Real-Space Bonding Indicator Analysis of the Donor–Acceptor

Article pubs.acs.org/JPCA

Real-Space Bonding Indicator Analysis of the Donor−Acceptor Complexes X3BNY3, X3AlNY3, X3BPY3, and X3AlPY3 (X, Y = H, Me, Cl) Stefan Mebs*,† and Jens Beckmann*,‡ †

Institut für Experimentalphysik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany Institut für Anorganische Chemie und Kristallographie, Universität Bremen, Leobener Straße 7, 28359 Bremen, Germany

‡

S Supporting Information *

ABSTRACT: Calculations of real-space bonding indicators (RSBI) derived from Atoms-In-Molecules (AIM), Electron Localizability Indicator (ELI-D), Non-Covalent Interactions index (NCI), and Density Overlap Regions Indicator (DORI) toolkits for a set of 36 donor−acceptor complexes X3BNY3 (1, 1a−1h), X3AlNY3 (2, 2a−2h), X3BPY3 (3, 3a−3h), and X3AlPY3 (4, 4a−4h) reveal that the donor−acceptor bonds comprise covalent and ionic interactions in varying extents (X = Y = H for 1−4; X = H, Y = Me for 1a−4a; X = H, Y = Cl for 1b−4b; X = Me, Y = H for 1c−4c; X, Y = Me for 1d−4d; X = Me, Y = Cl for 1e−4e; X = Cl, Y = H for 1f−4f; X = Cl, Y = Me for 1g−4g; X, Y = Cl for 1h−4h). The phosphinoboranes X3BPY3 (3, 3a−3h) in general and Cl3BPMe3 (3f) in particular show the largest covalent contributions and the least ionic contributions. The aminoalanes X3AlNY3 (2, 2a−2h) in general and Me3AlNCl3 (2e) in particular show the least covalent contributions and the largest ionic contributions. The aminoboranes X3BNY3 (1, 1a−1h) and the phosphinoalanes X3AlPY3 (4, 4a−4h) are midway between phosphinoboranes and aminoalanes. The degree of covalency and ionicity correlates with the electronegativity difference BP (ΔEN = 0.15) < AlP (ΔEN = 0.58) < BN (ΔEN = 1.00) < AlN (ΔEN = 1.43) and a previously published energy decomposition analysis (EDA). To illustrate the importance of both contributions in Lewis formula representations, two resonance formulas should be given for all compounds, namely, the canonical form with formal charges denoting covalency and the arrow notation pointing from the donor to the acceptor atom to emphasis ionicity. If the Lewis formula mainly serves to show the atomic connectivity, the most significant should be shown. Thus, it is legitimate to present aminoalanes using arrows; however, for phosphinoboranes the canonical form with formal charges is more appropriate.

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INTRODUCTION Borane-amine, H3BNH3 (1), a potential candidate for chemical hydrogen storage,1 comprises a prototypical Lewis pair complex between two main group compounds.2 Upon dissociation, H3BNH3 (1) undergoes heterolytical B−N bond cleavage into the electron pair acceptor BH3 (the Lewis acid) and the electron pair donor NH3 (the Lewis base).2 By contrast, in the isoelectronic ethane, H3CCH3, the C−C bond dissociates homolytically into two •CH3 radicals. In Lewis formula representations, Lewis pair complexes between main group compounds are often drawn with an arrow pointing from the electron pair donor to the acceptor, regardless of the nature of the bonds.2 The extensive use of the arrow notation has been scrutinized in a recent assay.3 It has been argued that strong covalent donor−acceptor bonds, often observed between phosphines or N-heterocyclic carbenes (NHCs) and low-valent and/or cationic main group fragments, might be better described by canonical Lewis formula using straight lines and formal charges. This assay has led to a vivid debate about the validity of the arrow notation that has not been settled with a generally accepted agreement.4−9 For donor−acceptor complexes of the general type X3ADY3 (acceptor A = B, Al; donor D = N, P; substituents X, Y = H, Me, Cl), the two opponent resonance structures are shown in Scheme 1. © XXXX American Chemical Society

Scheme 1. Lewis Formula Representations for Donor− Acceptor Complexes of the Type X3ADY3 (Acceptor A = B, Al; Donor D = N, P; Substituents X, Y = H, Me, Cl)

Donor−acceptor bonds may be distinguished by their bond polarity and classified as ionic, covalent, or in between those extremes on a relative scale, polar covalent. Energy decomposition analyses (EDA) of X3BNY3 (1, 1a−1h), X3AlNY3 (2, 2a−2h), X3BPY3 (3, 3a−3h), and X3AlPY3 (4, 4a−4h) have shown that the donor−acceptor bonds vary substantially on this relative scale within this set of 36 Lewis pair complexes (X = Y = H for 1−4; X = H, Y = Me for 1a−4a; X = H, Y = Cl for 1b−4b; X = Me, Y = H for 1c−4c; X, Y = Me for 1d−4d; X = Received: July 15, 2017 Revised: September 14, 2017 Published: September 15, 2017 A

DOI: 10.1021/acs.jpca.7b06977 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A

