EDA-NOCV Analysis of Donor-Base-Stabilized Elusive Monomeric Aluminum Phosphides [(L)P–Al(L′); L, L′ = cAACMe, NHCMe, PMe3]

Herein, we report on the stability and bonding analysis of donor-base-stabilized monomeric AlP species (1–6) of the general formula (L)P–Al(L′); [L = cAACMe, L′ = cAACMe, NHCMe, PMe3, (NiPr2)2 (1–4); L = L′ = NHCMe, PMe3 (5 and 6); cAAC = cyclic alkyl(amino) carbene; NHC = N-heterocyclic carbene]. Energy decomposition analysis coupled with natural orbitals for chemical valence (EDA-NOCV) analysis indicates the synthetic viability of this class of species, stabilized in their singlet ground state, in the laboratory. The CL–P bond is found to be a partial double bond (WBI ∼ 1.45), while the CL/PL–Al bond is a single bond (WBI ∼ 0.42–0.69). These bonds are mostly covalent or dative σ/π bonds depending upon the ligands attached. The central P–Al bond is an electron-sharing covalent polar single bond (WBI ∼ 0.80; P–Al) for 1–4 and a dative σ bond for 5 and 6 (WBI ∼ 0.89–0.93; P–Al). The calculated intrinsic interaction energies of the central P–Al bonds are found to be in the range from −116 to −216 kcal/mol (1–3 and 5 and 6). This value is the highest for compound 3, possibly due to the push and pull effects from the ligands PMe3 and cAAC, respectively.


■ INTRODUCTION
Having a similar outer valence shell with one crucial extra intranode in the more diffused orbitals, stabilization of multiple bonds between homo-and heterodiatomic third-row elements is of immense synthetic challenge. 1 Moreover, the weaker sideon overlap of the p-orbitals between these elements along with the significant Pauli repulsion energy keeps the synthetic chemists at the bay. 2 Sketching the structure of these species on the paper and subsequently trying to synthesize them in the laboratory are always intriguing. 3 However, for theoretical computational chemists, it is an ambitious goal to come up with the required theoretical calculations in this technologically advanced modern world to understand and predict the stability of such species. 3−15 In this regard, energy decomposition analysis coupled with natural orbital for chemical valence (EDA-NOCV) analysis 16 is a sufficiently powerful computational tool to rationalize and predict the stability of such synthetically elusive species. Hence, EDA-NOCV is called the state-of-the-art calculation. In the past, the stability of many unusual chemical species has been predicted, 17 and later on, they have been successfully synthesized by synthetic chemists and isolated in the laboratory 18 in reasonable yields. In this regard, bulky ligands and/or donor-base ligands played an extremely important role. Many of such species have been stabilized by phosphines and carbenes (cAAC and NHC; cAAC = cyclic alkyl(amino) carbene, NHC = N-heterocyclic carbene) by their electronic effect rather than the steric effect. 19 The synthetic success achieved by employing cAAC as a ligand in the past one and half decades 20 is enormous. Hence, cAAC can be compared to a unicorn among the ligands in the field of main group chemistry in modern days. 14,19,20 It is astonishing to take a look back at what chemists have achieved around the globe till now and yet much more to come. Many of such cAAC-containing species have now entered into the areas of application-based studies. 21 Aluminum phosphide has attracted the attention of chemists due to its usage as a fumigant, insecticide, rodenticide, and further application as a precursor for the AlP source as composite materials in the form of a crucial intermediate in hydrogen storage. 22−25 Very recently, the research group of H. Braunschweig isolated phospha-alumenes (B) with a PAl bond utilizing a bulky aryl ligand on a P atom and a cyclopentadienyl group (Cp*) on an Al atom 26 after the initial prediction on the stability of the PAl triple bond (A) by the group of Ming-Der Su (Scheme 1). 2 In this context, it is worth mentioning a few examples of the molecular dimers and/or trimers of the PAl species. 27 Fascinated by these results, we wondered whether the AlP monomer can be stabilized by introducing neutral donor-base ligands, and herein, we report on the NBO, QTAIM, and EDA-NOCV analysis of the donor- using the Gaussian 16 program package at the BP86-D3(BJ)/ def2-TZVPP level. 28 The absence of imaginary frequency assured the minima of the potential energy surface (PES). The natural bond orbital (NBO) 29 analysis for compounds 1−6 has been performed using the NBO 6.0 30 program to evaluate the partial charges, Wiberg bond indices (WBI), 31 and natural bond orbitals. EDA-NOCV analyses were performed using the ADF2020.102 program package. EDA-NOCV 32 calculations were carried out at the BP86-D3(BJ)/TZ2P level using the geometries optimized at the BP86-D3(BJ)/def2-TZVPP level. The details of EDA-NOCV calculations have been given in the Supporting Information (SI).

