DOI: 10.1002/chem.201304259
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& Squaric Acids
Spontaneous H2 Loss through the Interaction of Squaric Acid Derivatives and BeH2 M. Merced Montero-Campillo, Manuel YÇez,* Al Mokhtar Lamsabhi, and Otilia M[a]
Abstract: The most stable complexes between squaric acid and its sulfur- and selenium-containing analogues (C4X4H2 ; X = O, S, Se) with BeY2 (Y = H, F) were studied by means of the Gaussian 04 (G4) composite ab initio theory. Squaric acid derivatives are predicted to be very strong acids in the gas phase; their acidity increases with the size of the chalcogen, with C4Se4H2 being the strongest acid of the series and stronger than sulfuric acid. The relative stability of the C4X4H2·BeY2 (X = O, S, Se; Y = H, F) complexes changes with the nature of the chalcogen atom; but more importantly, the formation of the C4X4H2·BeF2 complexes results in a sub-
Introduction The traditional division between the different states of matter is directly related to the way atoms or molecules are associated to each other. Noncovalent interactions are weak interactions that have a crucial importance in nature and material science.[1] These interactions usually involve closed-shell species, as in the case of hydrogen bonds,[2] beryllium bonds,[3] halogen bonds,[4] or van der Waals complexes.[5] Apart from the difficulty in classifying them, there is a common characteristic, which is a certain amount of charge transfer from one interacting moiety to another. This concept is very well known in chemistry, as the interaction between a Lewis base and a Lewis acid is based on this, the acid-accepting electron pairs and the base that donates them.[6] For example, a proton in a typical hydrogen bond behaves like a Lewis acid. As an electropositive atom with available empty orbitals that can accept electrons, beryllium atoms can behave similarly to hydrogen and establish so-called beryllium bonds[3a] when interacting with electron donors. These weak forces might play a very important role in the properties of a given molecular system, and sometimes a coop-
[a] Dr. M. M. Montero-Campillo, Prof. M. YÇez, Dr. A. M. Lamsabhi, Prof. O. M Departamento de Qumica, Facultad de Ciencias Mdulo 13, Universidad Autnoma de Madrid Campus de Excelencia UAM-CSIC Cantoblanco, 28049 Madrid (Spain) Fax: (+ 34) 91-497-5238 E-mail: [email protected] Supporting information for this article is available on the WWW under http://dx.doi.org/10.1002/chem.201304259. Chem. Eur. J. 2014, 20, 5309 – 5316
stantial acidity enhancement of the squaric moiety owing to the dramatic electron-density redistribution undergone by the system when the beryllium bond is formed. The most significant consequence of this acidity enhancement is that when BeF2 is replaced by BeH2, a spontaneous exergonic loss of H2 is observed regardless of the nature of the chalcogen atom. This is another clear piece of evidence of the important role that closed-shell interactions play in the modulation of physicochemical properties of the Lewis acid and/ or the Lewis base.
erative effect between them is possible when more than one is present. We have recently studied some significant cases of this cooperativity between hydrogen and beryllium bonds.[3d, 7] Also, chemical properties such as the intrinsic acidity can change significantly when the system is perturbed by one or more weak interactions of this kind. This is the case of the acidity enhancement of BF3carbonyl complexes,[8] phosphine– boranes,[9] phosphine–alanes,[10] and amine–boranes[11] with respect to noncomplexed phosphines or amines. These effects are even stronger if the base interacts with BeX2 derivatives through the formation of beryllium bonds.[12] As a result, conventional gas-phase bases such as aniline, acetamide, or even unsaturated hydrocarbons become stronger acids in the gas phase than typical oxyacids.[12b] These acidity enhancements can lead to spontaneous proton-transfer processes[13] and to the spontaneous formation of ion pairs in the gas phase,[14] or can modulate the self-assembly of some molecular systems if the self-assembly process involves hydrogen bonds, the strength of which can be modified through the formation of beryllium bonds, as has been shown recently for squaric acid dimers.[7] Other interesting acidity enhancements are triggered by multiple hydrogen bonds to a single charged center.[15] The aim of this paper is to analyze whether a spontaneous intramolecular proton transfer from the squaric moiety, Sq, towards the beryllium derivative, triggered by the significant acidity enhancement induced by the formation of the beryllium bond, can occur. Hence, in a first step we will investigate the acidity enhancement of C4X4H2 (X = O, S, Se) Sq derivatives when they form beryllium bonds with BeF2. In a second step we will investigate what the effect of the beryllium bond is on the second deprotonation process. In a third step we will analyze what the behavior of these Sq acid derivatives is when
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Full Paper they interact with BeH2, which is able to yield dihydrogen bonds with the acidic hydrogen atoms bonded to the chalcogen atoms, in an effort to see if these dihydrogen bonds can be suitable precursors for the loss of H2.
Computational Details Although it has been shown[3d, 7] that the B3LYP functional[16] usually yields a good description of both hydrogen and beryllium bonds when a 6-311+G(3df,2p) basis set that is flexible enough is used, in the present work we have decided to increase the accuracy of the calculations by using the more sophisticated Gaussian 04 (G4) approach,[17] a composite technique based on B3LYP-optimized geometries 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 the strength of bonding in the complexes under investigation. With this method it is also possible to analyze natural charges and charge transfer by means of second-order interaction energies between the occupied orbitals of Sq acid derivatives and empty orbitals of BeY2, as well as to calculate the Wiberg bond order,[19] which is a good index of the nature of the bond. The topology of the electron density was analyzed within the framework of the atoms in molecules (AIM)[20] theory to obtain the critical points of the density, which give significant information about the nature and strength of the interactions present in the molecule. Bond critical points (BCPs) are first-order saddle points of the density on the bond paths that connect the nuclei. All electronic-structure calculations were carried out with the Gaussian 09 software package.[21] AIM calculations were performed with the AIMAll software package.[22] One of the properties that might influence the relative stability of these systems is aromaticity. To analyze this property we have decided to use two different criteria, one based on magnetic properties and the other on geometrical parameters. Among the former we have selected the magnetic susceptibility and the nucleus-independent chemical shift (NICS).[23] A strong diamagnetic susceptibility is an unequivocal characteristic of all aromatic compounds. Abnormal chemical shifts can also evidence electronic delocalization on cyclic compounds, as observed in benzene, which therefore present negative NICS values. NICS varies significantly with the distance to the molecular plane, and therefore a local value of this index such as NICS(1) is not always appropriate. Hence, in our survey, a scan of NICS along an axis perpendicular to the molecular plane[24] was carried out. Among all geometric indices we have chosen the Julg index,[25] which can be readily used for rings of different 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 (see Scheme 1). A third EE conformer that lies much higher in energy will not be considered in our study. Table 1 contains the relative stabilities of the EZ(X) and ZZ(X) conformers for X = O, S, Se, as well as the acidities that correspond to the first and second deprotonation processes of these compounds calculated at the G4 level of theory. Chem. Eur. J. 2014, 20, 5309 – 5316
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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 (DHrel, DGrel 298 K) of the two more stable conformers of C4X4H2 (X = O, S, Se) Sq derivatives and their gas-phase acidities (DHacid, DGacid 298 K). DHrel 298 K [kJ mol1] EZ(O) ZZ(O) EZ(S) ZZ(S) EZ(Se) ZZ(Se)
8.2 0.0 9.8 0.0 7.5 0.0
DHacid 298 K [kJ mol1] 1314.0[a] 1322.2/1771.6[b] 1276.9[a] 1286.6/1656.9[b] 1256.7[a] 1264.2/1614.4[b]
DGrel 298 K [kJ mol1] 8.0 0.0 8.9 0.0 6.8 0.0
DGacid 298 K [kJ mol1] 1283.0[a] 1291.0[a]/1741.4[b] 1247.1[a] 1256.0[a]/1626.7[b] 1226.6[a] 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 !C4X42 + H + . Note that this acidity is identical for the EZ and the ZZ conformers.
