Skip to main content
NCBI home page
ACS Omega logoLink to ACS Omega
. 2020 Aug 14;5(33):21271–21287. doi: 10.1021/acsomega.0c03237

In-Depth Investigation of a Donor–Acceptor Interaction on the Heavy-Group-14@Group-13-Diyls in Transition-Metal Tetrylone Complexes: Structure, Bonding, and Property

Huynh Thi Phuong Loan †, Thanh Q Bui †, Tran Thi Ai My †, Nguyen Thi Thanh Hai †, Duong Tuan Quang ‡, Pham Van Tat §, Dang Tan Hiep ∥, Nguyen Tien Trung ⊥, Phan Tu Quy #, Nguyen Thi Ai Nhung †,*
PMCID: PMC7450610  PMID: 32875264

Abstract

graphic file with name ao0c03237_0016.jpg

Stabilization for tetrylone complexes, which carry ylidone(0) ligands [(CO)5W-X (YCp*)2] (X = Ge, Sn, Pb; Y = B–Tl), has become an active theoretical research because of their promising application. Structure, bonding, and quantum properties of the transition-metal donor–acceptor complexes were theoretically investigated at the level of theory BP86 with several types of basis sets including SVP, TZVPP, and TZ2P+. The optimized structures reveal that all ligands X (YCp*)2 are strongly bonded in tilted modes to the metal fragment W(CO)5, and Cp* rings are mainly η5-bonded to atom X. DFT-based bonding analysis results in an implication that the stability of W–X bond strength primarily stems from the donation (CO)5W ← X(YCp*)2 formed by both σ- and π-bondings and the electrostatic interaction ΔEelstat. The W–X bond possesses a considerable polarizability toward atom X, and analysis on its hybridization is either sp2-characteristic or mainly p-characteristic. EDA-NOCV-based results further imply that the ligands XY perform as significant σ-donors but minor π-donors. The visual simulations of NOCV pairs and the deformation densities assemble a comprehensive summary on different components of the chemical bond via σ- and π-types in the complexes. This work contributes to the literature as an in-depth overview on predicted molecular structures and quantum parameters of the complexes [(CO)5W-X(YCp*)2] (X = Ge, Sn, Pb; Y = B–Tl), conducive to either further theoretical reference or extending experimental research.

Introduction

In general, the Group-14 ylidones XL2 with X = C–Pb, possessing two lone pairs at the X central atom, are called tetrylone ligands. They are composed of a central atom X(0) and two ligands L in a donor–acceptor coordination (L:→X(0)←:L).1,2 The latter was first reported as phosphines, i.e., PR3, including PPh3 and less bulky PH3.3,4 Regarding ligands L, there has been a variety of zero-valent Group-14 compounds XL2 that are of interest, such as L = N-heterocyclic carbenes (NHCs), YCp* (Y = B–Tl), cAAC (cyclic alkyl amino carbene), etc. It is proposed that the divalent X(0) compounds isolated are stabilized by the σ-donating induced from two lone pairs of the ligands according to the octet rule.5,6 The mechanism of two strong σ-donating carbones supporting the heavier X(0) species (X = Si, Ge) was discovered by Roesky et al. and Driess et al.6−8 In addition, the extension of the XL2 group of ylidones to other ligands was reported by Nikonov et al. and Flock et al. for germanium(0) compounds, Ge(0),9 and tin(0) compounds, Sn(0), respectively.10 Some theoretical studies projected the important role of tetrylone ligands for the stability of the X central atoms in the structures and electronic properties of the ylidone(0) ligands in complexes.11−13 Also, the marked dependence of X–L bond length on the donor–acceptor capability of ligand L was extensively demonstrated.12,13

A recent study investigated the structures and chemical bonding of the main Group-14 elements in transition-metal (TM) complexes that carry bulky tetrylone ligands, i.e., [W(CO)5-{X(PPh3)2}] (X = C–Pb).1 The work arrived at two main findings. First, the end-on bonding configuration was observable in carbone complexes and the heavier systems performed the side-on bonding manners. Second, the bond dissociation energy value has a positive correlation with molecular mass. Another research led to a conclusion that the tetrylones in the two systems [W(CO)4-{X(PPh3)2}] and [W(CO)5-{X(PPh3)2}] always utilize their two lone-pair orbitals available for donation ligand → transition-metal atoms.14 These results imply that the center atom of ligands in complexes can be a good electron-rich σ-donor ligand.15−17 It is also believed that an interesting topic in main-group chemistry regarding the coordination compounds of the monovalent Group-13 elements can pave the way for new research directions.18−20 In fact, the coordination chemistry of Group-13 elements in a low oxidation state has been extremely a topic of intensive research that has led to the successful synthesis of new types of transition-metal complexes.21−23 Several low-valent Group-13 diyl YR species (Y = Al, Ga, In; R = cyclopentadienyl-C5H5 denoted as Cp; pentamethylcyclopentadienyl-C5(CH3)5 denoted as Cp*) have emerged as versatile carbenoid ligands in coordination chemistry observing the metal-atom ligators.24−26 Klein and Frenking reported for the first time the structures and bonding configuration of the new class of stable carbenes CL2, in which L is a Group-13 diyl ligands YCp* (Y = B–Tl).27 Many theoretical studies reported that the diyl ligand YCp* appears as a stronger σ-donor and weaker π-acceptor, thus attracting much attention from scientists.20−22,28 This helps YCp* ligands act as suitable candidates for stabilizing a divalent carbon(0) atom in the carbone ligand C(YCp*)2.27

It was demonstrated that the Group-13 diyl compounds Cp*Y (Y = Al, Ga, In) play the role of Lewis bases thanks to the existence of the electron lone pair.29 In particular, monovalent MR′ metal ligands (M = Zn, Cd; R′ = Me, Et, Cp*; and M = Au; R′ = PMe3, PPh3) are considered as one-electron ligands of chemistry.30 If Cp* groups with soft and flexible binding mode were associated, the intrinsic tension of aluminium and gallium compounds would be reduced. The explanation relates to the unique steric and electronic features of the versatile ligand YCp*, including the strong electron-donating, carbenoid character, the high flexibility of the Cp* binding modes. In particular, Nhung et al. also reported the new complexes between silylone SiL2 (L = Group-13 diyls; B–Tl) with transition-metal compounds Mo(CO)5.31 The tetrylone ligands Si(YCp*)2 in complexes [(CO)5Mo-Si(YCp*)2] were theoretically predicted to perform as strong σ-donors and weak π-donors. The results suggested that the Group-13 diyls could effectively stabilize the central Si atom.31

In this work, a detailed comprehensive theoretical research of divalent ylidone(0) compounds on their geometric representation of coordination modes is compiled. The complexes [(CO)5W-X(YCp*)2] contain heavy-Group-14@Group-13-element ligands X(YCp*)2, in which X = Ge, Sn, Pb and Y = B–Tl, and W(CO)5. First, the equilibrium geometry, energy, and chemical bonding of tungsten complexes that carry Group-13 diyls [W(CO)5-X(YCp*)2] (W-XY) were calculated. The bond dissociation energies with and without dispersion corrections were then predicted with gradient corrected density functional theory (DFT). Bonding analysis was carried out by calculating the energetically low-lying occupied molecular orbitals for σ- and π-orbitals of the free ligands [X(YCp*)2] using natural bond orbital (NBO) analysis. Finally, the EDA-NOCV method combining energy decomposition analysis (EDA) and charge of natural orbitals for chemical valence (NOCV) was used to obtain in-depth information on the nature of chemical bonding for complexes. To the best of our knowledge, this is the first time that geometric structures, bonding properties, and complementary quantum parameters of tungsten complexes that carry the heavy-Group-14@Group-13-diyls ligands X(YCp*)2 are systematically summarized in an overview-based research. Scheme 1 illustrates the Lewis structures of donor–acceptor compounds investigated in this work, including the complete complexes (denoted as W-XY) and the free ligands (denoted as XY).

Scheme 1. Overview of Donor–Acceptor Compounds Investigated in This Work: (Left) Complexes: [W(CO)5-X(YCp*)2] (W-XY) and (Right) Tetrylone Ligands: [X(YCp*)2] (XY) with X = Ge, Sn, Pb; and Y = B–Tl.

Scheme 1

Open in a new tab

Results

Geometrical Parameters of Optimized Structures and Energies

Figure 1 presents quantum parameters, including bond lengths and bond angles, of all optimized geometries of complexes W-XY. W–X bond length is negatively correlated with the mass of Y, from the lightest boron complexes W-XB to the heaviest thallium systems W-XTl. This reveals that the thallium-complexes have the shortest W–X bonds in their germylones, stannylones, and plumbylones, i.e., W-GeTl (W-Ge at 2.612 Å), W-SnTl (W-Tl at 2.807 Å), and W-PbTl (W-Pb at 2.880 Å), respectively. In contrast, X–Y bonds register the opposite tendency as their length increases when the mass of the adducts is heavier. The shortest length values are 2.078 and 2.088 Å (Ge-B) in germylones, 2.337 and 2.348 Å (Sn-B) in stannylones, and 2.472 and 2.487 Å (Pb-B) in plumbylones. The results are consistent with our previous study on silylone systems [(CO)5Mo-Si(YCp*)2], in which the bond length value of Mo–Si increases if the YCp* homologue is heavier while a negative correlation was observed between the Si–Y bond length and the mass of the Group-13 Y adducts (Y = B–Tl).31 The bonding mode of the Y-Cp* homologue is also acquired from the optimized structures of the complexes W-XY. The bond length values of Y and carbon atoms in the rings in all lighter complexes with atoms Y from B to In are nearly equal regarding each complex. The figures for germylones, stannylones, and plumbylones vary in the range of 1.811–2.649, 1.804–2.651, and 1.805–2.646 Å, respectively. This indicates that they perform quasi-η5 bonded manners, interacting through the center of the ring-planes. Meanwhile, the bond length of Tl and the carbon atoms of Cp* rings in tetrylone@thallium complexes W-XTl varies significantly, i.e., 2.643–2.864 Å for W-GeTl, 2.642–2.860 Å for W-SnTl, and 2.649–2.854 Å for W-PbTl. These suggest that Tl–Cp* bonding is between η3- and η1-configurations. The bonding modes are further illustrated and summarized in Table 1.

