A Comparison of Donor-acceptor Interactions in Borane Complexes of Divalent Tetrylenes(II) and Divalent Tetrylones(0) using Energy Decomposition Analysis Method with Natural Orbital for Chemical Valence Theory

Abstract A scheme for chemical bond analysis by combining the energy decomposition analysis (EDA) method with natural orbitals for chemical valence (NOCV) theory has been investigated. Quantum chemical calculations at the BP86/TZ2P+ level of theory are performed for a comparison of chemical bond analysis between tetrylones [BH3-{E(PH3)2}] (B3-EP2) and tetrylenes [(BH3-{NHEMe}] (B3-NHE) (E = C to Pb). The EDA-NOCV results suggest that the B–E bond dissociation energies (BDEs) in tetrylones and tetrylenes decrease from the slighter to the heavier homologs. The decrease in the bond strengths from the lighter to the heavier homologs of B3-EP2 comes mainly from the decrease in the electrostatic attractions ΔEelstat and the orbital interactions ΔEorb, while the decrease in the bond strength from carbene B3-NHC to plumbylene B3-NHPb strongly correlates with the decrease in electrostatic term ΔEelstat.


Introduction
The first divalent carbon(0) compound (carbones) CL 2 synthesized already in 1961 by Ramirez et al. [1] is the carbodiphosphorane C(PPh 3 ) 2 . The carbon atom in CL 2 retains two electron lone pairs and is bonded to two σ-donor ligands L→C←L. [2,3] Carbones (CL 2 ) have two donoracceptor bonds L→C to a bare carbon atom in the 1 D exited singlet state. In contrast to carbones (CL 2 ), carbenes (CR 2 ) possess only one electron lone pair at the carbon, have two electron-sharing bonds (CR) to a carbon atom in the 3 P ground state. [4,5] Recent theoretical studies suggested that the bonding situation in CL 2 is not limited to carbon as the central atom, but that is can be extended to the heavier homologs EL 2 with E = Si to Pb [2,[5][6][7] in which the ligands EL 2 are strong σ-donors and weak π-donors. [5][6][7][8][9][10] The reaction of the carbodiphosphorane C(PPh 3 ) 2 complex (PPh 3 ) 2 C(BH 3 ) with the strong Lewis acid B(C 6 F 5 ) 3 yielded the first complex of a cation (PPh 3 ) 2 C→(BH 2 ) + that could be isolated in a condensed phase. [5,11] This is because the C(PPh 3 ) 2 always possesses two lone pair donor orbitals which leads the complex to be stabilized through double donation of the σ and π electron lone pairs of the carbone C(PPh 3 ) 2 into the vacant σ and π orbitals of the BH 2 + ligand. In contrast, carbenes NHCs possess only one lone pair for donation; this leads to the reaction of the carbene complex NHC(BH 3 ) with B(C 6 F 5 ) 3  were analyzed using DFT calculations by Frenking et al. [8,9,12,13] Further, new types of borane complexes that carry N-heterocyclic carbenes (NHC boranes) have been investigated theoretically as stable molecules. [14] Work focused first on structural determinations, [15,16] then gradually encompassed inorganic, [17][18][19][20][21][22] organic (inparticular astin hydride surrogates), [23][24][25][26][27][28][29] and organometallic chemistry. [30] Experimental and theoretical calculations on NHC-boranes have shown recently that coupling of NHC-BH 3 changes the electronic properties of the borane considerably. [14,24,25] The energy decomposition analysis (EDA)-natural orbitals for chemical valence (NOCV) [31] method combines charge (NOCV) and energy (EDA) In the Equation (1), the preparation energy ΔE prep is the energy that is required to promote the fragments in complexes from their equilibrium geometries in the ground electronic state to the geometries and electronic reference state which they have in the molecule. The interaction energy ΔE int can be further divided into three main components: where ΔE elstat is the quasi-classical electrostatic interaction energy between the fragments; ΔE Pauli refers to the repulsive interactions between the fragments, which are caused by the fact that two electrons with the same spin cannot occupy the same region in space, and can be calculated by enforcing the Kohn-Sham determinant on the superimposed fragments to obey the Pauli principle by anti-symmetrization and renormalization; and ΔE orb is the stabilizing orbital interaction term which is calculated in the final step of the energy partitioning analysis when the Kohn-Sham orbitals relax to their optimal forms.
