Hydride affinities of cationic maingroup-element hydrides across the periodic table

Results in Chemistry 1 (2019) 100007

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Hydride affinities of cationic maingroup-element hydrides across the periodic table Eva Blokker a, Caroline G.T. Groen a, J. Martijn van der Schuur b, Auke G. Talma b, F. Matthias Bickelhaupt a,c,⁎ a b c

Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling (ACMM), Vrije Universiteit Amsterdam, De Boelelaan 1083, NL–1081 HV Amsterdam, The Netherlands Polymer Chemistry, Nouryon, Zutphenseweg 10, NL–7418 AJ Deventer, The Netherlands Institute of Molecules and Materials, Radboud University, Heyendaalseweg 135, NL–6525 AJ Nijmegen, The Netherlands

a r t i c l e

i n f o

Article history: Received 12 July 2019 Accepted 30 August 2019 Available online xxxx

a b s t r a c t We have quantum chemically explored the gas-phase hydride affinities (HA) of archetypical cationic Lewis acids across the periodic table, using relativistic density functional theory (DFT) at ZORA-BP86/QZ4P. One purpose of this work is to establish an intrinsically consistent set of values of the 298 K HAs of all cationic maingroupelement hydrides (XH+ n–1) in which we have varied the central atom X along groups 14–17 and periods 2–6. Our main purpose is to understand the emerging trends in HA values in terms of the underlying bonding mechanism using Kohn-Sham molecular orbital (MO) theory together with a quantitative bond energy decomposition analysis (EDA). © 2019 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).

Keywords: Hydride affinities Bond theory Density functional calculations Thermochemistry

1. Introduction The hydride ion, H−, is the simplest Lewis base. It is believed that H− was necessary to form molecular hydrogen H2 in the early universe, which led to the cooling of primordial clouds and subsequently the formation of the first stars [1]. Furthermore, H− plays an important role in numerous chemical and biological processes, for instance, the hydrides LiAlH4, NaBH4 and AlH3 can reduce carbonyl compounds to alkoxides [2], and hydride transfer to the nicotinamide ring reduces NAD+ and NADP+ in metabolism [3]. Another example can be found in nickelmetal hydride battery electrochemistry [4]. An important thermodynamic quantity that characterizes the stability and reactivity for these species and processes is the hydride affinity (HA). The HA is defined as the enthalpy change associated with the heterolytic dissociation of the complex between the hydride and the Lewis acid, here a cationic acid XH+ n–1: XHn →XHn–1 þ þ H−

ΔH ¼ HA

ð1Þ

For chemical design and synthesis, it is in many cases helpful, if not essential, to know this quantity and understand the physical factors behind it. However, if compared to the situation for proton affinities (PAs), i.e., the affinities of Lewis bases for H+ [5], fewer research has been performed on systematically capturing HAs of Lewis acids and trends ⁎ Corresponding author at: Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling (ACMM), Vrije Universiteit Amsterdam, De Boelelaan 1083, NL–1081 HV Amsterdam, The Netherlands. E-mail address: [email protected] (F.M. Bickelhaupt).

therein. Parker and co–workers published experimental HA values on a selection of quinones, organic radicals and cations in 1993 [6], and Maksić and coworkers calculated the acidity of boranes and alkenes, by use of a triadic formula, more than a decade later [7]. Böhrer et al. augmented the HA scale of group 13 acids based on isodesmic reactions [8]. The purpose of this study is to explore and uncover trends of HAs of archetypal Lewis acids with electrophilic centers across the periodic table as well as getting insight into the underlying physical mechanisms behind the emerging trends. To this end, we have conducted a systematic and detailed quantum chemical exploration and analysis of the intrinsic (i.e., gas-phase) HA values of cationic Lewis acids XH+ n–1, using relativistic density functional theory (DFT). In our model Lewis acids XH+ n–1, we have varied the central atom X along groups 14–17 and periods 2–6. Besides the HAs (ΔH298), we also report the reaction entropies (ΔS298, provided as –TΔS298) and 298 K reaction Gibbs–free energies (ΔG298). The bonding mechanisms have been analyzed within the framework of Kohn-Sham molecular orbital (MO) theory in combination with a matching, canonical energy decomposition analysis (EDA) and Voronoi deformation density (VDD) analysis of the charge reorganization associated with bond formation. 2. Methods 2.1. 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 the largest uncontracted set of

https://doi.org/10.1016/j.rechem.2019.100007 2211-7156/© 2019 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

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E. Blokker et al. / Results in Chemistry 1 (2019) 100007