The first conspicuous fact is that regardless of the nature of the chalcogen atom the ZZ(X) isomer is predicted to be more stable than the EZ(X) one, likely reflecting the larger intrinsic basicity of the carbonyl, thiocarbonyl, and selenocarbonyl groups with respect to hydroxyl, thiol, and selenol groups. In this respect, it is interesting to note that for the selenium derivative, in which the size of the chalcogen atom reaches its maximum value, a BCP between the selenocarbonyl groups, which act as proton acceptors, and the SeH groups, which act as proton donors, has been found (see Figure 1), thereby suggesting the formation of an intramolecular SeH···Se hydrogen bond (HB). Also interestingly, the electron density of the four-membered ring changes significantly when O is replaced by S or Se. Owing to the decrease in the electronegativity of the heteroatom, this replacement is accompanied by an increase in the electron densities at the CC single bonds in which the thiocarbonyl or the selenocarbonyl groups participate, whereas the electron density at the HXC=CXH bond decreases. Consistently, C1C2, C1C3, and C1C4 shorten and the corresponding Wiberg bond index increases when O is replaced by S or Se, whereas the C3=C4 bond lengthens and the Wiberg bond index decreases (see Figure S1 in the Supporting Information). For the EZ(X) conformer it is found that the most acidic site is the X5H group. As a consequence, both EZ(X) and ZZ(X) structures lead to the same anion upon deprotonation. Therefore the most stable ZZ(X) conformer is always a slightly weaker acid than the EZ(X) one. It is worth noting that the in-
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Full Paper to those indicated above, our calculations predict the three C4X4H (X = O, S, Se) anions to be stronger acids than reported in the literature[28] by about 23 kJ mol1 for these second deprotonation processes as well. It should be noted, however, that the dianion produced in this second deprotonation process is not stable with respect to electron loss (see Table S3 in the Supporting Information). It is worth noting that the acidity trends predicted for these squaric acid derivatives, O < S < Se, is qualitatively similar to that observed for H2O, SH2, and SeH2,[27] as well as for carbonyl, thiocarbonyl, and selenocarbonyl derivatives.[29]
Acidity enhancement upon BeF2 association
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 in atomic units.
trinsic acidity of the Sq derivative increases when O is replaced by S and increases further if S is replaced by Se, likely reflecting the fact that second- and third-row atoms better accommodate the excess amount of charge produced by the deprotonation process. A second factor that contributes to an enhanced stability of the C4S4H and C4Se4H anions with respect to C4O4H is the intramolecular HB formed between the XH (X = S, Se) as proton donor and the C=X group as proton acceptor, as illustrated in the corresponding molecular graphs (see Figure S2 in the Supporting Information). An interesting consequence is that, whereas C4Se4H2 is predicted to be a stronger acid than sulfuric acid in the gas phase (DacidG0 = (1265 23) kJ mol1),[27] the Sq acid itself (C4O4H2) is predicted to be only as strong as chloric acid (DacidG0 = (1284 16) kJ mol1).[27] It is important to emphasize the significant disagreement between our estimates and previous theoretical studies,[28] which reported gas-phase acidities for these three compounds (DacidG0) about 24–29 kJ mol1 larger than ours. To check whether this disagreement could be due to the method used in the literature[28a] with respect to G4 theory, we have recalculated 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 disagreement of 26 kJ mol1 remains. Interestingly, this disagreement coincides with the value of the free energy of the proton, and this fact leads us to suspect that in all the calculations reported in the literature[28] the free energy of the proton was ignored. This would also explain why the acidity of these compounds measured in terms of enthalpies and in terms of free energies are almost identical in all these papers, which is conceptually erroneous. The same acidity trends are observed as far as the deprotonation of the C4X4H is concerned (see Table 1), with the C4Se4H being the strongest acid of the three C4X4H anions. In fact, the C4Se4H anion is predicted to be only 57 kJ mol1 less acidic than acetic acid (1427.0 8.4).[27] For similar reasons Chem. Eur. J. 2014, 20, 5309 – 5316
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Seven different complexes can be formed by association of the two more stable conformers, namely, EZ and ZZ, with BeF2 derivatives (see Scheme S1 in the Supporting Information). In a 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-
Scheme 2. Schematic structure of the most stable complexes formed by the interaction of EZ and ZZ conformers of C4X4H2 (X = O, S, Se) Sq derivatives.
tures and total energies of these complexes for X = O, S, Se as well as those of the corresponding deprotonated species are shown in Figure S3 and Table S1 in the Supporting Information. As found for the isolated Sq acid derivatives, ZZ(X)a is predicted to be more stable than EZ(X)a regardless of the chalcogen heteroatom involved (see Table 2). In all cases the most favorable deprotonation process corresponds to the heterolytic cleavage of the XH bond not interacting with the BeF2 molecule. This means that both EZ(X)a and ZZ(X)a complexes, as was 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 the significant acidity enhancement triggered by the association of the Sq derivatives with BeF2. Note that this acidity enhancement decreases upon going from O to Se. Hence, whereas the acidity changes by 105 kJ mol1 for the O-containing system, for S and Se this variation is only 69.9 and 60.9 kJ mol1, respectively. A rather substantial acidity enhancement, although approximately 40 % smaller than the one observed for the first proton loss, is observed for the second proton loss (see Table 2). In this case a decrease in the effect with the size of the chalcogen atom is also observed.
