2.1. Structural Results
We decided to use the five experimentally available tetrylidyne complex cations
NiSiTbbexp,
NiGeArMesexp,
NiSnArMesexp,
PtSiTbbexp, and
PtGeArMesexp from our group as anchor points of this study and completed the homologous series [(PMe
3)
3MER]
+ (M = Ni, Pd, Pt; E = C, Si, Ge, Sn, Pb) by including the 10 hitherto experimentally missing complex cations, resulting in overall 15 metal–tetrel combinations. The substituent was chosen to be Ar
Mes. In case of E = Si, the complex cations
MSiTbb were also studied in order to compare them with the experimentally known systems [(PMe
3)
3Ni≡SiTbb]
+ (
NiSiTbbexp) and [(PMe
3)
3Pt≡SiTbb]
+ (
PtSiTbbexp). For comparison reasons, we also studied the amino derivatives [(PPh
3)
3Ni≡EN(Si
iPr
3)(Dipp)]
+ (E = Ge (
B-Ge), E = Sn (
B-Sn)). The structures of all complexes were optimized at the B97-D3 (BJ)-ATM/def2-TZVP level of theory, abbreviated in the following as level
I (see also the Materials and Methods section for the full computational details) and confirmed as minima by successive numerical or analytical frequency calculations. A collection of selected bonding parameters is given in
Table 1, which indicates several trends, which are discussed in the following.
(a) The calculated M−E bond lengths are in all cases slightly longer than those obtained with single-crystal X-ray diffraction (sc-XRD) analyses. The difference Δ between the calculated and experimental values ranges from 1.4 to 7.0 pm and continuously increases with increasing atomic number of the tetrel (e.g., M = Ni: Δ = 1.4 pm (E = Si); Δ = 3.0 pm (E = Ge, using the mean value of the Ni−Ge bond lengths of the two complex cations found in the asymmetric unit of the crystal lattice); Δ = 7.0 pm (E = Sn)) and with increasing atomic number of the metal (e.g., E = Ge: Δ = 3.0 pm (M = Ni); Δ = 5.8 pm (M = Pt)).
The experimental M≡E bond lengths are the shortest reported to date. For example, the Ni≡Si bond of
NiSiTbbexp (203.11(7) pm) is shorter than the Ni=Si bond of [(PMe
3)
3Ni=Si(Br)Tbb] (210.2(2) pm) and of [(
η6-toluene)Ni=Si(C(SiMe
3)
2CH
2)
2] (209.4(1) pm), the latter one being the shortest Ni=Si bond reported to date [
54,
55]. Similarly, the Pt≡Si bond of
PtSiTbbexp (213.43(7) pm) is shorter than the Pt=Si bond of [(PMe
3)
3Pt=Si(Br)Tbb] (219.96(9) pm) and other reported Pt=Si bonds [
56]. Furthermore, the Ni≡Ge bond of
NiGeArMesexp (210.30(6) pm) is shorter than that of
B-Geexp (215.9(1) pm) and shorter than the Ni=Ge bond of [(PMe
3)
3Ni=Ge(Cl)Ar
Mes] (216.10(4) pm), the latter bond being the shortest Ni=Ge bond reported to date [
52]. Finally, the Ni≡Sn bond of
NiSnArMesexp (228.08(9) pm) is shorter than that of
B-Snexp (235.5(1) pm) and shorter than the Ni=Sn bond of [(PMe
3)
3Ni=Sn(Cl)Ar
Mes] (234.48(9) pm), the latter bond being the shortest Ni=Sn bond reported to date [
57]. All these bonding parameters provide structural evidence for the presence of M≡E triple bonds in these complexes.
At this point, we want to emphasize that the comparison between experimental solid-state structures obtained by single-crystal X-ray diffraction at 100–123 K versus theoretical single-molecule gas-phase calculations at 0 K is likely to exhibit certain deviations. However, we checked the reliability of our calculated structures at the level of theory
I with those obtained at the TPSS [
58] -D3(BJ)-ATM/def2-TZVP and PW6B95 [
59] -D3(BJ)-ATM/def2-TZVP levels of theory and found no considerable differences (see
Supplementary Materials). This is somewhat expected as the influence of the density functional approximation (DFA) on the structure is generally considered to be low in contrast to that of the employed basis set [
60,
61,
62,
63]. Furthermore, with the large differences found between the experimental and calculated M−E−C1 bond angles of
NiSnArMes and
PtGeArMes, we assessed the curvature of the potential energy hypersurface (PES) with PES scans, varying the M−E−C1 angle. Surprisingly, altering the angle by ±20° costs only 5.7 kJ·mol
−1 (
NiSnArMes) and 6.3 kJ·mol
−1 (
PtGeArMes), indicating a very flat PES (see
Section 2.5) with high flexibility regarding the M−E−C1 bond angle.
We also examined the relativistic influence on our compounds by all-electron calculations, explicitly treating relativistic effects with the zero-order regular approximation (ZORA) method [
64]. The structure optimization of
PtPbArMes at the ZORA-
I level of theory using the SARC-ZORA-TZVP basis set for platinum and lead resulted in a structure very similar to the one obtained at the level of theory
I, which uses effective core potentials (ECPs) for the heavier atoms (see the
SI). This is in line with previous reports that testify to an at least comparable performance of ECPs to explicit relativistic treatment with ZORA or Douglas–Kroll–Hess (DKH) techniques [
65,
66,
67].
