Computational Investigation of CarbeneâPhosphinidenes: Correlation

Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

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Computational Investigation of Carbene−Phosphinidenes: Correlation between 31P Chemical Shifts and Bonding Features to Estimate the π‑Backdonation of Carbenes Sayan Dutta,† Bholanath Maity,† D. Thirumalai,‡ and Debasis Koley*,† †

Department of Chemical Sciences, Indian Institute of Science Education and Research (IISER) Kolkata, Mohanpur 741 246, India Department of Chemistry, Thiruvalluvar University, Serkkadu, Vellore 632 115, India

‡

S Supporting Information *

ABSTRACT: Detailed investigations of the electronic structure and bonding scenario in different carbene−phosphinidenes have been presented using stateof-the-art computational methods (BP86/def2-TZVPP//BP86/def2-SVP). We have endeavored to find the correlation of the calculated 31P chemical shifts with different bonding parameters of compounds to access the relative πacceptor strengths of the carbenes. 31P chemical shifts exhibit a weak correlation with σ-polarizations of Ccarb−P bonds toward phosphorus; however excellent correlations are obtained in the case of π-polarizations of Ccarb−P bonds toward the carbene carbon (Ccarb) and NPA charges on phosphorus atoms. 31P chemical shifts also show excellent correlations with the electron densities and energy densities of Ccarb−P bonds at BCPs, as suggested by QTAIM calculations. Moreover, EDA-NOCV analysis is implemented to gain brief insight into the bonding scenario in this class of compounds. Good correlation exists between the interaction energies between the carbene and PPh fragments and 31P chemical shifts. Additionally, we have investigated the correlations of calculated 31P chemical shifts with different bonding parameters of the corresponding free carbenes. The bonding scenario in different carbene-substituted phosphinidenes is also explored to see how the bonding situation depends on various substituents on phosphinidenes. The other substituted carbene−phosphinidenes show correlations similar to those of carbene−phenylphosphinidenes.

1. INTRODUCTION After the discovery of the first stable and isolable singlet Nheterocyclic carbenes (NHCs) in 1988 by Bertrand et al.1,2 and in 1991 by Arduengo et al.,3 syntheses and characterization of several stable carbenes have been reported.4−8 The use of carbenes has become increasingly demanded globally in various areas of research, leading to a dramatic development in the field of catalysis.9−12 Despite the popularity of NHCs, it was the discovery of cyclic alkyl amino carbenes (cAACs)13 by Bertrand et al. that unveiled the ability of stable carbenes to activate small-molecule substrates.14,15 The stronger σ-donor and better π-acceptor properties of cAACs are utilized to stabilize various unstable chemical species, radicals, and elements in their different unusual oxidation states.16−21 Shortly following Bertrand’s initial results, several groups reported that the incorporation of π-acidic substituents into NHCs could drastically alter the electronic properties and associated reactivity.22−28 The most prominent contributions in this area have focused on the incorporation of carbonyl moieties into the NHC scaffold. In recent years, the focus has shifted toward deconvoluting the σ-donor and π-acceptor properties of carbenes, which is of utmost importance in elucidating the reactivity of complexes and its wider role in catalysis. Several techniques have been developed to estimate the donor properties of NHCs.29 The most commonly used method is © XXXX American Chemical Society

the Tolman electronic parameter (TEP), which measures the A1 stretching frequency of CO ligands (νCO) in [Ni(CO)3L] (L = carbene) complexes,30 although cis-[IrCl(CO)2L] and cis[RhCl(CO)2L] complexes provide less toxic alternatives.31−33 In these complexes, the C−O bond is weakened by the backdonation of metal d-electrons to π*CO; therefore, the stretching frequency (νCO) can be correlated to the amount of charge donated from the ligand (L) to the metal center. However, TEP has serious limitations, assuming that all ligands have similar π-accepting abilities.34 Furthermore, DFT calculations reveal the dependence of νCO only on the metal → ligand π-backdonation in linear gold(I) complexes,35 thus the correlation of the amount of charge donated from ligand to metal with νCO can be misleading in some cases. The second method, introduced by Lever and co-workers, is based on the assessment of electrochemical E0 values in a series of Ru(III)/ Ru(II) complexes containing NHCs of interest.36−39 The individual ligand electrochemical parameters (LEP) derived from these values are related to the donor strength of the ligands. The other available techniques are composed of the calorimetric measurements of [Cp*RuCl] complexes40 and the evaluation of 13C NMR chemical shifts in several palladium(II) Received: January 19, 2018

A

DOI: 10.1021/acs.inorgchem.8b00174 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry complexes.41 Although all of these methods render a convenient procedure to estimate the overall donor properties of carbenes, they have failed to evaluate the σ-donation and πbackdonation of the carbenes separately. Bertrand et al. reported a convenient method to evaluate the π-accepting properties of carbenes, independent of their σ-donation abilities, utilizing the 31 P NMR spectroscopy of the corresponding phenylphosphinidine adducts.42 A similar method for the assessment of the π-acceptor strength of NHCs has been developed by exploiting 77Se chemical shifts in the corresponding selanourea compounds by the groups of Ganter43,44 and Nolan.45 The ligating properties and bonding features of normal NHCs46−48 and the corresponding silylenes and germylenes49 have been explored earlier by employing the 31 P NMR chemical shifts of the carbene−phenylphosphinidene (C-PPh) adducts. Similar theoretical studies on the coordinating properties of boron-substituted heterocyclic carbenes of different ring sizes50,51 and that of remote NHCs52 have been previously reported. Hence, 31P NMR chemical shifts, acting as a paradigm for molecular electronic properties, serve as a reliable tool for finding a relative π-acidity scale for different carbenes. Similarly, 15N chemical shifts can be used to estimate the extent of σ-donation and π-backdonation in various cAACcontaining compounds as demonstrated by Roesky and Koley et al. employing combined experimental and computational methods.53 Several theoretical and experimental reports on carbene− phosphinidenes are documented in the literature.54−67 The carbene−phosphinidene adduct can be represented by three resonance forms (X, Y, and Z).42 Form X corresponds to a typical phosphaalkene showing a polar covalent CP bond with a lone pair at the phosphorus atom. Conversely, the C−P bonds in Y and Z are donor−acceptor in nature (Scheme 1).

four different substituents previously reported in the literature, namely, −H, −CMe3, −SiMe3, and −CF3.54,61,65,66

2. COMPUTATIONAL DETAILS All complexes were optimized using gradient-corrected BP86 functional68,69 in conjunction with def2-SVP basis set70,71 for all of the atoms with the Gaussian 09 suite of programs.72 BP86 is composed of Becke’s 1988 exchange and Perdew’s 1986 correlation functionals. No symmetry constraints were imposed during geometry optimizations. Frequency calculations were accomplished at the same level on the optimized geometries to characterize the nature of stationary points. All of the structures were verified as true minima on the potential energy surface by the absence of imaginary frequency. Single-point calculations were performed on optimized geometries using BP86 functional in combination with def2-TZVPP70,71 basis set for all atoms. Tight wave function convergence criteria and an “ultrafine” (99 950) grid were used in numerical integration during single-point calculations. Natural bond orbital (NBO)73,74 analysis was performed at the R-BP86/def2TZVPP//R-BP86/def2-SVP level using the NBO Version 3.1 program. Wiberg bond indices (WBI) were calculated at the same level of theory.75 The second-order perturbation theory analysis using the NBO method estimates the bonding and antibonding interactions. The magnitude of backbonding was determined by examining all possible interactions between filled Lewis and empty non-Lewis type NBOs. For each donor NBO (i) and acceptor NBO (j), the stabilization energy E(2) associated with delocalization i → j (2e stabilization) is calculated using the following equation E(2) = ΔEij = qi

