Introduction

The 11-vertex nido-cluster represents the most diverse family of heteroboranes and -borates. Many reactions are known [1–3] to incorporate a hetero-fragment into a smaller nido- or arachno-cluster, leading to 11-vertex nido-heteroboranes. Removal of one vertex from a 12-vertex closo-heteroborane cluster also leads to 11-vertex nido-heteroboranes and -borates [2, 4, 5]. Experimentally known 11-vertex nido-heteroborane and -borate clusters include: group 14 heteroatoms, i.e., carbon [6–9], silicon [10–13], germanium [14–17] and tin [6–8, 18–21]; group 15 heteroatoms, i.e., nitrogen, phosphorus [1, 2], arsenic [5, 22–32] and antimony [33]; group 16 heteroatoms, i.e., sulfur [34], selenium [35–41] and tellurium [35–37, 42, 53]. Williams’ qualitative rules predict isomers with low-coordinate heteroatoms and separated heteroatoms to be preferred [6, 54, 55]. While these rules suffice to select the most stable closo-heteroboranes, the presence of additional endo-hydrogen atoms, the large number of isomers and possibly irresolvable conflicts ask for more sophisticated rules to predict the most favorable isomer in the case of nido-clusters.

A set of quantitative rules was presented that reproduced the stability order of 6-vertex nido-carboranes on the basis of 15 structural increments [56]. Disfavoring structural features, e.g., neighboring carbon atoms, were identified and the so-called energy penalties were derived by a statistical fitting procedure. Applying these energy penalties additively, the stability order of isomeric 6-vertex nido-(carba)boranes and -borates can easily be derived by a paper-and-pencil approach. With only nine such fitted quantitative rules, the relative stability order of numerous 11-vertex nido-(carba)boranes and -borates [57] was reproduced successfully. The approach was applied to the 10-vertex nido-(carba)boranes and -borates [58], and to the 11-vertex nido-mixed hetero(carba)boranes and -borates [59] with H–C, P, H–P, N and H–N heteromoieties. Our work [56–59] quantified Williams’ rules [6, 54, 55] by corresponding energy penalties for each heteroatom and introduced some more rules due to open-face hydrogen characteristics of the nido-cluster. These quantitative rules allow us not only to predict the thermodynamically most stable isomer but also to estimate a stability order of various isomers easily [56–59]. Furthermore, these energy penalties successfully elaborate which two heteroatoms are more favorable choices for adjacent positions in the thermodynamically most stable mixed nido-heteroboranes. For example, quantitative rules indicate 7,8,10- rather than 7,8,9-, 7,9,10- and 7,9,8-positions for the heteroatoms in nido-[P2CB8H9]− to be thermodynamically most stable [59].

In our previous work [56–59], energy penalties (E inc) were determined by statistical fitting to a large number of structures. This procedure gives accurate values but requires extensive computations. Estimated energy penalties, (E inc′), which are the energy difference of two suitable reference structures differing with respect to one structural feature only, are usually very close to the energy penalties arising from statistical fitting to a large number of isomers [59]. This is to be expected when structural features behave additively. For instance, the estimated energy penalty for adjacent carbon atoms, i.e., the energy difference of 7,8-C2B9H 2−11 and 7,9-C2B9H 2−11 is 16.3 kcal mol−1, very close to the statistically fitted value (16.0 kcal mol−1) derived from 20 carboranes [57–59]. Here, we present the relative stability order (E relinc ′) for 11-vertex nido-sila-, germana-, stanna-, arsa-, stiba-, thia-, selena- and tellura(carba)boranes and -borates, phosphathiaboranes and -borates and selenathiaboranes produced by E inc′, which are more approximate but easier to determine and are accurate enough for the interpretation of general trends which we wish to investigate in the present study.

