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The effect of substitution on the potential energy surfaces of RE13≡BiR (E13 = B, Al, Ga, In, and Tl; R = F, OH, H, CH3, SiH3, Tbt, Ar*, SiMe(SitBu3)2, and SiiPrDis2) is investigated using density functional theories (M06-2X/Def2-TZVP, B3PW91/Def2-TZVP, and B3LYP/LANL2DZ+dp). The theoretical results suggest that all of the triply bonded RE13≡BiR molecules prefer to adopt a bent geometry (i.e., ∠RE13Bi ≈ 180° and ∠E13BiR ≈ 90°), which agrees well with the bonding model (model (B)). It is also demonstrated that the smaller groups, such as R = F, OH, H, CH3, and SiH3, neither kinetically nor thermodynamically stabilize the triply bonded RE13≡BiR compounds, except for the case of H3SiB≡BiSiH3. Nevertheless, the triply bonded RʹE13≡BiRʹ molecules that feature bulkier substituents (Rʹ = Tbt, Ar*, SiMe(SitBu3)2, and SiiPrDis2) are found to have the global minimum on the singlet potential energy surface and are both kinetically and thermodynamically stable. In other words, both the electronic and the steric effects of bulkier substituent groups play an important role in making triply bonded RE13≡BiR (Group 13–Group 15) species synthetically accessible and isolable in a stable form.
Department of Applied Chemistry, National Chiayi University, Chiayi, Taiwan
Ming-Chung Yang
Department of Applied Chemistry, National Chiayi University, Chiayi, Taiwan
Shih-Hao Su
Department of Applied Chemistry, National Chiayi University, Chiayi, Taiwan
Xiang-Ting Wen
Department of Applied Chemistry, National Chiayi University, Chiayi, Taiwan
Jia-Zhen Xie
Department of Applied Chemistry, National Chiayi University, Chiayi, Taiwan
Ming-Der Su*
Department of Applied Chemistry, National Chiayi University, Chiayi, Taiwan
Department of Medicinal and Applied Chemistry, Kaohsiung Medical University, Kaohsiung, Taiwan, Chiayi, Taiwan
*Address all correspondence to: midesu@mail.ncyu.edu.tw
1. Introduction
Triply bonded molecules are of great interest in structural and synthetic inorganic chemistry as well as in fundamental science. Molecules that have triple bonds, however, pose a more difficult challenge than analogous doubly bonded molecules from a synthetic viewpoint [1–8]. Acetylene is one of the most commonly triply bonded molecules in traditional organic chemistry. Thanks to Kira, Power, Sekiguchi, Tokitoh, Wiberg and many coworkers, the stable homonuclear alkyne analogues of all of the heavier group 14 elements have now been isolated and characterized [9–19]. Recently, heteronuclear ethyne-like molecules that possess C≡Ge [20, 21], C≡Sn [22], and C≡Pb [23] triple bonds have also been theoretically predicted and have been published elsewhere.
Nevertheless, to the authors’ best knowledge, neither experimental nor theoretical studies have been performed on acetylene-like compounds that feature an E13≡Bi (E = B, Al, Ga, In, and Tl) triple bond. It is surprising how little is known about the stability and molecular properties of E13≡Bi, considering the importance of bismuth compounds [24] that contain group 13 elements in inorganic chemistry [25–35] and material chemistry [36–45].
The aim of this study is to theoretically determine the existence and relative stability of RE13≡BiR triply bonded molecules, which can be synthesized as stable compounds when they are properly substituted. For the first time, the structures of RE13≡BiR with various substituents are reported. That is, theoretical calculations of RE13≡BiR are performed, using both smaller ligands (such as, R = F, OH, H, CH3, and SiH3) and larger ligands with bulky aryl and silyl groups (i.e., Rʹ = Tbt, Ar*, SiMe(SitBu3)2, and SiiPrDis2; Dis = CH(SiMe3)2; Scheme 1) [46–51]. As a result, the effect of substituents on these bismuth-group-13-element triple bonds is systematically investigated using density functional theory (DFT) calculations. It is expected that the theoretical interpretations of the effect of substituents, presented in this work, will help in the experimental preparation of the many precursors of RE13≡BiR.
Geometries were fully optimized using hybrid density functional theory at M06-2X, B3PW91, and B3LYP levels, using the Gaussian 09 program package [52]. It has been reported that M06-2X is proven to have excellent performance for main group chemistry [53]. In both the B3LYP and B3PW91 calculations, Becke’s three-parameter nonlocal exchange functional (B3) [54, 55] is used, together with the exact (Hartree-Fock) exchange functional, in conjunction with the nonlocal correlation functional of Lee, Yang, Parr (LYP) [56] and Perdew and Wang (PW91) [57]. Therefore, the geometries of all of the stationary points were fully optimized at the M06-2X, B3PW91, and B3LYP levels of theory. For comparison, the geometries and energetics of the stationary points on the potential energy surface were calculated using the M06-2X, B3PW91, and B3LYP methods, in conjunction with the Def2-TZVP [58] and LANL2DZ+dp [59–62] basis sets. Consequently, these DFT calculations are denoted as M06-2X/Def2-TZVP, B3PW91/Def2-TZVP, and B3LYP/LANL2DZ+dp, respectively.
The spin-unrestricted (UM06-2X, UB3PW91, and UB3LYP) formalisms are used for the open-shell (triplet) species. The <S2> expectation values for the triplet state for the calculated species all have an ideal value (2.00), after spin annihilation, so their geometries and energetics are reliable for this study. Frequency calculations were performed on all structures, in order to confirm that the reactants and products have no imaginary frequencies, and that the transition states possess only one imaginary frequency. Thermodynamic corrections to 298 K, heat capacity corrections, and entropy corrections (∆S) are applied at the three DFT levels. Therefore, the relative free energy (∆G) at 298 K is also calculated at the same levels of theory.
Sequential conformation analyses were performed for each stationary point, for species containing bulky ligands (Rʹ = Tbt, Ar*, SiMe(SitBu3)2, and SiiPrDis2) using Hartree-Fock calculations (RHF/3-21G*). The TbtE13≡Bi=Tbt, Ar*=E13≡Bi=Ar*, SiMe(SitBu3)2=E13≡Bi=SiMe(SitBu3)2, and SiiPrDis2=E13≡Bi=SiiPrDis2 (E =B, Al, Ga, In, and Tl) are used as model reactants in this work. It is known that the Hartree-Fock level of theory is insufficient for even a qualitative description of the chemical potential energy surface, so these stationary points were then further calculated at the B3LYP/LANL2DZ+dp level, using the OPT=READFC keyword with a tight convergence option (maximum gradient convergence tolerance = 5.0 × 10-5 hartree/bohr). Because of the limitations of the available CPU time and memory size, frequencies were not calculated for the triply bonded RʹE13≡BiRʹ systems with bulky ligands (Rʹ) at the B3LYP/LANL2DZ+dp level of theory. As a result, the zero-point energies and the Gibbs free energies for B3LYP/LANL2DZ+dp cannot be applied to these systems.
In order to understand the bonding interactions in the R=E13≡Bi=R molecule, R=E13≡Bi=R is divided into one E13=R and one Bi=R fragment. The theoretical calculations for these two fragments indicate that the ground states of E13=R and Bi=R are singlet and triplet states, respectively (vide infra). Therefore, there are two possible interaction modes (A and B) between the E13=R and Bi=R moieties in the formation of the triply bonded R=E13≡Bi=R species, as schematically illustrated in Figure 1. In model (A), both E=R and Bi=R units exist as triplet monomers. In this way, the combination between the group 13 element and bismuth can be considered as a triple bond, since it consists of 2 π bonds and 1 donor-acceptor σ bond, for these 2 triplet fragments. As a result, this bonding model allows a linear structure, as shown in Figure 1(A). In model (B), both E13=R and Bi=R units still exist as triplets, so this bonding scheme contains one σ bond and one p-π bond (indicated by two dashed lines), plus one donor-acceptor π-bond because of coupling between the lone pair in Bi=R and the empty p orbital at the E13 atom (indicated by the arrow). Accordingly, this bonding pattern results in a bent structure, as shown in Figure 1(B). The importance of the RE13←BiR donor-acceptor interaction is emphasized, as it is essential for the stabilization of the nonlinear structure. These analyses are used to explain the geometrical structures of triply bonded RE13≡BiR species in the following sections.
Figure 1.
Two interaction models, A and B, in forming triply bonded RE13≡BiR species.
3.2. Small ligands on substituted RE13≡BiR
Small ligands, such as R = F, OH, H, CH3, and SiH3, are firstly chosen to study the geometries of the RE13≡BiR (E13 = B, Al, Ga, In, and Tl) species. As mentioned in the Introduction, neither experimental nor theoretical results for the triply bonded RE13≡BiR species are available to allow a definitive comparison. As a result, three DFT methods were used (i.e., M06-2X/Def2-TZVP, B3PW91/Def2-TZVP, and B3LYP/LANL2DZ+dp) to examine their molecular properties. The selected geometrical parameters, natural charge densities (QE13 and QBi), binding energies (BE), and Wiberg bond order (BO) [63, 64] are shown in Table 1 (RB≡BiR), Table 2 (RAl≡BiR), Table 3 (RGa≡BiR), Table 4 (RIn≡BiR), and Table 5 (RTl≡BiR).
