Structural evolution, photoelectron spectra and vibrational properties of anionic GdGen− (n = 5–18) nanoalloy clusters: a DFT insight

The structural growth of Gd-doped germanium anionic nanoclusters, GdGen− (n = 5–18), has been explored via quantum chemistry calculations using the mPW2PLYP method and an unprejudiced structural searching technique known as ABCluster. The optimized geometries exhibited that when n = 10–14, the structural evolution favors the Gd-linked configuration where the Gd atom as a connector bridges two Ge subgroups, while the Gd atom is encapsulated in a closed cage-like Ge frame when n = 15–18. The properties like magnetic moment, charge transfer, relative stability, HOMO–LUMO gap, photoelectron spectra, and infrared and Raman spectra have been predicted. The information of these spectra could provide extra approaches to experimentally determine the electronic structures and equilibrium configuration of these compounds. The largest spin magnetic moment of 7 μB is attained via half-filled 4f states. The GdGe16− nanocluster is determined to be a superatom because its total valence of 75 electrons can be distributed to the orbital sequence of 1S21P6(4f7)1D101F142S22P21G182P42D10, which complies with not only Hund's rule, but also the spherical jellium model. Particularly, its UV-Vis spectra match well with solar energy distribution. Such materials act as nano multifunctional building units potentially used in solar energy converters or ultra-highly sensitive near-infrared photodetectors.


Introduction
In spite of the fact that silicon has served a critical role in the development of the modern semiconductor industry, it was not the rst material which was employed in such gadgets. Indeed, the usage of germanium is well known to build the rst transistor. 1,2 Now people's attention is back to germanium materials due to the fact that germanium-based materials have excellent electron and hole mobilities. Under the premise of low power and high-speed operation, germanium materials are more suitable for electronic equipment than silicon materials. 3,4 As an alternative to silicon, the use of germanium channel materials in MOS-FET is a strong illustration of its applications. 5,6 Moreover, germanium has different benets contrasted with silicon, like higher saturation velocity and lower electronic band gap, which can dispose of the issue of depleting current saturation in MOS-FETs, reduce the operation voltage for the equipment, and improve the performance of photodetector. [7][8][9] Germanium-based graphene directly realizes the integration of high-quality graphene and semiconductor substrates, which will promote the wide application of graphene in the semiconductor industry more quickly. 9,10 On the other hand, exploring the geometric mutations, electronic structures, photoelectron spectra and vibrational modes of nanoalloy clusters have considerable importance due to the fact that nanoalloy clusters play an incredibly essential role in the shi from molecular to condensed matter, with the ongoing progress and widespread application of nanotechnology. 11 Rare earth metals (REMs) have properties such as high magnetic moments and extremely narrow optical transitions. For example, rare earth molecular crystal has extremely narrow optical transitions and long-lived quantum states, which enables it to be used in elds such as quantum communication and quantum processors, thereby opening up optical quantum systems. 12 Doping of rare earth metals with Ge clusters not only enriches the properties of germanium-based compounds, but also produces synergistic effects to improve the germaniumbased compound's intrinsic properties, thereby obtaining novel functional materials. Ge clusters doped with rare earth metals can be employed as a building block for self-gathered novel functional materials. In addition, the stability of Ge clusters can be improved by doping with rare earth elements since pure Ge clusters possessing only sp 3 -hybridized bonding characteristics are unstable. [13][14][15] For instance, ScGe 16 À , 16 LuGe 16 À , 11 and LuGe 17 + (ref. 17 and 18) have been evaluated to be high-symmetry endohedral structures, which give prominence to enhance stability and render them possibly as a building block for new multi-functional nanomaterials. Although REM-doped germanium clusters are not much investigated until now, they are expected to fascinate broader interests since the synergistic effect induced by REM-doped germanium nanoalloys can produce multifunctional nanomaterials with novel properties such as magnetism, photoelectric properties and photosensitivity etc.
