Dihydrogen Bonding vs MetalâÏ Interaction in Complexes between H2

J. Phys. Chem. A 2011, 115, 201–210

201

Dihydrogen Bonding vs Metal-σ Interaction in Complexes between H2 and Metal Hydride Ibon Alkorta,*,† Jose Elguero,† Mohammad Solimannejad,‡ and Sławomir J. Grabowski*,§,| Instituto de Quı´mica Me´dica (CSIC), Juan de la CierVa, 3, 28006 Madrid, Spain, Quantum Chemistry Group, Department of Chemistry, Faculty of Sciences, Arak UniVersity, Arak 38156-8-8349, Iran, Kimika Fakultatea, Euskal Herriko Unibertsitatea and Donostia International Physics Center (DIPC), P.K. 1072, 20080 Donostia, Euskadi, Spain, and IKERBASQUE, Basque Foundation for Science, 48011, Bilbao, Spain ReceiVed: October 20, 2010; ReVised Manuscript ReceiVed: NoVember 12, 2010

The complexes formed by hydrogen with metal hydrides (LiH, NaH, BeH2, MgH2, BH3, AlH3, Li2H2, Na2H2, Be2H4, and Mg2H4) have been theoretically studied at the MP2/aug-cc-pVTZ, MP2/aug-cc-pVQZ and CCSD(T)/ aug-cc-pVTZ//CCSD/aug-cc-pVTZ levels of theory. The hydrogen molecule can act as a Lewis acid or base. In the first case, a dihydrogen bonded complex is obtained and in the second an interaction between the σ-bond of the hydrogen molecule and an empty orbital of the metal atoms is found. Quantum theory of atoms in molecules and natural bond orbitals methods have been applied to analyze the intermolecular interactions. Additionally, the cooperativity effects are analyzed for selected complexes with two H2 molecules where both kinds of interactions exist simultaneously. Introduction There are numerous studies on molecular hydrogen and its interactions in different environments1 because the topic of hydrogen storage is of great importance.2 It can be mentioned that the studies deal with the utilization of hydrogen as the energy source for fuel-cell vehicles,3 the search on candidates for storage materials,4 catalytic enhancement of hydrogen storage,5 hydrogen adsorption in metal-organic frameworks (MOF),6,7 and nanotubes as novel materials for hydrogen storage.8 In a parallel effort, theoretical studies have been carried out on the molecular hydrogen clusters,9 on the importance of the different components of the energy in the binding energy of hydrogen,10 and on the possibility to use organic frameworks in the storage.11 This is why the theoretical studies on the model systems where hydrogen interacts with species of different nature seem to be of importance to understand more complicated phenomena and ultimately resolve specific problems of hydrogen storage. There are studies where the σ-bond of H2 could act as a proton acceptor for hydrogen bonds. For example, the T-shaped H2 · · · HF complex is in the minimum on the Born-Oppenheimer potential energy surface.12 However, there are other numerous examples. The binding energies calculated at the MP2/6311++G(3df,3pd) level and corrected for BSSE for the complexes F-H · · · H2, HCCH · · · H2, H3NH+ · · · H2, and H2OH+ · · · H2 amount to 1.1, 0.3, 2.6, and 5.5 kcal/mol, respectively.13 It seems that the H2 molecule is rather a weak Lewis base but for the two latter cases the binding energies are not negligible. Especially, for the H2OH+ · · · H2 complex this value is greater, for instance, than the one obtained in the water dimer, where the typical and often investigated O-H · · · O hydrogen bond exists. It is also worth mentioning that for this complex the quantum theory of “atoms in molecules” * Authors to whom correspondence should be addressed. E-mail: [email protected] (I.A.), [email protected] (S.J.G.). † Instituto de Quı´mica Me´dica (CSIC). ‡ Arak University. § Kimika Fakultatea, Euskal Herriko Unibertsitatea and Donostia International Physics Center (DIPC). | Basque Foundation for Science.

(QTAIM)14 characteristics were analyzed and it was found that for the H · · · σ bond critical point the total electron energy density is negative, which indicates a partial covalent nature of the interaction. The H3NH+ · · · H2 complex and the related, more complicated clusters NH4+ · · · (H2)n (n ) 1-8) were analyzed much earlier.15 Even though interactions exist for such complexes, they were not considered as hydrogen bonds. However, a number of interesting results were obtained. For example, for the NH4+ · · · (H2)4 complex each of the H2 molecules is perpendicular to the N-H bond of ammonia ion. They were called “face bonded” NH4+ · · · H2 interactions, where the hydrogen molecules interact rather with the nitrogen center and they are not connected with the N-H proton-donating bonds. The H2 · · · HRgY complexes (Rg ) Ar, Kr; Y ) F, Cl, CN) were also analyzed to discuss more systematically the characteristics of H · · · σ interactions.16 Very recently the calculations on H2 · · · HX complexes (X ) CCH, CCLi, CCF, CN, NC, OH, F, and Cl) were performed and the correlation between the intermolecular distance (H2 and H-atom of the proton-donating bond) and the geometrical, electronic, and spectroscopic parameters was analyzed.17 This intermolecular distance may be treated as a rough measure of the strength of the X-H · · · σ interaction possessing the characteristics of hydrogen bonding. Thus, the shortening of the H · · · σ distance is accompanied by the elongation of the H-H bond, the increase of the electron density at the H · · · σ bond critical point, and the increase of the corresponding Laplacian value; also the decrease of the H-H bond stretching frequency is observed if the H · · · σ is enhanced.17 In other words, the H2 · · · HX interactions possess systematically the typical characteristics of hydrogen-bonded interactions. Similar observations were described for the other complexes with H2 molecule, where the elongation of the H-H bond was detected as a result of the enhancement of intermolecular interaction accompanied by a greater transfer of the electron charge from the Lewis base (H2) to the Lewis acid.13,17 Certainly, X-H · · · σ interactions seem to be much weaker than the X-H · · · π ones, and a systematic comparison of XH · · · H2 complexes with the corresponding XH · · · C2H2 species was

