3. Results and discussion

## 3.1. Theoretical models for RE13≡BiR

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/Def2TZVP, 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).


Several important conclusions can be found in Tables 1–5, which are shown as follows:

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

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-

the following sections.

74 Recent Progress in Organometallic Chemistry

3.2. Small ligands on substituted RE13≡BiR

Figure 1. Two interaction models, A and B, in forming triply bonded RE13≡BiR species.

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].

Table 1. Selected geometrical parameters, natural charge densities (Q<sup>B</sup> 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 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].

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.


Triple Bonds between Bismuth and Group 13 Elements: Theoretical Designs and Characterization http://dx.doi.org/10.5772/67220 77


R F OH H CH3 SiH3 ∠Al—Bi—R (°) 83.16 84.20 48.09 92.52 62.57

∠R—Al—Bi—R (°) 180.0 177.3 180.0 179.9 179.9

QAl (1) 0.5031 0.3942 0.1493 0.2692 0.1841

QBi (2) 0.3947 0.2709 −0.05788 0.03761 −0.1384

Wiberg BO (4) 1.393 1.403 1.746 1.634 1.602

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,

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

R F OH H CH3 SiH3 Ga≡Bi (Å) 2.639 2.625 2.463 2.543 2.512

∠R—Ga—Bi (°) 179.7 175.0 166.5 178.9 178.7

∠Ga—Bi—R (°) 86.32 86.85 52.56 91.27 65.56

∠R—Ga—Bi—R (°) 179.5 157.1 180.0 179.2 175.8

) (3) 22.61 20.28 50.55 38.69 53.41

BE (kcal mol−<sup>1</sup>

76 Recent Progress in Organometallic Chemistry

see Refs. [63, 64].

+dp (in square bracket) levels.

(84.59) (85.35) (49.85) (92.93) (61.82) [87.00] [88.32] [51.00] [93.77] [64.03]

(180.0) (176.0) (180.0) (179.6) (179.8) [180.0] 178.0] [180.0] [179.6] [180.0]

(0.4904) (0.3918) (0.1417) (0.2544) (0.2145) [0.6664] [0.4315] [0.3786] [0.2414] [0.1517]

(0.3196) (0.1834) (−0.04954) (0.02100) (−0.07446) [0.3044] [0.1982] [0.03410] [−0.05262] [−0.1074]

(30.36) (31.77) (85.64) (63.54) (57.96) [25.47] [20.51] [53.65] [42.77] [53.47]

(1.509) (1.511) (1.798) (1.690) (1.615) [1.521] [1.516] [1.787] [1.706] [1.653]

(2.602) (2.621) (2.465) (2.524) (2.510) [2.632] [2.629] [2.487] [2.550] [2.520]

(178.3) (173.3) (166.2) (177.8) (177.6) [177.3] [175.5] [167.0] [177.3] [177.0]

(88.49) (88.52) (56.24) (92.86) (66.28) [88.18] [90.75] [59.49] [93.37] [69.82]

(180.0) (159.8) (180.0) (178.8) (179.9)

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].

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 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].

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.



R F OH H CH3 SiH3

Wiberg BO (4) 1.312 1.403 1.590 1.543 1.553

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,

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

R F OH H CH3 SiH3 Tl≡Bi (Å) 2.859 2.843 2.713 2.742 2.707

∠R—Tl—Bi (°) 175.9 173.5 175.7 179.6 174.4

∠Tl—Bi—R (°) 81.34 86.72 78.87 91.91 76.03

∠R—Tl—Bi—R (°) 180.0 143.7 180.0 172.1 178.9

QTl (1) 0.6481 0.5672 0.3014 0.4162 0.2665

QBi (2) 0.4752 0.3214 −0.1836 0.008121 −0.2245

) (5) 7.90 6.61 30.74 26.94 30.56

) (3) 14.66 13.17 39.19 36.87 39.28

BE (kcal mol−<sup>1</sup>

78 Recent Progress in Organometallic Chemistry

see Refs. [63, 64].

BE (kcal mol−<sup>1</sup>

square bracket) levels.

