DOI: 10.1002/chem.200802641

Dihydrogen Bonding: Donor–Acceptor Bonding (AH···HX) versus the H2 Molecule (AH2X)

David Hugas,[a] Slvia Simon,*[a] Miquel Duran,[a] Clia Fonseca Guerra,[b] and F. Matthias Bickelhaupt*[b]

Abstract: Dihydrogen bonds (DHBs) density functional theory at the BP86/ H···H donor–acceptor DHB and the play a role in, among others, crystal TZ2P level of theory. First, we address formation of an H2 molecule by using packing, organometallic reaction mech- the questions of if and how one can the simple H4 model system. The re- anisms, and potential hydrogen-storage distinguish, in principle, between a sults of these analyses have been used materials. In this work we have ana- to gain an understanding of the bond- lyzed the central HH bond in linear ing in more realistic model systems Keywords: bond theory · density H , LiH···HX, BH ···HX, and (some of which have been studied ex- 4 4 functional calculations · donor–ac- AlH ···HX complexes with various X perimentally), and how this differs 4 ceptor systems · hydrogen bonds · by using the quantitative molecular or- from the bonding in H . hydrogen storage 4 bital model contained in Kohn–Sham

Introduction also a preorganization factor in solid-state proton transfer to hydridic hydrogen, leading to the elimination of molecular

Hydrogen bonds (HBs, I) are ubiquitous in chemistry and hydrogen. Recently, such H2 elimination processes (e.g., biology and have, therefore, been the subject of many stud- from BH3NH3) have been explored in connection with their ies, including theoretical studies.[1] Recently, an unconven- potential use in hydrogen storage materials.[5] tional type of hydrogen bonding, the dihydrogen bond (DHB, II), has received increased attention.[2–4] This interac- tion occurs when hydrogen atoms of different fragments have opposite charges, as shown in II. Here, AH acts as a proton acceptor in which A is an electropositive element (e.g., boron, lithium, or other metals) that accommodates a hydridic hydrogen. The protonic hydrogen in a typical Dihydrogen bonds have bond lengths and strengths simi- proton-donor group, HX, binds to the hydridic hydrogen lar to regular hydrogen bonds, that is, in the range of 1.7– in AH. Dihydrogen bonds play an important role in crystal 2.4 (H···H) and 3–10 kcalmol1, respectively. The elec- packing and molecular aggregation in the solid state.[4] It is tronic nature of classic hydrogen bonds has been the subject of much research in recent years, in particular, the question of the extent of covalent (orbital interaction) versus electro- [a] Dr. D. Hugas, Dr. S. Simon, Prof. Dr. M. Duran static character.[6] Kitaura and Morokuma have found that Institut de Qumica Computacional and Departament de Qumica hydrogen bonds in simple dimers, for example, of water, Universitat de Girona, Campus de Montilivi have a dominant electrostatic character, but a non-negligible E-17071 Girona, Catalonia (Spain) Fax : (+34)972-418356 contribution of some 20% from donor–acceptor orbital in- [7] E-mail: [email protected] teractions. Fonseca Guerra and co-workers have shown [b] Dr. C. Fonseca Guerra, Prof. Dr. F. M. Bickelhaupt that the hydrogen bonds in Watson–Crick pairs as well as in Department of Theoretical Chemistry and mismatches of DNA bases receive a contribution of some Amsterdam Center for Multiscale Modeling 40% from donor–acceptor orbital interactions between ni- Scheikundig Laboratorium der Vrije Universiteit trogen or oxygen lone pairs and NH s* acceptor orbitals.[8] De Boelelaan 1083, NL-1081 HV Amsterdam (The Netherlands) Fax : (+31)20-5987629 Furthermore, Isaacs et al. have confirmed through X-ray E-mail: [email protected] scattering measurements that the hydrogen bonds in ice

5814 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Chem. Eur. J. 2009, 15, 5814 – 5822 FULL PAPER

[9] indeed have partial covalent character. Likewise, the driv- from that of H4. Third, having examined the basic principles ing force for DHB formation has been ascribed to a combi- of DHBs, we turned to more realistic complexes, some of nation of a larger term of electrostatic attraction and a which have been studied experimentally, namely, BH4 ···HX smaller but non-negligible term of donor–acceptor interac- (3b, 3d–i) and AlH4 ···HX (4d, 4e). Our bonding analyses tions between the hydridic and protonic hydrogen were based on the quantitative molecular orbital (MO) atoms.[10–12] model contained in Kohn–Sham density functional theory More recently, complexes with very strong DHBs have (DFT)[17] at the BP86/TZ2P level of theory. For selected been studied.[13,14] These complexes feature extremely short model systems we performed a quantitative bond-energy de- H···H distances of 1.2–1.4 and relatively high binding en- composition,[17] as a function of the HH distance, of the ergies of around 20 kcalmol1. Theoretical analyses have classic electrostatic interaction, Pauli repulsive orbital inter- classified these DHBs as partially covalent.[13c,14b] They actions (between closed shells), and bonding orbital interac- appear as precursor complexes AH···HX to a proton trans- tions (e.g., donor–acceptor and electron-pair bonding). fer reaction, yielding cationic dihydrogen complexes + [15] A(H2) ···X . Very strong DHBs can achieve HH distan- ces not much longer than that in the H2 molecule. Interest- Theoretical Methods ingly, based on this HH distance, it has been argued that the H···H moiety in a DHB is a looser donor–acceptor bond General procedure: All calculations were performed by using the Am- between AH and HX(II) or that it can be conceived as sterdam Density Functional (ADF) program developed by Baerends and others.[17] The numerical integration was performed by using the proce- an H2 molecule with a strong H H electron-pair bond that dure developed by te Velde and co-workers.[17g,h] The MOs were expand- interacts with A and X (III). Liao, for example, classified ed in a large uncontracted set of Slater-type orbitals (STOs) containing the H···H moiety in microsolvated LiH···HF either as a diffuse functions: TZ2P (no Gaussian functions are involved).[17i] The basis set is of triple-z quality for all atoms and has been augmented with DHB or a H2 molecule based on the computed HH dis- tance, which varies as a function of the number of water two sets of polarization functions, that is, 3d and 4f on carbon, nitrogen, [16] and oxygen and 2p and 3d on hydrogen. The 1s core shells of carbon, ni- molecules. trogen, and oxygen were treated by the frozen-core approximation.[17c] An auxiliary set of s, p, d, f, and g STOs was used to fit the molecular density and to represent the Coulomb and exchange potentials accurately in each self-consistent field cycle.[17j] Equilibrium structures were optimized by using analytical gradient tech- niques.[17k] Geometries and energies were calculated at the BP86 level of In this study, we had three objectives: First, to address the the generalized gradient approximation (GGA): Exchange is described questions of if and how we can distinguish, in principle, be- by the Xa function[17l] with Becke[17m,n] nonlocal corrections added self- tween the formation of a DHB (II) and molecular hydrogen consistently and the correlation is treated in the Vosko–Wilk–Nusair [17 ] [17p] (III). For this fundamental issue, we used the simplest (VWN) parametrization 8 with Perdew nonlocal corrections added, again, self-consistently (BP86).[17q] model system possible: Linear H4 (1). Second, we wished to proceed to more realistic (but still simple) model systems For a selection of four representative DHB model complexes, we have verified that the trends emerging from our BP86/TZ2P approach are con- such as LiH···HX with X=Cl (2a), F (2b), and CN (2c), as firmed if we use dispersion-corrected DFT at the BP86-D/TZ2P and [18] well as BH4 ···HF (3b(l)), which feature hydridic and proton- BLYP-D/TZ2P levels and ab initio theory at the MP2/6-311++G(d,p)ACHTUNGRE ic hydrogen atoms forming a DHB. We also discuss how the level[19] (see below). electronic structure and the bonding of these species differ Bonding-energy analysis: The overall bond energy DE is made up of two major components [Eq. (1)].