Figure 1.

Figure 1

Open in a new tab

Selective parameters (bond lengths/Å and bond angles/°) of complex W-XY (X = Ge, Sn, Pb; Y = B–Tl) optimized structures at the BP86/def2-SVP level.

Table 1. Selective Parameters of Bond Length (Å), Bond Angle (°), Bending Angle (α/°), the Angle W–X–Z of Complexes W-XY Containing the Two Fragments [W(CO)5] and [X(YCp*)2] where Z Is the Midpoint of the Y–Y Distance, and Bonding Mode of YCp* with the Alternatives for the Cp* Ring for the Optimized Complexes W-XY (X = Ge, Sn, Pb; Y = B–Tl) Calculated at the BP86/def2-SVP Level.

graphic file with name ao0c03237_0014.jpg

complex bending angle (α/°) bonding mode of YCp* with the alternatives for the Cp* ring
W-GeB 125.1 η5
W-GeAl 98.8 η5
W-GeGa 104.4 η5
W-GeIn 106.5 η5
W-GeTl 110.9 η5 to η3
W-SnB 112.9 η5
W-SnAl 94.4 η5
W-SnGa 98.6 η5
W-SnIn 99.8 η5
W-SnTl 105.3 η5 to η3
W-PbB 107.3 η5
W-PbAl 91.6 η5
W-PbGa 96.2 η5
W-PbIn 97.4 η5
W-PbTl 102.7 η5 and η3
Open in a new tab

Table 1 and Figure 1 also provide information on bending angle α of the side-on bonding between ligands XY and metal fragment W(CO)5. In general, the bending angle value of W-XY bonds in the complexes follows the order germylones > stannylones > plumbylones in which bending angle α in W-SnY and W-PbY becomes more acute in the heavier systems (B–In). This resembles the tendency of other tetrylone ligands bonded in a tilted orientation relative to the metal fragment W(CO)x (x = 4, 5) in their optimized structures.1,14 The studies have recently reported a decrease of the corresponding bending angle from germylones to plumbylones, i.e., from 119.5° in [(CO)5W-Ge(PPh3)2] to 114.5° in [(CO)5W-Pb(PPh3)2] and from 105.5° in [(CO)4W-Ge(PPh3)2] to 99.3° for [(CO)4W-Pb(PPh3)2]. In each Group-14 homologue, boron systems exhibit the closest values to 180°, which are 125.1° for W-GeB, 112.9° for W-SnB, and 107.3° for W-PbB. Meanwhile, the smallest corresponding figures are observed in aluminum complexes, which are 98.8° for W-GeAl, 94.4° for W-SnAl, and 91.6° for W-PbAl. These reveal that the former is expected to be the most stable system as its main bonding is in highest alignment while the aluminum systems register the opposite property of stableness as their W-XY bonds approach right-angled arrangements. From Al to Tl, the bending angle α is in a positive correlation with the complex mass and stands at 110.9° for W-GeTl, 105.3° for W-SnTl, and 102.7° for W-PbTl.

The optimized geometries of free ligands XY were also investigated and are presented in Figure 2. B1–C and B2–C bonds of Cp* rings in complexes W-XY exhibit different bond length values when forming the two groups B1Cp* and B2Cp*. The ligand XB that embraces atom B1 is η5-connected to the carbon atoms of Cp* rings whose bonding length varies narrowly from 1.812 to 1.847 Å for GeB, from 1.808 to 1.835 Å for SnB, and from 1.813 to 1.839 Å for PbB. However, the atom B2 η3-bonds to the carbon atoms of Cp* rings whose bond lengths are in significantly wider ranges, i.e., 1.605–2.598 Å for GeB, 1.600–2.544 Å for SnB, and 1.597–2.549 Å for PbB. Also, Tl has a tendency of η3 bonding in its link toward Cp* with longest and shortest bonds being 2.458 and 3.208 Å for GeTl, 2.507 and 3.065 Å for SnTl, 2.513 and 3.064 Å for PbTl. Meanwhile, the calculated equilibrium structures of free ligands XY with Y = Al–In show that the YCp* is consistently η5-linked to atoms Y with the bond length values Y–C of Cp* rings.

Figure 2.

Figure 2

Open in a new tab

Selective parameters (bond lengths/Å and bond angles/°) of free ligand XY (X = Ge, Sn, Pb; Y = B–Tl) optimized geometries and bonding mode of Y-Cp* at the BP86/def2-SVP level.

Table 2 shows the theoretically predicted BDEs, DFT-De (kcal mol–1), of the bond W–X for W-XY. Overall tendency sees an increase along with the rise of the complex mass (from B to Tl). However, there are noticeable inconsistencies occurring at W-XAl systems in stannylones and plumbylones. In detail, the value De of the boron system in germylones W-GeB registers the smallest value of 44.4 kcal mol–1, and the corresponding figure for other homologues in this tetrylone family increases for the heavier complexes. Regarding stannylone systems, the BDE values of W-SnB, W-SnAl, W-SnGa, W-SnIn, and W-SnTl are 49.0, 46.7, 49.5, 49.9, and 53.9 kcal mol–1, respectively.

Table 2. Calculated Bond Dissociation Energies, DFT-De (kcal mol–1), and Bond Dissociation Energies with Corrections for Dispersion Interactions, DFT-D3 (kcal mol–1), at the BP86/def2-TZVPP Level Using BP86/def2-SVP Optimized Geometries for Complexes W-XY (X = Ge, Sn, Pb; Y = B–Tl).

graphic file with name ao0c03237_0015.jpg

complex DFT-De (kcal mol–1) DFT-D3 (kcal mol–1) ΔE
W-GeB 44.4 66.7 22.3
W-GeAl 45.5 68.9 23.4
W-GeGa 48.9 69.7 20.8
W-GeIn 50.0 69.9 19.9
W-GeTl 53.6 72.3 18.7
W-SnB 49.0 71.5 22.5
W-SnAl 46.7 66.6 19.9
W-SnGa 49.5 68.1 18.6
W-SnIn 49.9 70.6 20.7
W-SnTl 53.9 75.7 21.8
W-PbB 50.5 74.8 24.3
W-PbAl 46.2 66.9 20.7
W-PbGa 49.9 69.7 19.8
W-PbIn 49.6 70.5 20.9
W-PbTl 52.8 75.0 22.2
Open in a new tab

This is briefed that BDE values of the complexes decrease when their mass increases accordingly from B to Al before the overall tendency is observed thereafter. A similar inconsistency is also recorded in the plumbylone family, in which W-PbAl reaches a low at 46.2 kcal mol–1 between higher BDE values of W-PbB (50.5 kcal mol–1) and W-PbGa (49.9 kcal mol–1) and the thallium system that contains W-PbTl accounts for the highest BDE value (52.8 kcal mol–1). In summary, the results suggest that the heavier complexes possess stronger bonds W–X than their lighter counterparts, except for stannylone and plumbylone boron-complexes. From this, it can be pointed out that the longer bonds length do not involve that the strength bonds are weaker.32−34

In addition, dispersion forces might affect the theoretically calculated energy results, especially on the theoretical prediction for BDEs.35−37 These are especially significant if the structures comprise bulky ligands, such as Cp* groups in this study. Therefore, the calculated BDEs with dispersion interactions on the main bonding W–X in complexes W-XY (DFT-D3) are also included in Table 2. Overall, the DFT-De and DFT-D3 values of the (CO)5W-X(YCp*)2 bond strength experience a similar varying pattern. Thallium complexes W-XTl still hold the highest figure for BDEs, which are 72.3, 75.7, and 75.0 kcal mol–1 according to its germylone, stannylone, and plumbylone homologues, respectively. The two latter complexes are followed by borone complexes, while the second highest value among germylones is observed in W-GeIn. In detail, with the inclusion of dispersion forces, the BDE results of complexes W-XY register elevated values whose average rising index is ca. 20 kcal mol–1, representing the bulky factors of Cp* groups onto the BDEs of the W–X bond in W-XY. The reasoning for the elevation can be referred to the high affinity between XY and W(CO)5, which draws dispersive contribution from bulky Cp* groups.1,31,38 The contributions from dispersion interactions of germylone complexes W-GeY, stannylone complexes W-SnY, and plumbylone complexes W-PbY are expressed in term of De – D3 energy differences, i.e., 19.9–23.4, 18.6–22.5, and 19.8–24.3 kcal mol–1, respectively. Interestingly, the smallest values among stannylones and plumbylones standing for aluminum complexes are abnormal and still remain unexplained. Given the correlation with bonding stability, bond–bond dissociation energy values are markedly inconsistent with the corresponding bond length presented in Figure 1. Therefore, the length of a bond is not always a reliable parameter to evaluate its strength.

