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SCientifiC REPoRTS | (2018) 8:6702 | DOI:10.1038/s41598-018-25027-1
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Probing the Structural and
Electronic Properties of Dirhenium
Halide Clusters: A Density
Functional Theory Study
Li Huan Zhang1,2, Xin Xin Xia1, Wei Guo Sun1, Cheng Lu2,3, Xiao Yu Kuang1, Bo Le Chen1 &
George Maroulis4
Dirhenium halide dianions received considerable attention in past decades due to the unusual
metal–metal quadruple bond. The systematic structural evolution of dirhenium halide clusters has
not been suciently studied and hence is not well-understood. In this work, we report an in-depth
investigation on the structures and electronic properties of doubly charged dirhenium halide clusters
Re2X82− (X = F, Cl, Br, I). Our computational eorts rely on the well-tested unbiased CALYPSO (Crystal
structure AnaLYsis by Particle Swarm Optimization) method combined with density functional theory
calculations. We nd that all ground-state Re2X82− clusters have cube-like structures of D4h symmetry
with two Re atoms encapsulated in halogen framework. The reasonable agreement between the
simulated and experimental photoelectron spectrum of the Re2Cl82− cluster supports strongly the
reliability of our computational strategy. The chemical bonding analysis reveals that the δ bond is the
pivotal factor for the ground-state Re2X82− (X = F, Cl, Br, I) clusters to maintain D4h symmetric cube-like
structures, and the enhanced stability of Re2Cl82− is mainly attributed to the chemical bonding of 5d
orbital of Re atoms and 3p orbital of Cl atoms.
e discovery1 of the metal–metal quadruple bond in dirhenium halide Re2Cl82−, which is recognized as an
important milestone in the development of modern inorganic chemistry, has stimulated intensive research work
in the eld of transition metal chemistry2,3. Understanding the properties of the metal–metal multiple bond
is signicant to further elucidate the chemistry of transition metal complexes. As a prototypical metal–metal
multiple bonded ion, Re2Cl82− has been studied extensively in the past decades2,4–22. e experimental and theo-
retical investigations mainly focused on the preparation4–6, the molecular structure7,8, the metal–metal multiple
bond2,9–14 and the electronic properties4,10,15–22 of Re2Cl82− in the octachlorodirhenate salts. Previous studies7–13
have determined the geometry structure of Re2Cl82− to be of D4h symmetry, and conrmed the formation of
Re–Re quadruple bond isdue to the σ2π4δ2 subset of the bonding orbitals. Due to the diculty of preparing the
Re2Cl82− dianion in the gas phase, Wang et al.21 rst measured the photoelectron spectrum (PES) of gaseous
Re2Cl82− several decades aer the discovery of the metal−metal multiple bond, leading to a thorough under-
standing of the Re–Re quadruple bond and its electronic structure.
Compared to the extent of the investigations on Re2Cl82−, similar treatments of the heavier halogen derivative
Re2Br82−, which contains the Re–Re quadruple bond as well, are limited4,17,23,24. To our knowledge, sparse studies
have been reported on the lighter halogen derivative Re2F82−. Peters et al.25 initially synthesized (n-Bu4N)2[Re2F8]
·4H2O, which contains Re2F82−, via Re2Cl82− and (n-Bu4N)F·3H2O reacting in CH2Cl2 solution. Conradson et al.26
later conrmed the presence of the Re–Re quadruple bond in Re2F82− using X-ray absorption ne structure and
resonance Raman spectroscopy. e structure of Re2F82− was determined to be eclipsed D4h geometry by Henkel
et al.27. Recently, Balasekaran et al.28 prepared the (NH4)2[Re2F8]·2H2O salt in nearly 90% yield by the reaction of
(n-Bu4N)2[Re2Cl8] with molten NH4HF2. ey also investigated the molecular and electronic structure along with
1Institute of Atomic and Molecular Physics, Sichuan University, Chengdu, 610065, China. 2Department of Physics,
Nanyang Normal University, Nanyang, 473061, China. 3Department of Physics and High Pressure Science and
Engineering Center, University of Nevada, Las Vegas, Nevada, 89154, United States. 4Department of Chemistry,
University of Patras, GR-26500, Patras, Greece. Correspondence and requests for materials should be addressed
to C.L. (email: lucheng@calypso.cn) or X.Y.K. (email: scu_kuang@163.com) or G.M. (email: maroulis@upatras.gr)
Received: 15 February 2018
Accepted: 13 April 2018
Published: xx xx xxxx
OPEN
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SCientifiC REPoRTS | (2018) 8:6702 | DOI:10.1038/s41598-018-25027-1
the electronic absorption spectrum of Re2F82− relying on multicongurational quantum chemical calculations.
