Bond Pair

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Article Cite This: ACS Omega 2018, 3, 11331−11339

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On the Significance of Lone Pair/Lone Pair and Lone Pair/Bond Pair Repulsions in the Cation Affinity and Lewis Acid/Lewis Base Interactions Younes Valadbeigi*,† and Jean-François Gal*,‡ †

Department of Chemistry, Faculty of Science, Imam Khomeini International University, P.O. Box 288, Qazvin 3414896818, Iran Institut de Chimie de Nice, UMR 7272, Université Côte d’Azur, CNRS, 06108 Nice, France

‡

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S Supporting Information *

ABSTRACT: Interaction of H2O, H2S, H2Se, NH3, PH3, and AsH3 with cations H+, CH3+, Cu+, Al+, Li+, Na+, and K+ was studied from the energetic and structural viewpoint using B3LYP/6-311++G(d,p) method. The charge transfer from the Lewis bases to the cations reduces lone pair/lone pair (LP/LP) repulsion in H2O, H2S, and H2Se and LP/bond pair (LP/BP) repulsion in NH3, PH3, and AsH3. In parallel, changes in the H−M−H angles (M = O, S, Se, N, P, and As) are observed. The change in the H−M−H angle during the interactions was proportional to the amount of charge transferred from the bases to the cations and electron density (ρ) at the molecule/cation bond critical point. Also, the opposite trend for proton affinities of these two families, that is, NH3 > PH3 > AsH3 and H2O < H2S < H2Se, was interpreted on the basis of LP/BP repulsion in their neutral and protonated forms. Interaction of the Lewis bases with neutral Lewis acids including BeH2, BeF2, and BH3 was studied energetically and structurally. The calculated energies for interactions of H2O and NH3 with BeH2, BeF2, and BH3 are larger than the corresponding values for H2S, H2Se, PH3, and AsH3. This difference was interpreted on the basis of the lower stability of H2O and NH3 because of large LP/LP and LP/BP repulsion in H2O and LP/BP repulsion in NH3.

1. INTRODUCTION There are many models and theories which attempt to predict the geometry of the molecules and complexes.1 Lewis dot diagrams are the simplest molecular structures explained on the basis of the octet rule.2 Hybridization,3 valence bond theory,4 nonbonded interaction,5 and valence-shell electronpair repulsion (VSEPR)6−8 are further models giving a more realistic geometry as compared to Lewis structures. The VSEPR model is used to determine approximate structure of a molecule basis on the number of electron pairs of the central atom. Because the lone pair (LP) electrons are affected by one nucleus, whereas the bond pair (BP) electrons are influenced by two nuclei, the former occupy larger place.6 Because of the repulsive force between the LPs, they tend to arrange in a way to minimize the repulsion. It has been established that the repulsion trend is as LP/LP > LP/BP > BP/BP.6 Many researchers have attempted to interpret the VSEPR model on the basis of physical concepts,9−11 whereas others criticized this model.12,13 However, this model has been used for elucidation or prediction of many structures. Although the effect of LP repulsion on the structures of neutral and charged molecules and complexes has been considered,14−17 this repulsion effect on the cation/molecule interactions has not been studied from the energetic point of view. Cation affinity (CA) of a molecule is defined as −ΔH of attachment of a cation to the molecule.18 Although it is expected that the empty orbital of cations accepts the LP © 2018 American Chemical Society

electrons of molecules to form a bond via covalent interactions, complete electron transfer depends essentially on polarizability and dipole moment of the molecules,19 electron-withdrawing group (EWG) and electron-donating group (EDG),20 nature of the cation or acceptor atom, direction of cation/molecule interaction,21 electron affinity of the cation, and so on. Therefore, the cation attachment may occur through various combinations of covalent and electrostatic (charge/dipole) interaction.22,23 It is known that larger alkali metal cations (Na+, K+) attach to Lewis bases mainly via electrostatic interactions, whereas H+, CH3+, and to some extent Cu+ interact covalently.19,24 Li+ and Al+ exhibit intermediate behaviors with comparable electrostatic and covalent contributions. Effects of polarizability, dipole moment, and EWG and EDG on CA have been extensively studied. In this work, effect of LP and BP repulsions on the cation/molecule interaction is investigated from an energetic point of view. For comparison, interactions of neutral Lewis acids BeH2, BeF2, and BH3 with H2O, H2S, H2Se, NH3, PH3, and AsH3 are studied. Received: July 13, 2018 Accepted: September 7, 2018 Published: September 18, 2018 11331

