Periodic trends and easy estimation of relative stabilities in 11-vertex nido-p-block-heteroboranes and -borates.

Density functional theory computations were carried out for 11-vertex nido-p-block-hetero(carba)boranes and -borates containing silicon, germanium, tin, arsenic, antimony, sulfur, selenium and tellurium heteroatoms. A set of quantitative values called "estimated energy penalties" was derived by comparing the energies of two reference structures that differ with respect to one structural feature only. These energy penalties behave additively, i.e., they allow us to reproduce the DFT-computed relative stabilities of 11-vertex nido-heteroboranes in general with good accuracy and to predict the thermodynamic stabilities of unknown structures easily. Energy penalties for neighboring heteroatoms (HetHet and HetHet') decrease down the group and increase along the period (indirectly proportional to covalent radii). Energy penalties for a five- rather than four-coordinate heteroatom, [Het(5k)(1) and Het(5k)(2)], generally, increase down group 14 but decrease down group 16, while there are mixed trends for group 15 heteroatoms. The sum of HetHet' energy penalties results in different but easily predictable open-face heteroatom positions in the thermodynamically most stable mixed heterocarbaboranes and -borates with more than two heteroatoms.

Introduction

The <pan class="Chemical">span cln>an class="Chemical">ass="Chemical">11-vertex nido-cluster re<n>an class="Chemical">ass="Chemical">span class="Chemical">presents 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 wpan class="Chemical">as <span class="Chemical">presented that re<ass="Chemical">span class="Chemical">produced 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 <pan class="Chemical">span cln>an class="Chemical">ass="Chemical">previous work [56-59], energy penalties (Einc) were determined by statistical fit<n>an class="Chemical">ass="Chemical">span class="Chemical">ting to a large number of structures. This procedure gives accurate values but requires extensive computations. Estimated energy penalties, (Einc′), 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-C2B9H112− and 7,9-C2B9H112− 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 (Eincrel′) for 11-vertex nido-sila-, germana-, stanna-, arsa-, stiba-, thia-, selena- and tellura(carba)boranes and -borates, phosphathiaboranes and -borates and selenathiaboranes produced by Einc′, 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 <pan class="Chemical">span cln>an class="Chemical">ass="Chemical">11-vertex nido-cluster is shown in Fig. 1. The apical po<n>an class="Chemical">ass="Chemical">span class="Chemical">sition 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, kc=5 and five peripheral vertices with kp=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

Numbering scheme for the 11-vertex nido-cluster

Numbering scheme for the <pan class="Chemical">span cln>an class="Chemical">ass="Chemical">11-vertex nido-cluster

Computational details

For all <pan class="Chemical">span cln>an class="Chemical">ass="Chemical">hetero(carba)boranes and -<n>an class="Chemical">ass="Chemical">span class="Chemical">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 <pan class="Chemical">span cln>an class="Chemical">ass="Chemical">stanna, <n>an class="Chemical">ass="Chemical">span class="Chemical">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 fpan class="Chemical">eatures for ass="Chemical">hetero(carba)boranes and -<ass="Chemical">span class="Chemical">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

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

Table 1

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

aHeteroatom

bElectronegativity values, see Pauling, L. The Nature of the Chemical Bond. Cornell University Press: Ithaca, New York, 1960

cCovalent radii in pico meter, see Huheey, J.E.; Keiter, E.A.; Keiter, R.L. : , 4th edition, HarperCollins, New York, USA, 1993

dEnergy penalty for two identical adjacent heteroatoms in the 11-vertex nido-cluster

eEnergy penalty for a heteroatom adjacent to a carbon atom in the 11-vertex nido-cluster

fHet5k(1) is the structural feature for a heteroatom at a 5k apical position (vertex number 1) rather than the ideal 4k open face positions

gHet5k(2) is the structural feature for a heteroatom at vertices 2 through 6 rather than at the ideal 4k open face positions

hStructural feature Het(H) denotes the amount of destabilization caused by a heteroatom adjacent to a bridged hydrogen atom

iStatistically fitted values taken from ref. 31. For all other heteroatoms, energy penalties are estimated by comparing two suitable reference structures which differ with respect to one structural feature

jInitial starting 11-vertex nido-oxaborane geometries did not survive geometry optimizations due to the expected very high energy penalties of the oxygen atom

kThe NRNR energy penalty could not be accurately obtained as the structure rearranged. The rough energy penalty derived by fixing N7-B2 and N8-B2 distances to be 1.775 Å was even higher (76.5 kcal mol−1)

lThe energy penalty for SS (45 kcal mol−1) also needed to be derived by fixing the S(7)-S(8) bond distance to be 2.34 Å

a A heteroatom (Het) at a 5 k apical po<pan class="Chemical">span cln>an class="Chemical">ass="Chemical">sition (<n>an class="Chemical">ass="Chemical">span class="Chemical">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

