Stretching the P–C Bond. Variations on Carbenes and Phosphanes

The stability and the structure of adducts formed between four substituted phosphanes (PX3, X:H, F, Cl, and NMe2) and 11 different carbenes have been investigated by DFT calculations. In most cases, the structure of the adducts depends strongly on the stability of the carbene itself, exhibiting a linear correlation with the increasing dissociation energy of the adduct. Carbenes of low stability form phosphorus ylides (F), which can be described as phosphane → carbene adducts supported with some back-bonding. The most stable carbenes, which have high energy lone pair, do not form stable F-type structures but carbene → phosphane adducts (E-type structure), utilizing the low-lying lowest unoccupied molecular orbital (LUMO) of the phosphane (with electronegative substituents), benefiting also from the carbene–pnictogen interaction. Especially noteworthy is the case of PCl3, which has an extremely low energy LUMO in its T-shaped form. Although this PCl3 structure is a transition state of rather high energy, the large stabilization energy of the complex makes this carbene–phosphane adduct stable. Most interestingly, in case of carbenes with medium stability both F- and E-type structures could be optimized, giving rise to bond-stretch isomerism. Likewise, for phosphorus ylides (F), the stability of the adducts G formed from carbenes with hypovalent phosphorus (PX—phosphinidene) is in a linear relationship with the stabilization of the carbene. Adducts of carbenes with hypervalent phosphorus (PX5) are the most stable when X is electronegative, and the carbene is highly nucleophilic.

On the other hand, the reaction of PCl 3 with imidazol-2ylidenes having small substituents (R: Et, iPr, Mes) gave cationic (C) compounds 20 (the apparent byproduct Cl 2 being sequestered by a third molecule of NHC). Imidazol-2-ylidene (R:Dipp 33,34 and R:Me 35 ) formed adducts, 38−40 which, analogous to the silane case, were described with a single dative bond E (X = Cl) on the basis of the P−C distance. 38−40,44−48 These structures exhibit a "see-saw" arrangement at phosphorus. 38−40 Further interactions between carbenes and phosphanes have also been studied computationally, 49,50 with specific emphasis on weak pnictogen interactions. 51−53 According to these calculations, carbene− phosphane distances between ∼2.0 and 3.3 Å were reported for different stabilized singlet carbenes (including the NHC imidazol-ylidene and its oxygen analogue NOC) and various substituents at phosphorus. In case of the shortest (2.0−2.3 Å) distances, the energy of the interaction between carbene and phosphane approaches 15−20 kcal/mol, 49,50 and phosphorus has a distorted trigonal bipyramidal arrangement (E′ structure).
On the contrary, the bonding between a carbene R 2 C: and a phosphane :PR 3 is traditionally described as an ylidic double bond (λ 5 -PC bond). 54−72 While the charge separation (P + − C − character) can clearly be seen in the photoelectron spectrum, 73 the bond distance 74 is matching that of the λ 3 -PC bond. 75−79 Furthermore, Bader analysis provides similar characteristics (density and ellipticity) at the bond critical point for the λ 3 -PC and λ 5 -PC bonds. 80,81 Both the similarities and the differences can be understood, considering the presence of a hyperconjugative pseudo-π center (formed from the orbitals of the P-substituents) in case of the λ 5 -derivative. 80 In fact, this bonding model is equivalent to the model shown in Figure 2, considering the donation of the phosphine lone pair to the empty orbital of the (singlet) carbene augmented by a back donation of the carbene lone pair to the σ* orbitals at phosphorus (negative hyperconjugation). 82 The highest occupied molecular orbital (HOMO) of H 2 CPH 3 ( Figure  3 structure a) clearly shows the bond polarization (large contribution at carbon) but also the back donation toward phosphorus can easily be recognized.