Table 1. Topological and Integrated Bond Descriptors of the Donor−Acceptor Bonds of X3BNY3 (1, 1a−1h), X3AlNY3 (2, 2a− 2h), X3BPY3 (3, 3a−3h), and X3AlPY3 (4, 4a−4h; X, Y = H, Me, Cl)a X3BNY3

d [Å]

ρ(r)bcp [e·Å‑3]

∇2ρ(r) [e·Å−5]

H3BNH3 (1) H3BNMe3 (1a) H3BNCl3 (1b) Me3BNH3 (1c) Me3BNMe3 (1d) Me3BNCl3 (1e) Cl3BNH3 (1f) Cl3BNMe3 (1g) Cl3BNCl3 (1h) average

1.645 1.638 1.656 1.683 1.748 1.656 1.618 1.658 1.656 1.662

0.74 0.79 0.68 0.68 0.63 0.68 0.90 0.89 0.80 0.75

9.1 8.3 11.1 7.7 4.8 10.3 4.1 1.1 4.5 6.8

X3AlNY3

d [Å]

H3AlNH3 (2) H3AlNMe3 (2a) H3AlNCl3 (2b) Me3AlNH3 (2c) Me3AlNMe3 (2d) Me3AlNCl3 (2e) Cl3AlNH3 (2f) Cl3AlNMe3 (2g) Cl3AlNCl3 (2h) average

2.073 2.070 2.224 2.094 2.122 2.342 2.007 2.023 2.183 2.127

ρ(r)bcp [e·Å‑3] ∇2ρ(r) [e·Å−5] 0.33 0.36 0.23 0.32 0.32 0.18 0.41 0.43 0.27 0.32

5.5 5.5 3.3 5.1 4.5 2.1 6.6 6.2 3.6 4.7

ρ(r)bcp [e·Å‑3] ∇2ρ(r) [e·Å−5]

G/ρ(r) [he−1]

H/ρ(r) [he−1]

NELI [e]

VELI [Å3]

1.59 1.51 1.81 1.50 1.27 1.72 1.20 1.01 1.23 1.43 G/ρ(r) [he−1]

−0.72 −0.78 −0.65 −0.71 −0.74 −0.66 −0.89 −0.92 −0.83 −0.77 H/ρ(r) [he−1]

1.89 2.05 2.33 1.92 2.08 2.38 1.94 2.10 2.32 2.11 NELI [e]

1.23 1.20 1.07 1.20 1.12 0.92 1.27 1.21 1.06 1.14 G/ρ(r) [he−1]

−0.08 −0.13 −0.05 −0.08 −0.13 −0.07 −0.15 −0.19 −0.11 −0.11 H/ρ(r) [he−1]

X3BPY3

d [Å]

H3BPH3 (3) H3BPMe3 (3a) H3BPCl3 (3b) Me3BPH3 (3c) Me3BPMe3 (3d) Me3BPCl3 (3e) Cl3BPH3 (3f) Cl3BPMe3 (3g) Cl3BPCl3 (3h) average

1.920 1.905 1.887 2.037 1.989 2.038 2.005 1.973 2.076 1.981

0.75 0.83 0.78 0.60 0.72 0.57 0.77 0.89 0.66 0.73

0.2 −1.6 1.7 −0.2 −1.7 0.7 −5.6 −7.2 −3.9 −2.0

X3AlPY3

d [Å]

ρ(r)bcp [e·Å‑3]

∇2ρ(r) [e·Å−5]

0.91 0.78 1.03 0.79 0.70 0.87 0.31 0.20 0.30 0.65 G/ρ(r) [he−1]

H3AlPH3 (4) H3AlPMe3 (4a) H3AlPCl3 (4b) Me3AlPH3 (4c) Me3AlPMe3 (4d) Me3AlPCl3 (4e) Cl3AlPH3 (4f) Cl3AlPMe3 (4g) Cl3AlPCl3 (4h) average

2.531 2.466 2.559 2.618 2.526 2.681 2.494 2.427 2.564 2.541

0.25 0.31 0.23 0.21 0.27 0.18 0.29 0.37 0.25 0.26

2.0 2.4 1.9 1.5 2.0 1.3 1.9 2.3 1.7 1.9

0.79 0.82 0.81 0.73 0.79 0.71 0.76 0.78 0.73 0.77

YELI

RJI

Q(X)

Q(B)

Q(N)

Q(Y)

2.6 2.9 3.3 2.7 3.3 3.4 2.7 3.2 3.3 3.1 VELI [Å3]

1.79 1.88 1.95 1.85 1.88 1.94 1.88 1.89 1.96 1.89

96 96 98 96 96 97 93 92 95 95

−0.64 −0.63 −0.59 −0.67 −0.62 −0.60 −0.71 −0.70 −0.68 −0.65

1.82 1.83 1.82 1.94 1.92 1.89 2.04 2.01 2.02 1.92

−1.10 −1.07 −0.46 −1.09 −1.03 −0.44 −1.18 −1.12 −0.53 −0.89

0.39 0.38 0.14 0.39 0.32 0.12 0.43 0.41 0.19 0.31

YELI

RJI

Q(X)

