A theoretical study of the hydrogen bonding properties of H2BNH2: Some considerations on the basis set superposition error issue

Computational and Theoretical Chemistry 967 (2011) 147–151

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A theoretical study of the hydrogen bonding properties of H2B@NH2: Some considerations on the basis set superposition error issue Ibon Alkorta a,⇑, Cristina Trujillo a, Jose Elguero a, Mohammad Solimannejad b a b

Instituto de Química Médica (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

a r t i c l e

i n f o

Article history: Received 27 February 2011 Received in revised form 4 April 2011 Accepted 5 April 2011 Available online 14 April 2011 Keywords: HB complexes Ab initio calculations BSSE CBS

a b s t r a c t The HB complexes formed by H2B@NH2 with five small molecules that can act as hydrogen bond acceptors and donors have been theoretically studied. Three different kinds of complexes have been found to be minima: conventional hydrogen bonds, dihydrogen bonds and those with the p system of H2B@NH2. The geometric, electronic and spectroscopic properties of these complexes have been characterized at the MP2/aug-cc-pVDZ computational level. Special attention has been taken on the Basis Set Superposition Error (BSSE) issue using the full counterpoise (CP) method. The interaction energies have been calculated at MP2/aug-cc-pVXZ (X = D, T, Q, and 5) levels with and without BSSE counterpoise correction. These values have been used to extrapolate to the Complete Basis Set (CBS) energy. The results indicate that for the MP2/aug-cc-pVDZ calculations, the smallest errors in the interaction energy are obtained by correcting the interaction energy with the corresponding half of the BSSE correction. For the remaining cases, the CP corrected interaction energies are closer to the CBS ones than to those without correction. Ó 2011 Elsevier B.V. All rights reserved.

1. Introduction The interest in molecules with BN bonds has much increased in recent years. They have been proposed to be potential systems for hydrogen storage (Fig. 1) [1–9]. Borazanes and aminoboranes correspond to single and double BN bonds and are isoelectronic with ethane and ethene, while borazine is isoelectronic with benzene [10–14]. Compounds isoelectronic with benzyne, like borazynes, have been studied computationally [15]. Some authors named the B3N3 or (BN)3 six-membered ring that has no counterpart in carbocyclic aromatic chemistry, borazine, since it corresponds to the C6 cluster [16]. Iminoborane, HB„NH is isoelectronic with acetylene but much more reactive and it is only known as its trimer borazine [17]. Finally, boron nitride (BN)n corresponds to graphite and diamond, (C)2n [18]. In addition, it has been described the synthesis of 1,2-dihydro-1,2-azaborine (C4H6BN) [6] a organic/ inorganic hybrid of benzene, and several of their properties have been characterized [19,20]. Finally, the bonding properties and complexation pattern of systems with this type of BAN bond have been studied theoretically [21,22]. One of the smaller systems with a BAN bonded arrangement corresponds to aminoborane, H2B@NH2. The polymeric form of aminoborane is a white noncrystalline solid that can be obtained ⇑ Corresponding author. Fax: +34 91 564 48 53. E-mail address: [email protected] (I. Alkorta). URL: http://www.iqm.csic.es/are (I. Alkorta). 2210-271X/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.comptc.2011.04.008

by thermal decomposition of solid borazane H3BNH3 at temperatures below 370 K [23]. The use of finite basis in the calculation of molecular clusters by means of ab initio method is responsible of what is known as Basis Set Superposition Error (BSSE) [24,25]. This error is derived from the effective larger basis set used to compute the monomers within the complexes than the one used in the isolated monomers. Thus, the energy of the complex is overestimated with respect to the isolated monomers. The effect of the BSSE in weak interactions can be very important [26–29]. Thus, a large number of studies have been devoted to deal with this issue [30–34]. The most common method to evaluate the BSSE is the full counterpoise method (CP) which evaluates the energy of the monomers with the full basis set of the complex [35]. In the present study, the potential complexes of H2BNH2 with five small HBs donors/acceptor (HF, HCl, HCN, HNC, and HCCH) have been explored. The small size of the systems and the variety of non-bonding interactions established has allowed to analyze in detail the effect of the BSSE calculated with the counterpoise method at different computational levels for the different complexes formed. 2. Methods The geometry of the systems has been fully optimized at the MP2/aug-cc-pVDZ computational level [36,37]. Frequency calculations have been carried out to confirm that the structures obtained