DE ¼ DE þDE ð1Þ Abstract in Catalan: Els enllaÅos de dihidrogen (DHBs) prep int tenen un paper molt important, entre altres, en l’empaqueta- In Equation (1) the preparation energy (DEprep) is the amount of energy ment cristal·l, en mecanismes de reacci de sistemes organo- required to deform the separate molecular fragments from their equilibri- metl·lics i com a possibles materials per a l’emmagatzematge um structure to the geometry that they acquire in the DHB complex. The interaction energy (DE ) corresponds to the actual change in de hidrogen. En aquest article sanalitza l’enllaÅ central H···H int energy when the prepared fragments are combined to form the DHB en els sistemes lineals H4 i LiH···HX, i en els complexes, complex. It is analyzed within the framework of the Kohn–Sham MO BH4 ···HX and AlH4 ···HX amb diferents X, tot utilitzant el model by using a decomposition of the bond into electrostatic interac- model d’orbitals moleculars quantitatiu (MO) contingut en la tion, exchange repulsion (or Pauli repulsion), and (attractive) orbital in- [7, 20,21] teoria del funcional de la densitat (DFT) de Kohn–Sham a teractions [Eq. (2)]. nivell BP86/TZ2P. En primer lloc es discuteix si s possible DE ¼ DV þDE þDE ð2Þ distingir entre enllaÅos de dihidrogen donador-acceptor en- int elstat Pauli oi front de la formaci de una molcula de H2, utilitzant un The term DVelstat corresponds to the classic electrostatic interaction be- simple sistema model com s el H4. El resultat d’aquest anli- tween the unperturbed charge distributions of the prepared (i.e., de- sis servir per entendre altres sistemes molt ms realistes formed) molecular fragments and is usually attractive. The Pauli repul- sion DE comprises the destabilizing interactions between occupied or- ’ Pauli (alguns d ells han estat estudiat de forma experimental), i bitals and is responsible for the steric repulsion. The orbital interaction com aquests difereixen de l’enllaÅ en el sistema H 4. DEoi in any MO model, and therefore also in Kohn–Sham theory, ac- counts for charge transfer (i.e., donor–acceptor interactions between the

Chem. Eur. J. 2009, 15, 5814 – 5822 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim www.chemeurj.org 5815 S. Simon, F. M. Bickelhaupt et al.

occupied orbitals of one moiety and the unoccupied orbitals of the other, this turns out indeed to be the case. This follows from our including HOMO–LUMO interactions) and polarization (empty/occu- quantitative Kohn–Sham MO analyses at the BP86/TZ2P pied orbital mixing on one fragment due to the presence of another frag- level of theory, which are illustrated in Scheme 1 for the ment). Because the Kohn–Sham MO method of DFT in principle yields exact energies and in practice, with the available density functionals for frontier-orbital interactions between two H2 fragments in exchange and correlation, rather accurate energies, we have the special H4. situation that a seemingly one-particle model (an MO method) in princi- ple completely accounts for the bonding energy.[17a] Analysis of the charge distribution: The electron density distribution was analyzed by using the Voronoi deformation density (VDD) method.[22]

The VDD charge QA is computed as the (numerical) integral of the de- formation density D1(r)= 1(r)SB1B(r) associated with the formation of the molecule from its atoms over the volume of the Voronoi cell of atom A [Eq. (3)]. The Voronoi cell of atom A is defined as the compartment of space bound by the bond midplanes on and perpendicular to all the bond axes between nucleus A and its neighboring nuclei (cf. the Wigner- Seitz cells in crystals).[23]