Q(B)

Q(N)

Q(Y)

2.06 2.22 2.50 2.07 2.24 2.51 2.07 2.25 2.49 2.27 NELI [e]

4.9 4.7 5.1 4.9 5.0 5.4 4.7 5.0 5.2 5.0 VELI [Å3]

1.85 1.91 2.07 1.89 1.93 2.08 1.91 1.93 2.07 1.96

97 97 98 97 97 99 96 96 98 97

−0.76 −0.75 −0.74 −0.79 −0.81 −0.76 −0.83 −0.82 −0.81 −0.79

2.25 2.24 2.23 2.34 2.33 2.30 2.43 2.42 2.41 2.33

−1.16 −1.10 −0.44 −1.14 −1.08 −0.39 −1.19 −1.13 −0.48 −0.90

0.40 0.37 0.14 0.39 0.39 0.12 0.41 0.39 0.17 0.31

YELI

RJI

Q(X)

Q(B)

Q(N)

Q(Y)

−0.88 −0.92 −0.89 −0.81 −0.87 −0.78 −0.82 −0.77 −0.71 −0.83 H/ρ(r) [he−1]

2.01 2.08 2.13 1.98 2.07 2.10 2.02 2.09 2.10 2.06 NELI [e]

7.1 6.6 6.5 7.1 6.8 7.0 6.2 6.1 6.5 6.7 VELI [Å3]

1.84 1.96 1.86 1.92 2.03 1.91 2.09 2.20 2.07 1.99

90 88 91 89 87 92 81 75 84 86

−0.57 −0.59 −0.54 −0.63 −0.63 −0.61 −0.69 −0.69 −0.68 −0.63

1.64 1.62 1.64 1.78 1.77 1.77 1.81 1.71 1.84 1.73

1.48 1.49 1.47 1.50 1.50 1.50 1.56 1.60 1.61 1.53

−0.47 −0.45 −0.50 −0.46 −0.46 −0.48 −0.44 −0.42 −0.48 −0.46

YELI

RJI

Q(X)

Q(B)

Q(N)

Q(Y)

−0.24 −0.28 −0.21 −0.21 −0.26 −0.19 −0.30 −0.36 −0.27 −0.26

2.05 2.12 2.15 2.06 2.14 2.16 2.04 2.12 2.14 2.11

12.3 11.3 10.8 12.6 11.6 11.3 11.0 10.4 10.2 11.3

2.17 2.31 2.29 2.23 2.35 2.34 2.32 2.43 2.42 2.32

96 95 97 96 95 97 94 93 95 95

−0.74 −0.74 −0.72 −0.78 −0.78 −0.77 −0.82 −0.85 −0.80 −0.78

2.20 2.20 2.19 2.30 2.31 2.29 2.38 2.38 2.38 2.29

1.34 1.30 1.39 1.37 1.32 1.43 1.36 1.29 1.44 1.36

−0.44 −0.42 −0.47 −0.44 −0.43 −0.47 −0.43 −0.38 −0.48 −0.44

For all bonds, ρ(r) is the electron density at the bond critical point (bcp), ∇2ρ(r) is the corresponding Laplacian, G/ρ(r) and H/ρ(r) are the kinetic and total energy density over ρ(r) ratios, NELI and VELI are the electron populations and volumes of the donor−acceptor bonding basins (cut at the 0.001 au isosurface of the ED), YELI is the ELI-D value at the attractor position, RJI is the Raub−Jansen index, Q(X/Y) is the AIM charge of the substituents atoms attached to the acceptor or donor, and Q(A/D) is the AIM charge of the acceptor or donor atoms. a

Me, Y = Cl for 1e−4e; X = Cl, Y = H for 1f−4f; X = Cl, Y = Me for 1g−4g; X, Y = Cl for 1h−4h). For instance, the percentage orbital and electrostatic interactions are balanced and almost identical for H3BNH3 (1: 49.6/50.4%) and H3AlPH3 (4: 51.2%/48.8%). However, electrostatic interactions are predominate in H3AlNH3 (2: 66.4/33.6%), whereas orbital interactions are the most significant in H3BPH3 (3: 38.2/ 61.8%).10

A complementary picture of the donor−acceptor bonds may be obtained by a variety of real-space bonding indicators (RSBI).11 The RSBI applied here comprise topological and integrated bond descriptors derived from the electron densities (ED) according to the topological Atoms-In-Molecules (AIM)12 approach, and surface methods according to the Non-Covalent Interactions index (NCI)13 and Density Overlap Regions Indicator (DORI).14 Additionally, the electron pair B