Bonding Analysis

Electronic structures and the nature of chemical bonding in complexes W-XY and free ligands XY were analyzed using natural bond orbital (NBO) calculation whose results are presented in Table 3. These include Wiberg bond indices (WBI) and natural partial atomic charges (q). The tetrylones see a similar changing tendency regarding WBI values of W–X bonds, which are overall positively correlated with the complex mass in each family. The ranges are 0.58–0.98, 0.60–0.84, and 0.55–081 for germylone, stannylone, and plumbylone systems (from W-XB to WX-Tl), respectively. However, WBI values of the X–Y bond peak at 1.22, 1.13, and 1.10 for W-GeAl, W-SnAl, and W-PbAl, respectively. Meanwhile, the figures in their respective tetrylone family follow the order W-XB > W-XGa > W-GeIn > W-GeTl. In comparison to free ligands XY, the bond orders approximated by WBI indices of both X–Y and Y–Y bonds in their corresponding complexes are significantly lower. The calculated partial charges show that the metal fragment W(CO)5 in W-XY always carries a negative charge, which are between −0.76e and −0.86e in germylones, between −0.90e and −0.99e in stannylones, between −0.91e and −1.03e in plumbylones. This suggests that an inclination of charge donation (YCp*)2X → W(CO)5 is expected in complexes.12,51,74 Therefore, the positive charges are likely to be localized at germylone, stannylone, and plumbylone ligands.1,4,38 In detail, tungsten atoms are calculated carrying significantly large negative charges, which are over −1.80e in all the tetrylone complexes. In contrast, the Group-14 (X) and Group-13 (Y) atoms tend to be localized with a positive charge when in the systems W-XY. This excludes three aluminum atoms (−0.50 for W-GeAl; −0.10 for W-SnAl; −0.01 for W-PbAl). Without the contribution of tetrylone groups, the charge of the atoms (in the free ligands XY) both shifts toward more negative values. Resemble shifting tendencies have been reported.9,51 Briefly, because atoms W are strong electron acceptors, atoms Y are strong electron donors, and atoms X play the role of transitional channels, the charge donation (YCp*)2X → W(CO)5 might be slightly complemented by a contribution of the dimer ligands (YCp*)2 via charge transfers (Cp*Y)2 → X-W(CO)5.

Table 3. NBO Analysis with Wiberg Bond Indices (WBI) and Natural Partial Charges (NPA) at the BP86/def2-TZVPP//BP86/def2-SVP Level for Complexes W-XY (X = Ge, Sn, Pb; Y = B–Tl)a.

  W-XY
 XY
complex q [X] q [Y] q [W] q [W(CO)]5 WBI (W–X) WBI (X–Y) WBI (Y–Y) q [X] q [Y] WBI (X–Y) WBI (Y–Y)
W-GeB 0.01 0.31 –1.80 –0.86 0.58 1.20 0.10 –0.02 0.10, 0.24 1.24, 1.67 0.20
W-GeAl –0.50 1.17 –1.82 –0.76 0.59 1.22 0.25 –0.73 0.93 1.60 0.43
W-GeGa 0.11 0.92 –1.91 –0.79 0.68 1.04 0.18 –0.46 0.73 1.46 0.36
W-GeIn 0.02 0.94 –1.99 –0.78 0.84 0.83 0.20 –0.50 0.76 1.34 0.31
W-GeTl 0.15 0.80 –2.10 –0.80 0.98 0.42 0.11 –0.45 0.66 1.13 0.24
W-SnB 0.25 0.24 –1.84 –0.99 0.60 0.99 0.10 0.13 0.20 1.52 0.16
W-SnAl –0.10 1.04 –1.89 –0.90 0.59 1.13 0.23 –0.47 0.81 1.53 0.44
W-SnGa 0.27 0.81 –1.99 –0.93 0.70 0.89 0.14 –0.24 0.63 1.33 0.33
W-SnIn 0.24 0.91 –2.05 –0.92 0.76 0.80 0.16 –0.33 0.72 1.24 0.28
W-SnTl 0.42 0.78 –2.17 –0.98 0.84 0.43 0.10 –0.30 0.61 1.06 0.20
W-PbB 0.27 0.24 –1.82 –1.03 0.55 0.88 0.10 0.13 0.20 1.50 0.13
W-PbAl –0.01 1.02 –1.87 –0.91 0.57 1.10 0.19 –0.44 0.80 1.47 0.43
W-PbGa 0.33 0.80 –1.96 –0.96 0.66 0.81 0.10 –0.21 0.62 1.26 0.30
W-PbIn 0.30 0.90 –2.01 –0.93 0.74 0.72 0.13 –0.28 0.70 1.18 0.30
W-PbTl 0.48 0.78 –2.14 –1.01 0.81 0.40 0.10 –0.24 0.60 0.98 0.20
Open in a new tab
a

The partial charges, q, are given in electrons [e].

Figure 3 illustrates the highest σ- and π-occupied molecular orbitals of tetrylone complexes W-XY. The energy levels of the π-type donor orbitals of germylone and stannylone complexes W-XB, W-XAl, and W-XGa are lower than those of their σ-type donor counterparts, while W-XIn and W-XTl experience an opposite pattern. Regarding plumbylone complexes W-PbY, a different arrangement of occupied molecular orbitals and orbital energy levels of σ- and π-type MOs is observed. In detail, the energy levels of the σ-type donor orbitals are lower-lying than those of the π-type donor orbitals except W-PbB.1,4,39 Besides, although the molecules investigated possess C1 symmetry, their frontier molecular orbitals of easy σ- and π-type MOs obtained by visual inspection do not always occur as symmetrical. Germylone complexes W-GeY have π-type symmetry in HOMO-2 and HOMO-7 and σ-type symmetry in HOMO-4 and HOMO-8. In terms of plumbylone complexes W-PbY, HOMO-2 to HOMO-4 and HOMO-6 are in π-type symmetry; meanwhile, HOMO, HOMO-3, and HOMO-4 are in σ-type symmetry. In addition, the shape of the MOs in complexes W-XY indicates that both σ- and π-donations are (CO)5W ← X(YCp*)2.31,38 Given the energy levels of the σ- and π-orbitals from the frontier orbital plotting, W–X bonds are formed by significantly strong σ- and π-bonding molecular orbitals. Because of the possible interaction between π-lone-pair orbitals of the ligands X(YCp*)2 and the metal fragment W(CO)5, the strength of the π-orbitals is suggested with further examination.

Figure 3.

Figure 3

Open in a new tab

Frontier molecular orbitals and orbital energies (eV) of σ- and π-types for the complexes W-XY (X = Ge, Sn, Pb; Y = B–Tl) at the BP86/def2-TZVPP level.

The frontier orbitals with the plot of the energy levels of the highest energetically lying σ- and π-orbitals of the free ligands XY with X = Ge–Pb and Y = B–Tl are shown in Figure 4 for additional reference. Overall, W(CO)5 adducts seem to stabilize the systems given the lower HOMO energy of the complex (CO)5W-X(YCp*)2 than those of their corresponding free ligand X(YCp*)2 counterparts. The inconsistent exceptions are addressed at π-type bonding orbitals of heavy tetrylones, including GeY (Y = In–Tl), SnY (Y = In–Tl), and PbY (Y = Al– Tl). This could be explained by the shape of the HOMO making it flawlessly suitable as π-donor orbitals.1,2,4

Figure 4.

Figure 4

Open in a new tab

Molecular orbitals and orbital energies (eV) of σ- and π-type MOs for the ligands XY (X = Ge, Sn, Pb; Y = B–Tl) at the BP86/def2-TZVPP level.

The energy levels of the two highest-lying occupied MOs, which have σ- or π-symmetries for the free ligands X(YCp*)2, are briefed in Figure 5. It is clear that the energy level of the π- and the σ-orbitals of X–Y bonds decreases when its atom X becomes heavier. Also, the back-lobe of the tetrylone σ-lone-pair can raise a certain bonding contribution toward atom Y. Therefore, the consequence could be a tilted configuration formed in the structure of tetrylone ligands XY bonded with the metal fragment W(CO)5. This possibly explains the optimized structures of complexes W-XY, which are presented before in Figure 1 and Table 1.

Figure 5.

Figure 5

Open in a new tab

Energy levels (eV) of the σ- and π-type orbitals for the free ligands XY (X = Ge, Sn, Pb; Y = B–Tl) at the BP86/def2-TZVPP level.

Table 4 presents the polarization of the σ-bonds W–X between the transition-metal fragment and ylidone(0) ligands in W-XY and the hybridization of the W–X bonds at atom X (X = Ge, Sn, Pb) gained from NBO analysis. The polarization of atom W in the bonds W–X rises with the rise of the tetrylone mass, which are from 35.4 to 46.9% for W-GeY, from 36.8 to 54.6% for W-SnY, and from 38.7 to 56.2% for W-PbY (Y = B–Tl). Regarding each tetrylone family, the value is positively correlated with the complex mass. This also means that the corresponding figure for X sees an opposite changing pattern. The hybridization of atom X with %s characteristics registers the largest values in complexes W-XB, i.e., 40.8, 43.3, and 37.8% for W-GeB, W-SnB, and W-PbB, respectively. The corresponding figures for heavier tetrylones in each family do not see noticeable differences, and all are under 20%. These indicate that the contribution of p-hybridization in borane systems is slightly more than their s-counterparts while the heavier complexes witness the marked dominance of p-hybridization whose contribution is within the range of 82.6–91.6%. The former explains the slightly tilted bonding of W–XY bonds in borane complexes W-GeB, W-SnB, and W-PbB given the approximate sp2 hybridization; meanwhile, the W–XY bonds in heavier homologues exhibit mainly p-characteristics between σ-donation of the metal fragment W(CO)5 and π-lone-pair orbitals of the ligands, resulting in stronger side-on bonding configurations represented by smaller bending angles α.1,31,38 Overall, heavier tetrylones tend to be less polarized and more side-on bonded given their characteristics of W–X bonds whose explanation can be approached by the analysis of bonding polarization and hybridization.

