A comparison for donor-Acceptor interactions between E(PH3)2 and NHEMe ligands (E = C to Pb) of W(CO)5 complexes using energy decomposition analysis method with natural orbitals for chemical valence theory - Huynh Thi Phuong Loan

Vietnam Journal of Chemistry, International Edition, 54(4): 501-508, 2016 DOI: 10.15625/0866-7144.2016-00355 501 A comparison for donor-acceptor interactions between E(PH3)2 and NHEMe ligands (E = C to Pb) of W(CO)5 complexes using energy decomposition analysis method with natural orbitals for chemical valence theory Huynh Thi Phuong Loan 1 , Le Thi Hoa 1 , Duong Tuan Quang 2 , Tran Duc Sy 3 , Dang Tan Hiep 4 , Pham Van Tat 5 , Nguyen Thi Ai Nhung 1* 1 Department of Chemistry – Hue University of Sciences – Hue University, Hue City, Vietnam 2 Department of Chemistry – Hue University of Education – Hue University, Hue City, Vietnam 3 Department of Chemistry – Quang Binh University, Dong Hoi City, Vietnam 4 HCMC University of Food Industry, Ho Chi Minh City, Vietnam 5 Faculty of Science and Technology, Hoa Sen University, Ho Chi Minh City, Vietnam Received 17 March 2016; Accepted for publication 12 August 2016 Abstract Quantum chemical calculations at the BP86/TZ2P+ level of theory are performed for a comparison of density functional theory (DFT) between tetrylones [(CO)5W-{E(PH3)2}] (W5-EP2) and tetrylenes [(CO)5W-{NHEMe}] (W5- NHEMe) when E = C to Pb. The EDA-NOCV results suggest that the W-E bond dissociation energies (BDEs) in tetrylone complexes increase from the lighter to the heavier homologues. The W-E bond dissociation energies (BDEs) trend in W5-EP2 comes from the increase in (CO)5W←E(PH3)2 donation and strong electrostatic attraction, and that the ligands E(PH3)2 (EP2) are strong -donors and very weak π-donors. The W-E BDEs trend in tetrylene complexes W5- NHEMe is opposite to that of the W5-EP2 complexes which decrease from the lighter to the heavier homologues. The NHEMe ligands are strong -donors and weak π-acceptors. NOCV pairs were used in a description of the chemical bond between the W(CO)5 fragment and the ligands in the transition-metal complexes and the results indicated that the NOCV pairs lead to very valuable description of the bonding situation of the fragment-ligand bond in complexes. Keywords. Density functional theory; Bond dissociation energies (BDEs); Energy decomposition analysis (EDA); Natural Orbitals for Chemical Valence (NOCV). 1. INTRODUCTION The description of bonding in transition metal complexes in terms of synergic processes of the ligand metal electron donation and the metal ligand back-donation has much influenced the way of thinking about the properties of transition-metal- based systems [1]. The development of ab initio methods of quantum chemistry and in particular of density functional theory (DFT) has given rise to fast progress in the theoretical description of transition metal complexes thanks to the results obtained from high-quality computations [2]. Classification of ligands according to their donor- acceptor properties allows us to understand the electronic structure of metal complexes as well as to predict and to rationalize their chemical reactivity [1,3-5]. Numerous theoretical methods and concepts were applied in a description of donor-acceptor properties, including the interaction-energy partitioning schemes and energy decomposition analysis (EDA) [5, 6] techniques based on molecular orbital energies. The EDA gives very well-defined energy terms for the chemical bonds