism is identified as the global minimum structure of the (B3Si12+) cation A stochastic genetic algorithm is used to search for the global minima of the boron doped silicon clusters BxSi120/+ with x = 1, and 3, in which all probable initial structures are subjected to geometry optimizations.25 Additionally, to avoid missing any, guess geometries are also manually built by adding B atoms to the Si12 frameworks All guess geometries are optimized using density functional theory (DFT) with the hybrid TPSSh functional and the small LANL2DZ basis set.23,24 For each series, about twenty lower-lying structures are selected for geometry reoptimization using the 6-311+G(d) basis set27,28 with three different TPSSh, B3LYP and PBE functionals.26 Additionally, the energies This journal is © the Owner Societies 2018 Paper Fig Geometries of Si12, BSi12+, B2Si12 and B3Si12+ clusters (TPSSh/ 6-311+G(d)) Si12 structure is taken from ref 12 of the two lowest-energy isomers are recalculated using the G4 method.29 Structure optimizations are carried out using the Gaussian 09 package.30 Geometric features of BSi12+, B2Si12 and B3Si12+ clusters are shown in Fig Some lower-lying isomers of BSi12+, B2Si12 and B3Si12+ are given in Fig S1–S3 of the ESI.† The calculated results point out that doping with one B atom does not affect the Si12 host geometry The Si cage in the singly B-doped BSi12+ cation remains in fact unchanged (Fig 1) The appearance of two B atoms gives rise to a distorted tubular structure for the doubly doped B2Si12 as the global minimum isomer, according to both DFT and G4 calculations (Fig 1) A boron dimer B2 is thus inserted inside a low symmetry (6  2) Si12 prism The second isomer, a broken cage denoted as 2.n.B (Fig S2, ESI†) is only 2–3 kcal mol1 higher than the tubular isomer, as predicted by the G4 and TPSSh, B3LYP, PBE/6-311+G(d) calculations Although the emergence of the B2Si12 tubular isomer emphasizes a genuine effect of two B dopants on the Si12 host, the energetic neardegeneracy of both the distorted tube and broken cage isomers indicates that two B atoms are not sufficient to enhance the thermodynamic stability of a Si12 tube.31 Structural identifications emphasize that a B3@Si12+ cation is stable in a singlet D3h geometry (Fig and Fig S1, S3, ESI†) in which a B3 cycle is encapsulated by a (2  6) Si12 prism The high symmetry of the B3+ unit is maintained, but the B–B bond length of the B3 unit amounts to 1.75 Å which is significantly longer than that of free B3/0/+ clusters (1.55–1.57 Å by TPSSh/ 6-311+G(d)) The existence of the D3h B3@Si12+ structure emphasizes a remarkable effect of the B3 unit in stabilizing the Si12 tubular form, in view of the fact that the pure Si12 cluster has a Cs point group without any special shape (Fig 1) The stabilizing effect of B atoms can quantitatively be evaluated The binding energies per atom (BE) are calculated to be 3.7, 3.9, 3.9 and 4.2 eV for Si12, BSi12+, B2Si12 and B3Si12+, respectively The embedding energies, which are the energy This journal is © the Owner Societies 2018 PCCP differences between the doped cluster and the separated Si12 + Bn, amount to 7.2, 8.2 and 11.2 eV, for BSi12+, B2Si12 and B3Si12+, respectively (G4 values) This indicates that B3Si12+ is highly stabilized The B3 cycle gives a much greater enhancement in thermodynamic stability for the tubular Si12 host than the B2 dimer Preliminary computations suggest that embedding of B3 inside a Si12 cage is apparently spontaneous However, appropriate exploration of potential energy surface in searching for possible intermediates and transition structures needs to be carried out in future study to properly address this issue In B3Si12+, each B atom is connected with Si atoms, and additional bonds induce higher stability A tubular shape was identified for a Si12 cluster doped by two and three metals, but in all reported cases, a metal dopant is located outside the Si12 host due to the large distance between two dopants Indeed, the