R
F
OH
H
CH3
SiH3
B≡Bi (Å)
2.218
2.202
2.091
2.141
2.075
−2.210
−2.199
−2.083
−2.137
−2.084
[2.196]
[2.196]
[2.083]
[2.140]
[2.085]
∠R—B—Bi (°)
177.6
176
163.6
176.9
170.9
−178.8
−175.9
−163.6
−176.9
−169.4
[178.1]
[176.1]
[163.9]
[174.7]
[171.9]
∠B—Bi—R (°)
80.89
91.96
34.78
90.62
58.89
−88.58
−90.21
−34.83
−90.26
−58.47
[87.52]
[89.53]
[38.88]
[99.39]
[59.00]
∠R—B—Bi—R (°)
179.8
77.43
180
173.3
179.7
−179.1
−75.70
−180.0
−173.5
−179.5
[179.5]
[76.80]
[180.0]
[179.9]
[180.0]
QB(1)
0.1096
−0.0543
−0.3684
−0.3023
−0.5098
−0.124
(−0.0372)
(−0.2262)
(−0.1390)
(−0.4100)
[0.2303]
[0.0511]
[−0.1623]
[−0.01010]
[−0.4101]
QBi(2)
0.4759
0.3569
0.2189
0.1881
0.1784
−0.4975
−0.3431
−0.1331
−0.1602
−0.103
[0.4983]
[0.3552]
[0.1870]
[0.1430]
[0.1520]
Table 1.
Selected geometrical parameters, natural charge densities (QB and QBi), binding energies (BE), and Wiberg bond orders (BO) of RB≡BiR at the M06-2X/Def2-TZVP, B3PW91/Def2-TZVP (in round bracket), and B3LYP/LANL2DZ+dp (in square bracket) levels.
Notes: (1) The natural charge density on the central boron atom. (2) The natural charge density on the central bismuth atom. (3) BE = E (triplet state of R=B) + E (triplet state of R=Bi) – E(RB≡BiR). (4) Wiberg bond orders for the B=Bi bonds, see Ref. [18].
R
F
OH
H
CH3
SiH3
Al≡Bi (Å)
2.604
2.606
2.439
2.529
2.501
(2.601)
(2.601)
(2.463)
(2.539)
(2.532)
[2.621]
[2.624]
[2.483]
[2.561]
[2.542]
∠R—Al—Bi (°)
176.8
173.4
170.7
177.7
172.5
(175.4)
(172.9)
(168.1)
(177.6)
(170.4)
[177.3]
[174.2]
[166.9]
[177.1]
[174.5]
∠Al—Bi—R (°)
83.16
84.20
48.09
92.52
62.57
(84.59)
(85.35)
(49.85)
(92.93)
(61.82)
[87.00]
[88.32]
[51.00]
[93.77]
[64.03]
∠R—Al—Bi—R (°)
180.0
177.3
180.0
179.9
179.9
(180.0)
(176.0)
(180.0)
(179.6)
(179.8)
[180.0]
178.0]
[180.0]
[179.6]
[180.0]
QAl(1)
0.5031
0.3942
0.1493
0.2692
0.1841
(0.4904)
(0.3918)
(0.1417)
(0.2544)
(0.2145)
[0.6664]
[0.4315]
[0.3786]
[0.2414]
[0.1517]
QBi(2)
0.3947
0.2709
−0.05788
0.03761
−0.1384
(0.3196)
(0.1834)
(−0.04954)
(0.02100)
(−0.07446)
[0.3044]
[0.1982]
[0.03410]
[−0.05262]
[−0.1074]
BE (kcal mol−1) (3)
22.61
20.28
50.55
38.69
53.41
(30.36)
(31.77)
(85.64)
(63.54)
(57.96)
[25.47]
[20.51]
[53.65]
[42.77]
[53.47]
Wiberg BO (4)
1.393
1.403
1.746
1.634
1.602
(1.509)
(1.511)
(1.798)
(1.690)
(1.615)
[1.521]
[1.516]
[1.787]
[1.706]
[1.653]
Table 2.
Selected geometrical parameters, natural charge densities (QAl and QBi), binding energies (BE), and Wiberg bond orders (BO) of RAl≡BiR at the M06-2X/Def2-TZVP, B3PW91/Def2-TZVP (in round bracket), and B3LYP/LANL2DZ+dp (in square bracket) levels.
Notes: (1) The natural charge density on the central aluminum atom. (2) The natural charge density on the central bismuth atom. (3) BE = E (triplet state of R=Al) + E (triplet state of R=Bi) – E(RAl≡BiR). (4) Wiberg bond orders for the Al=Bi bonds, see Refs. [63, 64].
R
F
OH
H
CH3
SiH3
Ga≡Bi (Å)
2.639
2.625
2.463
2.543
2.512
(2.602)
(2.621)
(2.465)
(2.524)
(2.510)
[2.632]
[2.629]
[2.487]
[2.550]
[2.520]
∠R—Ga—Bi (°)
179.7
175.0
166.5
178.9
178.7
(178.3)
(173.3)
(166.2)
(177.8)
(177.6)
[177.3]
[175.5]
[167.0]
[177.3]
[177.0]
∠Ga—Bi—R (°)
86.32
86.85
52.56
91.27
65.56
(88.49)
(88.52)
(56.24)
(92.86)
(66.28)
[88.18]
[90.75]
[59.49]
[93.37]
[69.82]
∠R—Ga—Bi—R (°)
179.5
157.1
180.0
179.2
175.8
(180.0)
(159.8)
(180.0)
(178.8)
(179.9)
[180.0]
[158.0]
[180.0]
[179.3]
[180.0]
QGa(1)
0.6246
0.5224
0.2127
0.2266
0.1845
(0.5012)
(0.3464)
(0.1135)
(0.2356)
(0.1507)
[0.5700]
[0.3813]
[0.3031]
[0.1984]
[0.07925]
QBi(2)
0.3696
0.2435
−0.1367
0.03356
−0.2002
(0.3574)
(0.2743)
(−0.04212)
(0.05503)
(−0.05512)
[0.4000]
[0.2395]
[0.06523]
[−0.01620]
[−0.08931]
BE (kcal mol−1) (3)
18.03
16.41
45.28
46.24
46.10
(22.92)
(26.32)
(79.05)
(60.77)
(49.96)
[20.80]
[16.61]
[49.49]
[40.12]
[48.61]
Wiberg BO (4)
1.286
1.335
1.718
1.578
1.653
(1.382)
(1.393)
(1.787)
(1.633)
(1.646)
[1.403]
[1.431]
[1.758]
[1.656]
[1.673]
Table 3.
Selected geometrical parameters, natural charge densities (QGa and QBi), binding energies (BE), and Wiberg bond orders (BO) of RGa≡BiR at the M06-2X/Def2-TZVP, B3PW91/Def2-TZVP (in round bracket), and B3LYP/LANL2DZ+dp (in square bracket) levels.
Notes: (1) The natural charge density on the central gallium atom. (2) The natural charge density on the central bismuth atom. (3) BE = E (triplet state of R=Ga) + E (triplet state of R=Bi) – E(RGa≡BiR). (4) Wiberg bond orders for the Ga=Bi bonds, see Refs. [63, 64].
R
F
OH
H
CH3
SiH3
In≡Bi (Å)
2.804
2.790
2.659
2.696
2.667
(2.802)
(2.700)
(2.691)
(2.719)
(2.692)
[2.790]
[2.795]
[2.673]
[2.712]
[2.683]
∠R—In—Bi (°)
179.6
173.9
168.3
179.1
173.8
(178.0)
(172.2)
(175.2)
(177.3)
(174.3)
[177.0]
[174.5]
[174.1]
[177.6]
[174.7]
∠In—Bi—R (°)
84.16
85.14
67.00
92.20
70.37
(87.83)
(89.71)
(77.82)
(94.83)
(75.05)
[87.43]
[90.79]
[74.35]
[94.16]
[74.37]
∠R—In—Bi—R (°)
179.9
176.1
180.0
178.3
178.9
(180.0)
(177.3)
(180.0)
(179.1)
(177.5)
[180.0]
[176.5]
[180.0]
[179.4]
[179.8]
QIn(1)
0.7021
0.6352
0.3755
0.3297
0.3650
(0.5692)
(0.4640)
(0.2561)
(0.3403)
(0.2872)
[0.7571]
[0.5053]
[0.4055]
[0.3044]
[0.1756]
QBi(2)
0.3973
0.2452
−0.2474
−0.01187
−0.2599
(0.4000)
(0.2511)
(−0.08703)
(0.04410)
(−0.08023)
[0.3468]
[0.2141]
[0.02620]
[−0.05735]
[−0.1365]
BE (kcal mol−1) (3)
14.66
13.17
39.19
36.87
39.28
(15.06)
(12.88)
(42.01)
(35.00)
(40.94)
[18.80]
[13.70]
[44.04]
[35.54]
[41.83]
Wiberg BO (4)
1.312
1.403
1.590
1.543
1.553
(1.308)
(1.334)
(1.601)
(1.539)
(1.546)
[1.323]
[1.336]
[1.615]
[1.548]
[1.549]
Table 4.