Compared to Re2F82−, studies on Re2I82− are sparse as well. Glicksman et al.29 rstly reported a synthesis route of
Re2I82− via the reaction of the dirhenium complex Re2(O2CC6H5)4Cl2 and HI with Bu4N+ in ethanol or methanol
to produce the (Bu4N)2Re2I8 salt. Preetz et al.30 prepared (Bu4N)2Re2I8 successfully for the rst time in a simple
procedure by the reaction of (Bu4N)2Re2X8 with HI in dichloromethane. Preetz et al.31 also reported measure-
ments of the resonance Raman spectrum of (Bu4N)2Re2I8, while Cotton et al.32 studied its crystal structure until
a few years later. Extensive studies on Re2X82− have been reported, but almost all previous studies focused on
Re2X82− dianions in crystals. ere has been no systematic work on Re2X82− (X = F, Cl, Br and I) clusters until
now, so the following questions attract our interests: (i) It is not clear whether Re2X82− clusters are characterized
by the same molecular geometry as Re2X82− dianions in crystals. (ii) Does the chemical bonding in Re2X82− clus-
ters dier from that of dianions in crystals? (iii) What is the relative stability of Re2X82− clusters? Consequently, we
turn our attention to the systematic study of lowest-energy geometries and electronic structures of Re2X82− (X = F,
Cl, Br, I) clusters.
As a rst step of our study on the structural evolution of Re2X82− clusters, we perform a search for the the
low-energy structures of Re2X82− (X = F, Cl, Br, I) by means of the CALYPSO (Crystal structure AnaLYsis by
Particle Swarm Optimization) code combined with DFT (density functional theory) calculations. We get the
ground-state structures of Re2X82− clusters from the above calculations and subsequently investigate their relative
stabilities and chemical bonding. is paper is organized as follows. e obtained results and a pertinent discus-
sion are in the following. en we summarize our conclusions. Last, a detailed presentation of the computational
method is described.
Results and Discussion
Geometric Structure. e lowest-energy structures of the Re2X82− (X = F, Cl, Br, I) clusters, together with
other three typical low-lying isomers are shown in Fig.1. e optimized vibrational frequencies and atomic
coordinates of ground-state Re2X82− (X = F, Cl, Br, I) clusters are all collected in TableS1 and TableS2 of the sup-
plementary information. According to their energies from low to high, all isomers are denoted by na, nb, nc and
nd (n = 1, 2, 3,4), in which a, b, c and d stand for Re2F82−, Re2Cl82−, Re2Br82− and Re2I82−, respectively. e elec-
tronic states, point group symmetries, average binding energies, HOMO−LUMO (the highest occupied molec-
ular orbitals and the lowest unoccupied molecular orbitals) energy gaps, together with charge on Re atoms and
halogen atoms of the ground-state Re2X82− clusters are summarized in Table1. In addition, the electronic states,
point group symmetries, relative energies, HOMO−LUMO energy gaps of all isomers are given in TableS3.
It can be seen in Fig.1 that the ground state 1a, 1b, 1c and 1d of Re2X82− (X = F, Cl, Br, I) all possess cube-like
geometric structures with D4h symmetry. e geometric structures of ground-state Re2X82− (X = F, Cl, Br, I) clus-
ters favor low-spin 1A1g state and have the same symmetry with those in crystals2,7,11,23,27,32. With the increase of
the halogen atom size, the Re–Re bond length in Re2X82− varies from Re2F82− to Re2I82− as 2.20 Å, 2.21 Å, 2.22 Å,
2.24 Å, showing a little dierence to those of Re2X82− dianions in crystal2. e 2a isomer has a distorted cube-like
structure with C2 symmetry and the energy is 1.14 eV higher than its ground-state structure 1a. e metastable
isomer 3a of Re2F82− has Cs symmetry, at 1.71 eV higher than its global minimum 1a. Interestingly enough, the
structure of 3a is a small square-bottom boat, and the two rhenium atoms are located in its interior. e point
group symmetry of the 4a isomer is C2v, and its energy is 3.36 eV higher than its lowest-energy structure 1a. It is
obvious that the two rhenium atoms are exposed outside in the geometry structure of 4a. It can be clearly seen
from Fig.1 that 2b has similar structures with 3a. e isomer of 2b has C1 symmetry with its energy 1.16 eV
higher than the ground-state structure 1b. e isomers of 3b and 4b display cage-like structure with the two Re
atoms encapsulated in a chlorine framework. ey possess Cs and C2v symmetry with the energy 1.22 eV and
1.47 eV, respectively, higher than their lowest-energy structures 1b. e isomer 2c has C2v symmetry, with total
energy 0.28 eV higher than the ground-state 1c, whose structure is similar to that of 2b. e 3c structure of C2v
symmetry looks similar to the structure of 4b, with total energy higher than 1c by 1.31 eV. e C2v symmetry 4c
isomer is 3.07 eV less stable than the ground-state 1c. e 2d isomer of C2v symmetry has similar structure to the
isomers 2b and 2c with the total energy 0.43 eV higher than 1d structure. e structure of 3d, which possesses
D2d symmetry with total energy higher than the 1d one by 1.50 eV, is similar to that of 4b and 3c isomers. e C2v
symmetry 4d isomer, at 2.43 eV higher in energy than the ground-state 1d, has similar structure to 4c. It is worth
noting that, except for the 4a structure of Re2F82−, the two rhenium atoms are invariably inclined to stay inside for
all ground and excited state structures of Re2X82− (X = F, Cl, Br, I). In order to conrm the validity of our calcula-
tions, we have also optimized the Re2X82− (X = F, Cl, Br, I) clusters at the BP86 level of theory. e corresponding
lowest-energy geometries of Re2X82− clusters are presented in FigureS1 of the supplementary information. From
FigureS1 we can see all structures optimized at BP86 functional also have cube-like structures with D4h symmetry
and the same electronic state of 1A1g. e respective ground-state structures are in agreement with those obtained
by our B3LYP optimization, further supporting our claim for the reliability of our theoretical approach.