Table 4. Polarization of σ-Bonds W–X and Hybridization at Atom X from the NBO Analysis of the Complexes W-XY (X = Ge, Sn, Pb; Y = B–Tl) at the BP86/def2-TZVPP//BP86/def2-SVP Level.

  polarization W–X
 hybridization
complex % (W) % (X) %s (X) %p (X )
W-GeB 35.4 64.6 40.8 59.2
W-GeAl 39.0 61.0 10.4 88.5
W-GeGa 40.3 59.7 13.3 86.2
W-GeIn 43.8 56.2 15.7 83.9
W-GeTl 46.9 53.1 17.1 82.6
W-SnB 36.8 63.2 43.3 56.3
W-SnAl 44.7 55.3 9.4 89.5
W-SnGa 46.1 53.9 11.4 88.3
W-SnIn 48.7 51.3 11.7 88.0
W-SnTl 54.6 45.4 12.3 87.3
W-PbB 38.7 61.3 37.8 61.8
W-PbAl 45.6 54.4 7.8 91.6
W-PbGa 47.2 52.8 8.6 91.1
W-PbIn 48.4 51.6 9.3 90.3
W-PbTl 56.2 43.8 11.4 88.2
Open in a new tab

Table 5 summarizes the quantum chemical parameters related to molecular electronic structures of the studied complexes of W-XY (X = Ge, Sn, Pb; Y = B–Tl). In principle, EHOMO values represent the electron-accepting capability, and ELUMO values provide information on the capability of electron donation. The reasoning refers to the modern explanation of electron transfer including electron tunneling and the electron hopping.2,4 The obtained EHOMO values accord with the order W-XB > W-XAl > W-XGa > W-XIn > W-XTl regardless of tetrylone families. This is consistent with values of ELUMO, which are recorded with narrower differentials between systems. The HOMO energy varies from −3.35 to 4.83 eV, and the LUMO energy is within the range between −1.35 and −3.54 eV. These compile a rather inconsistent order of energy gap ΔEGAP = ELUMO – EHOMO, W-XAl > W-XB > W-XGa > W-XIn > W-XTl, and a contrary order of electronegativity (χ), W-XB < W-XAl < W-XGa < W-XIn < W-XTl. Regarding each tetrylone group, W-GeAl, W-SnAl, and W-PbAl register the highest values of energy gap with over 2 eV; meanwhile, electronegativity values of W-GeTl, W-SnTl, and W-PbTl are 4.19, 4.17, and 4.16, respectively, accounting for the highest figures. The noticeable quantum chemical parameters, including energy gap (ΔEGAP), ionization potential (I), electron affinity (A), and electronegativites (χ), imply that all the studied complexes can be considered as versatile ligands bondable with transition-metal fragments.

Table 5. Quantum Chemical Parameters for the Neutral Complexes of W-XY (X = Ge, Sn, Pb; Y = B–Tl) with the DFT at the BP86/def2-TZVPP Levela.

complex EHOMO (eV) ELUMO (eV) ΔE (eV) (ELUMO – EHOMO) I = −EHOMO A = −ELUMO χ = (I + A)/2
W-GeB –3.35 –1.43 1.92 3.35 1.43 2.39
W-GeAl –4.57 –2.29 2.28 4.57 2.29 3.43
W-GeGa –4.60 –2.45 2.15 4.60 2.45 3.53
W-GeIn –4.83 –3.02 1.81 4.83 3.02 3.92
W-GeTl –4.83 –3.54 1.29 4.83 3.54 4.19
W-SnB –3.43 –1.35 2.08 3.43 1.35 2.39
W-SnAl –4.48 –2.20 2.28 4.48 2.20 3.34
W-SnGa –4.55 –2.44 2.11 4.55 2.44 3.50
W-SnIn –4.78 –3.05 1.73 4.78 3.05 3.91
W-SnTl –4.81 –3.54 1.27 4.81 3.54 4.17
W-PbB –3.53 –1.38 2.15 3.53 1.38 2.45
W-PbAl –4.45 –2.14 2.31 4.45 2.14 3.29
W-PbGa –4.54 –2.47 2.07 4.54 2.47 3.49
W-PbIn –4.76 –3.05 1.71 4.76 3.05 3.90
W-PbTl –4.81 –3.52 1.29 4.81 3.52 4.16
Open in a new tab
a

ΔE (eV) was calculated from EHOMO and ELUMO values; electronegativites (χ) were obtained from ionization potential (I) and electron affinity (A).

EDA-NOCV calculations are utilized for in-depth analysis of chemical bonding energy in the interactions between divalent ylidone(0) ligands X(YCp*)2 and metal fragment W(CO)5 in complexes W-XY. The obtained results are presented in Table 6. The values of BDEs, −De (kcal mol–1), calculated by EDA-NOCV at the BP86/TZ2P+//BP86/def-SVP level approximate DFT-De values (Table 2). Therefore, the energy is still positively correlated with the heaviness of the studied complexes. The observations include all germylones W-GeY (44.6 to 54.7), stannylones W-SnY (from 49.3 to 54.2), and plumbylones W-PbY (50.9 to 54.3). Total instantaneous interaction energy ΔEint is composed of contributions from Pauli repulsion (ΔEPauli), attractive electrostatic interaction (ΔEelstat), and orbital interactions (ΔEorb). This represents the total interaction energy between substrates and functional groups in the complexes. EDA-NOCV data reveals that ΔEint registers its highest level at −74.1, −67.1, and −67.9 kcal mol–1 in each subgroup for W-GeTl, W-SnTl, and W-PbB, respectively. They were followed by W-GeB, W-SnB, and W-PbTl with the respective figures being −64.4, −66.5, and −66.2 kcal mol–1. Meanwhile, there are marginal differentials recorded among the medium-mass germylones, stannylones, or plumbylones. Also, −De values register rather consistent changing patterns relative with the complex mass in each tetrylone family, according to the order W-XTl > W-XIn > W-XGa > W-XAl > W-XB. There is no significant difference observable in respective values between the tetrylone groups. Overall, their calculated values are in good agreement with those obtained from DFT analysis (Table 2). However, preparation energy values resemble differently. The highest figures are those of boron-complexes W-XB, i.e., 19.8 (W-GeB), 17.2 (W-SnB), and 17.0 kcal mol–1 (W-PbB). These were followed by W-XTl with energy values of 19.4, 12.9, and 11.9 kcal mol–1, respectively. The other tetrylones saw irregular arrangements. The total attractive interaction attaching any two fragments together is deemed to be a sum of attractive electrostatic interaction (ΔEelstat) and orbital interaction energy (ΔEorb). Since both the energy levels increase along with the mass of the complexes in each tetrylone homologue, the bond W–X stability overall accords with the sequence W-XTl > W-XIn > W-XGa > W-XAl > W-XB. In detail, attractive electrostatic interaction contributes more than orbital overlapping to the total capacity of bonding Group-13 diyl adducts with W atoms. Similarly, orbital interaction energy ΔEorb positively correlates with the increase of the molecular mass, thus resulting in more stable orbital overlapping by heavier Group-13 diyl adducts than their lighter counterparts. Furthermore, the σ-orbital contributions ΔEσ dominate the π-orbital contributions ΔEπ, and they increase for the X@heavier Group-13 tetrylone ligands.1,38 The reasoning relates to the existence of the σ-lone-pair orbital leading to the significantly strong σ-orbital interactions.1,31

Table 6. EDA-NOCV Results for Complexes W-XY (X = Ge, Sn, Pb; Y = B–Tl) Using the Moieties [W(CO)5] and [XY(Cp*)2] as Interacting Fragments at the BP86/TZ2P+// BP86/def2-SVP Levela.

complex ΔEintb ΔEPauli ΔEelstatc ΔEorbd ΔEσe ΔEπe ΔEreste ΔEprep ΔE (= −De)
  [(YCp*)2X → W(CO)5] = (YCp*)2X + W(CO)5
W-GeB –64.4 115.2 –108.2 (60.2%) –71.5 (39.8%) –62.6 (87.6%) –7.9 (11.0%) –1.0 (1.4%) 19.8 –44.6 (−44.4)f
W-GeAl –51.2 102.3 –90.7 (59.1%) –62.8 (40.9%) –51.9 (82.6%) –8.6 (13.7%) –2.3 (3.7%) 3.6 –47.6 (−45.5)f
W-GeGa –55.1 117.2 –103.0 (59.8%) –69.2 (40.2%) –56.4 (81.5%) –10.8 (15.6%) –2.0 (2.9%) 3.2 –51.9 (−48.9)f
W-GeIn –57.2 127.4 –110.2 (59.7%) –74.3 (40.3%) –59.0 (79.4%) –13.4 (18.0%) –1.9 (2.6%) 4.9 –52.3 (−50.0)f
W-GeTl –74.1 170.8 –153.4 (62.6%) –91.6 (37.4%) –66.9 (73.0%) –22.7 (24.8%) –2.0 (2.2%) 19.4 –54.7 (−53.6)f
W-SnB –66.5 120.2 –112.8 (60.4%) –73.9 (39.6%) –63.7 (86.2%) –9.1 (12.3%) –1.1 (1.5%) 17.2 –49.3 (−49.0)f
W-SnAl –53.0 109.1 –95.5 (58.9%) –66.7 (41.1%) –56.6 (84.9%) –7.9 (11.8%) –2.2 (3.3%) 5.6 –47.4 (−46.7)f
W-SnGa –56.3 119.6 –105.9 (60.2%) –69.9 (39.8%) –59.5 (85.1%) –8.6 (12.3%) –1.8 (2.6%) 5.8 –50.5 (−49.5)f
W-SnIn –56.7 123.3 –108.2 (60.1%) –71.9 (39.9%) –59.9 (83.3%) –9.3 (12.9%) –1.7 (2.8%) 5.7 –51.0 (−49.9)f
W-SnTl –67.1 144.3 –130.5 (61.7%) –80.9 (38.3%) –65.3 (80.7%) –12.9 (15.9%) –2.7 (3.4%) 12.9 –54.2 (−53.9)f
W-PbB –67.9 117.5 –108.2 (58.3%) –77.3 (41.7%) –69.4 (89.8%) –6.7 (8.7%) –1.2 (1.5%) 17.0 –50.9 (−50.5)f
W-PbAl –53.5 109.2 –94.8 (58.2%) –68.0 (41.8%) –58.2 (85.6%) –7.9 (11.6%) –1.9 (2.8%) 6.3 –47.2 (−46.2)f
W-PbGa –56.4 115.9 –102.7 (59.6%) –69.6 (40.4%) –60.0 (86.2%) –8.2 (11.8%) –1.4 (2.0%) 5.8 –50.6 (−49.9)f
W-PbIn –55.9 117.8 –103.3 (59.5%) –70.4 (40.5%) –60.7 (86.2%) –8.7 (12.4%) –1.0 (1.4%) 4.8 –51.1 (−49.6)f
W-PbTl –66.2 135.0 –121.6 (60.4%) –79.6 (39.6%) –65.8 (82.7%) –12.0 (15.1%) –1.8 (2.2%) 11.9 –54.3 (−52.8)f
Open in a new tab
a

The complexes were analyzed under C1 symmetry. Energy values are in kcal mol–1.

b

The total instantaneous interaction energy, ΔEint = ΔEPauli + ΔEelstat + ΔEorb.

c

The values in parentheses are the percentage contributions to the total attractive interaction, ΔEelstat + ΔEorb.

d

The values in parentheses are the percentage contributions to the total attractive interaction, ΔEelstat + ΔEorb.

e

The values in parentheses are the percentage contributions to the total orbital interaction ΔEorb = ΔEσ + ΔEπ + ΔErest.

f

The values in parentheses give the bond dissociation energy, De, at the BP86/def2-TZVPP//BP86/def2-SVP level of theory.