Slater-type orbitals (STO): QZ4P [11]. The QZ4P basis set 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). The core electrons were treated without a frozen core approximation [11]. 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. 2.2. Density functional Energies and gradients were calculated using the local density approximation (LDA: Slater [12] exchange and VWN [13] correlation) with gradient corrections [14] due to Becke (exchange) and Perdew (correlation) added self-consistently. This is the BP86 density functional, which is one of the three best density functionals for the accuracy of geometries [5a–c,15a]. In a previous study [5a–c] on the proton affinities (PA) of anionic species, we compared the energies of a range of other density functionals, to estimate the influence of the choice of density functional which showed excellent performance of the BP86/QZ4P approach for computing PA values. These functionals included the Local Density Approximation (LDA), Generalized Gradient Approximation (GGAs), meta-GGA and hybrid functionals. It has also been shown that over-parametrized functionals are prone to larger errors in the computation of PAs [15b]. Scalar relativistic corrections were included self-consistently using the zeroth order regular approximation (ZORA) [16]. Spin-orbit coupling effects were neglected because they are small for closed-shell systems as they occur in this investigation. 2.3. Thermochemistry Enthalpies at 298.15 K and 1 atm (ΔH298) were calculated from electronic bond energies (ΔE) and vibrational frequencies using standard thermochemistry relations for an ideal gas, according to Eq. (2) [17]:
 ΔH 298 ¼ ΔE þ ΔEtrans;298 þ ΔErot;298 þ ΔEvib;0 þ Δ ΔEvib;0 298 þ ΔðpV Þ

ð2Þ

Here, ΔEtrans,298, ΔErot,298 and ΔEvib,0 are the differences between the reactant (i.e., XHn, the cation-hydride complex) and products − (i.e., XH+ n–1 + H , the cation and the hydride) in translational, rotational and zero-point vibrational energy, respectively. Δ(ΔEvib,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 re− actant XHn dissociating into two products XH+ n–1 and H . Thermal corrections for the electronic energy are neglected. 2.4. Activation strain and energy decomposition analysis For the bonding analysis, the overall bond energy ΔEbond [which corresponds to –ΔE in Eq. (2)] between the cation XH+ n–1 and the hydride H− is made up of two major components [18]: ΔEbond ¼ ΔEstrain þ ΔEint

ð3Þ

Here, the strain energy ΔEstrain is the amount of energy required to deform the cation from its equilibrium structure to the geometry that it acquires in the overall complex XHn. The hydride ion has zero strain energy, since it consists of solely one atom and therefore cannot undergo geometrical deformations. The interaction energy ΔEint corresponds to the actual energy change when the geometrically deformed cation and the hydride are combined to form the overall complex. We choose to further analyze the interaction ΔEint in the framework of the canonical Kohn-Sham molecular orbital (MO) model, by dissecting it through our canonical energy decomposition analyses (canonical

EDA) into electrostatic attraction, Pauli repulsion, and (attractive) orbital interactions [9,18]: ΔEint ¼ ΔV elstat þ ΔEPauli þ ΔEoi

ð4Þ

The term ΔVelstat corresponds to the classical electrostatic interaction between the unperturbed charge distributions of the prepared (i.e. deformed) cation and the hydride. This term is usually attractive. The Pauli-repulsion ΔEPauli comprises the destabilizing interactions between occupied orbitals and is responsible for the steric repulsion. The orbital interaction ΔEoi 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). 2.5. Charge distribution analysis The electron density distribution is analyzed by using the Voronoi deformation density (VDD) method [19,20] for atomic charges. The VDD atomic charge QVDD is computed as the (numerical) integral [21] A of the deformation density Δρ(r) = ρ(r) – ∑B ρB(r) in the volume of the Voronoi cell of atom A [Eq. (5)]. 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) [20c]. Z

Q VDD ¼– A

½ρðrÞ–∑B ρB ðrÞ dr

ð5Þ

Voronoi cell of A

In Eq. (5), ρ(r) is the electron density of the molecule and ∑B ρB(r) the superposition of atomic densities ρB 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 QVDD is rather straightforward and transparent. Instead of measuring A the amount of charge associated with a particular atom A, QVDD directly A monitors how much charge flows, due to chemical interactions, out of (QVDD N 0) or into (QVDD b 0) the Voronoi cell of atom A, that is, the reA A gion of space that is closer to nucleus A than to any other nucleus. The chemical bond between two molecular fragments can be analyzed by examining how the VDD atomic charges of the fragments change due to the chemical interactions. In Ref. [20a], however, we have shown that Eq. (5) leads to small artifacts that prohibit an accurate description of the subtle changes in atomic charges. This is due to the socalled front-atom problem that, in fact, all atomic-charge methods suffer from. To resolve this problem and, thus, enabling a correct treatment of even subtle changes in the electron density, the change in VDD atomic charges ΔQA is defined by Eq. (6), which relates this quantity directly to the deformation density Δρ(r) = ρcomplex(r) – ρfragment1(r) – ρfragment2(r) associated with forming the overall molecule from joining the molecular fragments, fragment1 and fragment2 [20a].

¼– ΔQ VDD A

Z

h

i ρcomplex ðrÞ–∑fragments i ρi ðrÞ dr

ð6Þ

Voronoi cell of A in complex

Again, ΔQA has a simple and transparent interpretation: it directly monitors how much charge flows out of (ΔQA N 0) or into (ΔQA b 0) the Voronoi cell of atom A as a result of the chemical interactions between fragment1 and fragment2 in the complex.