in molecules [6]. One of the several useful schemes that link the concepts of bond-order, bond-orbitals, and charge rearrangement with the deformation density is the method based on natural orbitals for chemical valence (NOCV) [7]. The EDA-NOCV method [1, 2, 8-10] combines both charge (NOCV) and energy (EDA) partitioning schemes for decomposition of the deformation density which is associated with the bond formation, Δρ, into different components of the chemical bonds. VJC, 54(4) 2016 Nguyen Thi Ai Nhung, et al 502 It has been known that the studies concerned with tetrylones (carbones, silylones, germylones, stannylones, plumbylones) EL2 possessing two lone pairs at E central atom (E = C to Pb) are increasingly interested [9, 11-14]. Comparison with tetrylones, the tetrylenes (ER2) (carbenes, silylenes, germylenes, stannylenes, plumbylenes) possess only one electron lone pair at E central atom and have two electron-sharing bonds (ER) to E atom [9, 12, 15]. Moreover, the structures and bonding situation of a complex of tungsten pentacarbonyl W(CO)5 with tetrylones-[W(CO)5-{C(PPh3)2}] and tetrylenes-[W(CO)5-{(NHCH)2}] were analyzed using DFT calculations by Nguyen and Frenking [9]. The main purpose of the present paper is to briefly review the application of the EDA-NOCV approach in a comparison for donor-acceptor interaction between the two typical ligands, carbodiphosphorane-analogues (tetrylones) E(PH3)2 and N-heterocyclic carbene-analogues (tetrylenes) NHEMe in transition metal complexes. We consider a comparative investigation of the bonding situation of the complexes [(CO)5W-{E(PH3)2}] (W5-EP2) and [(CO)5W-{NHEMe}] (W5-NHEMe) with E = C to Pb (Scheme 1). The electronic structures are analyzed using the energy partitioning method. We want to draw a thorough picture of electronic structures and natural of chemical bonding of free ligands (E(PH3)2 and NHEMe) as donor fragments bonded with W(CO)5 as acceptor fragments, and then a picture of structures and properties of parent complexes of the main group and transition metal complexes that carry tetrylone and tetrylene ligands. Scheme 1: Overview of the complexes investigated in this work. 2. COMPUTATIONAL DETAILS In the introduced EDA-NOCV [1, 2, 9, 10], the bond dissociation energy, De, of a molecule is divided into the instantaneous interaction energy ΔEint and the preparation energy ΔEprep. Bond- dissociation energy (BDE) is one measure of the strength of a chemical bond. For instance, the bond dissociation energy, De [kcal/mol], for a bond carbene/carbone W(CO)5 which is broken through the reaction: carbene/carbone W(CO)5 carbene/ carbone + W(CO)5 of a molecule and formed from the two fragments E 0 carbone/carbene and E 0 tungsten pentacarbonyl, is given by: E = Ecarbene/carbone tungsten pentacarbonyl E 0 carbone/carbene E 0 tungsten pentacarbonyl = -De (1) And ΔE (= -De) = ΔEint + ΔEprep (2) The preparation energy ΔEprep is the energy required to promote the fragments A and B from their equilibrium geometries in the electronic ground state to the geometries and electronic reference state that they have in the molecule. The interaction energy ΔEint can be further divided into three main components: ΔEint = ΔEelstat + ΔEPauli + ΔEorb (3) where Eelstat is the quasiclassical electrostatic interaction energy between the fragments, calculated by means of the frozen electron density distribution of the fragments in the geometry of the molecules. EPauli refers to the repulsive interactions between the