10.1021/jp1100544  2011 American Chemical Society Published on Web 12/14/2010

202

J. Phys. Chem. A, Vol. 115, No. 2, 2011

performed and all results indicate that an acetylene molecule is a stronger Lewis acid than molecular hydrogen.13 For the above-mentioned complexes, H2 molecule acts as the Lewis base losing electronic charge, and an elongation of the H-H bond length is observed. The similar behavior may be observed for the cation · · · H2 interactions, which are stronger than the X-H · · · σ hydrogen bonds.13 The other interesting topic concerns the interactions of metal hydrides with H2. Since for the metal hydrides there are negatively charged H-atom centers, the question arises if the neutral hydrogen molecule may play the role of the Lewis acid. In such a case, owing to the polarization of the H2 molecule, M-H-δ · · · +δH-H-δ (where M designates metal or boron) would exist. On the other hand, the positively charged metal atoms for hydrides may act as the Lewis acid centers and interact with σ-electrons of molecular hydrogen. Hence, one of the aims of the present study is to analyze different metal hydride-molecular hydrogen complexes. For such complexes H2 may play the role of the Lewis acid or the Lewis base, depending on the arrangement of the complex considered. The above-mentioned M-H-δ · · · +δH-H-δ may be classified as a dihydrogen bond (DHB), which can be considered as a subclass of hydrogen bonds. There are numerous studies on DHBs, both experimental18 and theoretical ones.19 Hence, it was suggested that a DHB may be treated as the primary stage of the reaction leading to the uptaking of the molecular hydrogen. Such an idea was supported by the theoretical calculations on the model FH · · · HLi complex, where the environment influence on such a process was also taken into account.20 Computational Details The calculations were performed with the Gaussian 09 set of codes.21 The systems chosen for analysis, complexes of metal hydrides with the molecular hydrogen, were optimized at the MP2/aug-cc-pVTZ, MP2/aug-cc-pVQZ, and CCSD/aug-ccpVTZ levels. The sample of complexes considered may be divided into groups. For the first subsample of complexes LiH · · · H2, NaH · · · H2, HBeH · · · H2, HMgH · · · H2, BH3 · · · H2 and AlH3 · · · H2, there are two configurations (few selected systems are presented in Figure 1). In the fist configuration (designated later as the A configuration) a linear H · · · H intermolecular contact is observed. In this configuration, the LiH · · · H2, NaH · · · H2, HBeH · · · H2, and HMgH · · · H2 complexes present C∞ symmetry, while the BH3 · · · H2 and AlH3 · · · H2 ones show C2V symmetry. For the second configuration (designated later as C), the metal atom is in contact with σ-electrons of H2. The LiH · · · H2, NaH · · · H2, HBeH · · · H2, and HMgH · · · H2 complexes in configuration C possess C2V symmetry. The second subsample contains the following complexes: Li2H2 · · · H2, Na2H2 · · · H2, Be2H4 · · · H2, and Mg2H4 · · · H2. Up to two different configurations with H · · · H contact (A and B) have been found. Initially, the symmetry of both configurations is C2V. A third configuration (C) is characterized for these complexes with M · · · σ interaction (see Figure 1). Finally, the complexes of the third subsample contain two H2 molecules, and these are H2 · · · LiH · · · H2, H2 · · · NaH · · · H2, and H2 · · · HBeH · · · H2. For these species both H · · · H and H · · · M (M ) Li, Na, Be) contacts exist. The complexes of lithium and sodium of the latter subsample are characterized by C2V symmetry (see Figure 2). Generally, all complexes analyzed are in the energetic minima, since no imaginary frequencies were found. The only exception is the BH3 · · · H2 complex of C2V symmetry calculated

Alkorta et al. at the MP2/aug-cc-pVQZ level, where two imaginary frequencies (below 20 cm-1) were found. For the other levels applied here, this system is a minimum. Besides in few cases, the abovementioned symmetries of some of complexes were broken during the optimizations to lead to the energetic minima. For some complexes in C configurations, only C1 symmetry is observed and both M · · · σ contacts are different (see Table 1). However, such symmetry was broken during optimization for Na2H2 · · · H2 complex. Similarly for the B-configuration of Mg2H4 · · · H2 complex, the C2V symmetry occurs while for Be2H4 · · · H2 it is broken. The binding energies were computed as the differences between the total energy of the complex and the energies of monomers. The binding energies were corrected for the basis set superposition error (BSSE) using the counterpoise method.22 The natural bond orbitals (NBO) method23,24 implemented within the Gaussian 09 set of codes was applied for the results of the B3LYP/aug-cc-pVTZ//MP2/aug-cc-pVTZ level to calculate the atomic charges and to perform the energetic analysis. QTAIM14,25 was used to analyze the electron density with the AIM2000 program.26 Results and Discussion Geometries and Energies. Table 1 presents geometrical parameters of the complexes analyzed here; these are H · · · H or H · · · M distances and the H-H bond lengths of molecular hydrogen. One can see that for complexes that may be classified as DHB systems (A and B configurations) the H-H bond length is rather insensitive to the interaction. The changes of H-H bond length are not greater than 0.004 Å for all levels of calculations. The greater differences for H-H bond occur for C configurations. The difference between the maximal and minimal H-H bond length is of about 0.06 Å, which is 1 order of magnitude larger than those observed in A and B configurations. This preliminary analysis suggests that metal-σ interactions are much stronger than dihydrogen bonds. For DHBs, the longest H-H bonds are observed for LiH · · · H2 and NaH · · · H2, 0.7403 and 0.7407 Å, respectively, which is accompanied by the shortest H · · · H distances of 2.6000 and 2.6030 Å (MP2/ aug-cc-pVTZ level). For the Na2H2 · · · H2 complex, the H-H bond is among the longest ones, 0.7404 Å, but the H · · · H distance is one of the longest, 2.7009 Å. Generally, there is no correlation between H-H bond length and H · · · H (or H · · · M) distance, even if the H · · · H contacts and the H · · · M interactions are considered separately. For the species with H · · · M interactions, the longest H-H bond is observed for BH3 · · · H2 complex (0.7983 Å) and the H · · · M contacts are the shortest ones here, since they are of about 1.4 Å. In view of the above geometrical results, it seems that H · · · H distance cannot be treated as a measure of the strength of the interaction. Table 2 presents the binding energies of the complexes analyzed. They are calculated as differences between the energy of the complex and the sum of energies of monomers optimized separately, including the BSSE correction. In other words, the deformation energy being the result of complexation is taken into account. The strongest interactions for DHBs are observed for LiH · · · H2 and NaH · · · H2 (0.7-0.8 kcal/mol), while for complexes with M · · · σ contacts the strongest interaction exists for BH3 · · · H2 (5.1 kcal/mol at CCSD(T)/aug-cc-pVTZ level). This is partly in line with the geometrical results, since for C-configurations the longest H-H bonds and the shortest intermolecular contacts were detected. However, there is no correlation between the intermolecular distance (H · · · H or H · · · M) and the binding energy. There is a linear correlation