DOI: 10.1021/acs.jpca.7b06977 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A densities are analyzed in terms of the Electron Localizability Indicator (ELI-D)15,16 scheme. By definition of surfaces of zero electron flux, AIM provides atomic basins with atomic properties as well as a topological bond path motif, which resembles the molecular structure in “simple” cases (e.g., organic compounds).12 ELI-D divides space into small regions containing equal amounts of same-spin electron pairs, thus providing basins of paired core, bonding, or lone pair electrons, which can be integrated in order to obtain basin volumes and electron populations. Core and lone-pair basins are denoted as monosynaptic (e.g., C(N) or V1(N), V = valence basin), whereas bonding basins are at least disynaptic (e.g., V2(N,B)), i.e., they topologically connect the core basins of two adjacent atoms.15,16 By mapping the reduced density gradient, s(r) = [1/ 2(3π2)1/3]|∇ρ|/ρ4/3, at special iso-values NCI uncovers (extended) regions in space where noncovalent interactions occur (other bond types are not visible then). NCI greatly complements ELI-D analyses since the latter is closely related to covalent bonding. Mapping the ED times the sign of the second eigenvalue of the Hessian (sign(λ2)ρ) on iso-surfaces of s(r) facilitates the assignment of different contact types including steric/repulsive (λ2 > 0), van der Waals-like (λ2 ≈ 0), and attractive (λ2 < 0) interactions.13 DORI is another scalar field, which is also derived from the ED and its derivatives: Θ(r) = (∇(∇ρ(r)/ρ(r))2)2/(∇ρ(r)/ρ(r)). DORI iso-surfaces display any kind of interaction, whether it is strong or weak, because it probes deviations of the ED from singleexponentiality (and is thus not related to electron localization). Since Θ(r) becomes infinite at bonding regions, a transformation is applied to restrict the values between zero and one: γ(r) = Θ(r)/(1 + Θ(r)). Like for NCI, sign(λ2)ρ may be mapped on γ(r) iso-surfaces to distinguish attractive from repulsive atom−atom interactions.14 Our interest in experimental charge density studies17,18 and donor−acceptor interactions in experimentally available peri-substituted (ace)naphthyl aminoboranes,19−21 aminoalanes,22 phosphinoboranes,23−29 and phosphinoalanes28 prompted an investigation of RSBI methods on the 36 donor−acceptor complexes X3BNY3 (1, 1a−1h), X3AlNY3 (2, 2a−2h), X3BPY3 (3, 3a− 3h), and X3AlPY3 (4, 4a−4h) already studied using EDAs (X, Y = H, Me, Cl).10

Table 2. ELI-D Properties of the Lone-Pairs within the Free Lewis Bases Y3N and Y3P (Y, H, Me, Cl)a H3N Me3N Cl3N H3P Me3P Cl3P

NELI [e]

VELI [Å3]

YELI

2.09 2.17 2.56 2.04 2.12 2.12

10.3 8.2 8.0 18.4 18.4 15.5

1.73 1.93 2.14 2.43 2.70 2.80

a

Much weaker effects are observed for the Me groups: H3BNMe3 (1a, 148 kJ mol−1), H3AlNMe3 (2a, 186 kJ mol−1), H3BPMe3 (3a, −54 kJ mol−1), and H3AlPMe3 (4a, 12 kJ mol−1).

of NCIplot (grid step size = 0.1 bohr),35 provided by the authors of ref 14. Bond paths are displayed with AIM2000, ELID, NCI, and DORI using MolIso.36 AIM bond topology, ELI-D localization domains (Y = 1.3), and iso-surfaces of NCI (s(r) = 0.5) and DORI (γ(r) = 0.95) are displayed in Figures 1−4.

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RESULTS AND DISCUSSION Geometries and Energies. With two exceptions all bond distances obtained in this study differ within 0.04 Å from literature values (see Supporting Information (SI) for details).10 The donor−acceptor distances vary in distinct ranges, being B− N = 1.62−1.75 Å < B−P = 1.89−2.08 Å < Al−N = 2.01−2.34 Å < Al−P = 2.43−2.68 Å. For longer donor−acceptor distances the Lewis acids X3B and X3Al approach the planar geometry of the free Lewis acid with X−B−X and X−Al−X angles of 120° (see SI for details). For some Lewis pairs, quite distinct effects of the substituents to the donor−acceptor distances are observed, which lead to the following bond length orders: B−N = Y3N no clear trend, Me3B > H3B ≈ Cl3B; Al−N = Cl3N > Me3N ≈ H3N, Me3Al > H3Al > Cl3Al; B−P = Y3P no clear trend, Me3B ≈ Cl3B > H3B; Al−P = Cl3P > H3P > Me3P, Me3Al > H3Al ≈ Cl3Al. As both substituents attached to the Lewis acids and bases have an influence to the donor−acceptor distances in same or opposite direction, the formation of unambiguous trends is, of course, largely hampered. Previously, the Lewis pair complexes were analyzed by means of energy decomposition analysis (EDA).10 Here, we estimate the bonding interaction (ΔBDE) in a quite basic manner by simply combining the molecular energies of the isolated (optimized) Lewis acid (LA) and Lewis base (LB) and comparing this value to the molecular energy of the respective Lewis pairs (LP) (ΔBDE = ELP − (ELA + ELB)); basis-set superposition error, BSSE, not taken into account. The results resemble those of Bessac and Frenking and are given in the SI. Both methods find the strongest BDE for H3BPMe3 (3a) and the weakest for Me3BNCl3 (1e) and Cl3BNCl3 (1h). In an effort to quantify (de)stabilizing effects of the substituents, the bond dissociation energies of inversely substituted pairs (e.g., Me3BNH3 (1c) vs H3BNMe3 (1a)) was compared. The analysis of these pairs revealed that Cl atoms attached to Lewis base heavily destabilize the Lewis pairs. The following Lewis pairs are highly destabilized with respect to their counterparts with inverted substituent patterns: H3BNCl3 (1b, 842 kJ mol−1), Me3BNCl3 (1e, 688 kJ mol−1), H3AlNCl3 (2b, 1126 kJ mol−1), Me3AlNCl3 (2e, 930 kJ mol−1), H3BPCl3 (3b, 137 kJ mol−1), Me3BPCl3 (3e, 213 kJ mol−1), H3AlPCl3 (4b, 465 kJ mol−1), and Me3AlPCl3 (4e, 465 kJ mol−1). Properties of the Donor−Acceptor Bonds. For the discussion of the general electronic characteristics of the B−N,