■ RESULTS AND DISCUSSION
The calculations at the BP86-D3(BJ)/def2-TZVPP level suggest that compounds 1−6 are stable in their singlet ground states (Figure 1), and the corresponding triplet states are higher in energy by 8.4 (1)−42.20 (4) kcal/mol (Table S3). Despite the fact that the BP86 functional is now obsolete, we used it for the current calculations as it yielded comparable results with the experimental values both in our previous studies and also in similar studies reported in the literature. 33 In compounds 1, 5, and 6, the P−Al fragment is flanked on both sides by cAAC Me , NHC Me , and PMe 3 , whereas in compounds 2−4, P is bound to cAAC Me and Al is bound to other donor ligands like NHC Me (2), PMe 3 (3), and N i Pr 2 (4). The variation of ligands is aimed at understanding the stability of the compounds in this study with different donor ligands. The geometries shown in Figure 1 illustrate that the ligands are arranged in trans fashion with respect to the P−Al moiety in 1, 2, 3, and 6, whereas in 5, the ligands are cis to each other, which is also supported by their corresponding torsion angles ( Figure 1). The C cAAC/NHC −P bond lengths of 1−5 ( Figure 1) correlate well with the recently reported theoretical/experimental values in (cAAC) 2 PSi(X) and NHC-PSi(X) (X = Cl, F) 33c and (cAAC)P−Cl, 34 respectively. The Al−L bond length varies considerably depending upon the ligands employed and is the shortest in 4, where L′ is two N i Pr 2 groups, and the longest in compounds 3, 5, where L′ is PMe 3 ( Figure 1, Table  S1). The Al−L′ bond lengths of 2 and 4 are longer than the single bond distances found in the experimentally synthesized dimethylaluminum supported by functional amine-linked NHC ligands (1.980−1.9832 Å) 35 37 The computed P−Al distances (2.33−2.57 Å) of 1−6 are longer than the reported PAl triple bond distance of 2.12 Å 2 and the PAl double bond distance of 2.21 Å in Ar−PAl(Cp*), 26 suggesting a P−Al single bond ( Figure 1). The P−Al bond distances of 1−6 ( Figure 1, Table S1) agree well with the P− Al single bond lengths of the Lewis base-coordinated phosphanylalumane, MesP(H)-Al(Br)(L)Bbp (2.407 Å). 38 The P−Al bond length (2.33 Å) in 4 is slightly shorter than the other compounds. While the cAAC−P−Al bond angle (106.2−108.2°; Figure 1, Table S2) remains almost the same in 1−5, the P−Al−L′ angle, on the other hand, varies with L′ in the order of 3 (79.4°, PMe 3 ) < 2 (85.1°, NHC Me ) < 1 (91.2°, cAAC Me ) < 4 (117.2°, N i Pr 2 ) ( Figure 1, Table S2). The difference in P−Al−L′ angles can be attributed to the steric effect and bulkiness of the ligands (L′).
We have performed NBO analysis 29 to understand the bonding pattern, charge distribution, and electron density distribution. The NBO results infer that the C cAAC/NHC −P bonds are similar for complexes 1−5.
The Wiberg bond indices (WBI) 32 of 1.45−1.56 (Tables 1,  S4−S6) indicate the presence of a CP double bond in compounds 1−4 and a partial double bond in 5 (CP, 1.25) and 6 (PP, 1.24), respectively. The C cAAC → P σ donation arising from the overlap of sp 2 −sp 3 hybrid orbitals is more polarized toward the ligand with an occupancy of ∼1.97 e and the π back donation from P → C cAAC resulting from the overlap of p-orbitals, which is more polarized toward P with an occupancy of ∼1.86e (Tables 1, S4−S6), indicating a donor− acceptor interaction. The WBI values of 0.42−0.69 for the Al− C/P L bond suggest a single bond character. In compounds 3, 5, and 6, the Al−C/P L bond is polarized toward the ligand, indicating a possible L → Al σ donation. The NBO analysis did not provide information on the occupancy and polarization of the Al−C cAAC bond of compounds 1, 2, and 4.
