Ligand Properties of Boron-Substituted Five‑, Six‑, and Seven-Membered Heterocyclic Carbenes: A Theoretical StudyAshwini K. Phukan,*,†,‡ Ankur Kanti Guha,† and Satyajit Sarmah†

†Department of Chemical Sciences, Tezpur University, Napaam 784028, Assam, India‡Institut fur Anorganische Chemie, Julius-Maximilians-Universitat Wurzburg, Am Hubland, D-97074 Wurzburg, Germany

*S Supporting Information

ABSTRACT: The electronic properties of boron-substituted five-,six-, and seven-membered heterocyclic carbenes have been studiedusing quantum chemical methods. The stability of carbenes has beenexamined from the values of their respective singlet−triplet andHOMO−LUMO gaps. Both the singlet−triplet and the HOMO−LUMO gaps indicate higher stability for six- and seven-membered P-heterocyclic carbenes (PHCs) containing boron atoms at the αposition with respect to phosphorus atoms. While PHCs are better πacceptors, the π acidities of NHCs can be tuned by substituting aboron atom in the α position with respect to nitrogen. This isrevealed by the energies of a π-symmetric unoccupied orbitalcentered at the central carbon atom. Reactivity of these carbenes has been discussed in terms of nucleophilicity andelectrophilicity index. The calculated relative redox potential values and 13C NMR parameters are found to correlate well with theπ acidities of the respective carbenes.

1. INTRODUCTION

N-Heterocyclic carbenes (NHCs) are a class of versatile ligandshaving a central divalent carbon atom in a singlet ground stateflanked by two amino groups with tunable electronic as well assteric properties.1 Since the 1960s, various research groups haveattempted the synthesis of metal-free NHCs.2−4 However, theycould synthesize only the transition-metal complexes of NHC.It was the careful work of Arduengo and co-workers thatresulted in the first isolation of a free stable NHC in 1991.5

This isolation of a free NHC inspired a series of experimentalstudies toward the synthesis of a large number of carbenes withstructural and electronic varieties.1 NHCs are found to haveexcellent σ-donating ability, and due to this special property,NHCs find extensive use in various chemical transformations.1

It will be intriguing to study whether the heavier analogues ofnitrogen can stabilize such a carbene system or not. The answerto this question came from a seminal study by Schleyer and co-workers in which the authors concluded that the π-donor abilityof heavier elements (such as phosphorus) are similar or largerthan that of lighter counterparts (such as nitrogen).6 Thepoorer π-donating abilities of heavier elements are traced totheir high inversion barrier. It was proposed that heavierelements, such as phosphorus, can be an effective donorprovided planarity around phosphorus is achieved so that theinversion barrier is reduced. Following this notion, in 2005,Bertrand and co-workers synthesized the first stable P-heterocyclic carbene (PHC) using bulky substituents atphosphorus to induce planarity.7 They have found that PHCsare a better candidate to compete with and/or complement

NHC as a ligand for transition-metal-based catalysis, which hasbeen substantiated theoretically by Jacobsen.8

Both five- and six-membered NHCs with an inorganicbackbone are known experimentally.9 In fact, some of theseNHCs demonstrate better ligating properties than that ofimidazol-2-ylidene.9a,c In recent years, various forms of ringexpanded six-10,11 and seven-membered11,12 NHCs have beenreported. Seven-membered heterocyclic carbenes are partic-ularly interesting because they exhibit a torsional twist thatresults in a chiral, C2 symmetric structure. On the basis of DFTcalculations, Stahl and co-workers concluded that unsaturatedseven-membered ring carbenes, a formally 8π-electronantiaromatic system, are likely to attain significant Mobiusaromatic stabilization upon undergoing torsional distortion ofthe heterocyclic ring.12b This has broaden the scope inchoosing the most appropriate NHCs for rational catalystdesign.10−16

According to earlier experimental17 and theoretical18 reports,the π-donation ability of NHCs is negligible. However, recentliterature shows that the π basicity and π acidity of NHCs arenot only significant, but also tunable.19−22 Moreover, NHCswith an inorganic backbone are found to have a larger πacidity.23 These findings have prompted us to study any effectthat may arise upon changing the ring atoms on the structure ofsix- and seven-membered ring carbenes. We present here asystematic theoretical study on the ligating properties of boron-substituted heterocyclic carbenes of different ring sizes

Received: February 27, 2013

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(Scheme 1) with special emphasis on their π acidity. In view ofthe diverse nature of the structures involving different ring sizesin this study, a uniform labeling scheme is necessary to keep thethread of discussion intact. Accordingly, we have devised alabeling scheme (Scheme 1) that takes into account all of thesecombinations. The ring size is indicated by a prefix, saturatedrings are indicated by putting a prime after the prefix, andboron-containing rings are indicated by putting a subscript “B”as suffix. Thus, 5-NHC, 5′-NHC, and 5-NHCB correspond tofive-membered unsaturated, saturated, and boron-substitutedNHCs, respectively. The substituents attached to either thenitrogen or the phosphorus atoms of these carbenes are shownwithin parentheses.