The numbering scheme for the 11-vertex nido-cluster is shown in Fig. 1. The apical position is numbered as 1. The vertices next to the apex (middle belt) are given numbers 2–6, while the vertices of the open face are numbered from 7 to 11 where 7 is connected to 2 and 3. There are six cage vertices with connections to five other cluster atoms, k c=5 and five peripheral vertices with k p=4, where, c and p denote cage and peripheral vertices, respectively. In the literature, different numbering patterns have been used for mixed heteroboranes.

Fig. 1
figure 1

Numbering scheme for the 11-vertex nido-cluster

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Computational details

For all hetero(carba)boranes and -borates except stanna, stiba and tellura(carba)boranes and -borates, geometries were consecutively optimized at B3LYP/3-21G and B3LYP/6-31G(d) using the Gaussian 98 program [60]. The structures presented in this paper are local minima at B3LYP/6-31G(d). Single point energies were computed at B3LYP/6-311+G(d,p). Zero point vibrational energies from B3LYP/6-31G(d) frequency calculations were included to derive the relative energies for all the isomers.

For stanna, stiba and telluraboranes, geometries were optimized at the B3LYP/LANL2DZ level with additional d-polarization functions [61] for Sn, Sb, Te, B and C atoms (ζ=0.183, 0.211, 0.237, 0.388, 0.600, respectively). Single point energies were determined at B3LYP/SDD together with p-polarization function for H (ζ=1.000) and d-polarization function for Sn, Sb, Te, B and C [61] along with an sp set of diffuse functions for Sn, Sb, Te (ζ=0.0231, 0.0259, 0.0306, respectively) [62] as well as for B and C (ζ=0.0315 and 0.0438, respectively) [63].

Results and discussion

Structural features for hetero(carba)boranes and -borates

Different structural features for hetero(carba)boranes and -borates are shown in Fig. 2 and their energy penalties are listed in Table 1. Energy penalties for carbon in Table 1 are statistically fitted values taken from our previous work [57, 59]. For all other heteroatoms, the energy penalties are estimated as the energy difference of two structures that differ with respect to one structural feature only.

Fig. 2
figure 2

a A heteroatom (Het) at a 5 k apical position (vertex number 1, structure B) or in the middle belt (positions 2 through 6, structure C) rather than at the open face (positions 7 through 11, structure A) represent the structural features Het5k(1) and Het5k(2), respectively. b Heteroatom adjacent (E) rather than heteroatom apart isomer (D) represent the structural feature HetHet′, where Het and Het′ may be equal or different heteroatoms. n and n′ are the number of electrons donated by two heteroatoms (Het and Het′) c μ-H-8,9 (hydrogen bridge adjacent to heteroatom, H) rather than μ-H-9,10 (hydrogen bridge far away from heteroatom, F) in nido-7-[HetB10H11](4−n)-, represent the structural feature Het(H). Hydrogen as an exo-substituent (G) rather than bridged between positions 9 and 10 (F) produces the structural feature HetR

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Table 1 Relative trends of energy penalties [kcal mol−1] for different features in 11-vertex nido-hetero(carba)boranes and -borates
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Het5k(1) and Het5k(2)

A heteroatom at a 5k position (1–6) rather than a 4k position (7–11) is indicated by the structural feature Het5k [57]. The apical position (number 1) differs from positions 2–6: the former has only 5k neighbors, the latter has two 4k and three 5k neighbors. Hence, higher energy penalties are observed for position 1, i.e., Het5k(1), as compared to positions 2 through 6, i.e., Het5k(2) [57]. Estimated Het5k(1) energy penalties for a given heteroatom were obtained by comparing the 7- and 1-isomers of [HetB10H10](6−n)− and that of Het5k(2) by comparing 7- and 2-isomers of [HetB10H10](6−n)− (Fig. 2a), where Het = H–C, H–Si, N, H–N, P or H–P etc. and n = number of electrons donated by a given hetero group. E inc′[Het5k(1)] and E inc′[Het5k(2)] for different heteroatoms are listed in Table 1. For the carbon atom at a 5k position in heterocarbaboranes, the statistically fitted energy penalty of 28.0 kcal mol−1 obtained originally from 11-vertex nido-carboranes will be used [57].