E. Blokker et al. / Results in Chemistry 1 (2019) 100007

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Table 1 Hydride affinity data and activation strain analysis (in kcal mol−1, Å) for cationic maingroup-element hydridesa. Group Period 2 Group 14 Group 15 Group 16 Group 17 Period 3 Group 14 Group 15 Group 16 Group 17 Period 4 Group 14 Group 15 Group 16 Group 17 Period 5 Group 14 Group 15 Group 16 Group 17 Period 6 Group 14 Group 15 Group 16 Group 17 a b

+ Acid XHn–1

ΔH

–TΔS

ΔG

ΔEbond

ΔEstrain

ΔEint

d(X–H)b

CH+ 3 NH+ 2 OH+ + F

316.7 383.6 475.8 613.7

−8.2 −7.6 −6.7 −5.7

308.5 376.1 469.1 608.0

−323.4 −392.3 −483.4 −618.5

27.9 1.6 2.7 0.0

−351.4 −393.9 −486.1 −618.5

1.095 1.021 0.969 0.931

SiH+ 3 PH2+ SH+ Cl+

260.0 292.6 356.0 435.4

−8.2 −7.5 −6.4 −5.4

251.9 285.1 349.6 430.0

−264.1 −297.5 −360.5 −438.6

19.6 0.1 0.3 0.0

−283.7 −297.6 −360.8 −438.6

1.489 1.429 1.351 1.289

GeH+ 3 AsH+ 2 + SeH Br+

250.0 274.4 326.7 389.3

−8.2 −7.5 −6.3 −5.3

241.9 266.9 320.4 384.0

−253.9 −278.7 −330.5 −392.1

20.2 0.0 0.1 0.0

−274.2 −278.7 −330.7 −392.1

1.532 1.532 1.477 1.431

SnH+ 3 SbH+ 2 + TeH I+

232.8 249.9 292.0 340.1

−8.1 −7.5 −6.2 −5.1

224.7 242.5 285.8 335.0

−236.0 −253.4 −295.1 −342.4

17.6 0.0 0.0 0.0

−253.6 −253.4 −295.1 −342.4

1.716 1.724 1.671 1.625

PbH3+ BiH+ 2 PoH+ + At

220.5 236.4 274.8 317.7

−8.0 −7.4 −6.2 −5.0

212.4 229.0 268.6 312.7

−223.4 −239.5 −277.5 −319.8

18.7 0.0 0.0 0.0

−242.0 −239.5 −277.5 −319.8

1.768 1.808 1.760 1.717

Computed at ZORA–BP86/QZ4P at 298.15 K and 1 atm. X–H equilibrium bond distances in XHn.

3. Results and discussion 3.1. Bond energies and distances The computed hydride affinities (HA) at 298.15 K (ΔH) with X–H equilibrium distances, entropies ΔS (provided as –TΔS) and free ener+ gies ΔG are summarized in Table 1 for the cationic acids XHn–1 of group 14–17 and periods 2–6. Furthermore, the bond energies ΔEbond [which correspond to –ΔE in Eq. (2)] are given with their strain (ΔEstrain) and interaction energies (ΔEint). The HA increases systematically from 316.7 to 383.6 to 475.8 to + + + + 613.7 kcal mol−1 along XH+ n–1 = CH3 , NH2 , OH , and F , respectively. In other words, F+ binds H− almost twice as strongly as does CH+ 3 . At the same time, the X–H equilibrium bond distance shortens from + + + 1.095 (CH+ 3 ) to 1.021 (NH2 ) to 0.969 (OH ) to 0.931 Å (F ). Thus, the stronger F\\H bond is approximately 1.2 times shorter than the C\\H bond. This systematic increase in HA from group 14–17 is the largest in period 2 and becomes less pronounced for the heavier elements. For example, the weakening in hydride affinity, ΔHA, along a period from group 14–17 decreases from 297.0 to 175.4 to 97.2 kcal mol−1 for periods 2, 3 and 6, respectively. Of all systems in Table 1, F+ is the strongest bound to H−, making it the strongest Lewis acid of all systems in our study. On the other hand, PbH+ 3 is the weakest Lewis acid in our study with an HA of only 220.5 kcal mol−1. The trend in Gibbs free energies ΔG is similar to that in hydride affinities ΔH, because the entropy values –TΔS are small and relatively constant (between −8.0 and − 5.0 kcal mol−1) on the scale of the ΔH values (between 220.5 and 613.7 kcal mol−1). The hydride affinity ΔH is an enthalpic quantity which is related to its associated electronic hydride affinity energy ΔE according to Eq. (2). The bond energy ΔEbond in Table 1 is equal to –ΔE, which refers − to the energy of the bond formation process XH+ n–1 + H → XHn. Note that ΔEbond largely determines the HA and that it is responsible for all major trends, even though zero-point vibrational energy effects can lead to differences in ΔE and ΔH of a few kcal mol−1, especially for period 2. Thus, F+–H− has again the most stable ΔEbond of − −618.5 kcal mol−1 and PbH+ the weakest one, with 3 –H −223.4 kcal mol−1.