Scheme 1. Canonical Structures of the Carbene− Phosphinidene Adducts

F(i , j)2 εj − εi

where qi is the donor orbital occupancy, εi and εj are the diagonal elements (energies of ith and jth NBO orbitals), and F(i,j) is the off-diagonal NBO Fock matrix element.73,74 Moreover, QTAIM (quantum theory of atoms in molecules) calculations were performed in the AIMAll program suite76 to characterize the electron distribution around some selected bonds in the chemical species by applying Bader’s AIM (atomsin-molecule) theory.77 Any bonded pair of atoms has a bond path, i.e., a connecting line with a maximum electron density [ρ(r)]. The bond critical point (BCP) is a point on this line where the gradient [∇ρ(r)] of the electron density is equal to zero. The magnitude of the electron density [ρ(r)] and its Laplacian [∇2ρ(r)] at the BCP provide information about the strength and type of bond. The Laplacian indicates whether the density is locally concentrated [∇2ρ(r) < 0] or depleted [∇2ρ(r) > 0]. The ellipticity (ε) measures the extent to which density is preferentially accumulated in a given path containing the bond path. The energy density (Hb) is used to quantify the extent of the covalent contribution to the donor−acceptor bonds. The energy density yields the total electronic energy when integrated over all space. Furthermore, to gain insight into the bonding scenario of the complexes, EDA (energy decomposition analysis), which was originally developed by Morokuma78,79 and later modified by Ziegler and Rauk, 80,81 calculations were performed in conjunction with the NOCV (natural orbital for chemical valence)82,83 method using the ADF 2013.01 program package.84,85 EDA-NOCV calculations were accomplished on

The stronger C: → P σ-donation in Y and Z makes the phosphorus atom electron-rich, while the phosphorus atom in phosphaalkene (X) is electron-deficient. Therefore, the electronic polarization of the carbon−phosphorus bond in X is opposite of that in the other two canonical forms (Y and Z). In this context, we have made an attempt to explore the electronic structure and bonding scenario in different carbene− phenylphosphinidene compounds, employing DFT calculations. We have considered 21 different types of carbenes in our present study, all of them collected in Scheme 2. Additionally, significant effort has been invested to correlate the calculated 31 P NMR chemical shifts with the different bonding parameters of the complexes in order to access the relative π-acceptor strength of various carbenes. Furthermore, we have extended our observations to find similar correlations for the corresponding free carbenes. To cast light on how the bonding situation depends on various substituents (R3) on phosphinidene, we have also investigated the bonding scenario in carbene adducts of substituted phosphinidenes. We have considered B


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Inorganic Chemistry Scheme 2. Schematic Representation of the Carbenes Considered in the Present Study

Figure 1. Optimized geometries of selected C-PPh adducts in singlet ground electronic states at the R-BP86/def2-SVP level. Color code: H, sky blue; C, gray; N, royal blue; and P, pink. X is the center of mass of the carbene ring.

polarization effects. ΔEorb can be further partitioned into the contributions of the orbitals belonging to different irreducible representations of the interacting system. The EDA-NOCV method merges charge (NOCV) and energy (EDA) partitioning schemes to decompose the deformation density (Δρ) into different components of the chemical bond. The EDA-NOCV calculations reveal pairwise energy contributions for each pair of interacting orbitals to the total bond energy. Further details on this method and its applications can be found in the literature.88,89 The bond dissociation energy (ΔE) between two fragments is given by eq 2

the BP86/def2-SVP optimized geometries at the BP86 level in conjunction with uncontracted Slater-type orbitals (STOs) as basis functions.86 The basis sets are triple-ξ quality augmented by two sets of polarization functions for all atoms without any frozen-core approximation. An auxiliary set of s, p, d, f, and g STOs were used to fit the molecular densities and to represent the Coulomb and exchange potentials accurately in each SCF cycle.87 This level of theory is denoted as R-BP86/TZ2P//RBP86/def2-SVP. The instantaneous interaction energy (ΔEint) between two fragments α and β in the molecule is composed of three main components: ΔE int = ΔEelstat + ΔE Pauli + ΔEorb

(1)

ΔE( = −De) = ΔEprep + ΔE int

In eq 1, ΔEelstat denotes the quasiclassical Coulomb interaction energy between the fragments and was calculated by means of the frozen electron density distribution of the fragments in the geometry of the adduct. ΔEPauli corresponds to the repulsive interactions between the fragments, originating by the fact that two electrons with the same spin cannot occupy the same region in space. Therefore, ΔEPauli accounts for the destabilizing interaction between the occupied orbitals. In contrast, stabilizing orbital interaction term ΔEorb represents the interaction between the occupied and virtual orbitals of the two fragments and also elucidates charge transfer and

(2)

in which the term ΔEprep (preparation energy) is the energy required to promote fragments α and β from their equilibrium geometry and electronic ground state to the geometry and electronic state in the molecule. Electron localization function (ELF)90,91 study and natural localized molecular orbital (NLMO)92 calculations were performed at the same level of theory. Scalar relativistic effects were considered using the zeroth-order regular approximation (ZORA) in all ADF calculations.93 C


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Table 1. Selected Geometrical Parameters of the C-PPh Adducts in Singlet Ground Electronic States at the R-BP86/def2-SVP Level of Theorya compound

d (Ccarb−P)

d (Ccarb−N1/ Ccarb−N2)

θ1b

θ2c

ϕd

1Ph 2Ph 3Ph 4Ph 5Ph 6Ph 7Ph 8Ph 9Ph 10Ph 11Ph 12Ph 13Ph 14Ph 15Ph 16Ph 17Ph 18Ph 19Ph 20Ph 21Ph

1.784 1.755 1.791 1.782 1.770 1.787 1.783 1.777 1.773 1.761 1.745 1.762 1.722 1.755 1.745 1.753 1.749 1.740 1.790 1.743 1.761

1.402/1.402 1.423/1.421 1.389/1.387 1.395/1.395 1.394/1.392 1.392/1.396 1.398/1.400 1.405/1.400 1.418/1.389 1.417/1.408 1.403/1.411 1.397/1.434 1.838/1.850e 1.384/1.545f 1.394/1.554f 1.392/1.483f 1.418/1.550f 1.422/1.563f 1.430/1.416f 1.428/1.434g 1.392/1.541f

104.0 102.2 104.7 105.3 107.2 116.4 106.2 106.2 115.2 115.4 106.4 115.7 110.3h 108.7i 106.3i 105.6i 117.1i 117.9i 103.1i 57.6j 110.6i

106.5 104.7 102.3 102.4 106.2 109.9 104.4 104.6 107.5 107.8 107.1 109.0 108.3 107.1 105.4 103.5 109.2 112.1 100.9 102.8 109.4

167.9 171.5 −165.3 −166.0 165.5 −157.5 167.5 174.9 −155.2 130.4 173.7 177.7 −173.6 179.9 1.7 −151.9 166.2 −171.4 168.6

Bond distances (d) are in angstroms (Å), and bond angles (∠) are in degrees (deg). bθ1 = ∠N1−Ccarb−N2. cθ2 = ∠Ccarb−P−CPh. dϕ = ∠X−Ccarb− P−CPh. ed (Ccarb−P1/Ccarb−P2). fd (Ccarb−N/Ccarb−C1). gd (Ccarb−C1/Ccarb−C2). hθ1 = ∠P1−Ccarb−P2. iθ1 = ∠N−Ccarb−C1. jθ1 = ∠C1−Ccarb−C2. X is the center of mass of the carbene ring. a

Table 2. Calculated 31P Chemical Shifts [δ(31P)]a and NBO Resultsb of the C-PPh Adducts compound

calculated 31P chemical shift

qPc

LPP(e)d

% Ccarb−P σ-polarization to P

% Ccarb−P π-polarization to Ccarb

WBI of Ccarb−P bonde

1Ph 2Ph 3Ph 4Ph 5Ph 6Ph 7Ph 8Ph 9Ph 10Ph 11Ph 12Ph 13Ph 14Ph 15Ph 16Ph 17Ph 18Ph 19Ph 20Ph 21Ph

−17.6 (−18.9)f +22.1 −62.3 (−53.5)f −43.1 −12.0 (−10.2)f +13.9 (+14.8)f −42.3 (−34.6)f −30.5 +39.8 (+39.7)f +70.2 (+83.0)f +66.6 (+78.6)f +119.2 +269.7 +74.2 (+68.9)f +102.6 +79.0 +172.8 +242.5 −47.9 −61.6 (−34.9)f +101.3 (+90.0)f

