Rational Design of Stable Dianions and the Concept of Super

Article Cite This: J. Phys. Chem. A 2019, 123, 5753−5761

pubs.acs.org/JPCA

Rational Design of Stable Dianions and the Concept of SuperChalcogens Gang Chen,†,‡ Tianshan Zhao,†,§ Qian Wang,§ and Puru Jena*,† †

Department of Physics, Virginia Commonwealth University, Richmond, Virginia 23284, United States Department of Physics, University of Jinan, Shandong 250022, China § Center for Applied Physics and Technology, BKL-MEMD, College of Engineering, Peking University, Beijing 100871, China ‡

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S Supporting Information *

ABSTRACT: Super-atoms are homo/heteroatomic clusters that mimic the chemistry of atoms in the periodic table. While a considerable amount of research over the past three decades has revealed many super-atoms that mimic group I (alkali metals) and group 17 (halogens) elements, little effort has been made to identify super-atoms that mimic the chemistry of chalcogens, i.e., those belonging to group 16 elements. This is particularly important as super-chalcogens can form the building blocks of new materials, just as super-alkalis and super-halogens form a variety of super-salts with unique properties. Using first-principles calculations and various electron counting rules, some of which have been prevalent in chemistry for a century, we provide a route to the rational design of dianions that are stable in the gas phase. And unlike the group 16 atoms, these super-chalcogens can retain the second electron without spontaneous electron emission or fragmentation. A new class of super-chalcogenides with unique properties could be formed with these super-chalcogens as building blocks. novel energy materials6 has stimulated the search for clusters that can mimic the chemistry of other elements. In this paper, we focus on a group of clusters that mimic the chemistry of chalcogens, the elements belonging to group 16 (S, Se, Te, Po). Note that the atoms in this group require two additional electrons to satisfy electronic shell closure. However, they cannot retain the second electron due to the coulomb repulsion between the added electrons. While large clusters carrying two or more additional electrons and containing thousands of atoms can be stable in the gas phase, this is not the case in small clusters composed of only a few atoms.19 Here, the coulomb repulsion between the added electrons would overwhelm their binding energy, and as a result, the electrons either autoeject or the cluster fragments. In bulk materials and solutions, on the other hand, doubly negatively charged clusters exist as they are stabilized by counterions in the former and by a solvent shell in the latter.20,21 Chalcogenides, composed of at least one chalcogen anion and one or more electropositive elements, are an important class of materials with applications as pigments, catalysts, and solid lubricants. However, the number of available chalcogens limits the number of chalcogenides that can be synthesized. If this limitation could be overcome by replacing chalcogens with super-chalcogens, a new class of materials can be assembled with the latter as building blocks. Note that it is not necessary for a doubly charged cluster to be stable in the gas phase in

1. INTRODUCTION The periodic table, formulated by Mendeleev about 150 years ago, is limited by the number of elements that occur in nature and by the few that can be created artificially in a laboratory. Nearly a quarter century ago, it was proposed that a cluster, with a given size and composition, can be designed such that it mimics the chemistry of an atom.1−3 It was hypothesized that these super-atoms can form the building blocks of a threedimensional periodic table and, when assembled, can lead to a new class of materials, called cluster-assembled materials. Examples of such super-atoms include super-halogens and super-alkalis. Proposed before the introduction of the superatom concept, super-halogens were initially designed to contain a metal atom M of maximal valence k at the center, surrounded by (k + 1) halogen atoms (e.g., LiF2).4 In contrast, super-alkalis were initially designed to consist of alkali and halogen atoms, with the number of alkali atoms exceeding that of halogen atoms by 1 (e.g., Li2F).5 The electron affinities (EAs) of super-halogens are larger than those of halogens, while the ionization potentials of super-alkalis are smaller than those of the alkalis. Research over the past two decades has considerably expanded the scope of these super-atoms.6−18 Using various electron counting rules, a wide range of superhalogens and super-alkalis have been designed and experimentally synthesized.3 It has been shown that a super-halogen (super-alkali) can be created without using halogens (alkalis) and/or metal atoms. More important, super-alkalis and superhalogens provide unprecedented opportunity to design and synthesize a new class of super-salts with unique properties. The potential of some of these salts in the recent synthesis of © 2019 American Chemical Society

