Alkali Metal Cation versus Proton and Methyl Cation Affinities: Structure and Bonding Mechanism.

We have analyzed the structure and bonding of gas-phase Cl-X and [HCl-X](+) complexes for X(+)= H(+), CH3 (+), Li(+), and Na(+), using relativistic density functional theory (DFT). We wish to establish a quantitative trend in affinities of the anionic and neutral Lewis bases Cl(-) and HCl for the various cations. The Cl-X bond becomes longer and weaker along X(+) = H(+), CH3 (+), Li(+), and Na(+). Our main purpose is to understand the heterolytic bonding mechanism behind the intrinsic (i.e., in the absence of solvent) alkali metal cation affinities (AMCA) and how this compares with and differs from those of the proton affinity (PA) and methyl cation affinity (MCA). Our analyses are based on Kohn-Sham molecular orbital (KS-MO) theory in combination with a quantitative energy decomposition analysis (EDA) that pinpoints the importance of the different features in the bonding mechanism. Orbital overlap appears to play an important role in determining the trend in cation affinities.

Introduction

Designing and optimizing routes in chemical synthesis requires knowledge of the thermochemistry involved in the targeted compounds or reactions. The alkali metal cation affinity (pan class="Chemical">AMCA) is a thermochemical quantity that plays an important role for predicting and understanding stability as well as reactivity in structures and processes in which such ions bind to, and/or dissociate from Lewis‐basic nitrogen, oxygen, and other atoms. Examples are lithium and sodium battery electrochemistry,1 alkali metal cation transport in biological systems (e.g., sodium or potassium cations in ion channels in cell membranes),2, 3 stabilization of nucleic acid structures (DNA, RNA and PNA),4 and the dissociation of salts.5, 6 However, the ACMA has received relatively little attention in the literature and if compared with, for example, the proton affinity (PA).7

The thermochemical quantity ACMA is defined as the enthalpy change associated with heterolytic dissociation of the complex between the alkali metal cation (X+) and the anionic (B−) or neutral base (B):

The purpose of the present study is twofold. The main objective is to obtain a better understanding of the physical factors behind the AMCA. To this end, we have carried out a detailed analysis of the bonding mechanism behind the intrinsic (i.e., in the absence of interfering solvent effects) ACMA of a negative and a neutral model base, namely, pan class="Chemical">chloride and hydrogen chloride, for both the lithium and the sodium cation (B− = Cl−, B = HCl, X+ = Li+, Na+ in [Equations (1)–(2)]. Our analysis has been carried out in the conceptual framework of Kohn–Sham molecular orbital (KS‐MO) theory in combination with a quantitative energy decomposition analyses (EDA).

In the second place, we wish to compare the nature of ACMA with that of the corresponding PA7a,7b,7c and methyl cation affinities (MCA).8 Thus, X+ = H+ and CH3 + are included in our discussion of the bonding mechanism. In addition to the ACMA values of all bases (ΔH 298 AMCA), we also report the corresponding 298 K reaction entropies (ΔS 298 AMCA, provided as −T ΔS 298 AMCA) and 298 K reaction Gibbs‐free energies (ΔG 298 AMCA).

Computational Methods

Basis sets

All calculations were performed with the Amsterdam Density functional (ADF) program developed by Baerends and others.9, 10 Molecular orbitals (MOs) were expanded using two large, uncontracted sets of Slater‐type orbitals (STO): TZ2P for geometry optimization and vibrational analysis, and QZ4P for single‐point energy calculations.11 The TZ2P basis set is of triple‐ζ quality, augmented by two sets of polarization functions (d and f on heavy atoms; 2p and 3d sets on H). The QZ4P basis, which contains additional diffuse functions, is of quadruple‐ζ quality, augmented by four sets of polarization functions (two 3d and two 4f sets on C, N, O; two 2p and two 3d sets on H). Core electrons (e.g., 1s for second‐period, 1s2s2p for third‐period, 1s2s2p3s3p for fourth‐period, 1s2s2p3s3p3d4s4p for fifth‐period, and 1s2s2p3s3p3d4s4p4d for sixth‐period atoms) were treated by the frozen core approximation.10 An auxiliary set of s, p, d, f, and g slater‐type orbitals was used to fit the molecular density and to represent the coulomb and exchange potentials accurately in each self‐consistent field (SCF) cycle.