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Fig. 1. The thermal decomposition of borazane with H2 release and formation of aminoborane and borazine.

are due to the double bond that connects boron and nitrogen and that they are shifted towards to more electronegative atom. Based on these results, it is expected that the H2BNH2 should act as HB acceptor in the hydrogen atoms attached to the boron and in the double bond and as HB donor through the NH moieties.

correspond to energetic minima. These geometries have been used to calculate the energy of the systems at the MP2/aug-cc-pVXZ (X = T, Q, and 5) level. The suitability of the MP2/aug-cc-pVDZ results has been confirmed by re-optimizing all the complexes at the MP2/aug-cc-pVTZ. The results at these two levels are almost identical (see Table S1 of Supporting Information). The full counterpoise method (CP), proposed by Boys–Bernardi, has been used to evaluate the Basis Set Superposition Error (BSSE) [35]. The electron density has been analyzed using the Quantum Theory of Atoms in Molecules (QTAIM) [38] with the AIMPAC and Morphy98 programs [39,40]. The electron localization function [41] (ELF) allows to analyze those region where the electron density is more concentrated and has been calculated with the TOPMOD programs [42].

3.2. Hydrogen bonded complexes Three different configurations have been found to be minima for the complexes of H2BNH2 and the considered HB donors/acceptors probes (HF, HCl, HCN, HNC and HCCH). The geometries obtained for the complexes with FH are shown in Fig. 3. The first complex (I) corresponds to a dihydrogen bond (DHB) between the electron rich hydrogen atom attached to the boron and the HB donors. The second complex (II) is the interaction with the polarized N@B double bond. Finally, in the third complex (III), two different situations can be found. For the complexes with HF, HCCH and HCl a double interaction is observed, DHB and conventional HB between the NH moiety of H2BNH2 and the HB acceptor group of our probe molecules. For the complexes with HCN and HNC only the interaction between the NH group of H2BNH2 and the HB acceptor (N and C, respectively) is present. All the complexes obtained show Cs symmetry. The interatomic distances of the moieties involved in the interactions are gathered in Table 1. The distances obtained in com-

3. Results and discussion 3.1. Isolated H2B@NH2 The molecular electrostatic potential of the isolated H2B@NH2 shows negative regions surrounding the hydrogen atoms attached to the boron and above and below the nitrogen atom (Fig. 2). The ELF indicates that the minima above and below the nitrogen atom

Fig. 2. Molecular electrostatic potential (MEP) (left) and ELF (right) of the isolated H2BNH2 calculated at the MP2/aug-cc-pVDZ computational level. The represented isosurfaces of the MEP are ±0.017 au and the ELF with a value of 0.8 is shown.

I

II

III

Fig. 3. Minima complexes of H2BNH2:HF calculated at MP2/aug-cc-pVDZ computational level.

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0.045

Table 1 Optimized intermolecular distances (Å) of the complexes optimized at the MP2/augcc-pVDZ computational level.

H2BNH2:FH H2BNH2:CNH H2BNH2:ClH H2BNH2:NCH H2BNH2:HCCH *

0.035

I

II

III

H  H

H  N

H  A*

H  H

1.788 1.942 2.038 2.293 2.380

1.944 2.088 2.145 2.441 2.520

2.329 2.339 2.765 2.211 2.498

1.713 1.894

0.025 0.02 0.015

2.492

A corresponds to the atom that acts as HB acceptor in the molecular probes.

0.01 0.005

plexes I and II follow the same trend being the shortest ones for the complexes with HF and the longest ones those with HCCH. In fact, a linear relationship of these parameters can be obtained with a square correlation coefficient of 0.994. The case of the complexes in disposition III is dependent on the interacting moiety of the molecular probes and the presence of one or two interactions. The analysis of the electron density of the complexes shows the presence of one intermolecular bond critical point (bcp) for all the complexes except for those with HF, HCl and HCCH in configuration III where two intermolecular bcp are found (Table 2). The small values of the electron density at the bcp and positive values of the Laplacian indicate that the interactions correspond to weak hydrogen bonds [43]. Exponential relationships have been found between the electron density at the bcp and the interatomic distances (Fig. 4) for all the H  H and H  N interactions in agreement with previous reports [44]. The shifts in the harmonic vibrational frequencies of the HB donors due to the complexation have been reported in Table 3. It is immediately clear from the results that the stretching vibrations corresponding to the DAH covalent bonds of the hydrogen bond donors undergo the red shifts that are characteristic for HB’s [45]. Larger red shifts of DAH bonds in complexes pairing via the DAH. . .p interactions comparing with complexes stabilized due to dihydrogen bonding are observed. An acceptable linear relationship (R2 = 0.92) is observed between the frequency shifts in complexes I and II. In complexes III, the frequency shift of the NH bond stretching of H2BNH2 ranges between 16 and 25 cm1 for those cases where the molecular probes act simultaneously as HB acceptor and donors (HF, HCl and HCCH) while it increases to 31 and 45 cm1 for the NCH and CNH complexes. The frequency shift of the molecular probes in III are larger than in the DHB complexes (I) but smaller than in those with the p-system (II).

