Bonding Situation in Dimeric Group 15 Complexes [(NHC)2

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Bonding Situation in Dimeric Group 15 Complexes [(NHC)

₂

(E

₂

)] (E = N–Bi)

Nicole Holzmann and Gernot Frenking

Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Strasse, D-35032 Marburg (Germany)

Reprint requests to N. H.; E-mail:holzmann@staff.uni-marburg.deand G. F.; E-mail:frenking@chemie.uni-marburg.de

Z. Naturforsch.69a, 385 – 395 (2014) / DOI: 10.5560/ZNA.2014-0033 Received May 8, 2014 / revised May 19, 2014 / published online July 15, 2014 Dedicated to Professor Dr. Jörg Fleischhauer on the occasion of his 75th birthday

Quantum chemical calculations using density functional theory at the BP86 level in conjunction with triple-zeta polarized basis sets have been carried out for the title compounds. The nature of the bonding between the diatomic fragment and the NHC ligands is investigated with an energy decomposition analysis. The chemical bonds in the [(NHC^Me)₂(E₂)] complexes can be discussed in terms of donor–acceptor interactions which consist of two NHC^Me→E2←NHC^Medonor components and two weaker components of the NHC^Me←E2→NHC^Meπ backdonation. The out-of-phase(+)/(−) contribution of theσdonation is always stronger than the in-phase(+)/(+)contribution. The electronic reference state of N₂in the dinitrogen complex [(NHC^Me)₂(N₂)] is the highly excited 1¹Γg

state which explains the anti-periplanar arrangement of the ligands. The gauche arrangement of the ligands in the heavier homologues [(NHC^Me)2(E2)] (E=P–Bi) may be discussed using either the excited 1¹Γgstate or the X¹Σ_g⁺ground state of E₂as reference states for the donor–acceptor bonds.

The EDA-NOCV calculations suggest that the latter bonding model is better suited for the complexes where E=As–Bi while the phosphorus complex is a borderline case.

Key words:Donor–Acceptor Complex; Bonding Analysis; Quantum Chemical Calculations.

1. Introduction

The stabilization of electronically unsaturated main group compounds by coordination of σ donor ligands L such as N-heterocyclic carbenes (NHCs) or phosphanes PR₃ has been an area of intensive experimental and theoretical research in recent years.

In particular, complexes of monoatomic species such as carbones CL₂ [1–18], silylones SiL₂ [19–25], germylones GeL₂[24,26,27], and adducts of diatomic molecules of groups 13 – 15 such as B₂L₂ [28–30], Si₂L₂[31], Ge₂L₂[32,33], Sn₂L₂[34], P₂L₂[35–39], and As₂L₂ [40] have been isolated, and they were investigated with quantum chemical methods. A par- ticularly interesting species is the dinitrogen complex N₂L₂. Quantum chemical calculations of group 14 and 15 complexes L→E₂←L by Wilson et al. [41]

showed that all complexes are stable toward dissocia- tion of the ligands L except for E=N. However, stable adducts [(NHC)2N2] [42] and even [(PPh3)2N2] [43],

which according to the calculations [41] is ther- modynamically unstable toward nitrogen loss by

∼90 kcal/mol, could become isolated and were found to be very stable. The surprisingly high kinetic stabil- ity of [(PPh₃)₂N₂] which melts at 184 – 186^◦C and de- composes only above 215^◦C has been explained with the very strong bidentate Lewis acidity of N₂ in the electronically highly excited 1¹Γgstate [44].

The ligands L in [(NHC)₂N₂] and [(PPh₃)₂N₂] exhibit an anti-periplanar arrangement in the complexes. In contrast, the conformation of the phosphorus analogues [(NHC^R)₂(P₂)] depends on the size of the substituents R at the nitrogen atoms. The X-ray structure of [(NHC^Dipp)₂(P₂)] (Dipp = 2,6- diisopropylphenyl) gives an anti-periplanar orientation of the ligands but the complex [(NHC^Mes)₂(P₂)]

(Mes = mesityl) possesses a gauche conformation with a dihedral angle C^NHC–P–P–C^NHCof 134.1^◦[35].

A gauche conformation is also found for the complex [(CAAC^Dipp)2(P2)] (CAAC=cyclic alkyl amino

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Table 1. EDA-NOCV results of the donor–acceptor interactions of [(NHC^Me)₂(E₂)] at BP86/TZ2P+. Fragments are (NHC^Me)2and (E2). All energies in kcal/mol.