In contrast, the HOMO of the λ 3 -PC bond (CH 2 PH) is nearly equally distributed between phosphorus and carbon ( Figure 3 structure b), in accordance with the similarity between the PC and CC bonds. 79,83 Accordingly, as an adduct between NHC and phosphane, the formation of an F-type structure, which is the λ 5 -PC counterpart of G, can also be envisaged. Stable singlet carbenes form G-type adducts with phosphinidene (known examples are  I−II, 22,84 which, as a strong nucleophile, has a key role in umpolung reactions. 117−119 Moreover, the 31 P NMR chemical shifts of these type of compounds were correlated with the π-polarizations of carbene−phosphorus bond as well. 120 Recently, these kind of adducts were reviewed, and their applications were highlighted as well. 121−123 Thus, the formation of any λ 5 -P containing F-type structure, where the NHC and the ylidic structure with opposing polarizing effects on the double bond (Figure 3), is clearly an interesting possibility; however, this type of adduct was not observed in the reactions between NHCs and phosphanes considered so far. This might be in accordance with the known destabilizing effect 72 of the amino substituents on phosphorus ylides; nevertheless, some C-amino-phosphorus ylides could be synthesized. 124,125 In view of the wide variation of the reaction products between phosphanes and different NHCs (Figure 1), the aim of the present computational study is the comprehensive investigation of the systems formed from the PX 3 (X = H, F, Cl, NMe 2 ) moiety and carbenes 1−11, yielding compounds with different electronic structures (in particular A, E, and F in Figure 1). The carbenes selected for our investigation (depicted in Figure 6) include mainly synthesized structures with (i) different σ-donor properties and (ii) with different stabilization (resulting mainly from π-donor interactions, raising the energy of the carbene empty orbital and consequently the singlet−triplet gap). The extent of the stabilizing interaction can be measured by singlet−triplet gap but more conveniently with the energy (ΔE ISO ) of the isodesmic reaction 1. 126 RR C: CH RR CH CH : (1) Figure 2. Bonding description of the λ 3 -PC and λ 5 -PC double bonds. The nonperpendicular (with respect to the bond) p-orbital lobes symbolize a σ* phosphorus-substituent orbital, which is involved in π-type back bonding. The stabilization energies (ΔE ISO ) from reaction 1 for the targeted carbenes are given in Figure 6 and Table S1. In the present work, we investigate the relative stability of the possible isomers, in case of the different carbenes, and discuss comprehensively the effect of the formal increase of the phosphorus valency on the P−NHC bond of the G-type compounds.

■ COMPUTATIONAL DETAILS
All calculations have been carried out with the Gaussian 09 program package. 127 Full geometry optimization was performed for all molecules at the ω-B97XD/cc-pVTZ 128 and M06-2X/cc-pVTZ 129 levels and also at the B3LYP-D3/cc-pVTZ level for calculations on isodesmic reaction 1 and on Gtype adducts, 130,131 followed by calculation of harmonic vibrational frequencies at the same levels to establish the nature of the stationary points obtained, as characterized by only positive eigenvalues of the Hessian for minima. Gibbs free energies were obtained from the calculated harmonic frequencies at 298 K and atmospheric pressure. During the discussion, we use M06-2X/cc-pvTZ results, the slightly different data obtained at the other levels of the theory are given in the Supporting Information. The Multiwfn program 132 was used for the determination of the bond critical points with the corresponding electron densities and ellipticities. For the visualization of the molecules and molecular orbitals, MOLDEN 133 and IQmol 134 programs were used.