2. COMPUTATIONAL DETAILSAll the structures were fully optimized with density functional theory(DFT) using the hybrid PBE1PBE exchange-correlation functional.24

We have used the 6-31+G* basis set for main group elements and theSDD basis set with the Stuttgart−Dresden relativistic effective corepotential for the rhodium atom.25 The effects of basis sets were testedby evaluating the singlet−triplet (ΔES−T) and HOMO−LUMO(ΔEH−L) gaps of two representative molecules employing higherbasis sets (Table S1, Supporting Information). We did not obtain anyappreciable differences in the values of ΔES−T and ΔEH−L, indicatingthat the basis set used in this study is a reasonable one and it can besafely used for other properties considered in this study. Frequencycalculations were performed at the same level of theory to characterizethe nature of the stationary point. All structures were found to beminimum on the potential energy surface with real frequencies.Natural bonding analysis was performed with the natural bond orbital(NBO) partitioning scheme26 as implemented in the Gaussian 03 suitof programs.27

For calculating the standard redox potential, we employed theprotocol of the Born−Haber cycle (Scheme 2). The standard Gibbsfree energy of the redox half reaction, ΔGsol

0,redox, consists of freeenergy changes in the gas and solution phases of the oxidized andreduced species.28

Solvent effects (CH2Cl2) have been estimated in single-pointcalculations on gas phase optimized structures using the polarizablecontinuum model, PCM.29 The values obtained from the Born−Habercycle has been used to calculate the standard free energy (kcal mol−1)of the overall reaction in solution according to eq 1.

Δ = Δ + Δ − ΔG G G Gsol gas s (Red) s (Ox)0,redox 0,redox 0 0(1)

The standard one-electron redox potential, E0 (in V), is thencalculated using the Nernst equation (eq 2)

Δ = −G FEsol0,redox 0calc (2)

where F is the Faraday constant and is equal to 23.06 kcal mol−1 V−1.We have used the PBE1PBE functional for standard redox potential

calculations as it provides accurate results for several early, middle, andlate transition metals.28 All the calculated values were referenced to thecalculated absolute half-cell potential of ferrocene at the same level oftheory. Isotropic 13C chemical shifts were calculated relative totetramethylsilane (TMS) at the same level of theory at whichgeometries of the molecules were optimized. The same level of theorywas also used for calculating the absolute isotropic chemical shift ofTMS. The nucleophilicity index has been calculated (vide infra) withreference to tetracyanoethylene (TCNE), which has been optimized atthe same level of theory.

3. RESULTS AND DISCUSSION3.1. Geometries. Even though we have considered various

substituents at the heteroatom (H, Me, tBu, Ph) in our study,here, we will discuss only the phenyl-substituted molecules as arepresentative one. The optimized geometrical parameters of allthe Ph-substituted molecules are given in Table 1, and the restare given in the Supporting Information (Table S2). In general,the computed geometrical parameters are in good agreementwith the experimentally reported ones.Among the optimized geometries of five-membered NHCs,

5-NHC and 5-NHCB are found to be planar irrespective of thesubstituents, whereas that of 5′-NHC is slightly distorted fromplanarity (except 5′-NHCB(Ph), vide infra). The order of five-membered NHCs with respect to Cc−N bond length (Cc is thecarbenic carbon atom) is 5′-NHC < 5-NHC < 5-NHCB andwith respect to the ECcE angle is 5-NHC < 5′-NHC < 5-NHCB. The longer Cc−N bond as well as smaller NCcN angleis consistent with the presence of 6π-electron delocalization in5-NHC, which is absent in 5′-NHC. The larger atomic radii ofboron may be responsible for the wider NCcN angle of 5-NHCB. However, the longer Cc−N bonds in the case of 5-NHCB compared to 5-NHC and 5′-NHC might be due to the

Scheme 1

Scheme 2. The Born−Haber Cycle

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presence of partial delocalization of π-electron density from thelone pair at nitrogen to the vacant p orbital on boron atom.Indeed, we obtained an occupancy of more than 0.220e for theformally empty p orbital at boron. It is noteworthy to mentionhere that the phosphorus atoms of the PHCs can havestructures displaying either syn- or anti-pyramidalization or canhave both forms. However, we have included only theminimum energy structures in this study irrespective of thenature of pyramidalization at the phosphorus atom. Theminimum energy structures of 5-PHC and 5′-PHC shownonplanar geometries with antipyramidalization at phosphorusatoms. (The syn-pyramidalized geometries are higher in energyby 2.7 and 6.7 kcal/mol, respectively. We have obtained a moreor less similar energy difference between the syn- and anti-geometries for other PHCs.) A distorted structure with unequalCc−P bond lengths is observed for 5-NHCB. Because ofineffective electron donation from the phosphorus lone pair tothe carbenic carbon, the PHCs show longer Cc−P bonds thanNHCs. Both the Cc−P bond lengths and PCcP angles followthe order 5-PHC < 5′-PHC < 5-PHCB.While the minimum energy structures of six-membered

saturated NHCs display a half-boat conformation with the sp3-hybridized carbon atoms projecting away from the plane of thering, the PHCs exhibit a chair conformation. The six-memberedNHCs exhibit a similar trend with respect to Cc−N bondlengths, that is, 6-NHC < 6-NHCB and ECcE bond angle(except for R = H, Ph where the ECcE bond angle follow thereverse order). The Cc−N bond lengths and NCcN angle of 6-NHC(Ph) are in excellent agreement with the experimentalgeometry (Table 1). It is to be noted that all the six-memberedcarbenes show a wider ECcE angle than five-membered ringcarbenes. Out of all the seven-membered carbenes, while 7-NHC and 7-NHCB exhibit nearly planar geometries, carbenes7′-NHC, 7′-NHCB, 7′-PHC, and 7′-PHCB show nonplanargeometries. 7-NHC and 7′-PHC show a twisted geometry.