Z hiX Q ¼ 1ðÞr 1 ðÞr dr A B B ð3Þ VoronoicellA

Here, 1(r) is the electron density of the molecule and SB1B(r) the super- position of atomic densities 1B of a fictitious promolecule without chemi- cal interactions that is associated with the situation in which all atoms are neutral. The interpretation of the VDD charge QA is rather straight- forward and transparent. Instead of measuring the amount of charge as- sociated with a particular atom A, QA directly monitors how much charge flows, due to chemical interactions, out of (QA > 0) or into (QA < 0) the Voronoi cell of atom A, that is, the region of space that is closer to Scheme 1. Schematic orbital-interaction diagram for linear H4 in terms of nucleus A than to any other nucleus. two H2 molecules. 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. [8h], however, we have shown that Thus, two closed-shell hydrogen molecules approaching Equation (3) leads to small artifacts that prohibit an accurate description each other in a linear manner yield an H molecule (1) with of the subtle changes in atomic charges that occur in the case of weak 4 chemical interactions such as hydrogen or dihydrogen bonds. This is due a closed-shell singlet (S) ground state that is essentially un- to the so-called front-atom problem that, in fact, all atomic-charge meth- bound. Pushing the H2 fragments together, that is, reducing ods suffer from. To resolve this problem and thus enable a correct treat- the central HH distance leads to 2-orbital–4-electron (or ment of even subtle changes in the electron density, the change in VDD Pauli) repulsion between the occupied H2 s orbitals, which atomic charges DQA is defined by Equation (4), which relates this quanti- form the occupied bonding H 1s and occupied antibonding ty directly to the deformation density D1(r)= 4 H 1s* MOs (see Scheme 1a). In this situation, any stabiliz- 1complex(r)1fragment1(r)1fragment2(r) associated with the formation of the 4 overall molecule (i.e., the DHB complex) from the joining the molecular ing contribution to the net interaction, in addition to an fragments, fragment1 and fragment2.[8h] electrostatic attraction, is provided by the donor–acceptor Z interaction between the occupied 1s orbital of one H2 frag- DQA ¼ 1complexðrÞ1fragment1ðrÞ1fragment2ðrÞ dr ment and the unoccupied s* orbital of the other H frag- ð4Þ 2 VoronoicellA incomplex ment and vice versa. Owing to the relatively large HOMO– LUMO gap between the s and s* orbitals in molecular hy- Again, DQA has a simple and transparent interpretation: It directly moni- drogen, this donor–acceptor interaction is weak and there- > < tors how much charge flows out of (DQA 0) or into (DQA 0) the Voro- fore dominated by the ss Pauli repulsion; for clarity, noi cell of atom A as a result of the chemical interactions between frag- ment1 and fragment2 in the complex. Scheme 1a only shows the latter. If the two H2 fragments are pushed together, below a cer-

tain critical central HH distance, the H2H2 antibonding

ss combination (1su in H4) rises above the H2H2 bonding

Results and Discussion s*+ s* combination (2sg in H4), as shown in Scheme 1b. The original closed-shell singlet configuration is no longer

Linear H4: Donor–acceptor H2···H2 dihydrogen bond versus the ground state at such a short central HH distance. In- C C electron-pair bonded central hydrogen molecule H···H2···H : stead, as shown in Scheme 1c, an open-shell triplet ground

The formation of linear H4 (1) from two hydrogen molecules state occurs as one of the electrons drops from the H2H2 is a generic and idealized model for analyzing the nature of antibonding 1su orbital into the H2H2 bonding orbital 2sg. dihydrogen bonding and, in particular, for addressing the This substantially reduces the ss Pauli repulsion and in- question as to whether one can distinguish qualitatively be- troduces a s*+s* one-electron bond. Thus, in effect, a cen- tween donor–acceptor H···H bonding and the formation of a tral HH electron-pair bond emerges in the linear C C hydrogen molecule with an electron-pair bond. Interestingly, H···H2···H diradical.

5816 www.chemeurj.org 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Chem. Eur. J. 2009, 15, 5814 – 5822 Dihydrogen Bonding FULL PAPER

The discussion so far has highlighted the important role of Finally, the experiment was repeated with long terminal the HOMO–LUMO gap between s and s* in each of the HH distances Rterminal of 2.5 (see Figure 1c). In this situa- two H2 fragments. This, in turn, depends on the internal tion, in which the s–s* gap in the terminal H2 moieties is

HH distance in the H2 fragments, that is, the terminal relatively small (1.3 eV as compared with 11.3 eV in the

HH distance in linear H4. In the following, we provide an equilibrium H2 molecule), the inversion of orbital energies overview of numerical experiments in which we have ex- between the H4 1su and H4 2sg occurs at an early stage of plored how the relative energy of the singlet (S) and triplet approach and the triplet state is thus easily reached. Indeed, states (T) of H4 depend on the central and terminal HH as can be seen in Figure 1c, the triplet state drops below the distances (see Figure 1). First, we consider two H2 mole- singlet state at all the central HH distances probed. In cules, each with a frozen internal HH distance RH of other words, H4 with long terminal HH bonds has a 0.75 , that are brought together from a central HH dis- ground state with an effective central HH electron-pair tance Rcentral in the resulting linear H4 (see Figure 1a). At bond. Note that the formation of a central H2 molecule any dihydrogen distance Rcentral that we probe, singlet H4 is agrees well with the optimum central HH distance of significantly more stable than triplet H4. Both configurations about 0.75 . Note also, however, that the optimum central present a minimum on the PES, the singlet at about Rcentral = HH distance in the singlet state also becomes shorter as 3 and the higher-energy triplet state, with its effective the terminal HH distances become longer (compare Fig- electron-pair bond, achieves a minimum at Rcentral =0.75 . ure 1a–c). Likewise, the energy wells become deeper. The

Note that this corresponds to the H2 equilibrium distance! reason for this is that, as the s–s* orbital-energy gap in H2

Next, we consider two H2 molecules that are brought to- becomes smaller, the s+s* donor–acceptor bonding be- gether in linear H4, but now each of these H2 fragments has tween the H2 moieties in H4 becomes stronger and eventual- a somewhat longer frozen internal HH distance Rterminal of ly prevails over the ss Pauli repulsion.