Relative trends of energy penalties [kcal mol−1] for different fpan class="Chemical">eatures in <span class="Chemical">11-vertex <ass="Chemical">span class="Chemical">nido-hetero(carba)boranes and -borates

bElectronepan class="Chemical">gativity values, see pan class="Chemical">Pauling, L. The Nature of the Chemical Bond. Cornell Univer<span class="Chemical">sity <ass="Chemical">span class="Chemical">Press: Ithaca, New York, 1960

dEnergy penalty for two identical ad<pan class="Chemical">span cln>an class="Chemical">ass="Chemical">jacent heteroatoms in the <n>an class="Chemical">ass="Chemical">span class="Chemical">11-vertex nido-cluster

eEnergy penalty for a heteroatom ad<pan class="Chemical">span cln>an class="Chemical">ass="Chemical">jacent to a <n>an class="Chemical">ass="Chemical">span class="Chemical">carbon atom in the 11-vertex nido-cluster

fHet5k(1) is the structural fpan class="Chemical">eature for a heteroatom at a 5k apn>ical po<span class="Chemical">sition (<ass="Chemical">span class="Chemical">vertex number 1) rather than the ideal 4k open face positions

gHet5k(2) is the structural fpan class="Chemical">eature for a heteroatom at vertices 2 through 6 rather than at the idn>an class="Chemical">eal 4k open face po<span class="Chemical">sitions

hStructural fpan class="Chemical">eature Het(H) denotes the amount of destabilization caused by a heteroatom ad<span class="Chemical">jacent to a bridged <ass="Chemical">span class="Chemical">hydrogen atom

iStatistically fitted values taken from ref. 31. For all other heteroatoms, energy penalties are estimated by comparing two suitable reference structures which differ with repan class="Chemical">spect to one structural fn>an class="Chemical">eature

<pan class="Chemical">span clpan class="Chemical">ass="Chemical">jInitial star<pan class="Chemical">ass="Chemical">span class="Chemical">ting 11-vertex nido-oxaborane geometries did not survive geometry optimizations due to the expected very high energy penalties of the oxygen atom

kThe NRNR energy penalty could not be accurately <pan class="Chemical">span cln>an class="Chemical">ass="Disease">obtained as the structure rearranged. The rough energy penalty derived by fixing N7-B2 and N8-B2 distances to be 1.775 Å was even higher (76.5 kcal mol−1)

Het5k(1) and Het5k(2)

A heteroatom at a 5k po<pan class="Chemical">span cln>an class="Chemical">ass="Chemical">sition (1–6) rather than a 4k po<n>an class="Chemical">ass="Chemical">span class="Chemical">sition (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. Einc′[Het5k(1)] and Einc′[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 pan class="Chemical">generally more favorable than heteroatom-adass="Chemical">jacent isomers in <ass="Chemical">span class="Chemical">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)

HetHet′	RHet [pm]	Einc′ [kcal mol−1]
NP	71	18.8
CP	77	15.1
PP	93	10.7
NRPR	71	42.5
PRPR	93	36.9
SPR	104	38.8
SePR	117	35.8

Energy penalties [kcal mol−1] for Het<pan class="Chemical">span cln>an class="Chemical">ass="Chemical">PR and HetP together with covalent radius of heteroatom (Het)

Very <pan class="Chemical">span cln>an class="Chemical">ass="Chemical">similar energy penalties were derived for CC (i.e., two ad<n>an class="Chemical">ass="Chemical">span class="Chemical">jacent 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 Einc[CC] in all heterocarbaboranes considered in this work.