+0.278 +0.399 +0.202 +0.242 +0.300 +0.297 +0.256 +0.290 +0.382 +0.487 +0.519 +0.385 +0.639 +0.401 +0.441 +0.414 +0.551 +0.518 +0.228 +0.277 +0.412

1.912 1.918 1.927 1.924 1.909 1.899 1.913 1.914 1.907 1.911 1.917 1.913 1.921 1.906 1.913 1.924 1.907 1.908 1.932 1.926 1.899

33.6 34.2 33.6 33.4 33.5 34.0 34.0 34.0 33.9 34.0 33.8 37.1 35.0 35.3 35.0 34.3 35.3 37.8 33.5 33.7 35.0

38.6 47.3 34.1 37.1 38.3 38.0 36.8 38.7 42.1 47.1 48.0 46.1 58.2 43.2 45.3 43.7 49.1 50.5 37.0 39.1 43.8

1.328 1.478 1.246 1.290 1.421 1.370 1.317 1.346 1.432 1.493 1.480 1.506 1.562 1.540 1.569 1.470 1.618 1.676 1.230 1.372 1.535

a

Calculated 31P chemical shifts at the R-PBE0/6-311G(2d,2p)//R-BP86/def2-SVP level. bNBO results at the R-BP86/def2-TZVPP//R-BP86/def2SVP level. cNPA charge on P atom. dLone pair occupancy on P atom. eWiberg bond index of Ccarb−P bond. fExperimental 31P chemical shifts in parentheses.

the most effective factors for the calculation of the 31P chemical shifts.104,107 Tetramethylsilane (TMS) and phosphoric acid (H3PO4) were taken as the standard for 13C and 31P NMR, respectively. The chemical shifts were calculated using the formula δ = σisoref − σiso, where σisoref is the nuclear shielding constant (or absolute isotropic value) of the reference compound and σiso is the nuclear shielding constant of the

NMR parameters were computed at the R-PBE0/6-311G(2d,2p)//R-BP86/def2-SVP level94,95 using the GIAO method.96,97 The PBE0 exchange-correlation hybrid functional finds its enormous applications in 1H, 13C, 15N, 31P, 77Se, and 119Sn NMR calculations.98−106 We have chosen the 6-311G(2d,2p) basis set for the 31P NMR calculations because the included triple-ξ valence shell and additional polarization functions are D


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Inorganic Chemistry substance. The three principal components (σ11, σ22, and σ33) and anisotropy (Δσ) of the shielding tensors in the compounds were also computed. Optimized geometries and orbital diagrams are rendered in the Chemcraft108 and CYLview109 visualization software.

abilities of carbenes, as indicated by a further downfield shift in 2Ph (+22.1 ppm) compared to that of 3Ph. The substitution of nitrogen atoms in the NHC framework by its next heavier congener in 13Ph results in an extreme downfield shift in the 31 P spectrum (+269.7 ppm). In general, higher delocalization from the adjacent heteroatom to the formally vacant 2pπ orbital results in reducing the electrophilicity of the carbene. This delocalization is much less in the case of PHCs compared to NHCs due to the pyramidalization at the P centers, making PHC more acidic. In this regard, we have calculated a significant downfield shift of +313.4 ppm for the phosphorus atom in the phenylphosphinidene adduct of the AsHC carbene because of an increased pyramidalization at the arsenic centers (Figure S2a). The calculated 31P NMR chemical shifts [δ(31P)] show excellent correlation with the pyramidalization at heteroatoms (R2 = 0.997, Figure S2b). In concurrence with this fact, Bertrand et al. earlier showed that the pyramidalization of one N atom in NHC appreciably increases its π-accepting ability.117 The delocalization of the N lone pairs to the vacant 2pπ orbital on Ccarb is drastically reduced, owing to the introduction of electron-withdrawing carbonyl groups (CO) into the NHC scaffold. Lesser electron density in the π-symmetric unoccupied molecular orbital centered on Ccarb significantly lowers the corresponding orbital energy. This results in greater π-accepting abilities of monoamido-aminocarbene (MAAC, 9) and cyclic di(amido)carbenes (cDAC, 10 and 11) compared to that of NHCs.27,28 The downfield shifts in 9Ph−11Ph (+39.8 ppm:9Ph, +70.2 ppm:10Ph, +66.6 ppm: 11Ph) are also in accordance with the greater π-accepting properties of the corresponding carbenes. Annulation in the NHC ring framework also enhances the electrophilicity of the carbene center, as indicated by the lowfield δ(31P) in 7Ph (−42.3 ppm) compared to that of 3Ph (−62.3 ppm). This is consistent with Heinicke’s ascertainment using rhodium complexes118 and the theoretical calculations performed by Phukan and co-workers.46 The greater π-acidity of cAACs compared to that of NHCs is also supported by the 31P NMR signals in 14Ph (+74.2 ppm) and 15Ph (+102.6 ppm), respectively. The phenylphosphinidene adduct of the recently synthesized bicyclic (alkyl)(amino)carbene (BICAAC, 21) shows a 31P NMR signal at +101.3 ppm, which is significantly downfield-shifted compared to the analogous adduct of saturated cAAC. This value, which is in accordance with the experimental findings,119 indicates a greater electrophilicity of BICAAC in comparison with that of saturated cAAC. However, the π-accepting capability of BICAAC is similar to that of unsaturated cAAC ligands. The significant deviation of the calculated 31P NMR chemical shift of 20Ph (−61.6 ppm) from the experimental value (−34.9 ppm) might be attributed to the significant deviation of the optimized geometry from the crystal structure. Unfortunately, we did not have the crystal structure of 20Ph. Additionally, we have performed 31P NMR calculations on the optimized geometry of 20Ph at other levels of theory to check the dependence of computed δ(31P) on functional and basis sets. The computed δ(31P) values in different levels are collected in Table S2. Meanwhile, the calculated 13C chemical shifts for the carbene carbon atoms, provided in Table S3, are in good agreement with the experimental values (R2 = 0.980, Figure S3a). Furthermore, we have found a moderately good correlation between the calculated 13C NMR signals and calculated 31P NMR signals (R2 = 0.7, Figure S3b).42

3. RESULTS AND DISCUSSION 3.1. Geometries. Singlet and triplet state optimizations of all the C-PPhs (1Ph−21Ph) at the R/U-BP86/def2-SVP level confirm the ground electronic state to be singlet. The singlet− triplet energy gaps (ΔES−T) in the compounds, provided in Table S1, are in the range of 25−47 kcal mol−1. Optimized geometries of selected compounds in singlet ground electronic states are presented in Figure 1. The P−CPh bonds are not coplanar with the carbene ring systems in the corresponding adduct. This noncoplanarity affirms that the lone pair on phosphorus is delocalized only into the vacant 2pz orbital of the carbene carbon atom (Ccarb) rather than to the phenyl ring bonded to phosphorus. The selected geometrical parameters of all compounds (1Ph−21Ph) are collected in Table 1. The Ccarb−N bond distances in the compounds are slightly longer than those in the corresponding free carbenes. This confirms that a larger π back-donation from phosphorus to Ccarb disrupts the delocalization of the lone pair on the adjacent nitrogen atom to the vacant p orbital on the carbene carbon (CcAAC ← N internal π back-donation). The significantly longer Ccarb−P1/Ccarb−P2 bond lengths (1.838/ 1.850 Å) in 13Ph compared to those in free carbene (1.726 Å) account for the strongest π-accepting property of the Pheterocyclic carbene (PHC)110,111 among all others considered in our present study. The significantly shorter Ccarb−P bond (1.722 Å) in 13Ph is comparable to that of nonconjugated phosphaalkenes (1.65−1.67 Å).112−115 3.2. 31P NMR Calculations and NBO Analysis. To investigate the π-accepting properties of the carbenes, we have performed 31P NMR calculations on the optimized geometries of C-PPhs. The calculated 31P NMR chemical shifts [δ(31P)], provided in Table 2, show similar trends with the experimental values collected from the literature (R2 = 0.973, Figure S1). Theoretical calculations of 31P NMR shifts reveal resonances at −17.6 and −12.0 ppm for 1Ph and 5Ph, indicating increased electrophilicity of the saturated NHC compared to that of the unsaturated analogue. This is consistent with Nolan’s findings in [PtCl2(DMSO)(NHC)] complexes using 1JPt−C coupling constants116and also the Wiberg bond indices (WBI) calculated for Ccarb−P bonds in these compounds (1.328/1.421 in 1Ph/ 5Ph). Thus, WBI indicate a relative measure of the Ccarb−P bond order and provide a qualitative description of the bond strength. The phosphorus atom in 6Ph is significantly lowfieldshifted (+13.9 ppm) in comparison with 1Ph and 5Ph, suggesting the increase in π-accepting abilities of carbenes with increasing ring size. However, the Ccarb−P bond in 6Ph possesses a slightly lower WBI value (1.370) compared to that of 5Ph. The substitution of bulky Dipp groups (Dipp = 2,6-diisopropylphenyl) in 1Ph by methyl groups in 3Ph leads to a remarkable upfield shift of P (−62.3 ppm). Therefore, our calculations suggest the importance of bulky aromatic groups around the heteroatoms in tuning the electrophilicity of the carbene carbon. The increased steric hindrance around the nitrogen atoms enhances the π-accepting abilities of carbenes.12 This finding is consistent with the appreciably lower WBI value (1.246) for the Ccarb−P bond in 3Ph. Similarly, the presence of electron-withdrawing −CF3 groups increases the π-accepting E