HetHet′

Heteroatom-apart isomers are generally more favorable than heteroatom-adjacent isomers in heteroboranes and -borates [6, 54–59]. The structural feature HetHet′ gives the amount of destabilization caused by two adjacent heteroatoms. For example 7,8-[C2B8H10]2− with two adjacent carbon atoms (CC) is 16.3 kcal mol−1 less stable than carbon apart 7,9-isomer [57, 59]. The estimated energy penalties for HetHet′ were obtained by comparing the 7,8- and 7,9-isomers of [HetHet′B9H9](8-n-n′)− (Fig. 2b), where Het or Het′ may be equal or different heteroatoms and n and n′ are the number of electrons donated by Het and Het′. When Het and Het′ are three-electron-donating heteroatoms (∑n=6), the structures to be compared are dianions, but they are neutral and monoanionic for two four-electron-donating heteroatoms (n+n′=8) and one three and one four-electron-donating heteroatom (n+n′=7), respectively. HetHet′ energy penalties for two adjacent carbon atoms, CC [57], and two adjacent phosphorus atoms, PP [59], are 16.0 and 10.7 kcal mol−1, respectively. HetHet′ energy penalties for Het′ = Het and for Het′ = C are listed in Table 1. The energy penalties for a heteroatom adjacent to a bare phosphorus atom (HetP) and to an exo-substituted phosphorus atom (HetPR) are listed in Table 2.

Table 2 Energy penalties [kcal mol−1] for HetPR and HetP together with covalent radius of heteroatom (Het)
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Very similar energy penalties were derived for CC (i.e., two adjacent carbon atoms) in carboranes (16.0 kcal mol−1) [57], phosphacarbaboranes (18.3 kcal mol−1) [59], exo-substituted azacarbaboranes (15.4 kcal mol−1) [59] and thiacarbaboranes (17.7 kcal mol−1). Hence, we use an average value of 17.0 kcal mol−1 for E inc[CC] in all heterocarbaboranes considered in this work.

Het(H)

This structural feature presents the amount of destabilization caused by a heteroatom (Het) adjacent to a hydrogen bridge. Comparing nido-7-[HetB10H11](5−n)− isomers, (n = number of electrons donated by Het) with μ-H-8,9 and μ-H-9,10 hydrogen positions, directly gives an estimated energy penalty for the structural feature Het(H) (Fig. 2c). This structural feature has a relatively small destabilizing effect. For example, the energy penalty for C(H) was determined to be 2.2 kcal mol−1 for carboranes [57]. The energy penalties of other heteroatoms adjacent to a hydrogen bridge are listed in Table 1. The largest Het(H) energy penalty (9.4 kcal mol−1) is observed for the four-electron-donating PR heterogroup, while tin has the smallest (even negative) energy penalty E inc′[Sn(H)] = −1.7 kcal mol−1. It is the only negative energy penalty observed for any heteroatom structural feature in 11-vertex nido-heteroboranes.

HetR

This structural feature allows to compare bare (three-electron donating) and exo-substituted (four-electron donating) group 14 heteroatoms. nido-7-[HetB10H11]2− (μ-H-9,10) and nido-7-[(HHet)B10H10]2− (Fig. 2c) give a direct estimate of the energy penalty of HetR for group 15 heteroatoms. Generally, three-electron-donating nitrogen and phosphorus atoms (N and P) have smaller energy penalties as compared to four electron donating exo-substituted nitrogen and phosphorus (NR and PR) atoms [59]. The same is true for bare arsenic (As) and antimony (Sb) atoms in the 11-vertex nido-cluster which have generally smaller energy penalties as compared to exo-substituted arsenic (AsR) and antimony (SbR) atoms (see Table 1).