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Full Paper Table 2. Relative free energies (DGrel 298 K [kJ mol1]) of the two more stable conformers of C4X4H2·BeF2 (X = O, S, Se) complexes, gas-phase acidity (DGacid) corresponding to the processes A) C4X4H2·BeF2 !(C4X4H )·BeF2 + H + and B) (C4X4H)·BeF2 !(C4X4 2)·BeF2 + H + , and values of DG1, DG2, DG3, and DG4 defined in Scheme 3.[a]
EZ(O)a ZZ(O)a EZ(S)a ZZ(S) a EZ(Se)a ZZ(Se)a
DGrel [kJ mol1]
DGacid [kJ mol1]
4.9 0.0 6.9 0.0 6.8 0.0
1178.0 1183.0 1177.2 1184.1 1165.7 1170.8
Process A DG1DG3 [kJ mol1]
DG2 [kJ mol1]
DG4 [kJ mol1]
105.0 108.0 69.9 71.9 60.9 62.6
95.2 92.2 31.1 29.1 25.1 23.4
200.2 200.2 101.0 101.0 86.0 86.0
DGacid [kJ mol1] 1678.3 – 1567.6 – 1533.3 –
Process B DG1DG3 DG2 [kJ mol1] [kJ mol1] 63.1 – 59.2 – 51.2 –
200.2 – 101.0 – 86.0 –
DG4 [kJ mol1] 263.3 – 160.2 – 137.2 –
[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.
What is the origin of this acidity enhancement and why does it decreases with the size of the chalcogen atom? This can be explained by the thermodynamic cycle shown in Scheme 3; in this scheme, DG01 and DG03 are the gas-phase acidities of the isolated Sq derivatives and of the complexes they formed with BeF2, respectively. DG02 and DG04 measure the stabilization of the neutral Sq derivatives and their deprotonated forms when interacting with BeF2. A similar scheme can be used for the loss of the second proton (see Scheme S2 in the Supporting Information). The enhanced stability of the C4X4H2 (X = O, S, Se) Sq derivatives and their deprotonated structures has a threefold origin: 1) the formation of a quite strong X···Be beryllium bond, 2) the formation of a XH···F intramolecular HB, and 3) a significant increase in the aromaticity of the system that is predicted both by magnetic properties and geometrical indexes. We present in Figure 2 the scan of the NICS along an axis perpendicular to the ring plane for the C4O4H2 as a suitable example. It can be seen that the NICS reaches its maximum absolute value at a distance of approximately 0.6 of the molecular plane, and that its value significantly increases upon going from the iso-
Scheme 3. Thermodynamic cycle associated with the acidity enhancement undergone by C4X4H2 (X = O, S, Se) Sq derivatives upon association with BeF2.
Figure 2. Scan of NICS along an axis perpendicular to the four-membered ring for C4O4H2 and C4O4H2·BeF2 and their corresponding deprotonated forms. Chem. Eur. J. 2014, 20, 5309 – 5316
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Full Paper lated Sq derivative to the corresponding Sq·BeF2 complex. Consistently, as shown in Table S2 of the Supporting Information, after BeF2 attachment both the magnetic susceptibility in absolute 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, DG04 is significantly larger than DG02, and this larger stabilization of the deprotonated structure upon association with BeF2 unavoidably leads to the observed substantial acidity enhancement. The enhanced stability of the deprotonated species has been proven very recently to be a general phenomenon in these kinds of derivatives.[12b] However, the relative changes vary strongly with the nature of the chalcogen. For X = O, DG04 is more than twice as large as DG02, but three times and four times as large for X = S and X = Se, respectively. Why, then, does the acidity enhancement decrease as O > S > Se? This is essentially due to the rather small value of DG02 for the S and Se derivatives, which is only about one third of the DG02 value for the O-containing analogues. This significant decrease in the stabilization of the neutral Sq derivatives when O is replaced by S or Se is essentially due to a significant decrease in the strength of both the XH···F hydrogen bond and the C=X···Be beryllium bond. This is apparent when comparing the molecular graphs of the Sq·BeF2 complexes (see Figure 3) with those of the isolated Sq derivatives in Figure 1. Although the electron densities at the OH···F BCP cannot be directly compared with those at the SH···F because of the different nature of the atoms involved, the relative strength of these linkages can be deduced from the changes undergone by the OH and SH, which participate in them. A comparison of the electron densities of the OH and SH proton donors in Figure 3 (0.310 and 0.207 a.u., respectively) with those of the
complex is larger than that of the sSH* (0.070 e) in the C4S4H2·BeF2 complex. Similar rationales show that the CO···Be beryllium bond is also stronger than the CS···Be one. Indeed, the electron density at the C=O BCP decreases 0.036 a.u. when the CO···Be bond is formed, whereas that of the C=S bond only decreases 0.007 a.u. Again, consistently, whereas the NBO shows that the interaction between the Sq subunit and BeF2 is the result of a charge transfer from the S lone pairs into the empty 2p orbital of Be, in the O-containing analogue this interaction is so strong that an OBe covalent bond strongly polarized toward the oxygen atom is formed. However, the aromaticity seems not to play any significant role in the enhanced stability of the anionic deprotonated species, as both magnetic properties and geometrical indices give almost equal values for the neutral and anionic systems (see Table S2 in the Supporting 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 fact that the three neutral compounds form strong HBs with one of the F atoms of the BeF2 subunit moved us to explore what the behavior of the same complexes would be when BeF2 is replaced by BeH2 and thus the XH···F HB is replaced by a XH···H dihydrogen bond.[3f] Indeed, when this replacement is carried out, the structures found for both the EZa and the ZZa conformers of C4O4H2·BeH2 shown in Figure 4 present a rather
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 densities are in a.u.