(b) The calculated E−C1 bond lengths of the silylidyne complexes MSiTbb compare very well to the experimental ones, but for E = Ge, Sn, the E−C1 bond lengths of the calculated structures are larger. Here, too, the deviation ranging from 2.3 to 5.4 pm continuously increases with increasing atomic number of the tetrel (e.g., M = Ni: Δ = 2.3 pm (E = Ge); Δ = 5.4 pm (E = Sn)) and the metal center (e.g., E = Ge: Δ = 2.3 pm (M = Ni); Δ = 3.9 pm (M = Pt)).
(c) Notably, the calculated M−E bond lengths for E = Si, Ge fit well to those obtained using Pyykkö’s covalent triple bond radii [
68], for example, for
NiSiArMes (204.2 pm found vs. 203 pm expected),
PtSiArMes (215.7 pm found vs. 212 pm expected), or
NiGeArMes (213.3 pm found vs. 215 pm expected). However, for E = Sn, Pb, the calculated M−E bond lengths are considerably larger than those suggested by Pyykkö, especially for the compounds
PdSnArMes (251.6 pm found vs. 244 pm expected),
PdPbArMes (263.1 pm found vs. 249 pm expected),
PtSnArMes (255.1 pm found vs. 242 pm expected), and
PtPbArMes (267.7 pm found vs. 247 pm expected), which rather appear in the region between metal–tetrel single- and double-bond lengths according to Pyykkö. Of course, conclusions from the latter comparison have to be cautiously made, as Pyykkö’s triple bond radii were obtained by adding up atomic radii that were derived from a limited benchmark set. It should be also considered that the calculated M−E bond lengths significantly depend on the M−E−C1 bond angle (vide infra). For example, a constrained structure optimization with the M−E−C1 bond angle of
PdSnArMes,
PdPbArMes,
PtSnArMes, and
PtPbArMes set to 180° yields structures with M−E bond lengths of 245.5 pm, 254.9 pm, 245.5 pm, and 257.1 pm, respectively. These bond lengths are much closer to those predicted using the triple bond radii of Pyykkö.
(d) The E−C1 bond lengths increase within group 14 as expected and stay roughly the same for E = Si when the metal atom is exchanged between Ni, Pd, and Pt. This is not the case for the compounds with E = Ge, Sn, Pb and M = Pd, Pt, for which slightly longer tetrel–carbon bonds are obtained (ca. 3–4 pm longer). This lengthening can be explained in terms of Bent’s rule [
69] with the decreased s character of the hybrid orbital of E used for the E−C1 bond reflecting the reluctance for hybridization of the heavier main group elements [
70,
71,
72].
(e) The M−E−C1 bond angles show a high degree of variability with values ranging from 168.4° (
NiCArMes,
PdCArMes) down to 127.3° (
PtPbArMes). The calculated M−E−C1 values of the silylidyne complexes (R = Tbb) only slightly vary with the metal (
NiSiTbb: 167.2°,
PdSiTbb: 163.1°, and
PtSiTbb: 168.1°), being ca. 6° smaller than the experimental values (
NiSiTbbexp: 172.40(8)°,
PtSiTbbexp: 173.83(9)°) and fall in the range of typical experimental M−E−C angles of heavier tetrylidyne complexes (156–179° [
1,
73]). This is also the case for
NiGeArMes (165.3°), but for M = Pd, Pt and E = Ge, Sn, Pb, the calculated M−E−C1 bond angles (e.g.,
NiSnArMes: 150.9°,
NiPbArMes: 142.7°,
PtGeArMes: 149.7°,
PtSnArMes: 132.1°, and
PtPbArMes: 127.3°) are considerably smaller as graphically shown in
Figure 2. The M−E−C1 angles generally decrease in the order C > Si > Ge > Sn > Pb, the decrease being more pronounced for palladium and platinum than for nickel. The only exception to this trend is
NiSiArMes with a Ni−Si−C1 angle of 163.8°, which is smaller than the Ni−Ge−C1 angle of
NiGeArMes (165.3°).
Based on these trends derived from the structures in combination with the analysis of the molecular orbitals (vide infra), the calculations suggest two different complex classes, namely tetrylidyne complexes with an approximately linear M−E−C1 linkage and a M≡E triple bond and compounds with a considerably bent M−E−C1 moiety and an increased lone pair density at the tetrel center, which are reminiscent of metallotetrylenes. This classification is given in
Scheme 3, with all carbon and silicon systems as well as
NiGeArMes belonging to the first class, whereas the systems
PdSnArMes,
PdPbArMes,
PtSnArMes, and
PtPbArMes belong to the second class of compounds. While
NiSnArMes,
NiPbArMes,
PdGeArMes, and
PtGeArMes also feature considerably bent M−E−C1 units, these complexes exhibit electronic structures close to those of the tetrylidyne complexes and therefore lie in between the two complex classes.
As mentioned in the Introduction, we also investigated the geometric and electronic structure of the cationic complexes [L
3Ni≡EN(Si
iPr
3)(Dipp)]
+ of T. J. Hadlingtonet al. We performed gas-phase structure optimizations starting from the solid-state structures of
B-Geexp and
B-Snexp available from ref. [
53] at the level of theory
I to be consistent with our other results. The structural parameters for both
B-Eexp and
B-E are listed in
Table 1, and a comparison with the calculated structures of ref. [
53] can be found in the
Supplementary Materials.
The calculated Ni−E and E−N bond lengths of the gas-phase structures are again 1.1–4.1 pm longer than those of the solid-state structures, and the calculated Ni−E−N angles 2.5° (B-Ge) and 5.9° (B-Sn) are smaller than the experimental ones. Compared with our systems, B-Ge and B-Sn feature longer Ni−E bond lengths (218.3 pm in B-Ge vs. 213.3 pm in NiGeArMes; 239.6 pm in B-Sn vs. 235.1 pm in NiSnArMes). The same holds for the solid-state structures. Another salient difference is the larger Ni−E−N angles of the complexes of T. J. Hadlington et al., with values of 173.4° and 167.8° for B-Ge and B-Sn, respectively, compared with the Ni−E−C1 bond angles of NiGeArMes (165.3°) and NiSnArMes (150.9°). A possible explanation is the increased repulsion between the sterically more demanding Ni(PPh3)3 fragment and the tetrylidyne ligand in B-Ge and B-Sn, which is reduced by an elongation of the Ni−E bond and a widening of the Ni−E−N bond angle.