Dihydrogen Bonding vs Metal-σ Interaction

J. Phys. Chem. A, Vol. 115, No. 2, 2011 203

Figure 1. Selected complexes with dihydrogen bonds where H-H · · · H interactions (A configurations) or H-H · · · H-M interactions (B configurations) exist and complexes with H · · · M interactions (C configurations).

between the H-H bond length of the H2 molecule and the binding energy for DHBs (Figure 3), with a square correlation coefficient of 0.97. Figure 3 presents the MP2/aug-cc-pVTZ results, but the remaining levels show similar correlations. For the complexes with H · · · M interactions, a second-order polynomial regression is obtained between the interaction energy and the H-H bond length of the H2 with a square correlation coefficient of 0.95. If all complexes are considered together,

the second-order polynomial regression also presents the correlation between H-H length and the binding energy, R2 ) 0.95. In other words, the H-H bond length may be treated as the measure of the strength of H · · · H or M · · · σ interaction. Charges and the Other NBO Results. It is interesting to notice that an elongation of the H-H bond is observed when the H2 molecule acts both as Lewis acid or Lewis base and that the effect is dependent on the interaction strength. For dihy-

204


Alkorta et al.

Figure 2. Two complexes containing two H2 molecules.

drogen-bonded systems, the H2 molecule is the Lewis acid, withdrawing electron charge from the base, while for M · · · σ interactions, H2 is the Lewis base, donating the electron charge.

Table 3 presents the NBO method results, which seem to explain this effect correctly. The charges of H2 molecule are also included. For DHB complexes, a negative charge on the molecular hydrogen is obtained due to the electron charge transfer from the Lewis base to H2. The most negative charge occurs for LiH · · · H2, NaH · · · H2, and Na2H2 · · · H2 complexes and it amounts to -0.005, -0.008, and -0.007 au, respectively. Associated with the charge transfer, a polarization of the H2 molecule occurs, with the interacting atom showing a positive net charge while the distant hydrogen atom shows negative charge. Hence, for dihydrogen bonds analyzed here, the following sequence of charges is observed: M-H-δ · · · +δH-H-δ. Table 3 presents the differences between the charges of H-atoms of a hydrogen molecule; such differences are greatest for the above-mentioned lithium and sodium complexes (0.06-0.07 au). It is worth mentioning that for these three complexes the greatest elongation of the H-H bond was observed (see Table 1) and the strongest interactions (see Table 2) for the complexes are connected through DHBs. There are the positive charges of H2 molecule for the complexes with M · · · σ interactions where the molecular hydrogen acts as the Lewis base, donating the electron charge. The greatest positive charge of H2 is observed for BH3 · · · H2 complex, +0.218 au. Also the binding energy for this complex is the greatest one among all systems analyzed here and there

TABLE 1: Geometrical Parameters (in Å) of the Complexes Analyzed, H-H Bond Lengths as Well as H · · · H Distances (for DHBs complexes) or H · · · M Onesa DHBs Systems, A and B Configurations MP2/aug-cc-pVTZ

MP2/aug-cc-pVQZ

CCSD/aug-cc-pVTZ

complex

H· · ·H

H2

H· · ·H

H2

H· · ·H

H2

LiH · · · H2 (A) NaH · · · H2 (A) HBeH · · · H2 (A) HMgH · · · H2 (A) BH3 · · · H2 (A) AlH3 · · · H2 (A) Li2H2 · · · H2 (A) Na2H2 · · · H2 (A) Be2H4 · · · H2 (A) Be2H4 · · · H2 (B) Mg2H4 · · · H2 (A) Mg2H4 · · · H2 (B)

2.6000 2.6030 2.6718 2.6634 2.7171 2.6589 2.6865 2.7009 2.8073 2.6611 2.7970 2.6531

0.7403 0.7407 0.7381 0.7387 0.7377 0.7381 0.7397 0.7404 0.7377 0.7383 0.7381 0.7388

2.6004 2.6037 2.6736 2.6644 2.7807 2.7154 2.7056 2.7066 2.8666 2.8261 2.8065 2.6465

0.7392 0.7397 0.7370 0.7377 0.7365 0.7370 0.7385 0.7392 0.7365 0.7371 0.7370 0.7377

2.6366 2.6609 2.6863 2.6928 2.7157 2.6579 2.7194 2.7390 2.8357 2.6661 2.8241 2.6833

0.7455 0.7457 0.7435 0.7441 0.7428 0.7432 0.7450 0.7456 0.7431 0.7437 0.7435 0.7441

Systems with M · · · σ Contacts, C Configurations MP2/aug-cc-pVTZ

MP2/aug-cc-pVQZ

CCSD/aug-cc-pVTZ

complex

M· · ·H

H2

M· · ·H

H2

M· · ·H

H2

LiH · · · H2 (C) NaH · · · H2 (C) HBeH · · · H2 (C) HMgH · · · H2 (C)

2.1809 2.7626 2.8975 2.6540 1.4066 1.4215 2.2568 2.2742 2.1360 2.6230 2.7699 1.7151 1.7678 2.4672 2.5220

0.7412 0.7394 0.7391 0.7418

2.1812 2.7626 2.8975 2.6538 1.4019 1.4159 2.2376 2.2530 2.1375 2.6168 2.7638 1.7118 1.7638 2.4586 2.5122

0.7401 0.7383 0.7380 0.7408

2.1858 2.7614 2.8981 2.6545 1.4427 1.4563 2.2773 2.2919 2.1353 2.6379 2.7584 1.7341 1.7903 2.4870 2.5409

0.7467 0.7450 0.7445 0.7468

BH3 · · · H2 (C) AlH3 · · · H2 (C) Li2H2 · · · H2 (C) Na2H2 · · · H2 (C) Be2H4 · · · H2 (C) Mg2H4 · · · H2 (C)