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DFT CALCULATIONS Relaxed gas phase structures of X3BNY3 (1, 1a−1h), X3AlNY3 (2, 2a−2h), X3BPY3 (3, 3a−3h), and X3AlPY3 (4, 4a−4h) were obtained by geometry optimization at the B3PW91/6-311+G(2df,p)30,31 level of theory applying Gaussian09 for a set of 36 Lewis pair complexes (X = Y = H for 1−4; X = H, Y = Me for 1a−4a; X = H, Y = Cl for 1b−4b; X = Me, Y = H for 1c−4c; X, Y = Me for 1d−4d; X = Me, Y = Cl for 1e−4e; X = Cl, Y = H for 1f−4f; X = Cl, Y = Me for 1g−4g; X, Y = Cl for 1h−4h).32 For all structures Cs symmetry was assigned. Subsequent frequency analysis proved all structures to be local minima. The resulting wave function (wfn) files were used for topological analysis of the ED according to the AIM space-partitioning scheme using AIM2000,33 whereas DGRID-4.634 was used to generate and analyze the ELI-D related real-space bonding descriptors (grid step size = 0.04 bohr). Topological and integrated bond descriptors of the donor−acceptor bonds are collected in Table 1. ELI-D properties of the lone pairs within in the free Lewis bases molecules are listed in Table 2. Additionally, the resulting wave function files were utilized for NCI indicator and DORI analyses applying a modified version C

DOI: 10.1021/acs.jpca.7b06977 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

Figure 1. AIM-topology and iso-surfaces of ELI-D (Y = 1.3), NCI (s(r) = 0.5), and DORI (γ(r) = 0.95) for H3BNH3 (1).

Figure 2. AIM-topology and iso-surfaces of ELI-D (Y = 1.3), NCI (s(r) = 0.5), and DORI (γ(r) = 0.95) for H3AlNH3 (2).

Figure 3. AIM-topology and iso-surfaces of ELI-D (Y = 1.3), NCI (s(r) = 0.5), and DORI (γ(r) = 0.95) for H3BPH3 (3).

D

DOI: 10.1021/acs.jpca.7b06977 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A

Figure 4. AIM-topology and iso-surfaces of ELI-D (Y = 1.3), NCI (s(r) = 0.5), and DORI (γ(r) = 0.95) for H3AlPH3 (4).

mainly determined by the type of Lewis base. The bond ellipticity (ε, not shown) as well as the distance of the ELI-D attractor position from the donor−acceptor axis (ΔELI, not shown), which are measures for deviations from cylindric symmetry along the donor−acceptor bond axis, are zero for all 36 cases. For the integrated RSBI, such as ELI-D basin populations and volumes, AIM atomic charges, and the Raub− Jansen index (RJI), which combines AIM and ELI-D and quantifies how the electron population within an ELI-D basin is distributed over adjacent AIM atomic basins,37,38 the situations is more complex. The highest NELI value = 2.27 e is observed for the N−Al contact in conjunction with the highest RJI of 97%, both indicating the lack of electron sharing between the Al and N atoms, which is typical for ionic bonds. In contrast, NELI = 2.06 e and RJI = 86% are observed for the B−P contacts, indicating considerable electron sharing typical for polarcovalent bonding. The B−N and Al−P contacts are in between the latter two and show similar behavior (NELI = 2.11 e, RJI = 95%). According to Pearsons concept of hard and soft acids and bases, the N and Al atoms are considered to be hard(er), whereas the B and P atoms are considered to be soft(er). Accordingly, the AIM atomic charges of the Al and N atoms are almost unchanged by the donor−acceptor pairing, whereas the B and P atoms are affected considerably (Q(B) = 1.92 e (BN), 1.73 e (BP); Q(P) = 1.53 e (BP), 1.36 e (AlP)). In summary, covalent bond contributions decrease in the order covalent > B−P > B−N ≈ Al−P > Al−N > ionic. Effects of the Substituents. In this part, the influence of the substituents X, Y = H, Me, Cl in the 36 donor−acceptor complexes of the types X3BNY3 (1, 1a−1h), X3AlNY3 (2, 2a− 2h), X3BPY3 (3, 3a−3h), and X3AlPY3 (4, 4a−4h; X, Y = H, Me, Cl) is analyzed. The electron density ρ(r)bcp of the donor− acceptor bond directly reflects the pronounced electronic impact of the substituents attached to the Lewis acid. With few exceptions, ρ(r)bcp increases in the order Me < H < Cl for any given set. The electron withdrawing effect of the Cl atoms results in an increased Lewis acidity of the X3B and X3Al fragments and thus in increased charge donation from the Lewis base fragments, Y3N and Y3P. As expected, electron donating Me groups attached to the Lewis acid exert the