As explained in the methods section, ΔEbond can be made up of the strain energy ΔEstrain and the interaction energy ΔEint with ΔEbond = ΔEstrain + ΔEint (see Table 1). The trend in bond energy is largely set by the electronic interaction energy ΔEint. The strain term ΔEstrain is much smaller and does not affect overall trends in ΔEbond or HA. ΔEstrain appears to be comparatively large only for the group-14 systems whereas it is small, essentially negligible, for all other groups. The reason is that the tricoordinate group-14 Lewis acids XH+ 3 have a planar equilibrium geometry but have to become pyramidal as, upon binding the H− ion, they form the tetra-coordinate XH4. The energy cost that goes with the pyramidalization of the XH+ 3 fragment is reflected by the higher, more destabilizing strain energy [22]. Note that the strain is most destabilizing for CH+ 3 (ΔEstrain = 28 kcal mol−1) and becomes significantly smaller for the heavier analogs (ca 18–20 kcal mol−1). The reason for the higher resistance of CH+ \H steric (Pauli) re3 to undergo pyramidalization, is the larger H\ pulsion associated with the fact that the hydrogen substituents in CH+ 3 are much closer, due to the shorter C\\H distance, than for example in SiH+ 3 in which hydrogen substituents are at larger mutual distance due to longer Si\\H bonds [22]. In the case of group-15 and -16 systems, + the corresponding Lewis acidic XH+ fragments are already 2 and XH bent or linear, and the additional distortion upon binding the hydride ion is anyway small or even negligible, respectively [22b]. In conclusion, the interaction energy ΔEint between the cationic acid − XH+ n–1 fragments and H is the main contributor to the ΔEbond trend. In the next section, we analyze the underlying bonding mechanism in more detail. 3.2. Bonding mechanism To obtain insight into the physical factors behind the HA and trends therein, we have decomposed the X–H interaction energy ΔEint between − XH+ n–1 and H into the electrostatic attraction ΔVelstat, the Pauli repulsion ΔEPauli and the orbital interaction ΔEoi according to Eq. (4). The results of this energy decomposition analysis (EDA) are shown in Fig. 1 (for numerical data, see Table S1 in the Supporting Information). Furthermore, we performed a quantitative analysis of the underlying Kohn-Sham orbital-interaction mechanism. These results, which can

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E. Blokker et al. / Results in Chemistry 1 (2019) 100007

(–) HA 15

Velstat 16

17

14

-100

-100

-200

-200

-300

P6 P5 P4 P3

-400 -500 -600

P2

Velstatkcal mol-1

(–) H kcal mol-1

14

15

P2 P3 P4 P5 P6

-400 -500 -600 -700

-800

-800

Eoi 15

EPauli 16

17

-100 P6 P5

-300

P4 -400

P3

-500 -600 -700

EPauli kcal mol-1

800

-200

Eoi kcal mol-1

17

-300

-700

14

16

700 600 500 400

P2 P3 P4 P5 P6

300 200

P2 -800

100 14

Group

15

16

17

Group

Fig. 1. Energy decomposition analysis of hydride affinity (HA) energies ΔE of cationic acids XH+ n–1 into the electrostatic interaction ΔVelstat, the orbital interaction ΔEoi and the Pauli repulsion energy ΔEPauli. Computed at ZORA–BP86/QZ4P.

Table 2 Analysis of the hydride-affinity bonding mechanism (in eV, a.u.) for cationic maingroupelement hydridesa. Group Period 2 Group 14 Group 15 Group 16 Group 17 Period 3 Group 14 Group 15 Group 16 Group 17 Period 4 Group 14 Group 15 Group 16 Group 17 Period 5 Group 14 Group 15 Group 16 Group 17 Period 6 Group 14 Group 15 Group 16 Group 17