V–V connections of V2Si12 and V3Si12 have a bond length of B2.2 Å,18 and similarly the bond length of 2.3–2.5 Å was found for the M–M connectivity of M2Si12q (M = Mo, Ta, Nb, W and q = 2, 0, 2).19 The appearance of B3@Si12+ with a B3 unit completely covered by a Si12 tube clearly demonstrates that the B3 cycle satisfies geometric requirements to form a threemembered cycle within a tube Along this line, triply transition metal doped silicon clusters in which an M3 cycle is completely covered, can be observed at larger size Sin In order to further verify the stability of the B3Si12+ tube, we perform molecular dynamic simulations for this structure at 600 K during 30 ps using the CP2K package.32 The root mean square deviation (RMSD) varies in the range of 0.11–0.25 Å, whereas the smallest bond length is 1.75 Å (Fig S4 of the ESI†) The connectivity of B3@Si12+ is maintained during the simulation time, indicating that this structure is dynamically stable As for a rationalization on bonding and stability, the electron distribution of B3@Si12+ is further examined using both the electron localization function (ELF)33 and quantum theory of atoms in molecules (QTAIM).34 Concerning the connection between the B3 and Si12 moieties, both analyses indicate that the B3 unit exhibits a delocalized bonding pattern interacting with a Si12 tube, and thereby stabilizing B3@Si12 in a D3h shape Fig S5 (ESI†) displays the Laplacian of the total electron density r2p(r) projected in the B3 plane This shows not only the bonding between the B3 unit and the Si12 moiety, but also that of the B3 unit As given in Fig S5 (ESI†), an electron concentration area pointing toward the Si atoms is observed resulting from electron delocalization between the B3 cycle and Si strings The electron density tends to increase around the B3 unit A similar result is found for B2Si12 in which electrons also concentrate around the B2 moiety The net charge of all B atoms amounts to around 1.3 electrons as the Si12 host massively transfers electrons to the B dopants The B3 and B2 units can be regarded as B3d and B2d For the B3 cycle, Fig S5 (ESI†) shows that a bond critical point (BCP, green ball) is located at the B–B bond, and more interestingly a ring critical point (RCP, red ball) is found at the central area of B3 As a consequence, three B atoms of B3@Si12+ connect to each other through a 2e–3c bond Fig S5 (ESI†) also shows a BCP (green ball) for each B–Si connection Phys Chem Chem Phys., 2018, 20, 7588 7592 | 7589 PCCP Fig ELF iso-surfaces produced at a bifurcation value of 0.7 (a) Side view and (b) top view RCPs are found in cycles formed by two Si atoms and one B atom, as well as by two B and one Si (Fig S5, ESI†) Three RCPs are identified in areas containing B–B and Si–Si edges which are perpendicular to each other QTAIM analysis illustrates the connection of the B3 cycle with the Si12 prism in forming a delocalized bond This conclusion is further supported by an ELF analysis As displayed in Fig 2, at a bifurcation value of ELF = 0.70, the isosurface map of B3@Si12+ establishes a localization domain located in a B3 region associated with a V(B,B,B) trisynaptic basin A delocalized bond of a free B3 unit is maintained when it is encapsulated by a Si12 tubular prism Three domains located in regions between the B atom and Si–Si edge are observed (Fig 2) indicating delocalized bonds between the B3 cycle and Si12 prism The bonding between B3 and Si12 moieties can also be understood from orbital interactions between B3+ and Si12 fragments, which is considered in a D3h tube and results in a high symmetry B3Si12+ (Fig 3) The empty and occupied MOs of B3+ enjoy strong Fig Orbital interactions between a Si12 tube (D3h) and B3+ cation resulting in B3Si12+ 7590 | Phys Chem Chem Phys., 2018, 20, 7588 7592 Paper stabilizing interactions with both occupied and unoccupied MOs of D3h Si12, and they produce a double aromaticity including 10s and 6p electrons, according to the classical 4N + counting rule Interactions of the unoccupied p-MOs of B3+(LUMO1,1 , e00 ) with both the HOMO and LUMO of Si12 (e00 symmetry) result in doubly degenerate HOMO1,1 for B3Si12+ The p-MO of B3+ enjoys a stabilizing interaction with HOMO (a200 ) of Si12 and produces subsequently HOMO2 of B3Si12+ These interactions provide p electrons for B3Si12+ A similar phenomenon is observed for s MOs Two pairs of doubly degenerate MOs of B3+ involving HOMO2,2 and LUMO0,0 (e ) interact with HOMO4,4 and HOMO5,5 of Si12 producing HOMO4,4 and HOMO5,5 for B3Si12+ HOMO6 of B3Si12+ is formed upon interaction of the HOMO of B3+ with HOMO6 of Si12 Interactions of s MOs between B3+ and Si12 create delocalized MOs for 10 s electrons Orbital interactions thus show that combination of B3+ and Si12 in the D3h point group gives rise to a double aromaticity for the resulting B3Si12+ D3h cluster, and thereby stabilizes it The above analysis indicates that delocalized bonds of a free B3 unit are conversed when it undergoes the formation of a B3@Si12+ tube The free B3 cycle is established as an aromatic species by ring current indicators.23 Thus the B3 unit brings in an aromatic character for B3@Si12+ The ring current density of the latter determined using the GIMIC method35 plotted in Fig displays a strongly diatropic current in the plane containing the B3 unit, thus confirming its aromatic feature Although B2@Si12 also has a tubular shape, it does not produce any current density flow (Fig S4, ESI†) This result suggests that the B3d unit is able to induce an aromatic character when it interacts with a Si12 double ring, whereas the B2 dimer is not A similar conclusion is drawn from Fig Within the GIMIC approach, electron delocalization can be considered bond by bond and thereby an aromatic pathway is revealed For free B3+/ clusters, the strength of the ring current that passes through the B–B bond is found to be 4.4 and 7.2 nA T1, Fig The line stream of current density provided by GIMIC calculation for the B3@Si12+ cluster This journal is © the Owner Societies 2018 Paper PCCP Acknowledgements Work at ICST was supported by the Department of Science and Technology of Ho Chi Minh City, Vietnam, under Grant 196/2016/HÐ-SKHCN DTTM thanks KU Leuven for a last year doctoral scholarship References There are no conflicts to declare W L Brown, R R Freeman, K Raghavachari and M Schluter, Science, 1987, 235, 860 E C Honea, A Ogura, C A Murray, K Raghavachari, W O Sprenger, M F Jarrold and W L Brown, Nature, 1993, 366, 42 G Pacchioni and J Koutecky, J Chem Phys., 1986, 84, 3301 N Veldeman, P Gruene, A Fielicke, P Claes, V T Ngan, M T Nguyen and P Lievens, in Handbook of Clusters, ed K D Sattler, CRC Press, Boca Raton, FL, USA, 2010, ch 5 O Cheshnovsky, S H Yang, C L Pettiette, M J Craycraft, Y Liu and R E Smalley, Chem Phys Lett., 1987, 138, 119 C B Winstead, S J Paukstis and J L Gole, Chem Phys Lett., 1995, 237, 81 ăthlisberger, W Andreoni and M Parrinello, Phys Rev U Ro Lett., 1994, 72, 665 N M Tam, H T Pham and M T Nguyen, Chem Phys Lett., 2014, 608, 255 S Li, R J Van Zee, W Weltner and K Raghvachari, Chem Phys Lett., 1995, 243, 275 10 K M Ho, A A Shvartsburg, B Pan, Z Y Lu, C Z Wang, J G Wacker, J L Fye and W L Brown, Nature, 1998, 392, 582 11 A A Shvartsburg, B Liu, M F Jarrold and K M Ho, J Chem Phys., 2000, 112, 4517 12 N M Tam and M T Nguyen, Chem Phys Lett., 2013, 586, 147 13 T Iwasa and A Nakajima, J Phys Chem C, 2012, 116, 14071 14 T Ohta, M Shibuta, H Tsunoyama, T Eguchi and A Nakajima, J Phys Chem C, 2016, 120, 15265 15 A K Singh, V Kumar, T M Briere and Y Kawazoe, Nano Lett., 2002, 2, 1243 16 H T Pham, T T Phan, N M Tam, L V Duong, M P P Ho and M T Nguyen, Phys Chem Chem Phys., 2015, 17, 17566 17 Z Liu, X Wang, J Cai and H Zhu, J Phys Chem C, 2015, 119, 1517 18 X Huang, H G Xu, S Lu, Y Su, R B King, J Zhao and W Zheng, Nanoscale, 2014, 6, 14617 19 H T Pham, D Majumdar, J Leszczynski and M T Nguyen, Phys Chem Chem Phys., 2017, 19, 3115 20 X Huang, S J Lu, X Liang, Y Su, L