In terms of experiments, Atobe et al. examined the atomic congurations and electronic properties of Ge clusters containing a lanthanide-or transition-atom (MGe n À ; M ¼ Lu, Sc, Y, Ti, Zr, Hf, V, Nb, and Ta, n ¼ 8-20) via scrutinizing the photoelectron spectra (PES) and reactivity. 19 On the theoretical aspect, Singh et al. investigated Th@Ge n (n ¼ 16,18,20) clusters with an ab initio calculation, and found that Th-encapsulating improved the stability of Th@Ge 16 and Th@Ge 20 , besides Th@Ge 16 has a wide HOMO-LUMO energy gap of 1.72 eV. 20 Recently, the structural evolution and electronic properties of Lu-doped Ge n (n ¼ 5-17) compounds in anionic states have been reported. 11 The 4f orbitals of the Lu atom are fully-lled. Its valence electron conguration is (4f 14 )5d 1 6s 2 . While 4f orbitals of Gd are half-lled, and its electron conguration is (4f 7 )5d 1 6s 2 . To compare the structure and properties of anionic germanium clusters doped with 4f orbital fully-lled Lu atom and 4f orbital half-lled Gd atom, in this study we have conducted a research for seeking the global minimum structure of doping Ge anionic clusters with Gd atom, i.e., GdGe n À (n ¼ 5-18). Global search scheme has been applied to explore their structural features and evolution systematically. Simulation of their PES, infrared and Raman spectroscopy, illumination of the electronic structure and ultraviolet-visible (UV-Vis) spectra of Gd@Ge 16 À as super atom with Frank-Kasper stable conguration has been performed. The ndings of this study could help researchers better understand the global minimal structural features and evolution, as well as the stabilities and spectroscopic properties of doping Ge clusters with REM atom, which are highly signicant for the construction of electronic equipment, solar cells and so on.

Computational details
The initial structures search for GdGe n À (n ¼ 5-18) nanoalloy clusters are rooted in two ways: (1) through the ABCluster unbiased global search technique 21-23 associated with Gaussian 09 package, 24 more than 400 geometries for each GdGe n À (n ¼ 5-18) nanoalloy clusters were optimized adopting PBE0 scheme 25 with the pseudopotential ECP28MWB basis set 26 for Ge atoms and ECP53MWB basis set 27,28 for Gd atoms. (2) Deduced from the earlier reported structures. 11,17,20 The lowlying geometries that come from above calculations were reoptimized by using PBE0 combined with cc-pVTZ-PP 29 and quasi-relativistic ab initio effective core potential def2-TZVP 30,31 basis set for Ge and Gd atoms, respectively. Aer optimization, vibrational frequency investigations were considered to proof the nature of stationary points. By the above process, mPW2PLYP hybrid functional 32 were deployed to select isomers for further optimization. However, the mPW2PLYP vibrational frequency was not performed due to limitations of computing capacity. Finally, the single-point energy was done through mPW2PLYP functional with basis set of aug-cc-pVTZ 33 for Ge and def2-TZVP for Gd. 30,31 Natural population analyses (NPA) were conducted via same scheme. The theoretical PES spectra of these anion nanoalloys were simulated by an outer-valence Green function (OVGF) approximation 34 combined with augcc-pVDZ 33 and def2-TZVP 30,31 basis set for Ge and Gd atoms, respectively. The infrared and Raman vibrational spectra of the global minimum structures have been performed by the PBE0 scheme. The DOS (density of states) and PDOS (partial DOS) of GdGe 16 À have been attained by Vienna Ab initio Simulation Package (VASP) [35][36][37][38] with PBE-GGA functional. 39 The projector augmented wave (PAW) was set to explore the inert core electron. 