1.25 (see Figure 1b). Still, singlet H4 is more stable than The question as to whether the central H2 moiety has a triplet H4, at any dihydrogen distance Rcentral, but the energy donor–acceptor DHB character or that it is best described difference is smaller. as a covalent H2 molecule clearly depends on the terminal HH distances. It is therefore instructive to consider an al- ternative decomposition of

linear H4, namely, the central

H2 fragment interacting on each side with a hydrogen C C atom, that is, H4 =H +H2 +H . In Figure 1d we show the corre- sponding energies of closed- shell singlet and open-shell trip- C C let H4 (relative to H +H2 +H ) as a function of the terminal HH distances (i.e., the ap- proach of the hydrogen· atoms)

for a central H2 moiety with its HH distance frozen at the equilibrium value of molecular hydrogen, that is, 0.75 . The corresponding frontier-orbital interactions that emerge from our quantitative Kohn–Sham MO analyses are schematically represented in Scheme 2. When the outer hydrogen atoms are far away from the

central H2 moiety (i.e., at large

terminal RH), the overall H4 species has a triplet ground state: The dashed curve is below the plain curve in Fig- Figure 1. Energy of the singlet (plain curves) and triplet ground state (dashed curves) of linear H4 as a function ure 1d. Importantly, the central of a) the central HH distance with terminal bonds frozen at 0.75 , b) the central HH distance with termi- H moiety in this situation has nal bonds frozen at 1.25 , c) the central HH distance with terminal bonds frozen at 2.5 , d) the terminal 2 HH distances with the central bond frozen at 0.75 , computed at the BP86/TZ2P level of theory relative to effectively an electron-pair ADF basic atoms. bonding valence configuration

Chem. Eur. J. 2009, 15, 5814 – 5822 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim www.chemeurj.org 5817 S. Simon, F. M. Bickelhaupt et al.

C Scheme 2. Schematic orbital-interaction diagram for linear H4 in terms of a central H2 molecule interacting with two outer H radicals, one to the left and one to the right. Bold fragment orbital levels belong to the bold (outer) HH fragment. that interacts with two hydrogen radicals, as shown in tween two hydrogen molecules is the most stable global sit-

Scheme 2c. uation for linear H4 and that this bonding cannot surmount As the two outer hydrogen atoms are brought closer to closed-shell Pauli repulsion between the two fragments in the central frozen H2 moiety (i.e., as Rterminal decreases while this particular model system (see Figure 1a). We proceeded

Rcentral remains fixed at 0.75 ), the singlet configuration is by modifying our linear AH···HX model system from stabilized and, at around Rterminal <1.5 , it becomes the A,X= H(1) towards somewhat more realistic DHB model ground state of H4 (see Figure 1d). Note that this corre- systems involving a hydridic hydrogen bound to an electro- sponds to a change in the valence configuration of the cen- positive A= Li (2), BH3 (3) and a protonic hydrogen bound tral H2 moiety from an electron-pair-bonded hydrogen mol- to an electronegative X= Cl (a), F (b), CN (c). Our results C C ecule to an excited triplet state HH that is intrinsically un- for the model systems 2a–c and 3b(l) are collected in Table 1 bound (see Scheme 2b). Such a valence excitation is facili- (bond analyses) and Figure 2 (geometries). Orbital-interac- tated as the central HH distance is expanded because this tion diagrams, as they emerge from our quantitative Kohn– leads to a small HOMO–LUMO (s–s*) orbital-energy gap Sham MO analyses, are schematically illustrated in in the central H2 moiety (see Scheme 2a). Scheme 3. For clarity, the latter have been simplified to

In conclusion, the central HH bond in linear H4 can show the essential frontier-orbital interactions in the s elec- exist in two qualitatively different bonding modes: 1) As a tron system. donor–acceptor DHB (with no net bonding in this model The donor–acceptor DHB is significantly stabilized (rela- system) and 2) as a central H2 molecule with an electron- tive to 1) in the linear AHHX model systems 2a–c and pair bond. Short terminal HH distances in H4 favor a cen- 3b(l), which are bound with respect to dissociation to AH tral donor–acceptor DHB, whereas long terminal HH and HX with the central HH bonds ranging from 1.13 1 bonds lead to an effectively electron-pair bonded central H2 and 13.7 kcalmol in LiH···HCl (2a) to 1.70 and 1 molecule. In the “H2 + H2 perspective”, this can be under- 8.5 kcalmol in LiH···HCN (2c) (see Table 1). Thus, stood in terms of a large (DHB) or small HOMO–LUMO except for LiH···HCN, these DHB complexes present rela- gap (central electron-pair bond) within the two terminal H2 tively short DHB distances, in agreement with the difference C C fragments. In the “H +H2 +H perspective”, on the other in the proton-donor acidity constant, as pointed out by Gilli hand, the same phenomenon arises from either strong Pauli and Gilli in the qualitative electrostatic–covalent model.[6d] repulsion, which leads to valence excitation of the central We have verified that the trends emerging from our BP86/

H2 molecule from bound singlet to unbound triplet, or weak TZ2P approach (i.e., DE values of 13.7, 15.1, 8.5, and 1 Pauli repulsion, which keeps the central H2 molecule in the 19.5 kcalmol for 2a, 2b, 2c, and 3b(l)) are confirmed if electron-pair-bonded singlet state. Both descriptions are, of we use dispersion-corrected BP86-D/TZ2P (i.e., 14.4, course, equivalent. 15.6, 9.0, and 20.5 kcalmol1), BLYP-D/TZ2P (i.e., 12.8, 15.1, 8.4, and 20.6 kcalmol1), or ab initio MP2/ Dihydrogen bonding in linear AH···HX: The above analyses 6-311+ +G(d,p)ACHTUNGRE methods (i.e., 9.9, 13.2, 8.1, and show that weak donor–acceptor dihydrogen bonding be- 17.2 kcalmol1).