(0.4000) (0.2511) (−0.08703) (0.04410) (−0.08023) [0.3468] [0.2141] [0.02620] [−0.05735] [−0.1365]

(15.06) (12.88) (42.01) (35.00) (40.94) [18.80] [13.70] [44.04] [35.54] [41.83]

(1.308) (1.334) (1.601) (1.539) (1.546) [1.323] [1.336] [1.615] [1.548] [1.549]

(2.812) (2.803) (2.698) (2.725) (2.705) [2.819] [2.822] [2.679] [2.713] [2.682]

(178.8) (172.5) (176.6) (178.5) (174.7) [177.2] [174.4] [176.3] [178.5] [175.9]

(87.73) (89.82) (79.00) (93.54) (76.50) [87.92] [92.34] [78.86] [93.25] [80.00]

(179.9) (132.9) (179.9) (178.6) (179.9) [180.0] [130.6] [180.0] [180.0] [179.2]

(0.6614) (0.5879) (0.2284) (0.2746) (0.3510) [0.7100] [0.4812] [0.3536] [0.2734] [0.1601]

(0.3615) (0.2201) (−0.05213) (−0.1282) (−0.09637) [0.3854] [0.2455] [0.04813] [−0.03131] [−0.1282]

(2.98) (8.17) (48.12) (35.39) (29.13)

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].

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.


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.

Triple Bonds between Bismuth and Group 13 Elements: Theoretical Designs and Characterization http://dx.doi.org/10.5772/67220 81

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.

80 Recent Progress in Organometallic Chemistry

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.

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.

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.

#### 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.

predicted to be a kinetically unstable isomer, so these could not be isolated in a matrix or even

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

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

as transient intermediates.

82 Recent Progress in Organometallic Chemistry

3.3. Large ligands on substituted RʹE13≡BiRʹ

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.

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.

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.

Triple Bonds between Bismuth and Group 13 Elements: Theoretical Designs and Characterization http://dx.doi.org/10.5772/67220 85

[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

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.

more electropositive than the small substituents, as mentioned earlier.

84 Recent Progress in Organometallic Chemistry

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.

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 (ΔH1 and ΔH2) 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=BiRʹ<sup>2</sup> 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).



Tables 6–10. The B3LYP/LANL2DZ+dp calculations indicate that the RʹE13≡BiRʹ species with Tbt, Ar\*, SiMe(SitBu3)2, and SiiPrDis2 substituents (ΔH1 and ΔH2) 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=BiRʹ<sup>2</sup> isomers are kinetically and thermodynamically unstable, so they rearrange spontaneously to the global minimum RʹE13≡BiRʹ triply bonded mole-

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),

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 Q<sup>B</sup> (1) −0.4310 −0.1711 −0.3251 −0.4742 QBi (2) 0.2915 0.3004 0.1426 0.1071

) (3) 37.58 41.68 36.25 51.07

cules, provided that significantly bulky groups are employed.

Table 14 (E13 = In), and Table 15 (E13 = Tl).

86 Recent Progress in Organometallic Chemistry

BE (kcal mol−<sup>1</sup>

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) ΔH<sup>1</sup> = E(:B=BiRʹ2) – E(RʹB≡BiRʹ); see Scheme 3. (6) ΔH<sup>2</sup> = E(Rʹ2B=Bi:) – E(RʹB≡BiRʹ); see Scheme 3

Table 6. Geometrical parameters, nature charge densities (Q<sup>B</sup> 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 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) ΔH<sup>1</sup> = E(:Al=BiRʹ2) – E(RʹAl≡BiRʹ); see Scheme 3. (6) ΔH<sup>2</sup> = E(Rʹ2Al=Bi:) – E(RʹAl≡BiRʹ); see Scheme 3.

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.

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


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) ΔH<sup>1</sup> = E(:Ga = BiRʹ2) – E(RʹGa≡BiRʹ); see Scheme 3. (6) ΔH<sup>2</sup> = E(Rʹ2Ga=Bi:) – E(RʹGa≡BiRʹ); see Scheme 3.

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 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) ΔH<sup>1</sup> = E(:In = BiRʹ2) – E(RʹIn≡BiRʹ); see Scheme 3. (6) ΔH<sup>2</sup> = E(Rʹ2In=Bi:) – E(RʹIn≡BiRʹ); see Scheme 3.

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.

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.

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) ΔH<sup>1</sup> = E(:Tl = BiRʹ2) – E(RʹTl≡BiRʹ); see Scheme 3. (6) ΔH<sup>2</sup> = E(Rʹ2Tl = Bi:) – E(RʹTl≡BiRʹ); see Scheme 3.

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.


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

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) ΔH<sup>1</sup> = E(:In = BiRʹ2) – E(RʹIn≡BiRʹ); see Scheme 3. (6) ΔH<sup>2</sup> = E(Rʹ2In=Bi:) – E(RʹIn≡BiRʹ); see Scheme 3.