[(NHC^Me)2(E2)] (¹Γg) [(NHC^Me)2(E2)] (X¹Σ_g⁺)

E=N C₂ –

∆E_int −374.3 –

∆E_Pauli 1237.7 –

∆E_elstat −530.5 (32.9%) –

∆E_orb −1081.6 (67.1%) –

∆E₁ −424.4 (39.2%) –

∆E2 −450.0 (41.6%) –

∆E₃ −92.0 (8.5%) –

∆E₄ −34.4 (3.2%) –

∆E_rest −80.8 (7.5%) –

E=P C₂ C₂

∆E_int −218.0 −78.0

∆E_Pauli 677.3 853.5

∆E_elstat −409.4 (45.7%) −441.9 (47.4%)

∆E_orb −485.9 (54.3%) −489.6 (52.6%)

∆E₁ −169.1 (34.8%) −163.0 (33.3%)

∆E₂ −204.6 (42.1%) −243.3 (49.7%)

∆E₃ −47.8 (9.8%) −28.4 (5.8%)

∆E₄ −26.5 (5.5%) −25.1 (5.1%)

∆Erest −37.9 (7.8%) −29.8 (6.1%)

E=As C₂ C₂

∆E_int −181.9 −65.5

∆E_Pauli 608.8 681.6

∆E_elstat −384.5 (48.6%) −385.9 (51.7%)

∆E_orb −406.1 (51.4%) −361.1 (48.3%)

∆E₁ −142.0 (35.0%) −135.7 (37.6%)

∆E₂ −190.4 (46.9%) −164.0 (45.4%)

∆E3 −28.2 (6.9%) −20.4 (5.6%)

∆E₄ −20.3 (5.0%) −19.9 (5.5%)

∆E_rest −25.2 (6.2%) −21.1 (5.8%)

E=Sb C2 C2

∆E_int −149.5 −53.6

∆E_Pauli 477.1 514.6

∆E_elstat −318.6 (50.9%) −318.5 (56.1%)

∆E_orb −308.0 (49.2%) −249.7 (44.0%)

∆E1 −103.4 (33.6%) −97.0 (38.8%)

∆E₂ −154.9 (50.3%) −108.7 (43.5%)

∆E₃ −17.5 (5.7%) −14.2 (5.7%)

∆E₄ −13.6 (4.4%) −13.6 (5.4%)

∆E_rest −18.6 (6.0%) −16.2 (6.5%)

E=Bi C₂ C₂

∆E_int −133.0 −46.9

∆E_Pauli 476.0 423.3

∆E_elstat −295.8 (48.6%) −272.2 (57.9%)

∆E_orb −313.2 (51.4%) −198.1 (42.1%)

∆E₁ −105.5 (33.6%) −67.3 (34.0%)

∆E₂ −173.5 (55.4%) −97.4 (49.2%)

∆E₃ −10.9 (3.5%) −9.8 (4.9%)

∆E4 −10.6 (3.4%) −10.8 (5.5%)

∆E_rest −12.7 (4.1%) −12.8 (6.5%)

carbene) which exhibits a dihedral angle C^CAAC–P–

P–C^CAAC of 149.2^◦ [36,37]. The arsenic complex [(NHC^Dipp)₂(As₂)] has an anti-periplanar arrangement

Table 2. Wiberg bond indices (WBI) of the E–E, E–C^NHC, and C^NHC–N bonds at BP86/def2-TZVPP.

E–E E–C^NHC C^NHC–N

NHC^Me – – 1.27

[(NHC^Me)2(N2)] 1.08 1.54 1.08/1.09

[(NHC^Me)2(P2)] 1.04 1.27 1.13/1.14

[(NHC^Me)2(As2)] 1.02 1.19 1.16

[(NHC^Me)2(Sb2)] 1.09 1.02 1.18/1.19

[(NHC^Me)2(Bi2)] 1.15 0.92 1.20

of the ligands [35]. The bonding analysis of the group 13 complexes L→E₂←L, where E=B–In, and the group 14 homologues with E=Si–Pb which pos- sess either a linear (E= B) or an anti-periplanar arrangement of the ligands L can straightforwardly be done because the choice of the electronic reference state of E₂was easy. This appears not the case for the heavier group 15 complexes [(NHC)₂(E₂)] where E= P–Bi. Therefore, we investigated the electronic structure of all group 15 adducts [(NHC)₂(E₂)] (E=N–Bi) using an energy decomposition analysis. The results are reported below.