Selected geometrical parameters, natural charge densities (QIn and QBi), binding energies (BE), and Wiberg bond orders (BO) of RIn≡BiR at the M06-2X/Def2-TZVP, B3PW91/Def2-TZVP (in round bracket), and B3LYP/LANL2DZ+dp (in square bracket) levels.
Notes: (1) The natural charge density on the central indium atom. (2) The natural charge density on the central bismuth atom. (3) BE = E (triplet state of R=In) + E (triplet state of R=Bi) – E(RIn≡BiR). (4) Wiberg bond orders for the In=Bi bonds, see Refs. [63, 64].
R
F
OH
H
CH3
SiH3
Tl≡Bi (Å)
2.859
2.843
2.713
2.742
2.707
(2.812)
(2.803)
(2.698)
(2.725)
(2.705)
[2.819]
[2.822]
[2.679]
[2.713]
[2.682]
∠R—Tl—Bi (°)
175.9
173.5
175.7
179.6
174.4
(178.8)
(172.5)
(176.6)
(178.5)
(174.7)
[177.2]
[174.4]
[176.3]
[178.5]
[175.9]
∠Tl—Bi—R (°)
81.34
86.72
78.87
91.91
76.03
(87.73)
(89.82)
(79.00)
(93.54)
(76.50)
[87.92]
[92.34]
[78.86]
[93.25]
[80.00]
∠R—Tl—Bi—R (°)
180.0
143.7
180.0
172.1
178.9
(179.9)
(132.9)
(179.9)
(178.6)
(179.9)
[180.0]
[130.6]
[180.0]
[180.0]
[179.2]
QTl(1)
0.6481
0.5672
0.3014
0.4162
0.2665
(0.6614)
(0.5879)
(0.2284)
(0.2746)
(0.3510)
[0.7100]
[0.4812]
[0.3536]
[0.2734]
[0.1601]
QBi(2)
0.4752
0.3214
−0.1836
0.008121
−0.2245
(0.3615)
(0.2201)
(−0.05213)
(−0.1282)
(−0.09637)
[0.3854]
[0.2455]
[0.04813]
[−0.03131]
[−0.1282]
BE (kcal mol−1) (5)
7.90
6.61
30.74
26.94
30.56
(2.98)
(8.17)
(48.12)
(35.39)
(29.13)
[11.34]
[7.38]
[37.14]
[31.09]
[35.03]
Wiberg BO (6)
1.000
1.132
1.652
1.448
1.792
(1.121)
(1.254)
(1.765)
(1.514)
(1.824)
[1.112]
[1.212]
[1.756]
[1.568]
[1.652]
Table 5.
Selected geometrical parameters, natural charge densities (QTl and QBi), binding energies (BE), and Wiberg bond orders (BO) of RTl≡BiR at the M06-2X/Def2-TZVP, B3PW91/Def2-TZVP (in round bracket), and B3LYP/LANL2DZ+dp (in square bracket) levels.
Notes: (1) The natural charge density on the central thallium atom. (2) The natural charge density on the central bismuth atom. (3) BE = E (triplet state of R=Tl) + E (triplet state of R=Bi) – E(RTl≡BiR). (4) Wiberg bond orders for the Tl=Bi bonds, see Refs. [63, 64].
Several important conclusions can be found in Tables 1–5, which are shown as follows:
As can be seen from Tables 1–5, the geometrical parameters of the RE13≡BiR triple bond species are quite analogous at the three levels employed. For instance, the predicted triple bond length for small ligands on RB≡BiR is 2.075–2.218 Å (M06-2X/Def2-TZVP), 2.083–2.210 Å (B3PW91/Def2-TZVP), and 2.083–2.196 Å (B3LYP/LANL2DZ+dp). For RAl≡BiR, the Al≡Bi triple bond length for small ligands is predicted to be 2.439–2.606 Å (M06-2X/Def2-TZVP), 2.463–2.601 Å (B3PW91/Def2-TZVP), and 2.483–2.624 Å (B3LYP/LANL2DZ+dp). For RGa≡BiR, the Ga≡Bi triple bond length for small ligands is predicted to be 2.463–2.639 Å (M06-2X/Def2-TZVP), 2.465–2.621 Å (B3PW91/Def2-TZVP), and 2.487–2.632 Å (B3LYP/LANL2DZ+dp). For RIn≡BiR, the In≡Bi triple bond length for small ligands is predicted to be 2.659–2.804 Å (M06-2X/Def2-TZVP), 2.691–2.802 Å (B3PW91/Def2-TZVP), and 2.673–2.795 Å (B3LYP/LANL2DZ+dp). For RTl≡BiR, the Tl≡Bi triple bond length for small ligands is predicted to be 2.707–2.859 Å (M06-2X/Def2-TZVP), 2.698–2.812 Å (B3PW91/Def2-TZVP), and 2.679–2.822 Å (B3LYP/LANL2DZ+dp).
It is apparent from Tables 1–5 that an acute bond angle ∠E13=Bi=R (close to 90°) in the triply bonded molecule RE13≡BiR is favored. The reason for this can be attributed to the “orbital nonhybridization effect,” also known as the “inert s-pair effect” [65–68], as discussed previously. Accordingly, these phenomena strongly indicate that mode (B) (Figure 1) is preferred in the RE≡BiR molecule, for which bent geometry is favored.
The Wiberg bond orders (WBOs) [63, 64] on the substituted RE13≡BiR compounds are also given in Tables 1–5. For all the triply bonded RE13≡BiR molecules with small substituents, their WBOs were computed to be less than 2.0, except for the cases of HB≡BiH and (SiH3)B≡Bi(SiH3). These WBO values imply that the bonding structure of RE13≡BiR may be due to the resonance structures, [I] and [II]. That is to say, the E13=Bi bond could be either double or triple bonds. From Tables 1–5, it seems that the resonance structure [II] prevails for the small ligands on the substituted RE13≡BiR species studied in this work. Indeed, since it is known that the electronegativities decrease in the order B (2.051) > Bi (2.01) > Tl (1.789) > Ga (1.756) > In (1.656) > Al (1.613) [69], the bonding mode of RE13≡BiR should prefer to adopt resonance structure [II] (Scheme 2).
With regard to the stability of RE13BiR, the results of theoretical calculations on the energy surface of the model RE13BiR (R = F, OH, H, CH3, and SiH3) system are depicted in Figures 2–6.
Figure 2.
Relative Gibbs free energy surfaces for RB≡BiR (R = F, OH, H, CH3, and SiH3). Energies are in kcal/mol, calculated at M06-2X/Def2-TZVP, B3PW91/Def2-TZVP, and B3LYP/LANL2DZ+dp levels of theory. For details see the text and Table 1.
Figure 3.
Relative Gibbs free energy surfaces for RAl≡BiR (R = F, OH, H, CH3, and SiH3). Energies are in kcal/mol, calculated at M06-2X/Def2-TZVP, B3PW91/Def2-TZVP, and B3LYP/LANL2DZ+dp levels of theory. For details see the text and Table 2.
Figure 4.
Relative Gibbs free energy surfaces for RGa≡BiR (R = F, OH, H, CH3, and SiH3). Energies are in kcal/mol, calculated at M06-2X/Def2-TZVP, B3PW91/Def2-TZVP, and B3LYP/LANL2DZ+dp levels of theory. For details see the text and Table 3.
Figure 5.
Relative Gibbs free energy surfaces for RIn≡BiR (R = F, OH, H, CH3, and SiH3). Energies are in kcal/mol, calculated at M06-2X/Def2-TZVP, B3PW91/Def2-TZVP, and B3LYP/LANL2DZ+dp levels of theory. For details see the text and Table 4.
Figure 6.
Relative Gibbs free energy surfaces for RTl≡BiR (R = F, OH, H, CH3, and SiH3). Energies are in kcal/mol, calculated at M06-2X/Def2-TZVP, B3PW91/Def2-TZVP, and B3LYP/LANL2DZ+dp levels of theory. For details see the text and Table 5.
This system exhibits a number of stationary points, including local minima that correspond to RE13≡BiR, R2E13=Bi:, :E13=BiR2, and the saddle points connecting them. The transition structures that separate the three stable molecular forms involve a successive unimolecular 1,2-shift TS1 (from RE13≡BiR to R2E13=Bi:) and a 1,2-shift TS2 (from RE13≡BiR to :E13=BiR2). As shown in Figures 1–5, these theoretical studies using the M06-2X, B3PW91, and B3LYP levels show that the RE13≡BiR species are local minima on the singlet potential energy surface, but they are neither kinetically nor thermodynamically stable for small substituents, except for the case of (SiH3)B≡Bi(SiH3). As a result, these triply bonded structures RE13≡BiR seem to be unstable on the singlet energy surface and undergo unimolecular rearrangement to the doubly bonded isomer. In brief, these triply bonded molecules (RE13≡BiR) possessing the small substituents are predicted to be a kinetically unstable isomer, so these could not be isolated in a matrix or even as transient intermediates.