Energy penalties as periodic properties of heteroatoms in 11-vertex nido-clusters

In this section, the general trends of HetHet′, Het5k(1) and Het5k(2) energy penalties will be discussed.

HetHet and HetC energy penalties decrease along group 14 (C → Sn), 15 (N → Sb) and 16 (S → Te) and increase along the periods (C → N, Si → S, Ge → Se, Sn → Te, see Table 1). The magnitude of energy penalties depends largely upon the extent of electron localization, which is determined primarily by the number of electrons donated by a heteroatom and secondarily by the electronegativity of the heteroatom. All the heteroatoms in Table 1 formally donate more than two electrons (two electrons are donated by a BH vertex) to the total of 26 skeletal electrons required in an 11-vertex nido-cluster and hence cause stronger electron localization as compared to a BH vertex. Two adjacent heteroatoms result in a larger degree of electron localization on two adjacent vertices and hence a positive HetHet energy penalty. This HetHet energy penalty is more positive for three-electron-donating group 15 heteroatoms as compared to the three-electron-donating group 14 heteroatoms. This is due to the larger electronegativity of three-electron-donating group 15 members. Four-electron-donating group 15 members have even higher electron localization due to four rather than three electrons localized at one vertex. Group 16 heteroatoms have even higher energy penalties as compared to group 15 heteroatoms due to larger electronegativity of the group 15 heteroatoms. It is interesting to note that neighboring NH groups have such a large destabilizing effect that the energy penalty could only be estimated by fixing the N(7)-B(2) and N(8)-B2 distances as the cluster shape was destroyed upon free geometry optimization [59]. Considering the general trends, the energy penalties for oxygen should be the largest but none of the five structural features for 11-vertex nido-oxaboranes could be determined as none of the oxaborane starting geometries optimized to a nido-11-vertex cluster geometry. Among the heteroatoms in Table 1, oxygen is the only one for which no experimentally known 11-vertex nido-heteroborane exists. The smallest HetHet energy penalty (3.1 kcal mol−1) is found for tin (on the left bottom of Table 1).

Geometric consequences also seem to be important. Incorporation of one large heteroatom requires geometric distortion of the cluster. Incorporating another large heteroatom next to the first enhances the geometric distortion but to a lesser extent as compared to placing it at a yet undistorted site. Although this effect is overruled by the opposing electronic effects, it considerably reduces the energy penalties for two adjacent larger heteroatoms. When there is a significant electronegativity difference between boron and the heteroatoms, the electronic effect dominates. However, when the electronegativity of the heteroatom is very close to that of boron, the relative position of hetero-groups does not influence the electronic situation much and the geometric consequences are important.

Figure 3 shows such general trends for HetHet′ and HetC energy penalties, which are indirectly proportional to the covalent radii (directly proportional to electronegativity) within one group. Table 2 also shows very similar effects for HetPR and HetP energy penalties, where one heteroatom is a phosphorus atom.

Fig. 3
figure 3

Covalent radii, HetHet and HetC energy penalties for group 14, group 15 and group 16 heteroatoms. HetHet and HetC energy penalties for heteroatoms increase with decrease in covalent radii

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Energy penalties for Het5k(1) and Het5k(2) increase down group 14 but decrease down group 16. For both three- as well as four-electron-donating heteroatoms in group 15, however, they show mixed trends (Fig. 4).

Fig. 4
figure 4

Het5k(1) and Het5k(2) energy penalties for group 14 heteroatoms decrease with decreasing covalent radii but increase for group 16 heteroatoms. Group 15 heteroatoms have mixed trends

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The importance of geometric consequences also becomes clear by the pronounced preference for open-face positions for larger heteroatoms. Larger heteroatoms have much larger Het5k(1) and Het5k(2) energy penalties. The larger heteroatoms cause more geometric distortion when connected to five cage vertices (at apical position or in the middle belt), and hence larger energy penalties as compared to the smaller heteroatoms which are closer to a BH vertex in size. In the open face, larger heteroatoms are connected to four cluster vertices and hence are more suitable.