Received: February 16, 2019 Revised: May 23, 2019 Published: June 14, 2019 5753

DOI: 10.1021/acs.jpca.9b01519 J. Phys. Chem. A 2019, 123, 5753−5761

Article

The Journal of Physical Chemistry A

(VASP)44 and the spin density functional theory to optimize the clusters and used these optimized structures as starting points for final optimization using the Gaussian 09 package. Calculations in VASP were carried out using the projectoraugmented wave method45 and the plane-wave basis set with a cutoff energy of 400 eV. To minimize interaction between clusters, a supercell with a vacuum space of more than 11 Å was used that separates the cluster from its periodic image. For such a supercell, only the Γ point was used to calculate the electronic properties. The exchange and correlation interaction was taken into account using the PBE functional.37 We note that the B3LYP functional used in the Gaussian code is not available in the VASP code.

order that it can be used to make a stable material, for it can be stabilized by counterions. However, our interest here is to rationally design small clusters that can be stable in the gas phase as a doubly charged anion. We define such clusters as super-chalcogens, which do not suffer from the spontaneous emission of electron or fragmentation. The composition and size of these clusters, as well as the energy with which the second electron is bound, are the most important characteristics of super-chalcogens. Ideally, one would like to find a cluster whose dianion is thermodynamically stable, even when the cluster contains only a few atoms. Among the most well-known dianions is B12H122− closoborane,22,23 which is stable, in the gas phase, against spontaneous electron emission by 0.9 eV. Stability of these species is explained by the Wade−Mingos rule, which requires (n + 1) pairs of electrons, where n is the number of vertices in the boron polyhedron.24−27 It was recently shown that the stability of these dianions could be substantially improved by ligand substitution.28−30 For example, B12(CN)122− and B12(SCN)122− are stable against electron emission by 5.3 and 3.3 eV,28,31 respectively. This prediction has recently been confirmed experimentally and the measured second electron affinity of B12(CN)122−, 5.55 eV,32 agrees well with the predicted value. Unlike super-alkalis and super-halogens, where a broad range of electron counting rules have been used for their design and synthesis, no such attempt has been made to design clusters mimicking chemistry of group 16 elements. In this paper, by using multiple electron counting rules, we have identified a broad range of super-chalcogens that do not contain even a single group 16 element. While we have demonstrated the stability of these clusters by considering a few examples, many more can be rationally designed using the procedure outlined here. A new class of super-chalcogenides could now be synthesized with super-chalcogens as the building blocks. In the following, we discuss each of these rules and determine the composition of super-chalcogens consistent with these rules. Stability of the doubly charged super-chalcogens is confirmed by frequency calculations.

3. RESULTS AND DISCUSSION The choice of size and composition of studied clusters is guided by electron counting rules. As pointed out earlier, a number of electron counting rules have been put forth in the past3 to account for the stability of atoms and clusters. These are the octet rule, the 18-electron rule, the aromatic rule, the Wade−Mingos rule, and the jellium rule. In the following, we describe each of these rules and accordingly design the size and composition of clusters such that they are stable as dianions. 3.1. Octet Rule. The octet rule, developed in the early 1900s, is a simple electron counting rule that accounts for the chemistry of light elements with atomic number less than 20.46−48 For example, the noble gas atoms such as Ne and Ar are chemically inert because their outermost s2 and p6 orbitals are closed. Similarly, the alkali (halogen) atoms that have one electron more (less) than needed for octet shell closure are chemically very reactive. A classic example of a compound stabilized due to the octet rule is Na+Cl−, where both Na+ and Cl− have their outermost s and p orbitals full, Na by giving up an electron and Cl by accepting that electron. We consider M(CN)42− as an example of a potential superchalcogen cluster that satisfies the octet rule. Here, M is a divalent metal atom such as Be, Mg, Ca, Zn, and Cd. CN, with valence electrons of C in 2s22p2 and that of N in 2s2p3 configuration, requires one electron to satisfy the octet rule. Thus, CN should mimic the chemistry of halogens. Indeed, with an electron affinity of 4.07 eV, CN is a super-halogen. Because metal atoms with ns2 valence electron can contribute two electrons, M(CN)4 would require two additional electrons for octet shell closure. Thus, we wondered if M(CN)42− cluster could be stable in the gas phase against spontaneous electron emission or fragmentation. We note that while many studies of M(CN)42− have been carried out in the past,49 their studies in the gas phase are limited. We are only aware of the work of Wang et al.36 who studied tetra- and hexacoordinated platinum−cyanide dianions Pt(CN)42− and Pt(CN)62− using photoelectron spectroscopy and density functional theory. The adiabatic detachment energies for the dianions to monoanions of Pt(CN)42− and Pt(CN)62− were measured to be 1.69 and 3.85 eV, respectively, confirming their stability. To see if this could be true for lighter metal−cyanide complexes, we optimized the geometries of M(CN)4, M(CN)4−, and M(CN)42− clusters (M = Be, Mg, Ca, Zn, Cd) and calculated the energy gain in adding successive electrons. These energy gains are defined as