The EDA-NOCV method combines charge (NOCV) and energy (EDA) partitioning schemes to decompose the deformation density that is associated with the bond formation, Δρ, into different components of the chemical bond. Furthermore, the EDA-NOCV calculations also provide pairwise energy contributions for each pair or interacting orbitals to the total bond energy. NOCV [35][36][37] is defined as the eigenvector of the valence operator, ν, given by Equation (4): In the EDA-NOCV scheme, the orbital interaction term, ΔE orb , is given by Equation 5: in which F TS −k,−k and F TS k,k are diagonal transition state Kohn-Sham matrix elements corresponding to NOCVs with the eigenvalues -υ k and υ k , respectively. The ΔE orb k term of a particular type of bond is assigned by visual inspection of the shape of the deformation density, Δρ k . The partitioning schemes to decompose the deformation density that is associated with the bond formation, Δρ, into different components of the chemical bonds. The EDA-NOCV calculations also provide pairwise energy contributions for each pair or interacting orbitals to the total bond energy. Moreover, it has been found that the set of orbitals which has been discussed in the recent past, NOCV, is defined as eigenvectors of the overall chemical valence operator and the NOCV set of orbitals can be especially useful for a description of bonding in transition metal complexes as it may allow for separation of the deformation density contributions originating from the ligand to metal donation and metal to ligand backdonation. [32] In view of the above, the main purpose of this study is to investigate donor-acceptor interactions between the two typical ligands carbodiphosphorane-analogs (called tetrylones) E(PH 3

Computational methods
We use the EDA [33,34] with the NOCV [35][36][37] to investigate the nature of chemical bonding in complexes. In the EDA-NOCV method, [31] the bond dissociation energy (BDE) of a molecule is divided into the instantaneous interaction energy ΔE int and the preparation energy ΔE prep : The BDE, D e (kcal/mol), for a bond carbene/carbone-BH 3 is broken through the reaction: carbene/carbone-BH 3 → carbene/carbone + BH 3 of a molecule and forms from the two fragments E 0 carbene∕carbone and E 0 borane , which is given by: EDA-NOCV scheme so provides information about the strength of orbital interactions in terms of both charge (Δρ orb ) and energy contributions (∆E orb ) in chemical bonds, even in molecules without symmetry. In this work, the parent compounds (B3-EP2 and B3-NHE) and free ligands (EP2 and NHE) were optimized for the EDA with the program package ADF 2013.01 [38] with BP86 in conjunction with a triple-zeta-quality basis set using un-contracted Slater-type orbitals (STOs) augmented by two sets of polarization function with a frozen-core approximation for the core electrons. [39] 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 SCF cycle.
[40] Scalar relativistic effects have been incorporated by applying the zeroth-order regular approximation. [41] The chemical bonding of the B-E bonds in B3-EP2 and B3-NHE was investigated at BP86/TZ2P+ level of theory using the EDA-NOCV method [31] under C1 symmetric geometries.

Results and discussion
In this study, we want to draw a picture that the EDA-NOCV calculations give a thorough insight into the nature of the BH 3 -ligands bonding in B3-EP2 and B3-NHE. Firstly, the structures of BH 3 -tetrylones and BH 3 -tetrylenes are presented. The optimized geometries of complexes B3-EP2 with calculated values for the most important bond lengths and angles are shown in Figure 1. All members of tetrylones in this study are experimentally unknown. Note that the borane complex that carries the more bulky ligand C(PPh 3 ) 2 was reported in the experimental study. [12] Figure 1 shows that the calculated B-C bond length of B3-CP2 gives the shortest value (1.691 Å) and is similar to the B-C bond length in BH 3 -C(PH 3 ) 2 (1.685 Å) and BH 3 -C(PPh 3 ) 2 (1.689 Å) which was recently calculated at the BP86/SVP level of theory by Frenking. [42] The borane complex with the more bulky ligand C(PPh 3 ) 2 exhibits the experimental B-C bond length of 1.673 Å. [12] The theoretically predicted B-E bond lengths of tetrylone complexes B3-CP2-B3-PbP2 in this study increased from 1.691 to 2.409 Å. This could be easily explained by the increasing radii of the group-14 atoms. The calculated equilibrium structures of tetrylone complexes B3-EP2 showed that all ligands EP2 were bonded in a tilted orientation relative to the fragment BH 3 . The bending angle, α, of B3-CP2 is 134.8° and becomes much more acute when E became heavier.