Schemes 2 and 3 are constructed in an attempt to illustrate the main interactions in the bondings X–Y and X–W, respectively, in W-XY complexes. The former exhibits the effects of electron stabilizing donation of the p-atomic orbital at the Y atom and π electron-sharing interactions as well as probable resonance of charge transfer between Y (Y = B–Tl) atoms of dimer (YCp*)2 and X (X = Ge, Sn, Pb) atoms of tetrylone ligands X(YCp*)2. The latter shows the orbital interaction between heavier main-group atoms X (Ge, Sn, Pb) of tetrylone ligands X(YCp*)2 and metal fragment W(CO)5 via σ- and π-donations of donor–acceptor bonding. The interactive mechanism meets the implication on the roles of main elements in the complexes proposed as the outcome of NBO calculations (Table 3), suggesting atoms W as strong electron acceptors, atoms Y as strong electron donors, and atoms X as transitional channels.

Scheme 2. Schematic View of the Chemical Bonding with Electron Stabilizing Donation of the p-Atomic Orbitals at the Y Atom, π Electron-Sharing Interactions, and Probable Resonance of Charge Transfers between Y (B–Tl) Atoms of Dimer (YCp*)2 and X (Ge, Sn, Pb) Atoms in Tetrylone Ligands X(YCp*)2.

Scheme 2

Open in a new tab

Scheme 3. Schematic Representation of the Orbital Interactions between the Heavier Main-Group Atoms X of Tetrylone Ligands X(YCp*)2 and Metal Fragment W(CO)5 with σ- and π-Donations of the Donor–Acceptor Bond in the Complexes W-XY (X = Ge, Sn, Pb and Y = B–Tl).

Scheme 3

Open in a new tab

We provide the charge transfer and energy levels to get insight into the chemical bonding in the variation of the donor–acceptor capacity in complexes between the substituted tetrylone@Group-13 ligands X(YCp*)2 and metal fragment W(CO)5. Furthermore, the orbital interaction energy, ΔEorb, of the EDA-NOCV results was additionally investigated in order to obtain more information on the nature of chemical bonding in complexes W-XY. The pairs of orbitals Ψk/Ψ–k for the most important σ- and π-orbital term contributions ΔEσ and ΔEπ and associated deformation densities Δρ characterized for bonding molecular orbitals in the representative complexes W-XY with X = Ge, Sn, Pb; Y = B, Al, T are depicted in Figures 6–9. Note that the complexes W-XGa and W-XIn demonstrate similar orbital shapes to the adducts W-XTl, so they are not shown in Figures 6–9. Bonding orbital pairs Ψk/Ψ–k are represented by red/blue colors. The blue/orange colors in the deformation densities Δρ describe the charge flow, in which the blue spaces exhibit charge depletion and the orange spaces present charge accumulation; ΔE and Δρ are included under each simulation model.

Figure 6.

Figure 6

Open in a new tab

Representative of NOCV pair, Ψ–1; Ψ1, with the eigenvalue, −υ1; υ1, in parentheses, and density deformation contour channel blue → orange, Δρ1, and orbital stabilization energy, ΔEkorb (kcal mol–1), describing the σ interaction of W(CO)5 ↔ X(YCp*)2 (X = Ge, Sn, Pb; Y = B, Al and Tl) at the BP86/TZ2P+ level: (a1) W-GeB, (a2) W-GeAl, (a3) W-GeTl; (b1) W-SnB, (b2) W-SnAl, (b3) W-SnTl; (c1) W-PbB, (c2) W-PbAl, (c3) W-PbTl.

Figure 9.

Figure 9

Open in a new tab

Contours plots of the representative π-types of NOCV interaction for thallium complexes W-XTl: (a1) W-GeTl, (a2) W-GeTl; (b1) W-SnTl, (b2) W-SnTl; (c1) W-PbTl, (c2) W-PbTl. The NOCV pairs, Ψ–k; Ψk (k = 2, 3), with the eigenvalues, −υk; υk, in parentheses and deformation densities blue → orange, Δρk, and orbital stabilization energies, ΔEkorb (kcal mol–1), were selected to describe the π interactions of W(CO)5 ↔ X(TlCp*)2 (X = Ge, Sn, Pb) at the BP86/TZ2P+ level.

Figure 6 displays the NOCV pairs Ψ1/Ψ–1 and the deformation densities Δρ1 of the most significant pairs of σ-molecular orbitals for ΔEσ in W-XY. Overall, the values of Δρσ1 are approximately 80% of the total energy ΔEσ (Table 6), which are from −59.2 to −68.5 kcal mol–1 for W-XB, from −49.8 to −57.6 kcal mol–1 for W-XAl, and from −63.4 to −64.9 kcal mol–1 for W-XTl. These are significantly higher than those of π molecular orbitals, which will be discussed later.

Therefore, the orbital pairs Ψ1/Ψ–1 can be considered as the dominant sources contributing to σ-bonding for the tetrylone ligands X(YCp*)2 in the three series W-XY. Also, the deformation density depicted reveals the charge flow in the molecular orbital from the donor atom X to the acceptor atom W. This confirms the direction of the σ-bond from the tetrylone ligand to the metal fragment (CO)5W ← X(YCp*)2 achieved by NBO analysis (Table 3).

Despite the fact that the contributions of the π stabilization ΔEπ is smaller than those of the σ-stabilization ΔEσ in the three families W-XY, their values of energy level are restrictedly lower than 10 kcal mol–1. The π energy in tetrylone complexes exhibits a significant contribution, which is shown by the shape of the molecular orbitals and charge transfer processes. Figures 7–9 illustrate the complementary NOCV pairs (Ψ2/Ψ–2 or Ψ3/Ψ–3) and the deformation densities (Δρk ; k = 2, 3) characterized for the most significant pairs of π molecular orbitals for ΔEπ in W-XY. It clearly shows that the π-lone-pair donation from the tetrylone ligands to the metal fragment W(CO)5 is very weak in terms of bonding energy. As those structural discussions mentioned above about the geometrically optimized structures of the complexes investigated W-XY (Figure 1 and Table 1), the tetrylone ligands XY bind to metal fragment W(CO)5 in a side-on mode conducive to π-type hybridization from the π-lone-pair orbital of the tetrylones@Group-13 ligands X(YCp*)2 into the second vacant coordination side of W(CO)5 in complexes W-XY, so the shape of NOCV orbitals was vizualized in order to answer a question that concerns the strength of the π ligand–metal fragment donation. In detail, the figures for W-XB, W-XAl, and W-XTl vary between −1.6 and −2.8, −1.9 and −3.4, and −5.3 and −12.5 kcal mol–1, respectively. This implies the geometrical structure of significance to the π molecular orbitals. In addition, the complexes experienced irregular patterns of charge flow in their π-bonding orbitals. The weak π-style orbital interactions in W-XY stem from either π-donation (CO)5W ← X(YCp*)2, or π-backdonation (CO)5W → X(YCp*)2, or partly each of the types. The contributing patterns depend on X and Y.

Figure 7.

Figure 7

Open in a new tab

Contour plots of the representative π-types of NOCV interaction for boron complexes W-XB: (a1) W-GeB, (a2) W-GeB; (b1) W-SnB, (b2) W-SnB; (c1) W-PbB, (c2) W-PbB. The NOCV pairs, Ψ–k; Ψk (k = 2, 3), with the eigenvalues, −υk; υk, in parentheses, and deformation densities blue → orange, Δρk, and orbital stabilization energies, ΔEkorb (kcal mol–1), were selected to describe the π interactions of W(CO)5 ↔ X(BCp*)2 (X = Ge, Sn, Pb) at the BP86/TZ2P+ level.

Figure 7 presents the corresponding deformation densities of W-XB with X = Ge, Sn, Pb in which the shape of the NOCV pairs Ψk/Ψ–k and the deformation densities clearly reveal the charge flow Δρk (k = 2, 3). We found that the energy stabilizations are −2.8 and −2.3 kcal mol–1 for germylone@boron W-GeB, −2.2. and −2.1 kcal mol–1 for W-SnB, and −1.7 and −1.6 kcal mol–1 for W-PbB, which mostly come from the relaxation of the metal fragment W(CO)5. Thus, it clearly shows that the π-lone-pair donation from the tetrylone ligands to the metal fragment W(CO)5 is very weak. Figure 8 lists the NOCV pairs for tetrylone@aluminum complexes W-XAl with X = Ge, Sn, Pb, and a comparison is made to get a detailed view of the NOCV shapes between tetrylone@aluminum and tetrylone@boron, which has the π-backdonation from atom W to X in a significant difference. The deformation density Δρπ2,3 exhibits that the weak π-style orbital interactions in W-XAl result not only from typical weak π-donation, (CO)5W ← X(AlCp*)2 but also from π-backdonation, (CO)5W → X(AlCp*)2, where the charge flow Δρπ2,3 shows energy stabilizations of −3.4 and −2.6 kcal mol–1 for germylone@aluminum W-GeAl; –2.6 and −2.2 kcal mol–1 for stannylone@aluminum W-SnAl, and −2.2 and −1.9 kcal mol–1 for plumbylone@aluminum W-PbAl.