2. COMPUTATIONAL DETAILS Calculations of optimized geometries of neutral and negatively charged clusters were carried out using density functional theory and the Gaussian 09 code.33 To treat exchange− correlation terms in the potential, we used the hybrid Becke three-parameter Lee−Yang−Parr (B3LYP) hybrid functional,34,35 as this is known for yielding accurate results for clusters composed of elements with low atomic number.36 To study the dependence of our results on exchange−correlation functional, we have also used the Perdew, Burke, and Ernzerhof (PBE) functional37 in the Gaussian 09 code.33 For Cd, Ti, Zr, Hf, and Au, we used the LANL2DZ basis set,38−40 while the 6-311+G(d,p) and 6-311++G(d,p) basis sets41 were used for all other atoms. All geometries were fully optimized without any symmetry constraint and their dynamic stability was confirmed by calculating the frequencies and confirming that they are positive. The convergence criteria for total energies and forces are 2.7 × 10−7 eV and 0.01 eV/Å, respectively. Charge analysis was performed using the natural bond orbital method.42,43 Because the optimization of geometries in the Gaussian code becomes increasingly difficult as the size of the cluster increases, we first used the Vienna ab initio simulation package

ΔE1 = E (X) − E (X−) ΔE2 = E (X−) − E (X2 −) 5754


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The Journal of Physical Chemistry A Here, X stands for the M(CN)4 cluster. X− and X2− represent, respectively, the monoanionic and dianionic clusters. E is the total energy of a given cluster. Note that as an electron is detached from a negatively charged cluster, it will undergo a structural change. The energy difference between a monoanion and its corresponding neutral, both in their respective ground states, is defined as the electron affinity (EA). The vertical detachment energy (VDE), on the other hand, is the energy difference between the monoanion and its corresponding neutral, both having the ground-state geometry of the monoanion. The difference between the EA and VDE, therefore, provides a measure of the energy gain as a cluster undergoes structural relaxation following electron detachment. We call ΔE1 as the first EA/VDE (FEA/FVDE) that measures the energy cost when the first electron is removed from the monoanionic cluster. Similarly, ΔE2 is the energy difference between the dianion and monoanion. When both are in their respective ground states, we name ΔE2 as the second electron affinity (SEA), and when the monoanion has the same geometry of its dianion, we name it the second vertical detachment energy (SVDE). In optimizing the geometries of neutral, monoanion, and dianion M(CN)4 complexes, we note that the metal atom can bind to either C or N of the CN molecule, and this choice may also depend upon the charge state of the cluster. In addition, the CN molecules can bind to the metal atom either individually or in a dimerized NCCN form. Thus, there are many choices and we have examined all possibilities. In Figure 1, we plot the ground-state geometries of neutral, monoanion, and dianion of M(CN)4 obtained using the Gaussian 09 code and B3LYP functional. The geometries of M(CN)42− isomers calculated using the Gaussian 09 code with B3LYP and PBE functionals are compared in Tables S1 and S2 of the Supporting Information, respectively. We only comment on the results obtained at the B3LYP level, while we refer the reader to the Supporting Information for the results obtained at the PBE level. Both functionals yield the same conclusion regarding the ground-state geometries of the M(CN)42− species. We note that all of the M(CN)42− dianions have a tetrahedral geometry with the metal atom bound to individual CN molecules. The nature of CN binding is consistent with the total number of available electrons. With M being divalent, the dianions of M(CN)42− have four available electrons, and hence, all of the CN molecules are bound individually. Be, Zn, and Cd atoms bind to C of CN, while Mg and Ca atoms bind to N of CN. This can be understood by examining the charges on individual atoms given in Figure 1. Note that in all cases, much of the negative charge is situated on the N atoms. However, in Be, Zn, and Cd tetracyanide complexes, the charge on the N atom is around −0.6, while in Mg and Ca tetracyanide complexes, the charge on the N atoms is larger, around −0.8. Similarly, the positive charges on Mg and Ca are larger than those on Be, Zn, and Cd. This explains why in one case, a metal atom prefers to bind to C of CN, while in the other case, it prefers to bind to N of CN. The energy differences between metal atom binding to C or N in M(CN)42− complexes are 0.18, 0.14, 0.39, 0.81, and 0.30 eV for M = Be, Mg, Ca, Zn, and Cd, respectively (see Table S1). In the case of M(CN)4− monoanions, all geometries are similar in the sense that two of the CN molecules are bound individually, while the other two dimerize and bind to the metal atoms. This is because there are three electrons (two electrons from the metal atom and one added electron) that