DOI: 10.1021/acsomega.8b01644 ACS Omega 2018, 3, 11331−11339

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Table 1. Comparison of the Calculated (B3LYP and CBS-Q) and Experimental CAs and CB of H2O, H2S, H2Se, NH3, PH3, and AsH3 Calculated Using B3LYP/6-311++G(d,p) Methoda B3LYP/6-311++G(d,p)

CBS-Q

experimental

reaction

CA

CB

CA

CB

H2O + H+ → H2O−H+ H2O + CH3+ → H2O−CH3+ H2O + Cu+ → H2O−Cu+ H2O + Al+ → H2O−Al+ H2O + Li+ → H2O−Li+ H2O + Na+ → H2O−Na+ H2O + K+ → H2O−K+ H2S + H+ → H2S−H+ H2S + CH3+ → H2S−CH3+ H2S + Cu+ → H2S−Cu+ H2S + Al+ → H2S−Al+ H2S + Li+ → H2S−Li+ H2S + Na+ → H2S−Na+ H2S + K+ → H2S−K+ H2Se + H+ → H2Se−H+ H2Se + CH3+ → H2Se−CH3+ H2Se + Cu+ → H2Se−Cu+ H2Se + Al+ → H2Se−Al+ H2Se + Li+ → H2Se−Li+ H2Se + Na+ → H2Se−Na+ H2Se + K+ → H2Se−K+ NH3 + H+ → H3N−H+ NH3 + CH3+ → H3N−CH3+ NH3 + Cu+ → H3N−Cu+ NH3 + Al+ → H3N−Al+ NH3 + Li+ → H3N−Li+ NH3 + Na+ → H3N−Na+ NH3 + K+ → H3N−K+ PH3 + H+ → H3P−H+ PH3 + CH3+ → H3P−CH3+ PH3 + Cu+ → H3P−Cu+ PH3 + Al+ → H3P−Al+ PH3 + Li+ → H3P−Li+ PH3 + Na+ → H3P−Na+ PH3 + K+ → H3P−K+ AsH3 + H+ → H3As−H+ AsH3 + CH3+ → H3As−CH3+ AsH3 + Cu+ → H3As−Cu+ AsH3 + Al+ → H3As−Al+ AsH3 + Li+ → H3As−Li+ AsH3 + Na+ → H3As−Na+ AsH3 + K+ → H3As−K+

687.9 274.0 171.7 116.7 148.7 104.59 75.5 705.9 327.2 190.4 70.7 98.1 65.9 40.16 716.74 339.74 202.96 76.76 99.30 67.50 39.23 852.76 431.54 244.42 143.18 167.85 118.22 81.1 783.8 427.4 228.4 80.2 106.5 73.0 44.1 751.0 386.2 210.6 69.7 93.4 62.2 34.8

659.6 230.8 145.5 90.7 121.7 77.2 51.4 677.2 282.6 161.6 45.8 71.8 41.0 17.7 688.1 295.6 174.2 51.9 73.1 42.7 16.6 824.5 386.5 215.5 116.4 140.5 92.2 57.0 755.4 382.5 199.5 56.4 80.8 48.8 22.3 719.9 339.3 179.3 43.7 65.3 35.5 10.7

686.2 275.1 144.1 114.8 136.4 92.6 62.4 703.1 337.9 160.1 71.5 89.2 59.8 27.1 703.7 341.6 179.7 82.7 95.4 58.8 39.5 854.1 439.4 214.6 146.6 156.5 107.0 69.3 785.4 445.0 201.9 79.5 97.7 68.9 36.0 740.5 389.3 171.9 59.6 77.3 47.6 29.2

658.2 235.4 116.6 88.7 109.3 65.1 38.5 674.3 296.1 132.4 47.9 63.4 35.7 5.8 675.0 299.7 151.0 57.5 68.9 33.5 16.6 819.8 397.4 186.2 119.2 129.3 81.2 45.6 757.0 403.2 173.9 56.0 72.3 45.1 15.0 709.5 344.9 141.1 33.2 49.1 21.2 5.4

CA

CB

691b 277c, 279d 157e 107.8e 140b 100b, 98.1f 74.9f 705b 339c, 340d

660b

707.8b, 716g

676.4b

853.6b 439c, 441d 241.6f 148.0e 164d 107b, 106.2f 84.1b, 82f 785.0b 438c, 440d

819.0b

93.1e 112.8f 74.4f 47.7f 673.8b

118.5e 134b, 132.9f 55f 750.9b

70.6f

747.9b 373c

712.0b

a

The values are in kJ/mol. bReference 25. cReference 26. dReference 27. eReference 28. fReference 29. gReference 30.