Density functional

Energies and gradients were calculated using the local density approximation (LDA: Slater12 exchange and VWN13 correlation) with gradient corrections14, 15 due to Becke (exchange) and Perdew (correlation) added self‐consistently. This is the BP86 density functional, which is one of the three best DFT functionals for the accuracy of geometries7a–7b, 16 with an estimated unsigned error of 0.009 Å in combination with the TZ2P basis set. In a previous study7a–7c on the proton affinities of anionic species, we compared the energies of a range of other DFT functionals, to estimate the influence of the choice of DFT functional. These functionals included the Local Density Approximation (LDA), Generalized Gradient Approximation (GGAs), meta‐GGA and hybrid functionals. Scalar relativistic corrections were included self‐consistently using the zeroth order regular approximation (ZORA).17 Spin‐orbit coupling effects were neglected because they are small for closed‐shell systems as they occur in this investigation.

Geometries, vibrational frequencies, and thermodynamic corrections have been computed using the TZ2P basis set: ZORA‐BP86/TZ2P level. All electronic energies have been computed in a single‐point fashion using the QZ4P basis set, based on the ZORA‐BP86/TZ2P geometries: ZORA‐BP86/QZ4P//ZORA‐BP86/TZ2P. For comparison, we have also computed the above‐mentioned quantities using the B3LYP hybrid functional18 in combination with TZ2P basis set for the geometries and frequencies calculations, and with QZ4P for the single‐point energies, that is, ZORA‐B3LYP/QZ4P//ZORA‐B3LYP/TZ2P. Note that bonding analyses have been carried out at the ZORA‐BP86/TZ2P level of theory.

Thermochemistry

Enthalpies at 298.15 K and 1 atmosphere (ΔH 298) were calculated from electronic bond energies (ΔE) at ZORA‐BP86/QZ4P//ZORA‐BP86/TZ2P and vibrational frequencies at ZORA‐BP86/TZ2P using standard thermochemistry relations for an ideal gas, according to [Eq. (3)]:19

Here, ΔE trans,298, ΔE rot,298 and ΔE vib,0 are the differences between the reactant (i.e., BX(+), the base‐cation complex) and products (i.e., B(−)+X+, the neutral or anionic base and the cation) in translational, rotational and zero point vibrational energy, respectively. Δ(ΔE vib,0)298 is the change in the vibrational energy difference as one goes from 0 to 298.15 K. The vibrational energy corrections are based on our frequency calculations. The molar work term Δ(pV) is (Δn)RT; Δn=+1 for one reactant BX dissociating into two products B− and X+. Thermal corrections for the electronic energy are neglected.

Bond‐energy decomposition

As mentioned above, bonding analyses have been carried out at the ZORA‐BP86/TZ2P level of theory. The overall bond energy ΔE bond (which corresponds to −ΔE in [Eq. (3)]) between base B(−) and cation X+ is made up of two major components:20

Here, the strain energy, ΔE strain, is the amount of energy required to deform the separate base and cation from their equilibrium structure to the geometry that they acquire in the overall complex BX(+). The interaction energy ΔE int corresponds to the actual energy change when the geometrically deformed base and cation are combined to form the overall complex.