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Inorganic Chemistry

Figure 2. Correlation plot of calculated δ(31P) of the C-PPh adducts with (a) π-polarization of the Ccarb−P bond to Ccarb (in %), (b) the NPA charge on phosphorus, and (c) the bonding scenario in C-PPh adducts.

Figure 3. Molecular orbitals of selected C-PPhs (isosurface = 0.06 au) at the R-BP86/def2-TZVPP//R-BP86/def2-SVP level. The orbital energies (in eV) are shown in parentheses. Hydrogen atoms are omitted for clarity.

In contrast to the Ccarb−P σ-polarization, the nature of Ccarb−P π-polarization is not similar in all of the complexes. In 1Ph, 3Ph− 8Ph, 19Ph, and 20Ph, the Ccarb−P π-bonded electron density is significantly polarized toward phosphorus, whereas the electron density is almost equally contributed by the bonding partners in 2Ph, 9Ph−12Ph, 14Ph−18Ph, and 21Ph. The stronger π-accepting ability of 13Ph is reflected in significant reverse π-polarization of the Ccarb−P bond toward the carbene carbon atom [Ccarb(π): 58.2%)]. The calculated δ(31P) values show poor correlation with the σ-polarization of the Ccarb−P bond toward phosphorus (R2 = 0.586, Figure S4a). On the contrary, a fairly good correlation exists between the π-polarization of the Ccarb−P bond to Ccarb and δ(31P) (R2 = 0.837, Figure 2a). These findings are consistent with the results reported by Nolan, Cavallo, and coworkers while studying similar relative π-accepting abilities of different carbenes using δ(31P).45

For further elucidation of the bonding features in C-PPhs and evaluation of π-accepting properties of the carbenes, we have performed NBO calculations on the optimized geometries. The Ccarb−P bonds in all of the compounds show partial double-bond character, as supported by the calculated WBI values for these bonds (Table 2). The Ccarb−P σ-bond is formed by the overlap of an almost pure p orbital of P and an sp2 hybrid orbital of the carbene carbon with a significant scontribution. The extent of s-mixing into the sp2 hybrid orbital of Ccarb is minimized in 18Ph (sp1.93) and maximized in 20Ph (sp1.19). Interestingly, the p-mixing is more in the phenylphosphinidene adduct of acyclic bis(amino)carbene (aBAC, 12) and acyclic (alkyl)(amino)carbene (aAAC, 18) than in the remaining cyclic variants (Table S4). The Ccarb−P σ-bonded electron density is polarized toward the Ccarb due to the higher electronegativity of carbon (2.5) compared to that of phosphorus (2.1).120 Besides, the Ccarb−P π-bond is formed by sideway overlap of pure p orbitals of the bonding partners. F


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Inorganic Chemistry The calculated δ(31P) values are found to have the least correlation with occupancy of the lone pair on a P atom (R2 = 0.113, Figure S4b). The chemical shift values depend on the electron pair on P that is involved in backdonation to the vacant pπ orbital on the Ccarb, as indicated by the extent of polarization of the Ccarb−P π-bond (Figure 2c). Similar to previous investigations,45 we have obtained a reasonably good correlation between δ(31P) and NPA charges on the P atoms in C-PPhs (R2 = 0.836, Figure 2b). Thus, the greater the πaccepting ability of the carbene, the higher the positive NPA charge on the phosphorus atom in the corresponding C-PPh adducts. So far, our calculations suggest that the computed δ(31P) values are satisfactorily correlated with the π-polarization of the Ccarb−P bond to the Ccarb atom and also with the NPA charges on P atoms. However, some anomalous trends have been traced from the comparative analyses. Though the polarization of the Ccarb−P π-bond toward the Ccarb is greater in 2Ph (47.3%) than in 9Ph (42.1%), the P atom in 2Ph is more upfield shifted (+22.1 ppm) than in 9Ph (+39.8 ppm). Additionally, in 2Ph/9Ph, the extent of σ-polarization of Ccarb−P bonds to P (34.2/ 33.9%) and NPA charges on P atoms (+0.399/+0.382 e) are also similar, indicating an alternative factor for the reverse trend. Likewise, the phosphorus atom in 5Ph is upfield shifted (−12.0 ppm) compared to 6Ph (+13.9 ppm) despite similar σ(33.5/34.0%) and π-polarizations (38.3/38.0%) of Ccarb−P bonds and NPA charges on P atoms (+0.300/+0.297 e) (refer to Table 2). For 17Ph and 18Ph, the qP in 17Ph is higher compared to that of 18Ph; nonetheless the calculated 31P signals are +172.8 and +242.8 ppm for 17Ph and 18Ph, respectively. These inconsistencies can be rationalized by looking at the HOMO−LUMO energy gaps (ΔEH−L) for the aforementioned adducts. As pointed out by Weber, there are two major contributions to δ(31P): the electron density associated with the low-coordinated P atom and the HOMO−LUMO separation energies (ΔEH−L) in the compounds.66,120 The ΔEH−L values for all the C-PPhs are collected in Table S1. The MOs of selected compounds are pictorially represented in Figure 3.121 Interestingly, the calculated ΔEH‑L value in 9Ph is 0.13 eV lower than in 2Ph. Similarly, the corresponding values in 6Ph and 18Ph are 0.20 and 0.30 eV lower than 5Ph and 17Ph, respectively. The lowest ΔEH−L value of 2.00 eV in 13Ph clearly indicates a much stronger π-acidic nature of PHC compared to that of other carbenes. Generally, the π orbitals of Ccarb−P bonds represent the HOMOs in all of the compounds. The fragment analyses suggest that the Ccarb−P π orbitals in 5Ph and 14Ph are formed mainly due to the overlap of the lone pair (LP) orbital on phosphorus in the PPh fragment [HOMO (63.2%: 55.2%) in 5Ph: 14Ph] and the formally empty 2pz orbital of the Ccarb in the carbene fragment [LUMO + 4 (18.1%): 5Ph, LUMO (28.9%): 14Ph]. Similarly, in phenylphosphinidene adduct of abnormal NHC (aNHC)122 19Ph, though the the Ccarb−P π orbital exhibits a major contribution from the LP [HOMO (36.0%)] and vacant 3pz orbital [LUMO (33.8%)] on P, the π orbital of the carbene ring framework and the empty 2pz orbital of the Ccarb contribute to a lesser extent [HOMO − 1 (9.6%), LUMO + 9 (9.1%)]. The lesser participation of the empty 2pz orbital of the Ccarb accounts for the relatively weaker Ccarb−P bond in 19Ph compared to that of 5Ph and 14Ph. It is also reflected in the WBI values calculated for the Ccarb−P bonds in these compounds (refer to Table 2). Unlike other compounds where phosphorus makes a major contribution to the Ccarb−P π