2. Methods

Geometry optimizations have been carried out using TurboMole 6.1 optimizer [45] and gradients at the BP86 [46,47] /def2-TZVPP [48] level of theory. Sta- tionary points were characterized as minima by calcu- lating the Hessian matrix analytically. For all calculations the resolution-of-identity method has been ap- plied [49].

For the bonding analyses we optimized the molecules at BP86 using uncontracted Slater-type orbitals (STOs) as basis functions [50] with the program package Amsterdam density functional ADF2009.01 [51,52]. The latter basis sets for all elements have triple-ζ quality augmented by two sets of polarization functions (ADF-basis set TZ2P). This

Table 3. NBO partial charges of the (E₂) moiety and the coor- dinating carbon atom at BP86/def2-TZVPP. All charges in e.

(E2) C^NHC

NHC^Me – 0.04

[(NHC^Me)2(N2)] −0.89 0.47 [(NHC^Me)2(P2)] −0.19 0.04 [(NHC^Me)2(As2)] −0.26 0.08 [(NHC^Me)2(Sb2)] −0.29 0.09 [(NHC^Me)2(Bi2)] −0.33 0.12

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Table 4. NBO results of the E–E and E–C^NHCbonds at BP86/def2-TZVPP.

orbital occupation occupation % (E) % s(E)â % p(E)â % (C) % s(C)â % p(C)â bonding anti-bonding

[(NHC^Me)2(N2)] N–N 1.97 0.02 50.0 25.0 74.8

N 1.89 39.8 60.1

N–C 1.99 0.02 56.0 35.4 64.1 44.0 39.6 60.4

N–C 1.94 0.49 64.7 0.0 99.8 35.3 0.0 100.0

[(NHC^Me)2(P2)] P–P 1.92 0.04 50.0 13.6 85.9

P 1.94 71.2 28.8

P–C 1.97 0.04 33.5 15.4 84.1 66.5 41.8 57.9

P–C 1.90 0.62 66.4 0.2 99.6 33.6 0.2 99.5

[(NHC^Me)2(As2)] As–As 1.93 0.04 50.0 9.2 90.5

As 1.96 80.2 19.7

As–C 1.97 0.05 31.4 10.6 89.0 68.6 41.2 58.8

As–C 1.91 0.64 70.3 0.2 99.6 29.7 0.1 99.7

[(NHC^Me)2(Sb2)] Sb–Sb 1.94 0.05 50.0 7.2 92.5

Sb 1.97 85.8 14.2

Sb 1.59 0.4 99.5

Sb–C 1.96 0.07 26.9 6.9 92.8 73.1 39.9 60.1

[(NHC^Me)2(Bi2)] Bi–Bi 1.95 0.03 50.0 4.7 95.1

Bi 1.98 91.4 8.6

Bi 1.64 0.4 99.6

Bi–C 1.96 0.09 25.0 3.9 95.9 75.0 39.2 60.8

aThe remaining small contributions which add to 100% come from polarization functions.

level of theory is denoted BP86/TZ2P. An auxiliary set of s, p, d, f, and g STOs was used to fit the molecular densities and to represent the Coulomb and exchange potentials accurately in each self-consistend field cy- cle [53]. Scalar relativistic effects have been incorpo- rated by applying the zero-order regular approximation (ZORA) in all ADF calculations [54].

The interatomic interactions were investigated by means of an energy decomposition analysis (EDA, also termed extended transition state method – ETS) devel- oped independently by Morokuma [55] and by Ziegler and Rauk [56]. The bonding analysis focuses on the instantaneous interaction energy∆E_intof a bond A–B between two fragments A and B in the particular electronic reference state and in the frozen geometry of AB. The interaction energy is divided into three main components:

∆E_int=∆E_elstat+∆E_Pauli+∆E_orb. (1) The term ∆E_elstat corresponds to the quasiclassi- cal electrostatic interaction between the unperturbed charge distributions of the prepared atoms and is usu- ally attractive. The Pauli repulsion ∆EPauli is the energy change associated with the transformation from the superposition of the unperturbed wavefunctions of the isolated fragments which corresponds to a Hartree product to the wavefunctionΨ⁰=NA[Ψˆ _AΨ_B], which

properly obeys the Pauli principle through explicit antisymmetrization ( ˆA operator) and renormalization (N= constant) of the product wavefunction.∆E_Pauli comprises the destabilizing interactions between elec- trons of the same spin on either fragment. The orbital interaction∆Eorb which can be associated with cova- lent bonding accounts for mixing of the fragment orbitals and polarization effects. The∆E_orbterm can be decomposed into contributions from each irreducible representation of the point group of the interacting system. Further details on the EDA method [51,52]

and its application to the analysis of the chemical bond [57–60] can be found in the literature.