2. RESULTS AND DISCUSSION 2.1. Interaction of the Lewis Bases with Cations. The B3LYP and CBS-Q calculated CAs of H2O, H2S, H2Se, NH3, PH3, and AsH3 are summarized in Table 1. There is an agreement between the calculated and experimental data; however, CBS-Q underestimates the Cu+ affinities. The proton affinities (PAs) of H2O, H2S, and H2Se increase as H2O < H2S < H2Se, whereas for NH3, PH3, and AsH3, the PA trend is as NH3 > PH3 > AsH3. The dipole moments (μ) of H2O, H2S, and H2Se are 1.85, 0.97, and 0.24 debye (D), respectively (Table S1 in Supporting Information), a trend opposite to their PAs. The reason is that H+ interacts with the Lewis bases mainly through covalent interaction, and the electrostatic contribution (ion/dipole interaction) is small. The PAs of

H2O, H2S, and H2Se and their polarizabilities (α) display the same trend (Table S1) which somewhat confirms the covalent nature of their interactions with H+. We intended to use electron densities (ρ) at bond critical points (BCPs) of O−H, S−H, and Se−H in H3O+, H3S+, and H3Se+ to compare the covalency nature of the bonds; however, because ρ also depends on bond length and atom type, it is not a good index of covalency. For example, the calculated values of ρ at BCPs of O−H, S−H, and Se−H in H3O+, H3S+, and H3Se+ are 0.33, 0.22, and 0.17, respectively (Table S2) which is not in agreement with the hypothetical covalent nature of the interactions. Therefore, Mulliken charge distributions for H3O+, H3S+, and H3Se+ were obtained to investigate the covalency of the bonds on the basis of the extent of transferred 11332


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Figure 1. Comparison of the angles in the neutral and protonated structures of H2O, H2S, H2Se, NH3, PH3, and AsH3. The angles have been obtained by optimization of the structures using the B3LYP/6-311++G(d,p) method.

charge from the molecules to the H+ (Figure S1). Comparison of the transferred charges shows that the covalency trend is as Se−H > S−H > OH which are in agreement with the PA trend. Therefore, charge transfer, electrostatic interaction, and polarizability influence the PA and generally CA. Effects of these parameters have been investigated by several authors.19−23 We advocate here that the LP repulsion may influence the CAs and can be used to explain the observed CA trend. Comparison of the angle between LP and BP vectors in H3O+ (105.0°), H3S+ (121.9°), and H3Se+ (123.4°) in Figure 1 shows that the LP/BP repulsion in H3O+ is larger than that in H3S+ and H3Se+; therefore, the latter is more stable. On the other hand, the trend in PA of NH3, PH3, and AsH3 is the same as their dipole moments (Table S1). Therefore, the simple interpretation of an electrostatic interaction would be in contradiction with the covalent bonding of the proton. Comparison of the LP/BP angles in Figure 1 shows that NH3 with H−N-LP angle of 111.0° suffers from the LP/BP repulsion more than PH3 and AsH3 with angles of 122.7° and 123.7°, respectively (smaller molecules suffer from more LP repulsions5). Protonation of NH3, PH3, and AsH3 removes completely the LP repulsion (angles = 109.5°), which results in stabilization of the protonated molecules, and this stabilization is larger for NH3 than for PH3 and AsH3. Therefore, the PA of NH3 is larger than the other two and the PA trend, NH3 > PH3 > AsH3, is in agreement with the trend in LP repulsions. In the case of H2O, H2S, and H2Se, both the neutral and protonated molecules suffer from LP/BP repulsion, whereas the neutral ones also experience LP/LP repulsion. Because the loss of stability due to LP/LP repulsion is larger than that due to LP/BP and BP/BP repulsions, we can assume that the loss of stability due to LP/LP repulsion in the neutral molecule is comparable, and what controls the stability of the protonated molecules and consequently the PA trends is LP/BP repulsion in the protonated molecules. In summary, because the repulsion effects in (H3O+, H3S+, and H3Se+) and (NH3, PH3, and AsH3) are similar, for NH3, PH3, and AsH3, the LP/BP repulsion in the neutral molecules controls the PA trend, whereas in the case of H2O, H2S, and