orbitals, the carbene carbon shows its dominance in 13Ph. In this case, the π orbital is composed of a vacant 2pz orbital of the Ccarb [LUMO (35.7%)] and LP orbitals on P1 and P2 centers [HOMO − 2 (10.7%)] in the carbene fragment along with LP [HOMO (27.7%)] and vacant 3pz orbitals [LUMO (9.1%)] on P in the PPh fragment. It is noteworthy to mention that in 9Ph− 11Ph and 17Ph, the Ccarb−P π orbitals have slight bonding interactions with lone pairs on oxygen atoms in carbonyl groups, while the Ccarb−P π* orbitals have antibonding interactions with the carbonyl π* orbitals. The Ccarb−P π* orbitals constitute the LUMOs in 2Ph−4Ph, 9Ph−18Ph, and 21Ph; LUMO + 3 in 20Ph; LUMO+4 in 7Ph and 8Ph; LUMO + 6 in 5Ph and 6Ph; LUMO + 7 in 1Ph; and LUMO + 8 in 19Ph. Meanwhile, the LUMOs in 1Ph, 5Ph, 6Ph, and 19Ph are π orbitals that are distributed predominantly on the aromatic rings in Dipp groups bonded to the nitrogen atoms. Similarly, in 7Ph and 8Ph, LUMOs comprise the π* orbitals of annulated ring frameworks, while in 20Ph, the LUMO represents the π* orbital of the phenyl ring bonded to P. Despite notably lower ΔEH−L values in 1Ph, 7Ph, 8Ph, and 19Ph (2.27 eV: 1Ph, 2.13 eV: 7Ph, 2.01 eV: 8Ph and, 1.40 eV: 19Ph), the phosphorus atoms in these compounds are significantly upfield shifted (refer to Table 2). This is attributed to the fact that though Ccarb−P π orbitals are HOMOs for all the compounds, LUMOs are not the corresponding Ccarb−P π* orbitals. As mentioned before, LUMOs in a few compounds represent aromatic π* orbitals distributed predominantly either on the carbene scaffold or the PPh fragment. In this regard, we have calculated H′−L′ separation energies (ΔEH′−L′) for all the compounds, where H′ and L′ are the respective Ccarb−P π and π* orbitals. Importantly, ΔEH′−L′ values calculated in 1Ph, 7Ph, 8Ph, and 19Ph are 3.25, 3.35, 3.40, and 3.25 eV, respectively (Table S1). These values are in accordance with the substantial upfield shift of phosphorus atoms in these compounds. As expected, 13Ph, with the lowest ΔEH′−L′ value (2.00 eV), perfectly correlates with the furthest downfield shift in the NMR signal. The 2e-stabilization energies, E(2), associated with the delocalization of lone pairs (LPs) on nitrogen (N1 and N2) and phosphorus (P1 and P2) atoms into the acceptor NBOs have been estimated by the second-order perturbation theory analysis. In general, the larger E(2) value indicates the more intensive interaction between the donor and acceptor NBOs. The computed perturbation energies of significant donor− acceptor interactions are presented in Table S6. The net 2e stabilization energies, associated with the delocalization of nitrogen LPs into the Ccarb−P π* orbitals are in the ranges of 80−95 kcal mol−1 in 1Ph and 3Ph−11Ph and 35−55 kcal mol−1 in 2Ph, 12Ph, 14Ph−17Ph, and 19Ph. Such stabilization is substantially reduced in 18Ph (6.0 kcal mol−1) and completely absent in 20Ph. In 13Ph, E(2) arising from the delocalization of phosphorus LPs into the Ccarb−P π* orbital is computed to be 10.4 kcal mol−1. The results of second-order perturbation theory analysis also suggest that the delocalization of the LP on the phosphorus atom into the Ccarb−N1/Ccarb−N2 σ* orbital stabilizes 1Ph−12Ph, and the corresponding stabilization energies are in the range of 9−14 kcal mol−1. In the PHCphenylphosphinidene adduct (13Ph), the interaction between the LP orbital on phosphorus and Ccarb−P1/Ccarb−P2 σ* orbital is favored (14.5 kcal mol−1) because of a smaller energy gap between the donor and acceptor orbitals. On the other hand, the phosphorus LP delocalizes to the formally empty Ccarb−C1 G


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Inorganic Chemistry

Figure 4. NLMO of the phosphorus lone pair in selected truncated C-PPh adducts (isosurface = 0.025 au).

σ* orbital to stabilize compounds 14Ph−20Ph. The computed associated energies are within 10−15 kcal mol−1. The small extent of 2e-stabilization (10.3 kcal mol−1) in 19Ph is due to the larger energy difference between the donor and acceptor orbitals. This delocalization is also revealed from the natural localized molecular orbital (NLMO) calculations, performed for selected truncated C-PPhs where Dipp groups bonded to the nitrogen atoms are replaced by methyl groups. The NLMOs of the phosphorus lone pair in these compounds are pictorially represented in Figure 4. To shed light on the electronic distribution in the complexes, we have performed electron localization function (ELF) study in selected truncated C-PPhs. Similar investigations on model NHC−PH systems were earlier reported by Frison and Sevin.123 ELF serves as a powerful method for the elucidation of the bonding scenario because it enables the localization of regions in the molecular space at which electrons concentrate.90,91 ELF isosurfaces, sketched in Figure S5, clearly show the extreme localization of LPs on phosphorus atoms (P1 and P2) in 13TPh, suggesting the utmost π-accepting ability of PHC compared to that of the other carbenes. 3.3. QTAIM Calculations. To gain insight into the bonding scenario in the C-PPh adducts, topological analyses are also performed using QTAIM (quantum theory of atoms in molecules) calculations. The important topological parameters at the (3, −1) bond critical points (BCPs) are given in Tables 3 and S7. The negative Laplacian [∇2ρ(r)] at BCPs of the Ccarb− P1 and Ccarb−P2 bonds in 13Ph and the Ccarb−N bonds in the other compounds indicates covalent interaction. On the other hand, the Ccarb−P bonds in all of the compounds have positive Laplacian values at BCPs, suggesting its donor−acceptor nature.66 The calculated ellipticities (εBCP) for the Ccarb−P bonds (0.564:1Ph; 0.599: 5Ph) in 1Ph and 5Ph divulge its less covalent nature in the saturated NHC-phenylphosphinidene adduct. Similarly, the increase in ring size further decreases the covalent character in the Ccarb−P bond (εBCP = 0.617) in 6Ph. This is also evidenced by the energy density (Hb) values for the donor− acceptor bonds in 5Ph and 6Ph (−0.456: 5Ph; −0.435: 6Ph). In contrast, ring annulation in the NHC framework causes a significant rise in the covalent contribution to Ccarb−P bond in 7Ph (εBCP = 0.523, Table 3). The εBCP values in 1Ph and 3Ph (0.564: 1Ph; 0.483: 3Ph) suggest that the covalent contribution to the donor−acceptor bond gets enhanced by reducing the steric hindrance around the nitrogen atoms. The covalent contribution is also increased in the presence of electronwithdrawing substituents either bonded to nitrogen atoms or in the ring skeleton, as reflected in the εBCP values in 2Ph and 4Ph, respectively (0.574: 2Ph; 0.507: 4Ph). Relatively lower ellipticity values for the Ccarb−P bonds in 9Ph and 10Ph compared to that of 6Ph implies an increase in the covalent character of the Ccarb− P bond with an increasing number of exocyclic carbonyl groups

Table 3. Topological Parameters of the Ccarb−P Bonds at (3,1) BCPs in the C-PPh Adducts compound

ρ(r)a

[∇2ρ(r)]b

εc

Hbd

qPBadere

Ph

0.152 0.157 0.151 0.152 0.157 0.154 0.153 0.155 0.158 0.161 0.165 0.165 0.173 0.164 0.166 0.164 0.168 0.172 0.152 0.158 0.163