40,41 To prevent interplay between adjacent nanoalloy clusters, the 40 Â 40 Â 40Å edge lengths cubic cells with periodic boundary condition were taken into consideration. The plane wave cut-off energy was set up to 500 eV. The structures, PES spectra, iso-surface maps, and orbitals were created by visualization soware of Multiwfn and VMD. 42,43 Only spin multiplicities of octuplet were reported in this study for GdGe n À (n ¼ 5-18) nano clusters based on the following case. (i) For GdGe n À (n ¼ 1-4) compounds, the spin multiplicities of sextuplet, octuplet, decuplet and twelve states were taken into account. The results revealed that in sextuplet, spin contamination is always present and energies are always high. In twelve state, there are no spin contamination, but energies are also high. Their ground states are either octuplet or decuplet. As can be seen from Fig. S1 in ESI † that GdGe À and GdGe 2 À compounds possess a 10 P and a 10 B 1 ground states respectively, which are more stable in energy than that of 8 P and 8 A 00 excited state by 0.31 eV and 0.36 eV, respectively. For GeGe 3 À alloy, 8 A 2 and 10 P electronic states compete with each for the ground state since their energy differences are within 0.01 eV. GeGe 4 À compound has 8 A 1 ground state, which is more stable than that of 10 A 00 by 0.65 eV in energy. This situation corresponds to the Ge n (n ¼ 1-4). The ground states of Ge and Ge 2 compounds are 3 P and 3 P g À , respectively. For Ge 3 compound, 1 A 1 (isosceles triangle) and 3 A 1 0 (equilateral triangle) electronic states compete with each other for the ground state structure. 13 And the ground state is singlet for pure Ge 4 clusters. 13,14 This means that when Gd À anion doped Ge n clusters, the 4f electrons of Gd atom do not participate in bonding, and the four valence electrons of Gd À anion interact with the Ge n clusters. If the ground states of Ge n cluster are originally a triplet, the Gd À anion doped Ge n compounds are a decuplet state, and if the Ge n clusters are originally a singlet, the Gd À anion doped Ge n compounds are an octuplet state. The ground state is singlet for Ge n with n ¼ 5-18. 13,14 (ii) Nonetheless, we calculated the energies of the octuplet and decuplet for GdGe n À (n ¼ 5-18) nanoclusters and listed them in Table S1 in ESI, † from which we can see that the energy of decuplet is larger than that of octuplet. Therefore, we only presented octuplet state for GdGe n À (n ¼ 5-18) compounds.
So as to conrm the quality of our employed method, test calculations had formerly been performed through the ROCCSD(T) method for ScSi n 0/À compounds with n ¼ 4-9 and compared them with several different DFT functions. 44 The results proved that only the ground state geometry and vertical detachment energy of ScSi n 0/À compounds calculated by the mPW2PLYP functional agree with that of ROCCSD(T) scheme. Furthermore, the bond lengths of Ge 2 , AgGe, and AuGe compounds calculated via mPW2PLYP are 2.38Å, 45

Structures and evolutions of GdGe n À compounds
All selected congurations, including most stable and low-lying congurations of doping Ge anionic clusters with Gd atom are displayed in Fig. 1. The compounds are designated as nAm, with n representing the number of Ge atoms, A representing anion, and m representing the number of compounds, based on their energies ranging from low to high. For GdGe 5 À compound, two isomers are reported. Its global minimum structure is predicted to be C 4v -symmetry tetragonal bipyramid (5A1) in 8 A 2 ground state. The C 2v -symmetry edge-capped trigonal bipyramid (5A2) of 8 A 2 electronic state is above 0.36 eV than the 5A1 in energy. For GdGe 6 À compound, there are three isomers which are presented here. The most stable structure is evaluated to be C 5vsymmetry pentagonal bipyramid (6A1) in 8 A 1 ground state. Both compounds of C 2v -symmetry pentagonal bipyramid (6A3) in 8 B 2 electronic state and C 1 -symmetry 6A2 are less stable in energy than that of 6A1 by 1.19 and 0.80 eV, respectively. For GdGe 7 À compound, four structures are reported. The C 2v -symmetry 7A1 in 8 A 2 ground state can be viewed by attaching two Ge atoms to the 5A1 structure. The C s -symmetry bicapped octahedron (7A-2) can be viewed as a Gd atom substituting for a Ge atom in the most stable structure of Ge 8 compound. 13 The C s -symmetry 7A3 can be regarded by attaching a Ge atom to the 6A1 geometries.
