& Squaric Acids

Spontaneous H2 Loss through the Interaction of Squaric AcidDerivatives and BeH2

M. Merced Montero-Campillo, Manuel Y�Çez,* Al Mokhtar Lamsabhi, and Otilia M�[a]

Abstract: The most stable complexes between squaric acidand its sulfur- and selenium-containing analogues (C4X4H2 ;X = O, S, Se) with BeY2 (Y = H, F) were studied by means ofthe Gaussian 04 (G4) composite ab initio theory. Squaric acidderivatives are predicted to be very strong acids in the gasphase; their acidity increases with the size of the chalcogen,with C4Se4H2 being the strongest acid of the series andstronger than sulfuric acid. The relative stability of theC4X4H2·BeY2 (X = O, S, Se; Y = H, F) complexes changes withthe nature of the chalcogen atom; but more importantly,the formation of the C4X4H2·BeF2 complexes results in a sub-

stantial acidity enhancement of the squaric moiety owing tothe dramatic electron-density redistribution undergone bythe system when the beryllium bond is formed. The mostsignificant consequence of this acidity enhancement is thatwhen BeF2 is replaced by BeH2, a spontaneous exergonicloss of H2 is observed regardless of the nature of the chalco-gen atom. This is another clear piece of evidence of the im-portant role that closed-shell interactions play in the modu-lation of physicochemical properties of the Lewis acid and/or the Lewis base.

Introduction

The traditional division between the different states of matteris directly related to the way atoms or molecules are associat-ed to each other. Noncovalent interactions are weak interac-tions that have a crucial importance in nature and material sci-ence.[1] These interactions usually involve closed-shell species,as in the case of hydrogen bonds,[2] beryllium bonds,[3] halogenbonds,[4] or van der Waals complexes.[5] Apart from the difficul-ty in classifying them, there is a common characteristic, whichis a certain amount of charge transfer from one interactingmoiety to another. This concept is very well known in chemis-try, as the interaction between a Lewis base and a Lewis acid isbased on this, the acid-accepting electron pairs and the basethat donates them.[6] For example, a proton in a typical hydro-gen bond behaves like a Lewis acid. As an electropositiveatom with available empty orbitals that can accept electrons,beryllium atoms can behave similarly to hydrogen and estab-lish so-called beryllium bonds[3a] when interacting with electrondonors.

These weak forces might play a very important role in theproperties of a given molecular system, and sometimes a coop-

erative effect between them is possible when more than oneis present. We have recently studied some significant cases ofthis cooperativity between hydrogen and beryllium bonds.[3d, 7]

Also, chemical properties such as the intrinsic acidity canchange significantly when the system is perturbed by one ormore weak interactions of this kind. This is the case of theacidity enhancement of BF3�carbonyl complexes,[8] phosphine–boranes,[9] phosphine–alanes,[10] and amine–boranes[11] with re-spect to noncomplexed phosphines or amines. These effectsare even stronger if the base interacts with BeX2 derivativesthrough the formation of beryllium bonds.[12] As a result, con-ventional gas-phase bases such as aniline, acetamide, or evenunsaturated hydrocarbons become stronger acids in the gasphase than typical oxyacids.[12b] These acidity enhancementscan lead to spontaneous proton-transfer processes[13] and tothe spontaneous formation of ion pairs in the gas phase,[14] orcan modulate the self-assembly of some molecular systems ifthe self-assembly process involves hydrogen bonds, thestrength of which can be modified through the formation ofberyllium bonds, as has been shown recently for squaric aciddimers.[7] Other interesting acidity enhancements are triggeredby multiple hydrogen bonds to a single charged center.[15]

The aim of this paper is to analyze whether a spontaneousintramolecular proton transfer from the squaric moiety, Sq, to-wards the beryllium derivative, triggered by the significantacidity enhancement induced by the formation of the berylli-um bond, can occur. Hence, in a first step we will investigatethe acidity enhancement of C4X4H2 (X = O, S, Se) Sq derivativeswhen they form beryllium bonds with BeF2. In a second stepwe will investigate what the effect of the beryllium bond is onthe second deprotonation process. In a third step we will ana-lyze what the behavior of these Sq acid derivatives is when

[a] Dr. M. M. Montero-Campillo, Prof. M. Y�Çez, Dr. A. M. Lamsabhi,Prof. O. M�Departamento de Qu�mica, Facultad de CienciasM�dulo 13, Universidad Aut�noma de MadridCampus de Excelencia UAM-CSICCantoblanco, 28049 Madrid (Spain)Fax: (+ 34) 91-497-5238E-mail : manuel.yanez@uam.es

Supporting information for this article is available on the WWW underhttp ://dx.doi.org/10.1002/chem.201304259.