+0.132 +0.205 +0.126 +0.146 +0.154 +0.105 +0.133 +0.142 +0.130 +0.146 +0.176 +0.091 +0.146 +0.134 +0.154 +0.148 +0.123 +0.099 +0.118 +0.187 +0.116

0.564 0.574 0.483 0.507 0.599 0.617 0.523 0.527 0.574 0.550 0.501 0.565 0.396 0.552 0.517 0.502 0.533 0.544 0.503 0.515 0.558

−0.471 −0.422 −0.422 −0.456 −0.435 −0.448 −0.457 −0.450 −0.470 −0.479 −0.468 −0.531 −0.492 −0.502 −0.491 −0.497 −0.515 −0.428 −0.459 −0.479

+0.828 +0.953 +0.768 +0.803 +0.830 +0.812 +0.811 +0.844 +0.904 +0.999 +1.060 +0.917 +1.131 +0.923 +0.964 +0.945 +1.039 +1.022 +0.782 +0.845 +0.919

1 2Ph 3Ph 4Ph 5Ph 6Ph 7Ph 8Ph 9Ph 10Ph 11Ph 12Ph 13Ph 14Ph 15Ph 16Ph 17Ph 18Ph 19Ph 20Ph 21Ph a c

Electron density at BCP (e/Å3). bLaplacian at BCP (e/Å5). Ellipticity. dEnergy density (hartree/Å3). eBader charge on a P atom.

adjacent to the heteroatoms (0.574: 9Ph; 0.550: 10Ph and; 0.617: 6Ph). The maximum covalent contribution to the donor−acceptor bond has been found for 13Ph, as indicated by the electron density at BCP and energy density values (ρ(r) = 0.173, Hb = −0.531). Furthermore, it is also supported by an appreciably lower εBCP value of 0.396. Meanwhile, the Ccarb−P bonds in cAAC-phenylphosphinidene adducts 14Ph−16Ph have slightly higher electron densities at BCP compared to that of NHC-phenylphosphinidene adducts. Similar to NHC, the replacement of alkyl groups by aryl groups affords a conspicuous increase in the covalent interaction (εBCP = 0.552/0.502 in 14Ph/16Ph). It is noteworthy to mention that the covalent contribution to the Ccarb−P bond significantly decreases in the BICAAC-phenylphosphinidene adduct (21Ph) (Hb = −0.479) compared to that in 14Ph−16Ph [(Hb = −0.491−(−0.502)]. Importantly, we have found an excellent correlation between the electron densities [ρ(r)] of Ccarb−P bonds at BCPs and δ(31P) (R2 = 0.887, Figure 5). The correlation can be justified by an increase in the electron densities at BCPs of Ccarb−P bonds, which correspond to an electron depletion from the phosphorus center. The removal of electron density on the phosphorus atom results in a downfield shift of the 31P NMR signal. On the other hand, the δ(31P) values are found to have H


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Inorganic Chemistry

fragments and pairwise orbital interactions are shown in Tables 4 and S8. The calculations reveal that the Ccarb−P bonds have slightly more covalent character (52−59%) than electrostatic nature (41−48%) in the studied C-PPhs. Examples of donor−acceptor bonds with significant covalent character are already documented in the literature.124−126 The calculated bond dissociation energies (ΔE) of Ccarb−P bonds lie in the range of 43−61 kcal mol−1 in 1Ph−10Ph, 12Ph, and 18Ph−20Ph, while slightly higher values within 65−75 kcal mol−1 are obtained for 11Ph, 13Ph−17Ph, and 21Ph, respectively. The destabilizing preparation energies (ΔEprep) in all of the compounds (30−70 kcal mol−1) mainly arise due to the energy required for the promotion of the β fragment from the triplet ground state to the singlet excited state. The ΔEprep values for acyclic carbenes in 12Ph and 18Ph are significantly higher than the cyclic ones (ΔEprep(α): 23.1 kcal mol−1:12Ph; 29.6 kcal mol−1: 18Ph). In order to compare the π-accepting abilities of NHC and PHC ligands, the pairwise orbital interactions in 5Ph and 13Ph are considered. The two major contributions to ΔEorb in 5Ph arise from the donation of the lone pair on the carbene carbon to the vacant 3pz orbital of P (−354.9 kcal mol−1, 86.8%) and the π* orbital of the phenyl group bonded to P (−37.2 kcal mol−1, 9.1%). The calculated eigenvalues (ν), which indicate the amount of charge flow from donor to acceptor fragments, are 2.00 and 0.45, respectively (Figure 6a). On the contrary, in 13Ph, though the minor contribution to the total covalent interaction, similar to that of 5Ph, shows LP(Ccarb) → 3pz(P) σdonation (−52.7 kcal mol−1, 14.3%), the major contribution (−288.2 kcal mol−1, 78.3%) is associated with the charge flow from the LP orbital of P into the LUMO of the PHC ligand. The plot of deformation densities of these pairwise orbital interactions are in accordance with the strong π-accepting ability of PHC (Figure 6b). The substantially higher interaction energy (ΔEint) in 13Ph (−129.5 kcal mol−1) compared to 5Ph

Figure 5. Correlation plot between electron density ([ρ(r)]) of the Ccarb−P bond at BCP and calculated 31P chemical shifts [δ(31P)] of the C-PPhs.

no correlation with the ellipticities of the Ccarb−P bonds (R2 = 0.063, Figure S6a). Instead, a fairly strong correlation exists between the energy density (Hb) values of Ccarb−P bonds at BCPs and δ(31P) (R2 = 0.786, Figure S6b). This shows that the covalent contribution to the donor−acceptor bond has a significant impact on δ(31P). Additionally, the calculated Bader charges on phosphorus atoms in the C-PPh adducts show a moderately strong correlation with δ(31P) (R2 = 0.766, Figure S6c). 3.4. EDA-NOCV Calculations. To better understand the nature of the chemical bonding in the C-PPh adducts, we have analyzed the bonding interaction between carbene (α) and PPh (β) fragments using energy decomposition analysis (EDA) in conjunction with the NOCV (natural orbital for chemical valence) method (refer to Computational Details). The energy terms associated with the interaction between the respective

Table 4. EDA Results of the Ccarb−P Bonds in the C-PPh Adducts at the BP86/TZ2P Level of Theorya compound

ΔE (−De)

ΔEint

ΔEPauli

ΔEelstat

ΔEorb

% ΔEelstat/ΔEorbb

ΔEprep

ΔEprep (α)c

ΔEprep (β)c

Ph

−43.4 −44.8 −54.9 −51.1 −50.5 −46.6 −51.8 −53.3 −53.9 −59.0 −68.3 −58.0 −71.7 −64.3 −72.6 −71.6 −74.7 −61.0 −57.6 −59.0 −67.2

−82.7 −94.7 −87.3 −83.9 −100.5 −87.5 −97.4 −87.7 −94.5 −98.6 −99.3 −123.9 −129.5 −99.2 −105.9 −104.3 −120.9 −131.5 −88.3 −89.2 −108.0

588.8 563.8 578.2 318.3 598.8 449.1 367.6 509.2 410.9 425.4 436.4 612.2 511.6 388.7 396.2 417.8 605.4 595.1 321.4 362.8 525.9

−276.2 −275.5 −276.4 −191.6 −290.5 −243.2 −221.8 −256.3 −231.8 −231.5 −234.4 −312.8 −272.9 −225.4 −227.9 −235.9 −305.2 −318.0 −194.0 −198.5 −277.3

−395.3 −383.0 −389.1 −210.7 −408.8 −293.4 −243.2 −340.6 −273.6 −292.5 −303.7 −423.2 −368.2 −265.0 −274.2 −286.2 −421.1 −408.7 −215.7 −253.5 −356.7