Previously, in a theoretical study, Rzepa et al. revealed that sucha twisted geometry might arise due to Mobius distortion.32d

The increase in the size of the ring from six to seven increasesthe ECcE angle. This, however, is much smaller in comparisonto that obtained while going from five- to six-membered ringcarbenes.Another important geometrical parameter, the torsional

angle (α), defined as the dihedral angle between the arylrings defined by the CAr−N···N−CAr atoms, is useful tomeasure the spatial disposition of aryl substituents. Thisparameter was widely used for six- and seven-memberedNHCs and their transition-metal complexes with arylsubstituents at nitrogen atoms.11c,d,12a−c Following this, wehave calculated the torsional angle α of phenyl-substitutedcarbenes (here, CPh−E···E−CPh), as represented in Scheme 3.

The respective α values of the phenyl-substituted carbenes arelisted in Table 1. The α value of 6-NHC agrees well with theexperimental one (Table 1).11c However, for 7′-NHC, thecalculated α value (21.9°) is found to be slightly larger than theexperimental one (13.6°).11c For both five- and six-memberedNHCs, the calculated values of the torsional angle is zero (α =0°). This indicates that the phenyl rings are coplanar in thesemolecules. In addition, to get insight into the extent ofdelocalization between the phenyl ring and the planar ECcEmoiety, we have measured the values of the dihedral angle β(Table 1), which is defined as the angle between the plane of

Table 1. PBE1PBE/6-31+G* Computed Bond Lengths of Cc−E Bonds r(Cc−E) (E = N, P), B−E Bonds r(B−E), E−CPh Bondsr(E−CPh), E−Cc−E Angle (∠ECcE), Torsional Angle CPhEECPh (α), and Dihedral Angle between the E−Cc−E Plane and thePlane of the Phenyl Ring (β). The Wiberg Bond Index (WBI) Values Are Given within Parentheses. The experimentallyObserved Values Are Given in Italicsa

r(Cc−E) r(B−E) ∠ECcE CArEECAr (α)

molecule calcd exptl calcd exptl calcd exptl calcd exptl CcECPhC (β) r(CE−CPh) ref

5-NHC 1.366 (1.227) 1.368 102.0 101.4 0.0 29.9 1.419 (0.988) 305′-NHC 1.347 (1.259) 1.349 105.9 104.7 0.0 0.0 1.406 (1.031) 315-NHCB 1.383 (1.151) 1.378 1.452 (0.883) 1.460 108.6 108.5 0.0 40.9 1.426 (0.979) 9c5-PHC 1.699 (1.472) 100.2 141 6.1 1.803 (0.938)5′-PHC 1.712 (1.453) 104.3 141.1 13.3 1.815 (0.926)5-PHCB 1.717 (1.353) 1.852 (1.204) 111.0 57.1 2.5 1.835 (0.910)

1.746 (1.260) 1.963 (0.901) 1.804 (0.938)6-NHC 1.348 (1.273) 1.346 116.6 114.7 0.0 0.0 25.0 1.424 (1.007) 11c6-NHCB 1.373 (1.198) 1.460 (0.855) 116.3 0.0 55.8 1.439 (0.961)6-PHC 1.696 (1.466) 117.4 0.0 24.5 1.820 (0.918)6-PHCB 1.692 (1.453) 1.885 (1.159) 117.7 0.0 10.0 1.810 (0.939)7-NHC 1.350 (1.284) 120.4 9.9 38.8 1.433 (0.993)7′-NHC 1.349 (1.286) 1.348 118.1 116.6 21.9 13.6 31.4 1.432 (0.996) 11c7-NHCB 1.360 (1.244) 1.469 (0.842) 122.3 28.2 49.7 1.444 (0.960)7′-NHCB 1.369 (1.215) 1.468 (0.838) 120.6 32.9 49.3 1.445 (0.959)7-PHC 1.686 (1.494) 123.5 0.0 8.2 1.824 (0.911)7′-PHC 1.678 (1.507) 125.7 89.3 1.8 1.822 (0.913)7-PHCB 1.671 (1.490) 1.864 (1.187) 124.2 3.5 23.3 1.808 (0.940)7′-PHCB 1.681 (1.467) 1.886 (1.134) 126.3 21.3 12.5 1.813 (0.930)

aBond lengths and angles are given in Å and degrees.

Scheme 3. Schematic Representation of Torsional Angle αand Dihedral Angle β

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the phenyl ring and the plane of the ECcE moiety (Scheme 3).It is expected that the extent of π-electron delocalizationbetween phenyl rings and the ECcE moiety will be larger whenthe value of β is smaller. Indeed, for five-membered NHCs, theβ value correlates well with the E−CPh bond length. That is, thesmaller the value of β, the shorter are the E−CPh bonds (Table1). The shortest E−CPh bond (1.406 Å) is obtained for 5′-NHC with β = 0°, and the longest E−Chi bond (1.426 Å) isfound for 5-NHCB with β = 40.9°. Such a correlation betweenβ values and E−CPh bonds is also obtained for six- and seven-membered NHCs. However, the correlation is less-pronouncedin the case of PHCs due to the presence of pyramidalizationaround phosphorus atoms. This suggests that the extent of π-electron delocalization between the phenyl rings and the ECcEmoiety depends on the value of the dihedral angle β, and thedegree of pyramidalization at the respective heteroatoms.3.2. Singlet−Triplet and HOMO−LUMO Gaps. The