The EDA-NOCV [61] method combines charge (NOCV) and energy (EDA) decomposition schemes to decompose the deformation density which is associated with the bond formation,∆ρ, into different components of the chemical bond. The EDA-NOCV calculations provide pair wise energy contributions for each pair of interacting orbitals to the total bond energy.

NOCV (natural orbital for chemical valence) [62–64]

is defined as the eigenvector of the valence operator ˆV given by

VΨˆ _i=υ_iΨ_i. (2) In the EDA-NOCV scheme the orbital interaction term

∆E_orbis given by

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Fig. 1. Optimized geometries at RI-BP86/def2-TZVPP and most important bond lengths [Å] and angles [°] of [(NHC^Me)2(E2)]. Experimental values of substituted analogues are given in parentheses.

∆E_orb=

∑

k

∆E_k^orb=

N 2

∑

k=1

v_k

h−F_−k,−k^TS +F_k,k^TSi

, (3)

in whichF_−k,−k^TS andF_k,k^TSare diagonal Kohn–Sham matrix elements corresponding to NOCVs with the eigenvalues−v_k andv_k, respectively. The∆E_k^orbterms are assigned to a particular type of bond by visual in-

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Fig. 2. Schematic view of the electronic reference states of E₂in the complexes [(NHC^Me)₂(E₂)] (E=N–Bi). (a) X¹Σ_g⁺ ground state; (b)¹Γgexcited state; (c) calculated excitation energies at RI-BP86/def2-TZVPP.

spection of the shape of the deformation density∆ ρ_k. The EDA-NOCV scheme thus provides both qualita- tive (∆ρ_orb) and quantitative (∆E_orb) information about the strength of orbital interactions in chemical bonds, even in molecules withC₁symmetry. For more details we refer to [63,64].

Wiberg bond indices (WBI), partial charges, and Lewis structures were obtained using natural bond orbitals NBO 3.1 [65] as implemented in Gaussian 09 Rev. C.01 [66]. NBO electron densities were generated from a single-point calculation of the molecules with BP86/def2-TZVPP basis sets in Gaussian09 from the TURBOMOLE 6.1 optimized geometries.

3. Results

The optimized geometries of the dimeric group 15 complexes [(NHC^Me)₂(E₂)] (E = N–Bi), including

most important bond lengths and angles, are displayed in Figure1. Experimental values of substituted analogues are given in parentheses [35–40,42].

The agreement between the experimental and the calculated structures for the nitrogen compound is good, both show a slight deviation from a perfect anti- periplanar arrangement of the NHC^Me ligands and a comparably long N–N bond of about 1.4 Å. As we described before for [(PPh₃)₂(N₂)] [44], the electronic reference state for the N₂moiety is the excited(1)¹Γ_g state (Fig.2b). The NHC^Me→N₂←NHC^Mecharge donation occurs from theσdonor orbitals of NHC^Meinto the vacant in-plane bonding 1π_u⁰ and anti-bonding 1π_g⁰ orbitals of N₂. The NHC^Me←N₂→NHC^Meπbackdo- nation takes place from the occupied out-of-plane π orbitals into the vacantπaccepting orbitals of NHC^Me. The charge flow which is associated with the NHC^Me→N₂←NHC^Me σ donation and the NHC^Me←N₂→NHC^Me π backdonation is nicely visualized by the calculated deformation densities∆ ρ which are shown in Figure3, along with the relevant molecular orbitals (MOs). The third and fourth column show the frontier orbitals of N₂ and NHC^Me which yield the occupied MOs of [(NHC^Me)₂(N₂)] that are shown in the second column. The first column displays the deformation densities which are coupled to the four major orbital interactions, i. e. (+)/(+) and (+)/(−) σ donation (Figs. 3a and b) and (+)/(−) and(+)/(+)πbackdonation (Figs.3c and d). Defor- mation densities visualize the electron density flow of the interactions: Areas of depleting electron density are shown in red (dark grey) and areas of accumulating electron density are shown in light blue (light grey).