same bonds in the isolated Sq derivatives (0.361 and 0.212 a.u., respectively; see Figure 1) shows that the activation of the OH bond, the electron density of which decreases 0.051 a.u., is much larger than that of the SH bond, the electron density of which decreases ten times less. This clearly indicates that the OH···F HB is significantly stronger than the S H···F one. This is consistent with the NBO analysis of these complexes, which shows that the charge transfer from the lone pairs of the F atom towards the sOH* antibonding orbital is larger than towards the sSH* antibonding orbital. Indeed, the natural population of the sOH* (0.085 e) in the C4O4H2·BeF2 Chem. Eur. J. 2014, 20, 5309 – 5316
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Figure 4. Most relevant optimized geometrical parameters of the EZ(O)a (left) and ZZ(O)a (right) complexes involving BeH2 and their corresponding molecular graphs. Dots denote BCPs and ring critical points (RCPs). Electron densities are in a.u.
strong OH···HBe dihydrogen bond, as reflected in the very short H···H distance as well as the significant elongation of both the OH and the BeH bonds. The electron density at the H···H bond critical point is significantly larger for this kind of weak interaction and the energy density is negative, thereby confirming its significant strength. In light of the significant strength of the aforementioned dihydrogen bond, we decided to study whether a proton trans-
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Figure 6. Potential-energy curve associated with the proton transfer in EZ(O)a complex.
Figure 5. Most relevant optimized geometrical parameters of the most stable complexes between the EZ and ZZ conformers of C4X4H2 (X = O, S, Se) Sq derivatives and BeH2.
fer to form a C4O4H·BeH3 + ion pair implies a significant activation barrier. As a result of this survey, we located for both conformers another local minima, namely, SqEZBeH(O)···H2 and SqZZBeH(O)···H2, which lie 19.3 and 14.4 kJ mol1 lower in energy, respectively. As illustrated in Figure 5, these complexes can 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 compounds yields only the structures SqZZBeH(X)···H2 (X = S, Se) shown in Figure 5, and any attempt to optimize structures EZ(X)a and ZZ(X)a (X = S, Se) similar to those shown in Figure 4 for the Ocontaining systems failed, because they collapsed into the structures in Figure 5 through a spontaneous proton transfer. To understand why the EZ(O)a and the ZZ(O)a complexes are found to be stable in the case of the oxygen analogues, we calculated the potential energy curve associated with the proton 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 low activation barrier of about 8 kJ mol1; but the most significant feature is that when free energies are used instead of enthalpies, the barrier disappears, thus indicating that the protontransfer (PT) process is spontaneous at 298 K. Indeed, as shown in Figure 7, the SqEZBeH(O)···H2 complex lies 93.0 kJ mol1 below the entrance channel C4O4H2 + BeH2. Furthermore, the SqEZBeH(O) + H2 dissociation limit lies 103.7 kJ mol1 even further below, thereby reflecting the stabiChem. Eur. J. 2014, 20, 5309 – 5316
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Figure 7. G4 relative free energies corresponding to the association of BeH2 to squaric acid to yield HC4O4BeH + H2.
lization of both the H2 moiety and the SqEZBeH(O), in which the BeH group interacts simultaneously with both carbonyl groups. In summary, the attachment of BeH2 to C4O4H2 leads to a spontaneous exergonic (by 196.7 kJ mol1) H2 loss. We have 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 the G4 level than the other heavier fragment. However, our estimates indicate that the BBSE is typically 0.6 kcal mol1 or lower. For the S- and Se-containing analogues, the proton-transfer process is barrierless both in terms of enthalpies and free energies, and the processes in which a spontaneous loss of H2 takes place are also exergonic (see Figure S4 in the Supporting Information). This finding might have important implications in the problem of hydrogen storage. Actually, the possibility of using beryllium hydride derivatives for this purpose has been discussed previously in the literature, owing to its high storage capacity,[30] although one of the important limitations is its high toxicity.[31]
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Full Paper Upon reaching this point, one final question arises. Why in the case of the complexes with BeF2 in which a strong XH···FBe HB is formed does no spontaneous proton transfer seem to be possible and therefore no spontaneous loss of HF is observed? The answer to this question is twofold. Whereas the PT in the complex between squaric acid and BeH2 is a low-barrier process in terms of enthalpies and barrierless in terms of free energies, the same process in the complex between squaric acid and BeF2 involves a significantly large activation barrier, both in terms of enthalpies (121 kJ mol1) and of free energies (125 kJ mol1). On top of that, the H2 loss process C4O4H2 + BeH2 !HC4O4BeH + H2 should be spontaneous because it is exergonic, and the HF loss process C4O4H2 + BeF2 !HC4O4BeF + HF is predicted to be endergonic by 96.6 kJ mol1.