5818 www.chemeurj.org 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Chem. Eur. J. 2009, 15, 5814 – 5822 Dihydrogen Bonding FULL PAPER

Table 1. Analysis of H···H dihydrogen bonds in selected complexes.[a] hydrogen atoms, respectively, which together form the LiH···HCl LiH···HF LiH···HCN BH4 ···HF DHB. (ACHTUNGRE ) (ACHTUNGRE ) (ACHTUNGRE ) (ACHTUNGRE ) 2a 2b 2c 3b(l) In line with this, we find that the overlaps ACHTUNGRE Rcentral(H···H) 1.13 1.30 1.70 1.27 of 0.44–0.67 are up to one order of magnitude larger than energy decomposition [kcal mol1] those of < s*AH j sHX >, which range from 0.04–0.08 (see DEoi 40.9 19.1 8.1 18.8 Table 1). Also, the gross populations of the s and s* DE 42.7 21.1 11.8 18.2 AH HX Pauli fragment orbitals show a donation of a few hundredths (2c) DVelstat 22.2 18.9 12.7 21.3

DEPauli +DVelstat 20.6 2.2 0.9 3.1 up to one third of an electron (2a) from the former to the DEint 20.4 16.9 8.9 21.9 latter. This is consistent with the net fragment VDD charges DEprep 6.7 1.8 0.4 2.4 DQAH =DQHX of 0.03 (2c) to 0.15 a.u. (2a). DE 13.7 15.1 8.5 19.5 [b] The corresponding DHB energy decomposition shows %DEoi 65 50 39 47 fragment orbital overlaps that the interaction energy DEint receives an important part

< sAH jsHX > 0.26 0.16 0.15 0.14 of its stabilizing character from the orbital interaction term < s js* > 0.56 0.67 0.59 0.44 AH HX DEoi (see Table 1). Thus, the electrostatic attraction DVelstat < > s*AH jsHX 0.08 0.05 0.04 0.08 ranges from 8.1 (2c)to40.9 kcalmol1 (2a), whereas the < s*AH js*HX > 0.04 0.01 0.01 0.43 fragment orbital energy [eV] corresponding orbital interaction DEoi ranges from 12.7 1 AH (2c)to22.2 kcalmol (2a). Note that the stronger the sAH 4.4 4.4 4.4 0.5 DHB, the greater the relative importance of the orbital in- s*AH 1.3 1.3 1.3 0.2 teractions. For example, along the series LiH···HCN (2c), HX LiH···HF (2b), LiH···HCl (2a), the interaction energy be- sHX 11.3 13.3 9.3 13.6 comes more stabilizing, from 8.9 to 16.9 to 20.4 kcal s*HX 2.1 1.1 1.1 1.1 1 fragment orbital population [a.u.] mol , whereas the percentage DEoi of all the bonding forces AH (i.e., DEoi +DVelstat) increases from 39 to 50 up to 65%. In- sAH 1.71 1.95 1.97 1.82 terestingly, the latter is even larger than the highest percent- s*AH 0.01 0.01 0.00 0.01 HX age (some 40%) orbital interactions found so far for regular [8] s*HX 0.34 0.07 0.05 0.19 hydrogen bonds. Important covalent contributions to dihy- fragment VDD charge [a.u.][c] drogen bonding also agree with topological analyses of the = [14] DQAH -DQHX 0.15 0.07 0.03 0.08 electron density. The variation from apolar HH···HH(1) to more polar [a] Computed at the BP86/TZ2P level of theory. [b] %DEoi =DEoi/ (and stable) AH···HX species 2a–c and 3b(l) forms a spec- (DEoi+DVelstat)100%. [c] Sum of the atomic charges DQA for all atoms A in a fragment as defined in Equation (4), that is, the net change in charge trum of donor–acceptor dihydrogen bonding mechanisms relative to separate AH and HX. that ranges from clear donor–acceptor bonding, that is, at variance to the qualitatively different electron-pair-bonded

central H2 molecule, to a situation in which the hydridic and

In the cases of 2a, 2b, and 3b(l), these linear stationary protonic character of the respective hydrogen atoms be- structures are second-order saddle points with doubly de- comes strong. Interestingly, the polar extreme of this spec- generate transition vectors with pronounced AHH and trum corresponds to a hydride H that enters into a 1s+1s HHX bending amplitudes, such that molecular hydrogen donor–acceptor interaction with the proton H+ (Scheme 3c). is eliminated from 2a and 2b [Eq. (5)], whereas a bent but This means that for very polar DHB complexes, we have still dihydrogen-bonded structure 3b(b) emerges from 3b(l) again a central H2 molecule. Thus, the clear-cut difference (see Figure 2). between a donor–acceptor DHB and the electron-pair- bonded central hydrogen molecule turns into a more gradu-

AH HX ! AX þ H2 ð5Þ ally changing spectrum in asymmetric model systems AH···HX. Similar conclusions were recently reached in a The essential change in the electronic structure and dihy- theoretical investigation of the structurally related radical- + C drogen bonding mechanism if one goes from 1 to 2 or 3 is cation complexes [HnEHHEnH] in which EnH is the [3] that the s*AH and sHX orbitals are no longer involved in the element hydride of an atom E of groups 15–18. frontier-orbital interactions. Instead, these interactions, to a good approximation, consist of a sAH + s*HX donor–acceptor Dihydrogen bonding in MH4 ···HX: To broaden the scope orbital interaction (compare Scheme 3a and b). This interac- of the above analyses, we have extended our set of model tion is reinforced as the sAH orbital is destabilized and local- systems (from 2a–c and 3b) to include DHB complexes that ized on the hydridic hydrogen, whereas the s*HX orbital is involve boron hydride (3) and aluminium hydride (4) frag- stabilized and more localized on the protonic hydrogen (see ments as hydride donors, and HCl (a), HF (b), HCN (c),

Scheme 3b). The s*AH and sHX orbitals are still present, of CF3OH (d), CH3OH (e), H2O(f), NH3 (g), SiH4 (h), and course, but the point is that their orbital energies have CH4 (i) as proton donors. The geometries and bond analyses moved out off the HOMO–LUMO regime and, in addition, are collected in Figure 2 and Table 2, respectively. Note that they only have little amplitude on the hydridic and protonic all the species discussed in this section are stable equilibri-

Chem. Eur. J. 2009, 15, 5814 – 5822 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim www.chemeurj.org 5819 S. Simon, F. M. Bickelhaupt et al.