■ RESULTS AND DISCUSSION
First, we discuss briefly the G-type carbene−phosphinidene adducts with carbenes 1−11. The P−C bond distance in these compounds (1.638−1.762 Åsee Table S2 of the Supporting Information) varies significantly, but it is in each case shorter than the P−C single bond (1.87 Å), 135 allowing to conclude that G is a (polarized) double bonded structure. As it can be expected, the molecules with longer P−C distances generally exhibit smaller dissociation energies (see Table S2 in the Supporting Information). The strongest bond (high adduct stability) belongs to those carbenes which exhibit the smallest stabilization energies (ΔE ISO ) in reaction 1, 126 as is evidenced by the linear correlation shown in Figure 7. It should be noted that for the most stabilized carbenes (ΔE ISO > 90 kcal/mol), the dissociation energy remains nearly unchanged showing a saturation effect, and accordingly, we have excluded these points from the correlation. The decrease of the double bond character results here in the polarization of the π-type HOMO, which then has a significant lone pair character as demonstrated in Figure 3c by the case of the most stabilized carbene 1. The polarization of this orbital decreases in case of the G-type compounds derived from less stabilized carbenes (see Figure S1 in the Supporting Information). Furthermore, these compounds also possess the "usual" in-plane lone pair orbital (shown also in Figure S1 of the Supporting Information) characteristic for the PC bond. Utilizing these two orbitals, the most polarized G-type compounds   . Correlation between ΔE ISO carbene stabilization energy and the dissociation Gibbs free energy of the CarbPH systems into carbene and (singlet) PH, and the F-type CarbPX 3 systems into carbene and PX 3 (X: H, F, Cl, NMe 2 ). The numbers of the "complexed" carbenes are given in the figure. Also the points for HClC: are added to provide additional points in the 0−40 kcal/mol ΔE ISO range. In case of the G-type compounds, the dissociation energy remains unchanged above ΔE ISO > 90 kcal/mol. These points (encircled) were excluded from the correlation.  The optimized structure (−10.8 kcal/mol) has a 2.41 Å C−Cl distance, indicating the easy formation of a C-type structure (see also Figure S2 in the Supporting Information). c The optimized structure has a 3.67 Å C−Cl distance, indicating the easy formation of a C-type structure (see also Figure S2 in the Supporting Information). d It should be noted that the prochiral carbene 4 can form two stereoisomers with phosphanes; however, the stability of the two structures does not differ significantly.  76 The ellipticity values (0.407−0.550) indicate an asymmetric electron distribution characteristic for π-systems (see Table S3 in the Supporting Information).
In a noteworthy contrast with the above discussed carbene− phosphinidene adducts, the optimized structures of the adducts between carbenes (1−11) and phosphanes PX 3 (X = H, F, Cl, NMe 2 ) exhibit high diversity, and the optimized structures can be classified as A, E, and F types on the basis of the atomic connectivity and the P−C distance. C-type structures from apparent reasons cannot be obtained in the gas phase optimization. However, in some cases, cationic like structures could be optimized, see footnotes a and b in Table  1. To characterize the different structures and their stability, we collected the P−C distances and the dissociation Gibbs free energies in Table 1 for the different carbene−phosphane adducts. Compounds with endoergic dissociation energies (stability against dissociation) are given in bold letters. Clearly, the least stabilized carbenes 9 and 10 (see Figure 6) form the most stable adducts throughout.
In case of the PH 3 adducts, only A-and F-type structures were obtained, the A-type structure being always the more stable one. This is in accordance with the general understanding 137 that in the condensed phase H-ylides of phosphorus (F) rearrange to their phosphane (A) counterparts via 1,2-H-shift 138 with the exception of some notable kinetically hindered cases. 139,140 In case of 1, 2, 7, and 8, no F-type structure could be optimized (neither at ω-B97XD/cc-pVTZ nor at M06-2X/cc-pVTZ see Tables 1 and S4), only very weakly bonded complexes with P−C distance over 3.2 Å could be obtained. Furthermore, among the F-type PH 3 adducts, only the least stabilized carbenes (ΔE ISO < ca. 50 kcal/mol) are stable against dissociation (Figure 7). It is noteworthy that in case of 1 and 7, also the A-type phosphanes tend to dissociate; in accordance, no reaction product was obtained in the reaction of PH 3 with an unsaturated imidazol-2-ylidene (flanked by bulky Dipp substituents). 22 In contrast, the saturated analogue (the Dipp substituted analogue of 2) gave the insertion product, 22 in agreement with its calculated stability against dissociation to PH 3 + 2. Altogether, these results provide an indirect evidence on the reliability of our calculations.
