2. Theoretical methods

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

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

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

group 13 elements in inorganic chemistry [25–35] and material chemistry [36–45].

been published elsewhere.

72 Recent Progress in Organometallic Chemistry

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 openshell (triplet) species. The <S<sup>2</sup> > 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 (ΔS) are applied at the three DFT levels. Therefore, the relative free energy (ΔG) 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.