Conclusion Squaric acid derivatives are predicted to be very strong acids in the gas phase. Importantly, our values predict all these compounds to be stronger acids by about 25 kJ mol1 than previous theoretical studies reported in the literature in which the free energy of the proton was ignored. The acidity increases with the size of the chalcogen, so that the C4Se4H2 is the strongest acid of the series, being even stronger than sulfuric acid. The association of these Sq derivatives with BeF2 leads to the formation of a rather strong C=X···Be beryllium bond and an XH···F hydrogen bond as well as to a significant increase in the aromaticity of the system. These three effects result in a significant stabilization of the C4X4H2·BeF2 complexes formed. However, the most important fact is that the stabilization undergone by the corresponding deprotonated species is two to four times larger than that undergone by the neutral compound, thereby resulting in a dramatic enhancement of the acidity of the C4X4H2·BeF2 complex. For instance, whereas, as mentioned above, C4O4H2 was predicted to be as acidic as chloric acid, the C4O4H2·BeF2 complex is estimated to be significantly stronger than perchloric acid. One of the most important consequences of this acidity enhancement triggered by the formation of a beryllium bond is that when BeF2 is replaced by BeH2, a barrierless spontaneous exergonic H2 loss is observed regardless of the nature of the chalcogen atom. An analogous loss of HF in complexes that involve BeF2 is, however, a rather endergonic process with a 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 MADRISOLAR2 project (S2009PPQ/1533) of the Comunidad de Madrid, by Consolider on Molecular Nanoscience CSC2007-00010, and by the COST Action CM1204. A generous allocation of computing time at the Centro de Computacin Cientfica of the UAM is also acknowledged. M.M.M.-C. thanks the MADRISOLAR2 project for financial support. Chem. Eur. J. 2014, 20, 5309 – 5316
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& Squaric Acids
Spontaneous H2 Loss through the Interaction of Squaric Acid Derivatives and BeH2 M. Merced Montero-Campillo, Manuel YÇez,* Al Mokhtar Lamsabhi, and Otilia M[a]
Abstract: The most stable complexes between squaric acid and its sulfur- and selenium-containing analogues (C4X4H2 ; X = O, S, Se) with BeY2 (Y = H, F) were studied by means of the Gaussian 04 (G4) composite ab initio theory. Squaric acid derivatives are predicted to be very strong acids in the gas phase; their acidity increases with the size of the chalcogen, with C4Se4H2 being the strongest acid of the series and stronger than sulfuric acid. The relative stability of the C4X4H2·BeY2 (X = O, S, Se; Y = H, F) complexes changes with the nature of the chalcogen atom; but more importantly, the formation of the C4X4H2·BeF2 complexes results in a sub-
Introduction The traditional division between the different states of matter is directly related to the way atoms or molecules are associated to each other. Noncovalent interactions are weak interactions that have a crucial importance in nature and material science.[1] These interactions usually involve closed-shell species, as in the case of hydrogen bonds,[2] beryllium bonds,[3] halogen bonds,[4] or van der Waals complexes.[5] Apart from the difficulty in classifying them, there is a common characteristic, which is a certain amount of charge transfer from one interacting moiety to another. This concept is very well known in chemistry, as the interaction between a Lewis base and a Lewis acid is based on this, the acid-accepting electron pairs and the base that donates them.[6] For example, a proton in a typical hydrogen bond behaves like a Lewis acid. As an electropositive atom with available empty orbitals that can accept electrons, beryllium atoms can behave similarly to hydrogen and establish so-called beryllium bonds[3a] when interacting with electron donors. These weak forces might play a very important role in the properties of a given molecular system, and sometimes a coop-
[a] Dr. M. M. Montero-Campillo, Prof. M. YÇez, Dr. A. M. Lamsabhi, Prof. O. M Departamento de Qumica, Facultad de Ciencias Mdulo 13, Universidad Autnoma de Madrid Campus de Excelencia UAM-CSIC Cantoblanco, 28049 Madrid (Spain) Fax: (+ 34) 91-497-5238 E-mail: [email protected] Supporting information for this article is available on the WWW under http://dx.doi.org/10.1002/chem.201304259. Chem. Eur. J. 2014, 20, 5309 – 5316
stantial acidity enhancement of the squaric moiety owing to the dramatic electron-density redistribution undergone by the system when the beryllium bond is formed. The most significant consequence of this acidity enhancement is that when BeF2 is replaced by BeH2, a spontaneous exergonic loss of H2 is observed regardless of the nature of the chalcogen atom. This is another clear piece of evidence of the important role that closed-shell interactions play in the modulation of physicochemical properties of the Lewis acid and/ or the Lewis base.
erative effect between them is possible when more than one is present. We have recently studied some significant cases of this cooperativity between hydrogen and beryllium bonds.[3d, 7] Also, chemical properties such as the intrinsic acidity can change significantly when the system is perturbed by one or more weak interactions of this kind. This is the case of the acidity enhancement of BF3carbonyl complexes,[8] phosphine– boranes,[9] phosphine–alanes,[10] and amine–boranes[11] with respect to noncomplexed phosphines or amines. These effects are even stronger if the base interacts with BeX2 derivatives through the formation of beryllium bonds.[12] As a result, conventional gas-phase bases such as aniline, acetamide, or even unsaturated hydrocarbons become stronger acids in the gas phase than typical oxyacids.[12b] These acidity enhancements can lead to spontaneous proton-transfer processes[13] and to the spontaneous formation of ion pairs in the gas phase,[14] or can modulate the self-assembly of some molecular systems if the self-assembly process involves hydrogen bonds, the strength of which can be modified through the formation of beryllium bonds, as has been shown recently for squaric acid dimers.[7] Other interesting acidity enhancements are triggered by multiple hydrogen bonds to a single charged center.[15] The aim of this paper is to analyze whether a spontaneous intramolecular proton transfer from the squaric moiety, Sq, towards the beryllium derivative, triggered by the significant acidity enhancement induced by the formation of the beryllium bond, can occur. Hence, in a first step we will investigate the acidity enhancement of C4X4H2 (X = O, S, Se) Sq derivatives when they form beryllium bonds with BeF2. In a second step we will investigate what the effect of the beryllium bond is on the second deprotonation process. In a third step we will analyze what the behavior of these Sq acid derivatives is when
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Full Paper they interact with BeH2, which is able to yield dihydrogen bonds with the acidic hydrogen atoms bonded to the chalcogen atoms, in an effort to see if these dihydrogen bonds can be suitable precursors for the loss of H2.
Computational Details Although it has been shown[3d, 7] that the B3LYP functional[16] usually yields a good description of both hydrogen and beryllium bonds when a 6-311+G(3df,2p) basis set that is flexible enough is used, in the present work we have decided to increase the accuracy of the calculations by using the more sophisticated Gaussian 04 (G4) approach,[17] a composite technique based on B3LYP-optimized geometries 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 the strength of bonding in the complexes under investigation. With this method it is also possible to analyze natural charges and charge transfer by means of second-order interaction energies between the occupied orbitals of Sq acid derivatives and empty orbitals of BeY2, as well as to calculate the Wiberg bond order,[19] which is a good index of the nature of the bond. The topology of the electron density was analyzed within the framework of the atoms in molecules (AIM)[20] theory to obtain the critical points of the density, which give significant information about the nature and strength of the interactions present in the molecule. Bond critical points (BCPs) are first-order saddle points of the density on the bond paths that connect the nuclei. All electronic-structure calculations were carried out with the Gaussian 09 software package.[21] AIM calculations were performed with the AIMAll software package.[22] One of the properties that might influence the relative stability of these systems is aromaticity. To analyze this property we have decided to use two different criteria, one based on magnetic properties and the other on geometrical parameters. Among the former we have selected the magnetic susceptibility and the nucleus-independent chemical shift (NICS).[23] A strong diamagnetic susceptibility is an unequivocal characteristic of all aromatic compounds. Abnormal chemical shifts can also evidence electronic delocalization on cyclic compounds, as observed in benzene, which therefore present negative NICS values. NICS varies significantly with the distance to the molecular plane, and therefore a local value of this index such as NICS(1) is not always appropriate. Hence, in our survey, a scan of NICS along an axis perpendicular to the molecular plane[24] was carried out. Among all geometric indices we have chosen the Julg index,[25] which can be readily used for rings of different 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 (see Scheme 1). A third EE conformer that lies much higher in energy will not be considered in our study. Table 1 contains the relative stabilities of the EZ(X) and ZZ(X) conformers for X = O, S, Se, as well as the acidities that correspond to the first and second deprotonation processes of these compounds calculated at the G4 level of theory. Chem. Eur. J. 2014, 20, 5309 – 5316
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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 (DHrel, DGrel 298 K) of the two more stable conformers of C4X4H2 (X = O, S, Se) Sq derivatives and their gas-phase acidities (DHacid, DGacid 298 K). DHrel 298 K [kJ mol1] EZ(O) ZZ(O) EZ(S) ZZ(S) EZ(Se) ZZ(Se)
8.2 0.0 9.8 0.0 7.5 0.0
DHacid 298 K [kJ mol1] 1314.0[a] 1322.2/1771.6[b] 1276.9[a] 1286.6/1656.9[b] 1256.7[a] 1264.2/1614.4[b]
DGrel 298 K [kJ mol1] 8.0 0.0 8.9 0.0 6.8 0.0
DGacid 298 K [kJ mol1] 1283.0[a] 1291.0[a]/1741.4[b] 1247.1[a] 1256.0[a]/1626.7[b] 1226.6[a] 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 !C4X42 + H + . Note that this acidity is identical for the EZ and the ZZ conformers.