Het(H)

This structural fpan class="Chemical">eature ass="Chemical">presents the amount of destabilization caused by a heteroatom (Het) ad<ass="Chemical">span class="Chemical">jacent 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 Einc′[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 fpan class="Chemical">eature allows to compn>are ass="Chemical">bare (three-electron dona<ass="Chemical">span class="Chemical">ting) 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 pan class="Chemical">general trends of HetHet′, Het5k(1) and Het5k(2) energy penalties will be discussed.

HetHet and HetC energy penalties decrepan class="Chemical">ase along groupn> 14 (C → Sn), 15 (N → n>an class="Chemical">Sb) and 16 (S → Te) and increase along the periods (C → N, <span class="Chemical">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 <ass="Chemical">span class="Chemical">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).

pan class="Chemical">Geometric consequences also seem to be impn>ortant. Incorpn>oration of one larn>an class="Chemical">ge heteroatom requires geometric distortion of the cluster. Incorpora<span class="Chemical">ting 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 <ass="Chemical">span class="Chemical">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 pan class="Chemical">general trends for HetHet′ and HetC energy penalties, which are indirectly ass="Chemical">proportional to the covalent radii (directly <ass="Chemical">span class="Chemical">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

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

Covalent radii, HetHet and HetC energy penalties for group 14, group 15 and group 16 heteroatoms. HetHet and HetC energy penalties for heteroatoms increpan class="Chemical">ase with decrepan class="Chemical">ase in covalent radii

Energy penalties for Het5k(1) and Het5k(2) increpan class="Chemical">ase down groupn> 14 but decrease down group 16. For both three- as well as four-electron-dona<span class="Chemical">ting heteroatoms in group 15, however, they show mixed trends (Fig. 4).

Fig. 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

Het5k(1) and Het5k(2) energy penalties for group 14 heteroatoms decrepan class="Chemical">ase with decrn>an class="Chemical">ea<span class="Chemical">sing covalent radii but increase for group 16 heteroatoms. Group 15 heteroatoms have mixed trends

The importance of pan class="Chemical">geometric consequences also becomes cln>an class="Chemical">ear by the ass="Chemical">pronounced <ass="Chemical">span class="Chemical">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 fpan class="Chemical">eature Het(H) hn>an class="Chemical">as very ass="Chemical">similar energy penalties for four-electron-dona<ass="Chemical">span class="Chemical">ting 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 (Eincrel′) derived from estimated energy penalties (Einc′) with DFT computed values (Ecalc) for the 11-vertex nido-hetero(carba)boranes and -borates

Estimated (Einc′) and statistically fitted (Einc) energy penalties pan class="Chemical">as well n>an class="Chemical">as Eincrel were reported for <span class="Chemical">11-vertex <ass="Chemical">span class="Chemical">nido-(carba)boranes and -borates, phospha(carba)boranes and -borates, and aza(carba)boranes and -borates [59]. In this section, the estimated relative stabilities (Eincrel′) are compared with the DFT-computed relative energies (Ecalc) 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 Eincrel′ and Ecalc.

Thia(carba)boranes and -borates

Twenty-five isomers of <pan class="Chemical">span cln>an class="Chemical">ass="Chemical">thia(carba)boranes and -<n>an class="Chemical">ass="Chemical">span class="Chemical">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 (Einc′), estimated relative energies (Eincrel′) and computed relative energies for thia(carba)boranes and -borates. All values are in kcal mol−1