The calculated [(NHC^Me)₂(E₂)] complexes of the heavier group 15 atoms all have gauche oriented ligands with decreasing dihedral angle C^NHC–E–E–C^NHC when E becomes heavier (Fig.1). For [(NHC^Me)₂(P₂)]

this orientation correlates with the experimentally known N-mesityl substituted analogue, where the C^NHC–P–P–C^NHCangles agree quite well with the calculated data (132.8^◦for [(NHC^Me)₂(P₂)] calc., 134.1^◦ for [(NHC^Mes)₂(P₂)] exp. [35]). However, the experimental structures of the diisopropyl substituted complexes of P₂and As₂show an anti-periplanar arrangement of the NHC^Dipp ligands [35,40]. Wilson et al.

could show that the distortion in different group 15 complexes [(NHC^X)2(E2)] (X=H, Me, Ph) decreases with the steric demand of the substituent H>Me>

Ph [41]. But the large deviation between the NHC^Dipp

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Fig. 3 (colour online). Plot of deformation densities∆ρ of the pairwise orbital interactions between N2in its¹Γgstate and (NHC^Me)2 in [(NHC^Me)2(N2)], associated energies∆E in kcal/mol and eigenvaluesε. Shape of the most important interacting occupied and vacant orbitals of N2and (NHC^Me)2and resulting molecular orbitals. Left:∆ρ<0 in red (dark grey),

∆ρ>0 in light blue (light grey).

and the NHC^Mesphosphorus complexes indicates that electronic reasons may also play a role.

While the electronic reference state of N₂ in [(NHC^Me)2(N2)] could easily be determined, the same is more complicated for the heavier homologues. Due to the gauche orientation of the ligands more than two frontier orbitals of E₂ can be considered to ac- cept electron density from theσ donor orbitals of the NHC^Meligands. Thus, it is also possible to donate electronic charge to the E₂ fragment in its ground state X¹Σ_g⁺where both anti-bonding 1π_gorbitals are vacant (Fig. 2a). The (+)/(−) σ donation could then take place into one 1π_gorbital, where the overlap with the σ donor orbitals of the ligands is also significant. Fur- thermore, this could be an explanation of the strong deviation from the planar ligand arrangement as in [(NHC^Me)₂(N₂)] and it would not require the excitation energy X¹Σ_g⁺→(1)¹Γ_g(Fig.2c).

In order to determine the correct reference state, we carried out two EDA-NOCV analyses of the heavier group 15 complexes [(NHC^Me)₂(E₂)] where E=P–Bi.

Besides the ligand fragment (NHC^Me)2with its high- est occupied molecular orbital (HOMO) and HOMO–

1 corresponding to the(+)/(+)and(+)/(−)combi- nation of theσ donating orbitals, the E₂ fragment is calculated in its excited (1)¹Γ_g state and the ground state X¹Σ_g⁺, respectively. The results are given in Ta- ble1.

The data in Table1show that the EDA-NOCV calculations using the excited¹Γgstate of E₂yield much larger interaction energies∆E_intthan the calculations which employ the X¹Σ_g⁺ ground state. However, the crucial term which indicates the most suitable choice of the electronic states of the interaction fragments is the orbital energy term ∆E_orb. The size of the latter is a measure for the change of the electronic struc-

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Fig. 4 (colour online). Plot of deformation densities∆ρof the pairwise orbital interactions between P2in its¹Γg state and (NHC^Me)2in [(NHC^Me)2(P2)], associated energies∆Ein kcal/mol and eigenvaluesεfor all [(NHC^Me)2(E2)] (E=P–Bi).

Shape of the most important interacting occupied and vacant orbitals of P2and (NHC^Me)2and resulting molecular orbitals.

Left:∆ρ<0 in red (dark grey),∆ρ>0 in light blue (light grey).

tures of the fragments. The smaller the absolute value of ∆E_orb, the closer is the electronic structure of the fragments to the final molecule. Table1 shows that the EDA-NOCV calculations of [(NHC^Me)₂(P₂)] give a slightly smaller value of∆E_orb=−485.9 kcal/mol when the excited ¹Γg state of P₂ is used, while the calculations using the electronic ground state give

∆E_orb= −489.6 kcal/mol. For the heavier systems [(NHC^Me)₂(E₂)] where E=As–Bi, the EDA calculations using the ground state of E₂give always a clearly

smaller value for∆E_orbthan the calculations with the excited¹Γgstate. The EDA-NOCV results thus suggest that the NHC^Me–E₂–NHC^Me bonds with E=As–Bi should be discussed in terms of donor–acceptor interactions using the ground state rather than the excited

1Γgstate of E₂while NHC^Me–P₂–NHC^Meis a borderline case.