The structures of tetrylene complexes B3-NHE are shown in Figure 2. The calculated BH 3 -NHC Me bond length of B3-NHC gives the shortest value (1.587 Å) and is extremely similar with the theoretical B-C bond length of 1.587 Å in BH 3 -NHC H which was recently calculated at the BP86/SVP level of theory by Frenking. [42] The B-E bond length increases from B3-NHC to B3-NHPb (2.564 Å). Note that a related carbene complex BH 3 -NHCs has an experimental the B-C bond length of 1.603 Å. [43] Unlike the structures of tetrylone complexes, the structures of tetrylene complexes B3-NHE have the NHE ligands (E = C to Ge) bonded in a head-on way to the BH 3 fragment with a bending angle, α, 180°. In contrast, the B3-NHSn complex has the NHSn Me ligand bonded in a side-on way to the BH 3 fragment with the bending angle 129.4°. The strongest side-on bonded ligand when E = Pb has a bending angle of 108.0°.
We continuously investigate bonding analysis for borane complexes of tetrylones and tetrylenes. In the EDA-NOCV calculations, the tetrylones B3-EP2 and tetrylenes B3-NHE are divided into the fragments {E(PH 3 ) 2 and NHE Me } as donor fragments and BH 3 as an acceptor fragment and both are in the singlet state. To the best of our knowledge, there are no experimental results available for complexes B3-EP2 and B3-NHE. Note that the EDA results of the borane complexes BH 3 that carry the more bulky carbodiphosphorane ligand as carbone have been recently described by Frenking et al. [8,12] In this study, we wanted to extend the carbone to heavier homologs as tetrylones and compare the bonding situation of tetrylone complexes B3-EP2 with tetrylene complexes B3-NHE (E = C to Pb). EDA-NOCV results at the BP86/TZ2P+ level for complexes B3-CP2-B3-PbP2 using the moieties [BH 3 ] and [E(PH 3 ) 2 ] as interacting fragments are shown in Table 1. The results demonstrate that the decrease in the borane-ligand bonding comes from the intrinsic interaction ΔE int , which slightly decreases from the lighter B3-CP2 to the heavier homologs. The trend of the bond dissociation energies (BDEs), D e (kcal/mol), for the B-E bond in the B3-EP2 system is B3-CP2 > B3-SiP2 > B3-GeP2 > B3-SnP2 > B3-PbP2. The decrease in BDEs is determined by the intrinsic strength of the borane-ligand bond ΔE int . The preparation energy of tetrylone-BH 3 complexes decreases from B3-CP2 (ΔE prep = 21.6 kcal/mol) to the B3-PbP2 (ΔE prep = 13.8 kcal/mol). The three main terms, Pauli repulsion ΔE Pauli , electrostatic interaction ΔE elstat , and orbital interaction ΔE orb , are considered to inspect their contribution to the intrinsic energy ΔE int of the complexes. The Pauli repulsion ΔE Pauli has the largest value of 135.9 kcal/mol for B3-CP2 and gets smaller from E = C to Pb (98.8 kcal/mol). Moreover, the electrostatic term ΔE elstat continuously decreases from B3-CP2 (−88.3 kcal/mol) to heavier complexes. Note that the largest contributions to the ΔE int values of the system come from the orbital term ΔE orb . The orbital interaction ΔE orb in B3-CP2 is −109.0 kcal/mol and becomes weaker for heavier homologs. The π-orbital contributions ΔE π as well as the associated deformation densities Δρ and stabilization energies are shown in Figure 3. Note that the shape of orbital pairs in the B3-EP2 exhibits the side-on mode between E(PH 3 ) 2 and BH 3 . The shapes of B3-SiP2-B3-SnP2 exhibit similar shapes like the adduct B3-PbP2 and are therefore not shown in Figure 3. Note that the white/red colors in the figures for Ψ −k /Ψ k indicate the sign of the orbitals, and the yellow/blue colors in the deformation densities Δρ indicate the charge flow which occurs in the direction from yellow to blue. Figure 3(a) and (d) gives the NOCV pairs of σ-orbitals for B3-CP2 and B3-PbP2. The orbital pairs Ψ −1 / Ψ 1 can be considered as the dominant sources of the σ-bonding of the ligands in the complexes. The shape of the orbital are much weaker than ΔE σ and they also decrease for heavier homologs in B3-EP2. The decrease in the bond strength from B3-CP2 to B3-PbP2 comes mainly from the decrease in the electrostatic attractions ΔE elstat and the orbital interactions ΔE orb . This is because the tetrylones have two lone pair orbitals available for donation and they use mainly one lone pair for strong σ-donation in