For the PX 3 (X: F, Cl, NMe 2 ) series in case of the least stabilized methylene (9) and dichlorocarbene (10), once more only the A-and F-type structures could be optimized, and all of them turned out to be stable against dissociation. Similar to the PH 3 adducts, A-type structures are more stable than F-type structures with the sole exception of F 3 PCH 2 . For the most stabilized carbenes (ΔE ISO larger than ca. 90 kcal/molFigure 6), no F-type structures could be optimized, while for carbenes with ΔE ISO between 70 and 90 kcal/mol, the F-type structures obtained are unstable against dissociation (Table 1). The decreasing stability of the carbenes (ΔE ISO ) correlates with the increasing stability (in terms of Gibbs free energy) of the Ftype adducts, as shown in Figure 7, exhibiting similar slope for all phosphorus compounds, including the above discussed Gtype phosphinidene adducts. Depending on the phosphane substituent, the dissociation Gibbs free energy of the F-type adducts is by about 70−100 kcal/mol smaller than that in the G series. Amongst the F-type systems, Carb + P(NMe 2 ) 3 (black points in Figure 7) exhibits the highest, while Carb + PH 3 (red points in Figure 7) exhibits the lowest stability. Similar linear correlation was also observed between ΔE ISO of a series of carbenes and the stability of the corresponding Breslow intermediates, which can be described as a hydroxycarbene adduct of the given carbene. 141 Also the dimerization Gibbs free energy of the carbene itself correlates with ΔE ISO . 126 Clearly, the raising energy of the carbene empty orbital (due to the stabilizing π-interactions) makes the donation from the lone pair of the attacking phosphane less effective. From this point of view, it is noteworthy that the above mentioned "saturation effect" in the stabilization of the G-type adducts for the carbenes with ΔE ISO > 90 kcal/mol is in line with the fact that we were not able to optimize F-type structures for the same carbenes. This fact further corroborates the importance of the donation from the phosphorus lone pair in the F-type structures.
Contrary to the PH 3 adducts in case of the PF 3 , PCl 3 , and P(NMe 2 ) 3 series, most carbenes (with the exception of the least stabilized 9 and 10) form single P−C bonded E-type structures. It is especially noteworthy that the PCl 3 series, where most of the E-type adducts were reported experimentally, is the most stable against dissociation. The P−C distance (1.831−1.948 Å in Table 1) in these compounds falls basically in the single bond regime. The most stable adduct is formed with 7, but even in this case, the ∼20 kcal/mol interaction Gibbs free energy (without BSSE correction) is far less than a usual P−C bond energy (ca. 63 kcal/mol). 142 These structures exhibit a see-saw arrangement, in accordance with the reported X-ray structures, 33−35 the chlorophosphane part having a T-shaped form. In this structure, the lone pair on the phosphorus is the HOMO, as shown on the example of the adduct formed between 4 and PCl 3 in Figure 8a. It is noteworthy that the HOMO of the T-shaped PCl 3 unit ( Figure  S3 in the Supporting Information) is similar to that of adduct 4, indicating that this feature is unperturbed upon complexation. The T-shaped PCl 3 structure is known as a transition state for the inversion of the phosphorus pyramid, 143,144 and the barrier of this inversion is 52.0 kcal/mol (55.8 kcal/mol in case of PF 3 ). This type of molecular geometry was also observed in case of tetrafluorophosphite anion. 145 Thus, it is reasonable to consider that a T-shaped chlorophosphane (fluorophosphane) is able to be complexed by the carbene. Although, the planarization energy is quite large, the lowest unoccupied molecular orbital (LUMO) of the T shaped PCl 3 , which is basically of "p" type ( Figure 9), is at −4.27 eV(!), which is much lower than the LUMO energy of the pyramidal phosphane (−0.46 eV). The presence of this easily accessible empty orbital facilitates the complex formation between the strongly nucleophilic carbenes and the T-shaped PCl 3 , by formation of a dative bond. In case of PF 3 , the The Journal of Physical Chemistry A pubs.acs.org/JPCA Article corresponding orbital appears at somewhat higher energy (−2.87 eV in Table S5 of the Supporting Information), and accordingly, the dative bond is weaker, explaining the lower dissociation Gibbs free energies in the fluorophosphine complexes. Altogether, the energy gain upon formation of the new P−C (dative) bond of the E structure should cover the energy demand for the formation of the T-shaped PX 3 structure. Because in the most strongly bound E-type structures (Table 1), the P−C distance falls in the usual single bond range, the usual bond strength (about 63 kcal/ mol 125 ) can be surmised. Because the energy requirement of the formation of the T-shaped structure is ca. 50 kcal/mol (see above), the calculated 10−20 kcal/mol binding Gibbs free energy of the E-type adducts (Table 1) is in reasonable accordance with the aforementioned considerations. The most stable adducts (Table 1) are indeed obtained with the most nucleophilic carbenes (4, 7, 8their HOMO energies are listed in Figure 6). On the contrary, 6 and 9−11 exhibit the most negative HOMO energies, and accordingly, their complexes are unstable against dissociation. Clearly, the plot of Δεthe energy difference of the carbene lone pair and the LUMO of the T-shaped PX 3 (X: F, Cl) fragmentagainst the adduct stabilization energy shows a common correlation ( Figure 10), for the PF 3 and PCl 3 adducts. It is noteworthy that 3, 5, and 11 (all large bond angle carbenessee Table S6 of the Supporting Information) are outliers, exhibiting smaller stability than expected on the basis of the HOMO−LUMO interaction energy of the fragments. Apparently, the steric requirement of these rings is larger than that of the smaller rings, reducing the stability of the adduct. Each PF 3 compound has reduced stability with respect to the corresponding PCl 3 counterpart, in accordance with the difference between the LUMO energies of the T-shaped PF 3 and PCl 3 structures (see Table S5 of the Supporting Information). It is also worthy to mention that the LUMOs of the T-shaped PH 3 and P(NMe 2 ) 3 are at significantly higher energies (see Table S5 in the Supporting Information); thus it is understandable that these phosphanes do not form stable "see-saw" adducts with the carbenes. Altogether, in contrast with the F-type structures, where the decisive stabilizing contribution comes from the donation of the phosphorus lone pair to the empty carbene orbital, which is available (having a low energy) only for the less stabilized carbenes, in case of the E-type structure, the donation from the carbene lone pair has the largest stabilizing contribution, in particular with those phosphanes, where the Tshaped structure has a low energy LUMO. It is worth mentioning that the formation of the E-type structure can alternatively be explained starting from the highly stable G-type carbene−phosphinidene adduct. By forming a 3c−4e hypercoordinate, X−P−X bond with the involvement of the HOMO of G (Figure 3c) and two halogens, the see-saw structure with the T-shaped PX 3 unit, and the residual HOMO − 1 in-plane phosphorus lone pair of G, which becomes then the HOMO (Figure 8a), can clearly be understood. Further type of complexes with somewhat extended P−C interatomic distance can also be optimized in case of X: Cl and F. These E′ structures (Figure 8b) not only exhibit extended P−C bond distances (2.041−3.025 Å with the stabilized carbenes: 1−8) compared to the E "see-saw" adduct, but they form a typical trigonal bipyramidal arrangement, with the carbene and one P−X bond aligned axially. The assembly is held together by the recently intensively discussed pnictogen interaction, 51,146,147 which is interpreted as (i) the electrostatic attraction between the positively charged region (σ-hole) next to the phosphorus lone pair and negative charge at the carbene lone pair and (ii) the donation of the carbene lone pair to the σ* orbital of the axially aligned P−X bond (see on Figure  8b). 48−51 The resulting structures were discussed in detail in case of the adducts between highly stabilized carbenes (as imidazol-2-ylidene) and PH 2 X (X: halogen). 48,49 This interaction is weaker than in case of the T-shaped PX 3 because the LUMO is at higher energy (in case of PCl 3 as much as by 3.81 eVsee Figure 9). However, because the T-shaped transition state itself is by about 50 kcal/mol higher energy as was mentioned above, the E and E′ structures have comparable stability. While for the PCl 3 series, E structures are more stable than E′ (Table 1) due to the highly stabilized LUMO of the Tshaped structure, the stability order is reversed for the PF 3 series, where the LUMO of the T-shaped PF 3 structure has higher energy (see Table S5 in the Supporting Information). Altogether, most of the E′ structures are unstable against dissociation. The P−C distances are varied over a wide range (2.041−3.025 Å in case of PCl 3 adducts, as seen in Table 1) for the different carbenes. Similarly, a large variation was found in the P−C distances in the case of the adducts of a single carbene (e.g. imidazol-2-ylidene) and a series of phosphanes (H 2 PX (X: F, Cl, Br, OH, NH 2 , CN, NC). 48,49 In that papers, Figure 9. Relative energies of the pyramidal ground state and the Tshaped transition state of PCl 3 (in kcal/mol), together with their LUMO (energies in eV). The direction of the attacking carbene nucleophile (Carb:) is shown by arrows pointing to the LUMO. Figure 10. Stability of the E-type complex with the T-shaped PX 3 ΔG (in kcal/mol), against Δε the energy difference of the carbene lone pair HOMO and the LUMO of the T-shaped PX 3 fragment (in eV). X: Cl and F. Carbenes 3, 5, and 11 are outliers due to the expanded bond angle around the carbene (as shown in Table S5 of the Supporting Information) and are not considered in the correlation. 9 and 10 do not form E-type adducts. It should also be mentioned that 6 also belongs to the large bond angle carbenes; however, due to its stable HOMO, it forms a weak complex with a long P−C distance, and thus the effect of the steric encumbrance is less important.