	Compound	μ-H-	C5k	C(H)	CC	S5k(1)′	S5k(2)′	S(H)′	SC′	∑Einc′	Eincrel′	Ecalc	ΔE′
			28.0	2.1	17.0	52.2	43.8	6.2	31.2
AAa	7-SB10H12	8,9; 9,10						2		12.4	0.0	0.0	0.0
AB	2-SB10H12	7,8; 9,10					1	1		50.0	37.6	39.8	-2.2
AC	1-SB10H12	7,8; 9,10				1				52.2	39.8	43.8	-4.0
BAa	7-SB10H111−	9,10								0.0	0.0	0.0	0.0
BBa	7-SB10H111−	8,9						1		6.2	6.2	6.2	0.0
BC	2-SB10H111−	8,9					1			43.8	43.8	44.3	-0.5
CAb	7-SB10H102−	–								0.0	0.0	0.0	0.0
CB	2-SB10H102−	–					1			43.8	43.8	43.8	0.0
CC	1-SB10H102−	–				1				52.2	52.2	52.2	0.0
DAa	7,9-S2B9H9	–								0.0	0.0	0.0	0.0
DB	1,7-S2B9H9	–				1				52.2	52.2	55.5	-3.3
EAa	7,9-SCB9H11	10,11		1				1		8.3	0.0	0.0	0.0
EB	7,8-SCB9H11	9,10		1					1	33.3	25.0	25.6	-0.6
EC	7,8-SCB9H11	10,11						1	1	37.4	29.1	27.9	1.2
ED	2,8-SCB9H11	9,10		1			1			45.9	37.6	35.0	2.6
FAa	7,9-SCB9H101−	–								0.0	0.0	0.0	0.0
FB	7,8-SCB9H101−	–							1	31.2	31.2	31.2	0.0
FC	7,1-SCB9H101−	–	1							28.0	28.0	33.3	-5.3
FD	1,7-SCB9H101−	–				1				52.2	52.2	54.4	-2.2
GAa	7,9,10-SC2B8H10	–			1					17.0	0.0	0.0	0.0
GBa	7,8,10-SC2B8H10	–							1	31.2	14.2	13.1	1.1
GCc	8,2,10-SC2B8H10	–	1							28.0	11.0	13.6	-2.6
GDc	7,1,9-SC2B8H10	–	1							28.0	11.0	17.5	-6.5
GEa	7,8,9-SC2B8H10	–			1				1	48.2	31.2	32.9	-1.7
GF	7,8,11-SC2B8H10	–							2	62.4	45.4	48.8	-3.4

aExperimentally known isomers

bOnly metal derivatives are experimentally known

cStrong candidates

Fig. 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

Estimated energy penalties (Einc′), estimated relative energies (Eincrel′) and computed relative energies for <pan class="Chemical">span cln>an class="Chemical">ass="Chemical">thia(carba)boranes and -<n>an class="Chemical">ass="Chemical">span class="Chemical">borates. All values are in kcal mol−1

bOnly <pan class="Chemical">span cln>an class="Chemical">ass="Chemical">metal derivatives are experimentally known

cStrong candipan class="Chemical">dates

Most stable <pan class="Chemical">span cln>an class="Chemical">ass="Chemical">thia(carba)borane and -<n>an class="Chemical">ass="Chemical">span class="Chemical">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

The experimentally known [3, 34, 68] most stable <pan class="Chemical">span cln>an class="Chemical">ass="Chemical">nido-SB10H12 isomer, i.e., <ass="Chemical">span class="Chemical">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 Eincrel′ and Ecalc have very similar relative energy values for AA (nido-2-SB10H12), AB (nido-2-SB10H12) and AC (nido-1-SB10H12 ) (Table 3).

One extra <pan class="Chemical">span cln>an class="Chemical">ass="Chemical">hydrogen atom in <ass="Chemical">span class="Chemical">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 Einc′[S(H)] = 6.2 kcal mol−1. BC, i.e., nido-2-[SB10H11]− has a sulfur atom at position number 2 (Einc′[S5k(2)] = 43.8 kcal mol−1) and hence the structure is higher in energy than both BA and BB.

The absence of <pan class="Chemical">span cln>an class="Chemical">ass="Chemical">hydrogen bridges in nido-[SB10H10]2− results in only three pos<ass="Chemical">span class="Chemical">sible isomers, i.e., nido-7-[SB10H10]2− (CA), nido-2-[SB10H10]2− (CB) and nido-1-[SB10H10]2− (CC), used to derive Einc′[S5k(2)] = 43.8 kcal mol−1 and Einc′[S5k(1)] = 52.2 kcal mol−1.

The experimentally known [69] nido-7,<pan class="Chemical">span cln>an class="Chemical">ass="CellLine">9-S2B9H9 (DA) is the most stable isomer as it lacks any structural feature. None of the <n>an class="Chemical">ass="Chemical">span class="Chemical">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.