B3-EP2. Thus, the EDA-NOCV results suggest that the ligand E(PH 3 ) 2 in B3-EP2 is a strong σ-donor and very weak π-donor. [5,42] The plots of the pairs of orbitals Ψ −k /Ψ k that yield the NOCVs providing the most important contributions to the σ-and π-orbital terms ΔE σ and ΔE π in B3-CP2 and B3-PbP2, notes: Bond lengths are given in Å; angles in degrees. the bending angle, α, is the angle B-e-X where X is the midpoint between the P-P distance: the associated energy stabilization comes not only from the weak π-donation BH 3 ←C(PH 3 ) 2 but also from the charge relaxation within the BH 3 donor fragment BH 3 →C(PH 3 ) 2 . Figure 3(e) clearly shows that deformation density Δρ 2 can be assigned to BH 3 →Pb(PH 3 ) 2 π-backdonation where the Pb-P vacant anti-bonding orbital in the ligand Pb(PH 3 ) 2 acts as an acceptor (∆E 2 = −3.1 kcal/mol). Figure 3(f) shows that the very weak π-type orbital interaction in B3-PbP2 comes from pairs clearly indicates that σ-orbital interactions take place between the donor orbital of CP2 and PbP2 ligands and the acceptor orbital of the BH 3 fragment. The contributions of the π-orbital stabilization ΔE π in B3-EP2 are quite small. Figure  3(b) and (c) shows the NOCV pairs Ψ −2 /Ψ 2 and Ψ −3 /Ψ 3 that dominate the total stabilization ΔE π in B3-CP2. The shape of the NOCV pairs and deformation densities Δρ 2 (∆E 2 = −6.1 kcal/mol) and Δρ 3 (∆E 3 = −3.3 kcal/mol) reveals that

-NHGe α = 180°B
3 -NHPb α = 108.0°F igure 2. Optimized geometries of B3-NHE at the BP86/tZ2P+ level. notes: Bond lengths are given in Å; angles in degrees. the bending angle, α, is the angle B-e-X where X is the midpoint between the n-n distance: We continuously consider the chemical bonding of borane complexes of tetrylenes B3-NHE. The EDA-NOCV results at the BP86/TZ2P+ level for complexes a very weak pi-donor BH 3 ←Pb(PH 3 ) 2 (∆E 3 = −2.7 kcal/mol) and a typical π-backdonation BH 3 →Pb(PH 3 ) 2 also appears in the deformation density Δρ 3 . The EDA-NOCV results suggest that the B-E BDEs decrease from slighter to heavier homologs and the decrease in the bond strength from B3-CP2 to B3-PbP2 comes mainly from the decrease in the electrostatic attractions ΔE elstat and the orbital interactions ΔE orb . The NOCV pairs show not only the ligands E(PH 3 ) 2 in B3-EP2 are strong σ-donors and very weak π-donors but also the π-interactions in B3-EP2 are due to weak π-acceptors BH 3 →Pb(PH 3 ) 2 which are also irrelevant for the bond strength (Scheme 2).  the values in parentheses are the percentage contributions to the total attractive interaction Δe elstat + Δe orb . [b] the values in parentheses are the percentage contributions to the total orbital interaction Δe orb .  lighter tetrylenes and is rather weak in the B3-NHPb (−17.8 kcal/mol). Table 2 also shows that the orbital interactions ΔE orb decrease for heavier homologs. The decrease in the bond strength from carbene B3-NHC to plumbylene B3-NHPb strongly correlates with the decrease in electrostatic term ΔE elstat . This can be explained as: the tetrylenes have only one lone pair orbital available for donation and the ligands NHE Me in B3-NHE are σ-donors and weak π-acceptors. [5,42] Figure 4 shows the plots of the pairs of orbitals Ψ −k / Ψ k that yield the NOCVs providing the most important contributions to the σ-and π-orbital terms ΔE σ and ΔE π , Table 2. The largest preparation energy ΔE prep is 22.0 kcal/mol for B3-NHC and strongly decreases from B3-NHC to B3-NHPb. The BDEs trend in tetrylene complexes B3-NHE strongly decreases from the lighter (−D e = −58.7 kcal/mol for B3-NHC) to the heavier homologs (−D e = −13.4 kcal/mol for B3-NHPb). The strong decrease in the BDEs from the lighter to heavier adduct is determined by the intrinsic strength ΔE int of the BH 3 -tetrylene bonds. The electrostatic term ΔE elstat decreases from B3-NHC (−120.5 kcal/mol) to  Table 2. eDa-nOcV results at the BP86/tZ2P+ level for compounds B3-NHC-B3-NHPb using the moieties [BH 3 ] and [nHe me ] as interacting fragments. the complexes are analyzed with c1 symmetry. energy values in kcal/mol. [a] the values in parentheses are the percentage contributions to the total attractive interaction Δe elstat + Δe orb . [b] the values in parentheses are the percentage contributions to the total orbital interaction Δe orb .