H2Se, the LP/BP repulsion in the protonated structures influences the PA trend. Although we can find several justifications in literature as to why PA of N site is larger than that of O site,31,32 it seems that the effect of LP repulsion has been ignored. Protonation of a nitrogen site completely removes the LP repulsion, whereas in the case of oxygen sites, only the LP/LP repulsion is diminished after protonation and LP/BP remains. However, we cannot always use LP repulsion to interpret the PA trend. For example, a recent study on the simple pnictogen oxides shows that the PA of the oxygen atom in these compounds increases as As−O > N−O > P−O.33 Interactions of the other cations including CH3+, Cu+, Al+, + Li , Na+, and K+ with H2O, H2S, H2Se, NH3, PH3, and AsH3 were also investigated. Figure 2 shows the optimized structures of the adduct cations as well as their angles and bond lengths. Previous studies show that the tendency of the cations to interact covalently with the molecules decreases as H+ > CH3+ > Cu+ > Al+ ≈ Li+ > Na+ > K+.19,26,28 In the covalent interactions, an empty orbital of the cation (Lewis acid) accommodates the LP electron of the Lewis base, and the LP/ BP repulsion is reduced. On the other hand, in highly electrostatic interactions, the charge/dipole dominates and a large part of the LP repulsion remains operative. Therefore, change in the H−M−H (M = O, S, Se, N, P, and As) angle upon cationization may be used as a marker of the nature of the interaction. For example, the H−O−H angle in H2O is about 105.1°, whereas this angle in H2O−H+, H2O−Na+, and H2O−K+ is 113.5°, 105.1°, and 104.6° respectively. These changes in the angles indicate that the H+ interacts covalently with H2O and reduces LP repulsion, whereas the highly electrostatic interactions of Na+ and K+ with H2O do not reduce significantly the LP repulsion. Also, Na+ and K+ are aligned with the direction of the dipole moment of H2O (planar structure of adduct ions), whereas H3O+ has a pyramidal structure.15 Therefore, the structure of the H2O− X+ adduct ions may be used as a measure of the nature of the H2O−X+ interactions so that planar structures correspond to the electrostatic interaction, and pyramidal geometries indicate more covalency. However, this is not a general index, and it is 11333


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Figure 2. Optimized structures of the adduct ions formed via interaction of H2O, H2S, H2Se, NH3, PH3, and AsH3 with H+, CH3+, Cu+, Al+, Li+, Na+, and K+. The angles and bond lengths are in degrees and Angstrom, respectively.

Figure 3. Plots of PAs of (a) amines and phosphines and (b) ethers and thioethers as functions of the number of the methyl groups (n).

covalency, it is expected that there is a relationship between the H−M−H angle in the adduct ions and ρ. Figure S1 (Supporting Information) shows the change in the H−M−H angles of the adduct ions versus the electron density (ρ) and the amount of the transferred charge. As the electron density and transferred charge (covalent contribution) increase, the

established only for H2O adduct ions because all of the H2S− X+ and H2Se−X+ form pyramidal adduct ions. It should be mentioned that the H−O−H angle in H2O−K+ is slightly smaller than that in H2O, which may be because of large size of K+ and increased LP/BP repulsion. Because electron density (ρ) at BCP of M−X (X = cation) is another good index of 11334


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Figure 4. Optimized structure for interaction of BeH2, BeF2, and BH3 with H2O, H2S, H2Se, NH3, PH3, and AsH3. The angles and bond lengths are in degree and Angstrom, respectively.