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Full PaperDOI: 10.1002/chem.201304259

they interact with BeH2, which is able to yield dihydrogenbonds with the acidic hydrogen atoms bonded to the chalco-gen atoms, in an effort to see if these dihydrogen bonds canbe suitable precursors for the loss of H2.

Computational Details

Although it has been shown[3d, 7] that the B3LYP functional[16] usual-ly yields a good description of both hydrogen and beryllium bondswhen a 6-311+G(3df,2p) basis set that is flexible enough is used, inthe present work we have decided to increase the accuracy of thecalculations by using the more sophisticated Gaussian 04 (G4) ap-proach,[17] a composite technique based on B3LYP-optimized geo-metries that provides final total energies at an effective CCSD(T,full)/G3LargeXP + HF limit level.

The natural bond orbital (NBO) analysis[18] was used to study thestrength of bonding in the complexes under investigation. Withthis method it is also possible to analyze natural charges andcharge transfer by means of second-order interaction energies be-tween the occupied orbitals of Sq acid derivatives and empty orbi-tals of BeY2, as well as to calculate the Wiberg bond order,[19] whichis a good index of the nature of the bond. The topology of theelectron density was analyzed within the framework of the atomsin molecules (AIM)[20] theory to obtain the critical points of thedensity, which give significant information about the nature andstrength of the interactions present in the molecule. Bond criticalpoints (BCPs) are first-order saddle points of the density on thebond paths that connect the nuclei.

All electronic-structure calculations were carried out with the Gaus-sian 09 software package.[21] AIM calculations were performed withthe AIMAll software package.[22]

One of the properties that might influence the relative stability ofthese systems is aromaticity. To analyze this property we have de-cided to use two different criteria, one based on magnetic proper-ties and the other on geometrical parameters. Among the formerwe have selected the magnetic susceptibility and the nucleus-inde-pendent chemical shift (NICS).[23] A strong diamagnetic susceptibili-ty is an unequivocal characteristic of all aromatic compounds. Ab-normal chemical shifts can also evidence electronic delocalizationon cyclic compounds, as observed in benzene, which thereforepresent negative NICS values. NICS varies significantly with the dis-tance to the molecular plane, and therefore a local value of thisindex such as NICS(1) is not always appropriate. Hence, in oursurvey, a scan of NICS along an axis perpendicular to the molecularplane[24] was carried out. Among all geometric indices we havechosen the Julg index,[25] which can be readily used for rings of dif-ferent sizes.[26]

Results and Discussion

Structure, stability, and intrinsic acidity of Sq derivatives(C4X4H2 ; X = O, S, Se)

Sq acids present two rather stable EZ and ZZ isomers (seeScheme 1). A third EE conformer that lies much higher inenergy will not be considered in our study.

Table 1 contains the relative stabilities of the EZ(X) andZZ(X) conformers for X = O, S, Se, as well as the acidities thatcorrespond to the first and second deprotonation processes ofthese compounds calculated at the G4 level of theory.

The first conspicuous fact is that regardless of the nature ofthe chalcogen atom the ZZ(X) isomer is predicted to be morestable than the EZ(X) one, likely reflecting the larger intrinsicbasicity of the carbonyl, thiocarbonyl, and selenocarbonylgroups with respect to hydroxyl, thiol, and selenol groups. Inthis respect, it is interesting to note that for the selenium de-rivative, in which the size of the chalcogen atom reaches itsmaximum value, a BCP between the selenocarbonyl groups,which act as proton acceptors, and the Se�H groups, whichact as proton donors, has been found (see Figure 1), therebysuggesting the formation of an intramolecular Se�H···Se hydro-gen bond (HB).