fragments, which are caused by 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-symmetrisation and renormalisation. The stabilising orbital interaction term Eorb 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 which is associated with the bond formation, Δρ, into different components of the chemical bond. Furthermore, the EDA-NOCV calculations also provide pair wise energy contributions for each pair or interacting orbitals to the total bond energy. NOCV (Natural Orbital for Chemical Valence) [1, 2, 9] is defined as the eigenvector of the valence operator, , given by Equation (4): ψi = υ ψi (4) In the EDA-NOCV scheme the orbital interaction term, ΔEorb, is given by equation 5: Eorb Ek orb k 1 N / 2 k F k, k TS Fk,k TS k 1 N / 2 (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 –υk and υk, respectively. The Ek orb term of a particular type of bond are assigned by visual inspection of the shape of the deformation density, Δρk. The EDA-NOCV E Complex Fragment C W5-CP2 CP2 Si W5-SiP2 SiP2 Ge W5-GeP2 GeP2 Sn W5-SnP2 SnP2 Pb W5-PbP2 PbP2 C W5-NHCMe NHCMe Si W5-NHSiMe NHSiMe Ge W5-NHGeMe NHGeMe Sn W5-NHSnMe NHSnMe Pb W5-NHPbMe NHPbMe VJC, 54(4) 2016 A comparison for donor-acceptor interactions 503 scheme thus provides information about the strength of orbital interactions in terms of both, charge (Δρorb) and energy contributions (∆Eorb) in chemical bonds, even in molecules without symmetry. In this work, the parent complexes (W5-EP2; W5-NHEMe) and free ligands (EP2; NHEMe) were optimized for the energy decomposition analysis with the program package ADF 2013.01 [16] 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 [17]. 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 [18]. Scalar relativistic effects have been incorporated by applying the zeroth-order regular approximation (ZORA) [19]. The nature of the W-E bonds in W5-EP2 and W5-NHEMe were investigated at BP86/TZ2P+ using the EDA-NOCV method [1, 2, 12-15, 20] combines the energy decomposition analysis (EDA) [21] with the natural orbitals for chemical valence (NOCV) [2,20] under C1 symmetric geometries. 3. RESULTS AND DISCUSSION The EDA-NOCV calculations give a thorough insight into the natural of the metal-ligand bonding in [(CO)5W-{E(PH3)2}] (W5-EP2) and [(CO)5W- {NHEMe}] (W5-NHEMe). This leads to a donor- acceptor description of the W-E bond in the two systems. Both W5-EP2 and W5-NHEMe molecules are divided into the fragments E(PH3)2; NHEMe and W(CO)5 which are in the singlet state. There are no experimental results available for complexes [(CO)5W-{E(PH3)2}] (W5-EP2) and [(CO)5W- {NHEMe}] (W5-NHEMe). Note that the transition metal complexes W(CO)5 that carry the more bulky tetrylone ligands as well as the less bulky tetrylene ligands have been recently described by Nguyen and Frenking [9]. This present work just focuses on the differences of the tetrylones and tetrylenes using the EDA scheme with the NOCV method. Firstly, the complexes W5-EP2 are investigated which the numerical results of EDA-NOCV calculations are shown in Table 1. The EDA-NOCV results demonstrate that the increase in the metal-ligand bonding comes from the intrinsic interaction Eint which rises from the lighter W5-CP2 to the heavier homologues W5-PbP2. The preparation energies Eprep change very little between 4.1 and 5.1 kcal/mol in W5-SiP2 and W5-PbP2. The increase of the BDEs from the lighter to heavier adduct is determined by the intrinsic strength of the metal- ligand bonds Eint. The trend of the