Orbital Interaction and Electron Density Transfer in PdII([9]aneB2A)L2 Complexes: Theoretical Approaches

The geometric structures of Pd-complexes {Pd([9]aneB2A)L2 and Pd([9]aneBAB)L2 where A = P, S; B = N; L = PH3, P(CH3)3, Cl−}, their selective orbital interaction towards equatorial or axial (soft A…Pd) coordination of macrocyclic [9]aneB2A tridentate to PdL2, and electron density transfer from the electron-rich trans L-ligand to the low-lying unfilled a1g(5s)-orbital of PdL2 were investigated using B3P86/lanl2DZ for Pd and 6-311+G** for other atoms. The pentacoordinate endo-[Pd([9]aneB2A)(L-donor)2]2+ complex with an axial (soft A--Pd) quasi-bond was optimized for stability. The fifth (soft A--Pd) quasi-bond between the σ-donor of soft A and the partially unfilled a1g(5s)-orbital of PdL2 was formed. The pentacoordinate endo-Pd([9]aneB2A)(L-donor)2]2+ complex has been found to be more stable than the corresponding tetracoordinate endo-Pd complexes. Except for the endo-Pd pentacoordinates, the tetracoordinate Pd([9]aneBAB)L2 complex with one equatorial (soft A-Pd) bond is found to be more stable than the Pd([9]aneB2A)L2 isomer without the equatorial (A-Pd) bond. In particular, the geometric configuration of endo-[Pd([9]anePNP)(L-donor)2]2+ could not be optimized.

The geometric structures of the active RPd(L) n X intermediates produced in various steps of Pd-mediated cross-coupling reactions (e.g., oxidative addition, transmetalation, reductive elimination) have been investigated both theoretically [9][10][11][12][13][14][15][16][17] and experimentally . The oxidative addition of substrates (R-X) to PdL n -precursor resulted in penta-, hexa-, and octacoordinate geometries [33][34][35][36] of the RPd II (L) n X intermediates with relative stability and a life time of 30 s [3]. The binding atoms in the penta-, hexa-, and octacoordinate Pd intermediates are not located on the x, y, and z-axis of trigonal bipyramidal, octahedral, and cubic structures. In particular, the geometric conformation of RPd(L) n X intermediates is altered by the cis-trans isomerization of L-ligand. The isomerization has been exclusively explained by the energy relationship between the isomers and low potential barrier (or binding energy of Pd-L) [3][4][5][6][7][8]44,45]. However, Goossen et al. [14,15] provided no evidence for mechanistic steps involving stable pentacoordinate Pd II intermediates in Pd-mediated cross-coupling reactions. To the best of our knowledge, the relative stabilities of various RPd(L) n X intermediates produced by oxidative addition of the substrate (R-X) to PdL n and the geometric changes in intramolecular interaction of RPd II (L) n X have not been investigated.