Figure 2. Structures of dihydrogen-bonded complexes (distances in ) computed at the BP86/TZ2P level of theory. Numbers correspond to different proton acceptors (2: LiH; 3:BH4 ; 4: AlH4 ), letters to different proton donors (a: HCl; b:HF;c: HCN; d:CF3OH; e:CH3OH; f:H2O; g:NH3 ; h:

SiH4 ; i:CH4). Subscripts refer to the connectivity: (l)=linear DHB, (b)=bifurcated DHB, (t)=trifurcated DHB, and (d) =double DHB.

um structures with zero imaginary frequencies, except for of charge from BH4 or AlH4 to the various proton donors

3f(d) which is a TS for the automerization reaction between HX (see Table 1). Note that the methane complexes 3i(l), two equivalent 3f(b) complexes. 3i(b), and 3i(t) (HX=CH4) are bound only very weakly, in

Our set of model systems covers the full range from very line with the high energy of the methane s*HX acceptor orbi- strong and short DHBs (e.g., 4d: DE=22.6 kcalmol1 and tals.

Rcentral = 1.16 ) to very weak and long (e.g., 3i(t): DE= As the energy of this s*HX acceptor orbital decreases, for 1 1.8 kcalmol and Rcentral =2.64 ). Important donor–ac- example, along BH4 ···HOCF3 (3e(b)), BH4 ···H2O(3b(b)), ceptor bonding is again revealed by a strong orbital interac- and BH4 ···HOCF3 (3d(b)), the DHB contracts, becomes tion component DEoi in combination with a sizeable transfer stronger, and acquires a higher percentage of donor–accept-

5820 www.chemeurj.org 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Chem. Eur. J. 2009, 15, 5814 – 5822 Dihydrogen Bonding FULL PAPER

nisms and potential hydrogen- storage materials is very similar to that of regular hydrogen bonds (Y···HX): It is provided by roughly 40–60% donor–ac- ceptor orbital interactions and a complementary percentage of electrostatic attraction. This fol- lows from our analyses of the central HH bond in LiH···HX, BH4 ···HX, and AlH4 ···HX complexes using the quantita- tive molecular orbital (MO) model contained in the Kohn– Scheme 3. Schematic orbital-interaction diagram showing relationships and differences between dihydrogen Sham density functional theory bonding (DHB) in a) HH···HH, b) AH···HX, and c) HH. (DFT) at the BP86/TZ2P level of theory. We have also shown that, in or orbital interactions. This trend in bonding may serve as principle, there can be a qualitative difference between the basis for the design of hydrogen-storage materials. Thus, donor–acceptor DHB and H2 formation, which, in the ge- by varying the electronegativity difference between H and neric (and idealized) case of H4, corresponds to two differ- XinHX (but also between A and H in AH), one can tune ent electronic states, namely, closed-shell HH···HH and the stability or lability of the DHB system towards conser- open-shell HC···HH···HC. This clear-cut difference can, how- vation or elimination of the central H2 unit, that is, the ever, turn into a more gradually changing spectrum in asym- uptake or release of molecular hydrogen as shown in Equa- metric model systems AH···HX that feature hydridic and tion (5). protonic hydrogen atoms. The results of our analyses suggest a design principle for hydrogen-storage materials. Thus, by varying the electrone- Conclusions gativity difference between H and X in HX (but also be- tween A and H in AH), one can tune the stability or lability The nature of the strong dihydrogen bonds (MH···HX) of the DHB system towards conservation or elimination of that occur, for example, in organometallic reaction mecha- the central H2 unit. The objective is then to arrive at a mate-

Table 2. Analysis of the H···H bond in 3b–4e in the order of ascending HH bond length.[a]

4d 3d(b) 3b(b) 4e 3e(b) 3f(b) 3f(d) 3g 3h(l) 3i(l) 3i(b) 3h(t) 3i(t) ACHTUNGRE Rcentral(H···H) 1.16 1.25 1.36 1.51 1.62 1.62 1.89 1.89 2.06 2.16 2.48 2.50 2.64 energy decomposition [kcal mol1]

DEoi 36.7 32.1 17.6 10.8 10.4 8.8 7.1 5.2 4.4 2.5 2.5 4.9 2.6

DEPauli 34.5 33.3 19.8 13.6 13.4 12.4 11.7 6.8 4.5 2.7 2.5 4.3 2.2

DVelstat 31.6 36.5 25.0 14.5 16.7 17.3 18.3 8.7 2.3 1.7 1.7 2.7 1.4

DEPauli +DVelstat 2.9 3.2 5.2 1.0 3.3 4.9 6.6 1.9 2.2 1.0 0.9 1.7 0.8

DEint 33.8 35.4 22.8 11.7 13.7 13.7 13.7 7.1 2.2 1.4 1.7 3.2 1.8

DEprep 11.2 9.5 2.3 0.8 0.7 0.8 1.3 0.3 0.4 0.0 0.0 0.6 0.0 DE 22.6 25.9 20.5 10.9 13.0 12.9 12.4 6.8 1.7 1.4 1.7 2.6 1.8 [c] %DEoi 54 47 41 43 38 34 28 37 66 60 60 65 65 fragment orbital overlaps [b] [b] [b] < sMH js*HX > 0.53 0.42 0.41 0.31 0.33 0.30 0.32 0.19 0.20 0.17 0.17 0.17 0.15 0.34[b] 0.30[b] 0.27[b] fragment orbital energy [eV] sAH 1.0 0.4 0.5 1.2 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.7 [b] [b] [b] s*HX 2.0 1.9 1.1 0.2 0.2 0.7 0.7 0.3 0.1 0.4 0.5 0.1 0.4 2.3[b] 2.3[b] 2.3[b] fragment orbital population [a.u.] sAH 1.74 1.80 1.89 1.89 1.93 1.93 1.94 1.96 1.94 1.97 1.98 1.95 1.97 s*HX 0.29 0.23 0.12 0.10 0.08 0.07 0.07 0.04 0.05 0.02 0.02 0.05 0.02 0.02 0.01 0.02 fragment VDD charge [a.u.][d] VDD VDD DQAH = DQHX 0.14 0.13 0.08 0.05 0.05 0.05 0.05 0.03 0.03 0.01 0.01 0.03 0.01

[a] Computed at the BP86/TZ2P level of theory. [b] CH4 has two s*HX acceptor orbitals available, of A and T symmetry, and values are displayed for these LUMO and LUMO +1, respectively. [c] %DEoi =DEoi/(DEoi+DVelstat)100%. [d] Sum of the atomic charges DQA of all atoms A in a fragment as de- fined by Equation (4), that is, net change in charge relative to separate AH and HX.