Alternatively, an electronic effect might be present originating from a (N→E) π donation, which in terms of the Lewis formalism is represented by the allenic form
B-E-b (
Scheme 4). To clarify which is the dominant effect causing the Ni≡E bond elongation and the widening of the Ni−E−N bond angle in
B-Ge and
B-Sn, the corresponding PMe
3-containing complex cation [(PMe
3)
3Ni≡GeN(Si
iPr
3)(Dipp)]
+ (
B-Ge-PMe3) was structurally optimized at the theoretical level
I. The obtained Ni−Ge bond length of 214.2 pm is close to that found for
NiGeArMes (213.3 pm), and the Ni−Ge−N angle of
B-Ge-PMe3 (163.7°) compares well with the Ni−Ge−C1 bond angle of
NiGeArMes (165.3°), suggesting that the longer bond length and larger Ni−Ge−N bond angle in
B-Ge result from the increased steric repulsion between the sterically demanding PPh
3 ligands and the tetrel-bonded amino substituent. A closer look at the MOs of
B-Ge and
B-Sn suggests a certain extent of (N→E) π donation, but this is apparently much smaller than in Fischer-type aminocarbyne [
6,
7,
74,
75,
76,
77,
78] complexes and does not influence the M≡E bond lengths.
2.2. Molecular Orbital Analysis
As one of the most direct results of an electronic structure calculation, we analyzed the canonical (Kohn−Sham) molecular orbitals (MOs) in the beginning. The MOs of the compounds
NiSiArMes (
Figure 3) and
PtPbArMes (
Figure 4) were selected as representatives for the discussion; the selected MOs of the other systems can be found in the
SI.
Although heavily delocalized, the low-lying HOMO−11 (highest occupied molecular orbital (HOMO)) in NiSiArMes corresponds to the σ(M−E) bond with σ(E−C) bond character. The metal-centered HOMO−8 and HOMO−7 represent the πxz(M−E) and πyz(M−E) bonds, respectively, with their antibonding, tetrel-centered counterparts being the lowest unoccupied molecular orbital (LUMO) and LUMO+1.
For PtPbArMes, the σ(M−E) bond is represented by HOMO−11, where the participation of the metal dz2 is evident. In contrast to NiSiArMes, no clear π bonds are found between the metal and tetrel, but rather metal-centered dxz (HOMO−10) and dyz (HOMO−9) orbitals without significant orbital contribution from the lead atom. Correspondingly, the antibonding π*(M−E) orbitals have a high contribution from the empty tetrel-px (LUMO, distorted due to M−E−C bending) and tetrel-py (LUMO+1) orbital, and only a small metal d-orbital participation.
As the canonical MOs are challenging to interpret due to their delocalized nature, we applied the Pipek−Mezey localization scheme to generate localized Pipek−Mezey MOs (LMOs) by a unitary transformation, not altering the physical meaningfulness of the orbitals [
79]. Again, the LMOs are shown for
NiSiArMes (
Figure 5) and
PtPbArMes (
Figure 6), being the anticipated extremes in terms of the bonding situation.
As already expected from the canonical MOs, localized σ(M−E), πxz(M−E), and πyz(M−E) bonds are found for NiSiArMes, resulting in a triply bonded M−E moiety. The corresponding Mulliken populations further show that the σ bond is strongly polarized toward the silicon atom (0.20 for Ni, 0.81 for Si), whereas both π bonds are polarized toward the metal atom (πxz: 0.80 for Ni and 0.16 for Si; πyz: 0.80 for Ni and 0.17 for Si). This bonding situation is reminiscent of that in Fischer-type carbyne complexes discussed in the Introduction. Furthermore, the Ni(0) 3d10 system demands the presence of three more metal-centered orbitals, which can be identified within the LMO framework as dxy, dz2, and dx2−y2, all with negligibly low contributions of the silicon atom (<0.04).
For the sake of completeness, the LMOs for the σ(Si−C1) and σ(Ni−P) bonds were also found and feature the expected orbital polarization toward carbon and phosphorus, respectively, based on electronegativity. It should be mentioned that the central phenyl ring of the Tbb and Ar
Mes substituents is also capable of delocalizing its aromatic π electrons over the formally empty p
x orbital of the tetrel. Such a π stabilization would, to some extent, compete with the d
xz back-donation of the metal atom, thus lowering the bond order between metal and tetrel. This effect, however, is assumed to be small due to the inferior π-donor ability of the phenyl substituent compared with that of the amino (NR
2) or alkoxy (OR) substituents (vide supra) and due to a decreasing p-orbital overlap between the tetrel and the phenyl group in the series C > Si > Ge > Sn > Pb. The Mulliken population for this π(E−C) LMO decreases—regardless of the metal—from 0.11 (Si) to rather insignificant values of 0.06 (Ge), 0.03 (Sn), and 0.02 (Pb). This conclusion was also drawn in a study by K. K. Pandey et al. in 2011 on cationic tetrylidyne complexes of molybdenum and tungsten bearing a mesityl substituent [
73].