3.3. Large ligands on substituted RʹE13≡BiRʹ
According to the above conclusions for the cases of small substituents, it is necessary to determine whether bulky substituents can destabilize R2E13=Bi: and :E13=BiR2 relative to RE13≡BiR (E13 = B, Al, Ga, In, and Tl), due to severe steric overcrowding. From Figure 7, it is easily anticipated that the presence of extremely bulky substituents at both ends of the RE13≡BiR compounds protects its triple bond from intermolecular reactions, such as polymerization. In order to examine the effect of bulky substituents, the structures of RʹE13≡BiRʹ optimized for Rʹ = Tbt, Ar*, SiMe(SitBu3)2, and SiiPrDis2 (Scheme 1) at the B3LYP/LANL2DZ+dp level. Selected geometrical parameters, natural charge densities on the central group 13 elements and bismuth (QE13 and QBi), binding energies (BE), and Wiberg bond order (BO) [69, 70] are summarized in Tables 6–10.
Rʹ
Tbt
Ar*
SiMe(SitBu3)2
SiiPrDis2
B≡Bi (Å)
2.230
2.214
2.117
2.131
∠Rʹ—B—Bi (°)
177.3
110.3
112.9
113.6
∠B—Bi—Rʹ (°)
115.6
115.5
112.5
114.3
∠Rʹ—B—Bi—Rʹ (°)
173.7
172.3
170.4
175.3
QB(1)
−0.4310
−0.1711
−0.3251
−0.4742
QBi(2)
0.2915
0.3004
0.1426
0.1071
BE (kcal mol−1) (3)
37.58
41.68
36.25
51.07
Wiberg BO (4)
2.385
2.249
2.640
2.701
∆H1 (kcal mol−1) (5)
62.6
61.04
76.52
77.24
∆H2 (kcal mol−1) (6)
98.51
88.38
68.72
78.13
Table 6.
Geometrical parameters, nature charge densities (QB and QBi), binding energies (BE), and Wiberg bond order (BO) of RʹB≡BiRʹ at the B3LYP/LANL2DZ+dp level of theory. Also see Figure 7.
Notes: (1) The natural charge density on the central boron atom. (2) The natural charge density on the central bismuth atom. (3) BE = E (triplet state of B−Rʹ) + E (triplet state of Bi−Rʹ) – E(RʹB≡BiRʹ). (4) Wiberg Bond Orders for the B−Bi bond, see Refs. [63, 64]. (5) ∆H1 = E(:B=BiRʹ2) – E(RʹB≡BiRʹ); see Scheme 3. (6) ∆H2 = E(Rʹ2B=Bi:) – E(RʹB≡BiRʹ); see Scheme 3
Rʹ
Tbt
Ar*
SiMe(SitBu3)2
SiiPrDis2
Al≡Bi (Å)
2.562
2.561
2.463
2.461
∠Rʹ—Al—Bi (°)
178.0
113.6
115.4
113.3
∠Al—Bi—Rʹ (°)
113.4
115.5
112.2
109.0
∠Rʹ—Al—Bi—Rʹ (°)
167.1
165.8
173.2
174.7
QAl(1)
0.4171
0.4111
0.2173
0.1585
QBi(2)
0.0773
0.2208
−0.1031
−0.1862
BE (kcal mol−1) (3)
38.62
66.78
33.65
31.76
Wiberg BO (4)
2.092
2.023
2.204
2.259
∆H1 (kcal mol−1) (5)
64.52
63.77
77.71
73.68
∆H2 (kcal mol−1) (6)
57.43
67.81
71.86
76.62
Table 7.
Geometrical parameters, nature charge densities (QAl and QBi), binding energies (BE), and Wiberg bond order (BO) of RʹAl≡BiRʹ at the B3LYP/LANL2DZ+dp level of theory. Also see Figure 7.
Notes: (1) The natural charge density on the central aluminum atom. (2) The natural charge density on the central bismuth atom. (3) BE = E (triplet state of Al=Rʹ) + E (triplet state of Bi=Rʹ) – E(RʹAl≡BiRʹ). (4) Wiberg Bond Orders for the Al=Bi bond, see Refs. [63, 64]. (5) ∆H1 = E(:Al=BiRʹ2) – E(RʹAl≡BiRʹ); see Scheme 3. (6) ∆H2 = E(Rʹ2Al=Bi:) – E(RʹAl≡BiRʹ); see Scheme 3.
Rʹ
Tbt
Ar*
SiMe(SitBu3)2
SiiPrDis2
Ga≡Bi (Å)
2.578
2.576
2.580
2.579
∠Rʹ—Ga—Bi (°)
178.1
113.4
115.2
112.1
∠Ga—Bi—Rʹ (°)
113.4
115.7
112.0
110.1
∠Rʹ—Ga—Bi—Rʹ (°)
167.9
164.1
175.4
178.5
QGa(1)
0.240
0.196
0.069
0.012
QBi(2)
0.120
0.261
−0.055
−0.140
BE (kcal mol−1) (3)
43.73
39.28
35.54
32.92
Wiberg BO (4)
2.091
2.181
2.262
2.313
∆H1 (kcal mol−1) (5)
68.10
69.08
61.74
58.83
∆H2 (kcal mol−1) (6)
78.07
71.28
77.43
64.13
Table 8.
Geometrical parameters, nature charge densities (QGa and QBi), binding energies (BE), and Wiberg bond order (BO) of RʹGa≡BiRʹ at the B3LYP/LANL2DZ+dp level of theory. Also see Figure 7.
Notes: (1) The natural charge density on the central gallium atom. (2) The natural charge density on the central bismuth atom. (3) BE = E (triplet state of Ga=Rʹ) + E (triplet state of Bi=Rʹ) – E(RʹGa≡BiRʹ). (4) Wiberg bond orders for the Ga=Bi bond, see Refs. [63, 64]. (5) ∆H1 = E(:Ga = BiRʹ2) – E(RʹGa≡BiRʹ); see Scheme 3. (6) ∆H2 = E(Rʹ2Ga=Bi:) – E(RʹGa≡BiRʹ); see Scheme 3.
Rʹ
Tbt
Ar*
SiMe(SitBu3)2
SiiPrDis2
In≡Bi (Å)
2.737
2.779
2.615
2.678
∠Rʹ—In—Bi (°)
178.7
111.7
110.0
110.9
∠In—Bi—Rʹ (°)
112.5
113.0
110.6
111.7
∠Rʹ—In—Bi—Rʹ (°)
170.7
174.6
164.3
162.0
QIn(1)
0.299
0.345
0.179
0.101
QBi(2)
0.066
0.293
−0.126
−0.132
BE (kcal mol−1) (3)
63.45
45.97
36.20
37.05
Wiberg BO (4)
2.052
2.153
2.211
2.304
∆H1 (kcal mol−1) (5)
64.06
60.17
55.72
62.99
∆H2 (kcal mol−1) (6)
79.38
61.44
56.03
67.61
Table 9.
Geometrical parameters, nature charge densities (QIn and QBi), binding energies (BE), and Wiberg bond order (BO) of RʹIn≡BiRʹ at the B3LYP/LANL2DZ+dp level of theory. Also see Figure 7.
Notes: (1) The natural charge density on the central indium atom. (2) The natural charge density on the central bismuth atom. (3) BE = E (triplet state of In=Rʹ) + E (triplet state of Bi=Rʹ) – E(RʹIn≡BiRʹ). (4) Wiberg Bond Orders for the In=Bi bond, see Refs. [63, 64]. (5) ∆H1 = E(:In = BiRʹ2) – E(RʹIn≡BiRʹ); see Scheme 3. (6) ∆H2 = E(Rʹ2In=Bi:) – E(RʹIn≡BiRʹ); see Scheme 3.
Rʹ
Tbt
Ar*
SiMe(SitBu3)2
SiiPrDis2
Tl≡Bi (Å)
2.816
2.833
2.820
2.789
∠Rʹ—Tl—Bi (°)
148.2
146.7
164.4
152.4
∠Tl—Bi—Rʹ (°)
116.5
121.4
114.1
125.1
∠Rʹ—Tl—Bi—R (°)
169.5
171.4
176.3
175.8
QTl(1)
0.3323
0.4221
0.1504
0.1282
QBi(2)
−0.0921
−0.0652
−0.3925
−0.3491
BE (kcal mol−1) (3)
41.66
37.59
36.66
51.07
Wiberg BO (4)
2.081
2.052
2.105
2.128
∆H1 (kcal mol−1) (5)
68.66
64.52
63.67
72.12
∆H2 (kcal mol−1) (6)
61.54
58.19
68.73
64.61
Table 10.
Geometrical parameters, nature charge densities (QTl and QBi), binding energies (BE), and Wiberg bond order (BO) of RʹTl≡BiRʹ at the B3LYP/LANL2DZ+dp level of theory. Also see Figure 7.
Notes: (1) The natural charge density on the central thallium atom. (2) The natural charge density on the central bismuth atom. (3) BE = E (triplet state of Tl=Rʹ) + E (triplet state of Bi=Rʹ) – E(RʹTl≡BiRʹ). (4) Wiberg bond orders for the Tl=Bi bond, see Refs. [63, 64]. (5) ∆H1 = E(:Tl = BiRʹ2) – E(RʹTl≡BiRʹ); see Scheme 3. (6) ∆H2 = E(Rʹ2Tl = Bi:) – E(RʹTl≡BiRʹ); see Scheme 3.
Figure 7.
The optimized structures of RʹE13≡BiRʹ (E13 = B, Al, Ga, In, and Tl; Rʹ = Tbt, Ar*, SiMe(SitBu3)2, and SiiPrDis2) at the B3LYP/LANL2DZ+dp level of theory. For details see the text and Tables 6–10.