thermodynamic stabilities of carbene were determined from

their singlet−triplet gap and are collected in Table 2. In general,the larger the value of the singlet−triplet gap (ΔES−T) of acarbene, the higher will be its stability and vice versa.1c Thecomputed singlet−triplet gap of 5-NHC(H) (79.9 kcal mol−1)is in agreement with previous calculations at different levels oftheory (80.0,32a 79.3,32b and 84.532c kcal mol−1). In general, thecomputed ΔES−T values of the parent five-, six-, and seven-membered NHCs are in very good agreement with thepreviously reported values (Table 2). From Table 2, it is seenthat the trend of ΔES−T values of NHCs are found to be almostindependent of substituents (R = H, Me, tBu, Ph). It isimportant to point out that most PHCs with sterically bulky Phand tBu groups at phosphorus atoms are found to have slightlylarger ΔES−T values than those PHCs with R = H, Me. This isin tune with an earlier observation where bulky groups atphosphorus atoms were used to reduce the pyramidalization atphosphorus atoms, which, in turn, increases the stability of thesystem.11 In the following discussion, we try to emphasize on

Table 2. PBE1PBE/6-31+G* Computed Singlet−Triplet (ΔES−T, in kcal/mol) and HOMO−LUMO (ΔEH−L, in eV) Gaps.Previously Reported Values at Different Levels of Theory along with the Respective Reference Numbers Are Given in Italics

molecule R ΔES−T ΔEH−L molecule R ΔES−T ΔEH−L5-NHC H 79.9 6.5 5-PHC H 16.8 4.8

80.032a 3.62b

Me 81.3 6.5 Me 20.5 4.8tBu 78.4 6.1 tBu 17.9 4.7

Ph 68.8 5.7 Ph 20.7 4.25′-NHC H 65.9 6.3 5′-PHC H 14.1 4.3

68.02b 3.72b

Me 68.7 6.3 Me 16.4 4.2tBu 66.7 5.9 tBu 17.6 4.2

Ph 63.7 5.0 Ph 16.2 3.85-NHCB H 28.0 3.8 5-PHCB H 11.9 3.7

Me 27.6 3.8 Me 13.9 3.8tBu 22.7 3.5 tBu 13.3 3.8

Ph 26.8 3.8 Ph 15.7 3.76-NHC H 59.3 5.7 6-PHC H 12.2 3.8

Me 58.0 5.7 Me 13.2 3.764.32c

tBu 55.0 5.2 tBu 15.1 3.7

Ph 51.9 5.3 Ph 12.7 3.56-NHCB H 39.6 4.7 6-PHCB H 16.3 3.8

Me 38.4 5.4 Me 22.2 3.9tBu 30.7 4.1 tBu 22.7 3.8

Ph 34.1 4.4 Ph 22.9 3.67-NHC H 47.1 5.4 7-PHC H 17.7 3.8

Me 46.8 5.4 Me 12.3 3.7tBu 4.8 tBu 15.4 3.7

Ph 37.7 4.8 Ph 14.2 3.67′-NHC H 48.1 5.5 7′-PHC H 15.1 4.1

Me 47.8 5.3 Me 16.2 4.050.42c

tBu 47.1 5.0 tBu 17.0 3.9

Ph 38.7 4.9 Ph 16.9 3.87-NHCB H 36.2 3.8 7-PHCB H 21.9 4.0

Me 29.5 3.6 Me 27.0 4.0tBu 26.8 3.6 tBu 25.4 3.7

Ph 32.1 3.6 Ph 33.5 3.67′-NHCB H 33.0 4.4 7′-PHCB H 18.0 3.8

Me 27.9 4.5 Me 22.1 3.7tBu 21.1 4.3 tBu 23.6 3.8

Ph 26.4 4.5 Ph 23.1 3.6

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the trends of ΔES−T values for all the molecules. The ΔES−Tvalues of five-membered NHCs decrease in the order 5-NHC >5′-NHC > 5-NHCB and is consistent with the increase of theECcE angle. The higher singlet−triplet gap of 5-NHCcompared to its saturated analogue 5′-NHC is due to thearomatic stabilization of the singlet state of the former. Previoustheoretical calculations also recognized this additional stabiliza-tion.33 It is noteworthy to mention here that the phosphorusatom has a higher inversion barrier compared with the nitrogenatom, which induces pyramidalization around it.34 Thisenhanced pyramidalization reduces its ability to donate itslone pair into the formally vacant pπ orbital on the carbenecarbon, which, in turn, reduces the stability of the singlet state.Indeed, this has been reflected in the calculated ΔES−T valuesfor five-membered PHCs, which are significantly smaller thanthe corresponding values for NHCs, and it decreases in theorder 5-PHC > 5′-PHC > 5-PHCB.For NHCs, it can be seen that an increase in the size of the

