Si11Mn0/+ cluster is endohedral or exohedral: a proof by DFT calculation - Cao Thi Thanh Huong

Vietnam Journal of Chemistry, International Edition, 55(5): 616-622, 2017 DOI: 10.15625/2525-2321.2017-00518 616 Si11Mn 0/+ cluster is endohedral or exohedral: a proof by DFT calculation Cao Thi Thanh Huong, Dao Thi Thao Linh, Nguyen Thi Minh Hue * , Ngo Tuan Cuong Faculty of Chemistry and Center for Computational Science, Hanoi National University of Education Received 8 June 2017; Accepted for publication 22 October 2017 Abstract The geometries of Si11, Si11Mn + and Si11Mn 0 clusters have been determined by the method of density functional theory using B3P86/6-311+G(d) level of theory. The pure silicon clusters Si11have cage structure associating with a low spin state.Although the geometrical structure of the most stable isomer of Si11Mn + cationic cluster is exohedral, the endohedral isomers have their calculated IR spectra fitting well with the experimental IRMPD spectra. The Si11Mn 0 neutral cluster is found to be most stable in both exohedral and endohedral forms. The most stable isomers of manganese-doped silicon clusters Si11Mn 0/+ possess high spin states and local magnetic moment of the Mn atom is reduced or even completely quenched when it is encapsulated inside the Si11 cage. Keywords. Silicon cluster doped manganese, density functional theory (DFT). 1. INTRODUCTION Silicon clusters doped with transition metal have been studied extensively in the last decade, owing to their prolific magnetic and optoelectronic properties that could lead to many application potentials [1-4]. Let us look a little more closely into the research work on this kind of cluster that has been done recently. It is shown in the literature that pure silicon clusters possess low spin states and are non magnetic type of materials. Transition metal atoms are magnetic owing to their non-fully filled d obitals. Of the transition metals, manganese has a maximum number of unpaired electrons on its 3d orbitals. Therefore doping manganese atoms into silicon clusters is very likely to create clusters which have prolific magnetic properties as well as improved band gaps [5-8]. Over the last few years, there has been much work on manganese doped silicon clusters. An interesting work on singly Mn-doped silicon clusters which combines experimental and theoretical investigation of small neutral vanadium and manganese doped silicon clusters SinX (n = 6-9, X = V, Mn) was reported [7]. These species were studied by infrared multiple photon dissociation and mass spectrometry. Structural identification is achieved by comparison of the experimental data with computed infrared spectra of low-lying isomers using density functional theory at the B3P86/6- 311+G(d) level. The assigned structures of the neutral manganese doped silicon clusters are compared with their cationic counterparts [9]. The structural, electronic and magnetic properties of singly Mn-doped SinMn + clusters with n = 6-10, 12- 14 and 16 have been investigated by using mass spectrometry and infrared spectroscopy in combination with density functional theory computations. This work has revealed that all the exohedral SinMn + (n = 6-10) clusters are found to be substitutive derivatives of the bare Sin+1 + cations, while the endohedral SinMn + (n = 12-14 and 16) clusters adopt fullerene-like structures. The clusters turn out to have high magnetic moments localized on Mn. In particular, the Mn atoms in the exohedral SinMn + (n = 6-10) clusters have local magnetic moments of 4 µB or 6 µB and can be considered as magnetic copies of the silicon atoms.[6] Recent theoretical work on manganese-doped silicon clusters has not yet confirmed the structures of Si11Mn + and Si11Mn 0 cluster. Whether the clusters are endohedral or exohedral, and whether or not the local magnetic moment of the Mn atom is completely quenched when doped in the silicon cluster. 