Figure 1. (a)−(e) are the globally optimized geometries for M(CN)40,1−,2− (M = Be, Mg, Ca, Zn, and Cd) clusters, respectively. Gray, pink, light green, dark green, purple, light blue, and dark blue spheres stand for C, N, Be, Mg, Ca, Zn, and Cd atoms, respectively. The charges on selected atoms are also given.

need to be shared by four CN moieties. Consequently, two of the CN moieties dimerize. Here, all metal atoms carry a substantial positive charge, while the N atoms carry a negative charge. Note that in the case of dianions, four available electrons (two from the metal atom and two added electrons) are shared by four electronegative N atoms. In the case of monoanions, there is one less electron, and hence, the metal atoms donate this extra charge, making them more positively charged than they are in the dianions. Naturally, in all of the monoanions, the metal atoms bind to the N atom of the NCCN moiety. The C atoms of the individually bound CN carry a positive charge in Be, Mg, and Ca complexes; hence, these metal atoms bind to the N atom as well. This is, however, not the case for Zn and Cd complexes where the C atoms also carry a negative charge. The geometries of neutral M(CN)4 complexes are a bit more complex. Here, one would have expected the CN molecules to dimerize and bind to the divalent metal atom. Instead, only two of them dimerize and bind to M, as seen in the case of M(CN)4− monoanions. This results from the hybridization of the s and p electrons of the metal atom. In the Supporting Information, we have given the geometries of other isomers and their energies (see Tables S1 and S2). 5755


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The Journal of Physical Chemistry A The first and second EAs, as well as the corresponding VDEs of M(CN)4 complexes calculated using B3LYP and 6-311+ +G(d,p) basis sets, are given in Table 1. The results obtained Table 1. First and Second EAs and VDEs of M(CN)4 (M = Be, Mg, Ca, Zn, Cd) Clusters clusters

FVDE

FEA

SVDE

SEA

Be(CN)4 Mg(CN)4 Ca(CN)4 Zn(CN)4 Cd(CN)4

3.93 3.82 3.75 3.71 3.41

3.13 2.94 2.89 2.78 2.59

2.67 2.54 2.66 2.80 2.71

0.32 0.97 1.21 0.83 0.56

using B3LYP and 6-311+G(d,p) basis sets are very similar, differing only in the second decimal place. The first EA lies between 2.59 and 3.13 eV in all cases, implying that all M(CN)4 species are pseudo-halogens. All M(CN)42− dianions are stable against electron emission with the second electron affinity ranging from 0.32 to 1.21 eV. Note that there is a large difference between the second EAs and second VDEs, reflecting the large changes in the geometry as an electron is detached from a negatively charged cluster. Recall that the second electron affinity of B12H12 is 0.9 eV. The stability of the M(CN)4 dianions indicates that the octet rule can be effectively used to rationally design doubly charged species that are stable in the gas phase. To facilitate corresponding experimental studies, we have provided the simulated IR and Raman spectra in the Figure S1, Supporting Information. 3.2. 18-Electron Rule. The 18-electron rule applies to compounds containing a transition-metal atom, where 18 electrons are needed to fill its s2p6d10 orbitals.50 An example of a compound that is stabilized by the 18-electron rule is Cr(C6H6)2.51 Here, Cr, with an outer electron configuration of 3d54s1, requires 12 electrons to satisfy the 18-electron rule, which the two C6H6 molecules supply. As a test case, we first tried to see if an all-metal cluster could be designed as a stable dianion. We note that WAu12, with 18 electrons in the valence pool, was earlier predicted and later experimentally verified to be a very stable cluster.52,53 The later experiment showed that TaAu12, with 17 electrons, is a superhalogen with a large electron affinity.54 We tried to see if TiAu122− cluster could be stable against the autodetachment of the second electron. Here, Ti with an electronic configuration of 3d24s2 and Au with an electronic configuration of 4d106s1 contribute four and one electrons, respectively, to the valence pool. Thus, with the added two electrons, TiAu122− would fulfill the 18-electron shell closure rule. In Figure 2a, we give the geometries of neutral, monoanion, and dianion of TiAu12. No imaginary frequencies were found, confirming that these geometries are dynamically stable and belong to minima in the potential energy surface. The corresponding first and second EAs and VDEs are given in Table 2. Note that the first electron affinity of TiAu12 is less than that of Cl. Hence, it cannot be identified as a superhalogen. The second EA is −0.23 eV. This means that TiAu122− is thermodynamically unstable and the 18-electron rule is not as effective as the octet rule discussed above for the rational design of super-chalcogens composed of all-metal atoms. This does not mean that the existence of TiAu122− cannot be verified in experiments. Many metastable dianions have been seen experimentally.19,55,56 To see if this could be the case with TiAu122−, we examine the geometries of the