0.7983 0.7467 0.7417 0.7404 0.7558 0.7424

0.7984 0.7459 0.7405 0.7393 0.7549 0.7414

0.7931 0.7515 0.7473 0.7457 0.7597 0.7476

If both H · · · M distances for any complex considered are equal to each other, one value is given; if they are not equal, two values are included. The results for three levels of theory are given. The H-H bond length in the isolated H2 molecule is 0.7374, 0.7363, and 0.7430 Å for the MP2/aug-cc-pVTZ, MP2/aug-cc-pVQZ, CCSD/aug-cc-pVTZ, computational levels, respectively. a



TABLE 2: Binding Energies (corrected for BSSE, in kcal/mol) of the Complexes Analyzed, with Four Levels of Theory Taken into Account

complex

MP2/augcc-pVTZ

DHBs LiH · · · H2 (A) NaH · · · H2 (A) HBeH · · · H2 (A) HMgH · · · H2 (A) BH3 · · · H2 (A) AlH3 · · · H2 (A) Li2H2 · · · H2 (A) Na2H2 · · · H2 (A) Be2H4 · · · H2 (A) Be2H4 · · · H2 (B) Mg2H4 · · · H2 (A) Mg2H4 · · · H2 (B)

MP2/augcc-pQTZ

CCSD/augcc-pVTZ

Systems, A and B Configurations -0.71 -0.73 -0.67 -0.76 -0.78 -0.68 -0.24 -0.25 -0.24 -0.45 -0.46 -0.43 -0.11 -0.11 -0.11 -0.22 -0.23 -0.21 -0.55 -0.57 -0.54 -0.67 -0.68 -0.64 -0.10 -0.10 -0.10 -0.27 -0.29 -0.26 -0.20 -0.21 -0.20 -0.39 -0.41 -0.38

CCSD(T)/ aug-ccpVTZ* -0.74 -0.76 -0.28 -0.48 -0.14 -0.25 -0.60 -0.71 -0.13 -0.30 -0.25 -0.43

Systems with M · · · σ Contacts, C Configurations -2.14 -2.16 -2.10 -2.14 LiH · · · H2 (C) NaH · · · H2 (C) -0.86 -0.87 -0.80 -0.83 HBeH · · · H2 (C) -0.48 -0.51 -0.48 -0.56 HMgH · · · H2 (C) -1.14 -1.22 -1.07 -1.19 BH3 · · · H2 (C) -5.39 -6.03 -3.67 -5.11 AlH3 · · · H2 (C) -2.58 -2.78 -2.44 -2.78 Li2H2 · · · H2 (C) -2.13 -2.16 -2.13 -2.21 Na2H2 · · · H2 (C) -0.98 -1.03 -1.00 -1.05 Be2H4 · · · H2 (C) -2.53 -2.80 -2.20 -2.85 Mg2H4 · · · H2 (C) -1.48 -1.57 -1.43 -1.62 * These results correspond to CCSD(T)/aug-cc-pVTZ//CCSD/ aug-cc-pVTZ calculations.

is the greatest elongation of the H-H bond. It is worth mentioning that for C configurations there is much greater donation of the electron charge by H2 than its reception for configurations A and B. Table 3 shows that for M · · · σ interactions the charges are in range 0.01-0.22 au, while for DHBs they are smaller than -0.01 au. The polarization of H2 for H · · · M interactions practically does not exist, since usually both H-atoms are positively charged and the H-charges are very close in value to each other. Figure 4a presents the relationship between the length of H-H bond and the polarization, i.e., the difference in H-atoms’ charges within the H2 molecule. In the DHB complexes (shown with open circles), there is a linear relationship between H-H bond length and the polarization. Figure 4b presents the secondorder polynomial dependence between the H-H bond length and the charge of the molecule of hydrogen for DHB systems (A and B configurations). The inset in Figure 4b presents the relationship between H-H bond length and the charge of H2 for all systems analyzed. One can observe the difference in the electron charge transfer for DHB complexes (open circles) and M · · · σ interactions (full circles). The question arises, why for both effects of donating and withdrawing of the electron charge is the H-H bond elongation observed accompanied by the increase of the binding energy? This may be simply explained in the terms of the molecular orbital theory. For the DHBs, the situation is similar to that one occurring for hydrogen bonds, where there is the electron charge transfer from the proton acceptor to the antibonding proton-donating bond orbital. For X-H · · · Y hydrogen bonds, it is usually n f σ*XH transfer (n designates the electron lone pair), while for Y-H-δ · · · +δH-X dihydrogen bonds, it is σYH f σ*XH transfer. For the M-H-δ · · · +δH-H-δ dihydrogen bonds analyzed here, this is σMH f σ*HH. In other words, the formation

of the dihydrogen bond where H2 molecule plays the role of the Lewis acid should lead to the increase of the occupancy of the antibonding σ H-H orbital (σ*HH). This leads to the weakening of the bond and its elongation. The other type of charge transfer is dominant for the M · · · σ interactions; this is σHH f σ*MH or σHH f n*(M), where n(M) designates an empty electron pair of the metal center. In both cases, a decrease of the occupancy of the σ bonding H-H orbital should be observed and consequently an elongation of the bond. One can see that for both H-δ · · · +δH and M · · · σ interactions the weakening of the H-H bond of the molecular hydrogen should be observed! Such a situation is really observed (see the H-H bond lengths in Table 1). Table 3 presents occupancies of σHH and σ*HH orbitals. The differences between occupancies of σHH for DHB complexes are meaningless, less than 0.001, but the occupancies of σ*HH are in the range 0.001-0.005. Figure 5 shows the relationship between the H-H bond length, which was found earlier here to be a good indicator of the strength of the interaction, and the occupancy of the σ*HH orbital, and the second-order polynomial regression line is plotted. Thus, the elongation of the H-H bond for DHB systems is really connected with the occupancy of the antibonding molecular H2 orbital. In the case of complexes connected through M · · · σ interactions, the occupancies of σ*HH are also observed; even for BH3 · · · H2 complex, such an occupancy amounts to 0.07. However, the most significant changes of the occupancy is found in the H-H bonding orbital, σHH. For the latter complex it is equal to 1.554. The lower occupancy of σHH is accompanied by the longer and weaker H-H bond and it is connected with the stronger H · · · M interaction. Figure 6 presents the secondorder polynomial dependence between the H-H bond length and the occupancy of the corresponding bonding orbital (R2 ) 0.98) for complexes linked through M · · · σ interaction. If the point that is out of the range of the other ones, corresponding to the BH3 · · · H2, is rejected, the correlation is still high (R2 ) 0.97). Figure 7 presents the correlation between the H-H bond length and the ∆E NBO energy. This energy is connected with the maximum σMH f σ*HH overlapping for the DHB complexes and with σHH f σ*MH or σHH f n*(M) overlapping for complexes linked by M · · · σ interactions. This interaction is calculated as the second-order perturbation theory energy, for DHBs, according to the following relation (eq 1):