<pan class="Chemical">span cln>an class="Chemical">ass="Chemical">nido-7,9-SCB9H11 with μ-H-10,11 (EA) [70], the most stable <n>an class="Chemical">ass="Chemical">span class="Chemical">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 <pan class="Chemical">span cln>an class="Chemical">ass="Chemical">nido-7,9,10-SC2B8H10 (GA) [3] is the most stable of the seven computed isomers. nido-7,8,<n>an class="Chemical">ass="Chemical">span class="CellLine">9-SC2B8H10 (GE) [3] and nido-7,8,10-SC2B8H10 (GB) [3] with Ecalc=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 pan class="Chemical">as determined from DFT compn>utations and from structural increments for a few ass="Chemical">phosphathiaboranes are compared in Table 4. [PSB9<ass="Chemical">span class="CellLine">H9]− 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 ∑Einc′, Eincrel′ and Ecalc 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 (Einc′), estimated relative energies (Eincrel′) for phosphathiaboranes. DFT computed relative energies are also reported for HA to HD. All values are in kcal mol−1

	Compound	μ-H-	P(H)	PR	S(H)′	PS′	PRS′	∑Einc′	Eincrel′	Ecalc	ΔE′
			2.2	13.3	6.1	21.4	38.8
HAa	7,9-PSB9H10	10,11	1		1			8.3	0.0	0.0	0.0
HBb	7,9-(HP)SB9H10			1				13.3	5.0	3.4	1.6
HC	7,8-PSB9H10	10,11	1			1		23.6	15.3	13.8	1.5
HD	7,8-(HP)SB9H10			1			1	52.1	43.8	42.2	1.6
IA	7,9-PSB9H9−							0.0	0.0	0.0	0.0
IB	7,8-PSB9H9−					1		21.4	21.4	21.4	0.0

aStrong candidate for synthesis

b7-Ph–HB, i.e., 7-Ph derivative of 7,9-PSB9H10 is experimentally known

Estimated energy penalties (Einc′), estimated relative energies (Eincrel′) for <pan class="Chemical">span cln>an class="Chemical">ass="Chemical">phosphathiaboranes. DFT computed relative energies are also reported for HA to HD. All values are in kcal mol−1

pan class="Chemical">aStrong candidate for synthe<span class="Chemical">sis

b<pan class="Chemical">span cln>an class="Chemical">ass="Chemical">7-Ph–HB, i.e., <ass="Chemical">span class="Chemical">7-Ph derivative of 7,9-PSB9H10 is experimentally known

Selena(carba)boranes and -borates

Estimated energy penalties were used to give the relative stability order of 25 <pan class="Chemical">span cln>an class="Chemical">ass="Chemical">selena(carba)boranes and -<n>an class="Chemical">ass="Chemical">span class="Chemical">borates (Tables 5 and 6). The relative stability order is correctly reproduced in most cases, yet ΔE′ (the difference of Eincrel′ and Ecalc) is larger for SeC2B8H10 isomers (up to 9.8 kcal mol−1 for PB).

Table 5

Estimated energy penalties (Einc′), estimated relative energies (Eincrel′) for selenaboranes and -borates. DFT computed relative energies are also reported for some structures. All values are in kcal mol−1

	Compound	μ-H-	Se5k(1)′	Se5k(2)′	Se(H)′	SeSe′	∑Einc′	Eincrel′	Ecalc	ΔE′
			48.2	40.7	6.1	35.1
JAa	7-SeB10H12	8,9; 10,11			2		12.2	0.0	0.0	0.0
JB	2-SeB10H12	7,8; 9,10		1	1		46.8	34.6	39.5	-4.9
KAa	7-SeB10H111−	9,10					0.0	0.0	0.0	0.0
KB	7-SeB10H111−	8,9			1		6.1	6.1	6.1	0.0
KC	1-SeB10H111−	7,8	1				48.2	48.2	52.6	-4.4
LAb	7-SeB10H102−						0.0	0.0	0.0	0.0
LB	2-SeB10H102−			1			40.7	40.7	40.7	0.0
MA	7,9-Se2B9H9						0.0	0.0	0.0	0.0
MBa	7,8-Se2B9H9					1	35.1	35.1	35.1	0.0

aExperimentally known isomers

bCyclopentadienyl metal derivatives are experimentally known

Table 6

Estimated energy penalties (Einc′), estimated relative energies (Eincrel′) for selenacarbaboranes and -borates. DFT computed relative energies are also reported for some structures. All values are in kcal mol−1