Acid XH+ n-1

εLUMOb

⟨HOMO|LUMO⟩c

ΔQ(H− in XHn)d

CH+ 3 NH+ 2 OH+ + F

−15.4 −18.3 −22.9 −29.5

0.45 0.27 0.26 0.23

+0.24 +0.46 +0.47 +0.56

SiH+ 3 PH+ 2 SH+ Cl+

−12.5 −13.9 −16.8 −20.4

0.53 0.41 0.38 0.34

+0.20 +0.30 +0.34 +0.42

GeH+ 3 AsH+ 2 + SeH Br+

−12.4 −13.3 −15.7 −18.4

0.50 0.42 0.40 0.37

+0.24 +0.30 +0.33 +0.40

SnH+ 3 SbH+ 2 + TeH I+

−11.6 −12.1 −14.1 −16.2

0.52 0.45 0.43 0.41

+0.26 +0.30 +0.33 +0.37

PbH+ 3 BiH+ 2 PoH+ At+

−11.5 −11.7 −13.4 −15.3

0.46 0.45 0.44 0.42

+0.31 +0.29 +0.32 +0.35

be found in Table 2 and Fig. 2, will be discussed after we have explored the trends in EDA. As shown in the previous section, the HA increases along a period and decreases down a group. The largest increase in HA occurs along pe−1 riod 2 from 316.7 kcal mol−1 for CH+ for F+, 3 to 613.7 kcal mol whereas the smallest increase happens along period 6 from −1 220.5 kcal mol−1 for PbH+ for At+. In Fig. 1, we 3 to 317.7 kcal mol compare the trends in (the negative of) HA with the various EDA terms. It can be seen that the trend in HA is dictated by the orbital interactions. Note that the electrostatic attraction ΔVelstat is also significant

a

Computed at ZORA–BP86/QZ4P. XH+ n–1 fragment orbital energy (in eV). ⟨H−|XH+ n–1⟩ fragment orbital overlap. d The VDD change in atomic charge ΔQ (in a.u.) associated with the formation of XHn from fragments. b c

Fig. 2. Donor–acceptor interaction of the H− HOMO with the XH+ n–1 LUMO.

E. Blokker et al. / Results in Chemistry 1 (2019) 100007

but this term stays relatively constant, especially within a period. Therefore, it does not affect the trend in HA significantly. The strong electrostatic attraction originates from the charge separation upon heterolytic dissociation of all neutral complexes into the oppositely − charged XH+ n–1 and H fragments between which Coulombic attraction occurs. ΔVelstat is however not exactly constant along all the model Lewis acids XH+ n–1 because of differences in bond distances (Table 1) as well as because ΔVelstat does not arise, here, between two point charges but between a molecular anion and an atomic anion. Each of these fragments are characterized by a more complex charge distribution of nuclei and electron charge density which gives rise to deviations from Coulombs law for two point charges, i.e., q1 x q2 / r12 [23]. Indeed, going down a group, i.e., towards heavier atoms X, the electrostatic attraction ΔVelstat becomes somewhat more stabilizing whereas, along a period, it is nearly constant. Thus, again, ΔVelstat plays no significant role in the HA trends. The orbital interaction ΔEoi, as already stressed above, clearly determines the trend in interaction energy and therefore that in HA (Fig. 1). The hydride affinity graph (top left) is the attenuated form of the orbital interaction graph (bottom left). In the case of F+, the orbital interaction ΔEoi is the most stabilizing with a value of −717.42 kcal mol−1 while −1 PbH+ . 3 goes with an orbital interaction of only −148.03 kcal mol The trend in Pauli repulsion ΔEPauli is not very pronounced, showing only a slight enhancement along a period (Fig. 1). Therefore, ΔEPauli has no major effect on the HA trend. The increase in Pauli repulsion correlates with the decrease in equilibrium bond distance (Table 1) between − the cationic acid XH+ n–1 and the hydride H . As can be seen in Table 1, the group 14 systems, and in particular CH+ 3 , go with a relatively large ΔEstrain. The reason is the relatively large steric repulsion between H− and the three other H substituents around the sterically crowded, tetra-coordinate carbon atom in the resulting complex, CH4. This causes the C\\H bonds to bend away from the approaching H− which results in the pyramidalization of the XH+ \H bonds reduces steric n–1 fragment. This bending away of the C\ (Pauli) repulsion for all group 14 systems (Fig. 1) [22b]. The strengthening in ΔEoi along the periods (Fig. 1) is a result of a feature in the covalent bonding mechanism, namely, the donor– + acceptor interaction of the H− HOMO with the XHn–1 LUMO (see Table 2 and Fig. 2). As the central atom X varies along period 2 from C to the more electronegative F, the LUMO energy decreases enormously + + from −15.4 to −18.3 to −22.9 to −29.5 eV along XH+ n–1 = CH3 , NH2 , + + OH , and F , respectively. This occurs also for the more electropositive elements in the higher periods, although to a lesser extent. For example, in period 6, the energy drops from −11.5 eV to −15.3 eV as we go from + group 14 (PbH+ 3 ) to group 17 (At ). The decrease in LUMO energy along a period is a direct consequence of the increasing nuclear charge. This trend in LUMO is also associated with the increasing electronegativity of the XH+ n-1 systems along a period, where atom X adopts, in Pauling units [24], the values 2.55 (C), 3.04 (N), 3.44 (O), and 3.98 (F) for period 2. Down a group, the LUMO of the Lewis acid XH+ n-1 goes up in energy which corresponds again with the decrease in electronegativity of X [24]. This leads to a larger HOMO–LUMO gap Δε down a group and, according to the approximate relationship ΔEoi ~ S2/Δε [25], to a weakening of the orbital interaction ΔEoi and the hydride affinity. Note that the trend in HOMO–LUMO gap Δε overrules the trend in the corresponding overlap S (Table 2, Fig. 1 for ΔEoi). Along a period, the overlap S decreases, i.e., becomes less favorable, as the atomic orbitals of X become more compact and no longer show a good spatial match with the diffuse hydride 1 s AO. Down a group, from period 2 to period 3, the overlap increases, i.e., becomes more favorable, as the atomic orbitals of X become more diffuse. In conclusion, the trend in LUMO energy across the periodic table dominates that in overlap and therefore determines the trend in orbital interaction energies and, eventually, the strength of the hydride affinity. The ΔEoi trend is reflected by the change in electronic charge ΔQ of H− when it binds to XH+ n-1 resulting in the formation of the XHn