Figure 2. (a)−(c) are the optimized geometries for MAu120,1−,2− (M = Ti, Zr, and Hf) clusters, respectively. Yellow, dark red, purple, and blue spheres stand for Au, Ti, Zr, and Hf atoms, respectively.

Table 2. First and Second EAs and VDEs of MAu12 (M = Ti, Zr, and Hf) Clusters clusters

FVDE

FEA

SVDE

SEA

TiAu12 ZrAu12 HfAu12

3.33 3.14 3.09

3.29 3.05 3.00

0.29 0.45 0.44

−0.23 0.05 0.05

mono- and dianions in Figure 2a; TiAu12 dianion has Ih symmetry, while the neutral and monoanion have Oh symmetry and its second VDE is 0.29 eV. This means that it will cost 0.29 eV to vertically detach the second electron. The monoanion, thus created, will undergo structural relaxation from Ih to Oh symmetry, gaining an additional 0.23 eV in the process. At the end, 0.52 eV energy will be gained. Because the ground-state geometry of the dianion is different from that of the monoanion, an accompanying energy barrier may make the observation of metastable TiAu122− possible. We note that C602−, although higher in energy than C60−, was observed due to the repulsive coulomb barrier.57,58 To facilitate comparison with future experiments, we show the IR and Raman spectra in the Figure S2, Supporting Information. To see if size matters, we have studied the stability of Zr@ Au122− and Hf@Au122− clusters. Note that as in Ti@Au122− cluster, the above two clusters also satisfy the 18-electron rule, but their sizes are larger than that of Ti@Au122−. Because the electron affinity increases with size, we hypothesized that Zr@ Au122− and Hf@Au122− clusters could be thermodynamically stable. We calculated the equilibrium geometries of neutral, monoanionic, and dianionic Zr@Au12 and Hf@Au12 clusters. The results are given in Figure 2b,c. Note that the neutral and monoanionic Zr@Au 12 and Hf@Au 12 clusters have O h symmetry, while their dianions have D5h symmetry. As a result, there is a significant difference between the vertical detachment energy and the electron affinity. These results are given in Table 2. The dynamic stabilities of these clusters are confirmed by frequency calculations. Note that Zr@Au122− and 5756