The computational results given in Tables 6–10 estimate that the E13≡Bi triple bond distances (Å) are about 2.117–2.230 (E13 = B), 2.461−2.562 (E13 = Al), 2.576–2.580(E13 = Ga), 2.615–2.779 (E13 = In), and 2.789–2.833 (E13 = Tl), respectively. Again, these theoretically predicted values are much shorter than the available experimentally determined E13=Bi single bond lengths [36, 70–72]. This strongly implies that the central group 13 element (E13) and bismuth in the RʹE13≡BiRʹ (Rʹ = Tbt, Ar*, SiMe(SitBu3)2, and SiiPrDis2) species are triply bonded. Indeed, as shown in Tables 6–10, the RʹE13≡BiRʹ molecules accompanied by bulky ligands can effectively produce the triply bonded species. That is, the WBOs in Tables 6–10 (with larger ligands) are apparently larger than those in Tables 1–5 (with smaller ligands). Additionally, from Tables 6–10, the central E13≡Bi bond lengths calculated for Rʹ = Tbt and Ar* are an average 0.095Å longer than those calculated for Rʹ = SiMe(SitBu3)2 and SiiPrDis2, respectively. The reason for these differences is that the Tbt and Ar* groups are electronegative, but the SiMe(SitBu3)2 and SiiPrDis2 ligands are electropositive. Further, the short length of the E13≡Bi bond in the RʹE≡BiRʹ species can be understood by noting that both SiMe(SitBu3)2 and SiiPrDis2 are more electropositive than the small substituents, as mentioned earlier.
Similar to the small ligands, these DFT results demonstrate that all the RʹE13BiRʹ molecules that possess bulky substituents (Rʹ) adopt a bent geometry, as illustrated in Figure 7. Our theoretical computations show that model (B), given in Figure 1, still predominates and can be used to interpret the geometries of the RʹE13≡BiRʹ systems that bear bulky substituents.
As shown in Tables 6–10, the RʹE13≡BiRʹ molecules can be separated into two fragments in solution, when the substituent Rʹ becomes bulkier. The BE that is essential to break the central E13≡Bi bond was computed to be at least > 32 kcal/mol for Rʹ = Tbt, Ar*, SiMe(SitBu3)2, and SiiPrDis2, for the B3LYP/LANL2DZ+dp method, as given in Tables 6–10. These BE values show that the central E13 and bismuth elements are strongly bonded and RʹE13≡BiRʹ molecules that contain bulky substituents do not dissociate in solution. Namely, the larger the dissociation energy of the E13≡Bi bond, the shorter and stronger the E13≡Bi triple bond.
As predicted previously, bulky groups destabilize the 1,2-Rʹ migrated isomers because they crowd around one end of the central E13≡Bi bond. As a consequence, the bulky substituents (Rʹ) can prevent the isomerization of RʹE13≡BiRʹ compounds, as outlined in Scheme 3 and Tables 6–10. The B3LYP/LANL2DZ+dp calculations indicate that the RʹE13≡BiRʹ species with Tbt, Ar*, SiMe(SitBu3)2, and SiiPrDis2 substituents (∆H1 and ∆H2) are at least 56 kcal/mol more stable than the 1,2-Rʹ shifted isomers, respectively. These theoretical results suggest that both doubly bonded Rʹ2E13=Bi: and :E13=BiRʹ2 isomers are kinetically and thermodynamically unstable, so they rearrange spontaneously to the global minimum RʹE13≡BiRʹ triply bonded molecules, provided that significantly bulky groups are employed.
Theoretical values from the natural bond orbital (NBO) [63, 64] and natural resonance theory (NRT) [73–75] analyses of the RʹE13≡BiRʹ molecules, computed at the B3LYP/LANL2DZ+dp level of theory, are summarized in Table 11 (E13 = B), Table 12 (E13 = Al), Table 13 (E13 = Ga), Table 14 (E13 = In), and Table 15 (E13 = Tl).
R′B≡BiR′
WBI
NBO analysis
NRT analysis
Occupancy
Hybridization
Polarization
Total/covalent/ionic
Resonance weight
R′=Tbt
2.39
σ = 1.95
σ: 0.7870 B (sp0.90) + 0.6170 Bi (sp9.90)
61.93% (B)
2.01/1.24/0.77
B=Bi: 12.58%
38.07% (Bi)
B=Bi: 53.81%
π = 1.93
π: 0.5938 B (sp1.00) + 0.8046 Bi (sp1.00)
35.26% (B)
B≡Bi: 33.61%
64.74% (Bi)
R′ = Ar*
2.25
σ = 1.94
σ: 0.8058 B (sp0.74) + 0.5922 Bi (sp19.46)
64.93% (B)
1.95/1.30/0.65
B=Bi: 6.78%
35.07% (Bi)
B=Bi: 62.97%
π = 1.90
π: 0.5587 B (sp99.99) + 0.8294 Bi (sp64.69)
31.22% (B)
B≡Bi: 30.25%
68.78% (Bi)
R′ = SiMe(SitBu3)2
2.64
σ = 1.96
σ: 0.7812 B (sp0.96) + 0.6242 Bi (sp10.68)
61.03% (B)
2.27/1.49/0.78
B=Bi: 5.77%
38.97% (Bi)
B=Bi: 54.1%
π = 1.89
π: 0.6146 B (sp62.48) + 0.7889 Bi (sp19.73)
37.77% (B)
B≡Bi: 40.11%
62.23% (Bi)
R′ = SiiPrDis2
2.7
σ = 1.83
σ: 0.6502 B (sp4.29) + 0.7598 Bi (sp1.07)
42.27% (B)
2.31/1.52/0.79
B=Bi: 6.01%
57.73% (Bi)
B=Bi: 54.39%
π = 1.80
π: 0.5606 B (sp1.73) + 0.8281 Bi (sp4.99)
31.43% (B)
B≡Bi: 39.96%
68.57% (Bi)
Table 11.
Selected results for the natural bond orbital (NBO) and natural resonance theory (NRT) analyses of RʹB≡BiRʹ compounds that have small substituents, at the B3LYP/LANL2DZ+dp level of theory [1–8, 76–80].
(1) The Wiberg bond index (WBI) for the B=Bi bond and occupancy of the corresponding σ and π bonding NBO: see Refs. [63, 64], and (2) the natural resonance theory (NRT): see Refs. [73–75].
R′Al≡BiR′
WBI
NBO analysis
NRT analysis
Occupancy
Hybridization
Polarization
Total/covalent/ionic
Resonance weight
R′ = Tbt
2.09
σ = 1.98
σ: 0.7538 Al (sp0.15) + 0.6571 Bi (sp22.99)
56.83% (Al)
2.12/1.10/1.02
Al=Bi: 12.76%
43.17% (Bi)
Al=Bi: 75.36%
π = 1.93
π: 0.4709 Al (sp1.00) + 0.8822 Bi (sp1.00)
22.17% (Al)
Al≡Bi: 11.88%
77.83% (Bi)
R′ = Ar*
2.02
σ = 1.84
σ: 0.7806 Al (sp0.15) + 0.6250 Bi (sp28.77)
60.93% (Al)
2.07/1.01/1.06
Al=Bi: 19.33%
39.07% (Bi)
Al=Bi: 74.20%
π = 1.94
π: 0.4960 Al (sp46.09) + 0.8673 Bi (sp15.43)
24.60% (Al)
Al≡Bi: 6.47%
75.40% (Bi)
R′ = SiMe(SitBu3)2
2.2
σ = 1.96
σ: 0.7169 Al (sp0.96) + 0.6971 Bi (sp21.26)
24.70% (Al)
2.24/1.38/0.86
Al=Bi: 11.69%
75.30% (Bi)
Al=Bi: 84.51%
π = 1.89
π: 0.8678 Al (sp19.21) + 0.4970 Bi (sp16.37)
37.77% (Al)
Al≡Bi: 3.80%
62.23% (Bi)
R′ = SiiPrDis2
2.26
σ = 1.86
σ: 0.7184 Al (sp0.93) + 0.6956 Bi (sp29.72)
51.61% (Al)
1.91/1.35/0.60
Al=Bi: 12.68%
48.39% (Bi)
Al=Bi: 83.75%
π = 1.90
π: 0.4430 Al (sp59.07) + 0.8965 Bi (sp35.38)
19.63% (Al)
Al≡Bi: 3.57%
80.37% (Bi)
Table 12.
Selected results for the natural bond orbital (NBO) and natural resonance theory (NRT) analyses of RʹAl≡BiRʹ compounds that have small substituents, at the B3LYP/LANL2DZ+dp level of theory [1–8, 76–80].
(1) The Wiberg bond index (WBI) for the Al=Bi bond and occupancy of the corresponding σ and π bonding NBO: see Refs. [63, 64], and (2) the natural resonance theory (NRT): see Refs. [73–75].