5

complex (Table 2). This change in atomic charge ΔQ for H− becomes in nearly all cases more positive along a period, indicating that more charge flows out of H− towards the XH+ n-1 fragment (+0.24, +0.46, +0.47, and +0.56 for the XHn complexes in period 2). This reflects the trend of increasing HA along a period. Within a group, the change in electronic charge ΔQ is less pronounced, but in most cases ΔQ becomes less positive, indicating that less charge flows out of H−. This reflects the trend of decreasing HA along a period. 4. Conclusion The hydride affinity (HA) of cationic maingroup-element hydrides XH+ n–1 in the gas phase systematically increases along a period from groups 14–17, with F+ having the strongest affinity towards the hydride ion. Furthermore, HA values decrease when going down a group from periods 2–6. We have demonstrated this through detailed quantum chemical analyses using relativistic density functional theory at ZORABP86/QZ4P. The trend in HA across the periodic table is determined by the HOMO–LUMO interaction between the hydride ion H− and the Lewis acid XH+ n–1. The main responsible factor is that, as X varies along a period towards the more electronegative side, on the right, the XH+ n–1 LUMO drops in energy which results in a smaller HOMO–LUMO gap and thus a more stabilizing orbital interaction. On the other hand, down a group, going to the heavier, more electropositive elements, + the XHn–1 LUMO rises in energy which results in a larger HOMO– LUMO gap and thus a less stabilizing orbital interaction. The electrostatic attraction between the fragments is strongly stabilizing because of charge separation upon heterolytic dissociation XHn − → XH+ n–1 + H . Within a period, however, the electrostatic attraction varies hardly and does not contribute to the trend in HA values. Likewise, the Pauli repulsion increases only slightly along a period and has therefore essentially no effect on the trend in HA values. Acknowledgments This work was supported by the Advanced Research Center Chemical Building Blocks Consortium (ARC CBBC) [grant number 2018.019. B]. We thank the Netherlands Organization for Scientific Research (NWO) for financial support, and Cynthia L. Kuiper for her contribution in early stages of the project. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.rechem.2019.100007. References [1] (a) V. Bromm, P.S. Coppi, R.B. Larson, The formation of the first stars. I. The primordial star-forming cloud, Astrophys. J. 564 (2002) 23–51, https://doi.org/10. 1086/323947; (b) J.H. Wise, M.J. Turk, M.L. Norman, T. Abel, The birth of a galaxy: primordial metal enrichment and stellar populations, Astrophys. J. 745 (2012) 1–10, https://doi. org/10.1088/0004–637X/745/1/50; (c) W.H. McCrea, The origin of the solar system, Proc. Roy. Soc., A 256 (1960) 245–266, https://doi.org/10.1098/rspa.1960.0108. [2] (a) A. Lipták, I. Jodál, P. Nánási, Stereoselective ring-cleavage of 3-O-benzyl- and 2,3-di-O-benzyl-4,6-O-benzylidenehexopyranoside derivatives with the LiAlH4–AlCl3 reagent, Carbohydr. Res. 44 (1975) 1–11, https://doi.org/10. 1016/S0008–6215(00)84330–X; (b) J.C. Hubert, J.B.P.A. Wijnberg, W.N. Speckamp, NaBH4 reduction of cyclic imides, Tetrahedron 31 (1975) 1437–1441, https://doi.org/10.1016/0040–4020(75) 87076–1; (c) E. Winterfeldt, Applications of diisobutylaluminium hydride (DIBAH) and triisobutylaluminium (TIBA) as reducing agents in organic synthesis, Synthesis 10 (1975) 617–630, https://doi.org/10.1055/s–1975–34049. [3] P. Belenky, K.L. Bogan, C. Brenner, NAD+ metabolism in health and disease, Trends Biochem. Sci. 32 (2007) 12–19, https://doi.org/10.1016/j.tibs.2006.11.006. [4] S.R. Ovshinsky, M.A. Fetcenko, J. Ross, A nickel metal hydride battery for electric vehicles, Science 260 (1993) 176–181, https://doi.org/10.1126/science.260.5105.176.