Also interestingly, the electron density of the four-mem-bered ring changes significantly when O is replaced by S or Se.Owing to the decrease in the electronegativity of the hetero-atom, this replacement is accompanied by an increase in theelectron densities at the C�C single bonds in which the thio-carbonyl or the selenocarbonyl groups participate, whereasthe electron density at the HXC=CXH bond decreases. Consis-tently, C1�C2, C1�C3, and C1�C4 shorten and the correspond-ing Wiberg bond index increases when O is replaced by S orSe, whereas the C3=C4 bond lengthens and the Wiberg bondindex decreases (see Figure S1 in the Supporting Information).

For the EZ(X) conformer it is found that the most acidic siteis the X5H group. As a consequence, both EZ(X) and ZZ(X)structures lead to the same anion upon deprotonation. There-fore the most stable ZZ(X) conformer is always a slightlyweaker acid than the EZ(X) one. It is worth noting that the in-

Scheme 1. EZ, ZZ, and EE conformers of squaric acid and its derivatives(X = O, S, Se) and numbering used in this study.

Table 1. Relative enthalpies and free energies (DH�rel, DG�rel 298 K) of thetwo more stable conformers of C4X4H2 (X = O, S, Se) Sq derivatives andtheir gas-phase acidities (DH�acid, DG�acid 298 K).

DH�rel 298 K[kJ mol�1]

DH�acid 298 K[kJ mol�1]

DG�rel 298 K[kJ mol�1]

DG�acid 298 K[kJ mol�1]

EZ(O) 8.2 1314.0[a] 8.0 1283.0[a]

ZZ(O) 0.0 1322.2/1771.6[b] 0.0 1291.0[a]/1741.4[b]

EZ(S) 9.8 1276.9[a] 8.9 1247.1[a]

ZZ(S) 0.0 1286.6/1656.9[b] 0.0 1256.0[a]/1626.7[b]

EZ(Se) 7.5 1256.7[a] 6.8 1226.6[a]

ZZ(Se) 0.0 1264.2/1614.4[b] 0.0 1233.4[a]/1584.4[b]

[a] Gas-phase acidity corresponding to the process C4X4H2!C4X4H�+ H+ .[b] Gas-phase acidity corresponding to the process C4X4H�!C4X4

2�+ H+ .Note that this acidity is identical for the EZ and the ZZ conformers.

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trinsic acidity of the Sq derivative increases when O is replacedby S and increases further if S is replaced by Se, likely reflect-ing the fact that second- and third-row atoms better accom-modate the excess amount of charge produced by the depro-tonation process. A second factor that contributes to an en-hanced stability of the C4S4H� and C4Se4H� anions with respectto C4O4H� is the intramolecular HB formed between the XH(X = S, Se) as proton donor and the C=X group as proton ac-ceptor, as illustrated in the corresponding molecular graphs(see Figure S2 in the Supporting Information). An interestingconsequence is that, whereas C4Se4H2 is predicted to bea stronger acid than sulfuric acid in the gas phase (DacidG0 =

(1265�23) kJ mol�1),[27] the Sq acid itself (C4O4H2) is predictedto be only as strong as chloric acid (DacidG0 = (1284�16) kJ mol�1).[27]

It is important to emphasize the significant disagreementbetween our estimates and previous theoretical studies,[28]

which reported gas-phase acidities for these three compounds(DacidG0) about 24–29 kJ mol�1 larger than ours. To checkwhether this disagreement could be due to the method usedin the literature[28a] with respect to G4 theory, we have recalcu-lated the acidity of Sq acid at the MP4/6-311+G(d,p) level,which was the approach used in the literature,[28a] and a dis-agreement of 26 kJ mol�1 remains. Interestingly, this disagree-ment coincides with the value of the free energy of theproton, and this fact leads us to suspect that in all the calcula-tions reported in the literature[28] the free energy of the protonwas ignored. This would also explain why the acidity of thesecompounds measured in terms of enthalpies and in terms offree energies are almost identical in all these papers, which isconceptually erroneous.

The same acidity trends are observed as far as the deproto-nation of the C4X4H� is concerned (see Table 1), with theC4Se4H� being the strongest acid of the three C4X4H� anions.In fact, the C4Se4H� anion is predicted to be only 57 kJ mol�1

less acidic than acetic acid (1427.0�8.4).[27] For similar reasons

to those indicated above, our calculations predict the threeC4X4H� (X = O, S, Se) anions to be stronger acids than reportedin the literature[28] by about 23 kJ mol�1 for these second de-protonation processes as well. It should be noted, however,that the dianion produced in this second deprotonation pro-cess is not stable with respect to electron loss (see Table S3 inthe Supporting Information).