Figure 8.

Figure 8

Open in a new tab

Contours plots of the representative π-types of NOCV interaction for aluminum complexes W-XAl: (a1) W-GeAl, (a2) W-GeAl; (b1) W-SnAl, (b2) W-SnAl; (c1) W-PbAl, (c2) W-PbAl. The NOCV pairs, Ψ–k; Ψk (k = 2, 3), with the eigenvalues, −υk; υk, in parentheses, and deformation densities blue → orange, Δρk, and orbital stabilization energies, ΔEkorb (kcal mol–1), were selected to describe the π interactions of W(CO)5 ↔ X(AlCp*)2 (X = Ge, Sn, Pb) at the BP86/TZ2P+ level.

Interestingly, the π interaction energy values ΔEπ of tetrylone@thallium complexes W-XTl given in Figure 9 are larger than those of tetrylone@boron W-XB and tetrylone@aluminum W-XAl. In detail, the germylone complex W-GeTl has the largest values (ΔEπ2 = −12.5 kcal mol–1; ΔEπ3 = −9.5 kcal mol–1), while the plumbylone complex W-PbTl exhibits the smallest values (ΔEπ2 = −5.4 kcal mol–1; ΔEπ3 = −5.3 kcal mol–1). Note that the shapes of the NOCV pairs Ψk/Ψ–k and the deformation density Δρk (k = 2, 3) in Figure 9 also show the weak π-type orbital interactions in tetrylone@thallium complexes W-XTl with the charge flow mainly coming from typical π-backdonation (CO)5W → X(TlCp*)2. It can be realized that the tetrylone ligands XY have two lone-pair orbitals, but they can use their π-lone-pair electrons for donor–acceptor interactions in the side-on complexes. We found a rationale for the stronger bonding of the ligands XY provided by the calculated values for ΔEσ and electrostatics attraction ΔEelstat, which is shown in the increase of the donation (CO)5W ← X(YCp*)2 when Y becomes heavier.

Conclusions

This study provides a comprehensive overview of the structures, chemical bonding, and properties in transition-metal complexes of divalent ylidone(0) ligands (CO)5W-X(YCp*)2 in which X = Ge, Sn, Pb and Y = B–Tl.

  • (a)

    Analysis on the geometrical structure reveals the main bonding configurations in the complexes, summarized as follows: (i) The ylidone(0) ligands XY in the complexes W-XY are bonded in a tilted orientation relative to the metal fragment W(CO)5; (ii) Cp* rings are mainly η5-bonded to Group-14 atoms (B-Tl).

  • (b)

    Investigation using DFT yields information on quantum parameters of the tetrylones and speculation for the main bonding properties, including the following: (iii) BDEs of the complex in each tetrylone family vary differently regarding the change of relative molecular mass. The energy orders of germylones, stannylones, and plumbylones are W-GeTl > W-GeIn > W-GeGa > W-GeAl > W-GeB, W-SnTl > W-SnIn > W-XGa > W-SnB > W-SnAl, and W-PbTl > W-PbB > W-PbGa > W-PbIn > W-PbAl, respectively; (iv) dispersion interactions considered as the effect of bulky ligands play an important role in the calculation of the total BDEs, accounting for ca. 20–30% of DFT-D3 values; (v) the bond W–X is inclined to polarize toward atom X, and the analysis on its hybridization suggests that borane systems W-GeB, W-SnB, and W-PbB contain sp2-characteristic W–X bonding while heavier homologues exhibit mainly p-characteristic configurations; (vi) bonding analysis speculates that the electron donation accords with the direction (CO)5W ← X(YCp*)2 formed by both σ- and π-types.

  • (c)

    EDA-NOCV calculations provide information on in-depth chemical bonding interactions and further confirm bonding suggestions speculated from DFT results, embracing the following: (vii) The values of De obtained from EDA-NOCV and DFT-De analyses are in good consistency; (viii) given attractive electrostatic interaction ΔEelstat and orbital interaction energy ΔEorb, the bond W–X stability overall accords with the sequence W-XTl > W-XIn > W-XGa > W-XAl > W-XB; (ix) EDA-NOCV calculations imply that the tendency of W–X bond strength in complexes came from the change of W(CO)5 ← X(YCp*)2 donation and electrostatic attraction. This also includes the additional weak π-style orbital interactions in W-XY stemming from either π-donation (CO)5W ← X(YCp*)2, or π-backdonation (CO)5W → X(YCp*)2, or partly each of the types; (x) the depictions for NOCV pairs Ψk/Ψ–k and the deformation densities Δρk illustrate a comprehensive overview of different components of the chemical bond via σ- and π-types in complexes W-XY.

Methods

Optimization of the Structure and Energy

Geometrical structures of the molecules were optimized by a combination of Gaussian 0940 and Turbomole 7.041 at the level of theory BP8642,43/def2-SVP44 without using symmetric constraints. The stationary points of molecules corresponding to the structures in global energetic minima on the potential energy surfaces (PES) were determined by vibrational frequency calculations. Single-point energy calculations with the same functional but a larger basis set def2-TZVPP45 were examined with the frozen-core approximation for non-valence-shell electrons. Small-core quasi-relativistic effective core potentials (ECPs) were applied46,47 for the heavier Group-14 atoms Sn and Pb and the heavier Group-13 atoms In and Tl. Resolution-of-identity (RI) approximation was used for all structure optimizations using the appropriate auxiliary basis sets.

Bonding Analysis

The BP86 functional in DFT calculations in conjunction with the def2-TZVPP45 basis set at BP86/def2-SVP level was used to calculate Wiberg bond indices (WBI), natural partial atomic (NPA) charges, and single-point energies (SPEs) using natural bond orbital methods.48 These were carried out on the NBO program version 5.1. The bond dissociation energy (BDE), De (kcal mol–1), was derived from the obtained SPE values. The effects of dispersion interactions on the calculated bond dissociation energies were estimated under the D3 dispersion corrections, suggested by Grimme’s DFT-D3 approximation.35,36 The influence of the ylidone(0) ligands X(YCp*)2 with X = Ge, Sn, Pb and Y = B–Tl on the BDEs to the intrinsic bond strength under the consideration of interactions in complexes with and without dispersion corrections was determined at the level of theory BP86/def2-TZVPP//BP86/def2-SVP. Also, HOMO energy (EHOMO) and LUMO energy (ELUMO) were calculated, and their electron density distributions were illustrated. Energy gap ΔE = ELUMO – EHOMO provides information on the reactivity tendency of inhibition efficiency of organic molecules toward the surface of metal elements. Ionization potential (I) and electron affinity (A) of inhibitory molecules were calculated by the application of Koopmans’ theorem49 related to HOMO and LUMO energies as I = −EHOMO and A = −ELUMO. The value of electronegativity (χ) was obtained by the following equation: χ = (I + A)/2.

The nature of chemical bonding for complexes was verified by further investigation using energy decomposition analysis (EDA)50−52 and charge of natural orbitals for chemical valence (NOCV)53,54 method. These were obtained via calculations with no restrictions at the relativistic DFT framework using the Amsterdam Density Functional (ADF)55 program package 2018.01. The level BP86 in conjunction was applied with a triple-zeta-quality basis set TZ2P+ using uncontracted Slater-type orbitals (STOs) augmented by two sets of polarization functions, with a frozen-core approximation for the core electrons.56 A standard triple-ξ basis set was employed for the heavier Group-14 elements Sn and Pb and the heavier Group-13 atoms In and Tl. 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.57 Scalar relativistic effects were incorporated by applying the zeroth-order regular approximation (ZORA).58 The BP86/TZ2P+ level using BP86/def2-SVP-optimized geometries was carried out to examine the nature of the W–XY bonds in complexes W-XY using the EDA-NOCV method under C1 symmetric geometries.

The EDA-NOCV scheme divides the total instantaneous interaction energy ΔEint into three main components: Pauli repulsion ΔEPauli, electrostatic interaction ΔEelstat, and total orbital interaction ΔEorb. This is expressed in eq 1.

graphic file with name ao0c03237_m001.jpg 1

The bond dissociation energy ΔE (= −De) is obtained by considering simultaneously the total instantaneous interaction energy ΔEint and the preparation energy ΔEprep, which gives the relaxation of the fragments into their equilibrium geometries in the electronic ground state to the geometries and electronic reference. The energy is achievable through eq 2.

graphic file with name ao0c03237_m002.jpg 2

In the EDA-NOCV analysis, the orbital interaction energy ΔEorb of the interacting fragments orbitals, forming the deformation density, which is associated with the bond formation, Δρorb, into different components of the chemical bond is given by eq 3. −F–k, – kTS and Fk, k are diagonal Kohn–Sham matrix elements corresponding to natural orbitals for chemical valence with the eigenvalues, equalized with a sum of pairs of complementary orbitals (Ψ–k, Ψk) and eigenvalues equal in absolute value and eigenvector of the valence operator (υ). They provide an expression for orbital interaction and estimate its symmetry, direction of the charge flow, and energetic contribution to the total orbital interaction (ΔEorb). This information is assigned by visual inspection to simulate the shape of the deformation density, Δρk. The function for the visualization is expressed in eq 4.

graphic file with name ao0c03237_m003.jpg 3
graphic file with name ao0c03237_m004.jpg 4

Acknowledgments

N.T.A.N. thanks Prof. Dr. Gernot Frenking for allowing the continuous use of her own resources within Frenking’s group. The program used in the studies was run via the Annemarie cluster operated by Reuti (Thomas Reuter) at the Philipps-Universität Marburg, Germany. This research is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 104.06-2017.303.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.0c03237.