R′Ga≡BiR′
WBI
NBO analysis
NRT analysis
Occupancy
Hybridization
Polarization
Total/covalent/ionic
Resonance weight
R′ = Tbt
2.09
σ = 1.78
σ: 0.7338 Ga (sp1.04) + 0.6794 Bi (sp31.81)
53.85% (Ga)
2.09/1.36/0.73
Ga=Bi: 11.42%
46.15% (Bi)
Ga=Bi: 87.53%
π = 1.94
π: 0.4586 Ga (sp1.00) + 0.8886 Bi (sp1.00)
21.04% (Ga)
Ga≡Bi: 1.05%
78.96% (Bi)
R′ = Ar*
2.18
σ = 1.93
σ: 0.8142 Ga (sp0.12) + 0.5806 Bi (sp40.52)
66.29% (Ga)
2.05/1.30/0.75
Ga=Bi: 10.87%
33.71% (Bi)
Ga=Bi: 88.05%
π = 1.84
π: 0.4810 Ga (sp50.27) + 0.8767 Bi (sp14.17)
23.13% (Ga)
Ga≡Bi: 1.08%
76.87% (Bi)
R′ = SiMe(SitBu3)2
2.26
σ = 1.80
σ: 0.7393 Ga (sp0.97) + 0.6733 Bi (sp27.39)
54.66% (Ga)
2.11/1.35/0.76
Ga=Bi: 11.84%
67.33% (Bi)
Ga=Bi: 82.11%
π = 1.86
π: 0.4937 Ga (sp22.70) + 0.8696 Bi (sp17.00)
24.38% (Ga)
Ga≡Bi: 6.05%
75.62% (Bi)
R′ = SiiPrDis2
2.31
σ = 1.90
σ: 0.7462 Ga (sp0.92) + 0.6657 Bi (sp58.99)
55.68% (Ga)
1.93/1.40/0.53
Ga=Bi: 12.93%
44.32% (Bi)
Ga=Bi: 80.74%
π = 1.84
π: 0.4201 Ga (sp99.99) + 0.9075 Bi (sp99.99)
17.65% (Ga)
Ga≡Bi: 6.33%
82.35% (Bi)
Table 13.
Selected results for the natural bond orbital (NBO) and natural resonance theory (NRT) analyses of RʹGa≡BiRʹ compounds that have small substituents, at the B3LYP/LANL2DZ+dp level of theory [1–8, 76–80].
(1) The Wiberg bond index (WBI) for the Ga=Bi bond and occupancy of the corresponding σ and π bonding NBO: see Refs. [63, 64], and (2) the natural resonance theory (NRT): see Refs. [73–75].
R′In≡BiR′
WBI
NBO analysis
NRT analysis
Occupancy
Hybridization
Polarization
Total/covalent/ionic
Resonance weight
R′ = Tbt
2.05
σ = 1.78
σ: 0.7626 In (sp0.09) + 0.6469 Bi (sp50.74)
58.15% (In)
2.10/1.15/0.95
In=Bi: 14.33%
41.85% (Bi)
In=Bi: 76.37%
π = 1.94
π: 0.4230 In (sp99.99) + 0.9061 Bi (sp95.23)
17.85% (In)
In≡Bi: 0.93%
82.11% (Bi)
R′ = Ar*
2.15
σ = 1.97
σ: 0.7145 In (sp0.07) + 0.6996 Bi (sp21.13)
51.05% (In)
2.11/1.04/1.07
In=Bi: 11.10%
48.95% (Bi)
In=Bi: 85.07%
π = 1.94
π: 0.4774 In (sp99.99) + 0.8787Bi (sp99.99)
22.79% (In)
In≡Bi: 3.83%
77.21% (Bi)
R′ = SiMe(SitBu3)2
2.21
σ = 1.74
σ: 0.7433 In (sp0.99) + 0.6690 Bi (sp35.62)
55.25% (In)
2.14/1.22/0.92
In=Bi: 14.20%
44.75% (Bi)
In=Bi: 81.22%
π = 1.88
π: 0.4468 In (sp42.13) + 0.8696 Bi (sp12.11)
19.96% (In)
In≡Bi: 4.58%
80.04% (Bi)
R′ = SiiPrDis2
2.3
σ = 1.92
σ: 0.7341 In (sp53.22) + 0.6790 Bi (sp0.98)
46.11% (In)
1.88/1.27/0.61
In=Bi: 15.31%
53.89% (Bi)
In=Bi: 81.02%
π = 1.78
π: 0.4357 In (sp26.46) + 0.9001 Bi (sp99.99)
18.99% (In)
In≡Bi: 3.67%
81.01% (Bi)
Table 14.
Selected results for the natural bond orbital (NBO) and natural resonance theory (NRT) analyses of RʹIn≡BiRʹ compounds that have small substituents, at the B3LYP/LANL2DZ+dp level of theory [1–8, 76–80].
Notes: (1) The Wiberg bond index (WBI) for the In=Bi bond and occupancy of the corresponding σ and π bonding NBO: see Refs. [63, 64], and (2) the natural resonance theory (NRT): see Refs. [73–75].
R′Tl≡BiR′
WBI
NBO analysis
NRT analysis
Occupancy
Hybridization
Polarization
Total/covalent/ionic
Resonance weight
R′ = Tbt
2.08
σ = 1.96
σ:0.8268 Tl (sp0.07) + 0.5625 Bi (sp99.99)
68.36% (Tl)
2.15/1.81/0.34
Tl=Bi: 18.71%
31.64% (Bi)
Tl = Bi: 71.54%
π = 1.94
π:0.4315 In (sp99.99) + 0.9021 Bi (sp99.99)
18.61% (In)
Tl≡Bi: 9.75%
81.37% (Bi)
R′ = Ar*
2.05
σ = 1.97
σ: 0.8159 Tl (sp0.05) + 0.5782 Bi (sp99.99)
66.57% (Tl)
2.11/1.70/0.41
Tl=Bi: 21.11%
33.43% (Bi)
Tl = Bi: 70.15%
π = 1.95
π: 0.4788 In (sp99.99) + 0.8779 Bi (sp99.99)
22.92% (In)
Tl≡Bi: 8.74%
77.08% (Bi)
R′ = SiMe(SitBu3)2
2.1
σ = 1.98
σ: 0.7986 Tl (sp0.02) + 0.6019 Bi (sp31.50)
63.77% (Tl)
2.21/1.40/0.81
Tl=Bi: 16.13%
36.23% (Bi)
Tl = Bi: 76.20%
π = 1.92
π: 0.3890 Tl (sp99.99) + 0.9212 Bi (sp1.00)
15.13% (Tl)
Tl≡Bi: 7.67%
84.87% (Bi)
R′ = SiiPrDis2
2.13
σ = 1.98
σ: 0.7757 Tl (sp0.03) + 0.6311 Bi (sp23.28)
60.17% (Tl)
1.85/1.23/0.62
Tl=Bi: 20.21%
39.83% (Bi)
Tl=Bi: 74.69%
π = 1.91
π: 0.4149 Tl (sp99.99) + 0.9099 Bi (sp99.99)
17.22% (Tl)
Tl≡Bi: 5.10%
82.78% (Bi)
Table 15.
Selected results for the natural bond orbital (NBO) and natural resonance theory (NRT) analyses of RʹTl≡BiRʹ compounds that have small substituents, at the B3LYP/LANL2DZ+dp level of theory [1–8, 76–80].
Notes: (1) The Wiberg bond index (WBI) for the Tl=Bi bond and occupancy of the corresponding σ and π bonding NBO: see Refs. [63, 64], and (2) the natural resonance theory (NRT): see Refs. [73–75].
All the NBO values listed in Tables 11–15 demonstrate that there exists a weak triple bond, or perhaps a bond between a double and a triple, in the ethyne-like RʹE13≡BiRʹ molecule. For instance, the B3LYP/LANL2DZ+dp data for the NBO [63, 64] analyses of the B≡Bi bonding in SiMe(SitBu3)2=B≡Bi=SiMe(SitBu3)2, which shows that NBO(B≡Bi) = 0.615(2s2p52.48)B + 0.789(6s6p19.73)Bi, strongly suggests that the predominant bonding interaction between the B=SiMe(SitBu3)2 and the Bi=SiMe(SitBu3)2 fragments originates from 2p(B) ← 6p(Bi) donation. In other words, boron’s electron deficiency and π bond polarity are partially balanced by the donation of the bismuth lone pair into the empty boron p orbital. This, in turn, forms a hybrid π bond. Again, the polarization analyses using the NBO model indicate the presence of the B≡Bi π bonding orbital, 38% of which is composed of natural boron orbitals and 62% of natural bismuth orbitals. There is supporting evidence in Table 11 that reveals that the B≡Bi triple bond in SiMe(SitBu3)2=B≡Bi=SiMe(SitBu3)2 has a shorter single bond character (5.8%) and a shorter triple bond character (40.1%) but a larger double bond character (54.1%), because the covalent part of the NRT bond order (1.49) is shorter than its ionic part (0.78). The same can also be said of the other three RʹB≡BiRʹ molecules, as shown in Table 11 as well as other RʹE13≡BiRʹ compounds represented in Tables 12–15. These theoretical evidences strongly suggest that these RʹE13≡BiRʹ species have a weak triple bond.
4. Overview of RE13≡BiR (E = B, Al, Ga, In, and Tl) systems
This study of the effect of substituents on the possibilities of the existence of triply bonded RE13≡BiR allows the following conclusions to be drawn (Scheme 4):
The theoretical observations strongly demonstrate that bonding mode (B) is dominant in the triply bonded RE13≡BiR species, since their structures are bent to increase stability, due to electron transfer (denoted by arrows in Figure 1) as well as the relativistic effect [65–68].