BDEs, De, for the W-E bond in the W5-EP2 system is W5-CP2 < W5-SiP2 < W5-GeP2 < W5-SnP2 < W5-PbP2. The three main terms EPauli, Eelstat, and Eorb are considered to inspect their contribution to the intrinsic energy Eint of the molecules. The Pauli repulsion EPauli has the smallest value of 95.2 kcal/mol for W5-CP2 and gets larger from E = C to E = Pb (131.4 kcal/mol). It follows that the increase in bond strength for the heavier homologues in W5- EP2 comes from stronger attraction rather than weaker repulsion [9]. Moreover, the electrostatic term Eelstat continuously increases from W5-CP2 (-94.9 kcal/mol) to the heavier complexes W5-GeP2 (-107.3 kcal/mol), W5-SnP2 (-118.5 kcal/mol) and it gives the strongest value in the lead complex W5- PbP2 (-120.3 kcal/mol). The same trend is shown for the orbital interactions that the increase in the orbital interactions from W5-CP2 (-47.4 kcal/mol) to W5-PbP2 (-70.8 kcal/mol) while the percentage contribution of the orbital interactions gives 33.3% in W5-CP2 and stays nearly the same from W5- SiP2 (37.7%) to W5-PbP2 (37.0%). The value of Eorb comes mainly from - and π-contributions. The increase in bond strength in W5-EP2 correlates with the decrease of Eelstat and Eorb. The increase in the attractive interaction Eelstat and Eorb of the heavier tetrylone ligands can be traced back to the - lone-pair orbital, which leads to stronger -orbital interaction Eorb and electrostatic attraction Eelstat. The -orbital contribution Eorb is much stronger for the heavier complexes which means they increase from W5-CP2 (-34.4 kcal/mol) to W5-PbP2 (-60.6 kcal/mol). In contract to this, the π-orbital contribution Eπ are much weaker than those of E and decrease for the heavier group-14 ligands in complexes. The Eorb term was examined of the EDA- NOCV results further in order to obtain more detailed information on the natural of the bonding in W5-CP2 to W5-PbP2. The plots of the pairs of orbitals k/ -k that yield the NOCVs providing the largest contributions to the - and -orbital terms E and E in W5-EP2 (E = C, Si) and the associated deformation densities and stabilization energies are shown in figure 1. The shape of orbital pairs in W5-CP2 exhibits the head-on mode between C(PH3)2 and W(CO)5, whereas the heavier homologues E(PH3)2 bind to W(CO)5 in W5-EP2 (E = Si – Pb) in side-on modes. The homologues W5- GeP2 – W5-PbP2 exhibit similar shapes to those of adduct W5-SiP2 and therefore, they are not shown in figure 1. Note that the green/red colors in the VJC, 54(4) 2016 Nguyen Thi Ai Nhung, et al 504 figures for k/ -k indicate the sign of the orbitals, and the white/black colors in the deformation density designate charge depletion, and the black areas point to charge accumulation. The charge flow occurs in the direction from white to black. Figures 1 (a) and 1 (d) give the NOCV pairs of - orbitals for W5-CP2 and W5-SiP2. The orbital pairs 1/ -1 can be considered as the dominant sources for the -bonding of the EP2 ligands in the two complexes. The shape of the orbital pairs clearly indicates that -orbital interactions take place between the donor orbital of CP2 and SiP2 ligands which are mainly localized at the carbon(0) or silicon(0) and the acceptor orbital of W(CO)5. The contributions of the π-orbital stabilization Eπ in W5-EP2 are small (Table 1). It has been pointed out that the ligand E(PH3)2 are double donor and therefore, there should be no significant contribution from (CO)5W→E(PH3)2 π-backdonation [9,11]. Figures 1(b) and 