3.3. Interaction energy The calculated values of the interaction energy with and without counterpoise correction for the four computational levels considered in the present article are gathered in Table 4.

-1.78(Distance) ρbcp = 0.86e R2 = 0.97

0.03 ρ bcp

Complex

0.04

-1.69(Distance) ρbcp = 0.33e R2 = 0.99

0 1.6

1.8

2 2.2 Interatomic distance

2.4

2.6

Fig. 4. Interatomic distance (Å) vs. qbcp (au) in the intermolecular bcp. Black and white square represents the values of the H  H and N  H interactions, respectively.

Table 3 Frequency shift (cm1) of the hydrogen bond donor calculated at the MP2/aug-ccpVDZ computational level. System

(I) HD

(II) HD

(III) H2BNH2

(III) HD

H2BNH2:FH H2BNH2:CNH H2BNH2:ClH H2BNH2:NCH H2BNH2:HCCH

117 54 47 31 5

328 218 184 80 16

17 45 16 31 25

179 87 9

The interaction energies smoothly vary as the size of the basis set increases (Fig. 5). The CP and noCP curves cannot cross each other and should tend to a common value that corresponds to that of the complete basis set (CBS). The values obtained at the MP2/ aug-cc-pV5Z with CP and noCP for each complex are very similar and provide a narrow range where the Ei(CBS) should be located. Two equations (Eqs. (1) and (2)) [46–49] have been used before to derive the CBS energy from a series of calculations using the Dunning basis sets, using as X values 2, 3, 4, and 5 for the augcc-pVDZ, aug-cc-pVTZ, aug-cc-pVQZ and aug-cc-pV5Z results, respectively. In general, Eq. (1) has been used to derive the CBS Hartree–Fock contribution while Eq. (2) has been used for the correlation contribution. In order to solve Eq. (1), three energetic values are needed while only two are needed for Eq. (2).

EðXÞ ¼ EðCBSÞ þ a e-bX

ð1Þ

E0 ðXÞ ¼ E0 ðCBSÞ þ c X -3

ð2Þ

In order to extrapolate the interaction energy at CBS, three different strategies have been followed. In the first one (A), the four MP2/ aug-cc-pvXZ total energy have been used to derived the MP2/CBS total energy of the monomers and complexes and from them the

Table 2 Electron density (q) and its Laplacian (»2q) (au) at the intermolecular bcp calculated with the MP2/aug-cc-pVDZ level. System

I

II

H  H

H2BNH2:FH H2BNH2:CNH H2BNH2:ClH H2BNH2:NCH H2BNH2:HCCH

III

H  N

X  H

H  H

q

»2q

q

»2q

q

»2q

q

»2q

0.0153 0.0129 0.0110 0.00742 0.00620

0.0510 0.0401 0.0322 0.0255 0.0225

0.0270 0.0215 0.0205 0.0115 0.00977

0.0854 0.0563 0.0473 0.0273 0.0245

0.0185 0.0136 0.0140 0.0149 0.0956

0.0561 0.0380 0.0359 0.0466 0.0279

0.0185

0.0561

0.0140

0.0359

0.0046

0.0170

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Table 4 Interaction energies (kJ mol1) obtained for all the complexes at the different computational levels considered with and without CP correction. Complexes

Ei (MP2/aug-cc-pVXZ)

Ei + CP (MP2/aug-cc-pVXZ)

X=D

X=T

X=Q

X=5

X=D

X=T

X=Q

X=5

H2BNH2:FH (I) H2BNH2:FH (II) H2BNH2:FH (III)

13.33 21.92 18.24

13.08 21.79 17.76

12.69 20.81 17.35

12.36 20.38 16.94

10.10 17.15 14.05

11.42 19.12 15.61

11.71 19.42 16.13

11.82 –19.63 16.32

H2BNH2:CNH (I) H2BNH2:CNH (II) H2BNH2:CNH (III)