Al−N, B−P, and Al−P donor−acceptor bonds, only the averaged values are considered (Table 1). The effect of the substituents is discussed below. Upon Lewis pair formation the formerly nonbonding ELI-D basin volumes of the Lewis base (VELI) undergo a remarkable change. They are as large as 8−18 Å3 in the free Lewis base but reduce to 3−12 Å3 in the Lewis pair complexes. For the electron populations (NELI) and the ELI-D values at the attractor position (Ymax), such clear trends are not observed. With several exceptions there is a tendency for NELI and Ymax to slightly decrease upon Lewis pair formation, resulting in the following ranges: NELI, 2.1−2.6 e (free) vs 1.9−2.5 e (bonded); Ymax, 1.7−2.8 (free) vs 1.8−2.4 (bonded). Both trends may be related to (partial) electron sharing between the Lewis acid and the Lewis base. Notably, some topological RSBI are determined by the type of Lewis acid (X3B vs X3Al) or base (Y3N vs Y3P). The average ED at the bcp of the donor−acceptor bond, ρ(r)bcp(D−A) or ρ(r)bcp, is 0.75 or 0.73 e·Å−3 for the B−N or B−P interactions, but reduces to 0.32 or 0.26 e·Å−3 for the Al−N or Al−P interactions, the latter being characteristic for predominantly ionic atom−atom contacts. The same trend is observed for the H/ρ(r)bcp values, a RSBI related to bond covalency, which is highly negative for the B−N (−0.77 au) and B−P (−0.83 au) contacts, indicating significant covalent bond contributions, but close to zero for the Al−N (−0.11 au) and Al−P (−0.26 au) contacts. Both RSBI are obviously mainly determined by the type of Lewis acid. In contrast, the G/ρ(r)bcp values, a RSBI related to mutual penetration and bond polarization, shows highly positive values for the B−N (1.43 au) and Al−N (1.14 au) contacts, but considerably smaller values for the Al−P (0.77 au) and the B−P (0.65 au) contacts. The trend in G/ρ(r)bcp fairly reproduces the trend of the electronegativity differences ΔEN (B−N, 1.0; Al−N, 1.4; Al−P, 0.6; B−P, 0.2, taking into account Pauling electronegativities (EN) of N = 3.0, P = 2.2, B = 2.0, and Al = 1.6. Although weaker, the same trend is observed for the Laplacian of the ED at the bcp (∇2ρ(r)bcp), which is more positive for the B−N (6.8 e·Å−5) and Al−N (4.7 e·Å−5) contacts, but closer to zero for Al−P (1.9 e·Å−5) and B− P (−2.0 e·Å−5) contacts. Apparently, the latter RSBIs are E