Chem. Eur. J. 2009, 15, 5814 – 5822 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim www.chemeurj.org 5821 S. Simon, F. M. Bickelhaupt et al.

rial that undergoes thermoneutral uptake and release of mo- Leszczynski, J. Phys. Chem. A 2004, 108, 10865; c) G. Merino, V. I. lecular hydrogen through a low activation barrier. Bakhmutov, A. Vela, J. Phys. Chem. A 2002, 106, 8491; d) I. Alkor- ta, J. Elguero, O. M, M. YÇez, J. E. Del Bene, J. Phys. Chem. A 2002, 106, 9325; e) T. Kar, S. Scheiner, J. Chem. Phys. 2003, 119, 1473. Acknowledgements [11] G. Orlova, S. Scheiner, J. Phys. Chem. A 1998, 102, 260. [12] H. Cybulski, M. Pecul, J. Sadlej, T. Helgaker, J. Chem. Phys. 2003, We thank the Spanish Ministerio de Educacin y Ciencia (MEC; Projects 119, 5094. CTQ2005-08797-C02-01/BQU and CTQ2005-02698), the Departament [13] a) S. Grabowski, T. L. Robinson, J. Leszczynski, Chem. Phys. Lett. d’Universitats, Recerca i Societat de la Informaci (DURSI; Project No. 2004, 386, 44; b) S. Grabowski, W. A. Sokalski, J. Leszczynski, J. 2005SGR-00238), the National Research School Combination—Catalysis Phys. Chem. A 2005, 109, 4331; c) H. Cybulski, E. Tymin´ska, J. (NRSC-C), and the Netherlands Organization for Scientific Research Sadlej, ChemPhysChem 2006, 7, 629. (NWO-CW) for financial support. [14] a) D. Hugas, S. Simon, M. Duran, Struct. Chem. 2005, 16, 257; b) D. Hugas, S. Simon, M. Duran, J. Phys. Chem. A 2007, 111, 4506. [15] a) S.-W. Hu, Y. Wang, X.-Y. Wang, T.-W Chu, X.-Q. Liu, J. Phys. [1] a) G. A. Jeffrey, An Introduction to Hydrogen Bonding, Oxford Uni- Chem. A 2003, 107, 9189; b) N. V. Belkova, E. Collange, P. Dub, L. versity Press, New York, 1997; b) G. R. Desiraju, T. Steiner, The Epstein, D. A. Lemenovskii, A. Lleds, O. Maresca, F. Maseras, R. Weak Hydrogen Bond, Oxford University Press, New York, 1999. Poli, P. O. Revin, E. S. Shubina, E. V. Vorontsov, Chem. Eur. J. 2005, [2] a) V. I. Bakhmutov, Eur. J. Inorg. Chem. 2005, 245; b) L. M. Epstein, 11, 873; c) A. Gil, M. Sodupe, J. Bertrn, Chem. Phys. Lett. 2004, E. S. Shubina, Coord. Chem. Rev. 2002, 231, 165; c) R. Custelcean, 395, 27. J. E. Jackson, Chem. Rev. 2001, 101, 1963; d) F. Maseras, A. Lleds, [16] H.-Y. Liao, Chem. Phys. Lett. 2006, 424, 28. E. Clot, O. Eisenstein, Chem. Rev. 2000, 100, 601; e) R. H. Crabtree, [17] a) G. te Velde, F. M. Bickelhaupt, S. J. A. van Gisbergen, C. Fonseca P. E. M. Siegbahn, O. Eisenstein, A. L. Rheingold, T. F. Koetzle, Guerra, E. J. Baerends, J. G. Snijders, T. Ziegler, J. Comput. Chem. Acc. Chem. Res. 1996, 29, 348, and references therein. 2001, 22, 931; b) C. Fonseca Guerra, O. Visser, J. G. Snijders, G. te [3] For a theoretical study of the structurally related radical-cation spe- Velde, E. J. Baerends in Methods and Techniques for Computational +C Chemistry (Eds.: E. Clementi, G. Corongiu), STEF, Cagliari, , cies [HnEHHEHn] , see: A. Krapp, G. Frenking, E. Uggerud, 1995 Chem. Eur. J. 2008, 14, 4028. pp. 305 –395; c) E. J. Baerends, D. E. Ellis, P. Ros, Chem. Phys. 1973, [4] a) J. Poater, R. Visser, M. Sol, F. M. Bickelhaupt, J. Org. Chem. 2, 41; d) E. J. Baerends, P. Ros, Chem. Phys. 1975, 8, 412; e) E. J. 2007, 72, 1134; b) J. Poater, M. Sol, F. M. Bickelhaupt, Chem. Eur. Baerends, P. Ros, Int. J. Quantum. Chem. Symp. 1978, 12, 169; f) C. J. 2006, 12, 2889; c) J. Dunitz, A. Gavezzotti, Angew. Chem. 2005, Fonseca Guerra, J. G. Snijders, G. te Velde, E. J. Baerends, Theor. 117, 1796; Angew. Chem. Int. Ed. 2005, 44, 1766; d) K. N. Robert- Chem. Acc. 1998, 99, 391; g) P. M. Boerrigter, G. te Velde, E. J. Baer- son, O. Knop, T. S. Cameron, Can. J. Chem. 2003, 81, 727; e) C. F. ends, Int. J. Quantum Chem. 1988, 33, 87; h) G. te Velde, E. J. Baer- Matta, J. Hernndez-Trujillo, T. H. Tang, R. F. W. Bader, Chem. Eur. ends, J. Comput. Phys. 1992, 99, 84; i) J. G. Snijders, E. J. Baerends, J. 2003, 9, 1940; f) D. Hugas, S. Simon, M. Duran, Chem. Phys. Lett. P. Vernooijs, At. Data Nucl. Data Tables 1981, 26, 483; j) J. Krijn, 2004, 386, 373; g) M. Remko, Mol. Phys. 1998, 94, 839; h) S. J. Gra- E. J. Baerends, Fit-Functions in the HFS Method; Internal Report (in bowski, J. Mol. Struct. 