Conclusion
The EDA-NOCV results suggest that the B-E BDEs in tetrylones and tetrylenes decrease from the slighter to the heavier homologs. The decrease in the bond strengths from the lighter to the heavier homologs of B3-EP2 comes mainly from the decrease in the electrostatic attractions ΔE elstat and the orbital interactions ΔE orb , while the decrease in the bond strength from carbene B3-NHC to plumbylene B3-NHPb strongly correlates with the decrease in electrostatic term ΔE elstat . The EDA-NOCV results show tetrylone ligands E(PH 3 ) 2 in B3-EP2 are strong σ-donors and very weak π-donors, and weak π-acceptors BH 3 →Pb(PH 3 ) 2 , while the ligands NHE Me in B3-NHE are σ-donors and weak π-acceptors, and very weak π-donors BH 3 ←{NHE Me }. These lead the tetrylone ligands to act as tetrylene ligands in borane complexes and vice versa. The theoretical results point toward new directions for experimental research in the field of lowcoordinate tetrylone and tetrylene compounds in the future.
the associated deformation densities ∆ρ, and stabilization energies in B3-NHC and B3-NHPb. Note that the shapes of complexes B3-NHSi and B3-NHGe are similar like the adduct B3-NHC, whereas B3-NHSn exhibits similar shape with the lead complex B3-NHPb and therefore the shapes of B3-NHSi, B3-NHGe, and B3-NHSn are not shown in Figure 4. NOCV pairs Ψ −1 /Ψ 1 , Ψ −2 /Ψ 2 , and Ψ −3 / Ψ 3 as well as the deformation densities of σ-and π-orbitals for ΔE orb of B3-NHC are shown in Figure 4(a)-(c). The σ-type interaction in Figure 4(a) is clearly from the donor fragment NHC Me to the acceptor fragment BH 3 . Figure 4(b) shows that weak π-type orbital interactions in B3-NHC do not come from a typical π-backdonation H 3 B→NHC Me only but also come from a very weak π-donor H 3 B←NHC Me with the charge flow Ψ −2 /Ψ 2 indicating stabilization at −9.8 kcal/mol. Figure 4(c) shows that a very weak π-type orbital interaction in B3-NHC comes from typical π-backdonation BH 3 →NHC Me with the charge flow Ψ −3 /Ψ 3 indicating stabilization at −5.9 kcal/mol. Note that the structures and orbital pairs of the lighter homologs B3-NHE with E = C to Ge have head-on modes between the ligands and BH 3 , whereas the heavier species B3-NHSn and B3-NHPb exhibit side-on bonded ligands to the BH 3 fragment. Figure 4(d)-(f) shows significant different EDA-NOCV results for B3-NHPb. Figure  4(d) clearly shows that the σ-type interaction has the direction from charge donation at the NHPb Me (yellow area) to BH 3 fragment H 3 B←NHPb Me with stabilization at −35.7 kcal/mol. Figure 4(e) shows that the very weak π-type orbital interactions in B3-NHPb come from typical π-backdonation BH 3 →NHPb Me with the charge flow Ψ −2 /Ψ 2 indicating stabilization at −1.5 kcal/mol. Like the Figure 4(b) of carbene, Figure 4(f) of plumbylene shows weak π-type orbital interactions in B3-NHPb which also exhibit a typical π-backdonation H 3 B→NHPb Me and a very weak π-donor H 3 B←NHPb Me with the charge flow Ψ −3 / Ψ 3 indicating stabilization at −1.1 kcal/mol. The fact is that the tetrylenes have only one lone pair orbital available for donation and the ligands NHE Me in B3-NHE are σ-donors and weak π-acceptors. However, a strange thing that was found is that the NOCV pairs also exhibit the