Table 2. Enthalpies and Gibbs Free Energies for the Interactions of BeH2, BeF2, and BH3 with H2O, H2S, H2Se, NH3, PH3, AsH3, (CH3)2O, (CH3)2S, (CH3)2Se, N(CH3)3, P(CH3)3, and As(CH3)3 Calculated by B3LYP/6-311++G(d,p) Methoda reaction

ΔH (kJ/mol)

ΔG (kJ/mol)

q (Mulliken)

q (MK)

H2O + BeH2 → H2O−BeH2 H2S + BeH2 → H2S−BeH2 H2Se + BeH2 → H2Se−BeH2 NH3 + BeH2 → H3N−BeH2 PH3 + BeH2 → H3P−BeH2 AsH3 + BeH2 → H3As−BeH2 H2O + BeF2 → H2O−BeF2 H2S + BeF2 → H2S−BeF2 H2Se + BeF2 → H2Se−BeF2 NH3 + BeF2 → H3N−BeF2 PH3 + BeF2 → H3P−BeF2 AsH3 + BeF2 → H3As−BeF2 (CH3)2O + BeH2 → (CH3)2O−BeH2 (CH3)2S + BeH2 → (CH3)2S−BeH2 (CH3)2Se + BeH2 → (CH3)2Se−BeH2 N(CH3)3 + BeH2 → (CH3)3N−BeH2 P(CH3)3 + BeH2 → (CH3)3P−BeH2 As(CH3)3 + BeH2 → (CH3)3As−BeH2 (CH3)2O + BeF2 → (CH3)2O−BeF2 (CH3)2S + BeF2 → (CH3)2S−BeF2 (CH3)2Se + BeF2 → (CH3)2Se−BeF2 N(CH3)3 + BeF2 → (CH3)3N−BeF2 P(CH3)3 + BeF2 → (CH3)3P−BeF2 As(CH3)3 + BeF2 → (CH3)3As−BeF2 H2O + BH3 → H2O−BH3 H2S + BH3 → H2S−BH3 H2Se + BH3 → H2Se−BH3 NH3 + BH3 → H3N−BH3 PH3 + BH3 → H3P−BH3 AsH3 + BH3 → H3As−BH3

−69.3, −69b −22.9, −24b −19.2 −86.8, −86b −23.5, −24b −11.2 −84.0, −81b −32.6, −31b −28.7 −109.4, −103b −31.7, −30b −19.1 −79.9 −50.0 −44.1 −89.9 −60.8 −39.2 −101.4 −61.4 −55.4 −112.9 −74.0 −51.8 −40.1 −36.8 −38.2 −104.7 −76.4 −50.8

−37.3 8.6 11.3 −57.0 5.0 18.5 −56.3 0.8 −0.7 −69.8 −1.2 15.6 −41.1 −14.2 −10.3 −51.0 −27.4 −7.9 −59.4 −22.5 −18.5 −70.8 −38.0 −19.7 0.5 5.2 3.2 −60.9 −33.3 −6.4

0.256 0.210 0.200 0.372 0.191 0.185 0.210 0.183 0.206 0.286 0.166 0.161 0.297 0.358 0.261 0.373 0.143 0.186 0.232 0.358 0.296 0.362 0.200 0.268 0.281 0.356 0.288 0.384 0.407 0.381

0.203 0.196 0.191 0.295 0.264 0.229 0.144 0.194 0.193 0.233 0.224 0.200 0.313 0.237 0.234 0.389 0.372 0.352 0.252 0.209 0.215 0.303 0.339 0.319 0.251 0.273 0.200 0.380 0.393 0.351

a

The charge on the Lewis bases in the complexes (q) was computed using Mulliken and MK charge distribution. bCalculated by B3LYP/6311+G(3df,2p) from ref 42.

because although more covalent interactions reduce LP/LP repulsion, these strong interactions lead in shorter cation/ molecule bond lengths and increased LP/BP and BP/BP repulsions.5 However, the general trend is that covalent

H−M−H angle becomes wider. Also, Figure S1 shows the widening of this angle as a function of the increase of the transferred charge from the Lewis base to the cation. In the case of H2O, the angle-ρ relationship is not completely linear 11335