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The Journal of Physical Chemistry A Hf@Au122− clusters are stable against the autoejection of the second electron, although the binding energy of this electron is rather small, namely, 0.05 eV. 3.3. Aromatic Rule. Hückel’s aromatic rule requires that (4n + 2) electrons are needed to stabilize an organic molecule, where n is an integer. For example, C6H6 with its six π electrons satisfies Hückel rule59,60 with n = 1. To see if the aromatic rule can be used to design a thermodynamically stable dianion, we first considered neutral B2C4H6, which would require two extra electrons to satisfy the aromatic rule as B is trivalent and C is tetravalent. The equilibrium geometries of neutral, monoanion, and dianion of B2C4H6 are given in Figure 3a. The corresponding first and second EAs and VDEs are given in Table 3. We see that B2C4H62− is unstable against electron emission by 3.27 eV. This is because C6H6 has a negative electron affinity, namely, −1.15 eV. It has been shown that substituting H by CN can substantially increase the EA of C6H6; e.g., the EA of C6(CN)6 is 3.49 eV.29 Thus, we first considered two examples of organic molecules, B2C4(CN)6 and B2C4(BO)6. Note that the EA of BO is 2.59 eV and can also be considered as a pseudo-halogen. When two electrons are added, each of these two dianions would possess six electrons, which would satisfy the aromatic rule. To examine their stability, we have optimized the geometries of their neutral, monoanion, and dianion forms. These geometries are given in Figure 3b,c. The first and second EAs and VDEs of these molecules are given in Table 3. Note that both these molecules are super-halogens with the first EA of 5.38 eV for B2C4(CN)6 and 6.11 eV for B2C4(BO)6. The corresponding VDEs are, respectively, 5.47 and 6.93 eV. The second EAs of B2C4(CN)6 and B2C4(BO)6 are, respectively, 1.12 and 1.58 eV. The corresponding second VDEs are, respectively, 1.59 and 1.71 eV. Thus, both the dianions are thermodynamically more stable than B12H122−. We also considered a third organic molecule C8(CN)6. Note that C8(CN)62− contains 10 electrons, and with n = 2, it satisfies the aromatic rule. As CN is more electronegative than H, our hypothesis was that C8(CN)62− may be stable. The geometries of the neutral, monoanion, and dianion C8(CN)6 molecules are also given in Figure 3. An analysis of the vibrational frequencies of the structures shown in Figure 3d revealed no imaginary frequencies, confirming that these geometries correspond to local minima in the potential energy surface. The corresponding first and second EAs and VDEs of this molecule are given in Table 3. Note that C8(CN)6 is a super-halogen and its second EA and VDE are 0.81 and 0.83 eV, respectively. To facilitate comparison with future experiments, we have also simulated their IR and Raman spectra (see the Figure S3, Supporting Information). Earlier calculation at the CCSD(T) level had shown that C8H82− is unstable against electron emission.61 We wondered if C8(CN)82− and C8(BO)82− would be stable against electron emission. Note that the dianions of these two clusters contain 10 electrons and hence satisfy the aromatic role (n = 2, 4 × 2 + 2 = 10). In addition, the replacement of H with CN and BO has already been known to increase the stability of their anion phases. The optimized geometries of neutral, monoanion, and dianion complexes of C8X82− (X = H, CN, BO) are given in Figure 3e−g. The corresponding first and second EAs and VDEs are given in Table 3. We see that C8H82− is unstable against electron emission, while C8(CN)82− and C8(BO)82− are stable with second electron affinities of 1.21 and 1.21 eV, respectively. We should point out that the stable dianionic

Figure 3. Optimized geometries of (a) B 2 C 4 H 6 0,1−,2− , (b) B2C4(BO)60,1−,2−, (c) B2C4(CN)60,1−,2−, (d) C8(CN)60,1−,2−, (e) C8H80,1−,2−, (f) C8(BO)80,1−,2−, and (g) C8(CN)80,1−,2− clusters. Gray, pink, brown, and red spheres stand for C, N, B, and O atoms, respectively.

Table 3. First and Second EAs and VDEs of the Studied Aromatic Molecules

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clusters

FVDE

FEA

SVDE

SEA

B2C4H6 B2C4(BO)6 B2C4(CN)6 C8(CN)6 C8H8 C8(BO)8 C8(CN)8

2.01 6.93 5.47 5.41 1.47 5.03 5.00

1.90 6.11 5.38 5.19 0.82 4.53 4.64

−2.68 1.71 1.59 0.83 −3.35 1.70 1.54

−3.27 1.58 1.12 0.81 −3.49 1.21 1.21


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The Journal of Physical Chemistry A organic molecules discussed here satisfy both the aromatic role and the octet rule of the ligands. 3.4. Wade−Mingos Rule. According to this rule, a borane complex is stable if it contains (n + 1) pairs of electrons, where n is the number of vertices in the boron polyhedron. As pointed out earlier, B12H122− is a classic example of a molecule whose stability is explained by the Wade−Mingos rule.22−27 The second electron in this closo-borane is bound by 0.9 eV. It was shown earlier that the stability of this dianion can be substantially improved by replacing H with other ligands such as CN, SCN, or BO. For example, the second electron affinities of B12X122− are found to be 5.33, 3.28, and 5.80 eV for X = CN, SCN, and BO, respectively. This colossal stability arises because CN, SCN, and BO are far more electronegative than H, a consequence of the octet shell closure rule. Using the B12(CN)122− as an example, we illustrate its geometries and those of the corresponding monoanionic and neutral species in Figure 4. The calculated EA and VDE are provided in Table 4.