2000, 553, 151; i) S. J. Grabowski, J. Phys. Dutch), Vrije Universiteit, Amsterdam, 1984; k) L. Versluis, T. Zie- Chem. A 2000, 104, 5551; j) S. A. Kulkarni, A. K. Srivastava, J. Phys. gler, J. Chem. Phys. 1988, 88, 322; l) J. C. Slater, Quantum Theory of Chem. A 1999, 103, 2836; k) S. A. Kulkarni, J. Phys. Chem. A 1998, Molecules and Solids, Vol. 4, McGraw-Hill, New York, 1974; 102, 7704. m) A. D. Becke, J. Chem. Phys. 1986, 84, 4524; n) A. Becke, Phys. [5] a) M. H. Matus, K. D. Anderson, D. M. Camaioni, S. T. Autrey, Rev. A 1988, 38, 3098; o) S. H. Vosko, L. Wilk, M. Nusair, Can. J. D. A. Dixon, J. Phys. Chem. A 2007, 111, 4411; b) C. R. Miranda, G. Phys. 1980, 58, 1200; p) J. P. Perdew, Phys. Rev. B 1986, 33, 8822 (Er- Ceder, J. Chem. Phys. 2007, 126, 184703; c) R. J. Keaton, J. M. Blac- ratum: J. P. Perdew, Phys. Rev. B 1986, 34, 7406); q) L. Fan, T. Zie- quiere, R. T. Baker, J. Am. Chem. Soc. 2007, 129, 1844; d) A. Stau- gler, J. Chem. Phys. 1991, 94, 6057. bitz, M. Besora, J. N. Harvey, I. Manners, Inorg. Chem. 2008, 47, [18] a) S. Grimme, J. Comput. Chem. 2004, 25, 1463; b) S. Grimme, J. 5910. Comput. Chem. 2006, 27, 1787. [6] a) P. Gilli, V. Bertolasi, L. Pretto, V. Ferretti, G. Gilli, J. Am. Chem. [19] W. J. Hehre, L. Radom, P. von R. Schleyer, J. A. Pople, Ab Initio Soc. 2004, 126, 3845; b) P. Gilli, V. Bertolasi, V. Ferretti, G. Gilli, J. Molecular Orbital Theory, Wiley-Interscience, New York, 1986. Am. Chem. Soc. 1994, 116, 909; c) J. Poater, X. Fradera, M. Sol, M. [20] a) F. M. Bickelhaupt, E. J. Baerends in Reviews in Computational Duran, S. Simon, Chem. Phys. Lett. 2003, 369, 248; d) G. Gilli, P. Chemistry, Vol. 15 (Eds.: K. B. Lipkowitz, D. B. Boyd), Wiley-VCH, Gilli, J. Mol. Struct. 2000, 552,1. Weinheim, 2000, pp. 1– 86; See also: b) F. M. Bickelhaupt, N. M. M. [7] a) K. Kitaura, K. Morokuma, Int. J. Quantum Chem. 1976, 10, 325; Nibbering, E. M. van Wezenbeek, E. J. Baerends, J. Phys. Chem. b) K. Morokuma, Acc. Chem. Res. 1977, 10, 294. 1992, 96, 4864; c) F. M. Bickelhaupt, A. Diefenbach, S. V. de Visser, [8] a) C. Fonseca Guerra, T. van der Wijst, F. M. Bickelhaupt, Chem. L. J. de Koning, N. M. M. Nibbering, J. Phys. Chem. A 1998, 102, Eur. J. 2006, 12, 3032; b) C. Fonseca Guerra, E. J. Baerends, F. M. 9549. Bickelhaupt, Int. J. Quantum Chem. 2006, 106, 2428; c) C. Fonseca [21] a) T. Ziegler, A. Rauk, Inorg. Chem. 1979, 18, 1755; b) T. Ziegler, Guerra, F. M. Bickelhaupt, E. J. Baerends, ChemPhysChem 2004, 5, A. Rauk, Inorg. Chem. 1979, 18, 1558; c) T. Ziegler, A. Rauk, 481; d) C. Fonseca Guerra, F. M. Bickelhaupt, J. Chem. Phys. 2003, Theor. Chim. Acta 1977, 46,1. 119, 4262; e) C. Fonseca Guerra, F. M. Bickelhaupt, Angew. Chem. [22] a) C. Fonseca Guerra, J.-W. Handgraaf, E. J. Baerends, F. M. Bickel- 2002, 114, 2194; Angew. Chem. Int. Ed. 2002, 41, 2092; f) C. Fonseca haupt, J. Comput. Chem. 2004, 25, 189; b) F. M. Bickelhaupt, N. J. R. Guerra, F. M. Bickelhaupt, E. J. Baerends, Cryst. Growth Des. 2002, van Eikema Hommes, C. Fonseca Guerra, E. J. Baerends, Organo- 2, 239; g) C. Fonseca Guerra, F. M. Bickelhaupt, Angew. Chem. metallics 1996, 15, 2923. 1999, 111, 3120; Angew. Chem. Int. Ed. 1999, 38, 2942; h) C. Fonseca [23] a) G. F. Voronoi, J. Reine Angew. Math. 1908, 134, 198; b) C. Kittel, Guerra, F. M. Bickelhaupt, J. G. Snijders, E. J. Baerends, Chem. Eur. Introduction to Solid State Physics, Wiley, New York, 1986. J. 1999, 5, 3581. [9] E. D. Isaacs, A. Shukla, P. M. Platzman, D. R. Hamann, B. Barbielli- ni, C. A. Tulk, Phys. Rev. Lett. 1999, 82, 600. [10] a) S. J. Grabowski, W. A. Sokalski, J. Leszczynski, J. Phys. Chem. A Received: December 16, 2008 2004, 108, 5823; b) P. Lipkowski, S. J. Grabowski, T. L. Robinson, J. Published online: April 22, 2009

5822 www.chemeurj.org 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Chem. Eur. J. 2009, 15, 5814 – 5822