	Compound	μ-H-	C5k	C(H)	CC	Se5k(1)′	Se5k(2)′	Se(H)′	SeC′	∑Einc′	Eincrel′	Ecalc	ΔE′
			28.0	2.1	17.0	48.2	40.7	6.1	30.3
NAa	7,9-SeCB9H11	10,11		1				1		8.2	0.0	0.0	0.0
NBb	7,8-SeCB9H11	9,10		1					1	32.4	24.2	24.8	-0.6
NC	7,8-SeCB9H11	10,11						1	1	36.4	28.2	26.5	1.7
ND	1,7-SeCB9H11	9,10		1			1			42.8	34.6	32.8	1.8
NE	1,7-SeCB9H11	8,9		1		1				50.3	42.1	46.7	-4.6
NF	2,4-SeCB9H11	9,10	1	1			1			70.8	62.6	65.0	-2.4
OA	7,9-SeCB9H10−									0.0	0.0	0.0	0.0
OB	7,8-SeCB9H10−								1	30.3	30.3	30.3	0.0
OC	7,1-SeCB9H10−		1							28.0	28.0	32.6	-4.6
PAc	7,9,10-SeC2B8H10				1					17.0	0.0	0.0	0.0
PB	7,8,10-SeC2B8H10								1	30.3	13.3	2.5	9.8
PC	7,1,9-SeC2B8H10		1							28.0	11.0	7.6	3.4
PD	7,8,9-SeC2B8H10				1				1	47.3	30.3	22.5	8.8
PE	7,8,11-SeC2B8H10								2	60.6	42.6	37.4	5.2

aStrong candidate

b7-Cycloheanamine derivative is experimentally known

cExperimentally known isomer

Estimated energy penalties (Einc′), estimated relative energies (Eincrel′) for <pan class="Chemical">span cln>an class="Chemical">ass="Chemical">selenaboranes and -<n>an class="Chemical">ass="Chemical">span class="Chemical">borates. DFT computed relative energies are also reported for some structures. All values are in kcal mol−1

<pan class="Chemical">span cln>an class="Chemical">ass="Chemical">bCyclopentadienyl metal derivatives are experimentally known

Estimated energy penalties (Einc′), estimated relative energies (Eincrel′) for <pan class="Chemical">span cln>an class="Chemical">ass="Chemical">selenacarbaboranes and -<n>an class="Chemical">ass="Chemical">span class="Chemical">borates. DFT computed relative energies are also reported for some structures. All values are in kcal mol−1

pan class="Chemical">aStrong candin>an class="Chemical">date

b7-<pan class="Chemical">span cln>an class="Chemical">ass="Chemical">Cycloheanamine derivative is experimentally known

The most stable <pan class="Chemical">span cln>an class="Chemical">ass="Chemical">SeB10H12 isomer i.e., <n>an class="Chemical">ass="Chemical">span class="Chemical">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 fpan class="Chemical">eature SSe wn>an class="Chemical">as ass="Disease">obtained as the energy difference of 7,8- and 7,<ass="Chemical">span class="CellLine">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 (Einc′), estimated relative energies (Eincrel′) for selenathiaboranes. All values are in kcal mol−1

	Compound	Eincrel′	Ecalc	ΔE	Structural feature
	7,9-SeSB9H9	0.0	0.0	0.0	None
QB	7,8-SeSB9H9	40.2	40.2	0.0	SSe′
QC	2,9-SeSB9H9	40.7	36.0	4.7	Se5k(2)′
QD	9,2-SeSB9H9	43.8	38.3	5.5	S5k(2)′
QE	1,7-SeSB9H9	48.1	51.9	−3.8	Se5k(1)′
QF	7,1-SeSB9H9	52.2	54.7	−2.5	S5k(1)′

Estimated energy penalties (Einc′), estimated relative energies (Eincrel′) for <pan class="Chemical">span cln>an class="Chemical">ass="Chemical">selenathiaboranes. All values are in kcal mol−1

Estimated energy penalties (Einc′) and corresponding estimated relative stabilities (Eincrel′) for other 11-vertex nido-hetero(carba)boranes and -borates