The interaction ΔE int can be further analyzed, in the framework of the Kohn–Sham molecular orbital (MO) model, using an energy decomposition into electrostatic interaction attraction, Pauli repulsion, and (attractive) orbital interactions:9, 20

The term ΔV elstat corresponds to the classical electrostatic interaction between the unperturbed charge distributions of the prepared (i.e., deformed) base and cation. This term is usually attractive. The Pauli‐repulsion ΔE Pauli comprises the destabilizing interactions between occupied orbitals and is responsible for the steric repulsion. The orbital interaction ΔE oi in any MO model, and therefore also in Kohn–Sham theory, accounts for charge transfer (i.e., donor–acceptor interactions between occupied orbitals on one moiety with unoccupied orbitals of the other, including the HOMO–LUMO interactions) and polarization (empty/occupied orbital mixing on one fragment due to the presence of another fragment).

Analysis of the charge distribution

The electron density distribution is analyzed at ZORA‐BP86/TZ2P using the Voronoi deformation density (VDD) method21, 22 for computing atomic charges. The VDD atomic charge Q A VDD is computed as the (numerical) integral23 of the deformation density Δρ(r)=ρ(r) − ΣB ρ B(r) in the volume of the Voronoi cell of atom A [Eq. (6)]. The Voronoi cell of atom A is defined as the compartment of space bound by the bond midplanes on and perpendicular to all bond axes between nucleus A and its neighboring nuclei (cf. the Wigner–Seitz cells in crystals).22c

In [Eq. (6)], ρ(r) is the electron density of the molecule and ΣB ρ B(r) the superposition of atomic densities ρ B of a fictitious promolecule without chemical interactions that is associated with the situation in which all atoms are neutral. The interpretation of the VDD charge Q A VDD is rather straightforward and transparent. Instead of measuring the amount of charge associated with a particular atom A, Q A VDD directly monitors how much charge flows, due to chemical interactions, out of (Q A VDD>0) or into (Q A VDD<0) the Voronoi cell of atom A, that is, the region of space that is closer to nucleus A than to any other nucleus.

Results and Discussion

Structures and energies

Our computed ZORA‐BP86/QZ4P//BP86/TZ2P geometries and affinities at 298 K (ΔH), the corresponding entropies ΔS (provided as −TΔS values) and free energies ΔG are summarized in Tables 1 and 2 for the chloride and pan class="Chemical">hydrogen chloride bases, respectively. In both tables we compare the results for ZORA‐BP86/QZ4P//BP86/TZ2P with ZORA‐B3LYP/QZ4P//B3LYP/TZ2P and MP2 calculations as well as with the experiment. As expected,7a,7b both functionals BP86 and B3LYP emerge as good functionals (vide infra), they agree for both ClX and [HCl−X]+ complexes within a few hundredths of an Å (Cl−X distances) and a few kcal mol−1 (298 K heterolytic bonds dissociation enthalpies ΔH) with the available experimental and/or other computational reference data.24, 25, 26, 27, 28, 29, 30, 31, 32, 33 Both functionals show mean absolute deviation (MAD) values of 2.0 kcal mol−1 with respect to the experimental values, while MP2 achieves a slightly worse MAD value of 2.5 kcal mol−1. Based on the results of previous studies7a,7b on the proton affinities, where BP86 functional emerges slightly more accurate than B3LYP, we have chosen to continue our calculation using BP86.

Table 1

Cation affinity data (in kcal mol−1, Å) for the chloride anion.

Cation	H+	CH3 +	Li+	Na+
−T ΔS [a]	−5.4	−7.9	−5.2	−5.1
ΔG [a]	328.2	223.5	147.7	126.9
ΔH BP86 [a]	333.6	231.4	152.9	132.0
ΔH B3LYP [b]	332.7	224.1	155.2	133.9
ΔH MP2 [c]	331.3	228.6	153.9	134.5
ΔH exp [d]	333.5±0.002	227.3±0.6	152.0	132.6
d(X−Cl)[a]	1.292	1.801	2.030	2.377
d(X−Cl)Exp [d]	1.275	1.785	2.021	2.361

[a] This work. Computed at ZORA‐BP86/QZ4P//ZORA‐BP86/TZ2P for 298.15 K and 1 atm. In parentheses: enthalpies computed at ZORA‐BP86/TZ2P. [b] This work. Computed at ZORA‐B3LYP/QZ4P//ZORA‐B3LYP/TZ2P for 298.15 K and 1 atm. [c] MP2 values from Refs. 24, 25 and 26. [d] Experimental values from Refs. 24, 27 and 28.