  • Cartesian coordinates and SCF energies from the systems at the BP86/def2-SVP level of theory (PDF)

The authors declare no competing financial interest.

Supplementary Material

ao0c03237_si_001.pdf (221.8KB, pdf)

References

  1. Nguyen T. A. N.; Frenking G. Transition-Metal Complexes of Tetrylones [(CO)5W-E (PPh3)2] and Tetrylenes [(CO)5W-NHE](E= C–Pb): A Theoretical Study. Chem. – Eur. J. 2012, 18, 12733–12748. 10.1002/chem.201200741. [DOI] [PubMed] [Google Scholar]
  2. Frenking G.; Tonner R.; Klein S.; Takagi N.; Shimizu T.; Krapp A.; Pandey K. K.; Parameswaran P. New bonding modes of carbon and heavier group 14 atoms Si–Pb. Chem. Soc. Rev. 2014, 43, 5106–5139. 10.1039/C4CS00073K. [DOI] [PubMed] [Google Scholar]
  3. Tonner R.; Öxler F.; Neumüller B.; Petz W.; Frenking G. Carbodiphosphoranes: the chemistry of divalent carbon (0). Angew. Chem., Int. Ed. 2006, 45, 8038–8042. 10.1002/anie.200602552. [DOI] [PubMed] [Google Scholar]
  4. Frenking G.; Hermann M.; Andrada D. M.; Holzmann N. Donor–acceptor bonding in novel low-coordinated compounds of boron and group-14 atoms C–Sn. Chem. Soc. Rev. 2016, 45, 1129–1144. 10.1039/C5CS00815H. [DOI] [PubMed] [Google Scholar]
  5. Kuwabara T.; Nakada M.; Hamada J.; Guo J. D.; Nagase S.; Saito M. (η4-Butadiene) Sn (0) Complexes: A New Approach for Zero-Valent p-Block Elements Utilizing a Butadiene as a 4π-Electron Donor. J. Am. Chem. Soc. 2016, 138, 11378–11382. 10.1021/jacs.6b07304. [DOI] [PubMed] [Google Scholar]
  6. Mondal K. C.; Roesky H. W.; Schwarzer M. C.; Frenking G.; Niepötter B.; Wolf H.; Herbst-Irmer R.; Stalke D. A stable singlet biradicaloid siladicarbene:(L:)2Si. Angew. Chem., Int. Ed. 2013, 52, 2963–2967. 10.1002/anie.201208307. [DOI] [PubMed] [Google Scholar]
  7. Li Y.; Mondal K. C.; Roesky H. W.; Zhu H.; Stollberg P.; Herbst-Irmer R.; Stalke D.; Andrada D. M. Acyclic germylones: congeners of allenes with a central germanium atom. J. Am. Chem. Soc. 2013, 135, 12422–12428. 10.1021/ja406112u. [DOI] [PubMed] [Google Scholar]
  8. Xiong Y.; Yao S.; Tan G.; Inoue S.; Driess M. A cyclic germadicarbene (“Germylone”) from germyliumylidene. J. Am. Chem. Soc. 2013, 135, 5004–5007. 10.1021/ja402477w. [DOI] [PubMed] [Google Scholar]
  9. Chu T.; Belding L.; van der Est A.; Dudding T.; Korobkov I.; Nikonov G. I. A Coordination Compound of Ge0 Stabilized by a Diiminopyridine Ligand. Angew. Chem., Int. Ed. 2014, 53, 2711–2715. 10.1002/anie.201309421. [DOI] [PubMed] [Google Scholar]
  10. Flock J.; Suljanovic A.; Torvisco A.; Schoefberger W.; Gerke B.; Pöttgen R.; Fischer R. C.; Flock M. The Role of 2, 6-Diaminopyridine Ligands in the Isolation of an Unprecedented, Low-Valent Tin Complex. Chem. – Eur. J. 2013, 19, 15504–15517. 10.1002/chem.201301340. [DOI] [PubMed] [Google Scholar]
  11. Andrada D. M.; Holzmann N.; Frenking G. Bonding analysis of ylidone complexes EL2 (E= C–Pb) with phosphine and carbene ligands L. Can. J. Chem. 2016, 94, 1006–1014. 10.1139/cjc-2016-0263. [DOI] [Google Scholar]
  12. Patel D. S.; Bharatam P. V. To bend or not to bend! The dilemma of allenes. J. Org. Chem. 2011, 76, 2558–2567. 10.1021/jo102432a. [DOI] [PubMed] [Google Scholar]
  13. Koput J. An ab initio study on the equilibrium structure and CCC bending energy levels of carbon suboxide. Chem. Phys. Lett. 2000, 320, 237–244. 10.1016/S0009-2614(00)00237-2. [DOI] [Google Scholar]
  14. Nguyen T. A. N.; Frenking G. Structure and bonding of tetrylone complexes [(CO) 4W {E (PPh3) 2}](E= C–Pb). Mol. Phys. 2013, 111, 2640–2646. 10.1080/00268976.2013.813593. [DOI] [Google Scholar]
  15. Jutzi P.; Reumann G. Cp* Chemistry of main-group elements. J. Chem. Soc 2000, 14, 2237–2244. [Google Scholar]
  16. Budzelaar P. H.; Engelberts J. J.; van Lenthe J. H. Trends in cyclopentadienyl– main-group-metal bonding. Organometallics 2003, 22, 1562–1576. 10.1021/om020928v. [DOI] [Google Scholar]
  17. Jutzi P.; Burford N. Structurally diverse π-cyclopentadienyl complexes of the main group elements. Chem. Rev. 1999, 99, 969–990. 10.1021/cr941099t. [DOI] [PubMed] [Google Scholar]
  18. Weiss D.; Steinke T.; Winter M.; Fischer R. A.; Fröhlich N.; Uddin J.; Frenking G. [(dcpe) Pt (ECp*) 2](E= Al, Ga): Synthesis, Structure, and Bonding Situation of the First Aluminum (I) and Gallium (I) Complexes of Phosphine-Substituted Transition Metal Centers. Organometallics 2000, 19, 4583–4588. 10.1021/om000310q. [DOI] [Google Scholar]
  19. Jutzi P.; Neumann B.; Schebaum L. O.; Stammler A.; Stammler H.-G. Unexpected Reactivity of Cp* Ga toward Fe– Cl Bonds: Synthesis and Structure of Cp*(Cp* Ga) 2FeGaCl2⊙ THF and of Cp*(CO) 2FeGa (η2-Cp*) Cl. Organometallics 2000, 19, 1445–1447. 10.1021/om990940w. [DOI] [Google Scholar]
  20. Murugavel R.; Chandrasekhar V. Monovalent Group 13 Organometallic Compounds: Weak Association to Monomeric, Versatile Two-Electron Donors. Angew. Chem., Int. Ed. 1999, 38, 1211–1215. . [DOI] [PubMed] [Google Scholar]
  21. Uhl W. Organoelement compounds possessing Al-Al, Ga-Ga, In-In, and Tl-Tl single bonds. Adv. Organomet. Chem. 2004, 51, 53–108. 10.1016/S0065-3055(03)51002-4. [DOI] [Google Scholar]
  22. Fischer R. A.; Weiß J. Coordination chemistry of aluminum, gallium, and indium at transition metals. Angew. Chem., Int. Ed. 1999, 38, 2830–2850. . [DOI] [PubMed] [Google Scholar]
  23. Dohmeier C.; Loos D.; Schnöckel H. Aluminum (I) and gallium (I) compounds: syntheses, structures, and reactions. Angew. Chem., Int. Ed. 1996, 35, 129–149. 10.1002/anie.199601291. [DOI] [Google Scholar]
  24. Nguyen T. A. N.; Huynh T. P. L.; Tran T. H.; Pham V. T.; Duong T. Q.; Dang T. H. Structures and Bonding Situation of Iron Complexes of Group-13 Half-Sandwich ECp*(E= B to Tl) Based on DFT Calculations. Z. Anorg. Allg. Chem. 2016, 642, 609–617. 10.1002/zaac.201600104. [DOI] [Google Scholar]
  25. Roesky P. W. Compounds with low-valent group 13 metals as ligands for electron poor main group and transition metals. Dalton Trans. 2009, 11, 1887–1893. 10.1039/B816377D. [DOI] [PubMed] [Google Scholar]
  26. Asay M.; Jones C.; Driess M. N-Heterocyclic carbene analogues with low-valent group 13 and group 14 elements: syntheses, structures, and reactivities of a new generation of multitalented ligands. Chem. Rev. 2011, 111, 354–396. 10.1021/cr100216y. [DOI] [PubMed] [Google Scholar]
  27. Klein S.; Frenking G. Carbodiylides C(ECp*)2 (E= B–Tl): another class of theoretically predicted divalent carbon (0) compounds. Angew. Chem., Int. Ed. 2010, 49, 7106–7110. 10.1002/anie.201002773. [DOI] [PubMed] [Google Scholar]
  28. Mondal S.; Osorio E.; Pan S.; Cabellos J. L.; Martínez S.; Florez E.; Merino G. Why CpAl–Cr(CO)5 is linear while CpIn–Cr(CO)5 is not? Understanding the structure and bonding of the CpE–Cr(CO)5 (E = Group 13 element) complexes. Theor. Chem. Acc. 2016, 135, 240. 10.1007/s00214-016-1993-7. [DOI] [Google Scholar]
  29. Schulz S.; Kuczkowski A.; Schuchmann D.; Flörke U.; Nieger M. Group 13– Group 13 Donor– Acceptor Complexes. Organometallics 2006, 25, 5487–5491. 10.1021/om0606946. [DOI] [Google Scholar]
  30. González-Gallardo S.; Bollermann T.; Fischer R. A.; Murugavel R. Cyclopentadiene based low-valent group 13 metal compounds: ligands in coordination chemistry and link between metal rich molecules and intermetallic materials. Chem. Rev. 2012, 112, 3136–3170. 10.1021/cr2001146. [DOI] [PubMed] [Google Scholar]