The C s -symmetry 7A4 can be considered as linked structure in which Gd atom connects a Ge 3 triangle and a Ge 4 tetrahedron. In 8 A 00 electronic state, they are 0.09, 0.19 and 0.33 eV higher in Fig. 1 Lowest energy structure and isomers of GdGe n À (n ¼ 5-18) anionic nanoclusters, point group and relative energy (in eV). The blue and red circles represent germanium and gadolinium atoms, respectively. energy than that of 7A1, respectively. For GdGe 8 À compound, ve isomers are presented. The C 1 -symmetry 8A1 is predicted to be the global minimum structure. It can be viewed by attaching a Ge atom to a face of 7A1 geometry. The 8A2, 8A4 and 8A5 can be viewed as adding dual Ge atoms to the 6A1 geometry. They are C s -symmetry in 8 A 00 electronic state, C 2v -symmetry in 8 A 2 electronic state, and C s -symmetry in 8 A 00 electronic state. The 8A3 geometry, similar to the most stable structure of GdSi 8 À compound, 50 is C 2 -symmetry with 8 A electronic state. It belongs to linked structure in which Gd atom links two germanium tetrahedral. The linked structures were rstly proposed by Kumar and co-workers. 51 Energetically, the 8A2, 8A3, 8A4 and 8A5 isomers are 0.08, 0.11, 0.14 and 0.33 eV higher than that of 8A-1, respectively. For GdGe 9 À compound, four congurations are presented. The global minimum structure is calculated to be a bicapped antitetragonal prism (9A1) with C 4v -symmetry and 8 A 2 ground state analogous to that of GdSi 9 À compound. 50 The 9A2 can be viewed by attaching a Ge 3 to the ground state structure of GdGe 6 À compound. The 9A2, 9A3, and 9A4 isomers have C ssymmetry with 8 A 00 electronic state. They are 0.44, 0.62, and 1.02 eV higher in energy than that of 9A1, respectively. For GdGe 10 À compound, four structures are presented. The global minimum structure is forecasted to be 10A1 linked structure with C s -symmetry in 8 A 00 ground state in which Gd atom connects a Ge 4 tetrahedron and a Ge 6 capped trigonal bipyramid. The C s -symmetry 10A2 of 8 A 00 electronic state can be noted as capping the lowest energy isomer (9A1) of GdGe 9 À by a Ge atom close to the metal atom. The C 1 -symmetry 10A3 can be viewed as substituting a Gd atom for a Ge atom in the ground state structure of Ge 12 . 13, 45 The C s -symmetry 10A4 of 8 A 00 electronic state, Gd-capped bicapped antitetragonal prism of Ge 10 , is comparable to the that of LuGe 10 compound. 17 They are higher in energy than that of 10A1 by 0.18, 0.34, and 0.91 eV, respectively. For GdGe 11 À compound, four geometries are reported.
The ground state 11A1 is linked conguration where Gd atom links two sub-groups of Ge 5 and a Ge 6 . 11A2 geometry can be considered as adding four Ge atoms to the face of 7A2 structure. The C s -symmetry 11A3 of 8 A 00 state can be considered as adding Ge 2 to the edge of the ground state bicapped antitetragonal prism of GdGe 9 À compound. These compounds and C s -symmetry 11A4 of 8 A 00 electronic state are less stable as compared with 11A1 by 0.11, 0.24, and 0.51 eV, respectively. For GdGe 12 À complex, four geometries are noted. They are linked structures in which Gd links two orthogonal Ge 6 distorted tetragonal bipyramid, links a Ge 3 isosceles triangle and a Ge 9 tricapped trigonal prism (TTP). It also links a Ge 5 trigonal bipyramid and a Ge 7 pentagonal bipyramid, and links a Ge 4 quadrilateral and a Ge 8 antitetragonal prism, respectively. Energetically, D 2dsymmetry 12A1 of 8 A 2 ground state is more stable than those of C s -symmetry in 8 A 00 state about 0.09, 0.39, and 0.41 eV. respectively. For GdGe 13 À compound, four geometries are presented.