The Journal of Physical Chemistry A pubs.acs.org/JPCA Article two types of adducts (nonplanar and coplanar) were distinguished based on the alignment of the phosphane to the carbene. In case of 1, 2, 5, 7, and 8 with PCl 3 , both nonplanar and coplanar structures could be optimized; however, the Gibbs free energy differences are within 2 kcal/ mol (more details in Supporting Information, Table S7). In fact, it was shown that while dominantly the carbene is the donor in these structures, 49 also the phosphorus lone pair contributes with some reverse donation effect. Accordingly, we were not able to find correlation between the P−C distance of the adducts and neither the HOMO nor the LUMO energy of the carbenes (see Table S8 in the Supporting Information). Nevertheless, the P−C distances of the PCl 3 adducts are in an inverse correlation with the PCl distances, and accordingly, the formation of the strongest complexes facilitates the cleavage of the PCl bond, in accordance with the formation of the B-and D-type ion pair structures.
In case of carbenes, which are not "too much" stabilized (ΔE ISO = 70−90 kcal/mol) and are also rather nucleophilic, two or three different types of adducts could be optimized with X: Cl and F. In case of 3, 5−6, and 11, these three structures are F, E, and E′, and in case of 4 and PF 3 , all the structures F, E, and E′ could be optimized. This is an interesting example of the rare and somewhat debated bond-stretch isomerism. 148−155 To our best knowledge, this is the first case where three distinct minima could be located from two reactants, without breaking the other bonds of the interacting units. We were also able to locate the transition states between the minima for the PF 3 adduct with carbene 4 (Figure 11). Because the reaction barriers are not too high, it seems unlikely that all three structures could be detected at room temperature.
As we mentioned above, the E-type structure can be derived from G, by the formation of a 3c−4e bond with the phosphorus localized HOMO (Figure 3c). Accordingly, it is reasonable to consider that the remaining phosphorus lone pair at E (see Figure 8a) is able to form a further 3c−4e bond with two halogens, yielding Carb → PX 5 adducts. Indeed, we could optimize stable adducts (I) between most carbenes (see footnote in Table 2) and PF 5 or PCl 5 (as an example, the PF 5 adduct of 7 is shown in Figure 12). A few adducts of this type have already been reported before in case of carbenes 1 and 2 with PF 5 . 156−161 The ΔG diss values of I for different carbenes cover a wide range (−12.5−41.1 kcal/mol in Table 2). The dissociation Gibbs free energies of the PF 5 adducts are higher than for the PCl 5 adducts for most carbenes. Likewise, carbene SiF 4 adducts were more stable than the analogous carbene SiCl 4 adducts. 40 The optimized P−C lengths (in the 1.85−2.15 Å range) correspond to somewhat extended P−C single bonds, again the (less stable) PCl 5 adducts exhibiting larger distances than their PF 5 counterparts. While the stability of the I-type compounds is related to the nucleophilicity of the carbene (similarly to the E-type adducts), no joint correlation line could be obtained for the chloro and the fluoro compounds (see Figures S4−S5 of the Supporting Information). Nevertheless, the trends are similar for the two series, although it is difficult to discuss correlation in statistical terms, due to the small number of data points. However, it is noteworthy that the outliers correspond to the same carbenes as in the case of the PX 3 series, assumedly in accordance with the steric effect.