The structural feature Het(H) has very similar energy penalties for four-electron-donating group 16 heteroatoms (S, Se and Te have energy penalties of 6.2, 6.1 and 6.3 kcal mol−1, respectively), however, Het(H) energy penalties do not follow any specific general trend for group 14 and −15 heteroatoms. Moreover, Het(H) energy penalties have a small disfavoring effect (~5 kcal mol−1 in many cases) and can be considered as a fine-tuning increment for two structural isomers differing with respect to open face hydrogen positions only.

Comparisons of the estimated relative stabilities (E relinc ′) derived from estimated energy penalties (E inc′) with DFT computed values (E calc) for the 11-vertex nido-hetero(carba)boranes and -borates

Estimated (E inc′) and statistically fitted (E inc) energy penalties as well as E relinc were reported for 11-vertex nido-(carba)boranes and -borates, phospha(carba)boranes and -borates, and aza(carba)boranes and -borates [59]. In this section, the estimated relative stabilities (E relinc ′) are compared with the DFT-computed relative energies (E calc) for thia(carba)boranes and -borates, phosphathiaboranes and -borates, selena-, and tellura(carba)boranes and -borates, and selenathiaboranes and -borates. ΔE′ is the difference between E relinc ′ and E calc.

Thia(carba)boranes and -borates

Twenty-five isomers of thia(carba)boranes and -borates from nido-SB10H12 to nido-SC2B8H10 are considered in this study. The estimated energy penalties for S5k(1), S5k(2), SS, SC, CC and S(H) were obtained as explained in the Structural features for hetero(carba)boranes and -borates section. A total of nine 11-vertex nido-thia(carba)borane and -borate clusters is experimentally known (labeled by “a” in Table 3, also see Fig. 5). Metal complexes of nido-[SB10H10]2− (CA) were also reported [64–67]. Two experimentally unknown SC2B8H10 isomers, GC and GD (see Table 3) are predicted as strong candidates for synthesis because of their competitive thermodynamic stabilities.

Table 3 Estimated energy penalties (E inc′), estimated relative energies (E relinc ′) and computed relative energies for thia(carba)boranes and -borates. All values are in kcal mol−1
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Fig. 5
figure 5

Most stable thia(carba)borane and -borate isomers. White, black and pink balls represent boron, carbon and sulfur atoms, respectively. AA, BA, DA–GA are experimentally known. Metal complexes of CA are also experimentally known

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The experimentally known [3, 34, 68] most stable nido-SB10H12 isomer, i.e., nido-7-SB10H12 (AA) has a sulfur atom at the open face with two bridged hydrogen atoms adjacent to the sulfur atom (structural feature S(H), twice). Both E relinc ′ and E calc have very similar relative energy values for AA (nido-2-SB10H12), AB (nido-2-SB10H12) and AC (nido-1-SB10H12 ) (Table 3).

One extra hydrogen atom in nido-7-[SB10H11]− (BA) [3] bridges positions 9 and 10, resulting in no disfavoring structural feature but is adjacent to the sulfur atom in isomer BB, resulting in E inc′[S(H)] = 6.2 kcal mol−1. BC, i.e., nido-2-[SB10H11]− has a sulfur atom at position number 2 (E inc′[S5k(2)] = 43.8 kcal mol−1) and hence the structure is higher in energy than both BA and BB.

The absence of hydrogen bridges in nido-[SB10H10]2− results in only three possible isomers, i.e., nido-7-[SB10H10]2− (CA), nido-2-[SB10H10]2− (CB) and nido-1-[SB10H10]2− (CC), used to derive E inc′[S5k(2)] = 43.8 kcal mol−1 and E inc′[S5k(1)] = 52.2 kcal mol−1.