It is worth noting that the acidity trends predicted for thesesquaric acid derivatives, O<S<Se, is qualitatively similar tothat observed for H2O, SH2, and SeH2,[27] as well as for carbonyl,thiocarbonyl, and selenocarbonyl derivatives.[29]

Acidity enhancement upon BeF2 association

Seven different complexes can be formed by association of thetwo more stable conformers, namely, EZ and ZZ, with BeF2 de-rivatives (see Scheme S1 in the Supporting Information). Ina previous survey[3f] we found that, as could be anticipated,the preferential sites for BeH2 attachment are the C=X groups,so that the most stable complexes when the Lewis acid is BeF2

are EZ(X)a and ZZ(X)a, respectively (see Scheme 2). The struc-

tures and total energies of these complexes for X = O, S, Se aswell as those of the corresponding deprotonated species areshown in Figure S3 and Table S1 in the Supporting Informa-tion.

As found for the isolated Sq acid derivatives, ZZ(X)a is pre-dicted to be more stable than EZ(X)a regardless of the chalco-gen heteroatom involved (see Table 2). In all cases the most fa-vorable deprotonation process corresponds to the heterolyticcleavage of the X�H bond not interacting with the BeF2 mole-cule. This means that both EZ(X)a and ZZ(X)a complexes, aswas the case for the corresponding isolated Sq derivatives,yield the same anion upon deprotonation.

A comparison of the acidities in Tables 1 and 2 shows thesignificant acidity enhancement triggered by the association ofthe Sq derivatives with BeF2. Note that this acidity enhance-ment decreases upon going from O to Se. Hence, whereas theacidity changes by 105 kJ mol�1 for the O-containing system,for S and Se this variation is only 69.9 and 60.9 kJ mol�1, re-spectively. A rather substantial acidity enhancement, althoughapproximately 40 % smaller than the one observed for the firstproton loss, is observed for the second proton loss (seeTable 2). In this case a decrease in the effect with the size ofthe chalcogen atom is also observed.

Figure 1. Molecular graphs of the ZZ isomers of C4X4H2; X = O (a), S (b), Se(c). Dots denote BCPs and ring critical points (RCPs). Electron densities are inatomic units.

Scheme 2. Schematic structure of the most stable complexes formed by theinteraction of EZ and ZZ conformers of C4X4H2 (X = O, S, Se) Sq derivatives.

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What is the origin of this acidity enhancement and whydoes it decreases with the size of the chalcogen atom? Thiscan be explained by the thermodynamic cycle shown inScheme 3; in this scheme, DG0

1 and DG03 are the gas-phase acid-

ities of the isolated Sq derivatives and of the complexes theyformed with BeF2, respectively. DG0

2 and DG04 measure the sta-

bilization of the neutral Sq derivatives and their deprotonatedforms when interacting with BeF2. A similar scheme can beused for the loss of the second proton (see Scheme S2 in theSupporting Information).

The enhanced stability of the C4X4H2 (X = O, S, Se) Sq deriva-tives and their deprotonated structures has a threefold origin:1) the formation of a quite strong X···Be beryllium bond, 2) theformation of a XH···F intramolecular HB, and 3) a significant in-crease in the aromaticity of the system that is predicted bothby magnetic properties and geometrical indexes. We presentin Figure 2 the scan of the NICS along an axis perpendicular tothe ring plane for the C4O4H2 as a suitable example. It can beseen that the NICS reaches its maximum absolute value ata distance of approximately 0.6 � of the molecular plane, andthat its value significantly increases upon going from the iso-

Table 2. Relative free energies (DG�rel 298 K [kJ mol�1]) of the two more stable conformers of C4X4H2·BeF2 (X = O, S, Se) complexes, gas-phase acidity (DG�acid)corresponding to the processes A) C4X4H2·BeF2!(C4X4H �)·BeF2 + H+ and B) (C4X4H�)·BeF2!(C4X4

2�)·BeF2 + H+, and values of DG�1, DG�2, DG�3, and DG�4defined in Scheme 3.[a]