  31. Loan H. T. P.; Van Duc H.; Quang D. T.; Van Tat P.; Hiep D. T.; Nhung N. T. A. Theoretically predicted divalent silicon (0) compounds: Structures and chemical bonding of silylone in molybdenum pentacarbonyl complexes [Mo(CO)5-Si(XCp*)2](X= B–Tl). Comput. Theor. Chem. 2018, 1131, 13–24. 10.1016/j.comptc.2018.03.021. [DOI] [Google Scholar]
  32. Frenking G.; Wichmann K.; Fröhlich N.; Grobe J.; Golla W.; Van D. L.; Krebs B.; Läge M. Nature of the Metal– Ligand Bond in M (CO) 5PX3 Complexes (M= Cr, Mo, W; X= H, Me, F, Cl): Synthesis, Molecular Structure, and Quantum-Chemical Calculations. Organometallics 2002, 21, 2921–2930. 10.1021/om020311d. [DOI] [Google Scholar]
  33. Fischer R. A.; Schulte M. M.; Weiss J.; Zsolnai L.; Jacobi A.; Huttner G.; Frenking G.; Boehme C.; Vyboishchikov S. F. Transition Metal Coordinated Al(X)L2 and Ga (X)L2 Fragments. J. Am. Chem. Soc. 1998, 120, 1237–1248. 10.1021/ja9716463. [DOI] [Google Scholar]
  34. Pidun U.; Frenking G. Theoretical Studies of Organometallic Compounds. XIX. Complexes of Transition Metals in High and Low Oxidation States with Side-On-Bonded. pi.-Ligands. Organometallics 1995, 14, 5325–5336. 10.1021/om00011a058. [DOI] [Google Scholar]
  35. Grimme S.; Antony J.; Ehrlich S.; Krieg H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 2010, 132, 154104. 10.1063/1.3382344. [DOI] [PubMed] [Google Scholar]
  36. Grimme S.; Ehrlich S.; Goerigk L. Effect of the damping function in dispersion corrected density functional theory. J. Comput. Chem. 2011, 32, 1456–1465. 10.1002/jcc.21759. [DOI] [PubMed] [Google Scholar]
  37. Goerigk L.; Grimme S. A thorough benchmark of density functional methods for general main group thermochemistry, kinetics, and noncovalent interactions. Phys. Chem. Chem. Phys. 2011, 13, 6670–6688. 10.1039/c0cp02984j. [DOI] [PubMed] [Google Scholar]
  38. Nguyen T. A. N.; Tran D. S.; Huynh T. P. L.; Le T. H.; Duong T. Q.; Nguyen T. T.; Vo T. C.; Pham V. T.; Dang T. H. Can tetrylone act in a similar fashion to tetrylene in Ni (CO)2 complexes? a theoretical study based on a comparison using DFT calculations. Z. Anorg. Allg. Chem. 2017, 643, 826–838. 10.1002/zaac.201700093. [DOI] [Google Scholar]
  39. Takagi N.; Shimizu T.; Frenking G. Divalent E (0) Compounds (E= Si–Sn). Chem. – Eur. J. 2009, 15, 8593–8604. 10.1002/chem.200901401. [DOI] [PubMed] [Google Scholar]
  40. Frisch M. J.; Trucks G. W.; Schlegel H. B.; Scuseria G. E.; Robb M. A.; Cheeseman J. R.; Scalmani G.; Barone V.; Mennucci B.; Petersson G. A.; Nakatsuji H.; Caricato M.; Li X.; Hratchian H. P.; Izmaylov A. F.; Bloino J.; Zheng G.; Sonnenberg J. L.; Hada M.; Ehara M.; Toyota K.; Fukuda R.; Hasegawa J.; Ishida M.; Nakajima T.; Honda Y.; Kitao O.; Nakai H.; Vreven T.; Montgomery J. J. A.; Peralta J. E.; Ogliaro F.; Bearpark M.; Heyd J. J.; Brothers E.; Kudin K. N.; Staroverov V. N.; Kobayashi R.; Normand J.; Raghavachari K.; Rendell A.; Burant J. C.; Iyengar S. S.; Tomasi J.; Cossi M.; Rega N.; Millam J. M.; Klene M.; Knox J. E.; Cross J. B.; Bakken V.; Adamo C.; Jaramillo J.; Gomperts R.; Stratmann R. E.; Yazyev O.; Austin A. J.; Cammi R.; Pomelli C.; Ochterski J. W.; Martin R. L.; Morokuma K.; Zakrzewski V. G.; Voth G. A.; Salvador P.; Dannenberg J. J.; Dapprich S.; Daniels A. D.; Farkas F. J. B.; Ortiz J. V.; Cioslowski J.; Fox D. J.. Gaussian 09, Revision A.1, Gaussian Inc, Wallingford CT. 2009
  41. Ahlrichs R.; Bär M.; Häser M.; Horn H.; Kölmel C. Electronic structure calculations on workstation computers: The program system turbomole. Chem. Phys. Lett. 1989, 162, 165–169. 10.1016/0009-2614(89)85118-8. [DOI] [Google Scholar]
  42. Perdew J. P.; Yue W. Accurate and simple density functional for the electronic exchange energy: Generalized gradient approximation. Phys. Rev. B 1986, 33, 8800. 10.1103/PhysRevB.33.8800. [DOI] [PubMed] [Google Scholar]
  43. Becke A. D. Density-functional exchange-energy approximation with correct asymptotic behavior. Phys. Rev. A 1988, 38, 3098. 10.1103/PhysRevA.38.3098. [DOI] [PubMed] [Google Scholar]
  44. Schäfer A.; Horn H.; Ahlrichs R. Fully optimized contracted Gaussian basis sets for atoms Li to Kr. J. Chem. Phys. 1992, 97, 2571–2577. 10.1063/1.463096. [DOI] [Google Scholar]
  45. Weigend F.; Ahlrichs R. Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy. Phys. Chem. Chem. Phys. 2005, 7, 3297–3305. 10.1039/b508541a. [DOI] [PubMed] [Google Scholar]
  46. Metz B.; Stoll H.; Dolg M. Small-core multiconfiguration-Dirac–Hartree–Fock-adjusted pseudopotentials for post-d main group elements: Application to PbH and PbO. J. Chem. Phys. 2000, 113, 2563–2569. 10.1063/1.1305880. [DOI] [Google Scholar]
  47. Andrae D.; Häußermann U.; Dolg M.; Stoll H.; Preuß H. Energy-adjustedab initio pseudopotentials for the second and third row transition elements. Theor. Chim. Acta 1990, 77, 123–141. 10.1007/BF01114537. [DOI] [Google Scholar]
  48. Reed A. E.; Weinstock R. B.; Weinhold F. Natural population analysis. J. Chem. Phys. 1985, 83, 735–746. 10.1063/1.449486. [DOI] [Google Scholar]
  49. Lukovits I.; Kálmán E.; Zucchi F. Corrosion inhibitors—correlation between electronic structure and efficiency. Corrosion 2001, 57, 3–8. 10.5006/1.3290328. [DOI] [Google Scholar]
  50. Morokuma K. Molecular orbital studies of hydrogen bonds. III. C= O··· H–O hydrogen bond in H2CO··· H2O and H2CO··· 2H2O. J. Chem. Phys. 1971, 55, 1236–1244. 10.1063/1.1676210. [DOI] [Google Scholar]
  51. Ziegler T.; Rauk A. On the calculation of bonding energies by the Hartree Fock Slater method. Theor. Chim. Acta 1977, 46, 1–10. 10.1007/BF02401406. [DOI] [Google Scholar]
  52. Zhao L.; von Hopffgarten M.; Andrada D. M.; Frenking G. Energy decomposition analysis. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2018, 8, e1345. [Google Scholar]
  53. Mitoraj M.; Michalak A. Applications of natural orbitals for chemical valence in a description of bonding in conjugated molecules. J. Mol. Model. 2008, 14, 681–687. 10.1007/s00894-008-0276-1. [DOI] [PubMed] [Google Scholar]
  54. Mitoraj M. P.; Michalak A.; Ziegler T. A combined charge and energy decomposition scheme for bond analysis. J. Chem. Theory Comput. 2009, 5, 962–975. 10.1021/ct800503d. [DOI] [PubMed] [Google Scholar]
  55. Te Velde G. T.; Bickelhaupt F. M.; Baerends E. J.; Fonseca Guerra C.; van Gisbergen S. J.; Snijders J. G.; Ziegler T. Chemistry with ADF. J. Comput. Chem. 2001, 22, 931–967. 10.1002/jcc.1056. [DOI] [Google Scholar]
  56. Snijders J. G.; Vernooijs P.; Baerends E. J. Roothaan-Hartree-Fock-Slater atomic wave functions: single-zeta, double-zeta, and extended Slater-type basis sets for 87Fr-103Lr. At. Data Nucl. Data Tables 1981, 26, 483–509. 10.1016/0092-640X(81)90004-8. [DOI] [Google Scholar]
  57. Krijn J.; Baerends E. J., Fit Functions in the HFS-Method: Internal Report ;Vrije Universiteit Amsterdam: The Netherlands, 1984. [Google Scholar]
  58. van Lenthe E.; Ehlers A.; Baerends E.-J. Geometry optimizations in the zero order regular approximation for relativistic effects. J. Chem. Phys. 1999, 110, 8943–8953. 10.1063/1.478813. [DOI] [Google Scholar]

Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

ao0c03237_si_001.pdf (221.8KB, pdf)

Articles from ACS Omega are provided here courtesy of American Chemical Society

RESOURCES