Table 2

Cation affinity data (in kcal mol−1, Å, degrees) for hydrogen chloride.

Cation	H+	CH3 +	Li+	Na+
−T ΔS [a]	−5.9	−8.7	−5.4	−5.0
ΔG [a]	130.2	46.1	10.3	4.8
ΔH BP86 [a]	136.2	54.8	15.7	9.9
ΔH B3LYP [b]	135.0	49.2	16.9	10.9
ΔH MP2 [c]	134.2	45.7	15.7	8.9
ΔH exp [d]	133.1	51.6	n.a.	12.1±1.5
d(X−Cl)[a]	1.324	1.876	2.351	2.755
d(Cl−H)[a]	1.324	1.315	1.302	1.299
(X−Cl−H)[a]	93.6	99.5	103.6	106.1

[a] This work Computed at ZORA‐BP86/QZ4P//ZORA‐BP86/TZ2P for 298.15 K and 1 atm. In parentheses: enthalpies computed at ZORA‐BP86/TZ2P. [b] This work. Computed at ZORA‐B3LYP/QZ4P//ZORA‐B3LYP/TZ2P for 298.15 K and 1 atm. [c] MP2 values from Refs. 29, 30 and 31. [d] Experimental values from Refs. 28, 32 and 33 (n.a.=not available).

In the neutral complexes ClX, between pan class="Chemical">chloride and the various cations, the X−Cl bond distance increases systematically from 1.292 to 1.801 to 2.030 to 2.377 Å along X+ = H+, CH3 +, Li+, and Na+, respectively (see Table 1). At the same time, the cation affinity of the chloride anion, that is, ΔH for reaction 1 (with B− = Cl−), decreases if one goes from 333.6 (H+) to 231.4 (CH3 +) to 152.9 (Li+) to 132.0 kcal mol−1 (Na+; see Table 1). The corresponding Gibbs free energies Δacid G 298 show the same trends because entropy corrections −TΔacid S 298 are relatively small, between −5.1 and −7.9 kcal mol−1.

Likewise, in the cationic complexes [HCl−X]+ between pan class="Chemical">hydrogen chloride and the various cations, the X−Cl bond distance increases again systematically from 1.324 to 1.876 to 2.351 to 2.755 Å along X+ = H+, CH3 +, Li+ and Na+, respectively (see Table 2). At the same time, as the X−Cl bond becomes longer, the H−Cl bond contracts, although only very slightly so (from 1.324 to 1.315 to 1.302 to 1.299 Å) and the H−Cl−X angle adopts a substantially less bent configuration (varying from 93.6° to 99.5° to 103.6° to 106.1°). The cation affinity of the hydrogen chloride molecule, that is, ΔH for reaction 2 (with B = HCl), decreases along the same series from 136.2 (H+) to 54.8 (CH3 +) to 15.7 (Li+) to 9.9 kcal mol−1 (Na+; see Table 2). Again, the corresponding Gibbs free energies ΔG show the same trends as ΔH.