The theoretical evidence shows that both the electronic and the steric effects of substituents are crucial to making the E13≡Bi triple bond synthetically accessible. Based on the present theoretical study, however, these E13≡Bi triple bonds should be weak, not as strong as the traditional C≡C triple bond. From our theoretical study, both bulky and electropositive substituents, such as the silyl groups demonstrated in Scheme 1, have a significant effect on the stability of E13≡Bi triply bonded compounds.
The authors are grateful to the National Center for High-Performance Computing of Taiwan in providing huge computing resources to facilitate this research. They also thank and the Ministry of Science and Technology of Taiwan for the financial support.
References
1.Power P P. π-Bonding and the lone pair effect in multiple bonds between heavier main group elements. Chem. Rev. 1999; 99:3463–3504.
2.Power P P. Silicon, germanium, tin and lead analogues of acetylenes. Chem. Commun. 2003; 17:2091–2101.
3.Lein M, Krapp A, Frenking G. Why do the heavy-atom analogues of acetylene E2H2 (E = Si-Pb) exhibit unusual structures? J. Am. Chem. Soc. 2005; 127:6290–6299.
4.Sekiguchi A, Ichinohe M, Kinjo R. The chemistry of disilyne with a genuine Si–Si triple bond: synthesis, structure, and reactivity. Bull. Chem. Soc. Jpn. 2006; 79:825–832.
5.Power P P. Bonding and reactivity of heavier group 14 element alkyne analogues. Organometallics 2007; 26:4362–4372.
6.Fischer R C, Power P P. π-bonding and the lone pair effect in multiple bonds involving heavier main group elements: developments in the new millennium. Chem. Rev. 2010; 110:3877–3923.
7.Sasamori T, Han J S, Hironaka K, Takagi N, Nagase S, Tokitoh N. Synthesis and structure of stable 1,2-diaryldisilyne. Pure Appl. Chem. 2010; 82:603–612.
8.Peng Y, Fischer R C, Merrill W A, Fischer J, Pu L, Ellis B D, Fettinger J C, Herber R H, Power P P. Substituent effects in ditetrel alkyne analogues: multiple vs. single bonded isomers. Chem. Sci. 2010; 1:461–468.
9.Sekiguchi A, Kinjo R, Ichinohe M. A stable compound containing a silicon-silicon triple bond. Science 2004; 305:1755–1757.
10.Kravchenko V, Kinjo R, Sekiguchi A, Ichinohe M, West R, Balazs Y S, Schmidt A, Karni M, Apeloig Y. Solid-state 29Si nmr study of RSiSiR: a tool for analyzing the nature of the Si-Si bond. J. Am. Chem. Soc. 2006; 128:14472–14473.
11.Sasamori T, Hironaka K, Sugiyama T, Takagi N, Nagase S, Hosoi Y, Furukawa Y, Tokitoh N. Synthesis and reactions of a stable 1,2-diaryl-1,2-dibromodisilene: a precursor for substituted disilenes and 1,2-diaryldisilyne. J. Am. Chem. Soc. 2008; 130:13856–13857.
12.Wiberg N, Vasisht S K, Fischer G, Mayer P. Disilynes. III [1] a relatively stable disilyne RSi≡SiR (R = SiMe(SitBu3)2). Z. Anorg. Allg. Chem. 2004; 630:1823–1828.
13.Stender M, Phillips A D, Wright R J, Power P P. Synthesis and characterization of a digermanium analogue of an alkyne. Angew. Chem. Int. Ed. 2002; 41:1785–1787.
14.Pu L, Phillips A D, Richards A F, Stender M, Simons R S, Olmstead M M, Power P P. Germanium and tin analogues of alkynes and their reduction products. J. Am. Chem. Soc. 2003; 125:11626–11636.
15.Stender M, Phillips A. D, Power P P. Formation of [Ar*Ge{CH2C(Me)C(Me)CH2}CH2C(Me)N]2 (Ar* = C6H3-2,6-Trip2; Trip = C6H2-2,4,6-i-Pr3) via reaction of Ar*GeGeAr* with 2,3-dimethyl-1,3-butadiene: evidence for the existence of a germanium analogue of an alkyne. Chem. Commun. 2002; 12:1312–1313.
16.Spikes G H, Power P P. Lewis base induced tuning of the Ge–Ge bond order in a “digermyne”. Chem. Commun. 2007; 1:85–87.
17.Sugiyama Y, Sasamori T, Hosoi Y, Furukawa Y, Takagi N, Nagase S, Tokitoh N. Synthesis and properties of a new kinetically stabilized digermyne: new insights for a germanium analogue of an alkyne. J. Am. Chem. Soc. 2006; 128:1023–1031.
18.Phillips A D, Wright R J, Olmstead M M, Power P P. Synthesis and characterization of 2,6-Dipp2-H3C6SnSnC6H3-2,6-Dipp2 (Dipp = H3-2,6-Pri2): a tin analogue of an alkyne. J. Am. Chem. Soc. 2002; 124:5930–5931.
19.Pu L, Twamley B, Power P P. Synthesis and characterization of 2,6-Trip2H3C6PbPbC6H3-2,6-Trip2 (Trip = C6H2-2,4,6-i-Pr3): a stable heavier group 14 element analogue of an alkyne. J. Am. Chem. Soc. 2000; 122:3524–3525.
20.Liao H-Y, Su M-D, Chu S-Y. A stable species with a formal Ge≡C triple bond — a theoretical study. Chem. Phys. Lett. 2001; 341:122–128.
21.Wu P-C, Su M-D. Theoretical designs for germaacetylene (RC≡GeR): a new target for synthesis. Dalton. Trans. 2011; 40:4253–4259.
22.Wu P-C, Su M-D. Effects of substituents on the thermodynamic and kinetic stabilities of HCGeX (X = H, CH3, F, and Cl) isomers. A theoretical study. Inorg. Chem. 2011; 50:6814–6814.
23.Wu P-C, Su M-D. A new target for synthesis of triply bonded plumbacetylene (RC≡PbR): a theoretical design. Organometallics 2011; 30:3293–3301.
24.Silvestru C, Breunig H J, Althaus H. Structural chemistry of bismuth compounds. I. Organobismuth derivatives. Chem. Rev. 1999; 99:3277–3328.
25.Bishop M B, LaiHing K, Cheng P. Y, Pesehke M, Duncan M A. Growth patterns and photoionization dynamics of In/Sb and In/Bi intermetallic clusters. J. Phys. Chem. 1989; 93:1566–1569.
26.Itami T, Masaki T, Kuribayasi K, Sato E, Hinada M, Yamasita M, Kawasaki K. Growth of fluctuations under microgravity in liquid Bi-Ga Alloys. J. Non-Cryst. Solids. 1996; 205–207:375–378.
27.Mudry S, Korolyshyn A. X-ray study of the structure of liquid Bi-T1. J. Alloys Compd. 1996; 235:120–123.
28.Boa D, Ansara I. Thermodynamic assessment of the ternary system Bi-In-Pb. Thermochimica Acta. 1998; 314:79–86.
29.Khairulin R A, Stankus S V, Sorokin A L. Determination of the two-melt phase boundary and study of the binary diffusion in liquid Bi–Ga system with a miscibility gap. J. Non-Cryst. Solids. 2002; 297:120–130.
30.Xi Y, Zu F-Q, Li X-F, Yu J, Liu L-J, Li Q, Chen Z-H. High-temperature abnormal behavior of resistivities for Bi–In melts. Phys. Lett. 2004; 329:221–225.
31.Mangalam R V K, Ranjith R, Iyo A, Sundaresan A, Krupanidhi S B, Rao C N R. Ferroelectricity in Bi26−xMxO40−δ (M = Al and Ga) with the γ -Bi2O3 structure. Solid State Commun. 2006; 140:42–44.
32.Brunetti B, Gozzi D, Iervolino M, Piacente V, Zanicchi G, Parodi N, Borzone G. Bismuth activity in lead-free solder Bi–In–Sn alloys. Comput Coupling Phase Diagr. Thermochem. 2006; 30:431–442.
33.Paliwal M, Jung I H. Thermodynamic modeling of the Al–Bi, Al Sb, Mg–Al–Bi and Mg–Al–Sb systems. Comput Coupling Phase Diagr. Thermochem. 2010; 34:51–63.
34.Gupta U, Reveles J U, Melko J J, Khanna S N, Castleman Jr. A. W. Origins of stability in mixed bismuth-indium clusters. J. Phys. Chem. C 2010; 114:15963–15972.
35.Aksöz S, Ocak Y, Maraşlı N, Keşlioğlu K. Thermal conductivity and interfacial energy of solid Bi solution in the Bi–Al–Zn eutectic system. Fluid Phase Equilib. 2010; 293:32–41.
36.Barbier J, Penin N, Cranswick L M. Melilite-type borates Bi2ZnB2O7 and CaBiGaB2O7. Chem. Mater. 2005; 17:3130–3136.
37.Curtarolo S, Kolmogorov A N, Cocks F H. High-throughput ab initio analysis of the Bi–In, Bi–Mg, Bi–Sb, In–Mg, In–Sb, and Mg–Sb systems. Comput. Coupling Phase Diagr. Thermochem. 2005; 29:155–161.
38.Li Z, Knott S, Mikula A. Calorimetric investigations of liquid Bi–In–Zn alloys. Acta Materialia 2007; 55:2417–2422.