Process A Process BDG�rel

[kJ mol�1]DG�acid

[kJ mol�1]DG�1�DG�3[kJ mol�1]

DG�2[kJ mol�1]

DG�4[kJ mol�1]

DG�acid

[kJ mol�1]DG�1�DG�3[kJ mol�1]

DG�2[kJ mol�1]

DG�4[kJ mol�1]

EZ(O)a 4.9 1178.0 105.0 �95.2 �200.2 1678.3 63.1 �200.2 �263.3ZZ(O)a 0.0 1183.0 108.0 �92.2 �200.2 – – – –EZ(S)a 6.9 1177.2 69.9 �31.1 �101.0 1567.6 59.2 �101.0 �160.2ZZ(S) a 0.0 1184.1 71.9 �29.1 �101.0 – – – –EZ(Se)a 6.8 1165.7 60.9 �25.1 �86.0 1533.3 51.2 �86.0 �137.2ZZ(Se)a 0.0 1170.8 62.6 �23.4 �86.0 – – – –

[a] Note that processes B are identical for EZ and ZZ conformers, so the values for the ZZ conformer are identical to those reported for the EZ one.

Scheme 3. Thermodynamic cycle associated with the acidity enhancementundergone by C4X4H2 (X = O, S, Se) Sq derivatives upon association withBeF2.

Figure 2. Scan of NICS along an axis perpendicular to the four-membered ring for C4O4H2 and C4O4H2·BeF2 and their corresponding deprotonated forms.

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lated Sq derivative to the corresponding Sq·BeF2 complex.Consistently, as shown in Table S2 of the Supporting Informa-tion, after BeF2 attachment both the magnetic susceptibility inabsolute value as well as the Julg index increase as well.

The important finding, however, is that, as shown in Table 2,whatever the nature of the chalcogen, DG0

4 is significantlylarger than DG0

2, and this larger stabilization of the deprotonat-ed structure upon association with BeF2 unavoidably leads tothe observed substantial acidity enhancement. The enhancedstability of the deprotonated species has been proven very re-cently to be a general phenomenon in these kinds of deriva-tives.[12b] However, the relative changes vary strongly with thenature of the chalcogen. For X = O, DG0

4 is more than twice aslarge as DG0

2, but three times and four times as large for X = Sand X = Se, respectively. Why, then, does the acidity enhance-ment decrease as O>S>Se? This is essentially due to therather small value of DG0

2 for the S and Se derivatives, which isonly about one third of the DG0

2 value for the O-containing an-alogues. This significant decrease in the stabilization of theneutral Sq derivatives when O is replaced by S or Se is essen-tially due to a significant decrease in the strength of both theX�H···F hydrogen bond and the C=X···Be beryllium bond. Thisis apparent when comparing the molecular graphs of theSq·BeF2 complexes (see Figure 3) with those of the isolated Sqderivatives in Figure 1.

Although the electron densities at the O�H···F BCP cannotbe directly compared with those at the S�H···F because of thedifferent nature of the atoms involved, the relative strength ofthese linkages can be deduced from the changes undergoneby the O�H and S�H, which participate in them. A comparisonof the electron densities of the O�H and S�H proton donors inFigure 3 (0.310 and 0.207 a.u. , respectively) with those of the

same bonds in the isolated Sq derivatives (0.361 and0.212 a.u. , respectively; see Figure 1) shows that the activationof the OH bond, the electron density of which decreases0.051 a.u. , is much larger than that of the S�H bond, the elec-tron density of which decreases ten times less. This clearly indi-cates that the O�H···F HB is significantly stronger than the S�H···F one. This is consistent with the NBO analysis of thesecomplexes, which shows that the charge transfer from thelone pairs of the F atom towards the sOH* antibonding orbitalis larger than towards the sSH* antibonding orbital. Indeed, thenatural population of the sOH* (0.085 e�) in the C4O4H2·BeF2

complex is larger than that of the sSH* (0.070 e�) in theC4S4H2·BeF2 complex. Similar rationales show that the CO···Beberyllium bond is also stronger than the CS···Be one. Indeed,the electron density at the C=O BCP decreases 0.036 a.u. whenthe CO···Be bond is formed, whereas that of the C=S bondonly decreases 0.007 a.u. Again, consistently, whereas the NBOshows that the interaction between the Sq subunit and BeF2 isthe result of a charge transfer from the S lone pairs into theempty 2p orbital of Be, in the O-containing analogue this inter-action is so strong that an O�Be covalent bond strongly polar-ized toward the oxygen atom is formed. However, the aroma-ticity seems not to play any significant role in the enhancedstability of the anionic deprotonated species, as both magneticproperties and geometrical indices give almost equal valuesfor the neutral and anionic systems (see Table S2 in the Sup-porting Information).