The experimentally known [69] nido-7,9-S2B9H9 (DA) is the most stable isomer as it lacks any structural feature. None of the dithiaborane starting geometries with two adjacent sulfur atoms optimized successfully but converged to rearranged structures. However, a rough estimate for the SS feature was obtained by fixing the S(7)-S(8) distance in 7,8-S2B9H9 to be 2.34 Å (45.5 kcal mol−1). Obviously, the SS feature, like NRNR [59], is incompatible with the nido-11-vertex cluster due to too large destabilization.

nido-7,9-SCB9H11 with μ-H-10,11 (EA) [70], the most stable SCB9H11 isomer, has non-adjacent carbon and sulfur atoms. Isomers EB through ED are at least 25 kcal mol−1 less stable than EA. A similar profound preference is found for the heteroatom apart nido-7,9-isomer (FA) [70] among [SCB9H10]− structures.

The experimentally known nido-7,9,10-SC2B8H10 (GA) [3] is the most stable of the seven computed isomers. nido-7,8,9-SC2B8H10 (GE) [3] and nido-7,8,10-SC2B8H10 (GB) [3] with E calc=32.9 and 14.2 kcal mol−1, respectively are also experimentally known. 8,2,10- (GC) and 7,1,9-SC2B8H10 (GD) are thermodynamically more stable than 7,8,9-SC2B8H10 (GE) [3], but are still experimentally unknown.

Phosphathiaboranes and -borates

The relative stabilities as determined from DFT computations and from structural increments for a few phosphathiaboranes are compared in Table 4. [PSB9H9]− structures lack extra hydrogen atoms and possess bare-phosphorus atom/s only. For nido-PSB9H10, however, both bare and exo-substituted phosphorus atoms are considered. The energy penalties derived for a phosphorus atom in phospha(carba)boranes and -borates [59] and for a sulfur atom in thia(carba)boranes and -borates (this paper) along with energy penalties for PS (derived by comparing nido-7,9-[PSB9H9]− with nido-7,8-[PSB9H9]−) and PRS (derived by comparing nido-7,9-(PH)SB9H9 with nido-7,8-(PH)SB9H9 can be used to estimate the relative stabilities of phosphathiaboranes. The estimated relative energies of four nido-PSB9H10 isomers (i.e., HA–HD that differ in more than one feature) were found to be in good agreement with the relative energies computed at B3LYP/6-311+G(d,p)//B3LYP/6-31G(d) (see Table 4, HA–HD). 7,9-PSB9H10 μ-H-10,11 (HA) with the structural features P(H) and S(H) has the least ∑E inc′, E relinc ′ and E calc values but is still experimentally unknown. nido-7,9-PSB9H10 with an exo-substituted phosphorus atom (HB) is computed to be 3.4 kcal mol−1 higher in energy than the former and its phenyl derivative i.e., nido-7-Ph-7,9-PSB9H9 was experimentally characterized [3].

Table 4 Estimated energy penalties (E inc′), estimated relative energies (E relinc ′) for phosphathiaboranes. DFT computed relative energies are also reported for HA to HD. All values are in kcal mol−1
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Selena(carba)boranes and -borates

Estimated energy penalties were used to give the relative stability order of 25 selena(carba)boranes and -borates (Tables 5 and 6). The relative stability order is correctly reproduced in most cases, yet ΔE′ (the difference of E relinc ′ and E calc) is larger for SeC2B8H10 isomers (up to 9.8 kcal mol−1 for PB).