ring results in a decrease of ΔES−T values except thosecontaining a boron atom in the ring framework. Thus, ΔES−Tvalues of 6-NHC are smaller by almost 10 kcal mol−1 thanthose of 5′-NHC. However, the ΔES−T values of PHCs do notchange appreciably with increases or decreases of ring size. Onthe contrary, the six-membered carbenes with a boron atom inthe ring framework are more stable than the five-memberedcounterparts. The calculated ΔES−T values for 7′-NHC and 7-NHCB are even smaller than those for 6-NHC. We could notcalculate the singlet−triplet gap of 7-NHC(tBu) (Table 2)because we have found a broken structure (the backboneconsisting of four carbon atoms moves away from the NCNmoiety) for its triplet state. The overall decreasing order ofseven-membered NHCs with respect to ΔES−T values is 7-NHC ≈ 7′-NHC > 7-NHCB > 7′-NHCB. Among the seven-membered PHCs, the ΔES−T values follow the order 7-PHCB ≈7′-PHCB > 7′-PHC > 7-PHC. The higher ΔES−T value for 7-PHCB may be attributed to the planarity of the molecule,whereas lower ΔES−T values of 7-PHC, 7′-PHC, and 7′-PHCBmay be attributed to the puckered nature of the molecule. Eventhough the ΔES−T values of PHCs are consistently lower thanthose for NHCs, indicating increased contribution from thetriplet state, the importance of singlet geometry cannot beneglected as the ΔES−T values are likely to increase with thesubstitution of more bulky groups at the phosphorus centers.The HOMO−LUMO gap, ΔEH−L, is an important parameter

that determines the kinetic stability of a molecule.35 Among thefive-membered NHCs, ΔEH−L values (Table 2) indicates that 5-NHC is kinetically the most stable, whereas 5-NHCB iskinetically the least stable. However, the five-membered PHCs5-PHC and 5′-PHC have lower kinetic stability than theirNHC analogues. Interestingly, the calculated ΔEH−L values for5-NHCB and 5-PHCB are comparable. With the exception ofmolecules containing a boron atom in the ring framework (suchas 5-NHCB), the kinetic stability of NHCs was found todecrease with an increase in the ring size. This is reflected incalculated ΔEH−L values for 6-NHC (≈5.5 eV) as compared tothose for 5′-NHC (≈5.9 eV). In contrast, 6-NHCB is kineticallymore stable than 5-NHCB. Similar to NHCs, 6-PHC has aslightly smaller ΔEH−L value than 5′-PHC. The ΔEH−L valuesof 7′-NHC and 7-NHCB are slightly smaller than that of 6-NHC. However, ΔEH−L values of seven-membered PHCs donot show any significant variation with respect to the ringmodification as well as substituents at E. The ΔEH−L values of

hydrogen- and methyl-substituted carbenes are slightly largerthan the tert-butyl- and phenyl-substituted ones.

3.3. Ligand Properties. 3.3.1. Frontier MolecularOrbitals. Heterocyclic carbene can act as an ambivalent liganddue to the presence of a σ-symmetric lone pair and empty π-symmetric orbital on the carbenic carbon. The reactivity36 aswell as ligand properties37 of a given carbene can be judgedfrom the nature and energies of these two key frontier orbitals.To investigate the relative σ-donation and π-accepting ability ofthe NHCs (R = Me) and PHCs (R = Me) as a function ofdifferent factors, such as saturation/unsaturation in the C−Cbackbone, different ring sizes, and the effect of boronsubstitution, the energies of the corresponding σ-symmetricoccupied molecular orbital (Eσ) and π-symmetric unoccupiedmolecular orbital (Eπ) of these molecules are depicted in Figure1. It is evident from Figure 1 that the increase in ring size

increases the σ-donation ability of NHCs. Saturation at the C−C backbone of five-membered NHCs has no dramatic effect onthe σ-donation ability; however, such an effect of saturation forthe seven-membered NHCs results in an increase in the σ-donation ability. Unlike NHCs, saturation at the C−Cbackbone of five-membered PHCs increases the σ-donationability. This is also true for six- and seven-membered PHCs. Itis also evident from Figure 1 that substituting a boron atom inthe ring framework of the NHCs does not lead to a dramaticchange in the σ-donation ability. However, boron substitutionat five-membered unsaturated PHC 5-PHCB leads to adramatic increase in the σ-donation ability. Despite the highdegree of pyramidalization at the phosphorus center, PHCs arefound to be better π acids than NHCs (Figure 1). In general,the higher the delocalization from the adjacent heteroatom tothe carbenic p orbital, the lower will be the acidity of thecarbene. This is because higher delocalization from the adjacentheteroatom results in a higher population at the unoccupied porbital. This, in turn, makes the central carbon atom moreelectron-rich. This delocalization is very less in the case ofPHCs due to the pyramidalization at phosphorus making itmore acidic. Moreover, boron substitution does not lead to anysignificant reduction of this delocalization, and accordingly, theπ acidity of PHCs is more or less unaffected. However, in thecase of NHCs, boron substitution reduces the delocalizationfrom the N lone pair to the carbenic carbon atom, resulting in

Figure 1. Plot of energies of σ-symmetric occupied molecular orbitals,Eσ, and π-symmetric unoccupied molecular orbitals, Eπ, of NHCs andPHCs (R = Ph).