In previous studies using hemilabile multidentate ligands [37][38][39][40][41][42][43][44][45][46][47], exceptional oxidation state and specific coordination selectivity have been observed for the Pd( [9]aneB 2 A)L 2 complexes with mixed soft A and hard B tridentates. The uncommon geometric structures of Pd( [9]aneB 2 A)L 2 complexes with an axial (A…Pd) interaction were mainly formed under the following restrictive conditions: (1) coordination bonds of P-and N-functionalized derivatives are present  and (2) polymeric side chain interactions exist [40][41][42]. In the Pd complex with an apical (hard N…Pd) interaction [42], the apical interaction was explained by an antibonding interaction between the lone pair of the apical N site and the d z2 -orbital of the Pd II species. In the ligand exchange reaction of square-planar Pd complexes, a vertical L…Pd interaction also has been optimized [43][44][45][46][47]. The mechanism of hydration exchange processes in the five-coordinate Pd II intermediates suggested two models for the axial interaction: σ-donor…d z 2 -orbital and HOH…d z 2 -orbital. The apical (A…Pd) orbital interaction of Pd([9]aneB 2 A)L 2 complex in mixed A and B sites has not been explained very well. Origins of the unusual coordination structures for the Pd complexes and the configurational changes in the ArPdL n X intermediates of Pd-mediated cross-coupling reaction have not been explored yet. To investigate these properties, the present study proposed the following geometric structures and the relative stabilities of macrocyclic Pd([9]aneB 2 A)L 2 complexes within the frameworks of its orbital interaction and electronic effect. For the Pd-mediated cross-coupling reactions, we suggest a two-step mechanism for the electron density transfer: the abundant electron density of the trans L-donor may transfer to a low-lying unoccupied a 1g (5s)-orbital of Pd II and then the partially unfilled a 1g (5s)-orbital can interact with the Lewis base substrate (σ-donor) as shown in Scheme 1. Scheme 1. Two-step mechanism for the electron density transfer from an equatorial trans L-donor {PH 3 , P(CH 3 ) 3 } and a σ-donor of substrate to a low-lying unoccupied a 1g (5s)-orbital of the Pd II center.
To justify the intermediate step for the additional reaction of [9]aneB 2 A to PdL 2 , the relative stabilities (Δ exo-endo , Δ BAB-B2A ) and the apical and equatorial orbital interactions [σ-donor…a 1g (5s), σ-donor…4d x2-y2 ] shown in Scheme 2 are suggested in this research exertion. The relative affinity of Pd towards the soft A (or hard B) in PdL 2 , the electronic characteristics owing to the donating (or withdrawing) property of the trans L-ligand, the axial σ-donor…a 1g (5s) interaction between the σ-donor of the A site and the low-lying unfilled a 1g (5s)-orbital of Pd II L 2 , and the relative stability of the uncommon Pd complexes were examined in detail.

Scheme 2.
A plausible orbital interaction of an equatorial or axial coordination bond of [9]aneB 2 A (or [9]aneBAB) with PdL 2 . (a): exo-type with an apical site pointing to outside. (b): endo-type with an apical site pointing to the Pd center. (c): endo-Pd complex with an apical (A…Pd) attraction. (d): endo-Pd complex without any axial interaction. (e): endo-Pd complex with an apical (A…Pd) repulsion.

Computational Methods
To explore the geometric structure and the relative stability of the Pd complexes, we selected the Pd([9]aneB 2 A)L 2 [A = P, S; B = N; L = donor {PH 3 , P(CH 3 ) 3 }, acceptor (Cl − )] complex as a model with [9]aneB 2 A, PH 3 , P(CH 3 ) 3 , and Cl − groups as ligands. The equilibrium structure of tetracoordinate Pd complexes was fully optimized with the B3P86/6-311+G** (lanl2DZ for Pd) level using Gaussian 03 [48]. The macrocyclic [9]aneN 2 P and [9]aneN 2 S ligands are 1,4-diaza-7-phospacyclononane and 1,4diaza-7-thiacyclononane, respectively (as shown in Scheme 2). The hybrid B3P86 density functional utilizes the exchange function of Becke [49,50] in conjunction with the Perdew 1986 correlation function [51] and yields good structural and energetic information, even for relatively large chemical systems such as transition metal complexes. For the optimized equilibrium Pd II complexes, the atomic charges obtained by the CHelpG method were analyzed using atomic radii (H = 0.53 Å, C = 0.67 Å, N = 0.56 Å, O = 0.48 Å, P = 0.98 Å, S = 0.88 Å, Cl − = 1.67 Å, Pd II = 0.78 Å) [52]. The relative energies of the Pd II complexes were compared. To confirm the existence of stable structures, the harmonic vibration frequencies of the species were analyzed at the B3P86 level. In addition, the geometric structures of endo-Pd( [9]aneA 2 B)L 2 {A = P, S; B = N; L = PH 3 , P(CH 3 ) 3 , Cl − } were optimized at the B3P86/6-311+G** (lanl2DZ for Pd) level. The optimized structures including HOMO and the geometric parameters are described in Supplementary Information Figure S1 and Table S1, respectively. To check the rationality of our results at the effective core potential level for Pd, the geometric structures of the equilibrium Pd complexes were also optimized at the CAM-B3LYP// 6-311+G** (lanl2DZ for Pd) and B3P86/6-311+G** (3-21g* for Pd) levels using Gaussian 09. Further, optimized structures and parameters are given in Supplementary Information Figures S2 and S3 and Tables S2 and S3.