16.62 21.09 16.31

15.28 19.35 15.55

14.15 17.78 14.74

13.76 17.28 14.38

11.64 14.86 12.42

12.90 16.24 13.62

13.27 16.58 13.95

13.38 16.75 14.05

H2BNH2:ClH (I) H2BNH2:ClH (II) H2BNH2:ClH (III)

10.33 15.44 14.01

9.88 14.50 13.76

9.45 13.82 13.33

9.24 13.54 13.13

7.13 10.91 9.81

8.24 12.07 11.60

8.57 12.60 12.18

8.66 12.74 12.33

H2BNH2:NCH (I) H2BNH2:NCH (II) H2BNH2:NCH (III)

11.51 11.11 16.48

10.61 10.02 15.66

9.72 8.81 14.93

9.39 8.43 14.51

7.95 7.05 12.71

8.79 7.76 13.68

9.03 8.00 14.03

9.10 8.09 14.13

H2BNH2:HCCH (I) H2BNH2:HCCH (II) H2BNH2:HCCH (III)

7.67 8.81 13.28

6.27 7.18 12.23

5.42 6.08 11.54

5.15 5.73 11.23

4.03 4.64 8.97

4.70 5.21 10.39

4.86 5.40 10.76

4.91 5.46 10.89

noCP CP

-12 Interaction energy (kJ/mol)

Table 5 Extrapolated interaction energies (kJ mol1) for each complex. (Values that are within of the range defined by the Ei and Ei-CP at the MP2/aug-cc-pV5Z are shown in bold.)

-14

-16

2

3

X

4

5

Fig. 5. Interaction energy as a function of the basis set used for the H2BNH2:CNH complex (I). X = 2, 3, 4, 5 correspond to the results at the MP2/aug-cc-pVDZ, MP2/ aug-cc-pVTZ, MP2/aug-cc-pVQZ and MP2/aug-cc-pV5Z, respectively.

Ei(CBS) has been evaluated as the difference between the complex and the sum of the monomers. In the second approach (B), the Ei at each computational level has been evaluated as the difference between the energy of the complex and the sum of the isolated monomers all of them calculated at the same computational level. The four Ei(MP2/augcc-pVXZ) in combination with Eq. (1) and (2) have provided an estimate of the Ei(CBS). The last approach (C) is analogous to the B one but using the CP corrected Ei’s. All these results have been gathered in Table 5. We have found that in our case, Eq. (1) provides better statistical parameters for both the Hartree–Fock and correlations contributions when using simultaneously the values of the four basis set considered here. In addition, since Eq. (1) can be used directly with the total energy, we have used the total energy with the different basis set and Eq. (1) to derive the Ei(CBS) for each system in approach A. In the case of approaches B and C, again, Eq. (1) provides better statistical parameters than Eq. (2). In addition, the statistical parameters applying approach C are better than the ones obtained in approach B for the same complex.

*

System

A⁄

B⁄

C⁄

H2BNH2:FH (I) H2BNH2:FH (II) H2BNH2:FH (III) H2BNH2:CNH (I) H2BNH2:CNH (II) H2BNH2:CNH (III) H2BNH2:ClH (I) H2BNH2:ClH (II) H2BNH2:ClH (III) H2BNH2:NCH (I) H2BNH2:NCH (II) H2BNH2:NCH (III) H2BNH2:HCCH (I) H2BNH2:HCCH (II) H2BNH2:HCCH (III)

11.99 19.67 16.57 13.29 16.63 14.00 8.86 13.09 12.72 8.99 7.89 14.17 4.88 5.37 11.00

11.83 19.60 16.41 13.43 16.76 14.08 8.70 12.90 12.42 9.12 8.13 14.20 4.92 5.49 10.92

15.99 23.82 12.29 12.71 15.79 12.92 8.52 12.97 9.02 8.25 6.87 13.08 4.73 5.10 10.73

See the text for an explanation of each approach method.