1(c) show two NOCV pairs k/ -k (k = 2, 3) that dominate the total stabilization Eπ in W5-CP2. The shape of the NOCV pairs 2/ -2 and 3/ -3 and deformation densities 2 and 3, reveal that the associated energy stabilization comes mainly from the charge relaxation within the W(CO)5 acceptor fragment (∆ρ2 (∆E = -3.9 kcal/mol); ∆ρ3 (∆E = -3.03 kcal/mol)). It follows that donation of the carbone π lone pair to the W(CO)5 is very weak. The charge flows, and the associated stabilization energies which are shown in Figures 1 (e) and 1 (f) of W5-SiP2 exhibits a strange trend compared with the NOCV pairs 2/ -2 and 3/ -3 as π-type orbitals in W5-CP2. The charge flow 2 can be assigned to (CO)5W→Si(PH3)2 π-back-donation where the Si-P vacant anti-bonding orbital acts as an acceptor. In contrast to this, the shape of the charge flow 3 indicates that the stabilization of -4.7 kcal/mol comes from the relaxation of the acceptor fragment W(CO)5. The W-E BDEs trend in W5-EP2 comes from the increase in (CO)5W←E(PH3)2 donation and from strong electrostatic attraction, and that the ligands E(PH3)2 (EP2) are strong -donors and very weak π-donors. Table 1: EDA-NOCV results at the BP86/TZ2P+ level for complexes W5-CP2 to W5-PbP2 using the moieties [W(CO)5] and [E(PH3)2] as interacting fragments. The complexes are analyzed with C1 symmetry. Energy values in kcal/mol Complex W5-CP2 W5-SiP2 W5-GeP2 W5-SnP2 W5-PbP2 Fragment W(CO)5 W(CO)5 W(CO)5 W(CO)5 W(CO)5 CP2 SiP2 GeP2 SnP2 PbP2 Eint -47.1 -53.3 -54.3 -58.3 -59.7 EPauli 95.2 119.9 118.2 129.6 131.4 Eelstat [a] -94.9 (66.7 %) -107.9 (62.3 %) -107.3 (62.2 %) -118.5 (63.1 %) -120.3 (63.0 %) Eorb [a] -47.4 (33.3 %) -65.3 (37.7 %) -65.2 (37.8 %) -69.4 (36.9 %) -70.8 (37.0 %) Eσ [b] -34.4 (72.6 %) -49.8 (76.3 %) -52.8 (81.0 %) -58.0 (83.6 %) -60.6 (85.6 %) Eπ [b] -10.6 (22.4 %) -13.8 (21.1 %) -10.2 (15.6 %) -8.3 (11.9 %) -7.8 (11.0 %) Erest [b] -2.4 (5.0 %) -1.7 (2.6 %) -2.2 (3.4 %) -3.1 (4.5 %) -2.4 (3.4 %) Eprep 4.2 4.1 4.8 5.0 5.1 E (= -De) -42.9 -49.2 -49.5 -53.3 -54.6 [a] The values in parentheses are the percentage contributions to the total attractive interaction Eelstat + Eorb. [b] The values in parentheses are the percentage contributions to the total orbital interaction Eorb. The EDA-NOCV results of tetrylenes [(CO)5W- {NHEMe}] (W5-NHEMe) are completely different from the tetrylone complexes. Table 2 shows that EDA-NOCV results at the BP86/TZ2P+ level for complexes W5-NHCMe–W5-NHPbMe using the moieties [W(CO)5] and [NHEMe] as interacting fragments. The W-E BDEs trend in W5-NHEMe is opposite to that of the W5-EP2 complexes which decrease from the lighter to the heavier homologues (W5-NHCMe: -De = -52.0kcal/mol; W5-NHPbMe: -De = -29.0 kcal/mol). The trend of the bond dissociations energies (BDEs) De for the W-E bond VJC, 54(4) 2016 A comparison for donor-acceptor interactions 505 Ψ-3 (-0.19) W5-CP2 (π) Ψ3 (0.19) ∆ρ3(∆E = -3.03) (c) W5-CP2 (π) Ψ2 (0.24) Ψ-2 (-0.24) ∆ρ2 (∆E = -3.9) (b) W5-SiP2 (σ) Ψ1 (0.83) Ψ-1 (-0.83) ∆ρ1(∆E = -48.96) (d) W5-SiP2 (π) Ψ2 (0.33) ∆ρ2(∆E = -6.2) (e) Ψ-2 (-0.33) Ψ-3 (-0.27) ∆ρ3(∆E = -4.7) (f) W5-SiP2 (π) Ψ3 (0.27) W5-CP2 (σ) Ψ1 (0.55) Ψ-1 (-0.55) ∆ρ1 (∆E = -32.34) (a) in W5-NHEMe system is W5-NHCMe > W5-NHSiMe > W5-NHGeMe > W5-NHSnMe > W5-NHPbMe. The decrease of the BDEs from the lighter to heavier adduct is determined by the intrinsic strength of the metal-ligand bonds Eint. The NOCV pairs of W5- NHEMe are considered like the tetrylone complexes. The shape of the NOCV pairs 1/ -1 and the deformation