As shown in Figure 2, when the soft A and hard B binding sites simultaneously coordinate to the 4d x2-y2 orbital, the large σ-donor of the A site overlaps more with the 4d x2-y2 orbital than the small σ-donor of B. With increasing atomic size (P:107 pm ≅ S:105 pm >> N:71 pm) [52], the larger σ-orbital of the soft A site in [9]aneBAB first interacts with the 4d x2-y2 orbital on the square-planar plane. In endo-Pd( [9]aneBAB)L 2 of (f) of Figure 2, due to its atomic size, the bond length (r Pd -P = 2.324 ~ 2.225 Å and r Pd-S = 2.402 ~ 2.324 Å) of the equatorial (A-Pd) bond is longer than the corresponding (N-Pd) bond (r Pd-N = 2.214 ~ 2.094 Å). Two equatorial bond lengths (r Pd-A , r Pd-B ) are unsymmetrical in nature. The axial distance between the axial N site and Pd II center is long (r Pd-N = 2.720 ~ 3.076 Å). As shown in (g) of Figure 2, in the endo-[Pd( [9]aneB 2 A)(L-donor) 2 ] 2+ complex, the average distance between the equatorial N site and Pd II center is short (R Pd-N = 2.138 ~ 2.195 Å). Because both the equatorial (N-Pd) bonds are short, the large σ-donor of the apical A site closely approaches to the Pd center. Thus, the large σ-donor of the soft A site can interact with the low-lying unoccupied a 1g (5s)-orbital of PdL 2 complex.
The ratio of products in Pd-catalyzed cross-coupling reactions was experimentally determined by the strength of the σ-donor ligand (e.g., n-Bu 3 N or an acetate anion) [6,30,31]. As the softness (P ≅ S > N) [47] and basicity (N > P > S) [6,26] of the binding site increases, the coordination bond of the soft A site to the 4d x2-y2 -orbital was more preferred than that of the hard B site. That is, the σ-donor of the soft A site demonstrates a stronger overlap on the 4d x2-y2 orbital than the hard B site. As shown in Table 1, exo-[Pd( [9]aneBAB)(L-donor) 2 ] 2+ and Pd([9]aneBAB)Cl 2 complexes with an equatorial (A-Pd) bond are more stable than the corresponding exo-[Pd( [9]aneB 2 A)(L-donor) 2 ] 2+ and Pd([9]aneB 2 A)Cl 2 isomers without the equatorial (A-Pd) bond, respectively. As described in Supplementary Information Figure S1 and Table S1, endo-[Pd( [9]anePNP)(L-donor) 2 ] 2+ could not be optimized. By strong softness and basicity of the binding A site, the relative energy of tetracoordinate endo-[Pd( [9] 2 ] 2+ complex with an axial fifth (A--Pd) quasi-bond, the pentacoordinate Pd complex is more stable than the tetracoordinate endo-[Pd( [9]aneBAB)(L-donor) 2 ] 2+ complexes. Therefore, in case of interaction of [9]aneB 2 A to PdL 2 , the relative stability of the Pd complexes and the selective formation of the coordination bond may depend on the strength of the hardness/softness and basicity of A (or B) and the position of the equatorial (or apical) binding atoms, and the existence of an axial (A--Pd) quasi-bond [6,26,30,31,47,55].