∆E(σMH f σ*HH) ) -2〈σMH |F|σHH*〉2 / [ε(σHH*) - ε(σMH)] (1) 〈σMH |F| σHH*〉 designates the Fock matrix element, and [ε (σHH*) - ε (σMH)] is the orbital energy difference. The NBO energies are presented in Table 3. Figure 7 and Table 3 show that the electron charge transfer energy expressed by eq 1 correlates with other geometrical, energetic, and NBO parameters. The QTAIM has also been applied here. The characteristics of the bond critical points are collected in Table 4. BCPs corresponding to the bond paths of H · · · H interactions (DHB complexes) and to the M · · · σ contacts (C configurations) are analyzed. Figure 8 presents the dependence between the H-H bond length and the electron density at H · · · H (H · · · M) BCP, FBCP. The empty circles represent DHB complexes, while full circles correspond to H · · · M interactions. This is the linear correlation where the low variety of FBCP is visible for DHBs. The FBCP values for the DHB interactions are in the range

206


Alkorta et al.

Figure 3. The linear relationship between the binding energy (kcal/mol) and the H-H bond length (Å) for DHB systems.

TABLE 3: NBO Parameters: Energies (see eq 1, in kcal/mol), the Charge of H2 Molecule (in au), the Difference between the Net Charges of H-Atoms of H2 for DHB Systems, and Occupancies of Bonding and Antibonding Orbitals of H2 complex

charge H2


-0.0051 -0.0077 -0.0007 -0.0015 -0.0007 -0.0006 -0.0039 -0.0065 -0.0005 -0.0007 -0.0010 -0.0011

LiH · · · H2 NaH · · · H2 HBeH · · · H2 HMgH · · · H2 BH3 · · · H2 AlH3 · · · H2 Li2H2 · · · H2 Na2H2 · · · H2 Be2H4 · · · H2 Mg2H4 · · · H2

0.0472 0.0080 0.0046 0.0146 0.2182 0.0651 0.0392 0.0109 0.1752 0.0408

∆ charge in H2 atoms

NBO energya

occupancy σ(H2)

occupancy σ*(H2)

DHBs Systems, A and B Configurations 0.0661 1.65 0.0641 2.1 0.0131 0.23 0.0255 0.54 0.0007 0.15 0.0098 0.35 0.0479 1.57 0.0583 2.13 0.0075 0.17 0.0177 0.27 0.0018 0.53 0.0275 0.6

1.99954 1.99899 1.99961 1.99936 1.99979 1.99958 1.99968 1.99966 1.99970 1.99951 1.99970 1.99926

0.00427 0.00504 0.00078 0.00136 0.00061 0.00074 0.00367 0.00507 0.00037 0.00090 0.00095 0.00125

Systems with M · · · σ Contacts, C Configurations 6.61 2.74 1.77 6.37 288.07 26.53 16.37 4.21 88.48 15.07

1.97762 1.99155 1.99417 1.98019 1.55442 1.92486 1.95703 1.98561 1.80243 1.95381

0.00000 0.00001 0.00081 0.00430 0.07005 0.00803 0.00343 0.00306 0.01924 0.00414

a In the DHB system the orbital interation is between the σMH f σ*HH orbitals, while in the M · · · σ contacts, it is between σHH f n*(M) or σHH f σ*MH ones.

0.002-0.005 au, while for H · · · M interactions they are between 0.004 and 0.086 au. Table 4 presents also the Laplacians of the electron density at BCP and the corresponding other QTAIM parameters: the total electron energy density at BCP, HBCP, and its components, the kinetic electron energy density, GBCP, and the potential electron energy density at BCP, VBCP. One can see that for few of complexes, BH3 · · · H2, AlH3 · · · H2, and Be2H4 · · · H2, the modulus of VBCP outweighs the GBCP value (bolded values). For such cases, the total electron energy density at BCP is negative, since HBCP ) VBCP + GBCP (VBCP is negative and GBCP is positive). It means that the corresponding interaction is partly covalent in nature.27,28 It is worth mentioning that for those H · · · M interactions where the negative HBCP values are observed, there is the greatest electron density at BCP, the

greatest positive charges of H2 molecule, the longest H-H bonds, the shortest H · · · M distances, and the strongest interactions (see Table 2 for the binding energies). Cooperativity Effects. The cooperativity effects for hydrogenbonded systems are often analyzed in the literature.29-31 There are various definitions of this phenomenon; however, it is usually understood as the enhancement of the hydrogen bonding between two species if still another species, a third one, is attached to that system.32 For most of the species such enhancement is observed,33 but there are also systems where an opposite effect of the weakening of hydrogen bond was found. For example, the cooperativity was analyzed for C-H · · · O and O-H · · · O hydrogen bonds in (H2CO)n and (HFCO)n aggregates.34 It was shown that for O-H · · · O interactions this



Figure 4. (a) Relationship between the H-H bond length (Å) and the polarization of the H2 molecule (e). (b) Relationship between the H-H bond length (Å) and the charge of the H2 molecule (e) for DHBs. The inset figure shows the latter dependence for all complexes analyzed.

effect enhances the H-bond, in the case of C-H · · · O hydrogen bonds the weakening of C-H · · · O interactions is observed. The cooperativity effect is observed not only for hydrogen bonds; for example, the enhancement of halogen bonding was found in the case of H2CO · · · (ClF)n and dihalogen clusters.35,36 Several studies were published where the cooperativity effects are analyzed where two or more different noncovalent interactions coexist. For example, the synergetic stability complexes have been calculated in ternary systems where ion-π and also

hydrogen-bonding, dihydrogen-bonding, or halogen-bonding interactions coexist.37 Very recently a review on cooperativity effects appeared38 where different combinations of various interactions were considered. In this study, the coexistence of both interactions described in the previous sections is analyzed, i.e., the dihydrogen-bonding and metal-σ interaction. Three aggregates have been considered: H2 · · · LiH · · · H2, H2 · · · NaH · · · H2, and H2 · · · HBeH · · · H2. For these systems, one of the hydrogen molecules acts as the

208


Alkorta et al.