It is noteworthy that the aNHC (7) adducts exhibit larger stability against dissociation than the isomeric NHC (1) adducts. This suggests that the aNHC (7) adducts of both the PF 5 and PCl 5 remain stable once synthesized, as was reported for CO 2 162,163 and SiCl 2 16 adducts before.

■ CONCLUSIONS
The structure and the properties of the carbene−phosphane adducts depend strongly on the interacting carbenes and phosphanes, yielding in principle three different types of structures. The stability of these adducts against dissociation is Figure 11. Bond-stretch isomers (E, E′, and F) and their connecting transition structures for the adducts between PF 3 and 4.  The Journal of Physical Chemistry A pubs.acs.org/JPCA Article rarely exceeding 50 kcal/mol (Table 2), andespecially in case of H-phosphanesthey can be stabilized by shifting one substituent from phosphorus to carbon, resulting in A-type structures. For the least stabilized carbenes, the double bonded/ylidic (F type) structure with some double bond character/back bonding is preferred. In case of these structures, the stability of the adduct is determined by the strength of the donation from the phosphorus lone pair to the empty orbital of the carbene augmented by back-bonding from the carbene lone pair to the proper σ* orbital of the P−X bonds. The stability of this type of adducts is in strong correlation with the (de)stabilization of the carbene, similarly to other double-bonded carbene adducts (e.g. the Breslow intermediates or the G-type carbene−phosphinidene adducts).
In case of the most stabilized carbenes, the stability of the adduct is determined by the nucleophilicity of the carbene (the energy of the HOMO, which is basically a carbon centered lone pair) and that of the phosphane LUMO. It is noteworthy that in case of PCl 3 , the energy of the LUMO in case of the Tshaped transition structure is extremely low. This facilitates the adduct formation even with the high energy T-shaped phosphane, yielding a "see-saw" structure (E), while for other P-substituents (F, NMe 2 ), the formation of the usual trigonal bipyramidal adduct (E′) is more preferred. These structures are mainly stabilized by pnictogen interactions; nevertheless, these E′ structures are rather unstable against dissociation, even with the most nucleophilic carbenes.
In case of medium stabilized and rather nucleophilic carbenes (with high HOMO energy) more structures can be optimized, giving rise to the formation of bond-stretch isomers. In case of some phosphanes and carbenes (e.g. PF 3 with CAAC 4) even three different types of bond-stretch isomers could be optimized.
The electronic structure of the adducts can also be understood from the phosphinidene carbene adducts (G structure), utilizing the lone pair for the formation of 3c−4e bond as was discussed before for simple phosphorus ylides. 80 The formation of a further 3c−4e bond with the remaining phosphorus lone pair of the resulting E-type structure yields Itype structures, which are neutral hexacoordinate phosphorus compounds.
Various DFT levels of theory stabilization energies for the investigated carbenes in the isodesmic reaction; various DFT levels of theory dissociation energies and P−C bond lengths of the carbene−phosphinidene adducts; the electron densities, the ellipticity values, and the Mayer covalent bond indices of the P−C bond in the optimized carbene−phosphinidene type of structures; ωB97X-D/cc-pVTZ dissociation Gibbs free energy and distance between the P moiety and the carbene unit of the investigated compounds; LUMO energy of the T-shaped transition structure of PX 3 , and its relative energy with respect to the pyramidal minimum; M06-2X/cc-pVTZ bond angle around the carbene center for the investigated carbenes; the lone pair orbitals of the G type phosphinidene adducts; the HOMO of the C type structures; the M06-2X/cc-pVTZ HOMO of the PCl 3 structure; relative stability and P−C distance of the coplanarly and nonplanarly aligned E′ type adducts with PCl 3 ; orbital and electronical parameters of the investigated carbenes 1−8; The correlation of the dissociation Gibbs free energy of the CarbPX 3 /CarbPX 5 (X: F, Cl) systems into carbene and (singlet) PX 3 /PX 5 and the difference between Tshaped PX 3 LUMO energy/tetragonal pyramidal PX 5 LUMO energy and the singlet carbene HOMO energy; and energies and XYZ coordinates of the investigated adducts and structures for the isodesmic reaction calculations (PDF)