Table 5 Estimated energy penalties (E inc′), estimated relative energies (E relinc ′) for selenaboranes and -borates. DFT computed relative energies are also reported for some structures. All values are in kcal mol−1
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Table 6 Estimated energy penalties (E inc′), estimated relative energies (E relinc ′) for selenacarbaboranes and -borates. DFT computed relative energies are also reported for some structures. All values are in kcal mol−1
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The most stable SeB10H12 isomer i.e., nido-7-SeB10H12 (JA) [39] has the selenium atom at vertex number seven with hydrogens bridging between 8/9 and 10/11 positions (structural feature Se(H) twice). The increment system suggests the deprotonated species, i.e., nido-7-[SeB10H11]− [35–41], with a hydrogen bridging positions 9/10 (KA) rather than positions 8/9 (KB) to be the most stable as in the case of exo-substituted nido-7-[(PH)B10H12]− [59]. nido-7-[SeB10H10]2− (LA) was reported as a ligand in complexes with different metal fragments [35–38, 42, 43, 71, 72]. The geometry of nido-7,8-Se2B9H9 (MB) [73–76] unlike that of nido-7,8-S2B9H9 could successfully be optimized and is 35.1 kcal mol−1 higher in energy than the experimentally still unknown but energetically more favorable 7,9-isomer (MA). Similarly, the heteroatom apart nido-7,9-SeCB9H11 (NA), the most stable SeCB9H11 isomer, is still experimentally unknown although the 7-cyclohexanamine derivative of the 7,8-isomer (NB) is experimentally known [77]. nido-7,9,10-SeC2B8H10 (PA) is experimentally known [73] and other computed SeC2B8H10 structures (PB–PE) are thermodynamically less stable (Table 6).

Selenathiaboranes

The energy penalty (40.2 kcal mol−1) for the structural feature SSe was obtained as the energy difference of 7,8- and 7,9-SeSB9H9. The latter is more stable and is experimentally known [69]. Relative energies of five SeSB9H9 isomers are given in Table 7.

Table 7 Estimated energy penalties (E inc′), estimated relative energies (E relinc ′) for selenathiaboranes. All values are in kcal mol−1
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Estimated energy penalties (Einc′) and corresponding estimated relative stabilities (E relinc ′) for other 11-vertex nido-hetero(carba)boranes and -borates

Estimated energy penalties for sila-, germa-, stanna-, bare and exo-substituted arsa- and stiba(carba)boranes and -borates are reported in Table 1, which can be used to produce the E relinc ′ for the 11-vertex nido-hetero(carba)boranes and -borates with H–Si, H–Ge, H–Sn, As, H–As, Sb and H–Sb heterogroups, respectively.

Prediction of thermodynamically most stable mixed heteroboranes and -borates with three open face heteroatoms

Energy penalties for the HetHet′ structural features describe the relative energies of open-face heteroboranes with two equal heteroatoms, for example, [C2B9H11]2− [57], P2B9H11 [59], Se2B9H9 or that of heteroboranes with two different heteroatoms, e.g., 7,8- and 7,9-isomers of [PSB9H9]− and PSB9H10, SeSB9H9 etc. However, it is complex to predict the thermodynamically most stable isomer in mixed heteroboranes with three open-face heteroatoms, e.g., [P2CB8H9]− [78], [PC2B8H10]− [79, 80], SC2B8H10 [3], SeC2B8H10 [73], NC2B8H11 [81], [NC2B8H10]− [81]. Here we present only [HetC2B8H10](4−n)- examples, (where n = number of electrons donated by a heterogroup, and Het may be a three-electron-donating heteroatom/group, i.e., H–C, H–Si, H–Ge, H–Sn, N, P, As, Sb, or a four-electron-donating heteroatom/group, i.e., H–N, H–P, H–As, H–Sb, S, Se, Te (Table 8). All four possibilities for [HetC2B8H10](4−n)- structures with open face heteroatoms, i.e., 7,9,10-, 7,8,10-, 7,8,9- and 7,8,11-[HetC2B8H10](4−n)- will be discussed.