The first conspicuous fact is that regardless of the nature of the chalcogen atom the ZZ(X) isomer is predicted to be more stable than the EZ(X) one, likely reflecting the larger intrinsic basicity of the carbonyl, thiocarbonyl, and selenocarbonyl groups with respect to hydroxyl, thiol, and selenol groups. In this respect, it is interesting to note that for the selenium derivative, in which the size of the chalcogen atom reaches its maximum value, a BCP between the selenocarbonyl groups, which act as proton acceptors, and the SeH groups, which act as proton donors, has been found (see Figure 1), thereby suggesting the formation of an intramolecular SeH···Se hydrogen bond (HB). Also interestingly, the electron density of the four-membered ring changes significantly when O is replaced by S or Se. Owing to the decrease in the electronegativity of the heteroatom, this replacement is accompanied by an increase in the electron densities at the CC single bonds in which the thiocarbonyl or the selenocarbonyl groups participate, whereas the electron density at the HXC=CXH bond decreases. Consistently, C1C2, C1C3, and C1C4 shorten and the corresponding Wiberg bond index increases when O is replaced by S or Se, whereas the C3=C4 bond lengthens and the Wiberg bond index decreases (see Figure S1 in the Supporting Information). For the EZ(X) conformer it is found that the most acidic site is the X5H group. As a consequence, both EZ(X) and ZZ(X) structures lead to the same anion upon deprotonation. Therefore the most stable ZZ(X) conformer is always a slightly weaker acid than the EZ(X) one. It is worth noting that the in-
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Full Paper to those indicated above, our calculations predict the three C4X4H (X = O, S, Se) anions to be stronger acids than reported in the literature[28] by about 23 kJ mol1 for these second deprotonation processes as well. It should be noted, however, that the dianion produced in this second deprotonation process is not stable with respect to electron loss (see Table S3 in the Supporting Information). It is worth noting that the acidity trends predicted for these squaric acid derivatives, O < S < Se, is qualitatively similar to that observed for H2O, SH2, and SeH2,[27] as well as for carbonyl, thiocarbonyl, and selenocarbonyl derivatives.[29]
Acidity enhancement upon BeF2 association
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 in atomic units.
trinsic acidity of the Sq derivative increases when O is replaced by S and increases further if S is replaced by Se, likely reflecting the fact that second- and third-row atoms better accommodate the excess amount of charge produced by the deprotonation process. A second factor that contributes to an enhanced stability of the C4S4H and C4Se4H anions with respect to C4O4H is the intramolecular HB formed between the XH (X = S, Se) as proton donor and the C=X group as proton acceptor, as illustrated in the corresponding molecular graphs (see Figure S2 in the Supporting Information). An interesting consequence is that, whereas C4Se4H2 is predicted to be a stronger acid than sulfuric acid in the gas phase (DacidG0 = (1265 23) kJ mol1),[27] the Sq acid itself (C4O4H2) is predicted to be only as strong as chloric acid (DacidG0 = (1284 16) kJ mol1).[27] It is important to emphasize the significant disagreement between our estimates and previous theoretical studies,[28] which reported gas-phase acidities for these three compounds (DacidG0) about 24–29 kJ mol1 larger than ours. To check whether this disagreement could be due to the method used in the literature[28a] with respect to G4 theory, we have recalculated 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 disagreement of 26 kJ mol1 remains. Interestingly, this disagreement coincides with the value of the free energy of the proton, and this fact leads us to suspect that in all the calculations reported in the literature[28] the free energy of the proton was ignored. This would also explain why the acidity of these compounds measured in terms of enthalpies and in terms of free energies are almost identical in all these papers, which is conceptually erroneous. The same acidity trends are observed as far as the deprotonation of the C4X4H is concerned (see Table 1), with the C4Se4H being the strongest acid of the three C4X4H anions. In fact, the C4Se4H anion is predicted to be only 57 kJ mol1 less acidic than acetic acid (1427.0 8.4).[27] For similar reasons Chem. Eur. J. 2014, 20, 5309 – 5316
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Seven different complexes can be formed by association of the two more stable conformers, namely, EZ and ZZ, with BeF2 derivatives (see Scheme S1 in the Supporting Information). In a 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-
Scheme 2. Schematic structure of the most stable complexes formed by the interaction of EZ and ZZ conformers of C4X4H2 (X = O, S, Se) Sq derivatives.
tures and total energies of these complexes for X = O, S, Se as well as those of the corresponding deprotonated species are shown in Figure S3 and Table S1 in the Supporting Information. As found for the isolated Sq acid derivatives, ZZ(X)a is predicted to be more stable than EZ(X)a regardless of the chalcogen heteroatom involved (see Table 2). In all cases the most favorable deprotonation process corresponds to the heterolytic cleavage of the XH bond not interacting with the BeF2 molecule. This means that both EZ(X)a and ZZ(X)a complexes, as was 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 the significant acidity enhancement triggered by the association of the Sq derivatives with BeF2. Note that this acidity enhancement decreases upon going from O to Se. Hence, whereas the acidity changes by 105 kJ mol1 for the O-containing system, for S and Se this variation is only 69.9 and 60.9 kJ mol1, respectively. A rather substantial acidity enhancement, although approximately 40 % smaller than the one observed for the first proton loss, is observed for the second proton loss (see Table 2). In this case a decrease in the effect with the size of the chalcogen atom is also observed.