Since the value of the Ei(CBS) for a given complex should lie between the Ei and Ei-CP for any computational level, we have used the values calculated with the MP2/aug-cc-pV5Z level to verify if the mentioned condition is fulfilled for the different extrapolations. The best results are those with approach C, where the Ei(CBS) of 14 of the complexes are within the range of those calculated at the MP2/aug-cc-pV5Z level and only one complex is out of this range by only 0.03 kJ mol1. The values derived from approach A are within the Ei’s at MP2/aug-cc-pV5Z level in 7 of the 15 complexes while those derived from approach B are within the range in only one case. Thus, the Ei(CBS) obtained with approach C have been used as reference for each complex in rest of the present work. In order to analyze the errors at the different levels with the inclusion or not of the CP correction, Eq. (3) have been used:

%Error ¼ jEiðZÞ  EiðCBSÞ ðZÞ=EiðCBSÞ ðZÞj

ð3Þ

where Ei(Z) corresponds to the calculated interaction energy of complex Z, with CP or without it (Table 4), and Ei(CBS) (Z) is the extrapolated CBS interaction energy for complex Z obtained with approach C (Table 5, last column). In addition, the average values of the Ei and Ei-CP for each complex have been considered. Some statistical parameters of this analysis are given in Table 6.

I. Alkorta et al. / Computational and Theoretical Chemistry 967 (2011) 147–151 Table 6 Statistical parameters of the errors in the interaction energies (kJ mol1) when compared to Ei(CBS)-approach C. MP2/aug-cc-pVXZ X=D

X=T

X=Q

X=5

151

MADRISOLAR2, ref. S2009/PPQ-1533). The authors thank the CTI (CSIC) for allocation of computer time. Appendix A. Supplementary material

Ei

Average error Max. error Min. error

24.61 60.47 11.16

15.09 30.72 8.27

7.00 10.67 4.66

3.80 6.26 2.15

Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.comptc.2011.04.008.

Ei-CP

Average error Max. error Min. error

14.70 20.99 10.52

4.38 6.60 2.47

1.38 2.29 0.91

0.41 1.18 0.05

References

Average error Max. error Min. error

5.88 22.50 0.32

5.35 12.74 1.72

2.81 4.51 1.85

1.71 2.88 0.85

(Ei + Ei-CP)/2

For a given basis set, larger errors are found without CP correction than considering it when compared to the CBS extrapolation. The larger deviation is obtained at the MP2/ aug-cc-pVDZ in the weak complexes where errors up to 60% are found. Obviously, the larger the basis set, the smaller errors found. Only in the case of the MP2/aug-cc-pVDZ calculations, the use of the average Ei values between CP and noCP is recommended. For the other cases, the Ei values with CP corrections are the best. These results indicate that the CP Ei with the aug-cc-pVTZ are between 2.5% and 6.6% less stable than those with the CBS extrapolation. The range of interaction energies obtained varies between 19.6 kJ mol1 for the H2BNH2:FH (II) and 4.9 kJ mol1 for the H2BNH2:HCCH (II) complex. In three of the dimers, the configuration II is the strongest one (complexes with HF, HNC and HCl) while configuration III is the preferred for two of them (with NCH and HCCH). In four cases, the weakest complex corresponds to that in configuration I being the H2BNH2:NCH (II) the only exception. 4. Conclusions A theoretical study of the HB complexes of H2BNH2 with five small systems that can act as HB acceptor and donors (HF, HCl, HCN, HNC, and HCCH) has been carried out. Three different complexes have been found to be minima for each probe molecule: dihydrogen bonded (I), one where the p-cloud of H2BNH2 acts as HB acceptor (II), and one a conventional hydrogen bond is formed. Thus, a total of 15 complexes have been considered. The interaction energy of the complexes has been evaluated with the MP2/aug-cc-pVDZ, MP2/aug-cc-pVTZ, MP2/aug-cc-pVQZ and MP2/aug-cc-pV5Z computational levels with and without the CP correction. Using these values the corresponding CBS interaction energy has been derived for each complex. The analysis of the differences between the calculated interaction energies and the CBS ones show that in all cases, the Ei(CP) values show smaller differences that the Ei(noCP) ones. Only in the case of the MP2/aug-cc-pVDZ results the average value between Ei(CP) and Ei(noCP) seems to be recommendable. For small complexes the Ei-CP evaluation at MP2/aug-cc-pVQZ is recommendable while for larger cases it is the Ei-CP at the MP2/aug-cc-pVTZ. Acknowledgements Thanks are given to Prof. Janet E. Del Bene and Prof. Isabel Rozas for helpful comments and suggestions. This work was supported by the Ministerio de Ciencia e Innovación (Project No. CTQ200913129-C02-02) and Comunidad Autónoma de Madrid (Project

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