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NH3, PH3, and AsH3 are summarized in Table 2. Interestingly, the calculated enthalpies for interaction of H2O and NH3 with BeH2 and BeF2 are about 3−4 times larger than the corresponding values for H2S, H2Se, PH3, and AsH3. This observation may be interpreted considering the large LP/LP and LP/BP repulsion in H2O and LP/BP repulsion in NH3. Because of the small size of N and O atoms, the LP/LP and LP/BP repulsions in H2O and NH3 are larger than H2S, H2Se, PH3, and AsH3 with larger central atoms. When H2O and NH3 interact with BeH2 and BeF2, donation of their electron pairs to an empty orbital of Be relieves the LP/LP repulsion, and a larger stabilization is achieved than for H2S, H2Se, PH3, and AsH3 adducts. We interpreted the strong interaction between NH3 and BeH2 basis on decrease in LP/BP; however, the change in the H−N−H angle before and after interaction is not considerable. The strong interaction results in a short distance between NH3 and BeH2, which increases the repulsion between BeH2 and N−H BP. In other words, although the BeH2 captures the LP electrons of NH3 and reduces LP/BP reduction, it substitutes the electrons and inserts a new type of repulsion. The amount of transferred charge from Lewis bases to BeH2 and BeF2 can confirm this hypothesis (Table 2). Although H2O and NH3 are less polarizable (Table S1) than H2S, H2Se, PH3, and AsH3, their transferred charges to BeH2 and BeF2 are larger. In addition to polarizability, the relief of LP repulsion is another factor that influences the amount of charge transfer. The large interaction energies of H2O and NH3 with BeH2 and BeF2 may be attributed in part to the large dipole moments of H2O and NH3 (Table S1) rather than the LP repulsion. To explore the effect of dipole moment, interaction between (CH3)2O, (CH3)2S, (CH3)2Se, N(CH3)3, P(CH3)3, and As(CH3)3 and BeH2 and BeF2 was studied. Although the dipole moments of (CH3)2O and N(CH3)3 are smaller than those of (CH3)2S, (CH3)2Se, P(CH3)3, and As(CH3)3 (Table S1), their interaction energies with BeH2 and BeF2 are larger (Table 2). In other words, the polarizability (α), dipole moment (μ), and transferred charge (q) trends are as (CH3)2Se > (CH3)2S > (CH3)2O, (CH3)2S > (CH3)2Se > (CH3)2O, and (CH3)2S > (CH3)2Se > (CH3)2O, respectively, whereas the interaction energy trend is as (CH3)2O > (CH3)2S > (CH3)2Se. These trends suggest that other factor(s) must be employed. Another effect strongly opposed to the three others is seemingly LP repulsion. Also, the difference between the interaction energies of the simple bases are larger than that for the methylated bases. The smaller difference in the interaction energies of the methylated Lewis bases may be attributed to smaller difference between LP/LP and LP/BP repulsions (Figure S3). For example, H2Se has a larger space to accommodate the two LP electrons compared to H2O; therefore, the LP/LP repulsion in H2O is larger than that in H2Se. On the other hand, because of CH3/CH3 repulsion in the both (CH3)2O and (CH3)2Se, there is not enough space for the LP electrons, and consequently their LP/LP repulsion is comparable in (CH3)2O and (CH3)2Se. In addition, in the methylated systems, the repulsive interaction between CH3 group and BeH2, for example, is considerable, and a determining factor for the H/BeH2 repulsive interaction in the simple base is not noticeable, and other factors influence the interaction energies. The short distance between N(CH3)3 and BeH2, because of their strong interaction, results in a large repulsion between BeH2 and methyl groups. Therefore, the

interactions with more charge transfer results in relief of the LP repulsion. 2.2. Effect of BP/BP and LP/BP Repulsions in NHn(CH3)3−n, PHn(CH3)3−n, (CH3)2−nHnO, and (CH3)2−nHnS. The effect of methyl groups on the PAs of simple amines, ethers, and alcohols has been previously studied.19,34 These studies showed that methyl group increases the PAs of the compounds; however, this increase is not linear (Figure 3). The observed curvature in the graph of PA versus the number of CH3 (n) group has been attributed to several physical and structural parameters such as saturation and electrostatic interaction.19 In our previous work, we showed that the graphs are fitted by a quadratic function19 PA = A + Bn + Cn2