Figure 5. Optimized geometries for BeAl120,1−,2− clusters. Light green and aqua spheres stand for Be and Al atoms, respectively.

and dianion of BeAl12 cluster. The first and second EA and VDE of BeAl12 cluster are given in Table 5. Note that the first Table 5. First and Second EAs and VDEs of BeAl12, MgAl12, Na2Al12, and Na3Al5

Table 4. First and Second EAs and VDEs of B12(CN)12 FEA

SVDE

SEA

8.71

8.62

5.42

5.33

FVDE

FEA

SVDE

SEA

3.34 3.31 2.21 1.43

3.03 2.58 2.03 1.33

0.14 −0.04 −0.75 −1.60

0.01 −0.27 −0.96 −1.60

EA is 3.03 eV, making BeAl12 a pseudo-halogen. Its second EA is 0.01 eV. The stabilities of the structures shown in Figure 5 for BeAl12, BeAl12−, and BeAl122− are confirmed by our frequency analyses. Also, the simulated IR and Raman spectra are given in the Supporting Information Figure S5 for comparison with future experiments. We note that the second electron affinity of BeAl122− is very small and is within the error of our computational approach. For example, the second electron affinity of BeAl122− calculated using the Gaussian 09 code and PBE exchange−correlation functional with 6-311++G(d,p) basis set gives an increased second EA value (∼0.11 eV). In addition, the calculated second EA may be affected by the composition of species, the geometry, and the cluster volume. To examine the role of size, composition, and geometry, we calculated the second EAs of Na2Al122−, MgAl122−, and Na3Al52−, which contain 40, 40, and 20 electrons, respectively (see the Supporting Information Figure S6 for geometries and Figure S7 for their IR and Raman spectra). The corresponding second electron affinities are −0.96, −0.27, and −1.60 eV, respectively. These results indicate that the dianions of metal clusters satisfying the jellium electron counting rule may not be as robust as those obeying the octet, aromatic, or Wade−Mingos rule for their rational design in the gas phase. 3.6. Simultaneous Use of Multiple Electron Counting Rules (Aromatic + Octet + 18-Electron Rule). The above examples clearly demonstrate that various electron counting rules can be individually used to rationally design the composition of clusters that could accommodate two extra electrons in the gas phase and, thus, be classified as superchalcogens. It has been shown earlier28,66 that a charged cluster can gain additional stability if it satisfies multiple electron counting rules, simultaneously. A good example, discussed earlier, is B12(CN)122− that is far more stable than B12H122−. This is because it satisfies the Wade−Mingos rule and octet rule, simultaneously.28 In this paper, we also showed that dianionic organic molecules satisfying the aromatic rule while the ligands satisfy the octet rule, such as C8(CN)82−, can gain extra stability against electron emission. In the following, we

Figure 4. Optimized geometries for B12(CN)120,1−,2− clusters. Gray, pink, and brown spheres stand for C, N, and B atoms, respectively.

FVDE

clusters BeAl12 MgAl12 Na2Al12 Na3Al5

Frequency calculations confirm that these structures belong to minima in their potential energy surface. The IR and Raman spectra of these clusters are given in the Supporting Information Figure S4 so that they can be compared with future experiments. These examples demonstrate that the stability of closo-boranes BnHn2− can be enhanced not only by increasing the values of n but also by replacing H with more electronegative ligands. 3.5. Jellium Rule. One of the electron counting rules that heightened interest in cluster science some 40 years ago is based on the jellium model. Applicable to clusters composed of simple metals, the jellium model replaces the cluster with a spherical distribution of a positive ion core, with compensating electrons. These electrons successively fill the electron shells, just as nucleons do in a nuclear shell model. Clusters containing 2, 8, 20, 40, etc. electrons satisfy the electron shell closure, corresponding to the closure of 1S, 1S1P, 1S1P1D2S, 1S1P1D2S1F2P, etc. orbitals. The discovery that Na clusters containing 2, 8, 20, 40, etc. atoms are more stable than their neighbors gave credence to the jellium model,62 which has been found to explain magic numbers of many simple metal clusters, such as Na8, Na20, Mg4, Al13−, Au20, etc.62−65 We studied if BeAl122− could serve as an example for a stable dianion, consistent with the jellium rule. Note that neutral BeAl12 cluster has 12 × 3 + 2 = 38 electrons and needs two extra electrons to satisfy the jellium shell closure requirement. In Figure 5, we present the geometries of neutral, monoanion, 5758