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lowering of the energy level of the π-symmetric unoccupiedmolecular orbital centered at the carbon atom. Thus, it is seenthat substitution of a boron atom in the ring framework ofNHCs significantly increases the π-accepting ability. The trendof Eσ and Eπ values as a function of different substituents (R) isgraphically represented in Figures 2 and 3, respectively (theenergies are provided in Table S3, Supporting Information). Itis evident from Figure 2 that both five-membered NHCs andPHCs show a similar trend in their σ donation abilities, that is,5-NHC < 5′-NHC < 5-NHCB and 5-PHC < 5′-PHC < 5-PHCB. The σ-donation ability of both NHCs and PHCsincreases with the increase in the size of the ring (expect thosecontaining boron atoms). However, such an increase is moreprominent for NHCs than that for PHCs (Figure 2). It is foundthat the alkyl-substituted (R = Me, tBu) carbenes have higherEσ values than with other substituents (R = H, Ph).Boron substitution has a dramatic effect on the π-accepting

abilities of NHCs, as evidenced by the lowering of Eπ values(Figure 3). The boron atoms at the α position to the nitrogenatoms can withdraw π-electron density from the nitrogen lonepair to its formally empty p orbital. This, in turn, results inreduced electron delocalization from the nitrogen lone pair tothe empty pπ orbital on the carbenic carbon, thereby loweringthe energies of the π-symmetric unoccupied molecular orbital.Surprisingly, the computed Eπ values of phenyl-substituted (R =Ph) NHCs are significantly lower than those with R = H, Me,and tBu. This might be due to the reason that phenyl canwithdraw π electrons from the lone pair on the nitrogen atomvia conjugation (mesomeric effect). To verify this, we did asingle-point calculation by keeping the two phenyl ringsperpendicular to the plane of the NHC ring of 5-NHC(Ph),thereby effectively removing the overlap of the nitrogen lonepair with the phenyl ring. As expected, this has raised theenergy of the empty π-symmetric orbital by 1.3 eV (the Eπ

values for parallel and perpendicular conformation are −0.7 and+0.6 eV, respectively). Interestingly, the π acidities of all theparent NHCs are nearly comparable, as revealed by more orless similar values of Eπ. The change of the heteroatom from

nitrogen to phosphorus results in a significant lowering of theEπ values. However, the π acidities of PHCs do not changesignificantly as a result of boron substitution (Figure 3).Contrary to NHCs, the change of R from H (or Me and tBu) toPh in PHCs does not lead to any significant lowering of the Eπ

values. Like five- and six-membered PHCs, all seven-memberedPHCs are found to have a significantly higher π acidity incomparison to seven-membered NHCs.

3.3.2. Nucleophilicity and Electrophilicity. We havecalculated the nucleophilicity index, N, using a similar methodas that reported by Domingo et al.38a In this method, N iscalculated as N = EHOMO − EHOMO(TCNE), where tetracyano-ethylene (TCNE) is considered as the reference. In addition,the global electrophilicity, ω, is computed by employing theexpression ω = (μ2/2η), where μ is the chemical potential (μ ≈

Figure 2. Plot of energies of σ-symmetric occupied molecular orbitals, Eσ, of the carbenes for all the substituents.

Figure 3. Plot of energies of π-symmetric unoccupied molecularorbitals, Eπ, of the carbenes for all the substituents.

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(EHOMO + ELUMO)/2) and η is the chemical hardness (η =(EHOMO − ELUMO).

38b−d

The reactivity parameters, such as nucleophilicity index, N,and electrophilicity index, ω, are computed for carbenes (Table3) and discussed here for Me-substituted carbene as arepresentative case.

The five-membered NHCs have comparable nucleophilicity(>3.5 eV). However, the electrophilicity of 5-NHCB(Me) (ω =4.35 eV) is much larger than that for 5-NHC(Me) and 5′-NHC(Me) (ω = 1.22 eV). This is consistent with thecomparable σ-donating ability and higher π-accepting abilityof these NHCs. 5-PHC(Me) and 5′-PHC(Me) exhibit thelowest nucleophilicity among the carbenes under consideration.However, their N values are slightly smaller (3.42 eV for 5-PHC(Me) and 3.52 eV for 5′-PHC(Me)) than those for theirNHC counterparts. The effect of saturation of the backbone offive-membered PHCs on the nucleophilicity is the same as thatof NHC analogues. 5-PHC(Me) and 5′-PHC(Me) exhibithigher electrophilic character (3.11 eV for 5-PHC(Me) and3.82 eV for 5′-PHC(Me)) than their NHC counterparts. Theorder of ω values among five-membered PHCs is 5-PHC(Me)< 5′-PHC(Me) < 5-PHCB(Me).It is found that an increase in ring size of simple NHCs

(except those containing B atoms in the ring framework)results in an increase in the nucleophilicity of the carbene. It isto be noted that no significant variation in ω values is seen inthe case of simple NHCs as the ring size increases from five toseven. However, NHCs containing a B atom in the ringframework exhibit more electrophilicity. The N values of six-membered PHCs are larger than those of five-memberedPHCs, but smaller than those of six-membered NHCs.7-NHC(Me) and 7′-NHC(Me) are most nucleophilic

among the studied carbenes. In general, the calculated valuesof N and ω are found to correlate well with the energies of theσ-donating and π-accepting orbitals of carbenes.3.3.3. Electrochemistry and 13C NMR Spectroscopy of the