Spontaneous H2 loss when BeF2 is replaced with BeH2

The significant acidity enhancement experienced by C4X4H2

(X = O, S, Se) when interacting with BeF2 together with the factthat the three neutral compounds form strong HBs with oneof the F atoms of the BeF2 subunit moved us to explore whatthe behavior of the same complexes would be when BeF2 is re-placed by BeH2 and thus the XH···F HB is replaced by a XH···Hdihydrogen bond.[3f] Indeed, when this replacement is carriedout, the structures found for both the EZa and the ZZa con-formers of C4O4H2·BeH2 shown in Figure 4 present a rather

strong OH···HBe dihydrogen bond, as reflected in the veryshort H···H distance as well as the significant elongation ofboth the O�H and the Be�H bonds. The electron density atthe H···H bond critical point is significantly larger for this kindof weak interaction and the energy density is negative, therebyconfirming its significant strength.

In light of the significant strength of the aforementioned di-hydrogen bond, we decided to study whether a proton trans-

Figure 3. Molecular graph of the complexes between C4X4H2, X = O (a), S (b),and BeF2. Dots denote BCPs and ring critical points (RCPs). Electron densitiesare in a.u.

Figure 4. Most relevant optimized geometrical parameters of the EZ(O)a(left) and ZZ(O)a (right) complexes involving BeH2 and their correspondingmolecular graphs. Dots denote BCPs and ring critical points (RCPs). Electrondensities are in a.u.

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fer to form a C4O4H�·BeH3+ ion pair implies a significant activa-

tion barrier. As a result of this survey, we located for both con-formers another local minima, namely, SqEZBeH(O)···H2 andSqZZBeH(O)···H2, which lie 19.3 and 14.4 kJ mol�1 lower inenergy, respectively. As illustrated in Figure 5, these complexescan be seen as the result of a weak interaction between H2

and the neutral HC4O4BeH molecule.The most striking result is that the geometry optimization of

complexes that involve S- and Se-containing compoundsyields only the structures SqZZBeH(X)···H2 (X = S, Se) shown inFigure 5, and any attempt to optimize structures EZ(X)a andZZ(X)a (X = S, Se) similar to those shown in Figure 4 for the O-containing systems failed, because they collapsed into thestructures in Figure 5 through a spontaneous proton transfer.To understand why the EZ(O)a and the ZZ(O)a complexes arefound to be stable in the case of the oxygen analogues, wecalculated the potential energy curve associated with theproton transfer for the particular case of the EZ(O)a complex.The result of this survey is shown in Figure 6.

It is apparent that the proton transfer implies a rather lowactivation barrier of about 8 kJ mol�1; but the most significantfeature is that when free energies are used instead of enthal-pies, the barrier disappears, thus indicating that the proton-transfer (PT) process is spontaneous at 298 K. Indeed, asshown in Figure 7, the SqEZBeH(O)···H2 complex lies93.0 kJ mol�1 below the entrance channel C4O4H2 + BeH2. Fur-thermore, the SqEZBeH(O) + H2 dissociation limit lies103.7 kJ mol�1 even further below, thereby reflecting the stabi-

lization of both the H2 moiety and the SqEZBeH(O), in whichthe BeH group interacts simultaneously with both carbonylgroups. In summary, the attachment of BeH2 to C4O4H2 leadsto a spontaneous exergonic (by 196.7 kJ mol�1) H2 loss. Wehave also verified whether the basis set superposition error(BSSE) could have some significant effect in these predictions,since H2 would in principle be more poorly described at theG4 level than the other heavier fragment. However, our esti-mates indicate that the BBSE is typically 0.6 kcal mol�1 or lower.For the S- and Se-containing analogues, the proton-transferprocess is barrierless both in terms of enthalpies and free ener-gies, and the processes in which a spontaneous loss of H2

takes place are also exergonic (see Figure S4 in the SupportingInformation). This finding might have important implications inthe problem of hydrogen storage. Actually, the possibility ofusing beryllium hydride derivatives for this purpose has beendiscussed previously in the literature, owing to its high storagecapacity,[30] although one of the important limitations is itshigh toxicity.[31]

Figure 5. Most relevant optimized geometrical parameters of the moststable complexes between the EZ and ZZ conformers of C4X4H2 (X = O, S,Se) Sq derivatives and BeH2.