(1)

where, A, B, and C are constants. The calculated PAs of the methylated Lewis bases have been collected in Table S3. Comparison of the PA versus n graphs of amines and phosphines (Figure 3a) or ethers and thioethers (Figure 3b) reveals that the curvature for the amines and ethers with smaller central atoms (N and O) are larger. The constant C, which stands for the curvature, is small for phosphines and thioethers and large for amines and ethers. Because there is a relationship between the curvature and the size of the acceptor atom, the curvature may be attributed to LP repulsion. Figure S2 compares the geometrical parameters of N(CH3)3, P(CH3)3, (CH3)2O, and (CH3)2S with their protonated forms. The CH3−N−CH3 and CH3−P−CH3 angles in the neutral molecules are 111.7 and 99.4°, respectively. After protonation, the CH3−P−CH3 angle increases to 111.3°, whereas the CH3−N−CH3 angle remains constant. In other words, P(CH3)3 gets rid of CH3/CH3 (BP/BP) repulsion because of protonation, whereas protonation does not decrease CH3/CH3 repulsion in N(CH3)3. Therefore, the graph slope of PA versus the number of CH3 groups is larger for the methyl phosphines. In the case of (CH3)2O and (CH3)2S, the change in the CH 3 −O−CH 3 and CH 3 −S−CH 3 angles after protonation is comparable; however, the CH3/LP repulsion in (CH3)2S−H+ is smaller (compare the angles between LP and CH3 in Figure S2). 2.3. Interaction between Lewis Bases and Neutral Lewis Acids. Lewis acids relieve LP/BP and LP/LP repulsion in the Lewis bases by withdrawing their electron pairs. In the previous section, the interaction of cations with the Lewis bases was investigated, and in this section, interactions of the Lewis bases with some neutral Lewis acids are studied. Because of their electron deficiency, the boron atom in BX3 and the beryllium atom in BeX2 are electron-acceptor centers, therefore, BH3, BeH2, and BeF2 are known as neutral Lewis acids.35−40 BF3 is also a neutral Lewis acid; however, it was not considered here because we could not fully optimize some adducts due to strong interaction between F atom of BF3 and H atoms of the Lewis bases H2O, H2S, H2Se, and AsH3. The net dipole moments of isolated BH3, BeH2, and BeF2 are zero; however, BeX2 becomes bent and BH3 pyramidal when coordinated; therefore, their interactions are slightly electrostatic. Figure 4 shows the optimized structures for interaction of BeH2, BeF2, and BH3 with H2O, H2S, H2Se, NH3, PH3, and AsH3. Because the H−H distance in the Lewis bases is directly proportional to BP/BP repulsion,5 these distances are also shown in Figure 4. The calculated enthalpies and Gibbs free energies for the interactions of BeH2, BeF2, and BH3 with H2O, H2S, H2Se, 11336


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C−N−C angle in BeH2−N(CH3)3 complex is slightly smaller than that in isolated N(CH3)3. Interaction of BH3 with H2O, NH3, H2S, and H2Se does not lead in considerable change in the H−M−H angles, whereas it changes the H−P−H and H−As−H angles. Interaction of H2O with BeH2 is about 30 kJ/mol stronger than its interaction with BH3. This difference may not be attributed solely to the larger tendency of BeH2 to accept an electron pair of the oxygen atom and reduction of LP repulsion because the Mulliken charge distribution shows that the amount of transferred charge in the case of BeH2 and BH3 interactions are not so different (Table 2). Hence, this difference in the interaction energies may be interpreted on the basis of the electrostatic interaction. Mo and Gao41 showed that the Lewis base/Lewis acid interactions with interaction energies between 12 and 38 kJ/mol are mainly electrostatic. Therefore, we calculated the dipole moments of BeH2, BeF2, and BH3 molecules in their complexes (Table S4). The dipole moments of BeH2 and BeF2 with bent geometry and pyramidal BH3 are about 1.5, 2.0, and 0.5 D, respectively. Comparison of the dipole moments shows that the electrostatic contributions to BeH2 and BeF2 interactions are about 3 and 4 times stronger than that for BH3. Because of small dipole moments of PH3 and AsH3 (0.55 and 0.2 D, respectively), their large interaction energies with BH3 (76.4 and 50.8 kJ/mol, respectively) may not only be because of electrostatic contribution. Furthermore, both Merz-Kollman (MK) and Mulliken charge analyses show large amount of transferred charge in the PH3/BH3 and AsH3/ BH3 complexes. This nonelectrostatic interaction materializes as considerable changes in the H−P−H and H−As−H angles because of complexation with BH3 (Figure 4).

used for interpreting observed trends in CA. Interaction of the Lewis bases with BeH2 , BeF2, and BH3 was studied energetically and structurally. H2O and NH3 interact with BeH2, BeF2, and BH3 more strongly compared to PH3, AsH3, H2S, and H2Se. The difference in the interaction energies was attributed to the larger relief of LP repulsion in H2O and NH3 after interaction with BeH2 and BeF2, and BH3.