The bond order of 0.79−0.93 for the P−Al bond suggests a single bond character, which is polarized toward P since it is comparatively more polar. As expected, 4 shows two different bonding occupancies for the P−Al bond, which are polarized toward the P atom. The highest occupied molecular orbital (HOMO) represents the lone pair of P and Al atoms in all compounds ( Figure 2). In 1, we could observe a slight interaction between the lone pair of Al atoms and cAAC with a significant coefficient residing on the Al center ( Figure 2). The HOMO-1 represents the C cAAC P π bond, which is slightly extended toward Al atoms, and HOMO-2 illustrates the interaction of a lone pair on the P atom with Al ( Figures  We investigated the topological properties of electron density (ρ(r)) and its Laplacian (∇ρ(r)) using quantum theory of atoms in molecules (QTAIM) analysis. 39 The wave functions for the QTAIM studies were computed at the BP86/ def2-TZVPP level of theory on the optimized geometries of compounds 1−6. The electron densities (ρ(r)) between 0.1 and 0.2, 39 as well as positive Laplacian (∇ 2 ρ(r)) at the bond critical point (BCP) of the L−P and Al−L′ bonds in compounds 1−6, indicate closed-shell interactions (Tables S7−S12). The ellipticity, ε, measures the π character of the bond. When the bond is cylindrically symmetrical, as in the case of single and triple bonds, ε is close to zero because of the cylindrical contours of electron density. For a double bond, it is greater than zero due to the asymmetric distribution of electron density, perpendicular to the bond path. 39 The ε values of 0.157−0.308 for the C cAAC −P bonds in compounds 1−4 and 0.057−0.068 (Tables S7−S12) for C cAAC −P and P− P bonds in compounds 5 and 6 correlate well with the WBI values from NBO analysis and indicate a double bond character in 1−4 and a partial double character in 5 and 6. However, unlike the NBO analysis, the ε values of Al−L′ (0.163−0.312) also reveal a double bond character. The ε values for the P−Al bond, on the other hand, support the single bond character in almost all complexes except compounds 4 and 5 (Tables S7−S12).
We have employed energy decomposition analysis coupled with natural orbitals for chemical valence (EDA-NOCV) 16 6)]. The EDA-NOCV method is more appropriate in explaining the nature of the bond, as one of the major strengths of the method is its ability to provide the best bonding model to represent the bonding situation in the equilibrium geometry. The details of the method are given in the Supporting Information (SI). The bonding model with the lowest ΔE orb is considered the best bonding representation since it involves the least change in the electronic charge of the fragments to create the electronic structure of the molecule. 40 To arrive at the best bonding description, we considered four different bonding possibilities (Scheme 2) Table S14 (see SI) indicate that the best bonding description in compounds 1, 2, 5, and 6 comes from the interactions of neutral [L L′] and [PAl] fragments in the singlet state forming dative bonds (Scheme 2a) since it gives the lowest ΔE orb . However, it is worth mentioning that the bonding in compound 2 can also be described in terms of a mixture of dative and electron-sharing bonds, as shown in Scheme 2d, due to the low ΔE orb difference between the two bonding possibilities. Similarly, in compound 3, the bonding can be described both in terms of a mixture of dative and electron-sharing (Scheme 2d) and exclusively dative bonds (Scheme 2a) since the orbital energies of possibility (a) match closely with that of possibility (d). On the other hand, for compound 4, the bonding can be best discussed as electronsharing (Scheme 2b). We have categorized and discussed the compounds showing similar bonding situations in Tables 2, S15, and S16 for clarity.
The dissociation energy (−De) and the interaction energy (ΔE int ) demonstrate the strength of the bond. Tables 2, S15, and S16 show that the L−PAl−L′ bonds are relatively stronger in compound 4 (L = cAAC, L′ = (N i Pr 2 ) 2 ) and weaker in compound 6 (L = L′ = PMe 3 ). The difference between interaction energy (ΔE int ) and dissociation energy (−De) is termed preparative energy (ΔE prep ). The preparative energies originate from the distortions in the geometry of the fragments from their equilibrium structure to the geometry and electronic states in the compound. It often takes a significant amount of energy to excite the electrons of the fragments to the suitable excited energy states to make them ready for the formation of bonds. Therefore, the compounds with high ΔE prep values indicate that the relaxed fragments are very different from the fragments in the molecules and hence only poorly reflect the electronic situation in the total molecule. According to the results, compound 3 (Table S15) show relatively higher preparative energy followed by 4 (Table S16) and 6 ( Table 2). Compounds 1−3 and 5 possess slightly higher electrostatic (Coulombic) contributions, while 4 and 6 show higher orbital (covalent) contributions toward the total attractive interactions (ΔE int ) (Tables 2, S15, and S16). The contributions due to attractive dispersion interactions (ΔE disp ) are quite low (2.2−3.6%).