The C 1 -symmetry 13A1, C s -symmetry 13A11, 13A2 and 13A4 in 8 A 00 state belong to linked shapes where Gd atom connects a Ge 4 tetrahedron and a Ge 9 TTP, a Ge 4 rhombus and a Ge 9 TTP, and a Ge 5 trigonal bipyramid with a Ge 8 subcluster, respectively. The energy difference compared with the most stable structure of 13A1 is 0.13, 0.14, and 0.36 eV, respectively. For GdGe 14 À compound, four congurations are described. Its most stable structure is calculated to be Gd-linked motif (14A1) with C ssymmetry and 8 A 00 state where Gd atom attaches a Ge 5 and a Ge 9 motif. The C s -symmetry 14A2 in 8 A 00 state belongs to a linked structure where Gd atom joins a Ge 5 tetragonal pyramid and a Ge 9 TTP. The C 2v -symmetry 14A3 in 8  isomers are presented. One of them is Gd-encapsulated vecapped FPTQ (four pentagonal faces and two quadrangles) cage framework (17A1) with C 4v -symmetry and 8 A 2 ground state. It is more stable in energy than the C 1 -symmetry 17A2 linked geometry by 0.83 eV. For GeGe 18 À compound, two structures are presented. The most stable geometry is Gd-encapsulated endohedral conguration (18A1) with C s -symmetry in 8 A 00 ground state, of which energy is lower than that of 18A2 linked structure with C s -symmetry and 8 A 00 electronic state by 0.11 eV. Before the discussion of most stable structure, we concentrate on the structural transformation of GdGe n À (n ¼ [5][6][7][8][9][10][11][12][13][14][15][16][17][18] compounds at present. In the light of their structural characteristic of the determined global minimum conguration, the structural evolution favors Gd-linked conguration where metal atom connects two Ge subclusters starting from n ¼ 10, and Gdencapsulated germanium cage-like conguration is favored when n reaches to 15. Compared with LuGe n À (n ¼ 5-17) clusters, 11 except for the different electronic states (the ground states of LuGe n À (n ¼ 5-17) clusters are singlet), the most stable geometries of GdGe n À with n ¼ 8, 10, and 15 are different from those of LuGe n À clusters.

Magnetic moment and charge transfer
To learn more about the interaction between Gd atom and germanium nanoclusters, NPA of the GdGe n À (n ¼ 5-18) global minimum structure is carried out. The results including NPA congurations and NPA charges on Gd atom, the 4f, 5d, 6s, 6p and total magnetic moments of Gd, and total magnetic moments of compounds are shown in , the charge of Gd is from À3.17 to À4.87 a.u., demonstrating that Gd is an electron acceptor and the bond nature between Gd and the host of the germanium cluster may be principally metallic bonds. And for linked structures (n ¼ 10-15), the charge of Gd is from +0.25 to À0.26 a.u., revealing the fact that the characteristics of bonding between Gd and germanium clusters may be mixed with ionic bonds and covalent bonds in essence. (iv) The total magnetic moments of GdGe n À (n ¼ 5-18) compounds are kept at the value of 7 m B , and provided by the 4f electrons of Gd atom which are le nearly unperturbed.

Stability
Average atomization energy (AAE) and second energy difference (D 2 E) as two substantial parameters to evaluate thermodynamic and relative stability, have been performed on the most stable structures of GdGe n À (n ¼ 5-18) compounds via atomization and disproportional reaction as follow: GdGe n À / (n À 1)Ge + Ge À + Gd (1) Incremental AAE is an effective approach to examine the local relative stability of different size compounds. The AAE of GdGe n À (n ¼ 5-18) compounds as a function of the size of the compound is shown in Fig. 2(a), from which it can be deduced that GdGe 9 À and GdGe 16 À compounds are more stable than proposed by at rising background. In addition to AAE, D 2 E can not only mirror the local relative stability, but also gives a susceptible measure as shown in Fig. 2(b). The larger the D 2 E, the stronger the relative stability. The results of AAE are clearly reproduced in Fig. 2(b). It is noted that GdGe 9 À compound has only good relative stability, not the best thermodynamic stability. However, GdGe 16 À compound not only has good relative stability, but also has the best thermodynamic stability due to the fact that its AAE is the largest. Compared to anionic LuGe n À (n ¼ 5-17) clusters, 11 the AAE curves of LuGe n À and GdGe n À are in parallel as can be seen from with 4f orbital fully-lled Lu atom is slightly better than that of doped with 4f orbital half-lled Gd atom.