41.1/58.9 41.8/58.2 41.5/58.5 47.6/52.4 41.5/58.5 45.3/54.7 47.7/52.3 42.9/57.1 45.9/54.1 44.2/55.8 43.6/56.4 42.5/57.5 42.6/57.4 46.0/54.0 45.4/54.6 45.2/54.8 42.0/58.0 43.8/56.2 47.4/52.6 43.9/56.1 43.7/56.3

39.3 49.9 32.4 32.8 50.0 40.9 45.6 34.4 40.6 39.6 31.0 65.9 57.8 34.9 33.3 32.7 46.2 70.5 30.7 30.2 40.8

6.9 6.7 4.0 4.3 5.8 8.1 4.1 4.2 6.1 7.2 2.7 23.1 16.7 6.5 5.2 4.0 7.8 29.6 2.2 1.2 4.8

32.4 43.2 28.4 28.5 44.2 32.8 41.5 30.2 34.5 32.4 28.3 42.8 41.1 28.4 28.1 28.7 38.4 40.9 28.5 29.0 36.0

1 2Ph 3Ph 4Ph 5Ph 6Ph 7Ph 8Ph 9Ph 10Ph 11Ph 12Ph 13Ph 14Ph 15Ph 16Ph 17Ph 18Ph 19Ph 20Ph 21Ph

a Fragments carbene and PPh are labeled as α and β, respectively. Energy values are given in kcal mol−1. bPercentage contribution to the total attractive interactions ΔEelstat+ ΔEorb. cΔEprep(α) and ΔEprep(β) are the preparation energies of the carbene and PPh fragments, respectively.

I


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Inorganic Chemistry

Figure 6. Plot of deformation densities Δρ of the pairwise orbital interactions in (a) 5Ph and (b) 13Ph between respective fragments (α and β). The associated energies ΔEorb,n (kcal mol−1) are given in parentheses. The charge flow is color coded red → blue. NOCV pairs (Ψn/Ψ−n) with charge eigenvalues ν (in e) in parentheses are shown. The negative and positive eigenvalues give the amounts of donated and accepted electronic charge, respectively. The most important interacting occupied and vacant orbitals of the fragments are also included.

(−100.5 kcal mol−1) indicates that PHC is more strongly bonded to phenylphosphinidene. Although stabilizing interaction terms ΔEelstat and ΔEorb are significantly higher for 5Ph than 13Ph, it is the destabilizing ΔEPauli term that is predominant in the reverse trend.127 The interaction energy is significantly higher in the C-PPh adduct of saturated NHC compared to that of the unsaturated analogue (−100.5 kcal mol−1: 5Ph; −82.7 kcal mol−1: 1Ph). The substitution of bulky Dipp groups in 1Ph by simple methyl groups in 3Ph slightly reduces the ΔEPauli value (588.8 kcal mol−1:1Ph; 578.2 kcal mol−1: 3Ph) and the Ccarb−P bond gets marginally strengthened (ΔEint: −82.7 kcal mol−1:1Ph; −87.3 kcal mol−1: 3Ph). Similarly, the substitution by electronwithdrawing CF3 groups in 2Ph slightly strengthens the Ccarb− P bond (ΔEint: −94.7 kcal mol−1:2Ph; −87.3 kcal mol−1: 3Ph).

With the increase in ring size, the covalent interaction is drastically reduced (ΔEorb: 598.8 kcal mol−1:5Ph; 449.1 kcal mol−1: 6Ph), leading to significant weakening of the Ccarb−P bond. It is indicated by the corresponding interaction energies (ΔEint: −100.5 kcal mol−1: 5Ph; −87.5 kcal mol−1:6Ph), though the calculated bond dissociation energies are similar because of the preparation energy of the β fragment in 5Ph, which lowers the ΔEint. While considering the bonding effects in the case of cAAC and aNHC ligands, it was observed that the major orbital interaction in 14Ph and 19Ph originates from σ-donation of the Ccarb LP to the vacant 3pz orbital of P in the β fragment (−180.6 kcal mol−1 {68.2%}: 14Ph; −154.8 kcal mol−1 {71.8%}: 19Ph). The greater π-accepting ability of a cAAC compared to aNHC is reflected in the minor contribution to the ΔEorb, where the π-back donation of P LP to the formally empty 2pz J


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Inorganic Chemistry orbital of the Ccarb in an α fragment (−56.8 kcal mol−1 {21.4%}:14Ph; −36.2 kcal mol−1 {16.8%}:19Ph) occurs. Interestingly, we have observed that δ(31P) values show poor correlation with the bond dissociation energies (ΔE) of Ccarb− P bonds in C-PPhs (R2 = 0.422, Figure S7), indicating that the 31 P chemical shifts exhibit less dependence on Ccarb−P bond strengths. This is attributed to the fact that ΔEprep of the fragments may significantly change the trend of the bond strength, hence, the bond dissociation energy is not a reliable measure of the intrinsic donor−acceptor strength.128 Rather, a fairly good correlation exists between δ(31P) and ΔEint between the fragments (R2 = 0.850, Figure 7). Indeed, the calculated δ(31P) shows a dependence on the intrinsic donor−acceptor strengths of Ccarb−P bonds.

orbital on Ccarb with the exception of PHC carbene 13. The HOMO and HOMO−1 in 13 comprise LP orbitals on P atoms (P1 and P2) and Ccarb, respectively. On the other hand, the vacant pπ orbital on the carbene carbon is LUMO in 2, 10, 12− 18, and 21; LUMO + 1 in 3 and 20; LUMO + 2 in 4, 7, and 8; LUMO + 4 in 5 and 6; LUMO + 5 in 1, 9, and 11; and LUMO + 7 in 19. The LUMOs in 1, 5, 6, and 19 are π-type orbitals that are distributed predominantly on the aromatic rings in Dipp groups bonded to the nitrogen atoms. Similarly, the LUMOs in 3, 7, and 8 represent the π* orbitals of the NHC ring framework. Hence, δ(31P) values in most of the carbenes do not correlate directly with the HOMO−LUMO energy gaps. Instead, we have found a moderate correlation (R2 = 0.736, Figure S8c) between δ(31P) values and the ΔEH′−L′ of free carbenes, where H′ and L′ are the σ-symmetric lone pair orbital and π-symmetric unoccupied molecular orbital centered at Ccarb. The stronger π-accepting properties of cAACs (14− 16) are attributed to lower ΔEH′−L′ values (2.3−3.0 eV). Similarly, an even lower ΔEH′−L′ (1.7 eV) accounts for the greater electrophilicity of cyclic (alkyl)(amido)carbene 17.129 Figure 8 collects all of the correlations of δ(31P) with different observables as calculated and discussed in this current

Figure 7. Correlation plot between the interaction energy (ΔEint) between the respective fragments (α and β) and the calculated δ(31P) of the C-PPhs.

3.5. Correlation with Singlet−Triplet and HOMO− LUMO Gaps in Free Carbenes. To rationalize the πaccepting abilities of the carbenes, we decided to search for a correlation between the δ(31P) in C-PPhs with singlet−triplet separation (ΔE S−T) and HOMO−LUMO energy gaps (ΔEH−L) in the corresponding free carbenes (1−21; Scheme 2). The ΔES−T and ΔEH‑L values which provide a measure of their respective thermodynamic and kinetic stabilities for the free carbenes are tabulated in Table S9. The ΔES−T values of free carbenes do not correlate well with the calculated δ(31P) (R2 = 0.698, Figure S8a), with 11 and 20 largely deviating from the trend line. This result can be reasoned from the fact that the triplet electronic state in 11 is a biradical located on two carbonyl groups. Similarly, unlike other carbenes where the spin density is almost entirely localized on Ccarb, the triplet state in 20 arises from the distribution of spin between the carbene carbon and one of the neighboring carbon atoms. It is manifested in a significant change in Ccarb−C1/Ccarb−C2 distances in the triplet state (1.501/1.352 Å) over the singlet electronic state (1.428/1.434 Å). An even weaker correlation was observed between the HOMO−LUMO energy gaps (ΔEH−L) of free carbenes and δ(31P) (R2 = 0.404, Figure S8b). It is because of the fact that the carbene carbon donates its lone pair to phosphorus for Ccarb−P σ-bond formation, while phosphorus backdonates its electron pair to the vacant pπ orbital on the carbene carbon. Therefore, δ(31P) values should have a strong dependence on the energy differences between the σ-symmetric LP orbital and the π-symmetric unoccupied molecular orbital concentrated on the carbene carbon atom. Meanwhile, HOMOs in all of the free carbenes are a lone pair