Bonding mechanism: Cl− cation affinities

Our heterolytic Cl−X bonding analyses have been carried out at ZORA‐BP86/TZ2P and comprise three complementary approaches: 1) quantitative analysis of the Kohn–Sham orbital interaction mechanism; 2) the associated bond energy decomposition; and 3) analysis of the electron‐density distribution (see Table 3 and Figure 1). The trend in cation affinity ΔH, an enthalpic quantity, is determined by that in the electronic cation affinity energy ΔE associated with reaction 1. Note that, for the bonding analysis, we use the bond energy ΔE bond=−ΔE, that is, the energy change associated with bond formation Cl−+X+ → ClX (see Table 3). The main contributor to ΔE bond=ΔE strain+ΔE int, in turn, is the interaction energy ΔE int between the two fragments which determines the overall trend in stability. ΔE int weakens strongly from −339.5 to −261.6 to −155.5 to −134.0 along H+, pan class="Chemical">CH3 +, Li+ and Na+. The strain energy ΔE strain does not affect this trend in interaction. ΔE strain is exactly zero kcal mol−1 for all monoatomic fragments (chloride, proton, alkali metal cations). Only in the case of the methyl cation, there is a destabilizing strain energy of 24.7 kcal mol−1 which originates from the fact that planar CH3 + must deform into a pyramidal geometry as it binds to Cl−. This strain effect is too small to change the overall trend in relative stability ΔE bond.

Table 3

Analysis of the X−Cl bonding mechanism between Cl− and X+.[a]

		Cation X+
		H+	CH3 +	Li+	Na+
Bond energy decomposition (in kcal mol−1)
ΔE σ		−157.5	−184.6	−13.6	−8.1
ΔE π		−22.1	−21.6	−12.5	−6.9
ΔE oi		−179.6	−206.2	−26.1	−14.9
ΔE Pauli		0.0	156.4	30.2	26.0
ΔV elstat		−159.9	−211.9	−159.6	−145.1
ΔE int		−339.5	−261.6	−155.5	−134.0
ΔE strain		0.0	24.7	0.0	0.0
ΔE bond		−339.5	−236.9	−155.5	−134.0
ΔH bond=−ΔH TZ2P		−336.3	−234.4	−155.4	−134.2
X + Fragment orbital energy (in eV)
ɛLUMO		−13.6	−15.4[b]	−6.9	−7.1
〈Cl−|X+〉 Fragment orbital overlap		〈3p σ|1s〉	〈3p σ|2a1〉	〈3p σ|2s〉	〈3p σ|3s〉
〈HOMO|LUMO〉		0.52	0.35	0.29	0.26
Fragment orbital populations (in e) [c]
Cl−	HOMO−1	1.89 (3s)	1.96 (3s)	1.96 (3s)	1.98 (3s)
	HOMO	1.27 (3p σ)	1.22 (3p σ)	1.82 (3p σ)	1.84 (3p σ)
X+	LUMO	0.74 (1s)	0.81 (2a 1)	0.08 (2s)	0.12 (3s)
	LUMO+1	0.02 (2s)[d]	0.01 (3a 1)	0.08 (2p σ)	0.03 (3p σ)
VDD atomic charges (in a.u.)
Q(X in XCl)		+0.098	+0.131[e]	+0.475	+0.567

[a] Computed at ZORA‐BP86/TZ2P. See also Methods section. [b] Orbital energy of CH3 + in the geometry it adopts in ClCH3. [c] Pertinent orbital indicated in parentheses. [d] P(2p σ)=0.04 e. [e] Sum of atomic charges on CH3 moiety.

Figure 1

Orbital interaction diagram for XCl composed of Cl− and X+, emerging from our Kohn–Sham orbital analyses at ZORA‐BP86/TZ2P (X+ = H+, CH3 +, Li+, Na+). In bold: Gross Mulliken frontier molecular orbital (FMO) contributions to the molecular orbital (MO). Parentheses indicate no Pauli repulsion for X+ = H+.

[a] Computed at ZORA‐BP86/TZ2P. See also Methods section. [b] Orbital energy of CH3 + in the geometry it adopts in pan class="Chemical">ClCH3. [c] Pertinent orbital indicated in parentheses. [d] P(2p σ)=0.04 e. [e] Sum of atomic charges on CH3 moiety.