For the main LMOs of PtPbArMes, a σ(Pt-Pb) LMO was found, which—in contrast to NiSiArMes—is not polarized toward the tetrel but toward the metal center (0.82 for Pt and 0.13 for Pb). The involved metal orbital is also different and can be rationalized as a dx2−z2 orbital (in terms of symmetry the same as the dz2 orbital). This orbital is filled, as stated above, due to the presence of a d10 metal system, so it seems clear that this M−E interaction comes from the overlap of a filled metal orbital with an empty p orbital at the tetrel atom.
No π(M−E) LMOs were found for PtPbArMes, although the dxz and dyz orbitals on Pt show the correct orientation. The hereby resulting metallotetrylene picture is confirmed by the presence of an electron lone pair (LP) at Pb without significant contribution of the platinum atom, as shown by the Mulliken population (0.02 for Pt and 0.96 for Pb).
Ultimately, this leads to the formulation of two types of bonding situations, which are qualitatively presented in
Scheme 5. Case a involves tetrylidyne complexes for which the M≡E bonding can be described by a σ(E→M) donation and two π(M→E) back donations between a neutral ML
3 and an ER
+ fragment in the singlet state. As both the empty metal sp
z (according to a Loewdin population analysis of the LUMO of Ni(PMe
3)
3) and the filled d
z2 orbital have the appropriate symmetry to interact with the filled sp hybrid orbital of the tetrel, three MOs result: a σ-bonding and a σ*-antibonding orbital as well as a nonbonding σ
nb MO that can be approximately considered as a metal-centered d
z2 orbital, as confirmed by the LMOs above (
Figure 5). The degenerate π
xz and π
yz bonds result from the interaction of the filled, almost degenerate metal-d
xz and -d
yz orbitals (the d
xz and d
yz orbitals are degenerate only in the case of a
C3v-symmetric ML
3 fragment) with the empty, approximately degenerate tetrel-p
x and -p
y orbitals. The degeneracy of the p
x and p
y orbitals is lifted in case of a π-donor substituent at the tetrel atom, such as an amino or alkoxy group, leading to a π
oop(E−N) or π
oop(E−O) MO as well as a π*
oop(M−E) MO with π*(E−N) or π*(E−O) contribution. The remaining orbitals on the metal atom are used for bonding to the phosphane ligands, whereas the second sp hybrid orbital on the tetrel is responsible for the bond to the substituent R.
The other case (b), found especially for
PtPbArMes, is the metallotetrylene type, with one σ(M→E) donation constituting the M−E single bond, and an electron lone pair at the tetrel center, causing a considerably bent M−E−C moiety. Here, the sp hybridization on the tetrel is not favored anymore, and the electron lone pair resides in an s orbital, further stabilized by relativistic effects that is not participating in bonding to the metal atom. The empty tetrel-p
z acceptor orbital interacts with the filled metal d
z2 orbital but is also partially involved in bonding to the substituent R (see HOMO−11 in
Figure 4).
After investigating the Mos and LMOs of all compounds in this study, the classification of
Scheme 3 was obtained: All carbon and silicon compounds and the
NiGeArMes complex can be described as tetrylidyne complexes (case a), whereas
PdSnArMes,
PdPbArMes,
PtSnArMes, and
PtPbArMes are best described as metallotetrylenes (case b). The germanium systems
PdGeArMes and
PtGeArMes as well as
NiSnArMes and
NiPbArMes lie between cases a and b and show a similar σ bonding to the tetrylidyne complexes, which is why we consider them more like tetrylidyne complexes, albeit with weakened π(M−E) bonds, compared with the silicon compounds.
We also studied the canonical Mos of compound
B-Ge and found three Mos resulting from the interaction of the d
xz(Ni), p
x(Ge), and p
x(N) orbitals (
Figure 7), which are the π
xz, π
nbxz, and π*
xz orbitals. The bonding π
xz orbital is the low-lying HOMO−27, which shows mostly π(Ge−N) bonding with a very small d
xz(M) orbital contribution. The nonbonding combination π
nbxz with one nodal plane is HOMO−3. It shows no contribution from the germanium atom but only from the metal and nitrogen atoms. Finally, LUMO+1 comprises the antibonding combination π*
xz with a large contribution of the p
x orbital at the tetrel atom. As can be seen in HOMO−27, some π
xz(M−E) bonding interaction is present but is diminished by the presence of the nitrogen atom, leading to a π(E−N) interaction.
The MOs mentioned above were not discussed in the publication of T. J. Hadlington et al. The MO description was limited to HOMO, HOMO−1, and HOMO−2, which were presented by the authors as two π- and one M−E σ-bonding orbital. However, by employing a more modest isosurface value of 0.04 e
1/2·Bohr
−3/2 and comparing it with similar orbitals in our compounds, we suggest that these orbitals correspond to the metal-centered d
x2−y2, d
xy, and σ
nb orbitals, respectively (more details on this can be found in the
SI).
The aromatic groups of the triphenylphosphane ligands in
B-Ge further amplify the delocalized character of the canonical frontier MOs, making them harder to interpret. This is why we also carried out a Pipek−Mezey orbital localization for
B-Ge, and selected LMOs (localized molecular orbitals) are presented in
Figure 8. It can be seen that apart from the σ(Ni−Ge) and σ(Ge−N) bonds, three π-type orbitals emerge from the orbital localization (π
yz(Ni−Ge), π
xz(Ni−Ge), and π
xz(Ge−N)). Whereas π
yz LMO corresponds to a (Ni−Ge) π bond, the presence of two xz-oriented π-type LMOs (one π(Ni−Ge) and one π(Ge−N) LMO) suggests the presence of both the ylidyne and allenic Lewis resonance forms in compound
B-Ge, as discussed in
Scheme 4. Furthermore, the Mulliken populations of these LMOs clearly suggest the typical Fischer-type characteristic of these complexes, with high tetrel contributions for the σ bond (0.73, E→M donation) and low ones for the two π bond orbitals (0.18, 0.12, M→E back-donation).