Transition-Metal Complexes [LRh(CO)2Cl; L = CarbeneLigand]. The relative π acidity of the carbenes is further

assessed from the relative redox potential (ΔE1/2) and theaverage CO stretching frequencies (υavCO) of the cis-LRh(CO)2Cl complexes (Scheme 4). Here, we have considered

only the methyl-substituted carbenes as a representative case.The calculated ΔE1/2 values (Table 4) are within the range of

other NHC supported [M(CO)2Cl] complexes (0.88−1.16V).39 It should be noted that such relative redox potential(ΔE1/2) values were used as a probe to measure the donationability of carbenes.39 However, in general, a carbene with higherπ acidity can withdraw more electron density from the metalcenter through dπ → pπ* back-donation, thereby making themetal center electron-deficient. This electron deficiency at themetal center is reflected in the lowering of the energy level ofthe HOMO (concentrated at the metal center) of the neutralmetal complex, thus increasing the first ionization energy. Inother words, the calculated relative redox potential values(ΔE1/2) may be taken as a measure of such electron deficiencyat the metal center caused by the associated ligands. In general,the higher is the π-accepting ability of the carbenes, the higherwill be the ΔE1/2 and υavCO of the respective metal complexes.We found reasonable correlation (Figure 4, R2 = 0.80) betweenthe ΔE1/2 values and the energy of the π-symmetric unoccupiedorbital (Eπ) centered at the central carbon atom of thecarbenes. For example, the π-accepting ability of 5-NHCB, 5′-PHC, 5-PHCB, 6-PHC, 6-PHCB, 7-PHCB, and 7′-NHCB issignificantly higher than that of 5-NHC. Consequently, theoxidation potential of the complexes of these ligands withRh(CO)2Cl is 60−100 mV higher than that of 5-NHC-Rh(CO)2Cl. However, the correlation between the average COstretching frequencies (υavCO) of the respective complexes andEπ values is poor (R

2 = 0.56). This implies that the ΔE1/2 valuemay be taken as a measure of π acidity of carbene. All the

Table 3. PBE1PBE/6-31+G* Computed Values ofNucleophilicity Index (N) and Electrophilicity Index (ω) ofCarbenes with R = Me

ligand N (eV) ω (eV)

5-NHC 3.58 1.215′-NHC 3.75 1.225-NHCB 3.72 4.355-PHC 3.42 3.115′-PHC 3.52 3.825-PHCB 3.83 4.116-NHC 4.23 1.186-NHCB 4.08 2.326-PHC 3.88 4.096-PHCB 3.91 3.727-NHC 4.45 1.187′-NHC 4.56 1.147-NHCB 4.15 3.817′-NHCB 4.27 2.27-PHC 3.91 4.037′-PHC 3.89 3.457-PHCB 3.66 4.037′-NHCB 4.04 3.81

Scheme 4

Table 4. Relative Redox Potential (ΔE1/2, in Volts) Values ofcis-LRh(CO)2Cl (L = Carbenes) Complexes (R = Me)

L E1/2 (V) υavCO (cm−1)

5-NHC 0.82 2154.35′-NHC 0.84 2150.25-NHCB 0.91 2161.35-PHC 0.87 2169.75′-PHC 0.88 2174.95-PHCB 0.92 2176.96-NHC 0.82 2157.36-NHCB 0.83 2148.66-PHC 0.90 2169.66-PHCB 0.89 2165.67-NHC 0.80 2139.67′-NHC 0.82 2138.57-NHCB 0.83 2144.57′-NHCB 0.83 2161.27-PHC 0.88 2156.57′-PHC 0.86 2170.27-PHCB 0.88 2166.47′-NHCB 0.89 2164.0

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calculated transition-metal complexes are found to be quitestable, as indicated by their binding energies (∼40 kcal/mol;Table S4, Supporting Information).

13C chemical shifts of all the NHCs have been calculated tounderstand the ligating properties of these NHCs. Theextensive use of 13C NMR spectroscopy in elucidating thestructure and bonding in carbenes has been recentlyreviewed.40 The calculated 13C chemical shifts are found tobe very close to the experimental values (Table 5), whichjustifies the adequacy of this DFT methodology in calculatingNMR chemical shifts. As suggested by Arduengo et. al,41 theorientation of the chemical shift tensor at the carbenic carboncan be represented as shown in Figure 5. It is evident fromFigure 5 that the tensor component, σ22, lies along the directionof the carbene lone pair. Its magnitude is the smallest. Theother component, σ11, which lies in the molecular plane alongthe nitrogen atoms, is the most deshielded one. The mostshielded tensor component, σ33, lies perpendicular to the

molecular plane and is along the direction of vacant p orbital atthe carbenic carbon. During the formation of the transitionmetal−carbene bond, this σ33 component may becomedeshielded due to the mechanism of dπ−pπ* back-donation.In general, the higher the π-accepting ability of the carbene, the

Figure 4. Correlation plot between the energies of the π-symmetric unoccupied molecular orbitals (Eπ) and the relative redox potential (ΔE1/2) andaverage CO stretching frequencies (υavCO).

Table 5. Calculated Absolute Chemical Shift, σiso, and the Chemical Shift Tensor Components, σii, of the Carbenic Carbon inFree NHCs and in their cis-LRh(CO)2Cl Complexes

chemical shift

free ligand complex

ligand L σiso σ11 σ22 σ33 δrela σiso σ11 σ22 σ33 δrel

a Δσ33b ΔδCc

5-NHC −20.14 −192.3 14.6 117.2 208.4 9.5 −93.4 30.0 91.9 178.8 25.3 29.6(213.7)30 (182.6)13c

5′-NHC −39.6 −235.8 121.5 112.1 227.8 −18.1 −155.6 16.1 85.1 206.4 27.0 21.4(244.5)31 (205.7)13b