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Full Paper Table 2. Relative free energies (DGrel 298 K [kJ mol1]) of the two more stable conformers of C4X4H2·BeF2 (X = O, S, Se) complexes, gas-phase acidity (DGacid) corresponding to the processes A) C4X4H2·BeF2 !(C4X4H )·BeF2 + H + and B) (C4X4H)·BeF2 !(C4X4 2)·BeF2 + H + , and values of DG1, DG2, DG3, and DG4 defined in Scheme 3.[a]
EZ(O)a ZZ(O)a EZ(S)a ZZ(S) a EZ(Se)a ZZ(Se)a
DGrel [kJ mol1]
DGacid [kJ mol1]
4.9 0.0 6.9 0.0 6.8 0.0
1178.0 1183.0 1177.2 1184.1 1165.7 1170.8
Process A DG1DG3 [kJ mol1]
DG2 [kJ mol1]
DG4 [kJ mol1]
105.0 108.0 69.9 71.9 60.9 62.6
95.2 92.2 31.1 29.1 25.1 23.4
200.2 200.2 101.0 101.0 86.0 86.0
DGacid [kJ mol1] 1678.3 – 1567.6 – 1533.3 –
Process B DG1DG3 DG2 [kJ mol1] [kJ mol1] 63.1 – 59.2 – 51.2 –
200.2 – 101.0 – 86.0 –
DG4 [kJ mol1] 263.3 – 160.2 – 137.2 –
[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.
What is the origin of this acidity enhancement and why does it decreases with the size of the chalcogen atom? This can be explained by the thermodynamic cycle shown in Scheme 3; in this scheme, DG01 and DG03 are the gas-phase acidities of the isolated Sq derivatives and of the complexes they formed with BeF2, respectively. DG02 and DG04 measure the stabilization of the neutral Sq derivatives and their deprotonated forms when interacting with BeF2. A similar scheme can be used for the loss of the second proton (see Scheme S2 in the Supporting Information). The enhanced stability of the C4X4H2 (X = O, S, Se) Sq derivatives and their deprotonated structures has a threefold origin: 1) the formation of a quite strong X···Be beryllium bond, 2) the formation of a XH···F intramolecular HB, and 3) a significant increase in the aromaticity of the system that is predicted both by magnetic properties and geometrical indexes. We present in Figure 2 the scan of the NICS along an axis perpendicular to the ring plane for the C4O4H2 as a suitable example. It can be seen that the NICS reaches its maximum absolute value at a distance of approximately 0.6 of the molecular plane, and that its value significantly increases upon going from the iso-
Scheme 3. Thermodynamic cycle associated with the acidity enhancement undergone by C4X4H2 (X = O, S, Se) Sq derivatives upon association with BeF2.
Figure 2. Scan of NICS along an axis perpendicular to the four-membered ring for C4O4H2 and C4O4H2·BeF2 and their corresponding deprotonated forms. Chem. Eur. J. 2014, 20, 5309 – 5316
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Full Paper lated Sq derivative to the corresponding Sq·BeF2 complex. Consistently, as shown in Table S2 of the Supporting Information, after BeF2 attachment both the magnetic susceptibility in absolute 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, DG04 is significantly larger than DG02, and this larger stabilization of the deprotonated structure upon association with BeF2 unavoidably leads to the observed substantial acidity enhancement. The enhanced stability of the deprotonated species has been proven very recently to be a general phenomenon in these kinds of derivatives.[12b] However, the relative changes vary strongly with the nature of the chalcogen. For X = O, DG04 is more than twice as large as DG02, but three times and four times as large for X = S and X = Se, respectively. Why, then, does the acidity enhancement decrease as O > S > Se? This is essentially due to the rather small value of DG02 for the S and Se derivatives, which is only about one third of the DG02 value for the O-containing analogues. This significant decrease in the stabilization of the neutral Sq derivatives when O is replaced by S or Se is essentially due to a significant decrease in the strength of both the XH···F hydrogen bond and the C=X···Be beryllium bond. This is apparent when comparing the molecular graphs of the Sq·BeF2 complexes (see Figure 3) with those of the isolated Sq derivatives in Figure 1. Although the electron densities at the OH···F BCP cannot be directly compared with those at the SH···F because of the different nature of the atoms involved, the relative strength of these linkages can be deduced from the changes undergone by the OH and SH, which participate in them. A comparison of the electron densities of the OH and SH proton donors in Figure 3 (0.310 and 0.207 a.u., respectively) with those of the
complex is larger than that of the sSH* (0.070 e) in the C4S4H2·BeF2 complex. Similar rationales show that the CO···Be beryllium bond is also stronger than the CS···Be one. Indeed, the electron density at the C=O BCP decreases 0.036 a.u. when the CO···Be bond is formed, whereas that of the C=S bond only decreases 0.007 a.u. Again, consistently, whereas the NBO shows that the interaction between the Sq subunit and BeF2 is the result of a charge transfer from the S lone pairs into the empty 2p orbital of Be, in the O-containing analogue this interaction is so strong that an OBe covalent bond strongly polarized toward the oxygen atom is formed. However, the aromaticity seems not to play any significant role in the enhanced stability of the anionic deprotonated species, as both magnetic properties and geometrical indices give almost equal values for the neutral and anionic systems (see Table S2 in the Supporting 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 fact that the three neutral compounds form strong HBs with one of the F atoms of the BeF2 subunit moved us to explore what the behavior of the same complexes would be when BeF2 is replaced by BeH2 and thus the XH···F HB is replaced by a XH···H dihydrogen bond.[3f] Indeed, when this replacement is carried out, the structures found for both the EZa and the ZZa conformers of C4O4H2·BeH2 shown in Figure 4 present a rather
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 densities are in a.u.