Together with the very similar results obtained for the tin analogue
B-Sn (see the
SI), the canonical and localized molecular orbital analysis suggests a similar bonding situation as in Fischer-type aminocarbyne complexes. However, the π(E−N) interaction in
B-Ge and
B-Sn is expected to be weaker than in the Fischer aminocarbyne complexes as evidenced by the small contribution of the tetrel atom in the π
xz LMOs.
2.3. Bond Dissociation Energies and Natural Population Analysis
Bond dissociation energies provide insights into the strength of bonds and create a basis for the discussion of the correlation between bond strengths and bond orders. Herein, we differentiate between the bond cleavage energy (
BCE), which describes the cleavage of a molecule without structural relaxation of the fragments in which the total spin of the fragments must be equal to the spin of the unfragmented molecule, and the bond dissociation energy (
BDE), in which the structural relaxation of the fragments is taken into consideration. Both energies are purely electronic.
BDEs that were corrected by the zero-point vibrational energies (ZPVEs) as well as the respective inner energies Δ
U, enthalpies Δ
H°, entropies Δ
S°, and Gibbs free energies Δ
G° at standard ambient conditions 298.15 K and 1 atm are given in the
SI together with their definitions.
The first step in obtaining the lowest possible BCEs and BDEs is determining the charges and spin states of the fragments. For gas-phase calculations, a cleavage into oppositely charged fragments is heavily unfavored due to strong coulombic attraction between the fragments. As a result of the cationic nature of the compounds presented herein, there are two reasonable schemes for the fragmentation of the M−E bond:
[(PMe3)3ME−R]+ → [M(PMe3)3] + [E−R]+: An investigation of the electronic states of the fragments [ML3] and [E−R]+ revealed that all fragments have a singlet ground state, with the only exception being the structurally relaxed [C−ArMes]+ fragment, which is stabilized in the triplet state after activation of the Mes substituent (see the calculated structure file). The singlet−triplet excitation energies range from 191.4 kJ·mol−1 ([Ni(PMe3)3]) to 214.3 kJ·mol−1 ([Pd(PMe3)3]) for the metal fragments and from 140.8 kJ·mol−1 ([Si−Tbb]+) to 174.7 kJ·mol−1 ([Sn−ArMes]+) for the tetryliumylidene ions.
[(PMe
3)
3ME−R]
+→[M(PMe
3)
3]
+ + [E−R]: This fragmentation scheme involves an interaction of two open-shell fragments either in their doublet or quartet states. The doublet state is preferred by all fragments with doublet−quartet excitation energies ranging from 232.5 kJ·mol
−1 ([Ni(PMe
3)
3]
+) to 284.0 kJ·mol
−1 ([Pd(PMe
3)
3]
+) for the metal fragments and from 120.3 kJ·mol
−1 ([C−Ar
Mes]) to 218.7 kJ·mol
−1 ([Pb−Ar
Mes]) for the tetrylidyne fragments (see the
SI for details).
The following trends in the
BCEs and
BDEs given in
Table 2 and
Figure 9 were found:
- (a)
Concerning the BCEs, the fragmentation into the [ML3]+ and [ER] fragments is favored for all compounds by 2.4 kJ·mol−1 (PdSnArMes) to 181.0 kJ·mol−1 (PtCArMes), except for PdPbArMes, for which the cleavage into the [ML3] and [ER]+ fragments is favored by 15.7 kJ·mol−1.
- (b)
The BDEs are lower for the dissociation into the [ML3]+ and [ER] fragments in all cases, and the energetic differences between the two fragmentation schemes are lower than for the BCEs in most cases, ranging from 6.1 kJ·mol−1 (NiPbArMes) to 74.7 kJ·mol−1 (PtCArMes).
- (c)
When comparing the energetic differences ΔBCE and ΔBDE between the two fragmentation schemes in dependence on the transition metal, the observed trend is Ni ≈ Pt > Pd for the ΔBCEs and Pt > Pd > Ni for the ΔBDEs (ΔBCE = BCE(i) − BCE(ii) and ΔBDE = BDE(i) − BDE(ii), where i and ii denote the fragmentation schemes).
- (d)
The energetic difference between the two fragmentation schemes (ΔBCE and ΔBDE) follows the order C >> Si > Ge > Sn > Pb regarding the tetrel for both the ΔBCE and ΔBDE. The substituent effect (ArMes vs. Tbb) in the silylidyne complexes on the BCEs and BDEs is minute. However, because the BCEs of MSiTbb are slightly lower for the fragmentation into the ML3 + ER+ fragments than those of MSiArMes but slightly higher for the fragmentation into the ML3+ + ER fragments, the ∆BCEs of the MSiTbb complexes are lower than the ∆BCEs of the MSiArMes and MGeArMes complexes. For ΔBDE, the difference between Si and Ge is negligible.
For the remaining trends, only the values in
Table 2 given in bold are discussed in the following:
- (e)
The BCEs, if ordered by transition metal, follow the order Pt > Ni > Pd for E = C and Si and the order Ni > Pt > Pd for E = Ge, Sn and Pb. In comparison, the BDEs, if ordered by the transition metal, follow the order Ni > Pt >Pd for all tetrels. The reason for this difference is a significantly higher structural relaxation energy of the Pt(PMe3)3 fragment (avg. 104.4 kJ·mol−1) followed by the Pd(PMe3)3 (avg. 63.9 kJ·mol−1) and Ni(PMe3)3 fragments (avg. 54.8 kJ·mol−1), which lowers the BDEs of the PtER complexes more than the BDEs of the PdER and NiER complexes in comparison with the respective BCEs.