HOMO-LUMO energy gaps
An important physical parameter closely involved in chemical stability is HOMO-LUMO energy gap (E gap ). In the E gap quantitative evaluation, Baerends et al. 53 mentioned that the E gap calculated via pure density functional theory (DFT) is closer to the real optical gap than that evaluated by hybrid DFT due to the fact that the energy of HOMO and LUMO predicted in Kohn-Sham molecular orbital approximations experience in general the alike quantity increase. However, HF approach moves the LUMO up a much higher energy levels than the HOMO up, which results in the E gap of hybrid DFT becomes larger than that of pure DFT. Recently, An Wei 15 calculated the E gap of Ge n (3 # n # 20) by using the PBE scheme, compared them with experiment data, and found that the theoretical E gap match well with those in experiment. Therefore, the PBE scheme 39 are employed to evaluate the E gap of GdGe n À (n ¼ 5-18) compounds. The used basis sets are aug-cc-pVTZ 32 and def2-TZVP 29,30 for Ge and Gd atoms, respectively. They along with energies of HOMO and LUMO are shown in Fig. 2(c). We can see from it that the E gap of GdGe n À (n ¼ 5-18) compounds range from 0.75 to 1.96 eV.

PES of GdGe n À compounds
Spectral information is of considerable importance because the PES is an exceedingly hypersensitive approach for examining both electronic structures and equilibrium conguration of anionic atom, molecules and compounds. In particular, there is no experimental approach for directly determining the ground state conguration of compounds by now. One can only indirectly determine the ground state structures via detailed comparison of theoretical and experimental results. And PES is one of the most effective strategies. Therefore, we simulated the PES of GdGe n À (n ¼ 5-18) compounds in order to provide strong motivation and theoretical information for future experimental investigations. In the PES simulation, to t all peaks in the region of less than 5.00 eV, a Gaussian FWHM of 0.25 eV is utilized. The theoretical PES spectra are shown in Fig. 3 peaks (X, A-C) located at 3.18, 3.57, 4.31 and 4.66 eV are observed. For n ¼ 18, the rst peak (X) resided at 3.29 eV is a weaker shoulder. Its third and fourth peaks (B and C) are also relatively weaker peaks resided at 4.09 and 4.34 eV, respectively. The second and h peaks (A and D) centered at 3.62 and 4.69 eV are resolved easily. There are no experimental counterparts for comparison. We hope that our theoretical simulations will provide great incentive for further experimental research on these crucial Gd-doped germanium nanoalloys.

Infrared and Raman spectra
In addition to PES, infrared and Raman spectra are also one of the effective schemes to indirectly determine the ground state structures. The infrared and Raman spectra of GdGe n À (n ¼ 5-18) compounds have been computed using the PBE0 method to better understand their vibrational features. The basis set used are aug-cc-pVTZ and def2-TZVP for Ge and Gd atoms, respectively. They are shown in Fig. 4 where no imaginary frequency was observed, which demonstrates that the structure is stable.
In the infrared and Raman spectra of the GdGe 5 À compound, there are four and two prominent peaks observed, respectively. An angle-bending is doubly degenerated vibration mode at 67 cm À1 , and it leads to the highest intense infrared frequency. The second lowest vibration mode at 143 cm À1 with infrared active is breathing mode of GdGe 5 bipyramid. The vibration modes at 179 cm À1 and 240 cm À1 with Raman and infrared active are breathing mode of LuGe 5 tetragonal bipyramid and stretching mode of Ge 5 tetragonal pyramid respectively. For GdGe 6 À compound, only one resolved infrared peak at 85 cm À1 is doubly degenerated angle-bending vibration mode. Two vibration modes at 143 and 220 cm À1 in Raman spectra are stretching mode of GdGe 5 pentagonal pyramid and breathing mode of Ge 6 pentagonal pyramid respectively. In infrared and Raman spectra of GdGe 7 À compound, four and one prominent peaks are seen, respectively. The vibration modes at 95 cm À1 and 155 cm À1 belong to the bending mode of GdGe 7 , that at 199 cm À1 and 220 cm À1 belong to the stretching mode of GdGe 7 , and that at 205 cm À1 of Raman spectra is the breathing mode of GdGe 7 . In infrared and Raman spectra of GdGe 8 À compound, ve and three prominent peaks are seen, respectively. The strongest peak in infrared spectra is at 179 cm À1 , which is resulted from the stretching mode of the Ge 4 tetrahedron, and that in Raman spectra is at 183 cm À1 , which is resulted from the breathing mode of the GdGe 8 . In infrared and Raman spectra of GdGe 9 À compound, there