The trend in ΔE int originates from a combination of two phenomena in the bonding mechanism (see Table 3): 1) the orbital interactions ΔE oi and electrostatic attraction ΔV elstat are strongest for CH3 + (−206.2 and −211.9 kcal mol−1) and become systematically weaker as we further proceed to H+, Li+ and Na+; 2) a sizeable Pauli repulsion ΔE Pauli of 156.4 kcal mol−1 causes the methyl cation affinity (MCA) to become smaller than the proton affinity (PA). The strong Pauli repulsion in the case of CH3 + results from the overlap of the Cl− 3s and especially 3p σ AOs with the C−H bonding valence 1a 1 orbital of CH3 +.8 Such Pauli repulsion was shown to play an even more important role in complexes between sterically more demanding bases and alkyl cations.37, 38 The chloride anion has zero Pauli repulsion with the proton (the latter has no electrons at all) and only little Pauli repulsion (26‐30 kcal mol−1) with the alkali metal cations which have electrons only in very compact core AOs.

The weakening in ΔE oi along CH3 +, H+, Li+, and Na+ can be traced directly to covalent features in the bonding mechanism, in particular, the HOMO–LUMO interactions in the σ‐electron system (see Figure 1 and Table 3). First, the energy of the cation LUMO increases drastically as we go from the methyl cation and proton (−15.4 eV and −13.6 eV) to the alkali pan class="Chemical">metal cations (−6.9 and −7.1 eV). Second, the HOMO–LUMO bond overlap decreases systematically when the LUMO, as can be seen in Figure 2, contains more nodal surfaces and becomes more diffuse along H+ (0.52), CH3 + (0.35), Li+ (0.29) and Na+ (0.26). The combined result of these two factors of HOMO–LUMO gap and overlap results in the steady decrease of the σ‐orbital interactions ΔE σ from −184.6 to −157.5 to −13.6 to −8.1 kcal mol−1 along CH3 +, H+, Li+ and Na+. This trend is reflected by the orbital‐interaction diagram in Figure 1 which shows that the bonding HOMO+LUMO combination in the overall complex is increasingly polarized towards the chloride fragment if one goes from ClCH3 to ClH to ClLi to ClNa. In line with the trend in orbital interactions, the VDD charges of the cation‐group show that the polarity of the chloride‐cation bond increases if we go from hydrogen in ClH (+0.098 au) and methyl in ClCH3 (+0.131 au), on one hand, to the alkali metals in ClLi and ClNa (0.475 and 0.567 au; see Table 3).

Figure 2

Contour plots of cation LUMOs (scan values: ±0.0, ±0.02, ±0.05, ±0.1, ±0.2, ±0.5).

The weakening in ΔE σ from ClLi to ClNa is reinforced by the fact that the former complex gains stabilization from the involvement of a low‐lying pan class="Chemical">lithium 2p σ AO which accepts 0.08 electrons from the chloride lone pair. The corresponding sodium 3p σ AO accepts much less, only 0.03 electrons (see Table 3; cf. 6, 36).

The π‐orbital interactions ΔE π are in all model complexes smaller than the ΔE σ term, only slightly so for lithium and pan class="Chemical">sodium cations and even significantly in the case of the proton and methyl cation. Still they follow approximately the same trend which therefore comes out even more pronouncedly in the overall orbital interactions ΔE oi. The origin of the π stabilization ΔE π is that the chloride 3p π orbitals are stabilized in the presence of the cation. This stabilizing effect diminishes as the chloride‐cation distance increases along Cl−H, Cl−Li and Cl−Na. In Cl−CH3, these ΔE π do not only consist of a stabilization of the chloride 3p π orbitals in the electrostatic field of the cation but they also gain stabilization due to π‐donor‐acceptor interactions with the empty C−H antibonding 2 e orbitals of CH3 +.