Figure 5. Relationship between the H-H bond length (Å) and the occupancy of σ*HH orbital for DHB complexes (au).

Figure 8. Relationship between the H-H bond length (Å) and the electron density at H · · · H (M · · · σ) BCP (au).

Figure 6. Relationship between the H-H bond length (in Å) and the occupancy of σHH orbital for complexes with H · · · M interactions (au).

Figure 7. Relationship between the H-H bond length (Å) and the NBO energy (kcal/mol; see eq 1).

Lewis acid (M-H · · · H-H dihydrogen bonding) and the second one as the Lewis base (M · · · σ interaction). Table 5 presents the interaction energies of these trimers and the cooperativity energies. The interaction energies were calculated in a similar way as for the calculation of the binding energy for dimers, i.e., as a difference between the total energy of the trimer and the energies of monomers. The cooperativity energy is expressed by eq 238

Coop-Energy ) Ei(ABC) - Ei(AB) - Ei(BC) - Ei(AC) (2) where Ei(ABC) is the interaction energy of the trimer, Ei(AB) and Ei(BC) are the interaction energies of the isolated dimers being in their energetic minima and Ei(AC) is the interaction energy of the molecules A and C in the geometry they have in the trimer. The following sequence is applied here for A, B, and C designations; A is the H2 molecule interacting with the metal center, B is the metal hydride (LiH, NaH, or BeH2), and

C is the second H2 molecule involved in dihydrogen bonding. In case of H2 · · · LiH · · · H2 and H2 · · · NaH · · · H2 complexes, a favorable cooperativity is observed (Table 5), while for H2 · · · HBeH · · · H2 aggregate it depends on the level of theory applied. However, this effect seems to be meaningless, since for all three systems analyzed and for all levels of theory applied, the modulus of the cooperativity energy is not greater than 0.05 kcal/mol. It is worth mentioning that the AC species is not a real complex but two H2 molecules separated by a spacer, metal hydride. For AC dimer, the interaction energy is meaningless; only for the MP2/aug-cc-pVQZ level, for H2 · · · HBeH · · · H2 aggregate, it is equal to -0.08 kcal/mol. However, usually the modulus of AC energy is less than 0.01 kcal/mol. The geometrical parameters for the trimers and also the parameters of the corresponding dimers are presented for comparison in Table S1 of the Supporting Information. One can see that the bond lengths of H2 molecules in trimers do not change if compared with dimers. The changes, if they are observed, are smaller than 0.0001 Å. Similarly, no meaningful changes for M-H bonds are observed. The greater differences are observed for H · · · H and H · · · M contacts. However, also they are not significant; sometimes there is elongation of the H · · · H contact (or H · · · M) and sometimes shortening, depending on the level of theory applied. Table S2 (Supporting Information) shows the charges and energies obtained from the NBO method. The charges of monomers within trimers and the charges of monomers within the corresponding dimers are given for comparison. It is interesting that the charges of H2 molecules practically do not change in trimers when compared with dimers. It means that the amount of the electron charge that is transferred from the metal hydride to H2 acting as the Lewis acid (DHB interaction) is the same in the dimer as in the trimer. The same concerns the metal-σ interaction; the electron charge transfer is the same for trimers and dimers. It means that both kind of interactions act independently in trimers, and it explains why the cooperativity energies (Table 5) are meaningless. Table S2 (Supporting Information) also presents the total charges of metal hydrides (B systems), where only bold values for trimers are given; for dimers they have the opposite signatures as the corresponding values for H2 molecules. One can also see (Table S2, Supporting Information) that NBO energies in trimers are close to the corresponding energies in dimers; the only exception is the H2 · · · HBeH · · · H2 aggregate, where such a difference is greater. This also confirms the previous finding concerning the weak cooperativity effects for three species analyzed here.



TABLE 4: QTAIM Parameters (in au) of the Complexes Analyzeda

a

complex

FBCP

32FBCP


0.0043 0.0045 0.0028 0.0033 0.0022 0.0030 0.0039 0.0041 0.0021 0.0030 0.0028 0.0034

DHBs Systems, A and B Configurations 0.0109 0.0022 0.0109 0.0022 0.0088 0.0017 0.0093 0.0018 0.0073 0.0014 0.0090 0.0017 0.0100 0.0020 0.0098 0.0020 0.0070 0.0013 0.0090 0.0017 0.0080 0.0015 0.0095 0.0019

-0.0017 -0.0018 -0.0011 -0.0013 -0.0009 -0.0012 -0.0015 -0.0015 -0.0008 -0.0012 -0.0010 -0.0013

0.0005 0.0004 0.0006 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005 0.0006

LiH · · · H2 NaH · · · H2 HBeH · · · H2 HMgH · · · H2 BH3 · · · H2 AlH3 · · · H2 Li2H2 · · · H2 Na2H2 · · · H2 Be2H4 · · · H2 Mg2H4 · · · H2

0.0080 0.0038 0.0042 0.0059 0.0863 0.0151 0.0086 0.0043 0.0284 0.0075

Systems with M · · · σ Contacts, C Configurations 0.0487 0.0094 0.0201 0.0037 0.0114 0.0023 0.0125 0.0030 0.0716 0.0788 0.0494 0.0129 0.0560 0.0108 0.0244 0.0045 0.0374 0.0171 0.0320 0.0066

-0.0067 -0.0023 -0.0017 -0.0028 -0.1397 -0.0134 -0.0076 -0.0028 -0.0248 -0.0052

0.0027 0.0014 0.0006 0.0002 -0.0609 -0.0005 0.0032 0.0017 -0.0077 0.0014

GBCP

VBCP

HBCP

For bolded values, the interactions are partially covalent in nature.