The relevant deformation densities of the EDA- NOCV with their corresponding molecular and fragment orbitals are given in Figure4(¹Γ_g) and Figure5

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Fig. 5 (colour online). Plot of deformation densities∆ρof the pairwise orbital interactions between P₂in its X¹Σ_g⁺state and (NHC^Me)2in [(NHC^Me)2(P2)], associated energies∆Ein kcal/mol and eigenvaluesεfor all [(NHC^Me)2(E2)] (E=P–Bi).

Shape of the most important interacting occupied and vacant orbitals of P₂and (NHC^Me)₂and resulting molecular orbitals.

Left:∆ρ<0 in red (dark grey),∆ρ>0 in light blue (light grey).

(X¹Σ_g⁺). Two of the orbital interactions for the different occupations are qualitatively and quantitatively alike: The NHC^Me→E₂←NHC^Me (+)/(+) σ donation from the (NHC^Me)₂HOMO–1 into the vacant in- plane anti-bonding 1π_g orbital on E₂. It contributes with 30 – 40% to the orbital energy and can be assigned to the HOMO–8 of the complex (Figs. 4a and 5a).

The NHC^Me←E₂→NHC^Meπ backdonation from the occupied out-of-plane bonding 1π_u orbital of E₂into

the lowest unoccupied molecular orbital (LUMO) of (NHC)₂ accounts for about 3 – 6% of the orbital energy (Figs.4d and5d). The resulting molecular orbital is the HOMO–1.

The(+)/(−)σdonation in the complex with E₂in the excited¹Γgstate (Fig.4b) occurs into the vacant in- plane bonding 1πuorbital. The shape of the resulting molecular HOMO–7 features both fragment orbitals which can easily be identified. Additionally, the defor-

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mation density∆ρ1shows areas of electron density de- pletion on the E₂moiety perpendicular to the accepting 1π_uorbital. These are in shape of the occupied out-of- plane anti-bonding 1π_gorbital, which according to the EDA-NOCV participates in this interaction. As a result, the amount of shifted electron density gets quite large and also the energetic contribution dominates the orbital term by 42.1% for the phosphorus complex and up to 55.4% for [(NHC^Me)₂(Bi₂)]. A smaller part of less than 10% of the orbital term is the π backdonation from the occupied out-of-plane anti-bonding 1π_g orbital of E₂ into the LUMO+1 on (NHC^Me)₂ (Fig.4c). The [(NHC^Me)2(P2)] HOMO matches the occupied anti-bonding 1π_gorbital of P₂(HOMO), which is delocalized towards the carbon atoms of NHC inπ fashion.

For the complexes with E₂ in its ground state, the(+)/(−)σdonation NHC^Me→E₂←NHC^Metakes place into the in-plane anti-bonding 1π_gorbital, which is occupied in the excited state (Fig. 5b). The resulting molecular HOMO lies energetically higher than its corresponding fragment orbitals. Still, the associated energy contribution of this donation dominates the orbital term by 40 – 50%. The amount of the electron density shift shown in deformation density∆ ρ₁is even larger than in the(+)/(−)σdonation into E₂of its excited state as described above. In the ground state, the electron density shift into the E₂1π_goccurs not only from the ligands, the occupied in-plane bonding 1π_u (HOMO) participates as well. This is the reversed situation as for the major contribution∆E₁to the orbital term of the excited case. But there, the shape of the resulting molecular HOMO is better represented by the chosen fragment orbitals than for the complexes with E2in its ground state. This is also the case for the interaction shown in Figure5c, theπbackdonation into the accepting orbital on (NHC^Me)₂from the occupied in- plane bonding 1π_uorbital on E₂. Although the corresponding molecular orbital HOMO–7 is low in energy, the contribution of this interaction to∆E_orbis only mi- nor (5 – 6%). Also, its shape shows predominantly features of the participating E₂HOMO, but the accepting LUMO+1 of (NHC)₂is not represented well.