Article


emission than those designed using the 18-electron rule and the jellium rule alone. (2) Clusters satisfying multiple electron counting rules are generally more stable than those satisfying only one electron counting rule. (3) Composition of a cluster also plays an important role in stability, as seen by comparing the second electron affinity of B2C4X62− (X = CN, BO) and C8X82− (X = CN, BO) with that of TiC12(CN)122−. Even though the latter satisfies three electron counting rules while the former only two, B2C4X62− (X = CN, BO) and C8X82− (X = CN, BO) are more stable than TiC12(CN)122− against electron emission. It is expected that super-chalcogens can form the building blocks of a new class of super-chalcogenides with potential applications in energy conversion. Electron counting rules can play a major role in identifying the size and composition of such super-atoms.

use the same procedure to design super-chalcogens by simultaneously satisfying three electron counting rules. We first consider TiC12(CN)122−. This cluster is stabilized by fulfilling the octet rule for CN, the aromatic rule for C6(CN)6, and the 18-electron rule for TiC12(CN)122−. Note that the total number of electrons in TiC12(CN)12 is 2 × 6 + 4 = 16. In Figure 6, we present the geometries of neutral,

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Figure 6. Optimized geometries for TiC12(CN)120,1−,2− clusters. Gray, pink, and barn red spheres stand for C, N, and Ti atoms, respectively.

S Supporting Information *

monoanion, and dianion of TiC12(CN)12, where the Ti atom is sandwiched between two C6(CN)6 rings. Frequency calculations confirm that the geometries of these clusters belong to minima in the potential energy surface. Note that there is a very little distortion of the C6(CN)6 planar structure. In addition, the geometry of the monoanion changes little from that of its neutral; however, the changes are large when the second electron is attached. These are reflected in the electron affinity and corresponding vertical detachment energy. The first EA and VDE of TiC12(CN)12 are, respectively, 5.38 and 5.42 eV (see Table 6). The second EA and VDE, on the other

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.9b01519.

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Table 6. First and Second EAs and VDEs of TiC12(CN)12 FVDE

FEA

SVDE

SEA

5.42

5.38

1.26

0.76

ASSOCIATED CONTENT

Calculated total energies of the tetrahedral, planar, and chain structural configurations of M(CN)40,1−,2− (M = Be, Mg, Ca, Zn, and Cd) clusters (Tables S1 and S2); to facilitate corresponding experimental studies, the simulated IR and Raman spectra for the ground states of our studied dianions (Figures S1−S5 and S8); the geometries of Na2Al12, MgAl12, and Na3Al5 clusters (Figure S6), and their simulated IR and Raman spectra (Figure S7) (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

hand, are 0.76 and 1.26 eV. Thus, TiC12(CN)122− is thermodynamically more stable than that of TiAu122−. This is not only because TiC12(CN)122− satisfies the octet, aromatic, and 18-electron rules simultaneously while TiAu122− satisfies only the 18-electron rule but also because C6(CN)6, which fulfills the aromatic rule, has a large electron affinity of 3.53 eV due to the cyano ligand. We should point out that B2C4X62− (X = CN, BO), as well as C8X82− (X = CN, BO), clusters are more stable against electron emission than TiC12(CN)12, even though the latter fulfills three electron counting rules, while the former fills only two electron counting rules. This shows that the composition of a cluster also matters; note that B is electron-deficient and C8H8 is larger in size than C6H6. The IR and Raman spectra presented in the Figure S8 (Supporting Information) could be used to facilitate experimental studies.

Gang Chen: 0000-0003-0780-5234 Qian Wang: 0000-0002-9766-4617 Puru Jena: 0000-0002-2316-859X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge the computing resources from the University of Jinan. G.C. acknowledges the financial supports from the National Natural Science Foundation of China (NSFC) (Grant 11674129) and the China Scholarship Council (CSC) for sponsoring his visit to Virginia Commonwealth University. Q.W. acknowledges the support of the National Natural Science Foundation of China (NSFC21773004). P.J. acknowledges the support of the U.S. DOE, Office of Basic Energy Sciences, Division of Material Sciences and Engineering under Award No. DE-FG02-96ER45579.

4. CONCLUSIONS Using density functional theory and generalized gradient approximation, as well as hybrid functionals for exchange− correlation potential, different basis sets, and computational codes, we have rationally designed the size and composition of dianionic clusters that could be stable against spontaneous electron emission. A series of stable dianionic clusters have been identified, which could be described as super-chalcogens. Our results can be summarized as follows: (1) dianionic clusters designed using the octet, aromatic, and Wade−Mingos rules are generally more stable against spontaneous electron

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Rational Design of Stable Dianions and the Concept of Super

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