39.Madouri D, Ferhat M. How do electronic properties of conventional III–V semiconductors hold for the III–V boron bismuth BBi compound? Phys Stat Sol. 2005; 242:2856–2863.
40.Gave M A, Malliakas C D, Weliky D P, Kanatzidis M G. Wide compositional and structural diversity in the system Tl/Bi/P/Q (Q = S, Se) and observation of vicinal P−Tl J coupling in the solid state. Inorg. Chem. 2007; 46:3632–3644.
41.Witusiewicz V T, Hecht U, Böttger B, Rex S. Thermodynamic re-optimisation of the Bi–In–Sn system based on new experimental data. J. Alloys Compounds. 2007; 428:115–124.
42.Sun Z, Zhu Z, Gao Z, Tang Z. Experimental and theoretical investigation on binary anionic clusters of Al(m)Bi(n)(-). Rapid Commun. Mass Spectrom. 2009; 23:2663–2668.
43.Ropero-Vegaa J L, Rosas-Barrerab K L, Pedraza-Avellaa J A, Laverde-Catañob D A, Pedraza-Rosasb J E, Niño-Gómeza M E. Photophysical and photocatalytic properties of Bi2MNbO7 (M = Al, In, Ga, Fe) thin films prepared by dip-coating. Mater. Sci. Eng. 2010; 174:196–199.
44.Geng L, Cheng W D, Lin C S, Zhang W L, Zhang H, He Z Z. Syntheses, crystal and electronic structures, and characterizations of quaternary antiferromagnetic sulfides: Ba2MFeS5 (M = Sb, Bi). Inorg. Chem. 2011; 50:2378–2384.
45.Rosas-Barrera K L, Pedraza-Avella J A, Ballén-Gaitán B P, Cortés-Peña J, Pedraza-Rosas J E, Laverde-Cataño D A. Photoelectrolytic hydrogen production using Bi2MNbO7 (M = Al, Ga) semiconductor film electrodes prepared by dip-coating. Mater. Sci. Eng. 2011; 176:1359–1363.
46.Kobayashi K, Nagase S. Silicon−silicon triple bonds: do substituents make disilynes synthetically accessible? Organometallics 1997; 16:2489–2491.
47.Nagase S, Kobayashi K, Takagi N. Triple bonds between heavier group 14 elements. A theoretical approach. J. Organomet. Chem. 2000; 611:264–271.
48.Kobayashi K, Takagi N, Nagase S. Do bulky aryl groups make stable silicon−silicon triple bonds synthetically accessible? Organometallics 2001; 20:234–236.
49.Takagi N, Nagase S. Substituent Effects on germanium−germanium and tin−tin triple bonds. Organometallics 2001; 20:5498–5000.
50.Takagi N, Nagase S. A silicon–silicon triple bond surrounded by bulky terphenyl groups. Chem. Lett. 2001; 30:966–967.
51.Takagi N, Nagase S. Theoretical study of an isolable compound with a short silicon-silicon triple bond, (tBu3Si)2MeSiSi≡SiSiMe(SitBu3)2. Eur. J. Inorg. Chem. 2002;2002: 2775–2778.
52.Frisch M J, Trucks G W, Schlegel H B, Scuseria G E, Robb M A, Cheeseman J R, Scalmani G, Barone V, Mennucci B, Petersson G A, Nakatsuji H, Caricato M, Li X, Hratchian H P, Izmaylov A F, Bloino J, Zheng G, Sonnenberg J L, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Montgomery Jr. J A, Peralta J E, Ogliaro F, Bearpark M, Heyd J J, Brothers E, Kudin K N, Staroverov V N, Keith T, Kobayashi R, Normand J, Raghavachari K, Rendell A, Burant J C, Iyengar S S, Tomasi J, Cossi M, Rega N, Millam J M, Klene M, Knox J E, Cross J B, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann R E, Yazyev O, Austin A J,Cammi R, Pomelli C, Ochterski J W, Martin R L, Morokuma K, Zakrzewski V G, Voth G A, Salvador P, Dannenberg J J, Dapprich S, Daniels A D, Farkas O, Foresman J B, Ortiz J V, Cioslowski J, Fox D J. Gaussian, Inc., Wallingford, CT; 2013.
53.Zhao Y, Truhlar D G. Density functionals with broad applicability in chemistry. Acc. Chem. Res. 2008; 41:157–167.
54.Becke A D. Density-functional exchange-energy approximation with correct asymptotic behavior. Phys. Rev. A 1988; 38:3098–3100.
55.Becke A D. Density-functional thermochemistry. III. The role of exact exchange. J. Chem. Phys. 1993; 98:5648–5652.
56.Lee C, Yang W, Parr R G. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B 1998; 37:785–789.
57.Perdew J P, Wang Y. Accurate and simple analytic representation of the electron-gas correlation energy. Phys. Rev. B 1992; 45:13244–13249.
58.Weigend F, Ahlrichs R. Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: design and assessment of accuracy. Phys. Chem. Chem. Phys. 2005; 7:3297–3305.
59.Hay P J, Wadt W R. Ab initio effective core potentials for molecular calculations. Potentials for the transition metal atoms Sc to Hg. J. Chem. Phys. 1985; 82:270–283.
60.Hay P J, Wadt W R. Ab initio effective core potentials for molecular calculations. Potentials for main group elements Na to Bi. J. Chem. Phys. 1985; 82:284–298.
61.Hay P J, Wadt W R. Ab initio effective core potentials for molecular calculations. Potentials for K to Au including the outermost core orbitals. J. Chem. Phys. 1985; 82:299–310.
62.Check C E, Faust T O, Bailey J M, Wright B J, Gilbert T M, Sunderlin L S. Addition of polarization and diffuse functions to the LANL2DZ basis set for p-block elements. J. Phys. Chem. A 2001; 105:8111–8116.
63.Wiberg K B. Application of the pople-santry-segal CNDO method to the cyclopropylcarbinyl and cyclobutyl cation and to bicyclobutane. Tetrahedron 1968; 24:1083–1096.
64.Reed A E, Curtiss L A, Weinhold F. Intermolecular interactions from a natural bond orbital, donor-acceptor viewpoint. Chem. Rev. 1988; 88:899–926.
65.Pyykkö P, Desclaux J-P. Relativity and the periodic system of elements. Acc. Chem. Res. 1979; 12:276–281.
66.Kutzelnigg W. Chemical bonding in higher main group elements. Angew. Chem. Int. Ed. Engl. 1984; 23:272–295.
67.Pyykkö P. Relativistic effects in structural chemistry. Chem. Rev. 1988; 88:563–594.
68.Pyykkö P. Strong closed-shell interactions in inorganic chemistry. Chem. Rev. 1997; 97:597–636.
69.Allen L C. Electronegativity is the average one-electron energy of the valence-shell electrons in ground-state free atoms. J. Am. Chem. Soc. 1989; 111:9003–9014.
70.Jones C. Recent developments in low coordination organo-antimony and bismuth chemistry. Coord. Chem. Rev. 2001; 215:151–169.
71.Geng L, Cheng W D, Lin C S, Zhang W L, Zhang H, He Z Z. Syntheses, crystal and electronic structures, and characterizations of quaternary antiferromagnetic sulfides: Ba2MFeS5 (M = Sb, Bi). Inorg. Chem. 2011; 50:5679–5686.
72.Chattopadhyay A, Das K K. Electronic states of TlX (X = As, Sb, Bi): a configuration interaction study. J. Phys. Chem. A 2004; 108:7306–7317.
73.Glendening E D, Weinhold F. Natural resonance theory: I. General formalism. J. Comp. Chem. 1998; 19:593–609.
74.Glendening E D, Weinhold F. Natural resonance theory: II. Natural bond order and valency. J. Comp. Chem. 1998; 19:610–627.
75.Glendening E D, Badenhoop J K, Weinhold F. Natural resonance theory: III. Chemical applications. J. Comp. Chem. 1998; 19:628–646.
76.Bino A, Ardon M, Shirman E. Formation of a carbon-carbon triple bond by coupling reactions in aqueous solution. Science 2005; 308:234–235.
77.Su P, Wu J, Gu J, Wu W, Shaik S, Hiberty P C. Bonding conundrums in the c2 molecule: a valence bond study. J. Chem. Theory Comput. 2011; 7:121–130.
78.Ploshnik E, Danovich D, Hiberty P C, Shaik S. The nature of the idealized triple bonds between principal elements and the σ origins of trans-bent geometries—a valence bond study. J. Chem. Theory Comput. 2011; 7:955–968.
79.Danovich D, Bino A, Shaik S. Formation of carbon−carbon triply bonded molecules from two free carbyne radicals via a conical intersection. J. Phys. Chem. Lett. 2013; 4:58–64.
80.Kuczkowski A, Thomas F, Schulz S, Nieger M. Synthesis and X-ray crystal structures of novel Al−Bi and Ga−Bi compounds. Organometallics 2000; 19:5758–5762.
Written By
Jia-Syun Lu, Ming-Chung Yang, Shih-Hao Su, Xiang-Ting Wen, Jia-
Zhen Xie and Ming-Der Su
Submitted: 24 October 2016Reviewed: 12 December 2016Published: 05 July 2017
Open access peer-reviewed chapter