Finally, the electrostatic attraction ΔV elstat is in all case larger than the orbital interactions ΔE oi, especially in the case of the alkali metal cation complexes. The latter have a relatively weak ΔE oi term and are predominantly electrostatically bound. The relatively strong electrostatic attraction in all four model systems results from the charge separation associated with dissociation of a neutral complex into two oppositely charged fragments [Eq. (1)]. The exact trend in electrostatic attraction depends in an intricate manner on the shape and mutual penetration of the fragment charge distributions. Therefore, significant deviations of Coulombs law q 1⋅q 2/r 12 for two point charges occur. Still, one can observe a slight weakening in ΔV elstat from −159.9 to −159.6 to −145.1 kcal mol−1 as the equilibrium bond length increases along pan class="Chemical">ClH to ClLi and ClNa (see Table 1 and 3).

Bonding mechanism: HCl cation affinities

The ZORA‐BP86/TZ2P results of our heterolytic HCl−X+ bonding analyses have been collected in Table 4. The cation affinity ΔH for the neutral base pan class="Chemical">HCl (9 to 136 kcal mol−1) are substantially smaller than those for the anionic base Cl− (134 to 336 kcal mol−1) but the trend along the four cations is the same for both bases (compare Tables 3 and 4).

Table 4

Analysis of the Cl−X Bonding Mechanism between HCl and X+.[a]

		Cation X+
		H+	CH3 +	Li+	Na+
Bond energy decomposition (in kcal mol−1)
ΔE A′		−151.6	−131.3	−11.3	−5.9
ΔE A′′		−9.4	−6.7	−2.3	−1.2
ΔE oi		−161.0	−138.0	−13.7	−7.1
ΔE Pauli		0.0	103.9	6.8	4.7
ΔV elstat		21.0	−39.0	−8.5	−6.9
ΔE int		−140.0	−73.1	−15.3	−9.4
ΔE strain		0.3	15.2	0.0	0.0
ΔE bond		−139.7	−57.9	−15.3	−9.4
ΔH bond=−ΔH TZ2P		−135.8	−54.5	−15.0	−9.3
X + Fragment orbital energy (in eV)
ɛLUMO		−13.6	−15.1[b]	−6.9	−7.1
〈ClH|X+〉 Fragment orbital overlap		〈2 π|1s〉	〈2 π|2a 1〉	〈2 π|2s〉	〈2 π|3s〉
〈HOMO|LUMO〉		0.48	0.32	0.24	0.19
Fragment orbital populations (in e) [c]
HCl	HOMO−1	1.95 (5 σ)	1.96 (5 σ)	1.98 (5 σ)	1.98 (5 σ)
	HOMO	1.34 (2 π)	1.41 (2 π)	1.87 (2 π)	1.92 (2 π)
X+	LUMO	0.66 (1s)	0.61 (2a 1)	0.05 (2s)	0.04 (3s)
	LUMO+1	0.03 (2s)[d]	0.00 (3a 1)	0.04 (2p σ)	0.02 (3p σ)
VDD atomic charges (in a.u.)
Q(X in [X−ClH]+)		+0.311	+0.412[e]	+0.702	+0.777

[a] Computed at ZORA‐BP86/TZ2P. See also Methods section. [b] Orbital energy of CH3 + in the geometry it adopts in ClCH3. [c] Pertinent orbital indicated in parentheses. [d] P(2p σ)=0.03 e. [e] Sum of atomic charges on CH3 moiety.

[a] Computed at ZORA‐BP86/TZ2P. See also Methods section. [b] Orbital energy of CH3 + in the geometry it adopts in pan class="Chemical">ClCH3. [c] Pertinent orbital indicated in parentheses. [d] P(2p σ)=0.03 e. [e] Sum of atomic charges on CH3 moiety.