endo-Pd([9]aneB 2 A)L 2 , (g)
In some Pd II complexes with terminal amino derivatives [37][38][39][40][41][42], both apical soft S…Pd and hard N…Pd interactions were observed under the strong strain of a polymeric side chain. In particular, the apical (hard N…Pd) distances (r Pd…N = 2.523 ~ 2.638 Å) [40] are slightly shorter as explained by an axial σ*…d z2 interaction between an antibonding orbital of the apical N site and the filled d z2 -orbital [42]. Meanwhile, in the ligand exchange processes of the Pd complexes [46,47], an axial water…Pd interaction was also observed. The mechanism of the hydration reactions is described by two models: axial H 2 O…d z 2 -orbital and OH 2 …d z 2 -orbital interactions with the former being rarely formed due to electrostatic repulsions. In studies by Kozelka et al. [56], both the axial O 2 H…Pt and H 2 O…Pt interactions in the Pt complex were explained by an electrostatic attraction between the dispersion components. Until now, the axial L…d 8 -metal interaction between the axial L-ligand and d 8 -metal have not been explained in detail using an orbital interaction. The 3a 1g (5s)-orbital [(h), (j), (l)] and the 2a 1g -orbital [(i), (k), (m)] of endo-Pd complexes are illustrated in Figure 3. As shown in (h), (j), and (l) of Figure 3, the orbital shape of the 3a 1g (5s)-orbital of the endo-Pd( [9]aneB 2 A)L 2 complexes is largely varied by the donating (or withdrawing) property of the trans L-ligand. Due to the electron donating property of trans L-donor, its electron density moves to the Pd II center, and then the increased electron density at the Pd II center is transferred to the low-lying unoccupied 3a 1g (5s)-orbital. The orbital lobe of the 3a 1g (5s)-orbital around the Pd II center is huge [as shown in tetracoordinate endo-[Pd ([9]aneBAB)(L-donor) 2 ] 2+ complex of (h) and (j) of Figure 3]. This huge lobe of the 3a 1g (5s)-orbital can interact with the σ-donor of the soft A site [or filled π-donor orbital of substrates]. In the endo-[Pd( [9] Figure 3], the shape of the 3a 1g (5s)-orbital is not symmetric. The partially unfilled and lowered a 1g (5s)-orbital strongly interacts with the large σ-donor of A to make the apical (A--Pd) quasi-bond. The upper part of the a 1g (5s)-orbital lobe is used for the apical (A…Pd) interaction. Meanwhile, in the endo-[Pd ([9]aneBAB)(L-donor) 2 ] 2+ complex without the apical (A--Pd) quasi-bond [(h) and (j) of Figure 3], the orbital lobe of the 3a 1g (5s)-orbital is huge and symmetric. The 3a 1g (5s)orbital of endo-[Pd ([9]aneBAB)(L-donor) 2 ] 2+ complex is quite different from that of endo-[Pd([9]aneB 2 A)(L-donor) 2 ] 2+ . As shown in (l) of Figure 3 with trans Cl-acceptor, the lobe size of the 3a 1g (5s)-orbital is very small. No interaction between the σ-donor of the soft A site and the 3a 1g (5s)orbital is formed. The orbital shapes of the 3a 1g (5s)-orbital and the 2a 1g -orbital are very similar to those given in Supplementary Information Figures S2 and S3. As listed in Table 1   Based on Figure 3, orbital interaction between the σ-donor of the apical soft A (or hard B) site and the partially unfilled a 1g (5s)-orbital of Pd II center as well as the direction for the electron transfer of trans L-ligand (electron-donor or acceptor) are schematically depicted in Figure 4. In endo-[Pd( [9]aneB 2 A)(L-donor) 2 ] 2+ and endo-[Pd ([9]aneBAB)(L-donor) 2 ] 2+ complexes, the electron density of the unfilled a 1g (5s)-orbital of Pd II center is greatly increased by the strong electron-donating property of the trans L-donor. The spatial distribution of electron density of the a 1g (5s)-orbital is larger than that of the a 1g (4d z 2 )-orbital, thus positioning the lobe of a 1g (5s)-orbital at the outer space of the a 1g (4d z 2 )-orbital. As represented in (n) of Figure 4, the soft σ-donor of the axial A site (or substrate of Lewis base) first interacts with the partially unoccupied a 1g (5s)-orbital (or Pd-complex of Lewis acid). A fifth apical (soft A--Pd) quasi-bond is formed as shown in Figure 1. In (o) of Figure 4, the size of σ-donor in an axial B site is small [covalent radius of the N atom: 71 pm [52]]. In the regular Pd tetracoordinate, the axially hard N atom cannot easily interact with the Pd center. Meanwhile, in endo-Pd( [9]aneB 2 A)Cl 2 and endo-Pd( [9]aneBAB)Cl 2 complexes with a trans Cl-acceptor, the filled a 1g (4d z 2 )-orbital of Pd II center lies spatially outside than that of the a 1g (5s)-orbital. There is no interaction between the soft σ-donor of A and the filled a 1g (4d z 2 )-orbital. Experiments to analyze the electronic effect of a donating (or withdrawing) Z group were performed by some research groups [30,31]. The results of these experiments indicated that the rate of catalytic activity of the neutral Pd 0 (dba-n,n'-Z) 2 precursor is greatly dependent on the electronic property (donor or acceptor) of the bulky dba-n,n'-Z ligand. Owing to the increase in the strength of electron donating dba-n,n'-Z ligand, the overall rate of the oxidative addition of phenyl iodide to Pd 0 (dba-n,n'-Z) 2 precusor is faster than that of the Pd 0 complex with an electron withdrawing Z group. In particular, the rate of oxidative addition of aryl halide to Pd 0 L n depends on the concentration of the active Pd 0 L n precursor with a strong electron-donating trans L-ligand. Scrivanti et al. [38,39] found that the rate of oxidative addition of an aryl halide to the (iminophosphine)Pd 0 (η 2 -olefin) complex also increased. The increase in reaction rate is explained by the catalyst stability of the moderate π-accepting ligand. These experimental results [31,39] showing an increased rate in the catalytic activity may have originated from the electronic property of a strong electron-donating trans L-ligand in Pd 0 L n . Based on Figures 3 and 4, in the oxidative addition of ArX to Pd 0 L n , the donating π-orbital of the aryl halide can interact with the low-lying unfilled a 2u (5p)-orbital of Pd. Thus, an a 2u (5p)… π-orbital interaction between the low-lying unfilled a 2u (5p)-orbital of Pd and the filled π-orbital of ArX can take place. These experimental results can be understood with the help of results shown in Figure 3.

aneB 2 A)(L-donor) 2 ] 2+ complex with an apical (A--Pd) quasibond [(h) and (j) of
The orbital energy levels for the orbital interaction associated with the coordination bond of [9]aneB 2 A to PdL 2 are drawn in Figure 5. As shown in (r) of Figure 5, there is a large gap in the energy level between the A site of [9]aneB 2 A and the a 1g (5s)-orbital of PdL 2 . Therefore, the σ-orbital of A cannot easily interact with the unoccupied a 1g (5s)-orbital. Meanwhile, as shown in (s) of Figure 5, the energy gap between the axial A site and a 1g (5s)-orbital is largely reduced. In the endo-[Pd ([9]aneBAB)(L-donor) 2 ] 2+ complex as shown in (h) and (j) of Figure 3, the unoccupied 3a 1g (5s)-orbital is partially filled by the electron density transfer from trans L-donor and the level of the partially filled 3a 1g (5s)-orbital decreases. In endo-[Pd( [9]aneB 2 A)(L-donor) 2 ] 2+ complex as shown in (i) and (k) of Figure 3, the huge σ-orbital of the soft A site can overlap with the partially filled 3a 1g (5s)-orbital and then the energy level of the A site is increased by the [σ-donor ↔ 3a 1g (5s)] overlap. Therefore, the electron density of increased energy level in σ-orbital of A can share with that of the decreased energy level of 3a 1g (5s)-orbital. The unfilled 3a 1g -molecular orbital is occupied and the energy level is largely lowered as HOMO. The energy difference between the HOMO and LUMO is also reduced {ΔE2 H-L = 2.67~3.51 eV for endo-[Pd( [9]aneB 2 A)(L-donor) 2 ] 2+ }. As shown in (t) of Figure 5, the orbital energy levels are similar to that in (r) of Figure 5. The σ-orbital cannot interact with the 3a 1g (5s)-orbital and the energy gap between the HOMO and LUMO is large {ΔE1 H-L = 3.77 and 3.84 eV for endo-Pd( [9]aneB 2 A)Cl 2 }.