2. METHODS OF CALCULATIONS We use the method of density functional theory (DFT) which is implemented in the Gaussian 09 software [10, 11] to investigate the pure and manganese doped silicon clusters Si11, Si11Mn + and Si11Mn 0 . The B3P86/6-311+G(d) functional/basis set has been used for our calculations [12-14], since this combination of functional and basis set are suitable for treating silicon clusters doped with manganese as VJC, 55(5), 2017 Nguyen Thi Minh Hue et al. 617 well as some other transition metals [6-8, 15-17]. The optimization calculations followed by frequency calculations have been done for searching minima of the clusters. Geometries, relative energies with zero point energy correction are deduced from these calculations. 3. RESULTS AND DISCUSSION 3.1. Searching for the stable isomer of pure silicon cluster Si11 Stable structures of the Si11 cluster have been determined as follows. Firstly, we have used the Gauss View program for building as many structures of Si11 cluster as possible. These input structures have been optimized converging to 14 stable isomers which have been confirmed by frequency calculations. The stable isomers are shown in figure 1. Of all the isomers found, the most stable isomer belongs to the Cs point group and has the structure that could be described as such: The structure has three layers. Both the first and the second layers contain five Si atoms, while in the third layer lies only one Si atom. This structure arises from the Si8 cluster with three other Si atoms adding to faces of the distorted cube of the Si8 cluster. 11A (Cs, 1A’, 0.00eV) 11B (Cs, 1A’, 0.03eV) 11C (Cs, 1A’, 0.08eV) 11D (C1, 1 A, 0.09eV) 11E (Cs, 1A’, 0.21eV) 11F (C01, 1 A, 0.36eV) 11G (Cs, 1A’, 0.39eV) 11H (Cs, 1A’, 0.50eV) 11I (Cs, 1A’, 0.86eV) 11K (Cs, 1A’, 0.89eV) 11L (Cs, 1A’, 1.03eV) 11M (C1, 1 A, 1.28eV) 11N (C1, 1 A, 1.88eV) 11O (C2, 1 A, 2.17eV) Figure 1: Stable isomers of the Si11 cluster, which have been optimized using DFT calculation with B3P86/6-311+G(d) functional/basis set. The grey balls represent Si atoms VJC, 55(5), 2017 Si11Mn 0/+ cluster is endohedral or 618 Three other isomers 11B, 11C, 11D are found lying at 0.03 eV, 0.08 eV and 0.09 eV barely above the most stable isomer, respectively. All the isomers are in their singlet spin states. 3.2. Searching for the most stable isomers of singly Mn-doped silicon cluster Si11Mn + The searching for the stable isomers of the singly Mn-doped silicon cluster Si11Mn + has been performed as follows. After the optimization calculations for stable isomers of the Si11 cluster, we added the Mn atom onto the low-lying energy isomers of the Si11 structures in as many positions as possible. The optimization calculations on the 54 input structures of the Si11Mn + clusters resulting in 21 stable isomers. All of them have 3-dimensional structure and 17 ones of them lying at below 1.50 eV are represented in figure 2 accompanying with their point groups, electronic states as well as relative energies (in parenthesis). A (C1, 5 A, 0.00eV) B (C1, 5 A, 0.24eV) C (C1, 7 A, 0.27eV) D (C1, 5 A, 0.32eV) E (C1, 5 A, 0.35eV) F (C1, 5 A, 0.37eV) G (Cs, 3A”, 0.42 eV) H (C1, 3 A, 0.49eV) I(C1, 3 A, 0.52eV) J (C2v, 1 A1, 0.62 eV) K (C1, 7 A, 0.71eV) L (C1, 3 A, 0.74eV) M (C1, 3 A, 0.78eV) N (C1, 3 A, 0.85eV) O (C1, 3 A, 0.90eV) P (Cs, 7A’, 1.38eV) Q (Cs, 1A’, 1.43eV) Figure 2: Stable isomers of the Si11Mn + cluster, which have been optimized using DFT calculation with B3P86/6-311+G(d) functional/basis set. The grey balls represent Si atoms, the pink ball represents the Mn atom For the most stable isomer of the Si11Mn + cluster, isomer A (C1, 5 A, 0.00 eV), the Mn atom capes onto the quadrilateral faces of the Si11. This structural isomer associates with four unpaired electrons locating in the Mn atom. This structure