DOI: 10.1021/acs.jpca.7b06977 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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highest NELI values are observed for the (small) X3BNCl3 (1b, 1e, 1h) and X3AlNCl3 (2b, 2e, 2h) basins. As the ELI-D localization domain shape, which is closely related to covalent bonding aspects, is mainly determined by the Lewis base, the NCI iso-surface shape, which is closely related to noncovalent bonding aspects, is mainly determined by the Lewis acid. For the H3BNY3 (1, 1a, 1b) and H3BPY3 (3, 3a, 3b), red-colored interligand NCI basins are observed, suggesting weak H···H repulsion (for NCI and DORI, the term “basin” refers to a region in space, which is enclosed by an arbitrarily chosen isovalue). In contrast, pronounced donor−acceptor NCI basins are observed for H3AlNH3 (2) and H3AlPH3 (4), the discshaped blue regions of which indicate considerable ionic bond contributions. Notably, the ELI-D and NCI trends correlate with the trends observed for the AIM-derived RSBI discussed above. All X3BNY3 (1, 1a−1h) and X3AlNY3 (2, 2a−2h) series exhibit small but high populated donor−acceptor ELI-D basins and high positive G/ρ(r)bcp values, whereas the opposite is observed for the X3BPY3 (3, 3a−3h) and X3AlPY3 (4, 4a−4h) series. All X3BNY3 (1, 1a−1h) and X3BPY3 (3, 3a−3h) series exhibit negligible NCI basins in conjunction with large numbers for ρ(r)bcp and H/ρ(r)bcp, whereas the X3AlNY3 (2, 2a−2h) and X3AlPY3 (4, 4a−4h) series show the opposite; see SI. DORI is an ED-derived RSBI, which depicts all types of chemical interactions at the given iso-value (including covalent and noncovalent) in terms of deviations from singleexponentially in the underlying ED. In all X3BNY3 (1, 1a− 1h) and X3AlNY3 (2, 2a−2h) series, the DORI basins are observed at the N atoms valence regions approximating a spherical shape. Obviously, the N atoms are only little affected by donor−acceptor bond formation. For the larger and softer P atoms, a large DORI basin is observed, the blue-red color scheme of which indicates considerable effects of the donor− acceptor bond to the P atoms valence region. Moreover, in H3BPH3 (3) an excrescence toward the B atoms is detected. For the B atoms, heavily distorted DORI basins indicate major impacts of the N and P atoms to its valence electron distribution. As the shape is flat in the direction of the Lewis base for the more polar B−N contact (resembling the Al DORI and NCI shape, see below), it is drastically shifted toward the P atom in the X3BPY3 (3, 3a−3h) series, almost resulting in a fusion of the B and P DORI basins; an effect that is finally realized in Cl3BPMe3 (1g) and H3BPMe3 (1a, see SI for details). In contrast to the heavily deformed valence region of the B atoms, the valence region of the Al atoms is exclusively deformed at the atom−atom borders, resulting in disc-shaped blue-colored DORI shapes, which closely resemble the corresponding NCI surfaces. Like the harder N atoms, the harder Al atoms valence region is only little affected by donor− acceptor bond formation. Real-Space Bond Indicators (RSBI) vs Energy Decomposition Analysis (EDA). Previously, the nature of the donor−acceptor bonds of the same 36 Lewis pair complexes was analyzed by means of bond dissociation energies (ΔBDE) and energy decomposition analysis (EDA).5 According to ΔBDE = ΔEprep + ΔEint, the bonding interaction is constituted by repulsive ΔEprep and attractive ΔEint terms. ΔEprep is the energy needed to form the tetrahedrally distorted fragments as found in the Lewis pair complexes from the originally planar X3B and X3Al acceptors and the tetrahedral Y3N and Y3P donors (Eprep: X3B > X3Al ≫ Y3N/Y3P). ΔEint is the interaction energy between Lewis acid and Lewis base fragments and is constructed from attractive ΔEelstat and ΔEorb and repulsive

opposite effect. Less pronounced trends are observed for the variation of the substituents of the Lewis base. Here, ρ(r)bcp tends to increase in the opposite order Cl < H < Me, as the electron withdrawing Cl atoms of the Lewis base withdraw electron density from the donor−acceptor bond. In the ELI-D scheme, however, a quite different trend is observed. In contrast to ρ(r)bcp, the electron population within the donor−acceptor bonding basin (NELI) is highly determined by the type of substituent of the Lewis base and decreases in the order Cl > Me > H for all four types of donor−acceptor complexes. As this effect is strong for complexes of types X3BNY3 (1, 1a−1h) and X3AlNY3 (2, 2a−2h), it is much weaker (but still visible) for complexes of the type X3BPY3 (3, 3a−3h) and X3AlPY3 (4, 4a−4h). Although the reason for this observation is not yet clear, it might be related to intramolecular charge polarization. Notably, the EN values of the ligands follow the same order: Cl > CMe > H. The differences between ELI-D population analysis and AIM topology reflects the fact that the number of electrons in a (bonding) region is not equal to its concentration. With few exceptions, the highest positive G/ρ(r)bcp values are observed for H3BNY3 (1, 1a, 1b), H3AlNY3 (2, 2a, 2b), H3BPY3 (3, 3a, 3b), and H3AlPY3 (4, 4a, 4b), which may be related to reduced steric hindrance between the ligands and hence increased mutual penetration of donor and acceptor atoms. For the polarcovalent B−P bonds, this also holds for the (negative) H/ ρ(r)bcp values, indicating the highest degree of covalency for the H3BPY3 (3, 3a, 3b) complexes. However, for the more polar B−N, Al−N, and Al−P bonds, the highest negative H/ρ(r)bcp values are observed for the Cl3BNY3 (1f−1h), Cl3AlNY3 (2f− 2h), and Cl3AlPY3 (4f−4h) complexes. Again, with few exceptions, the Cl3BNY3 (1f−1h), Cl3 AlNY 3 (2f−2h), Cl3BPY3 (3f−3h), and Cl3AlPY3 (4f−4h) series exhibit the highest negative (N) and positive (P, B, Al) AIM atomic charges and the lowest RJI in comparison to the H3BNY3 (1, 1a, 1b), H3AlNY3 (2, 2a, 2b), H3BPY3 (3, 3a, 3b), and H3AlPY3 (4, 4a, 4b) series and Me3BNY3 (1c−1e), Me3AlNY3 (2c−2e), Me3BPY3 (3c−3e), and Me3AlPY3 (4c−4e) series. In addition, with a Pauling electronegativity of 3.2, the Cl atoms have a drastic effect on the N atom AIM charges (loss of ca. 0.6 e in comparison H or Me). As the P, B, and Al atomic charges already are determined by the higher electronegativities of three H, Me, or Cl substituents, such dramatic effects are not visible. In summary, major (and in parts contradictory) effects are exerted to the donor−acceptor bonds by the Cl atoms. Situated at the Lewis acid, they increase the ED at the donor−acceptor bcp; located at the Lewis base, they decrease the ED at the donor−acceptor bcp but increase the electron population of the donor−acceptor bonding basin. Iso-Surface Analysis. The ELI-D is colored representing the basin size order: small basins are greenish and solid; large basins are increasingly bluish and transparent (Figures 1−4). The color scheme, however, is not on an absolute scale and thus cannot directly be compared between the different compounds. As expected, the donor−acceptor bcp is located much closer to the acceptor atoms (30−40% of d) as the dative bonds are formed from the formerly non-bonding (lone-pair) electrons of the Lewis base. The ELI-D shows the localization domain at Y = 1.3 within the donor−acceptor bonding basin (V2(LB,LA)) to be small and located close to the N atom for the B−N and Al−N contacts, but larger and significantly shifted toward the acceptor atom for the B−P and Al−P contacts (compare basin volumes in Table 1). The volume trends do not directly relate to the electron population within these basins as by far the F