The breaking down of ΔE orb into pairwise contributions brings more insight into the orbital interactions involved between the fragments, leading to the formation of the particular bonds in the present study. The calculations manifest four relevant orbital contributions, ΔE orb(1) − Table 2 ΔE orb(4) for compounds 1, 2, 5, and 6, which show similar bonding situations. The type of interactions and the direction of charge flow can be well understood from the deformation densities Δρ n and associated fragment orbitals (Figures S17, S7, S9−10). The first two pairwise contributions ΔE orb(1) and ΔE orb(2) represent strong out-of-phase (+ −) σ-donation from HOMO of the ligands into the LUMO of the [PAl] fragment and rather weak in-phase (+ +) σ-donation from HOMO − 1 of the ligands into the LUMO + 1 of the [PAl] fragment, respectively, in compounds 1, 2, 6. However, in compound 5, the in-phase (+ +) σ-donation (ΔE orb (1) ) is stronger than the out-of-phase (+ −) σ-donation (ΔE orb (2) ). The other two pairwise contributions ΔE orb (3) and ΔE orb(4) denote weak π back donations from the HOMO-1 and HOMO of the [PAl] fragment into the vacant orbitals LUMO−LUMO + 4 of the ligands in compounds 1, 2, 5, and 6. The L → P−Al ← L′ σ donations together contribute 59.6−79.3%, while L ← P−Al → L′ π back donations together contribute 13.9−32.5% of the total orbital interactions. Compound 1 shows relatively stronger π back donations followed by 2, 5, and the least in compound 6. The strength of the π back donations falls in line with the π-accepting capacity of the ligands. However, the strength of the σ donations follows the reverse order.
The major contribution to the ΔE orb in compound 3 (Table  S16) is from electron-sharing σ interaction (61.7%) occurring between the singly occupied molecular orbital (SOMO) of [(cAAC) PMe 3 ] + and [PAl] − (ΔE orb (1) ). The ΔE orb (2) represents in-phase σ donation (11.9%) from the [(cAAC)-(PMe 3 Figure  S8). However, the second orbital term, ΔE orb (2) , arises due to the electron-sharing σ interaction between the cAAC ligand and P of the [PAl] moiety. The other two orbital terms (ΔE orb (3)(4) ) represent π electron-sharing contributions between SOMO-1, SOMO and SOMO, SOMO-3 of the interacting fragments, respectively. The last contribution is due to the outphase dative σ donation from HOMO of the ligand fragments to the LUMO of the [PAl] fragment. It can be expressed as cAACP−Al(N i Pr 2 ) 2 . The σ interactions together contribute ∼64% and π interactions together contribute 28% of the total orbital interactions. The nature of P−Al bonds of 1−6 has been also studied by EDA-NOCV analyses, which is schematically shown in Scheme 3 (see SI for detailed analyses).

■ CONCLUSIONS
We have theoretically studied the bonding and stability of monomeric AlP species by EDA-NOCV analysis, which suggests that these exotic species (1−4 and 5 and 6) are possible to stabilize and isolate in the laboratory. Ligands play an important role in their stabilizations. Both σ-donating and π-accepting properties of L and L′ are in the following order: Me 3 P < N i Pr 2 <NHC < cAAC. The phosphine being a poor π  (4) . The eigenvalues |ν n | give the size of the charge migration in e. The direction of the charge flow of the deformation densities is red → blue.
acceptor is more suitable for an Al atom in terms of stability. The instantaneous interaction energy is computed to be lowest when L L′ is PMe 3 and highest when L = cAAC and L′ = N i Pr 2 . Ligands stabilize the AlP unit by σ donation and this electron-rich AlP unit gains further stability by donating back the electron densities to the adjacent ligands (←P−Al→) when the ligands are cAAC. This π back donation is significantly weak when donor ligands are NHC and Me 3 P. Species 1−2 and 4−5 are most likely to have donor−acceptor dative bonds between AlP and ligands, while 3 can have two equally possible bonding scenarios (schemes 2 and 3). The P− Al bonds of 1−4 are electron-sharing σ bonds, while it is a σ dative P → Al bond for 5 and 6 due to strong σ donation of NHC/Me 3 P ligands.