Photoelectron Spectra of Re2X82−. Photoelectron spectrum (PES) is a powerful tool, which can pro-
vide important information about the electronic conguration of ground-state structures. In order to verify the
validity of our obtained structures in this work, as shown in Fig.2, we have simulated the photoelectron spectra
of all global minimum geometries of Re2X82− (X = F, Cl, Br, I) and compared to the available experimental PES.
Moreover, the values of adiabatic detachment energy (ADE), extracted from the threshold of the rst peak, and
the values of vertical detachment energy (VDE), obtained from the rst peak maximum of the spectra, are sum-
marized in TableS5 together with the available experimental data21.
As shown in Fig.2, all spectra exhibit rich features, which correspond to transitions from the ground state of
Re2X82− to the ground and excited states of singly charged Re2X8−. Overall, the binding energies, spacings and
intensities are dierent in each spectrum, but the spacings and intensities of spectra features for Re2Br82− and
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SCientifiC REPoRTS | (2018) 8:6702 | DOI:10.1038/s41598-018-25027-1
Re2I82− are nearly similar to each other. e most prominent spectral feature of Re2F82− is the observation of
a lower adiabatic detachment energy measured as 0.05 eV. is phenomenon is normal for multiply charged
anions, largely due to the presence of intramolecular Coulomb repulsion33,34. It can be clearly seen that the rst
two peaks of the Re2F82− spectrum are very weak and appear in very lower binding energies. e following rela-
tively intense peaks locate at 1.25 and 1.70 eV, respectively, and the most intense peak locates at 3.80 eV. For the
Figure 1. e geometrical structures of low-lying Re2X82− (X = F, Cl, Br, I) clusters, along with the point group
symmetry and relative energy (eV). Rhenium atoms are in yellow. Fluorine, chlorine, bromine and iodine atoms
are in orange, pink, green and purple, respectively.
Cluster State Sym. EbEgap Q (Re) Q (X)
Re2F82−1A1g D4h3.91 1.94 1.29 −0.57
Re2Cl82−1A1g D4h2.49 1.71 −0.03 −0.24
Re2Br82−1A1g D4h2.07 1.66 −0.32 −0.17
Re2I82−1A1g D4h1.72 1.43 −0.60 −0.10
Table 1. Electronic states, point group symmetries, average binding energies Eb (eV), HOMO−LUMO energy
gaps Egap (eV) along with charge Q (e) on Re atoms and halogen atoms of Re2X82− (X = F, Cl, Br, I) clusters.
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SCientifiC REPoRTS | (2018) 8:6702 | DOI:10.1038/s41598-018-25027-1
simulated PES of Re2Cl82−, the ADE, namely the second electron binding energy, is 0.98 eV, which is consistent
with the experimental datum of 1.00 eV. e rst peak is located at 1.19 eV, in reasonable agreement with the
rst peak location of the experimental spectrum of Re2Cl82− centered at 1.16 eV. e following three peaks are
relatively intense, located at 2.21, 2.80, and 3.24 eV, respectively. In the simulated PES of Re2Br82−, the rst peak is
quite intense, and emerges at 2.09 eV. In addition, there is a relatively sharp peak, which is the most intense one,
located at 3.95 eV. e simulated spectrum of Re2I82− exhibits three obviously intense peaks and the rst relatively
weak peak emerges at 1.21 eV. e agreement of the ADE and VDE values of the simulated and experimental PES
for Re2Cl82− supports the validity of our computational approach. We hope that the simulated PES of dirhenium
halides can provide a helpful reference for the spectroscopic studies of Re2X82− (X = F, Br, I) dianions.