The decrease in cation affinities from anionic to neutral base by 125–200 kcal mol−1 mainly stems from a similar weakening, that is, by 138–187 kcal mol−1, in the electrostatic attraction ΔV elstat. The latter is even 21 kcal mol−1 repulsive in the case of the proton affinity.39 This is a direct consequence of the fact that, upon heterolytic dissociation of HCl−X+, no charge separation occurs [Eq. (2)] while charge separation does occur for Cl−X [Eq. (1)]. Likewise, also the orbital interactions ΔE oi of the neutral base pan class="Chemical">HCl with the various cations (see Table 4) are weaker than the corresponding one for the anionic base (see Table 3) which has orbitals that are effectively at higher energy due to the much more negative electrostatic potential. Altogether, the weaker ΔV elstat and ΔE oi terms in the case of the HCl−X+ systems lead to substantially longer Cl−X equilibrium distances (compare Tables 1 and 2) and smaller Pauli repulsion ΔE Pauli (compare Tables 3 and 4). Note also the somewhat smaller deformation strain for the more weakly bound methyl cation complex HClCH3 + as compared with ClCH3.

The trend in ΔE int stems directly from the orbital interactions ΔE oi and not from the rather weak electrostatic attraction ΔV elstat anymore. The orbital interactions ΔE oi become weaker from −161 to −138 to −14 to −7 kcal mol−1 along H+, CH3 +, Li+, and Na+. The trend in orbital interactions correlates directly with the HOMO–LUMO bond overlap (0.48, 0.32, 0.24, and 0.19) and is reflected by the population of the LUMO (0.66, 0.61, 0.05, and 0.04 e), both of which decrease along the series (see Table 4). In line with this, the polarity of the pan class="Chemical">HCl−X+ bond increases along the series, as indicated by the cation's VDD atomic charge (+0.3, +0.4, +0.7, and +0.8 a.u.).

A sizeable Pauli repulsion ΔE Pauli of 103.9 kcal mol−1 of the HCl HOMO and HOMO−1 with the C−H bonding valence 1a 1 orbital of CH3 + significantly weakens the MCA but does not change the trend.8 Hydrogen chloride has zero Pauli repulsion with the proton (the latter has no electrons at all) and only little Pauli repulsion (4.7–6.8 kcal mol−1) with the alkali metal cations which have electrons only in very compact core AOs.

Conclusion

Alkali metal cation affinities (pan class="Chemical">AMCA) of both the anionic and neutral Lewis bases Cl− and HCl are smaller than the corresponding proton (PA) and methyl cation affinities (MCA). Besides, all cation affinities of the neutral base HCl are weaker than those of Cl−. This follows from our quantum chemical analyses using relativistic density functional theory.

The reason for the smaller AMCAs is mainly a weaker HOMO–LUMO interaction between the base and the alkali pan class="Chemical">metal cations if compared with the proton. The AMCA therefore has a relatively large electrostatic component. The weaker HOMO–LUMO interaction originates from a higher energy (and thus a larger HOMO–LUMO gap) and more diffuse character (and thus a smaller bond overlap) of the alkali metal cation 2s (Li) or 3s (Na) LUMO. Pauli repulsion with the alkali metal cation core orbitals is relatively unimportant (although not negligible) for the weaker AMCA. At variance, Pauli repulsion is the main responsible factor for the weaker MCA as compared with PA.

The weakening of all cation affinities, if we go from anionic to the neutral base, is mainly (although not only) caused by the loss in electrostatic attraction in the latter case. In the complexes of Cl−, there is a strong Coulomb attraction that goes with the charge separation upon heterolytic dissociation ClX→Cl−+X+. Such charge separation does not occur for heterolytic dissociation pan class="Chemical">HClX+→HCl+X+ in the case of the neutral base HCl.

As a service to our authors and readers, this journal provides supporting information supplied by the authors. Such materials are peer reviewed and may be re‐organized for online delivery, but are not copy‐edited or typeset. Technical support issues arising from supporting information (other than missing files) should be addressed to the authors.

Supplementary

Click here for additional data file.