Sai, Z G Zhang, J Zhao, H G Xu and W Zheng, J Phys Chem C, 2015, 119, 10987 21 Y Li, A Fielicke, P Lievens and E Janssens, in Clusters: Structure, Bonding and Reactivity, ed M T Nguyen and B Kiran, Springer, 2017, ch 2, and references therein This journal is © the Owner Societies 2018 Phys Chem Chem Phys., 2018, 20, 7588 7592 | 7591 Fig Potential silicon tubes made by B3Si12+ units (TPSSh/6-31G(d) computations) respectively Under the D3h geometry, the (6  2) Si12 tube has two types of Si–Si connections including the horizontal Si1–Si2 and the vertical Si2–Si3, and the current density strength passing through these bonds amounts to 26.5 and 5.8 nA T1 The current density going via the B1–B2 connection of B3@Si12+ of 13.4 nA T1 is much higher than the corresponding value of free B3+/ clusters Similarly, two types of Si–Si connections of B3@Si12+ produce a current density with a strength of B33.5 nA T1, which is much higher than that of the pure D3h Si12 fragment Accordingly, the combination of both B3 and D3h (6  2) Si12 fragments results in a great enhancement in aromaticity, and this provides a significant contribution to the high stability of D3h B3@Si12+ As the B3@Si12+ cluster is a dynamic and thermodynamic stable species, it is possible to establish the silicon nanotube by connecting (B3@Si12) units along their vertical axis To illustrate this possibility, some oligomers constructed by joining B3@Si12+ units are geometrically optimized and displayed in Fig The optimized geometry of a (B3@Si12+)2 dimer is indeed a superposition of two B3Si12+ units along the C3 axis The (B3@Si12+)3 and (B3@Si12+)4 oligomers are extensions of the (B3@Si12+)2 dimer by adding (B3@Si12+) units along the C3 axis Such an extension suggests that a silicon nanotube can be made in which (B3@Si12+) serves as a building block In summary, we report on new findings emphasizing remarkably strong effects of the B3 unit on the geometry, bonding, aromaticity and stability of a silicon cluster containing 12 atoms Both B2Si12 and B3Si12+ clusters are found to be global minima in a tubular prism shape in which the B2 and B3 units are encapsulated in a (6  2) Si12 double ring The dynamic stability of the B3@Si12+ cluster is confirmed by molecular dynamic simulations Both the B2 and B3 moieties gain electron transfer from their Si12 counterpart In particular, the B3 unit enjoys a delocalized bonding pattern when interacting with the unstable Si12 tube Emergence of a double aromaticity from such interaction subsequently stabilizes the resulting doped B3@Si12+ tubular cluster in a high symmetry (D3h) Conflicts of interest PCCP 22 L V Duong and M T Nguyen, Chem Phys Lett., 2017, 685, 377, and references therein 23 H T Pham, K Z Lim, R W A Havenith and M T Nguyen, Phys Chem Chem Phys., 2016, 18, 11919 24 X Wu, S J Lu, X Liang, X Huang, Y Qin, M Chen, J Zhao, H G Xu, R B King and W Zheng, J Chem Phys., 2017, 146, 044306 25 H T Pham, D V Long, B Q Pham and M T Nguyen, Chem Phys Lett., 2013, 577, 32 26 J M Tao, J P Perdew, V N Staroverov and G E Scuseria, Phys Rev Lett., 2003, 91, 146401 27 R Krishnan, J S Binkley, R Seeger and J A Pople, J Chem Phys., 1980, 72, 650 28 P J Hay, J Chem Phys., 1977, 66, 4377 29 L A Curtiss, J Chem Phys., 2007, 126, 084108 7592 | Phys Chem Chem Phys., 2018, 20, 7588 7592 Paper 30 M J Frisch, H B Schlegel, G E Scuseria, M A Robb, J R Cheeseman, J A Montgomery, T Vreven, K N Kudin, J C Buran and J M Millam, et al., Gaussian 09 Revision: D.01, Gaussian Inc., Wallingford, CT, USA, 2009 31 N M Tam, T B Tai and M T Nguyen, J Phys Chem C, 2012, 116, 20086 32 J Vande Vonele, M Krack, F Mohamed, M Parrinello, Y Chassaing and J Hutter, Comput Phys Commun., 2005, 8, 1314 33 A D Becke and K E Edgecombe, J Chem Phys., 1990, 92, 5397 34 T A Keith, AIMAll (Version 17.01.25), TK Gristmill Software, Overland Park KS, USA, 2017, aim.tkgristmill.com ´lius, D Sundholm and J Gauss, J Chem Phys., 2004, 35 J Juse 121, 3952 This journal is © the Owner Societies 2018