4. COMPUTATIONAL DETAILS Structures of all molecules and complexes were fully optimized employing density functional theory using the B3LYP functional in the gas phase. The 6-311++G(d,p) basis set was used for all calculations which includes diffuse and polarization functions for both hydrogen and heavy atoms. Frequency calculations were performed at the same level of theory and at 298.15 K to obtain thermodynamic quantities of Lewis base/Lewis acid interactions such as ΔH and ΔG. Accuracy of the B3LYP method for the ion/molecule systems has been confirmed previously.43 For the systems including ions, B3LYP with affordable basis sets exhibits better performance compared to X3LYP, M06-2X, and M06-L methods.44 For more comparison, CAs and cation basicities (CBs) were also computed using a complete basis set method, CBS-Q.45 MK and Mulliken charge distributions were used to compute the transferred charge from the Lewis bases to the Lewis acids. The van der Waals radii of As and Se atoms, 1.85 and 1.90 Å, respectively, were used in the MK charge calculations. All calculations were performed using Gaussian 09 software.46 The atom in molecule (AIM) calculations were carried out using AIM2000 software47 to determine the electron density, ρ, and its Laplacian, −∇2ρ at BCPs. CA of a molecule (M) is calculated as −ΔH of reaction 2

3. CONCLUSIONS Interactions of NH3, PH3, AsH3, H2O, H2S, and H2Se with some typical singly charged cations (H+, CH3+, Cu+, Li+, Na+, K+, and Al+) and neutral Lewis acids (BeH2, BeF2, and BH3) were (re)examined from the viewpoint of the internal repulsion between electron pairs. The bases H2O, H2S, and H2Se suffer from both LP/LP and LP/BP repulsions, whereas NH3, PH3, and AsH3 experience only LP/BP repulsion. Because of the donor/acceptor interaction, the LP electrons of the base are in part localized in an empty orbital of the Lewis acid, leading in reducing the LP repulsion and change in the H−M−H angles (M = N, P, As, O, S, and Se). However, because the charge transfer is not complete and it is different for different bases and cations, the change in the H−M−H angles is different. Therefore, changes in the H−M−H angle because of the interaction can be used to interpret the nature of the interaction, that is, charge transfer or covalency of the interaction. However, there is not a straightforward relationship between angle change and transferred charge, for example, because many factors influence these interactions. Namely, CA of a molecule is multifactorial, involving essentially polarizability (α) and dipole moment (μ) of the molecule, electron affinity of the cation, EWG and EDG connected to the cationacceptor site, and orientation of the cation relative to the molecule. The influence of these factors on the CA has been extensively investigated. In this work, we observed that in some cases the CAs cannot be interpreted on the sole basis of these factors, and LP repulsion should also be considered. In other words, change in LP repulsion in a molecule during its interaction with a cation becomes significant as regards to other factors. In summary, LP repulsion affects CA and can be

M (g) + X + (g) → MX + (g)

(2)

where X+ is the cation. The −ΔG of reaction 2 is reported as CB of M.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsomega.8b01644.

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Dipole moment and polarizability values, calculated ρ, ∇2ρ, G(r), and V(r), relationship between H−M−H angle and ρ, structures of N(CH3)3, P(CH3)3, (CH3)2O, and (CH3 ) 2S, structures of the Lewis base/BeX2 complexes, PA values, and dipole moments of BeX2 and BF3 (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. Phone: +98 28 3390 1367 (Y.V.). *E-mail: [email protected]. Phone: +33 49207 6361 (J.-F.G.). ORCID

Younes Valadbeigi: 0000-0002-4189-2987 Jean-François Gal: 0000-0002-5500-5461 Notes

The authors declare no competing financial interest. 11337


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ACKNOWLEDGMENTS Y.V. wishes to express his thanks to Imam Khomeini International University in Qazvin, Iran.

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