6

E. Blokker et al. / Results in Chemistry 1 (2019) 100007

[5] (a) M. Swart, F.M. Bickelhaupt, Proton affinities of anionic bases: trends across the periodic table, structural effects, and DFT validation, J. Chem. Theory Comput. 2 (2006) 281–287, https://doi.org/10.1021/ct0502460; (b) M. Swart, E. Rosler, F.M. Bickelhaupt, Proton affinities of maingroup-element hydrides and noble gases: trends across the periodic table, structural effects, and DFT validation, J. Comput. Chem. 27 (2006) 1486–1493, https://doi.org/10. 1002/jcc.20431; (c) M. Swart, E. Rösler, F.M. Bickelhaupt, Proton affinities in water of maingroupelement hydrides – effects of hydration and methyl substitution, Eur. J. Inorg. Chem. (2007) 3646–3654, https://doi.org/10.1002/ejic.200700228; (d) A. Moser, K. Range, D.M. York, Accurate proton affinity and gas-phase basicity values for molecules important in biocatalysis, J. Phys. Chem. B 114 (2010) 13911–13921, https://doi.org/10.1021/jp107450n; (e) J.L. Reed, Electronegativity – proton affinity, J. Phys. Chem. 98 (1994) 10477–10483, https://doi.org/10.1021/j100092a016; (f) S. Kolboe, Proton affinity calculations with high level methods, J. Chem. Theory Comput. 10 (2014) 3123–3128, https://doi.org/10.1021/ct500315c. [6] (a) J.-P. Cheng, K.L. Handoo, V.D. Parker, Hydride affinities of carbenium ions in acetonitrile and dimethyl sulfoxide solution, J. Am. Chem. Soc. 115 (1993) 2655–2660, https://doi.org/10.1021/ja00060a014; (b) K.L. Handoo, J.-P Cheng, V.D. Parker, Hydride affinities of organic radicals in solution. A comparison of free radicals and carbenium ions as hydride ion acceptors, J. Am. Chem. Soc. 115 (1993) 5067–5072, https://doi.org/10.1021/ja00065a017; (c) J.-P. Cheng, K.L. Handoo, J. Xue, V.D. Parker, Free energy hydride affinities of quinones in dimethyl sulfoxide solution, J. Org. Chem. 58 (1993) 5050–5054, https://doi.org/10.1021/jo00071a011. [7] (a) R. Vianello, Z.B. Maksić, Hydride affinities of borane derivatives: novel approach in determining the origin of lewis acidity based on triadic formula, Inorg. Chem. 44 (2005) 1095–1102, https://doi.org/10.1021/ic048647y; (b) Z.B. Maksić, R. Vianello, Physical origin of chemical phenomena: interpretation of acidity, basicity, and hydride affinity by trichotomy paradigm, Pure Appl. Chem. 79 (2007) 1003–1021, https://doi.org/10.1351/pac200779061003; (c) R. Vianello, N. Peran, Z.B. Maksić, Hydride affinities of substituted alkenes: their prediction by density functional calculations and rationalisation by triadic formula, Eur. J. Org. Chem. (2007) 526–539, https://doi.org/10.1002/ejoc.200600640. [8] H. Böhrer, N. Trapp, D. Himmel, M. Schleep, I. Krossing, From unsuccesful H2activation with FLPs containing B(Ohfip)3 to a systematic evaluation of the Lewis acidity of 33 Lewis acids based on fluoride, chloride, hydride and methyl ion affinities, Dalton Trans. 44 (2015) 7489–7499, https://doi.org/10.1039/C4DT02822H. [9] ADF2017; SCM, Theoretical Chemistry, Vrije Universiteit Amsterdam, http://www. scm.com. [10] G. te Velde, F.M. Bickelhaupt, E.J. Baerends, C. Fonseca Guerra, S.J.A. van Gisbergen, J.G. Snijders, et al., Chemistry with ADF, J. Comput. Chem. 22 (2001) 931–967, https://doi.org/10.1002/jcc.1056. [11] E. van Lenthe, E.J. Baerends, Optimized slater–type basis sets for the elements 1–118, J. Comput. Chem. 24 (2003) 1142–1156, https://doi.org/10.1002/jcc.10255. [12] J.C. Slater, A simplification of the hartree-fock method, Phys. Rev. 81 (1951) 385–390, https://doi.org/10.1103/PhysRev.81.385. [13] S.H. Vosko, L. Wilk, M. Nusair, Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis, Can. J. Phys. 58 (1980) 1200–1211, https://doi.org/10.1139/p80–159. [14] (a) J.P. Perdew, Erratum: density-functional approximation for the correlation energy of the inhomogeneous electron gas, Phys. Rev. B 34 (1986) 7406, https:// doi.org/10.1103/PhysRevB.34.7406; (b) J.P. Perdew, Density-functional approximation for the correlation energy of the inhomogeneous electron gas, Phys. Rev. B 33 (1986) 8822–8824, https://doi. org/10.1103/PhysRevB.33.8822;

[15]

[16] [17]

[18]

[19]

[20]

[21] [22]

[23] [24]

[25]