are four and one prominent peaks, and the strongest peaks locate at 235 cm À1 and 185 cm À1 with breathing and stretching mode of GdGe 9 , respectively. Three lowest vibration modes of 64, 116 and 137 cm À1 are doubly degenerated bending vibration mode. In infrared and Raman spectra of GdGe 10 À compound, four and one prominent peaks are respectively reported. The vibration mode at 267 cm À1 with Raman and infrared active is breathing mode of Ge 4 tetrahedron. The most prominent peak in infrared spectra at 172 cm À1 results from the breathing mode of the Gd-linked Ge 4 tetrahedron and Ge 6 capped trigonal bipyramid together. The second most prominent peak in infrared spectra at 140 cm À1 is the breathing mode of Gd-linked Ge 6 . The infrared vibration mode at 236 cm À1 is the stretching mode of Gd 6 capped trigonal bipyramid. In infrared and Raman spectra of GdGe 11 À compound, three prominent peaks are reported. The two most intense infrared peaks at 152 and 175 cm À1 are resulted from the breathing mode of Ge 6 and Gd-linked Ge 5 together. The vibration mode at 189 cm À1 with infrared active is breathing mode of Gd-linked Ge 5 . The strongest peak in Raman spectral located at 147 cm À1 is bending mode of Gd-linked Ge 6 . The vibration mode at 251 cm À1 in Raman spectra results from the breathing mode of Ge 6 , and that at 203 cm À1 results from doubly degenerated stretching vibration mode. In infrared and Raman spectra of GdGe 12 À compound, the most prominent peak at 373 cm À1 results from the doubly degenerated breathing mode of Gd-linked Ge 6 . In addition, there are three dominant peaks in infrared spectra at 114, 140 and 180 cm À1 related to bending mode of GdGe 12 . In infrared and Raman spectra of GdGe 13 À compound, four and three prominent peaks are seen. The most intense peak in infrared spectra at 249 cm À1 results from stretching mode. The second most intense peak in infrared and the most intense peak in Raman located at 172 cm À1 results from bending mode of GdGe 13 . The vibration modes at 104 cm À1 and 132 cm À1 with infrared active are stretching and bending mode respectively. And that at 224 cm À1 in Raman spectra results from bending mode. For GdGe 14 À compound, two dominant peaks are reported. The most prominent peak in infrared spectra at 157 cm À1 results from the breathing mode of Gd-linked Ge 5 trigonal bipyramid. In Raman and infrared spectra, the vibration mode at 242 cm À1 results from the breathing mode of Gd-linked Ge 9 TTP, and that in Raman spectra at 264 cm À1 is the breathing mode of Ge 5 trigonal bipyramid. For GdGe 15 À compound, only one prominent peak at 219 cm À1 in infrared spectra arises from the doubly degenerated bending mode. There are two major peaks in the Raman spectra at 171 cm À1 and 185 cm À1 in the bending mode of Gddoped Ge 15 motif and the breathing mode of peripheral Ge cage conguration (Gd atom remains static), respectively. In infrared and Raman spectra of GdGe 16 À compound, only one main peak resides at 214 cm À1 with the threefold degenerate bending mode and 161 cm À1 for breathing mode of peripheral Ge cage (Gd atom motionless). For GdGe 17 À compound, there is also single peak in infrared and Raman spectra, which resides respectively at 181 cm À1 with the doubly degenerate bending mode and 164 cm À1 in breathing mode. In infrared and Raman spectra of GdGe 18 À nanocluster, there are three prominent peaks respectively. The most intense peak in infrared spectra resides at 127 cm À1 consisted of approximately triple times of degenerate bending mode. In infrared spectra the vibration modes at 164 cm À1 and 191 cm À1 are stretching mode. In Raman spectra the largest peak resides at 176 cm À1 with the approximately doubly degenerated breathing mode, and those at 119 cm À1 and 152 cm À1 are bending mode. As we could know from the description above, infrared and Raman activity manifests different spectra for these compounds and reects the inuence of geometrical changing. According to infrared analysis, breathing mode of the Gd-linked Ge subclusters for Gd-linked congurations excluded GdGe 13 À compound give rise to the most intense peak, and it is degenerated bending mode for Gd-encapsulated frameworks. In Raman spectra, the strongest peak is largely breathing or bending mode of Ge subclusters or Gd-linked Ge subclusters for Gd-linked geometries, and it is breathing mode of peripheral Ge cage (Gd atom hardly moves) for Gd-encapsulated structures. They occur in the infrared range of these compounds in comparison with the 400-10 cm À1 far-infrared region. Therefore, the most stable compounds with component might be useful for far-infrared sensing devices.