Table 9. Geometrical parameters, nature charge densities (QIn and QBi), binding energies (BE), and Wiberg bond order

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

) (3) 43.73 39.28 35.54 32.92

) (5) 68.10 69.08 61.74 58.83

) (6) 78.07 71.28 77.43 64.13

Wiberg BO (4) 2.091 2.181 2.262 2.313

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) ΔH<sup>1</sup> = E(:Ga = BiRʹ2) – E(RʹGa≡BiRʹ); see Scheme 3. (6) ΔH<sup>2</sup> = E(Rʹ2Ga=Bi:) – E(RʹGa≡BiRʹ); see

Table 8. Geometrical parameters, nature charge densities (QGa and QBi), binding energies (BE), and Wiberg bond order

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

) (3) 63.45 45.97 36.20 37.05

) (5) 64.06 60.17 55.72 62.99

) (6) 79.38 61.44 56.03 67.61

Wiberg BO (4) 2.052 2.153 2.211 2.304

(BO) of RʹGa≡BiRʹ at the B3LYP/LANL2DZ+dp level of theory. Also see Figure 7.

(BO) of RʹIn≡BiRʹ at the B3LYP/LANL2DZ+dp level of theory. Also see Figure 7.

BE (kcal mol−<sup>1</sup>

88 Recent Progress in Organometallic Chemistry

ΔH<sup>1</sup> (kcal mol−<sup>1</sup>

ΔH<sup>2</sup> (kcal mol−<sup>1</sup>

Scheme 3.

BE (kcal mol−<sup>1</sup>

ΔH<sup>1</sup> (kcal mol−<sup>1</sup>

ΔH<sup>2</sup> (kcal mol−<sup>1</sup>


(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].

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].



R′B≡BiR′ WBI NBO analysis NRT analysis

π = 1.89 π: 0.6146 B (sp62.48) + 0.7889 Bi (sp19.73)

π = 1.80 π: 0.5606 B (sp1.73) + 0.8281 Bi (sp4.99)

compounds that have small substituents, at the B3LYP/LANL2DZ+dp level of theory [1–8, 76–80].

R′Al≡BiR′ WBI NBO analysis NRT analysis

(sp1.07)

R′ = SiiPrDis2 2.7 σ = 1.83 σ: 0.6502 B (sp4.29) + 0.7598 Bi

90 Recent Progress in Organometallic Chemistry

[63, 64], and (2) the natural resonance theory (NRT): see Refs. [73–75].

R′ = Tbt 2.09 σ = 1.98 σ: 0.7538 Al (sp0.15) + 0.6571 Bi

R′ = Ar\* 2.02 σ = 1.84 σ: 0.7806 Al (sp0.15) + 0.6250 Bi

R′ = SiiPrDis2 2.26 σ = 1.86 σ: 0.7184 Al (sp0.93) + 0.6956 Bi

R′ = SiMe (SitBu3)2

(sp22.99)

(sp28.77)

2.2 σ = 1.96 σ: 0.7169 Al (sp0.96) + 0.6971 Bi (sp21.26)

(sp29.72)

π = 1.93 π: 0.4709 Al (sp1.00) + 0.8822 Bi (sp1.00)

π = 1.94 π: 0.4960 Al (sp46.09) + 0.8673 Bi (sp15.43)

π = 1.89 π: 0.8678 Al (sp19.21) + 0.4970 Bi (sp16.37)

Occupancy Hybridization Polarization Total/covalent/

(1) The Wiberg bond index (WBI) for the B=Bi bond and occupancy of the corresponding σ and π bonding NBO: see Refs.

Table 11. Selected results for the natural bond orbital (NBO) and natural resonance theory (NRT) analyses of RʹB≡BiRʹ

Occupancy Hybridization Polarization Total/covalent/

ionic

ionic

56.83% (Al) 2.12/1.10/1.02 Al=Bi: 12.76% 43.17% (Bi) Al=Bi: 75.36%

22.17% (Al) Al≡Bi: 11.88%

60.93% (Al) 2.07/1.01/1.06 Al=Bi: 19.33% 39.07% (Bi) Al=Bi: 74.20%

24.60% (Al) Al≡Bi: 6.47%

24.70% (Al) 2.24/1.38/0.86 Al=Bi: 11.69% 75.30% (Bi) Al=Bi: 84.51%

37.77% (Al) Al≡Bi: 3.80%

51.61% (Al) 1.91/1.35/0.60 Al=Bi: 12.68% 48.39% (Bi) Al=Bi: 83.75%

62.23% (Bi)

68.57% (Bi)

77.83% (Bi)

75.40% (Bi)

62.23% (Bi)

37.77% (B) B≡Bi: 40.11%

42.27% (B) 2.31/1.52/0.79 B=Bi: 6.01% 57.73% (Bi) B=Bi: 54.39%

31.43% (B) B≡Bi: 39.96%

Resonance weight

Resonance weight

(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].

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 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].

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].


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].

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 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].

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].