- (f)
If ordered by tetrel, the
BCEs and
BDEs follow the trend C >> Si > Ge > Sn ≈ Pb. This means that the M−E bonds of the carbyne complexes are, as expected, the strongest. However, the heavier ylidyne complexes exhibit considerable
BCEs and
BDEs. These are lower than those of the carbyne complexes, with the difference, though, being considerably smaller than those of the ditetrylynes. For example, the experimental dissociation enthalpy ∆
H° of acetylene of 964.8 ± 2.9 kJ·mol
−1 [
81] (∆
H°
calc(HCCH) = 953.0 kJ·mol
−1 at the level of theory
I and 970.2 kJ·mol
−1 at the level of theory
II) is ca. 13 times larger than that of the distannyne Ar
DippSnSnAr
Dipp (∆
Hexp = 72.0 ± 7.1 kJ·mol
−1) [
82]. Similarly, a calculation of the gas-phase dissociation enthalpy ∆
H°
calc of Ar
DippSnSnAr
Dipp at the level of theory
I leads to a value of 160.7 kJ·mol
−1, which is still only a small fraction of that of the analogous acetylene derivative Ar
DippC≡CAr
Dipp (∆
H°
calc = 721.7 kJ·mol
−1). In comparison, the
BDE of
NiSnArMes is still 63 % and 66 % of the
BDE of
NiCArMes on the level theory
I and
II, respectively, illustrating the considerable bond strength of the M≡E triple bonds. An important implication of this comparison is that C≡C bonds are stronger than M≡C bonds, whereas the opposite is true for the heavier group 14 elements Si–Pb (i.e., the
BDEs of the E−E bonds in E
2R
2 are smaller than those of the M≡E bonds).
- (g)
The choice of tetrel generally has a larger influence on the BCEs and BDEs than the choice of the transition metal. For example, the BCEs of NiGeArMes, PdGeArMes, and PtGeArMes are within 40 kJ·mol−1 of each other, whereas the BDEs of NiSiArMes and NiPbArMes differ by 83.3 kJ·mol−1.
As the charge distribution in the group 10 ylidyne complex cations is an important consideration for the comprehension of these compounds, atomic charges were calculated at the level of theory
I from a natural population analysis (NPA) in the natural bond orbital (NBO) framework using natural atomic orbitals (NAOs). The results are given in
Table 3 and
Figure 10. The metal atoms Ni, Pd, and Pt are either almost electroneutral for E = Si and Ge, with charges in the range of −0.03 e (
PdSiR) to +0.05 e (
NiGeArMes), or slightly negatively charged for E = Sn, Pb, with charges from −0.21 e (
PtPbArMes) to −0.09 e (
NiSnArMes,
NiPbArMes). A significant positive charge of +0.58 e (
PtGeArMes) to +1.07 e (
NiPbArMes) is carried by the tetrel atoms Si, Ge, Sn, and Pb, where the positive charges of the Si and Ge atoms are smaller than those of the Sn and Pb atoms. The entire ML
3 units carry total charges of +0.46 e (
NiPbArMes) to +0.76 e (
PtGeArMes), and the ER unit charges range for E = Si–Pb from +0.24 e (
PtGeArMes) to +0.54 e (
NiPbArMes). Overall, the silylidyne and germylidyne complexes behave very similarly but slightly differ from the charge distribution in the stannylidyne and plumbylidyne complexes. The dependence of the NPA charges on the tetrel atom is also much higher than on the metal atom.
These charges are comparable to the NPA charges for the complexes
B-Ge and
B-Sn, where the Ni atoms carry only small charges (
B-Ge: +0.05 e,
B-Sn: −0.19 e), and the tetrel atoms carry high positive charges of +1.01 e (
B-Ge) and +1.42 e (
B-Sn) [
53]. The charges on the Ge and Sn atoms of
B-Ge and
B-Sn are higher than the charges in the Ar
Mes-containing complexes due to the more electronegative amino substituent.
The group 10 ylidyne complexes with the heavier tetrel atoms have a quite different charge distribution from the group 10 carbyne complexes. This can be attributed to the special position of carbon among the group 14 elements in the periodic table reflected in its much higher electronegativity than that of its heavier congeners. This results in negative partial charges on the carbon atoms in the carbyne complexes, whereas the heavier tetrel atoms carry positive partial charges. Additionally, a clear shift in electron density from the ML3 to the ER unit is observed, leading to negatively charged ER ligands in the carbyne complexes, whereas the heavier tetrylidyne ligands ER (E = Si–Pb) are positively charged. For the same reason, the metal center carries a positive partial charge in the carbyne complexes but is electroneutral or slightly negatively charged in the heavier tetrylidyne complexes, and the ML3 unit carries a much larger positive partial charge in the carbyne complexes than in the heavier group 14 analogues.
2.4. ETS-NOCV and EDA
A very useful tool in the analysis of the chemical bond is the combination of the extended-transition state (ETS) [
83] method and natural orbitals of chemical valence (NOCV) [
84,
85]. The ETS-NOCV analysis was carried out on the level
I optimized structures using the ADF program package, as described in
Section 3. Within the ETS-NOCV scheme, an energy decomposition analysis (EDA) is used to decompose the interaction energy (Δ
Eint) of the complexes [L
3M≡E−R]
+ into chemically meaningful components (Equation (1)):
The orbital interaction energy ΔEorb represents the attractive interactions between the occupied molecular orbitals and the virtual orbitals of the two fragments. The Pauli repulsion energy ΔEPauli results from the destabilizing interaction between the occupied orbitals of the fragments. The third term, ΔEelstat, is the electrostatic interaction energy between the fragments as they are combined in the final molecule with the densities kept frozen, and the dispersion interaction energy ΔEdisp describes the long-ranged dispersive interactions of the fragments.