Figure 8. Summary of the correlations of calculated δ(31P) with different bonding parameters in the C-PPhs.

study. It is obvious from the plot that the best correlations are obtained with the following computed parameters: (a) Ccarb−P π-polarization to Ccarb, (b) NPA charges on phosphorus atoms, (c) electron densities [ρ(r)] of Ccarb−P bonds at BCPs, and (d) interaction energies (ΔEint) between the coupling fragments. 3.6. Bonding Scenario in the Carbene−Substituted Phosphinidene Compounds. To cast light on how the bonding situation depends on various substituents on phosphinidene, we have considered four substituents of diverse steric and electronic effects, namely, −H, −CMe3, −SiMe3, and −CF3.54,61,65,66 It is evident that 13 possesses the shortest Ccarb−P bonds of all of the substituents (13H: 1.723 Å; 13CMe3: K


Article

Inorganic Chemistry

of Ccarb−P bonds at BCPs and δ(31P). Moreover, EDA-NOCV analysis is performed to gain better insight into the bonding scenario in C-PPhs. The calculations reveal significant covalent character of the donor−acceptor Ccarb−P bonds. Gratifyingly, the interaction energies (ΔEint) between the carbene (α) and PPh (β) fragments show a fairly strong correlation with δ(31P). To rationalize the π-accepting abilities of the carbenes, our next attempt was to find the correlation of δ(31P) in the compounds with different bonding parameters of the corresponding free carbenes. Our calculations show that singlet−triplet (ΔES−T) and HOMO−LUMO energy gaps (ΔEH−L) in the free carbenes are poorly correlated with δ(31P). Instead, δ(31P) values bear a moderately strong correlation with the energy difference between the σ-symmetric lone pair orbital and the π-symmetric unoccupied molecular orbital centered at the carbene carbon (ΔEH′−L′). We have also explored the bonding scenario in different carbene-substituted phosphinidene compounds to shed light on how the bonding situation depends on various substituents on phosphinidene. It is encouraging to note that the other carbene−phosphinidenes also show correlations similar to those of carbene−phenylphosphinidenes. Hence, our computational endeavor affirms the reliability of 31P NMR chemical shifts in all of the carbene−phosphinidenes for assessment and quantification of the relative π-acidity strengths of carbenes.

1.721 Å; 13SiMe3: 1.731 Å; and 13CF3: 1.724 Å). On the other hand, similar to C-PPhs, 3 possesses the longest Ccarb−P bonds for −CMe3 and −SiMe3 substituents. For −H- and −CF3substituted phosphinidenes, the longest Ccarb−P bonds are shown by 6H and 6CF3. The Ccarb−P bonds have significant partial double-bond character in all the substituted compounds. NBO analysis shows that the σ- and π-polarizations of Ccarb−P bonds follow similar trends with the exception of 5H (Tables 2 and S13). In comparison to other substituents, the Ccarb−P σbond in 5H is significantly polarized toward phosphorus atoms [Ccarb(σ): 5H: 45.9%; 5CMe3: 32.9%; 5SiMe3: 33.7%; and 5CF3: 33.8%]. Similarly, the Ccarb−P π-bond in 5H shows substantial polarization toward the carbene carbon center [Ccarb(π): 5H, 52.7%; 5CMe3, 39.3%; 5SiMe3, 35.5%; and 5CF3, 34.7%]. We have observed that in 5H, Ccarb projects an sp2 hybrid orbital with a prominent p-contribution for the formation of a Ccarb−P σbond [Ccarb(σ): 5H, sp2.64; 5CMe3, sp1.38; 5SiMe3, sp1.38; and 5CF3, sp1.51]. Furthermore, unlike other substituents, where the Ccarb−P π-bonds are formed by the overlap of pure 2pz and 3pz orbitals of Ccarb and P, respectively, the Ccarb in 5H utilizes a 2pz orbital with significant 2s-mixing [s/p: 19.4/80.3%]. Similar to C-PPhs, HOMOs in all the compounds represent the π orbitals of Ccarb−P bonds. Additionally, we have calculated HOMO− LUMO energy gaps (ΔEH−L) for all of the substituted carbenephosphinidene species. It is noteworthy to mention that the least ΔEH‑L values are obtained for all aNHC-phosphinidenes [19H: 1.43 eV; 19CMe3: 1.36 eV; 19SiMe3: 1.53 eV; and 19CF3: 1.69 eV]. On the contrary, the highest ΔEH‑L values are obtained for 20 for all the substituents [20H: 3.13 eV; 20CMe3: 3.06 eV; 20SiMe3: 3.17 eV; and 20CF3: 3.29 eV]. We have also examined whether the correlations obtained for C-PPhs remain valid for other substituents. Analogous to CPPhs, the δ(31P) show fairly strong correlations with the πpolarization of Ccarb−P bonds to Ccarb and NPA charges on phosphorus atoms (Figures S10 and S11). Additionally, the δ(31P) show a weak correlation with the σ-polarization of Ccarb−P bonds toward P and no correlation with the lone pair occupancies on P, similar to the observations made in C-PPhs (Figures S9 and S12). Hence, our systematic computational investigation shows that δ(31P) in substituted carbenephosphinidenes are reliable for the estimation of relative πaccepting abilities of carbenes, though only few such carbene adducts are experimentally and theoretically explored so far.42,45

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.8b00174. The singlet−triplet (ΔES−T) and HOMO−LUMO (ΔEH−L) energy gaps in C-PPhs (Table S1); 31P chemical shifts of 20Ph (Table S2); calculated 13C chemical shifts [δ(13C)] of the carbene carbon atoms (Table S3); NBO results (Tables S4−S6); topological parameters (Table S7); ELF isosurfaces (Figure S5), EDA-NOCV results (Table S8); ΔES−T and ΔEH−L of free carbenes (Table S9); the principal components, isotropic values, and anisotropy of 13C and 31P shielding tensors in C-PPhs (Tables S10−S12); calculated δ(31P) and NBO results of different carbene−phosphinidenes (Table S13); several correlation plots (Figures S1−S4 and S6−S12); and XYZ coordinates of the optimized geometries of carbene−phosphinidenes (Table S14) (PDF)

4. CONCLUSIONS The present study illustrates a detailed in silico investigation of the electronic structure and bonding scenario in 21 various carbene−phenylphosphinidenes. The calculated 31P NMR chemical shifts [δ(31P)] of these compounds in singlet ground electronic states are found to have a very strong correlation with the experimental values. We made an attempt to find a similar correlation of δ(31P) with the different bonding parameters of the compounds to access the relative π-acceptor strength of the carbenes. Our calculations reveal that σpolarizations of Ccarb−P bonds toward phosphorus exhibit a weak correlation with δ(31P). Rather, the chemical shifts show excellent correlations with the π-polarizations of Ccarb−P bonds toward Ccarb and NPA charges on phosphorus atoms. The donor−acceptor nature of Ccarb−P bonds are confirmed by QTAIM calculations. We have obtained an even better correlation between the calculated electron densities [ρ(r)] of Ccarb−P bonds at BCPs and δ(31P). Furthermore, a fairly strong correlation also exists between the energy density (Hb) values

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Debasis Koley: 0000-0002-7912-3972 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS S.D. and B.M. acknowledge the Council of Scientific and Industrial Research (CSIR) for the Senior Research Fellowship (SRF) and IISER Kolkata for the computational facility. D.K. is grateful to DST-SERB for the fast-track fellowship (no: SR/ L


Article

Inorganic Chemistry

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FT/CS-72/2011). We are thankful to the reviewers for their valuable suggestions to improve the quality of the manuscript.

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DEDICATION Dedicated to Professor Gernot Frenking for his remarkable contribution to the field of chemical bonding.

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Inorganic Chemistry

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