Figure 6. Potential-energy curve associated with the proton transfer inEZ(O)a complex.

Figure 7. G4 relative free energies corresponding to the association of BeH2

to squaric acid to yield HC4O4BeH + H2.

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Upon reaching this point, one final question arises. Why inthe case of the complexes with BeF2 in which a strong XH···FBeHB is formed does no spontaneous proton transfer seem to bepossible and therefore no spontaneous loss of HF is observed?The answer to this question is twofold. Whereas the PT in thecomplex between squaric acid and BeH2 is a low-barrier pro-cess in terms of enthalpies and barrierless in terms of free en-ergies, the same process in the complex between squaric acidand BeF2 involves a significantly large activation barrier, bothin terms of enthalpies (121 kJ mol�1) and of free energies(125 kJ mol�1). On top of that, the H2 loss process C4O4H2 +BeH2!HC4O4BeH + H2 should be spontaneous because it is ex-ergonic, and the HF loss process C4O4H2 + BeF2!HC4O4BeF + HFis predicted to be endergonic by 96.6 kJ mol�1.

Conclusion

Squaric acid derivatives are predicted to be very strong acidsin the gas phase. Importantly, our values predict all these com-pounds to be stronger acids by about 25 kJ mol�1 than previ-ous theoretical studies reported in the literature in which thefree energy of the proton was ignored. The acidity increaseswith the size of the chalcogen, so that the C4Se4H2 is the stron-gest acid of the series, being even stronger than sulfuric acid.

The association of these Sq derivatives with BeF2 leads tothe formation of a rather strong C=X···Be beryllium bond andan XH···F hydrogen bond as well as to a significant increase inthe aromaticity of the system. These three effects result in a sig-nificant stabilization of the C4X4H2·BeF2 complexes formed.However, the most important fact is that the stabilization un-dergone by the corresponding deprotonated species is two tofour times larger than that undergone by the neutral com-pound, thereby resulting in a dramatic enhancement of theacidity of the C4X4H2·BeF2 complex. For instance, whereas, asmentioned above, C4O4H2 was predicted to be as acidic aschloric acid, the C4O4H2·BeF2 complex is estimated to be signifi-cantly stronger than perchloric acid.

One of the most important consequences of this acidity en-hancement triggered by the formation of a beryllium bond isthat when BeF2 is replaced by BeH2, a barrierless spontaneousexergonic H2 loss is observed regardless of the nature of thechalcogen atom. An analogous loss of HF in complexes that in-volve BeF2 is, however, a rather endergonic process witha rather high activation barrier.

Acknowledgements

This work has been partially supported by the DGI projects no.CTQ2012-35513-C02-01 and CTQ2010-17006, by the MADRISO-LAR2 project (S2009PPQ/1533) of the Comunidad de Madrid,by Consolider on Molecular Nanoscience CSC2007-00010, andby the COST Action CM1204. A generous allocation of comput-ing time at the Centro de Computaci�n Cient�fica of the UAMis also acknowledged. M.M.M.-C. thanks the MADRISOLAR2project for financial support.

Keywords: beryllium · chalcogens · cooperative phenomena ·hydrogen · noncovalent interactions

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Received: October 31, 2014Published online on && &&, 0000

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& Squaric Acids

M. M. Montero-Campillo, M. Y�Çez,*A. M. Lamsabhi, O. M�

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Spontaneous H2 Loss through theInteraction of Squaric Acid Derivativesand BeH2

Acid test : The dramatic acidity en-hancement induced on squaric acid de-rivatives (O, S, Se) when associated withBeH2 leads to a spontaneous exergonicloss of H2 regardless of the nature ofthe chalcogen atom (see figure).

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