3.7 Iso-chemical shielding surface of GdGe 16 À compound Because of great potential application of GdGe 16 À nanocluster in optoelectronic devices, we further evaluated its stability via the method of iso-chemical shielding surface (ICSS), which is the negative value of nuclear independent chemical shielding (NICS), and was carried out by gauge-independent atomic orbital (GIAO) way. 54,55 In Fig. 5(a), it is displayed that the whole real space displays the red region that means the chemical shielding opposed the external magnetic eld with the isovalue of 0.05 ppm, and the blue region represents the chemical deshielding area with the isovalue of À0.05 ppm. Both of them have symmetry because GdGe 16 À nanocluster has a high symmetry of T d . Clearly, inner cage area has a larger chemical shielding effect and outer has vice versa. In the Fig. 5(b), the curve map shows one direction shielding value which relates to the distance. Generally, the shielding value in the distance of 1 angstrom is a standard parameter to evaluate the aromaticity of the system, i.e., ICSS(1) ¼ 46 ppm. Besides that, the maximum shielding value is 78 ppm in a distance of 1.91Å. In short, the stability of GdGe 16 À nanocluster has been revealed by the ICSS methods. Moreover, the excellent stability of such cluster has been further proved.
To further understand the outstanding chemical and thermal stabilities of GdGe 16 À nanocluster, the total and partial density of states analysis are shown in Fig. 6. In the near Fermi level of which the most contribution belongs to the 4p orbital of Ge atom which was mixed with the major of 5d and 6s orbital of Gd atom to form the hybrid bonds which stabilizes the whole structure. In the whole range, the spin up curve and spin down curve are asymmetric that indicates the system has magnetism and spin polarization effect. Combined with NPA analysis, we have known that Gd 4f electrons in half-lled state do not participate in the bonds, and hence provide magnetism. The total valence of 75 electrons of GdGe 16 À system can be distributed to the orbital sequence of 1S 2 1P 6 (4f 7 ) 1D 10 1F 14 2S 2 2P 2 1G 18 2P 4 2D 10 , which complies with not only Hund's rule, but also spherical jellium model. Hence, it proves that GdGe 16 À nanocluster is a superatom.

UV-Vis spectra of GdGe 16 À molecule
Owing to the high stability and proper semiconductor characteristics of anion cluster of GdGe 16 À , the ultraviolet-visible (UV-Vis) spectra have been simulated by time-dependent density functional theory (TD-DFT) calculation by the PBE scheme with aug-cc-pVDZ and ECP28MWB basis set for Ge and Gd atoms respectively. To ensure the accuracy of calculation, enough bands were required to be considered, so the 120 excited states were performed to satisfy the described system. Full results are assembled in Fig. 7 with the Gaussian broadening value of 0.30 eV. Overall, the UV-Vis absorption spectrum of GdGe1 6 À anion produces three absorption bands, two of them fall in the visible region and one in the near-infrared region. Compared to UV-Vis spectra of LuGe 16 À , 11 the UV-Vis spectra of GdGe 16 À have obvious red shi. The rst absorption band is from 350 nm to 465 nm. The strongest peak is at 413 nm. The second absorption band, with the strongest peak at 525 nm, is from 465 nm to 628 nm. The third absorption band having range of 628 nm to 1050 nm has the most intense peak at 767 nm. For summit of 413 nm, it is made of S 0 / S 109 , S 0 / S 95 , S 0 / S 86 with the contribution of 74.9%, 8.4%, 7.1%, respectively. For the peak of 525 nm, it is composed of S 0 / S 35 , S 0 / S 40 , S 0 / S 44 with the contribution of 46.7%, 45.1%, 7.6%, respectively. The last peak of 767 nm is attributed to the transition of 99% of S 0 / S 9 . As we know, the solar energy distribution is 43% visible light with the most intensity, and 52% near-infrared with the energy