TABLE 5: Interaction Energies of Trimers and the Cooperativity Energies (see eq 2), Both in kcal/mol, of Three Complexes Analyzed Here and Containing Two H2 Molecules, with Four Levels of Theory Taken into Account interaction energy

a

level

ABC H2 · · · MH1-2 · · · H2

AB H2 · · · MH1-2

BC MH1-2 · · · H2

AC H 2 · · · H2

MP2/aug-cc-pVTZ MP2/aug-cc-pQTZ CCSD/aug-cc-pVTZ CCSD(T)/aug-cc-pVTZa

-3.07 -2.98 -2.96 -3.07

H2 · · · LiH · · · H2 -2.25 -2.20 -2.20 -2.24

-0.78 -0.75 -0.72 -0.79

0.01 0.01 0.00 0.00

-0.05 -0.03 -0.05 -0.05


-1.78 -1.76 -1.62 -1.73

H2 · · · NaH · · · H2 -0.92 -0.94 -0.86 -0.89

-0.84 -0.81 -0.73 -0.81

0.00 0.01 0.00 0.00

-0.03 -0.02 -0.03 -0.03


-0.91 -0.90 -0.88 -1.00

H2 · · · HBeH · · · H2 -0.54 -0.54 -0.53 -0.61

-0.38 -0.26 -0.37 -0.40

-0.01 -0.08 -0.01 -0.02

0.02 -0.02 0.03 0.03

Coop-Energy

These results corresponds to CCSD(T)/aug-cc-pVTZ//CCSD/aug-cc-pVTZ calculations.

Summary Two types of interactions are considered, dihydrogen bonds and metal-σ interactions for complexes containing H2 molecules. For dihydrogen bonds, H2 plays the role of the Lewis acid, and these interactions for the systems considered here are weak; the elongation of the H-H bond and the changes of the other parameters being the effect of complexation are small. For example, for NaH · · · H-H complex the binding energy amounts to ∼0.7 kcal/mol. However, it is possible to detect few correlations for DHB complexes between the parameters analyzed. The metal-σ bond interactions are stronger. For BH3 · · · H2 complex, the binding energy is of about 5-6 kcal/ mol, depending on the level of theory considered. For both types of interactions, the elongation of H-H bond of the molecular hydrogen is observed in spite of the fact that for DHB H2 is the

Lewis acid while for metal-σ interaction H2 is the Lewis base. This is connected with the electron charge transfer into the antibonding and from bonding H2 orbitals, respectively. Several trimers containing two hydrogen molecules where both interactions exist have been considered. The comparison of the properties in these trimers with those of the corresponding dimers shows that no significant cooperative effect is observed. These results could be very important in the process of designing new materials based on metal hydrides for hydrogen storage. Acknowledgment. Technical and human support provided by IZO-SGI SGIker (UPV/EHU, MICINN, GV/EJ, ESF) is gratefully acknowledged (S.J.G.). We also thank the Ministerio de Ciencia e Innovacioń (Project No. CTQ2009-13129-C0202), the Spanish MEC (CTQ2007-62113), and the Comunidad Autońoma de Madrid (Project MADRISOLAR2, ref S2009/

210


PPQ-1533) for continuing support. Thanks are given to the CTI (CSIC) for an allocation of computer time. Supporting Information Available: Geometry and charges in the calculated trimers. This material is available free of charge via Internet at http://pubs.acs.org. References and Notes (1) (a) Kubas, G. J. Metal Dihydrogen and σ-Bond Complexes; Kluwer Academic Publishers: New York, 2001. (b) Crabtree, R. H. The Organometallic Chemistry of the Transition Metals; John Wiley and Sons, Inc.: Hoboken, NJ, 2005. (2) (a) Elam, C. C.; Padr, C. E. G.; Sandrock, G.; Luzzi, A.; Lindblad, P.; Hagen, E. F. Int. J. Hydrogen Energy 2003, 28, 601. (b) Conte, M.; Iacobazzi, A.; Ronchetti, M.; Vellone, R. J. Power Sources 2001, 100, 171. (c) Bogdanovic, B.; Schwickardi, M. J. Alloys Compd. 1997, 253, 1. (3) National Hydrogen Energy Road Map; USDOE: Washington, DC, 2002. (4) (a) Grochala, W.; Edwards, P. P. Chem. ReV. 2004, 104, 1283. (b) Dillon, A. C.; Heben, M. J. Appl. Phys. A: Mater. Sci. Process. 2001, 72, 133. (c) Zu¨ttel, A. Mater. Today 2003, 6, 24. (5) Zaluska, A.; Zaluski, L.; Strom-Olsen, J. O. Appl. Phys. A: Mater. Sci. Process. 2001, 72, 157. (6) Yang, Q.; Zhong, C. J. Phys. Chem. B 2006, 110, 655. (7) Murray, L. J.; Dinca, M.; Long, J. R. Chem. Soc. ReV. 2009, 38, 1294. (8) (a) Dillon, A. C.; Jones, K. M.; Bekkedahl, T. A.; Kiang, C. H.; Bethune, D. S.; Heben, M. J. Nature 1997, 386, 377. (b) Chen, P.; Wu, X.; Lin, J.; Tan, K. L. Science 1999, 285, 91. (c) Mpourmpakis, G.; Froudakis, G. E.; Lithoxoos, G. P.; Samios, J. Nano Lett. 2006, 6, 1581. (9) Carmichael, M.; Chenoweth, K.; Dykstra, C. E. J. Phys. Chem. A 2004, 108, 3143. (10) Lochan, R. C.; Head-Gordon, M. Phys. Chem. Chem. Phys. 2006, 8, 1357. (11) Gomez, D. A.; Combariza, A. F.; Sastre, G. Phys. Chem. Chem. Phys. 2009, 11, 9250. Sastre, G. Theor. Chem. Acc. 2010, 127, 259. (12) Grabowski, S. J.; Sokalski, W. A.; Leszczynski, J. Chem. Phys. Lett. 2006, 432, 33. (13) Grabowski, S. J. J. Phys. Chem. A 2007, 111, 3387. (14) Bader, R. F. W. Atoms in Molecules. A Quantum Theory; Oxford University Press: New York, 1990. (15) Urban, J.; Roszak, S.; Leszczynski, J. Chem. Phys. Lett. 2001, 346, 512. (16) Solimannejad, M.; Alkorta, I. Chem. Phys. Lett. 2007, 439, 284. (17) Alkorta, I.; Elguero, J.; Del Bene, J. E. Chem. Phys. Lett. 2010, 489, 159. (18) (a) Park, S.; Ramachandran, R.; Lough, A. J.; Morris, R. H. J. Chem. Soc. Chem. Commun. 1994, 2201. (b) Lough, A. J.; Park, S.; Ramachandran, R.; Morris, R. H. J. Am. Chem. Soc. 1994, 116, 8356. (c) Lee, J. C., Jr.; Rheingold, A. L.; Mu¨ller, B.; Pregosin, P. S.; Crabtree, R. H. J. Chem. Soc. Chem. Commun. 1994, 1021. (d) Lee, J. C., Jr.; Peris, E.; Rheingold, A. L.; Crabtree, R. H. J. Am. Chem. Soc. 1994, 116, 11014. (e) Peris, E.; Lee, J. C., Jr.; Crabtree, R. H. J. Chem. Soc. Chem. Commun. 1994, 2573. (f) Wessel, J.; Lee, J. C., Jr.; Peris, E.; Yap, G. P. A.; Fortin, J. B.; Ricci, J. S.; Sini, G.; Albinati, A.; Koetzle, T. F.; Eisenstein, O.; Rheingold, A. L.; Crabtree, R. H. Angew. Chem., Int. Ed. Engl. 1995, 34, 2507. (g) Crabtree, R. H.; Siegbahn, P. E. M.; Eisenstein, O.; Rheingold, A. L.; Koetzle, T. F. Acc. Chem. Res. 1996, 29, 348. (h) Peris, E.; Lee, J. C., Jr.; Rambo, J.; Eisenstein, O.; Crabtree, R. H. J. Am. Chem. Soc. 1995, 117, 3485. (i) Peris, E.; Wessel, J.; Patel, B. P.; Crabtree, R. H. J. Chem. Soc. Chem. Commun. 1995, 2175.