Relative Stabilities. To explore the relative stabilities of the ground state structures of the dirhenium halide
system, we have calculated the average binding energies (Eb). For Re2X82− (X = F, Cl, Br, I) clusters, the Eb can be
dened as follow:
=++−
−−
EE EEE[2 (Re) 6(X) 2(X) (ReX )]/10(1)
b282
Where E(Re2X82−), E(Re), E(X), and E(X−) represent the energy of Re2X82− clusters, neutral Re atom, neutral X
atom, and anionic X−, respectively. e average binding energies of Re2X82− (X = F, Cl, Br, I) clusters are displayed
in Fig.3. From Fig.3 we can nd that Re2F82− is relatively stable due to its large average binding energy value.
Besides, the Eb values of Re2X82− decrease monotonically from Re2F82− to Re2I82−, indicating that the relative sta-
bilities of Re2X82− (X = F, Cl, Br, I) decrease with increasing size of the halogen atom.
Figure 2. e simulated photoelectron spectra of the ground-state structures of Re2X82− (X = F, Cl, Br, I)
clusters, along with the available experimental spectrum of Re2Cl82− in the inset.
Figure 3. e average binding energies per atom Eb and HOMO−LUMO energy gaps of Re2X82− (X = F, Cl, Br, I).
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SCientifiC REPoRTS | (2018) 8:6702 | DOI:10.1038/s41598-018-25027-1
Another important parameter related to the relative stabilities of the Re2X82− clusters is the HOMO−LUMO
energy gap (Egap), which represents the ability of an electron to jump from the highest occupied molecular orbital
(HOMO) to the lowest unoccupied molecular orbital (LUMO). A large value of Egap implies the corresponding
molecular structure is chemically inert. e evolution of the HOMO−LUMO energy gap for the ground-state
Re2X82− clusters is shown in Fig.3. It is clearly seen that the Egap decrease monotonically, that is to say, the clusters
are relatively less reactive as the halogen atom size increases, in agreement with the obtained results for the aver-
age binding energies. However, in contrast to the average binding energy rapid decrease from Re2F82− to Re2I82−,
the HOMO−LUMO energy gap decreases less steeply.
Charge Transfer. Electronegativity35–39 is an important chemical property to describe the ability of an atom
to attract electrons. A large electronegativity value is interpreted as a strong ability to attract electrons. In order
to investigate the charge transfer between Re atoms and halogen atoms for ground-state Re2X82− clusters and
compare to the electronegativity, we utilize natural population analysis (NPA) to obtain the charge on each atom.
e results are summarized in Table1. From Table1 we can see that the negative charge on halogens gradually
decreases from Re2F82− to Re2I82−. is phenomenon agrees with the decreasing values of Pauling electronegativ-
ity, which are 3.98, 3.16, 2.96 and 2.6640 for F, Cl, Br and I, respectively. Meanwhile, the charge on Re changes from
positive to negative and the negative charge on Re is increasing with the halogen atom size increasing. All this
indicates that it becomes more competitive for Re to attract electrons as the electronegativity values of halogens
decrease. Although the electronegativity value of Re (1.93 on the Pauling scale)36 is lower than that of all halogen
atoms, the negative charge on Re atoms is more than that of Br and I for Re2Br82− and Re2I82−, clearly not in accord
with the electronegativity. is is perhaps related to the weak ability of Br and I halogen atoms to attract electrons
caused by their large atomic radii and the strong intramolecular Coulomb repulsion observed in multiply charged
anions34. In summary, the two excess negative charges shi from peripheral halogens to Re atoms in the case of
heavier halogen atoms.
Chemical Bonding Analysis. In order to explore the nature of the chemical bonding in Re2X82−, we have
carried out a detailed analysis on the HOMO−LUMO molecular orbitals (MOs). Figure4 shows the molecular
orbital diagrams of Re2X82− clusters together with their orbital energy levels, which feature their HOMO−LUMO
energy gaps. Herein we take the Re–Re bond as z axis and the Re–Cl bond as ± x and ± y axes to analyze the
Figure 4. Molecular orbital maps and energy levels of Re2X82− (X = F, Cl, Br, I). e HOMO−LUMO energy
gap is indicated (in blue).
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SCientifiC REPoRTS | (2018) 8:6702 | DOI:10.1038/s41598-018-25027-1
chemical bonding. As shown in Fig.4, the HOMO of Re2F82− displays a large overlap between the 5dxy orbitals of
the two Re atoms, and the overlap forms a δ bond. e HOMO–1 and HOMO−2 are doubly degenerate, which
feature π bonds formed by the overlap of the 5dyz orbitals. From the HOMO of Re2Cl82−, it can be seen that the
5dxy orbitals of the Re atoms overlap and this leads to the formation of the δ bond. In Re2Cl82−, the HOMO-2
and HOMO–3 are doubly degenerate, leading to π bonds formation by the overlap of the 5dyz orbitals. In the
HOMO of Re2Br82−, the 5dxy orbitals of Re atoms have an overlap, leading to the formation of the δ bond. As for
Re2I82−, there is no bonding between Re and Re in HOMO, while the HOMO-2 reveals an overlap between the
5dxy orbitals of the Re atoms, forming a δ bond. Both the HOMO of Re2X82− (X=F, Cl, Br) and the HOMO−2 of
Re2I82− are δ bonds. Compared to σ and π bonds10,13,21, the δ bond is weak and contributes relatively a little to the
total strength of the Re–Re bond. Nevertheless, it plays a vital role in geometric structure. e δ bond strength
achieves its maximum only when the conformation is eclipsed. Its strength reduces as the conformation becomes
staggered19. us, we can deduce that the δ bond is the pivotal factor for the ground-state Re2X82− (X = F, Cl, Br,
I) clusters to maintain D4h symmetric cube-like structures.