densities 1 of W5-NHCMe exhibit typical features for (CO)5W NHCMe -donation. Fig. 1: Most important NOCV pairs of orbitals Ψ-k, Ψk with their eigenvalues -υk, υk given in parentheses, and the associated deformation densities ∆ρk and orbital stabilization energies ∆E (kcal/mol) for the complexes W5-CP2 and W5-SiP2. The charge flow in the deformation densities is from the white →black region. (a) σ-NOCV of W5-CP2; (b) and (c) π-NOCVs of W5-CP2; (d) σ-NOCV of W5-SiP2; (e) and (f) π-NOCVs of W5-SiP2 Figure 2 (a) shows that the - type interaction is clearly from the donating NHCMe fragment to the accepting W(CO)5 fragment. The shapes of the NOCV pairs 2/ -2 and the deformation density 2 in Figure 2 (b) show that stabilization of -7.1 kcal/mol can be assigned to (CO)5W NHCMe - donation while the stabilization of also comes from relaxation of the acceptor fragment W(CO)5 in W5- NHCMe. In contrast to this, the shapes of the NOCV pairs 3/ -3 and particularly the deformation density 3 in figure 2(c) clearly show that the small stabilization of -3.6 kcal/mol comes mainly from VJC, 54(4) 2016 Nguyen Thi Ai Nhung, et al 506 relaxation of the acceptor fragment W(CO)5. Figure 2-(d, e, f) shows significantly different EDA-NOCV results for W5-NHPbMe because of the surprising structure of the plumbylene ligand, which is bonded through its - electron density. Note that the structures and orbitals pairs of the lighter homologues W5-NHEMe with E = C, Si, Ge have head-on modes between the ligands and W(CO)5, whereas the heavier species W5-NHSnMe and W5- NHPbMe exhibit a side-on bonded ligands to the W(CO)5 fragment. Figure 2 (d) shows that the -type interaction has the direction of the charge flow of (CO)5W NHPbMe. The deformation density 1 exhibits an area of charge donation (white area) at the NHPbMe moiety associated with the deformation density 1 and stabilization energy is 39.5 kcal/mol. Figures 2 (e) and 2 (f) show that the very weak -type orbital interactions in W5- NHPbMe come from typical -back-donation (CO)5W NHPbMe with the charge flow 2/ -2 indicates stabilization of -2.4 kcal/mol and the relaxation of the W(CO)5 fragment with the charge flow 3/ -3 indicates stabilization of -1.3 kcal/mol. Thus, the bonding in the tetrylene complexes W5- NHEMe exhibits the typical feature in terms of strong -donation and weak -donation. From the above results, it can be asserted that the weaker bonds of the heavier complexes [(CO)5W-{NHEMe}] result from a strong decrease in the electrostatic component of the W-E bonds. The -interactions in [(CO)5W-{NHEMe}] are due to very weak - backdonation and are also irrelevant for the bond strength. The decrease in the donation (CO)5W NHEMe, which is manifested in the calculated values for E and in the electrostatic attraction, Eelstat, provides a rationale for the weaker bonding of the heavier atoms E. The differences between [(CO)5W-{E(PH3)2}] (W5-EP2) and [(CO)5W- {NHEMe}] (W5-NHEMe) can be mainly explained that the tetrylones-{E(PH3)2} have two lone pairs for donation while the tetrylenes NHEMe only retains one lone pair at central atom E. Table 2: EDA-NOCV results at the BP86/TZ2P+ level for complexes W5-NHCMe to W5-NHPbMe using the moieties [W(CO)5] and [NHEMe] as interacting fragments. The complexes are analyzed with C1 symmetry. Energy values in kcal/mol Complex W5-NHCMe W5-NHSiMe W5-NHGeMe W5-NHSnMe W5-NHPbMe Fragment W(CO)5 W(CO)5 W(CO)5 W(CO)5 W(CO)5 NHCMe NHSiMe NHGeMe NHSnMe NHPbMe Eint -56.7 -48.2 -36.7 -32.1 -34.0 EPauli 