Because the choice of the electronic reference states of the fragments has a significant influence on all of the energy components and their sum, there is a certain degree of arbitrariness involved in the ETS scheme. The best way to determine the most appropriate electronic reference state of the interacting fragments is dependent on Δ
Eorb [
85]. It is assumed that the combination of electronic reference states for which |Δ
Eorb| becomes minimal most closely represents the electronic states of the fragments that are formed upon fragmentation. Another argument is that |Δ
Eorb| could otherwise be arbitrarily increased by the choice of arbitrary electronic states.
Interestingly, the electronic reference states for most fragments are the low-spin singlet states (
Table 4), which means the compounds are fragmented into L
3M and ER
+. This contrasts the preference for the cleavage into the L
3M
+ and ER fragments according to the
BCEs. The electronic reference state of the fragments in case of the carbyne complexes and
NiGeArMes and
PtGeArMes are the L
3M
+ and ER fragments in their doublet states, in line with the preferred fragmentation scheme according to the
BCEs.
The carbyne complexes prefer fragmentation into L3M+ and ER rather than fragmentation into L3M and ER+ due to the higher electronegativity of the carbon atom compared with its heavier homologs. Because ΔEorb directly depends on the charge transfer between and within the fragments, the fragments in which the atomic charges are closest to the respective atomic charges of the unfragmented molecule are favored. In case of the carbyne complexes, the natural charges of the carbon atoms in the CArMes fragments are +0.23 e (NiCArMes), +0.28 e (PdCArMes), and +0.27 e (PtCArMes); in the [CArMes]+ fragment, they are +0.53 e, independent of the metal. The charges of the carbyne carbon atoms in the carbyne complexes are −0.13 e (NiCArMes), −0.15 e (PdCArMes), and −0.24 e (PtCArMes), which are more similar to the respective charges of the CArMes fragments than to those of the [CArMes]+ fragments.
The ETS-NOCVs were also carried out using the triplet electronic reference states of the ML3 and ER+ fragments and the quartet electronic reference states of the ML3+ and ER fragments, but these resulted in much higher orbital interaction energies than the low-spin calculations.
The notable results are that |ΔEorb| is highest for the carbyne complexes ranging from −645.3 kJ·mol−1 (NiCArMes) to −903.3 kJ·mol−1 (PtCArMes), followed by the silylidyne and germylidyne complexes with a ΔEorb of −426.8 kJ·mol−1 (PdGeArMes) to −585.8 kJ·mol−1 (PtSiTbb), and the Sn and Pb compounds with a ΔEorb of −291.1 kJ·mol−1 (PdPbArMes) to −380.4 kJ·mol−1 (PtSnArMes).
The same trends were observed for Δ
EPauli and |Δ
Eelstat| (see the
SI). The dispersion interaction energy is almost identical for all complexes. The total interaction energy corresponds to the
BCE, with slightly different values due to the different levels of theory (see
Section 2.3).
Interestingly, the NiSnArMes and NiPbArMes complexes show no appreciable differences in the orbital interaction energies from their metallotetrylene counterparts (PdSnArMes, PdPbArMes, PtSnArMes, and PtPbArMes).
The orbital interaction energy can be further split into contributions of individual NOCVs, which allows for a detailed delineation of the bonding situation. Because the NOCVs are related to the fragment MOs, the fragment MOs involved in the bonding can be inferred by inspection of the NOCVs.
For the sake of simplicity, we only discuss the deformation densities of
NiSiTbb,
NiGeArMes and
PtPbArMes. All compounds marked as tetrylidyne complexes in
Scheme 3 exhibit similar NOCVs to either
NiSiTbb or
NiGeArMes, and all compounds marked as metallotetrylenes are similar to
PtPbArMes. More details can be found the
SI.
As shown in the top row of
Figure 11, the three largest contributions to the orbital interaction energy of
NiSiTbb are two π-symmetric and one σ-symmetric interaction. The first interaction (Δ
Eorb,1 = −199.6 kJ·mol
−1) is identified as the π-back donation from the HOMO−1 of Ni(PMe
3)
3 to the LUMO+1 of SiTbb
+. This interaction is marginally weaker than the second π-back donation (Δ
Eorb,2 = −206.8 kJ·mol
−1) from the HOMO of Ni(PMe
3)
3 to the LUMO of SiTbb
+. This slight difference is due to the competition of the first π donation with the π interaction of the empty p
x orbital on the Si atom with the phenyl ring of the substituent R (vide supra). The last interaction is the σ donation (Δ
Eorb,3 = −53.5 kJ·mol
−1) from the HOMO−10 of SiTbb
+ to the LUMO of Ni(PMe
3)
3. Remarkably, there is a substantial difference in the contribution to the bond strength between the π- and σ-type interactions, in which the σ-donation is weaker by a factor of roughly four compared with each of the π-back donations.