(c) A.D. Becke, Density-functional exchange-energy approximation with correct asymptotic behavior, Phys. Rev. A 38 (1988) 3098–3100, https://doi.org/10.1103/ PhysRevA.38.3098. (a) M. Swart, J.G. Snijders, Accuracy of geometries: influence of basis set, exchangecorrelation potential, inclusion of core electrons, and relativistic corrections, Theoret. Chem. Acc. 110 (2003) 34–41, https://doi.org/10.1007/s00214–003– 0443–5; (b) S. Kolboe, Proton affinity calculations with high level methods, J. Chem. Theory Comput. 10 (2014) 3123–3128, https://doi.org/10.1021/ct500315c. E. van Lenthe, E.J. Baerends, J.G. Snijders, Relativistic regular two-component Hamiltonians, J. Chem. Phys. 99 (1993) 4597–4610, https://doi.org/10.1063/1.466059. (a) P.W. Atkins, J. de Paula, Physical Chemistry, 9th ed. W.H. Freeman, New York, 2010; (b) F. Jensen, Introduction to Computational Chemistry, Wiley, 2007. (a) F.M. Bickelhaupt, E.J. Baerends, Kohn-Sham density functional theory: predicting and understanding chemistry, in: K.B. Lipkowitz, D.B. Boyd (Eds.), Reviews in computational chemistry, Wiley-VCH, New York 2000, pp. 1–86; (b) T. Ziegler, A. Rauk, On the calculation of bonding energies by the Hartree Fock Slater method, Theoret. Chim. Acta 46 (1977) 1–10, https://doi.org/10.1007/ BF00551648; (c) T. Ziegler, A. Rauk, A theoretical study of the ethylene-metal bond in complexes between copper+, silver+, gold+, platinum0 or platinum2+ and ethylene, based on the Hartree-Fock-Slater transition-state method, Inorg. Chem. 18 (1979) 1558–1565, https://doi.org/10.1021/ic50196a034; (d) T. Ziegler, A. Rauk, CO, CS, N2, PF3, and CNCH3 as σ donors and π acceptors. A theoretical study by the Hartree-Fock-Slater transition-state method, Inorg. Chem. 18 (1979) 1755–1759, https://doi.org/10.1021/ic50197a006. F.M. Bickelhaupt, N.J.R. van Eikema Hommes, C. Fonseca Guerra, E.J. Baerends, The carbon−lithium electron pair bond in (CH3Li)n (n = 1, 2, 4), Organometallics 15 (1996) 2923–2931, https://doi.org/10.1021/om950966x. See also: (a) C. Fonseca Guerra, F.M. Bickelhaupt, J.G. Snijders, E.J. Baerends, The nature of the hydrogen bond in DNA base pairs: the role of charge transfer and resonance assistance, Chem. Eur. J. 5 (1999) 3581–3594, https://doi.org/10.1002/(SICI)1521-3765(19991203)5:12%3C3581:: AID-CHEM3581%3E3.0.CO;2-Y; (b) C. Fonseca Guerra, J.W. Handgraaf, E.J. Baerends, F.M. Bickelhaupt, Voronoi deformation density (VDD) charges: Assessment of the Mulliken, Bader, Hirshfeld, Weinhold, and VDD methods for charge analysis, J. Comput. Chem. 25 (2004) 189–210, https://doi.org/10.1002/jcc.10351 Voronoi cells are equivalent to Wigner-Seitz cells in crystals; for the latter, see:; (c) C. Kittel, Introduction to solid state physics, Wiley, New York, 1986. G. te Velde, E.J. Baerends, Numerical integration for polyatomic systems, J. Comput. Phys. 99 (1992) 84–98, https://doi.org/10.1016/0021–9991(92)90277–6. (a) F.M. Bickelhaupt, T. Ziegler, P. von Ragué Schleyer, CH•3 is planar due to H–H steric repulsion. Theoretical study of MH•3 and MH3Cl (M = C, Si, Ge, Sn), Organometallics 15 (1996) 1477–1487, https://doi.org/10.1021/om950560k; (b) J. van Zeist, F.M. Bickelhaupt, Trends and anomalies in H–AHn and CH3–AHn bond strengths (AHn = CH3, NH2, OH, F), Phys. Chem. Chem. Phys. 11 (2009) 10317–10322, https://doi.org/10.1039/B914873F. A. Krapp, F.M. Bickelhaupt, G. Frenking, Orbital overlap and chemical bonding, Chem. Eur. J. 12 (2006) 9196–9216, https://doi.org/10.1002/chem.200600564. (a) L. Pauling, The Nature of the Chemical Bond, Cornell University Press, Ithaca, NY, 1960; (b) A.L. Allred, Electronegativity values from thermochemical data, J. Inorg. Nucl. Chem. 17 (1961) 215, https://doi.org/10.1016/0022–1902(61)80142–5. T.A. Albright, J.K. Burdett, M.H. Whangbo, Orbital Interactions in Chemistry, 2nd ed. Wiley, Hoboken, 2013.