Estimated energy penalties for <pan class="Chemical">span cln>an class="Chemical">ass="Chemical">sila-, germa-, <n>an class="Chemical">ass="Chemical">span class="Chemical">stanna-, bare and exo-substituted arsa- and stiba(carba)boranes and -borates are reported in Table 1, which can be used to produce the Eincrel′ 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 fpan class="Chemical">eatures describe the relative energies of opn>en-face ass="Chemical">heteroboranes with two equal heteroatoms, for example, [C2B9H11]2− [57], P2B9H11 [59], Se2B9<ass="Chemical">span class="CellLine">H9 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

aHet may be a three- or four-electron-donating heteroatom. n corresponds to the number of electrons donated by a given heteroatom

bB3LYP/6-311+G(d,p)//B3LYP/6-31G(d)+ZPE computed relative stabilities of various [HetC2B8H10](4-n)- isomers are listed in parenthesis for various heteroatoms. These values are usually very close to the values predicted by estimated energy penalties

c7,9,10-[NC2B8H10]−, 7,9,10-(HN)C2B8H10, 7,9,10-SC2B8H10, 7,9,10-SeC2B8H10 are experimentally known

d7,8,10-SC2B8H10 is experimentally known

e7,8,9-[NC2B8H10]− and 7-Me and 7-Ph derivatives of 7,8,9-(HP)C2B8H10 are experimentally known

f7-Ph derivatives of 7,8,11-(HP)C2B8H10 is experimentally known

aHet may be a three- or four-electron-dona<pan class="Chemical">span cln>an class="Chemical">ass="Chemical">ting heteroatom. n corren>an class="Chemical">ass="Chemical">sponds to the number of electrons donated by a given heteroatom

bB3LYP/6-311+G(d,p)//B3LYP/6-31G(d)+ZPE computed relative stabilities of various [HetC2B8H10](4-n)- isomers are listed in parenthe<pan class="Chemical">span cln>an class="Chemical">ass="Chemical">sis for various heteroatoms. These values are usually very close to the values <n>an class="Chemical">ass="Chemical">span class="Chemical">predicted by estimated energy penalties

<pan class="Chemical">span cln>an class="Chemical">ass="Chemical">d7,8,10-SC2B8H10 is experimentally known

pan class="Chemical">e7,ass="Chemical">8,9-[NC2B8H10]− and <ass="Chemical">span class="Chemical">7-Me and 7-Ph derivatives of 7,8,9-(HP)C2B8H10 are experimentally known

f<pan class="Chemical">span cln>an class="Chemical">ass="Chemical">7-Ph derivatives of 7,8,11<ass="Chemical">span class="Chemical">-(HP)C2B8H10 is experimentally known

Both 7,9,10- and 7,8,10-isomers of [HetC2B8H10]− have one structural fpan class="Chemical">eature n>an class="Chemical">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–<span class="Chemical">Si, H–Ge and H–Sn, the HetC, i.e., <ass="Chemical">span class="Chemical">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-dona<pan class="Chemical">span cln>an class="Chemical">ass="Chemical">ting heteroatoms are listed in Table 8. H–N and H–P have HetC energy penalties (Einc′[NRC] =36.0 kcal mol−1 and Einc′[<n>an class="Chemical">ass="Chemical">span class="Chemical">PRC] =23.6 kcal mol−1) much larger than CC (Einc′[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 (Einc′[AsRC] =17.3 kcal mol−1) and 7,9,10-AsC2B8H11 with the structural feature CC (Einc′[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 Einc′[CC] > Einc′[SbRC].

HetC energy penalties for all four-electron-dona<pan class="Chemical">span cln>an class="Chemical">ass="Chemical">ting 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, ren>an class="Chemical">ass="Chemical">spectively, and therefore have even larger <n>an class="Chemical">ass="Chemical">span class="Chemical">disfavoring effects for four-electron-donating heteroatoms.

Conclusions

Estimated energy penalties <pan class="Chemical">span cln>an class="Chemical">ass="Chemical">present a convenient method to <n>an class="Chemical">ass="Chemical">span class="Chemical">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

Carte<pan class="Chemical">span cln>an class="Chemical">ass="Chemical">sian coordinates of the optimized geometries of <n>an class="Chemical">ass="Chemical">span class="Chemical">11-vertex nido-heterocarbaboranes and -borates considered in this paper are listed in Appendices I through V.

Supplementary material