Similar to the interaction suggested above [σ-donor…unfilled a 1g (5s)], the fifth [sixth, eighth] axial olefin-Pd coordination bond in the oxidative addition of olefin to Pd (0) L n can be formed by an axial π-donor…unfilled a 2u (5p x,y ) interaction between the π-donor of olefin and an unfilled a 2u (5p x,y )-orbital of Pd. The electron density transfer from the trans L-donor to the unfilled a 2u (5p x,y )-orbital makes it partially occupied, and thus the energy level of the partially unfilled a 2u (5p x,y )-orbital is lowered. Consequently, the π-donor electron-rich substrates such as olefin can interact with the partially unfilled and lowered a 2u (5p x,y )-orbital of Pd. In the Pd-mediated cross-coupling reactions, the results of this study can describe the mechanism for the formation of the apical σ-donor…unfilled a 1g (5s) and π-donor…unfilled a 2u (5p x,y ) interactions in ArPdL n X. Furthermore, in d 9 -electron systems such as [Cu(NH 3 ) 4 (H 2 O) 2 ] 2+ [57,58], a distorted octahedron with two water molecules at a longer distance than four ammonias is formed via the long range interactions. The vertical Cu-OH 2 bond length (R Cu-O = 2.204 Å) is longer than that (R Cu-N = 1.933 Å) of the equatorial Cu-NH 3 bond [55]. The two longer Cu-OH 2 bonds along the z-axis are explained by the interaction between the half unoccupied 3d z2 -orbital of Cu II and the filled σ-orbital of the oxygen atom in water.
In the Pd-catalyzed coupling reactions, the PdL n intermediates are activated by an electron-rich trans L-donor possessing a strong Lewis base character. The strong Lewis base character of the trans L-donor allows its electron density to transfer to the low-lying unoccupied orbitals [a 1g (5s) or a 2u (5p)] of Pd and the energy level of the partially unfilled a 1g (5s)-orbital of Pd is decreased. Therefore, an axially fifth substrate…PdL 2 interaction between the σ(or π)-donor of substrates (such as hemilabile multidentates, olefinic halides, and solvents) and the PdL 2 precursor should occur energetically, resulting in the electronic and steric effects of the bulky and electron-rich ligand. Because of the low transition barrier and an axial substrate…PdL 2 interaction, the configurational and conformational changes of RPd II (L) n X can easily take place (e.g., axial-equatorial and cis-trans exchanges and interconversions in RPd II (L) n X intermediates). Consequently, the geometric structure and relative stability of the Pd complexes are influenced by the relative strength of the axial or equatorial (soft A…Pd) interaction, donating electron property of the trans L-ligand, and relative Pd affinity of the A and B donors. The mechanisms for orbital interaction and electron density transfer proposed in this study can be considerably valuable in the design of useful Pd-catalyst and synthetic applications for the Pd-catalyzed cross-couplings of substrates.