To further understand the bonding mechanism in Re2X82−, we select Re2Cl82− as a representative example in
order to perform a chemical bonding analysis using the adaptive natural density partitioning (AdNDP) method,
which is particularly suitable to decipher the nature of the chemical bond. e AdNDP results displayed in Fig.5
reveals 25 localized bonds and 11 delocalized bonds with occupation numbers (ONs) ranging from 1.9684 to
2.0000 |e|, very close or nearly equal to the ideal values (2.000 |e|). ere are eight 1c–2e lone pairs (3 s) with
the ON of 1.9684 |e|. e seventeen 2c–2e bonds can be divided into three sets, which contain one Re–Re bond
(ON = 1.9991 |e|), eight Cl–Cl bonds (ON = 1.9989 |e|), and eight Re–Cl bonds (ON = 1.9947 |e|), respectively.
e Re–Re bond is formed by the overlap of 5d orbital between the two Re atoms. For the Cl–Cl bonds, the 3p
orbital in the peripheral Cl atoms results in the formation of the 2c–2e bonds. e interaction between Re and Cl
is mainly dominated by the 5d orbital of Re atom and the 3p orbital of the Cl atom. e eight 3c–2e bonds with
ON = 1.9886 |e| are formed by the 5d orbitals of two Re atoms and the 3p orbital of one Cl atom. ere are three
10c−2e bonds with the ONs of 2.0000 |e| between the two Re atoms and the Cl8 framework, which strengthen the
interactions between the inside Re atoms and the peripheral Cl atoms. In addition, the high occupation number
among the localized and delocalized bonds may point to its stability. Overall, the enhanced stability of Re2Cl82− is
mainly caused by the chemical bonding of 5d orbital of Re atoms and 3p orbital of Cl atoms.
Conclusions
We have performed a comprehensive research on the structural and electronic properties of dirhenium halide
clusters via unbiased CALYPSO structure searches combined with DFT optimizations. e results clearly reveal
that the ground states of Re2X82− (X = F, Cl, Br, I) all possess cube-like geometry with D4h symmetry. is nd-
ing has been further tested by performing calculations at the BP86 level. e simulated PES of Re2Cl82− shows
reasonable agreement with the experimental spectrum, which further conrms the validity of our computational
approach. According to the average binding energy and HOMO−LUMO energy gap, Re2X82− clusters are pro-
gressively less stable as halogen atoms become heavier. e chemical bonding analysis indicates that the δ bond
is the pivotal factor for the ground-state Re2X82− (X = F, Cl, Br, I) clusters to retain D4h symmetric cube-like
structures, and the enhanced stability of Re2Cl82− is mainly due to the chemical bonding of 5d orbital of Re atoms
Figure 5. e results of AdNDP analysis for Re2Cl82−. ON represents the occupation number.
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SCientifiC REPoRTS | (2018) 8:6702 | DOI:10.1038/s41598-018-25027-1
and 3p orbital of Cl atoms. We expect our ndings provide stimulations and guidance to researchers for further
experimental or theoretical investigations on binuclear transition metal halide clusters.
Computational Method
e low-lying isomers of Re2X82− (X = F, Cl, Br, I) clusters are determined via the CALYPSO method which
is based on the particle swarm optimization (PSO) algorithm. is theoretical method has been described in
sucient detail previously41–43. In brief, it can explore the global minima of the potential energy surfaces of
predicted system only based on the chemical compositions at given external conditions. It has achieved great
success in predicting the ground-state structures of various systems44–49. Herein, initial structures for Re2X82−
clusters are achieved by the CALYPSO method. Each generation contains 50 structures and 60% of those are
generated by PSO, while the other structures are generated randomly. We have followed 30 generations for each
cluster to achieve convergence to the global minima on the potential energy surfaces. e candidates within
4 eV of the lowest-energy structure are further optimized using the B3LYP50,51 exchange-correlation functional.
The 6-311 + G(d) basis set for F and the LANL2DZ52,53 basis with effective core potentials for Cl, Br, I and
transition-metal Re are employed throughout all calculations. All these calculations are carried out using the
Gaussian 09 soware package54. e choice of the B3LYP functional and e LANL2DZ basis leans heavily on
experience acquired from the previous investigations11,13,55. Dierent spin multiplicities are taken into consider-
ation in the geometric optimization process (up to quintet for all clusters). e harmonic vibrational frequencies
are calculated in order to ensure that the optimized structures are true minima without any imaginary frequen-
cies. We also perform the natural bond orbital (NBO)56 and adaptive natural density partitioning (AdNDP)57 to
get further insight into the chemical bonding mechanism.