DOI: 10.1021/acs.jpca.7b06977 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A ΔEPauli contributions.39−41 It was found that both, bond lengths and ΔBDE, are not good measures for the estimation of the donor−acceptor bond strength, the former being affected by electronic and steric effects, the latter being largely affected by ΔEprep, especially for the X3B fragments. For Cl3BNCl3 (1h) and Me3BNCl3 (1e), ΔEprep actually causes dissociation of the donor−acceptor bond. The EDA analysis revealed trends in the steric repulsion (ΔEPauli) between the ligands, which are reflected in the donor−acceptor bond lengths and also in the formation of interligand NCI and DORI basins. ΔEPauli decreases in the order: B−N > B−P > Al−N > Al−P. Considering the pronounced effects of the substituents at the acceptor atoms, the order for ΔEPauli was Cl > Me > H (B−N) and Cl > Me ≈ H (Al−N, B−P, Al−P). Considering the much weaker effects of the substituents at the Lewis base, the order for ΔEPauli was Me > H > Cl for Al−N, B−P, and Al−P (no clear trend for B−N). Consequently, the repulsive terms of the dative bonding interaction, ΔEprep and ΔEPauli, are mainly controlled by the acceptor atom type and its substituents. AIM, ELI-D, NCI, and DORI representations are given for all 36 Lewis pair complexes in the SI. For all series Cl3BNY3 (1f−1h), Cl3AlNY3 (2f−2h), Cl3BPY3 (3f−3h) and Cl3AlPY3 (4f−1h) containing Cl atoms at the acceptor atom, red-colored NCI basins are detected at the outer parts of the acceptor atom, indicating repulsive interactions. In most cases, they are in conjunction with green-colored interligand NCI and DORI basins, indicating nonbonding atom−atom contacts. For the longer donor−acceptor bonds, the interligand basins become smaller or even vanish in the order B−N > Al−N > B−P > Al− P. Interestingly, for all X3AlNY3 and X3AlPY3 series, additional blue-colored regions are observed in the three X3B/Al···N/P axes indicating attractive secondary H/CMe/Cl···N/P interactions. This might be related to the fact that the percentile electrostatic interaction energy between the fragments (ΔEelstat) is higher for the X3AlNY3 (2, 2a−2h) and X3AlPY3 (4, 4a−4h) series (%ΔEelstat: Al−N = 50−70%, Al−P = 40−60%) than for the X3BNY3 (1, 1a−1h) and X3BPY3 (3, 3a−3h) series (%ΔEelstat: B−N = 40−55%, B−P = 35−50%). The relative electrostatic contributions (ΔEelstat) decrease, while the relative covalent contributions (ΔEorb) increase. These results fully resemble the above-discussed trends for H/ρ(r)bcp, NELI, and RJI: Al−N > Al−P (>) B−N > P−B and make clear that the Al−N contacts are dominated by ionic contributions, whereas the B−P contacts are dominated by covalent contributions. For all investigated Lewis pair complexes, by far the smallest ΔBDE values were observed for the Cl3BNY3 (1f−1h), Cl3AlNY3 (2f− 2h), Cl3BPY3 (3f−3h), and Cl3AlPY3 (4f−4h) series. This is in part due to considerable reduced ΔEorb but mostly due to drastic losses in ΔEelstat (notably, ΔEPauli is reduced as well in most cases). In their paper, Bassac and Frenking stated that “the electronegative chlorine atoms make the lone pair orbital at nitrogen in Cl3N much more compact than in H3N and Me3N,” and they related this to a heavily increased percentile s character of 74% in the Cl3N lone-pair compared to 27% in H3N and 17% in Me3N42 (similar arguments are given for Cl3P). Hence, one would expect the donor−acceptor ELI-D bonding basin volumes to show the same trend, which, however, was not observed. Instead, they vary only little (