Because the interaction of the fragments in NiGeArMes takes place between the two open-shell doublet fragments GeArMes and Ni(PMe3)3+, the orbital interaction energies are further split into the α- and β-spin contributions. The first interaction is a π donation (ΔEorb,1,α = −108.4 kJ·mol−1) from the singly occupied MO (SOMO) of GeArMes to the SOMO of Ni(PMe3)3+, which is completed by the π-back donation (ΔEorb,1,β = −71.2 kJ·mol−1) from the SOMO of Ni(PMe3)3+ to the SOMO of GeArMes. Expectedly, the π donation is significantly stronger than the π-back donation and is accompanied by a larger charge transfer of 0.87 e vs. 0.41 e due to the cationic nature of the Ni(PMe3)3+ fragment. The sum ΔEorb,1,α, + ΔEorb,1,β gives the total orbital interaction energy ΔEorb,1 of −179.6 kJ·mol−1, which is slightly weaker than the first π interaction in NiSiTbb. The second interaction in NiGeArMes is also composed of an α- and β-spin component; both components involve, in this case, a charge transfer in the same direction from the metal to the tetrel (M→E π-back donation). The total interaction energy ΔEorb,2 of −135.7 kJ·mol−1 is albeit weaker than that in NiSiTbb. This is also the case for the third interaction, which is the σ donation (ΔEorb,3 = −77.4 kJ·mol−1) from the HOMO−1 of GeArMes to the LUMO of Ni(PMe3)3+. This σ interaction is slightly stronger than that in NiSiTbb, which can be explained by the direction of the charge flow from the neutral fragment GeArMes to the cationic fragment Ni(PMe3)3+ in NiGeArMes, whereas, in NiSiTbb, the charge flow from SiTbb+ to Ni(PMe3)3 via the σ donation occurs against the charge gradient.
Lastly, the three strongest contributions of the metallotetrylene-like compound PtPbArMes feature one strong σ-back donation (ΔEorb,1 = −180.1 kJ·mol−1) from the HOMO−4 of Pt(PMe3)3 to the LUMO+1 of [PbArMes]+. Notably, the acceptor orbital of this interaction is the pz orbital of the tetrel atom. The direction of the σ donation of the tetrylene-like compounds is opposite to that of the ylidyne complexes. The second interaction can be identified as a weak π-back donation (ΔEorb,2 = −74.7 kJ·mol−1) from the HOMO−3 of Pt(PMe3)3 to the LUMO of [PbArMes]+. This interaction is significantly weaker than in the compounds NiSnArMes (ΔEorb,2 = −136.3 kJ·mol−1) and NiPbArMes (ΔEorb,2 = −113.7 kJ·mol−1). The third interaction still indicates a weak π donation (ΔEorb,3 = −26.8 kJ·mol−1) from the HOMO−6 of PbArMes+ to the LUMO of Pt(PMe3)3. However, there is a significant amount of intrafragment charge-redistribution present, which is why this interaction plays a negligible role in the bonding between the Pt and Pb atoms.
In
Figure 12, we present the three bonding situations that describe the cationic group 10 tetrylidyne complexes discussed herein. Additionally, the tetrylidyne complexes with one σ-donating and two π-back interactions can be formulated with one π-type electron spin-pairing interaction bond replacing one of the π-back interactions. Although the formal charge of the latter type is located at the transition metal atom, no notable difference between the two types is observed regarding the charge distribution of the compounds including the heavier group 14 elements. The metallotetrylene type entails a cationic ER
+ fragment, which receives electron density from the metal fragment ML
3 via a σ bond and features notably smaller M−E−R angles (vide infra).
2.5. Metallotetrylene Isomers by PES Scans
When we optimized the structures of our complexes, we were surprised by the variability in the M−E−C1 bond angle, which significantly deviates from 180° for most structures (
Table 1). To energetically address this variability, we carried out PES scans of the M−E−C1 angle from 180° to 90° in steps of 10° for all heavier tetrylidyne complexes (
Figure 13). As can be seen, the steepness of the PES decreases in the order Si > Ge > Sn > Pb; more importantly, isomers with much smaller M−E−C1 angles of around 95° were found for most systems, abbreviated in the following as
MER-2, which were confirmed to be minima on the PES. These isomers are energetically not favored for most compounds as the energy difference between the isomers with the smaller and larger M−E−C angle shows (e.g.,
PdSiTbb-2: +47.1 kJ·mol
−1;
NiGeArMes-2: +83.5 kJ·mol
−1;
NiSnArMes-2: +55.3 kJ·mol
−1, at the level of theory
II; see the
SI). However, the more bent isomers,
PdSnArMes-2,
PdPbArMes-2,
PtSnArMes-2, and
PtPbArMes-2, were found to be energetically favored by 13–29 kJ·mol
−1. In the following, the isomer
PtPbArMes-2 is representatively discussed, and key properties of the other
MER-2 isomers are included in the
SI.
A comparison of the structural parameters of
PtPbArMes-2 (
Figure 14) and
PtPbArMes (
Table 5) shows a further elongation of the M−E bond from 267.7 to 281.9 pm when decreasing the M−E−C1 angle to 94.3°, whereas the E−C1 bond length stays nearly the same (233.7 pm). Notably, the metal adopts a distorted square-planar coordination in
PtPbArMes-2 (see the
SI) [
86].
Expectedly, the analysis of the LMOs of
PtPbArMes-2 (
Figure 15) shows an electron lone pair at Pb, a σ(Pt−Pb) bond that is highly polarized toward Pt (0.75 at Pt, 0.20 at Pb), and a σ(Pb−C) bond that is highly polarized toward the carbon atom (0.81 at C1, 0.28 at Pb).
The first deformation density of
PtPbArMes-2 given in
Figure 16 indicates that the σ(Pt−Pb) bond is best described as a donation from the Pt atom to the Pb atom. Notably, the orbital interaction energy Δ
Eorb,1 of 299.0 kJ·mol
−1 is larger in
PtPbArMes-2 than the corresponding orbital interaction energy in
PtPbArMes, as shown in
Table 6. The remaining orbital interactions of
PtPbArMes-2 are weaker than those of
PtPbArMes. However, the much higher Δ
Eorb,1 of
PtPbArMes-2 compared with that of
PtPbArMes ultimately leads to a net preference of the strongly bent isomer of 67.2 kJ·mol
−1 based on Δ
Eorb.