grows up from the Si11 pure silicon cluster-isomer3, which has the relative energy of 0.08eV, with the Mn atom added to the face of four Si atoms. VJC, 55(5), 2017 Nguyen Thi Minh Hue et al. 619 The most stable isomer of Si11Mn + cluster is exohedral. This means that the Mn atom attaches the outer sphere of the Si11 one. The spin density of the Mn atom, which is deduced from the calculation and listed in table 1, shows that the local magnetic moment of the Mn atom does not change significantly when doping outer of the Si11 cage. Several low-energy lying isomers of the Si11Mn + cluster have been found, in which the Mn atom capes onto the outer faces of the Si11 cluster and they all have unpaired electrons. Interestingly, we have found the two isomers G (Cs, 3A”, 0.42 eV) and J (C2v, 1 A1, 0.62 eV) which are endohedral with the Mn atom locating inside the Si11 cage. They have relative energies of 0.42 eV and 0.62 eV as compared to the most stable isomer A. We also found other endohedral isomers P, Q in which the Mn atom is encapsulated inside the cage of Si11 which are low spin with the spin multiplicity being equal to 1. They are much less stable with relative energies of 1.38 and 1.43 eV, respectively. The calculation results also show that isomers of Si11Mn + with quintet spin state are stable and those with singlet spin state have very high relative energies, as compared to the ground state. On a recent research work by Vu Thi Ngan et al. [6], the theoretical investigation has been performed on the geometrical structures of SinMn + on the basis of comparison the calculated vibrational spectra and the experimental ones. The structural identification is made by fitting the simulated spectra of stable isomers and the experimental Infrared Multi-photon Dissociation (IRMPD) spectra for each cluster stoichiometry. In that in tense work, although the structural assignments have been made for SinMn + (n = 6-10, 12-14, 16) clusters, the Si11Mn + cluster was left unsolved. As a complementary to that research work, this one is done for searching the structural identification of the Si11Mn + cluster. Table 1: Mulliken atomic spin density Cluster Mulliken atomic spin density on Mn Si11Mn + - isomer A 3.97 Si11Mn + - isomer G 2.18 Si11Mn 0 - isomer A 2.21 Si11Mn 0 - isomer B 4.37 Figure 3: Calculated IR spectra of Si11Mn + exohedral cluster (red dashed curve), endohedral clusters isomer G (light blue curve) and isomer J (pink curve). The experimental IRMPD spectrum of the Si11Mn + cluster, which is taken from the reference [6], is presented in the insert VJC, 55(5), 2017 Si11Mn 0/+ cluster is endohedral or 620 In order to assign the geometrical structure of the Si11Mn + cluster, we have plotted the IR spectra of all the low-energy isomers of the cluster, including the most stable isomer A-exohedral as well as the endohedral isomers G and J. The theoretical IR spectra are then compared with the experimental Infrared Multi-photon Dissociation (IRMPD) spectrum of the Si11Mn + cluster [6]. The calculated IR spectra of the endohedral isomers G and J turn out to fit better with the experimental one, as this could be seen in figure 3. Both of the two endohedral isomers have strong absorption bands at ~420 cm -1 , and less intense band at 270 cm -1 which are found in the experimental one. The calculated spectrum of the exohedal isomer A - the lowest energy one - which is also plotted in figure 3 for inspection, has strong absorption peaks at ~ 470 cm -1 which are not observed in the experimental spectrum. This analysis allows us to conclude that the Si11Mn + cluster appears in its endohedral forms, though they locate at 0.42 eV and 0.62 eV higher energies as compared to the exohedral isomer A. The magnetic moment of the Si11Mn + cluster is decreased from quintet state as the Mn atom dopes outer of the Si11 cage, to triplet as