5-NHCB −133.1 −434.0 −29.5 64.1 376.4 −72.1 −202.9 −7.1 −6.5 260.4 70.6 116.06-NHC −35.9 −227.2 −4.1 123.5 224.2 −9.1 −134.5 3.9 103.2 197.4 20.3 26.86-NHCB −102.4 −389.5 −13.7 96.1 290.7 −52.1 −228.1 −1.7 42.6 240.4 53.5 50.37-NHC −47.8 d d d 236.1 −43.8 d d d 232.1 4.07′-NHC −54.2 d d d 242.5 −23.5 d d d 211.8 30.7

(244.0)11c

7-NHCB −93.1 d d d 281.4 −47.6 d d d 233.8 47.67′-NHCB −122.6 d d d 310.9 −58.5 d d d 246.8 64.1

aWith reference to tetramethylsilane (TMS). bσ33 (free ligand) − σ33(complex).cδ(free) − δ(complex). dThe NHC ligands in free form and in

complexes are not planar, and hence, no perfect axes system can be defined.

Figure 5. Components of the chemical shielding tensor of NHCs.41

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higher deshielded will be the tensor component, σ33. Thus, wecalculated the change in magnitude of this tensor component,Δσ33 = σ33 (free ligand) − σ33(complex). This gives a measureof the π-accepting ability of the carbene. We could not assignΔσ33 for seven-membered NHCs as these ligands are notperfectly planar in their free form as well as in their complexes,and hence, the assignment of the proper axes system becamedifficult. This also accounts for the noninclusion of PHCs inNMR calculations. However, the calculated values of Δσ33 forthe other NHCs were found to correlate well (R2 = 0.97) withthe energies of the π-accepting orbital, Eπ, of the free carbenes(Figure 6).The magnitude of the change in the chemical shift values,

ΔδC, upon complexation may also be taken as a measure of theπ-accepting ability of the carbene. The magnitude of the ΔδCvalues of the 13C signal for these carbenes follows the order 5-NHCB > 7′-NHCB > 6-NHCB > 7-NHCB > 7′-NHC > 5-NHC> 6-NHC > 5′-NHC > 7-NHC. This order is almost similar tothat of the π-accepting abilities of these carbenes (Table S3,Supporting Information). In fact, we also obtained a goodcorrelation (R2 = 0.87) between ΔδC values and the energy ofthe π-accepting orbital, Eπ (Figure 6). However, the chemicalshift difference may not be attributed solely to a change in π-acceptor properties as the σ-donation ability of these carbenesalso varies appreciably, which may affect the overall chemicalshift values.

4. CONCLUSIONQuantum chemical calculations have been carried out on theelectronic structure and stability of boron-substituted five- toseven-membered carbenes with a special emphasis on their π-accepting ability. Calculated singlet−triplet and HOMO−LUMO gaps indicate that the hitherto unknown carbenes 6-NHCB, 6-PHCB, 7-NHC, 7′-NHCB, 7-PHCB, and 7′-PHCBare stable. Substituents at the nitrogen atoms of NHCs arefound to have a negligible effect on the singlet−triplet gap.However, the bulkiness of the substituents has a significanteffect on the singlet−triplet gap of PHCs; that is, the singlet−triplet gap of PHCs increases with an increase in bulkiness ofthe substituents attached to phosphorus. Introduction of aboron atom in the ring framework of these carbenes decreasesthe singlet−triplet as well the HOMO−LUMO gap. An

increase of the ring size decreases the singlet−triplet gap ofNHCs except for boron-containing rings.In general, PHCs are found to be better π acceptors than

NHCs. The introduction of a boron atom in the ringframework significantly affects the σ-donation and π-acceptanceabilities of these carbenes. Phenyl-substituted NHCs are foundto have better π-accepting ability than those with R = H, Me,and tBu. A recent study reveals that aromatic N-substitutedNHCs have π-face donation abilities too.42 Thus, phenylsubstitution at the heteroatoms seems exciting as far as itsimplication in catalysis is concerned. The calculated reactivityparameters, such as nucleophilicity and electrophilicity index,are in accord with the respective σ-donation and π-acceptanceability of the carbenes. The relative redox potential values of therhodium complexes of these carbenes are found to correlatewell with the π-accepting abilities of these carbenes. However,the correlation of π acidity and average CO stretchingfrequency is somewhat poor. The calculated 13C NMRparameters of the NHCs were also found to correlate wellwith the π acidity of these carbenes. This implies that relativeredox potential values and 13C NMR parameters of transition-metal complexes of carbenes may be used as a measure of πacidity of carbenes even though the contribution of σ donationcannot be ruled out completely.

■ ASSOCIATED CONTENT*S Supporting InformationTables S1−S4 and Cartesian coordinates of all the moleculesalong with their total energies including zero-point vibrationalcorrection. This material is available free of charge via theInternet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: ashwini@tezu.ernet.in.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSS.S and A.K.G thank the Council of Scientific and IndustrialResearch (CSIR) for a Senior Research Fellowship (SRF). We

Figure 6. Correlation plot between the changes in the chemical shielding tensor, Δσ33, along the vacant pπ orbital at the carbenic carbon; changes inthe chemical shift upon complexation, ΔδC; and the energies of the π-accepting orbital of the carbenes, Eπ (eV).

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thank all the reviewers for their helpful comments. This articleis dedicated to Prof. Pradip K. Gogoi.

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Organometallics Article

dx.doi.org/10.1021/om400162a | Organometallics XXXX, XXX, XXX−XXXJ

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Organometallics Article

dx.doi.org/10.1021/om400162a | Organometallics XXXX, XXX, XXX−XXXK