same bonds in the isolated Sq derivatives (0.361 and 0.212 a.u., respectively; see Figure 1) shows that the activation of the OH bond, the electron density of which decreases 0.051 a.u., is much larger than that of the SH bond, the electron density of which decreases ten times less. This clearly indicates that the OH···F HB is significantly stronger than the S H···F one. This is consistent with the NBO analysis of these complexes, which shows that the charge transfer from the lone pairs of the F atom towards the sOH* antibonding orbital is larger than towards the sSH* antibonding orbital. Indeed, the natural population of the sOH* (0.085 e) in the C4O4H2·BeF2 Chem. Eur. J. 2014, 20, 5309 – 5316
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Figure 4. Most relevant optimized geometrical parameters of the EZ(O)a (left) and ZZ(O)a (right) complexes involving BeH2 and their corresponding molecular graphs. Dots denote BCPs and ring critical points (RCPs). Electron densities are in a.u.
strong OH···HBe dihydrogen bond, as reflected in the very short H···H distance as well as the significant elongation of both the OH and the BeH bonds. The electron density at the H···H bond critical point is significantly larger for this kind of weak interaction and the energy density is negative, thereby confirming its significant strength. In light of the significant strength of the aforementioned dihydrogen bond, we decided to study whether a proton trans-
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Figure 6. Potential-energy curve associated with the proton transfer in EZ(O)a complex.
Figure 5. Most relevant optimized geometrical parameters of the most stable complexes between the EZ and ZZ conformers of C4X4H2 (X = O, S, Se) Sq derivatives and BeH2.
fer to form a C4O4H·BeH3 + ion pair implies a significant activation barrier. As a result of this survey, we located for both conformers another local minima, namely, SqEZBeH(O)···H2 and SqZZBeH(O)···H2, which lie 19.3 and 14.4 kJ mol1 lower in energy, respectively. As illustrated in Figure 5, these complexes can 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 compounds yields only the structures SqZZBeH(X)···H2 (X = S, Se) shown in Figure 5, and any attempt to optimize structures EZ(X)a and ZZ(X)a (X = S, Se) similar to those shown in Figure 4 for the Ocontaining systems failed, because they collapsed into the structures in Figure 5 through a spontaneous proton transfer. To understand why the EZ(O)a and the ZZ(O)a complexes are found to be stable in the case of the oxygen analogues, we calculated the potential energy curve associated with the proton 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 low activation barrier of about 8 kJ mol1; but the most significant feature is that when free energies are used instead of enthalpies, the barrier disappears, thus indicating that the protontransfer (PT) process is spontaneous at 298 K. Indeed, as shown in Figure 7, the SqEZBeH(O)···H2 complex lies 93.0 kJ mol1 below the entrance channel C4O4H2 + BeH2. Furthermore, the SqEZBeH(O) + H2 dissociation limit lies 103.7 kJ mol1 even further below, thereby reflecting the stabiChem. Eur. J. 2014, 20, 5309 – 5316
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Figure 7. G4 relative free energies corresponding to the association of BeH2 to squaric acid to yield HC4O4BeH + H2.
lization of both the H2 moiety and the SqEZBeH(O), in which the BeH group interacts simultaneously with both carbonyl groups. In summary, the attachment of BeH2 to C4O4H2 leads to a spontaneous exergonic (by 196.7 kJ mol1) H2 loss. We have 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 the G4 level than the other heavier fragment. However, our estimates indicate that the BBSE is typically 0.6 kcal mol1 or lower. For the S- and Se-containing analogues, the proton-transfer process is barrierless both in terms of enthalpies and free energies, and the processes in which a spontaneous loss of H2 takes place are also exergonic (see Figure S4 in the Supporting Information). This finding might have important implications in the problem of hydrogen storage. Actually, the possibility of using beryllium hydride derivatives for this purpose has been discussed previously in the literature, owing to its high storage capacity,[30] although one of the important limitations is its high toxicity.[31]
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Full Paper Upon reaching this point, one final question arises. Why in the case of the complexes with BeF2 in which a strong XH···FBe HB is formed does no spontaneous proton transfer seem to be possible and therefore no spontaneous loss of HF is observed? The answer to this question is twofold. Whereas the PT in the complex between squaric acid and BeH2 is a low-barrier process in terms of enthalpies and barrierless in terms of free energies, the same process in the complex between squaric acid and BeF2 involves a significantly large activation barrier, both in terms of enthalpies (121 kJ mol1) and of free energies (125 kJ mol1). On top of that, the H2 loss process C4O4H2 + BeH2 !HC4O4BeH + H2 should be spontaneous because it is exergonic, and the HF loss process C4O4H2 + BeF2 !HC4O4BeF + HF is predicted to be endergonic by 96.6 kJ mol1.
Conclusion Squaric acid derivatives are predicted to be very strong acids in the gas phase. Importantly, our values predict all these compounds to be stronger acids by about 25 kJ mol1 than previous theoretical studies reported in the literature in which the free energy of the proton was ignored. The acidity increases with the size of the chalcogen, so that the C4Se4H2 is the strongest acid of the series, being even stronger than sulfuric acid. The association of these Sq derivatives with BeF2 leads to the formation of a rather strong C=X···Be beryllium bond and an XH···F hydrogen bond as well as to a significant increase in the aromaticity of the system. These three effects result in a significant stabilization of the C4X4H2·BeF2 complexes formed. However, the most important fact is that the stabilization undergone by the corresponding deprotonated species is two to four times larger than that undergone by the neutral compound, thereby resulting in a dramatic enhancement of the acidity of the C4X4H2·BeF2 complex. For instance, whereas, as mentioned above, C4O4H2 was predicted to be as acidic as chloric acid, the C4O4H2·BeF2 complex is estimated to be significantly stronger than perchloric acid. One of the most important consequences of this acidity enhancement triggered by the formation of a beryllium bond is that when BeF2 is replaced by BeH2, a barrierless spontaneous exergonic H2 loss is observed regardless of the nature of the chalcogen atom. An analogous loss of HF in complexes that involve BeF2 is, however, a rather endergonic process with a 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 MADRISOLAR2 project (S2009PPQ/1533) of the Comunidad de Madrid, by Consolider on Molecular Nanoscience CSC2007-00010, and by the COST Action CM1204. A generous allocation of computing time at the Centro de Computacin Cientfica of the UAM is also acknowledged. M.M.M.-C. thanks the MADRISOLAR2 project for financial support. Chem. Eur. J. 2014, 20, 5309 – 5316
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