Table 8 Estimated relative energies (kcal mol−1) of 7,9,10-, 7,8,10-, 7,8,9- and 7,8,11-isomers in [HetC2B8H10](4−n)- a,b
Full size table

Both 7,9,10- and 7,8,10-isomers of [HetC2B8H10]− have one structural feature each, i.e., CC and HetC, respectively. However, 7,8,9- and 7,8,11-isomers of [HetC2B8H10]− have two structural features each, i.e., HetC+CC and 2·HetC, respectively. For group 14 heteroatoms, i.e., H–Si, H–Ge and H–Sn, the HetC, i.e., SiC, GeC and SnC energy penalties are smaller than that of CC and therefore 7,8,10-isomers (i.e., isomers with the HetC structural feature) are more stable. The 7,8,11-isomers with twice the structural feature HetC for three-electron-donating group 14 heteroatoms is not a too high energy option. HetC is very small for group 14 heteroatoms and therefore the 7,8,11-isomers of SnC2B8H10 is only 2.4 kcal mol−1 higher in energy than the 7,8,10-isomer (see Table 8). In the case of three-electron-donating bare nitrogen atom (N), however, the NC structural feature has a larger disfavoring effect than CC, and therefore the 7,9,10-isomer (with structural feature CC) is more stable than the 7,8,10-isomer (with structural feature NC). But for other three-electron-donating group 15 heteroatoms, i.e., P, As, Sb, HetC has less disfavoring effect than CC and therefore the 7,8,10-isomer is more favorable for [PC2B8H10]−, [AsC2B8H10]−, [SbC2B8H10]−.

The estimated relative stabilities for HetC2B8H10 structures for four-electron-donating heteroatoms are listed in Table 8. H–N and H–P have HetC energy penalties (E inc′[NRC] =36.0 kcal mol−1 and E inc′[PRC] =23.6 kcal mol−1) much larger than CC (E inc′[CC] =17.0 kcal mol−1) and hence 7,9,10-isomers with structural feature CC are more favorable than the 7,8,10-isomers. For H–As, however, 7,8,10-AsC2B8H11 (with structural feature AsRC (E inc′[AsRC] =17.3 kcal mol−1) and 7,9,10-AsC2B8H11 with the structural feature CC (E inc′[CC] =17.0 kcal mol−1) are very similar in energy. Since HetHet′ energy penalties decrease down the group, the HetC energy penalty (SbRC) for a four-electron-donating antimony atom (SbRC) is 4.8 kcal mol−1 less than that of AsRC and therefore the 7,8,10-isomer is more stable for (HSb)C2B8H10 as compared to the 7,9,10-isomer (7,9,10-isomer has structural feature CC and E inc′[CC] > E inc′[SbRC].

HetC energy penalties for all four-electron-donating group 16 heteroatoms are much higher than CC and therefore 7,9,10-HetC2B8H10 isomers are thermodynamically more stable than 7,8,10-isomers. 7,8,9- and 7,8,11-isomers have more than one structural feature, i.e., HetHet+HetC and 2·HetC, respectively, and therefore have even larger disfavoring effects for four-electron-donating heteroatoms.

Conclusions

Estimated energy penalties present a convenient method to predict the relative stabilities of 11-vertex nido-heteroboranes and -borates. Energy penalties for adjacent heteroatoms increase along the period and decrease down the group. Four-electron-donating heteroatoms generally have larger energy penalties than those of three-electron-donating heteroatoms. Larger heteroatoms usually have larger Het5k(1) and Het5k(2) energy penalties and smaller HetHet′ energy penalties, indicating that they prefer open-face vertices and that the destabilizing effect of adjacent heteroatoms is smaller for larger heteroatoms. Most stable mixed heteroboranes with more than two open-face heteroatoms have different but easily predictable heteroatom positions in the thermodynamically most stable 11-vertex nido-heteroborane isomers. Energy penalties are likely to have periodic trends in other polyborane clusters.

Supplementary material

Cartesian coordinates of the optimized geometries of 11-vertex nido-heterocarbaboranes and -borates considered in this paper are listed in Appendices I through V.