well as completely quenched to singlet as the Mn atom is embedded inside the Si11 cage. 3.3. Searching for the most stable isomers of singly Mn-doped silicon cluster Si11Mn From stable isomers of the Si11Mn + cluster we construct the Gaussian input files for searching the geometrical structures of the Si11Mn 0 neutral cluster with spin multiplicities ranging from 2 to 8. The results of optimized geometries as well as their point groups, electronic states and relative energies are represented in figure 4. A (Cs, 4A”, 0.00eV) B (C1, 6 A, 0.00eV) C (C1, 4 A, 0.34eV) D (C1, 6 A, 0.58eV) E (C1, 4 A, 0.60eV) F (C1, 6 A, 0.69eV) G (C1, 8 A, 0.75eV) H (C1, 4 A, 0.78eV) I (C1, 4 A, 0.85eV) K (C1, 4 A, 1.01eV) L (C1, 4 A, 1.07eV) M (C1, 8 A, 1.12eV) N (C1, 4 A, 1.20eV) O (Cs, 2A’, 1.32eV) P (Cs, 8A’, 1.38eV) Figure 4: Stable isomers of the Si11Mn neutral cluster, which have been optimized using DFT calculation with B3P86/6-311+G(d) functional/basis set. The grey balls represent Si atoms, the pink ball represents the Mn atom The results show that for the Si11Mn neutral cluster, there are two different geometrical structures with the same electronic energy, isomer A(Cs; 4A’’; 0.00 eV), and isomer B(C01; 6 A; 0.00eV). In isomer VJC, 55(5), 2017 Nguyen Thi Minh Hue et al. 621 A, the Mn atom is embedded inside the Si11 cluster binding with all the Si atoms. This structure associates with the quartet spin state and belongs to the Cs point group. In the second isomer, the Mn atoms locates outer of the Si11 cage binding with 5 Si atoms. This isomer, which is similar to that of the lowest energy-lying isomer of the Si11Mn + cationic cluster, belongs to the C1 point group and has the spin multiplicity of 6. On the optimization of structures, we have also found many other low energy-lying isomers of the Si11Mn 0 cluster. They all belong to low point groups (C1, Cs) and almost all of them have spin multiplicities of 4, 6 and 8. The spin density of the Mn atom, which is listed in table 1, shows that the local magnetic moment of the Mn atom does not change when doping outer of the Si11 cage and it is reduced to a triplet state rather than it is quenched completely when embedded inside the Si11 cage. We also found several isomers for this cluster, which are illustrated in figure 4. In this section, for the sake of providing persuasive information on the Si11Mn 0 neutral cluster, the IR spectra of the Si11Mn 0 cluster in its exohedral as well as endohedral forms have been plotted and represented in figure 5. The result shows that for the Si11Mn 0 cluster of endohedral form – isomer A in figure 4, the IR spectrum has an intense absorption band at ~430 cm -1 wavenumber and bands at ~380 cm -1 , ~300 cm -1 and ~250 cm -1 with lower intensities. The exohedral isomer B has absorption bands at ~465, ~390, ~350 as well as ~250 cm -1 wavenumbers and all of them are less intense as compared with the endohedral one. Figure 5: The calculated IR spectra of Si11Mn 0 exohedral cluster (a) And endohedral cluster (b) 4. CONCLUSION The B3P86/6-311+G(d) quantum chemical calculation method has been employed for searching the stable geometrical structures of Si11, Si11Mn + , and Si11Mn 0 clusters. While for the lowest energy structure of Si11Mn + cationic cluster, the Mn dopant locates outer the Si11 cage forming the exohedral isomer, the endohedral isomers which have relative energies of 0.42 and 0.62 eV possess the calculated IR spectra fitting well with the experimental IRMPD spectrum. The geometrical structures of the most stable isomers of Si11Mn 0 neutral cluster are both endohedral and exohedral. The Mn-doped silicon clusters Si11Mn + and Si11Mn 0 prefer high spin states and they are reduced or even quenched completely as the Mn dopant moves into the cage of the silicon cluster. Acknowledgement. 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