In order to identify the reliability of our calculations, we have optimized the structures of dirhenium halide
clusters with the non-hybrid BP86 functional and the same basis set as above. It is readily seen that the optimized
results of Re2X82− clusters obtained by BP86 method are in accordance with our B3LYP results. In addition,
compared with the Re–Re bond length of Re2X82− dianions in previous study2 (TableS4), we can see the results
calculated by the B3LYP level agree better than those from the BP86 functional. us we conclude that the results
obtained at B3LYP level are reliable. To further conrm the reliability of our computational method, we simulate
the photoelectron spectra (PES) of all lowest-energy dirhenium halide clusters and compare to the available
experimental PES21. e rst VDE is obtained based on the energy dierence between the singly charged anion
and dianion at the ground-state geometry of the dianion. e excited-state energies of the singly charged anion
are calculated via the time-dependent density functional theory (TD-DFT) method58. e reasonable agreement
between the simulated and the experimental PES of Re2Cl82− strongly supports our choice of B3LYP functional.
References
1. Cotton, F. A. et al. Mononuclear and polynuclear chemistry of rhenium(III): Its pronounced homophilicity. Science 145, 1305–1307
(1964).
2. Cotton, F. A., Murillo, C. A. & Walton, . A. Multiple Bonds Between Metal Atoms. 8, 271−280. (Springer Science and Business
Media, Inc., New Yor, 2005).
3. Cotton, F. A. Highlights from recent wor on metal−metal bonds. Inorg. Chem. 37, 5710–5720 (1998).
4. Cotton, F. A., Curtis, N. F., Johnson, B. F. G. & obinson, W. . Compounds containing dirhenium(III) octahalide anions. Inorg.
Chem. 4, 326–330 (1965).
5. Barder, T. J. & Walton, . A. eductive coupling of perrhenate to form the octachlorodirhenate(III) anion: A new, convenient, and
high-yield synthetic procedure. Inorg. Chem. 21, 2510–2511 (1982).
6. Shtemeno, A. V., ozhura, O. V., Paseno, A. A. & Domasevitch, . V. New octachlorodirhenate(III) salts: Solid state manifestation
for a certain conformational exibility of the [e2Cl8]2− ion. Polyhedron 22, 1547–1552 (2003).
7. Cotton, F. A. & Harris, C. B. The crystal and molecular structure of dipotassium octachlorodirhenate(III) dihydrate,
2[e2Cl8]·2H2O. Inorg. Chem. 4, 330–333 (1965).
8. Cotton, F. A., Frenz, B. A., Stults, B. . & Webb, T. . Investigations of quadruple bonds by polarized crystal spectra. I. The
interpretation of the spectrum of tetra(n-butylammonium) octachlorodirhenate. e disordered crystal structure. J. Am. Chem. Soc.
98, 2768–2773 (1976).
9. Cotton, F. A. Metal–metal bonding in [e2X8]2− ions and other metal atom clusters. Inorg. Chem. 4, 334–336 (1965).
10. Cotton, F. A. & Harris, C. B. Molecular orbital calculations for complexes of heavier transition elements. III. e metal–metal
bonding and electronic structure of e2Cl82−. Inorg. Chem. 6, 924–929 (1967).
11. Ponec, . & Yuzhaov, G. Metal–metal bonding in e2Cl8(2−) from the analysis of domain averaged fermi holes. eor. Chem. Acc.
118, 791–797 (2007).
12. rapp, A., Lein, M. & Frening, G. e strength of the σ-, π- and δ-bonds in e2Cl82−. eor. Chem. Acc. 120, 313–320 (2008).
13. Ponec, ., Bučinsý, L. & Gatti, C. elativistic eects on metal–metal bonding: Comparison of the performance of ECP and scalar
DH description on the picture of metal–metal bonding in e2Cl82−. J. Chem. eory Comput. 6, 3113–3121 (2010).
14. Hay, P. J. Ab initio studies of the metal–metal bond in octachlorodirhenate(2−). J. Am. Chem. Soc. 100, 2897–2898 (1978).
15. Cowman, C. D. & Gray, H. B. Low-temperature polarized spectral study of the lowest electronic absorption band in e2Cl82− and
related binuclear complexes. J. Am. Chem. Soc. 95, 8177–8178 (1973).
16. Mortola, A. P., Mosowitz, J. W., ōsch, N., Cowman, C. D. & Gray, H. B. Electronic structure of e2Cl82−. Chem. Phys. Lett. 32,
283–286 (1975).