119.4 117.5 84.6 67.2 58.4 Eelstat [a] -123.3 (70 %) -104.8 (63.3 %) -72.2 (59.5 %) -53.9 (54.3 %) -46.0 (49.8 %) Eorb [a] -52.8 (30 %) -60.9 (36.7 %) -49.1 (40.5 %) -45.3 (45.7 %) -46.3 (50.2 %) Eσ [b] -36.3 (68.8 %) -42.1 (69.1 %) -35.0 (71.3 %) -37.2 (82.1 %) -41.1 (88.8 %) Eπ [b] -12.5 (23.7 %) -12.8 (21.0 %) -12.8 (26.1 %) -7.1 (15.7 %) -3.7 (8.0 %) Erest [b] 4.0 (7.5 %) -6.0 (9.9 %) -1.3 (2.6 %) -1.0 (2.2 %) -1.5 (3.2 %) Eprep 4.7 2.9 2.3 2.0 5.0 E (= - De) -52.0 -45.3 -34.4 -30.1 -29.0 [a] The values in parentheses are the percentage contributions to the total attractive interaction Eelstat + Eorb. [b] The values in parentheses are the percentage contributions to the total orbital interaction Eorb. 4. CONCLUSION The EDA scheme with the NOCV method has been combined for comparing the differences between W(CO)5 complexes that carry E(PH3)2 and NHEMe ligands (E = C to Pb). The EDA-NOCV charge and energy decomposition scheme based on the Kohn-Sham approach not only makes it possible to decompose the deformation density, Δρ, into the different components of the chemical bond ( , π , π ) of the chemical bond but also provides the corresponding energy contributions to the total bond energy. The EDA-NOCV results suggest that the W- E bond dissociation energies trend in W5-EP2 comes from the increase in (CO)5W←E(PH3)2 donation and from strong electrostatic attraction and VJC, 54(4) 2016 A comparison for donor-acceptor interactions 507 that the ligands E(PH3)2 are strong -donors and very weak π-donors. The W-E BDEs trend in W5- NHEMe is opposite to that of the W5-EP2 complexes which the NHEMe ligands are strong -donors and weak π-acceptors. The results show that the set of orbitals applied in the two fragments in complexes allows for a separation and quantitative assessment of the contributions to the deformation density of donation from ligand metal to back-donation ligand metal electron transfer processes. Fig. 2: Most important NOCV pairs of orbitals Ψ-k, Ψk with their eigenvalues -υk, υk given in parentheses, and the associated deformation densities ∆ρk and orbital stabilization energies ∆E for the complexes W5-NHCMe and W5-NHPbMe. The charge flow in the deformation densities is from the white → black region. (a) σ-NOCV of W5-NHCMe; (b) and (c) π-NOCVs of W5-NHCMe; (d) σ-NOCV of W5-NHPbMe; (e) and (f) π-NOCVs of W5-NHPbMe. Energy values in kcal/mol Acknowledgements. This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 104.06-2014.13 (Nguyen Thi Ai Nhung). The jobs of this study were run via Erwin cluster which is an excellent service provided by the Hochschulrechenzentrum of the Philipps-Universität Marburg-Germany. NTAN would like to thank Prof. Dr. Gernot Frenking for allowing to continuously use her own allocation at Frenking’s group. Further W5-NHPbMe (π) Ψ3 (0.17) Ψ-3 (-0.17) ∆ρ3(∆E = -1.3) (f) W5-NHPbMe (π) Ψ2 (0.24) Ψ-2 (-0.24) ∆ρ2(∆E = -2.4) (e) W5-NHPbMe (σ) Ψ1 (0.85) Ψ-1 (-0.85) ∆ρ1(∆E = -39.5) (d) W5-NHCMe (σ) Ψ1 (0.53) Ψ-1 (-0.53) ∆ρ1(∆E = -34.4) (a) W5-NHCMe (π) Ψ2 (0.32) Ψ-2 (-0.32) ∆ρ2(∆E = -7.1) (b) Ψ-3 (-0.16) W5-NHCMe (π) Ψ3 (0.16) ∆ρ3(∆E = -3.6) (c) VJC, 54(4) 2016 Nguyen Thi Ai Nhung, et al 508 computer time was provided by the HLRS Stuttgart, the HHLRZ Darmstadt, and the CSC Frankfurt. REFERENCES 1. M. Mitoraj, A. Michalak. Donor-Acceptor properties of Ligands from Natural Orbitals for Chemical Valence, Organometallic, 26, 6576-6580 (2007). 2. M. Mitoraj, A. Michalak. 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