For further information on the bonding situation in [(NHC^Me)₂(E₂)] (E = P–Bi) and the electronic reference state of E₂, we carried out NBO calculations which are independent of the reference state. The calculated Wiberg bond indices (WBIs) of the E–E, E–

C^NHC, and C^NHC–N bonds are shown in Table2, while

the partial charges of the bonding atoms are given in Table3.

The charge donation from the ligands to the E₂moiety is large only for the [(NHC^Me)₂(N₂)] complex. This corresponds to the high electronegativity of nitrogen that exceeds those of the higher group 15 elements by far. The high WBI for the E–C^NHC donor–acceptor bond of the nitrogen complex of 1.54 indicates some double bond character which correlates with the large amount of shifted electron density in theπ backdonation seen in the EDA-NOCV. Additionally, this backdonation lowers the bond index of the C^NHC–N bond by raising the electron density in the C^NHC–N anti- bonding orbital. The bond index of the donor–acceptor bond is still larger than one for the complexes with E

=P and As but decreases continuously for the heavier analogues. This is represented well in the EDA- NOCV of the phosphorus and arsenic complexes with E₂in its excited¹Γg state, where theπ backdonation in∆ρ₃(Fig.4c) shows a larger energetic contribution and more shifted electron density than in their heavier analogues. The E–E bond index which varies only slightly from nitrogen to bismuth indicates essentially a single bond for all complexes. This can be interpreted in different ways. There is an E–E single bond present in E₂in the excited¹Γgstate. In the EDA-NOCV, the (+)/(−) σ donation contributes most to the orbital energy and occurs into a vacant E–E bonding orbital (Fig.4b), which should increase the WBI of this single bond. The σ donation (Fig.4a) into the corresponding anti-bonding orbital is weaker. Additionally, the π backdonation from the occupied anti-bonding E–

E π orbital (Fig. 4c) exceeds the backdonation from bonding the E–E orbital (Fig.4d). On the other hand, there is a triple bond in E2 in its ground state ¹Σ_g⁺. In the EDA-NOCV it could be seen that bothσ do- nations occur into vacant anti-bonding orbitals of E₂ (Figs.5a and b) while bothπbackdonations take place from occupied bonding orbitals on E₂(Figs.5c and d).

This would decrease the bond order of the triple bond massively, which would also correspond to the given WBIs in Table2. Thus, the NBO data in Table2do not discriminate between the models using different electronic reference states.

Orbital information on the E–E and E–C bonds and E lone pair orbitals from the Lewis structure determi- nation of the NBO calculation are given in Table4.

The results suggest that the [(NHC^Me)₂(E₂)] complexes have a E–E single bond where the hybridiza-

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tion changes toward higher %p character from E = N (74.8%) to E =Bi (95.1%). The calculations give Lewis structures with E=C^NHCdouble bonds and one lone-pair orbital at atom E for E =N, P, As. For the heavier system where E=Sb, Bi the calculations give E–C^NHCsingle bonds and two lone-pair orbitals at An- timony and Bismuth. Note, however, that the E–C^NHC π bonds in the lighter systems have a large occupation from the antibonding orbital. The NBO data should rather be interpreted as evidence for strongerπ backdonation in the lighter complexes which agrees with the EDA-NOCV results.

4. Summary and Conclusion

The results of this work can be summarized as follows. The chemical bonds of the diatomic fragments E₂ and the NHC^Me ligands in the

[(NHC^Me)₂(E₂)] complexes can be discussed in terms of donor–acceptor interactions which consist of two NHC^Me→E₂←NHC^Me donor components and two weaker components of the NHC^Me←E₂→NHC^Me π backdonation. The out-of-phase(+)/(−)contribution of theσdonation is always stronger than the in-phase (+)/(+) contribution. The electronic reference state of N2 in the dinitrogen complex [(NHC^Me)2(N2)] is the highly excited 1¹Γgstate which explains the anti- periplanar arrangement of the ligands. The gauche arrangement of the ligands in the heavier homologues [(NHC^Me)₂(E₂)] (E =P–Bi) may be discussed using either the excited 1¹Γgstate or the X¹Σ_g⁺ground state of E₂as reference states for the donor–acceptor bonds.

The EDA-NOCV calculations suggest that the latter bonding model is better suited for the complexes where E=As–Bi while the phosphorus complex is a borderline case.

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