Alkorta et al. (19) (a) Liu, Q.; Hoffman, R. J. Am. Chem. Soc. 1995, 117, 10108. (b) Alkorta, I.; Elguero, J.; Foces-Foces, C. Chem. Commun. 1996, 1633. (c) Rozas, I.; Alkorta, I.; Elguero, J. J. Phys. Chem. A 1997, 101, 4236. (d) Lipkowski, P.; Grabowski, S. J.; Robinson, T. L.; Leszczynski, J. J. Phys. Chem. A 2004, 108, 10865. (e) Robertson, K. N.; Knop, O.; Cameron, T. S. Can. J. Chem. 2003, 81, 727. (20) Rozas, I.; Alkorta, I.; Elguero, J. Chem. Phys. Lett. 1997, 275, 423. (21) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, Jr., J. A.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, N. J.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, ¨ .; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian 09, O ReVision A.1, Gaussian, Inc., Wallingford CT, 2009. (22) Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553. (23) Reed, A. E.; Curtiss, L. A.; Weinhold, F. Chem. ReV. 1988, 88, 899. (24) Weinhold, F.; Landis, C. Valency and Bonding, A Natural Bond Orbital Donor-Acceptor PerspectiVe: Cambridge University Press: New York, 2005. (25) (a) Popelier, P. Atoms in Molecules. An Introduction.: Prentice Hall, Pearson Education Limited: New York, 2000. (b) Quantum Theory of Atoms in Molecules: Recent Progress in Theory and Application;. Matta, C., Boyd, J. J., Eds.; Wiley-VCH: New York, 2007. (26) Biegler-Ko¨nig, F. AIM2000; University of Applied Sciences: Bielefeld, Germany. (27) (a) Cremer, D.; Kraka, E. Croat. Chem. Acta 1984, 57, 1259. (b) Jenkins, S.; Morrison, I. Chem. Phys. Lett. 2000, 317, 97. (c) Arnold, W. D.; Oldfield, E. J. Am. Chem. Soc. 2000, 122, 12835. (28) (a) Rozas, I.; Alkorta, I.; Elguero, J. J. Am. Chem. Soc. 2000, 122, 11154. (b) Gatti, C.; Cargnoni, F.; Bertini, L. J. Chem. Phys. 2003, 24, 422. (c) Sobczyk, L.; Grabowski, S. J.; Krygowski, T. M. Chem. ReV. 2005, 105, 3513. (d) Mariam, Y. H.; Musin, R. J. Phys. Chem. A 2008, 112, 134. (29) Del Bene, J.; Pople, J. A. Chem. Phys. Lett. 1969, 4, 426. (30) Kollman, P. J. Am. Chem. Soc. 1977, 99, 4875. (31) Mo´, O.; Yań˜ez, M.; Elguero, J. J. Chem. Phys. 1992, 97, 6628. (32) Sanz, P.; Alkorta, I.; Mo´, O.; Yań˜ez, M.; Elguero, J. Chem. Phys. Chem. 2007, 8, 1950. (33) (a) Hunt, S. W.; Higgins, K. J.; Craddock, M. B.; Brauer, C. S.; Leopold, K. R. J. Am. Chem. Soc. 2003, 125, 13850. (b) Parra, R. D.; Bulusu, S.; Zeng, X. C. J. Chem. Phys. 2005, 122, 184325. (c) Kobko, N.; Dannenberg, J. J. J. Phys. Chem. A 2003, 107, 6688. (d) Parra, R. D.; Ohlssen, J. J. Phys. Chem. A 2008, 112, 3492. (e) Zio´łkowski, M.; Grabowski, S. J.; Leszczynski, J. J. Phys. Chem. A 2006, 110, 6514. (f) Grabowski, S. J.; Leszczynski, J. Chem. Phys. 2009, 355, 169. (g) Grabowski, S. J.; Ugalde, J. M. Can. J. Chem. 2010, 88, 769. (34) Kar, T.; Scheiner, S. J. Phys. Chem. A 2004, 108, 9161. (35) Grabowski, S. J.; Bilewicz, E. Chem. Phys. Lett. 2006, 427, 51. (36) Alkorta, I.; Blanco, F.; Elguero, J. Struct. Chem. 2009, 20, 63. (37) (a) Estalleras, C.; Frontera, A.; Quinõnero, D.; Alkorta, I.; Deya`, P. M.; Elguero, J. J. Phys. Chem. A 2009, 113, 3266. (b) Solimannejad, M.; Malekani, M.; Alkorta, I. J. Phys. Chem. A 2010, 114, 12106. (38) Alkorta, I.; Blanco, F.; Deya`, P. M.; Elguero, J.; Estalleras, C.; Frontera, A.; Quinõnero, D. Theor. Chem. Acc. 2010, 126, 1.

JP1100544

Dihydrogen Bonding vs MetalâÏ Interaction in Complexes between H2

Recommend Documents

Dihydrogen Bonding vs MetalâÏ Interaction in Complexes between H2