17. Trogler, W. C., Cowman, C. D., Gray, H. B. & Cotton, F. A. Further studies of the electronic spectra of octachlorodirhenate(2−) and
octabromodirhenate(2−). Assignment of the wea bands in the 600−350-nm region. Estimation of the dissociation energies of
metal–metal quadruple bonds. J. Am. Chem. Soc. 99, 2993–2996 (1977).
18. Trogler, W. C. & Gray, H. B. Electronic spectra and photochemistry of complexes containing quadruple metal–metal bonds. Acc.
Chem. Res. 11, 232–239 (1978).
19. C otton, F. A. Spectroscopic and quantum theoretical studies of species with metal–to–metal bonds. J. Mol. Struct. 59, 97–108 (1980).
20. Hay, P. J. Electronic states of the quadruply bonded e2Cl82− species: An ab initio theoretical study. J. Am. Chem. Soc. 104, 7007–7017
(1982).
21. Wang, X. B. & Wang, L. S. Probing the electronic structure and metal–metal bond of e2Cl82− in the gas phase. J. Am. Chem. Soc.
122, 2096–2100 (2000).
22. Gagliardi, L. & oos, B. O. e electronic spectrum of e2Cl82−: A theoretical study. Inorg. Chem. 42, 1599–1603 (2003).
www.nature.com/scientificreports/
8
SCientifiC REPoRTS | (2018) 8:6702 | DOI:10.1038/s41598-018-25027-1
23. Cotton, F. A., Deboer, B. G. & Jeremic, M. Some reactions of the octahalodirhenate (III) ions. VIII. Definitive structural
characterization of the octabromodirhenate (III) ion. Inorg. Chem. 9, 2143–2146 (1970).
24. Huang, H. W. & Martin, D. S. Single-crystal polarized spectra for the δ → δ* band of tetrabutylammonium octachlorodirhenate(III)
and tetrabutylammonium octabromodirhenate(III). Crystal structure of the octabromo salt. Inorg. Chem. 24, 96–101 (1985).
25. Peters, G. & Preetz, W. Synthesis and properties of the octauorodirhenate(III) anion, [e2F8]2−. Z. Naturforsch. 34, 1767−1768
(1979).
26. Conradson, S. D., Sattelberger, A. P. & Woodru, W. H. X-ray absorption study of octauorodirhenate(III): EXAFS structures and
resonance aman spectroscopy of octahalodirhenates. J. Am. Chem. Soc. 110, 1309–1311 (1988).
27. Henel, G., Peters, G., Preetz, W. & Sowrone, J. Crystal structure and vibration spectra of [(n-C4H9)4N]2[e2F8]·2(C2H5)2O. Z.
Naturforsch. 45, 469–475 (1990).
28. Balasearan, S. M. et al. Octauorodirhenate(III) revisited: Solid-state preparation, characterization, and multicongurational
quantum chemical calculations. Inorg. Chem. 55, 5417–5421 (2016).
29. Glicsman, H. D. & Walton, . A. Studies on metal carboxylates. 14. eactions of molybdenum(II) and rhenium(III) carboxylates
with the gaseous hydrogen halides in alcoholic media. Synthesis, characterization, and reactivity of the new haloanions of
molybdenum and rhenium, Mo2Br6−, Mo4I112−, and e2I82−. Inorg. Chem. 17, 3197–3202 (1978).
30. Preetz, W. & udzi, L. Synthesis and properties of tetrabutylammonium octaiododirhenate(III), [(n-C4H9)4N]2[e2I8]. Ang ew.
Chem. Int. Ed. Engl. 18, 150–151 (1979).
31. Preetz, W., Peters, G. & udzi, L. esonance aman spectrum of tetrabutylammonium octaiododirhenate(III), [(n-C4H9)4N]2[e2I8].
Z. Naturforsch. 34, 1240–1242 (1979).
32. C otton, F. A., Daniels, L. M. & Vidyasagar, . e crystal structure of [(n-C4H9)4N]2e2I8: ree-fold disorder of the eectively cubic
anion. Polyhedron 7, 1667−1672 (1988).
33. Wang, X. B., Yang, X. & Wang, L. S. Probing solution-phase species and chemistry in the gas phase. Int. Rev. Phys. Chem. 21, 473–498
(2002).
34. Dreuw, A. & Cederbaum, L. S. Multiply charged anions in the gas phase. Chem. Rev. 102, 181–200 (2002).
35. Pauling, L. e nature of the chemical bond. IV. e energy of single bonds and the relative electronegativity of atoms. J. Am. Chem.
Soc. 54, 3570–3582 (1932).
36. Gordy, W. & omas, W. J. O. Electronegativities of the elements. J. Chem. Phys. 24, 439–444 (1956).
37. Allred, A. L. & ochow, E. G. A scale of electronegativity based on electrostatic force. J. Inorg. Nucl. Chem. 5, 264–268 (1958).
38. Allred, A. L. Electronegativity values from thermochemical data. J. Inorg. Nucl. Chem. 17, 215–221 (1961).
39. Parr, . G., Donnelly, . A., Levy, M. & Pale, W. E. Electronegativity: The density functional viewpoint. J. Chem. Phys. 68,
3801–3807 (1978).
40. Murphy, L. ., Mee, T. L., Allred, A. L. & Allen, L. C. Evaluation and test of Pauling’s electronegativity scale. J. Phys. Chem. A 104,
5867–5871 (2000).
41. Wang, Y. C., Lv, J., Zhu, L. & Ma, Y. M. Crystal structure prediction via particle-swarm optimization. Phys. Rev. B 82, 094116 (2010).
42. Wang, Y. C., Lv, J., Zhu, L. & Ma, Y. M. CALYPSO: A method for crystal structure prediction. Comput. Phys. Commun. 183,
2063−2070 (2012).
43. Lv, J., Wang, Y. C., Zhu, L. & Ma, Y. M. Particle-swarm structure prediction on clusters. J. Chem. Phys. 137, 084104 (2012).
44. Zhu, L. et al. Substitutional alloy of Bi and Te at high pressure. Phys. Rev. Lett. 106, 145501 (2011).
45. Zhu, L., Liu, H. Y., Picard, C. J., Zou, G. T. & Ma, Y. M. eactions of xenon with iron and nicel are predicted in the earth’s inner
Core. Nat. Chem. 6, 644–648 (2014).
46. Lv, J., Wang, Y. C., Zhu, L. & Ma, Y. M. Predicted novel high-pressure phases of lithium. Phys. Rev. Lett. 106, 015503 (2011).
47. Xing, X. D. et al. Insights into the geometries, electronic and magnetic properties of neutral and charged palladium clusters. Sci.
Rep-uk. 6, 19656 (2016).
48. Jin, Y. Y. et al. Probing the structural evolution of ruthenium doped germanium clusters: Photoelectron spectroscopy and density
functional theory calculations. Sci. Rep-uk. 6, 30116 (2016).
49. Ding, L. P., Shao, P., Lu, C., Zhang, F. H. & Wang, L. Y. Iron-based magnetic superhalogens with pseudohalogens as ligands: An
unbiased structure search. Sci. Rep-uk. 7, 45149 (2017).
50. Bece, A. D. Density functional thermochemistry. III. e role of exact exchange. J. Chem. Phys. 98, 5648–5652 (1993).
51. Lee, C., Yang, W. & Parr, . G. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density.
Phys. Rev. B 37, 785–789 (1988).
52. Wadt, W. . & Hay, P. J. Ab initio eective core potentials for molecular calculations. Potentials for main group elements Na to Bi. J.
Chem. Phys. 82, 284–298 (1985).
53. Hay, P. J. & Wadt, W. . Ab initio eective core potentials for molecular calculations. Potentials for to Au including the outermost
core orbitals. J. Chem. Phys. 82, 299–310 (1985).
54. Frisch, M. J. et al. Gaussian 09 (evision C.0). Gaussian, Inc., Wallingford, CT, 2009. UL http://www.gaussian.com.
55. Taylor, C. J., Wu, B., Nix, M. G. D. & D essent, C. E. H. Probing the gas-phase stability of the e2X82− (X = Cl, Br) and e2XnY8-n2−(X = Cl,
Y = Br, n = 1−3) metal–metal bond complexes. Chem. Phys. Lett.479, 184–188 (2009).
56. ead, A. E., Curtiss, L. A. & Weinhold, F. Intermolecular interactions from a natural bond orbital, donor–acceptor viewpoint. Chem.
Rev.88, 899–926 (1988).
57. Zubarev, D. Y. & Boldyrev, A. I. Developing paradigms of chemical bonding: Adaptive natural density partitioning.Phys. Chem.
Chem. Phys.10, 5207–5217 (2008).
58. Casida, M. E., Jamorsi, C., Casida, . C. & Salahub, D. . Molecular excitation energies to high-lying bound states from time-
dependent density-functional response theory: Characterization and correction of the time-dependent local density approximation
ionization threshold.J. Chem. Phys.108, 4439–4449 (1998).
Acknowledgements
is work was supported by the National Natural Science Foundation of China (Grants 11574220, 11304167,
and 21671114), the 973 Program of China (Grant 2014CB660804), the Special Program for Applied Research on
Super Computation of the NSFC–Guangdong Joint Fund (the second phase; Grant U1501501), and the Program
for Science & Technology Innovation Talents in Universities of Henan Province (Grant 15HASTIT020).
Author Contributions
C.L. and X.Y.K. conceived the idea. L.H.Z., X.X.X. and C.L. performed the calculations. L.H.Z., X.X.X., W.G.S.
B.L.C. and G.M. wrote the manuscript.
Additional Information
Supplementary information accompanies this paper at https://doi.org/10.1038/s41598-018-25027-1.
Competing Interests: e authors declare no competing interests.
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