Complex pairing of B2H4 with H2O, CH3OH, NH3, NH2CH3, NH(CH3)2 and N(CH3)3

Ab initio calculations were carried out to analyze the interactions between a molecule of B2H4 with H2O, CH3OH, NH3, NH2CH3, NH(CH3)2 and N(CH3)3 molecules at the MP2/aug-cc-pvdz computational level. B2H4 through its bridged hydrogens (Hb) could act as a hydrogen bond donor while its B-B act as hydrogen bond acceptor. Thus, interaction of B2H4 with the mentioned molecules resulted in formation of Hb...X or B-B...H hydrogen bond complexes. In contrast, Ht atoms of B2H4 have not enogh strength to form Ht...H dihydrogen bond complexes with the above molecules. Results showed that the B-B...H interactions are stronger than its Hb...X counterpart. The obtained structures were analyzed by the natural bond orbital (NBO) and Atoms in Molecules (AIMs) methodologies.


Introduction
Borane complexes have been studied extensively and have even been the subject of Nobel Prize work by Brown [1,2]. It has been the subject of proton affinity experiments in chemical ionization mass spectrometers. Among non-covalent interactions which have been known in boron chemistry, both dihydrogen bonding and hydrogen bonding types are particularly significant [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. B 2 H 4 , designated as diborane (4), probably is the best known electron-deficient analogue of ethylene [22][23][24][25][26]. The molecule B 2 H 4 bears 10 valence electrons for chemical bonding. There are two standard two electron terminal B-H bonds, thus accounting for a total of four electrons. This leaves a total of six electrons to share between the two bridging H atoms and the two B atoms. Consequently, there are two 3c-2e curved 'banana' B-H-B bridging bonds. According to the above illustrations, B 2 H 4 has two types of terminal (H t -B) and bridging (B-H b -B) hydrogen atoms which differ in nature and characteristics. The bridging hydrogens of B 2 H 4 are participating in electron deficient 'three-center, two-electron bonds' thus, they bear enough partial positive charge to act as hydrogen bond donor (HBD) to form H b …X (X= N, O) hydrogen bonds with electron donating molecules [13,14,[17][18][19][20][21]26]. On other hand, recent studies are showing that B-B bond also could act as HBA in the interactions of borane clusters with HBD species to form H…B-B hydrogen bonds [13,20,26].
From a fundamental point of view, the present work aims to extend the knowledge of the intrinsic activity of H t , H b and B-B bond of diborane(4) as hydrogen bond acceptor or hydrogen bond donor towards other molecules. For this propose, we investigated interaction of B 2 H 4 toward H 2 O, CH 3 OH and NH n (CH 3 ) 3-n , n= 0-3 derivatives thorough theoretical calculation.

Computational methods
Calculations were performed using the Gaussian 03 system of codes [27]. The geometries of the isolated B 2 H 4 and H 2 O, CH 3 OH and NH n (CH 3 ) 3-n molecules as well as their complexes were fully optimized at the mp2/aug-cc-pVDZ computational level. Harmonic vibrational frequency calculation confirmed the structures as minimal and enabled the evaluation of zero point energy (ZPE). The counterpoise procedure was used to correct the interaction energy for basis set superposition error [28]. The AIM package was used to obtain bond properties and molecular graphs [29,30]. The natural bond orbitals (NBO) method implemented within the Gaussian 03 set of codes was applied to perform NBO analysis [31]. The association of B 2 H 4 and NH n (CH 3 ) 3-n (n=0-3) derivatives led to the formation of the 1:1 hydrogen bond complexes which has been denoted as B 2 H 4 -NH 3 , B 2 H 4 -NH 2 Me, B 2 H 4 -NHMe 2 and B 2 H 4 -NMe 3 , Figure 1. In these complexes hydrogen bond interactions has been found between a bridging proton of the B 2 H 4 as a proton donor and nitrogen atom of amine as a proton acceptor (H b …N). According to the data given in Table 1, stabilities of B 2 H 4 -NH n (CH 3 ) 3-n complexes increased with enhancing basicity of amines in the following order:

Results and discussion
The results due to the intermolecular bond lengths are given in the Table 2 and Figure 1. In the B 2 H 4 -H 2 O and B 2 H 4 -CH 3 OH complexes, the B1-B4 bond has elongation (0.0015); but, other bonds of B 2 H 4 are shortened (from -0.0009 to -0.0053) upon complex formation. Moreover, a 0.0061 lenthening was observed for O-H bond in these complexes.
On the other hand, the N…H b distances in the B 2 H 4 -NHn(CH 3 ) 3-n complexes are in the range of 2.6196 to 2.4997 Å. These distances could be considered as weak bonding interactions between the two components. Comparison of the H b …N distances showed that the obtaine trend was in agreement with the stability of these complexes.
The selected vibrational stretching frequencies (cm -1 ) with the corresponding intensities (km mol -1 ) for the studied complexes are listed in Table 3 3 OH complexes showed -8 cm -1 red shift, which is in agreement with its lengthening due to the complex formation. In contrast, in B 2 H 4 -NH n (CH 3 ) 3-n complexes, this bond was less affected by complex formation; thus, the observed shifts were negligible. In agreement with the lengthening of B1-H5 and B4-H6 bonds, their unsymetric stretching frequencies, which observed at 2811 cm -1 in free B 2 H 4 , showed -6 to -9 cm -1 red shift in the B 2 H 4 -NH n (CH 3 ) 3-n complexes.

Aim analysis
The atoms in molecules (AIM) theory is applied here to analyze the characteristics of the H…N and H…B-B interactions through the location of Bond Critical Points (BCP) with (3,-1) coordinates in the Hessian matrix fitted to the intermolecular contact area [29,30]. In Table 4, the results of the QTAIM topological parameters, namely as electronic density (ρ), Laplacian (∇ 2 ρ) and the ratios between the kinetic (G) and potential (U) electron energy density are listed [32]. These last ones are embodied into the QTAIM formalism as follows: (ħ 2 /4m)∇ 2 ρ = 2G + U This equation indicates which type of interaction may exist between the two nuclei, wherein, the profile of ∇ 2 ρ is embodied into the contribution of G and U. If the potential electron energy density is outweighed by the kinetic, the positive profile of ∇ 2 ρ indicates a depletion of charge density along the inter-nuclear connecting Bond Path (BP) [33]. Furthermore, the atomic connection is recognized as close-shell interaction, which is often designated to H-bonds or other intermolecular weakly bound contacts, such as halogen bonds, dihydrogen bonds, and π-staking [34][35][36][37][38][39][40]. Regarding the values gathered in Table 4, it should be highlighted that the positive values of ∇ 2 ρ ensure that all H-bonds are closed-shell interactions due to the low charge density concentration. The inter-atomic and inter-molecular interactions are also studied in terms of local electron energy density (H) and its components, the local kinetic electron energy density (G), and local potential electron energy density (V) at the BCPs. The relation between these energetic parameters is given in Equation 1.
Also it has been suggested that both ∇ 2 BCP and the H should be used for characterizing hydrogen bond [41]. The weak hydrogen-bonds means that both ∇ 2 BCP and H are positive, medium hydrogen-bonds show that ∇ 2 BCP >0 and H<0; while, strong hydrogen-bonds bearing both ∇ 2 BCP and H<0. For the investigated complexes (Table 4), ∇ 2 BCP and H at BCP for H…N and H…B-B interactions are positive. This means that these interactions belong to close shell weak HB interactions.
The balance between G and V could be used to show the nature of interactions [42]. If >1, then, the nature of the interaction is purely non-covalent. For all the examined complexes, this ratio was greater than 1, which confirmed the existence of weak interactions between the two systems and nature of the interaction was purely non-covalent.
Topological parameters ρ and ∇ 2 BCP , also describe the stability of complexes through the identification of charge density centres within the intermolecular bonds. Considering the results of the topological analysis presented in Table 4, good agreement could be found between the values of ∇ 2 BCP , ρ, and stabilization energies of complexes (Figures 2 and 3).

Natural bond orbital analysis
Natural bond orbital (NBO) analysis was performed for the minima found on the studied B 2 H 4 complexes. These complex formations are associated with an orbital interaction between the bonding pairs in the electron donor and the antibonding orbital in the electron acceptor. The quantity of charge transferred from donor to the acceptor (∆Q) due to the interaction of donor and acceptor orbitals were 0.0060, 0.    transferred from HBA to HBD molecules. Thus, charge transfer is not concentrated on the interacting atoms; but, is mostly dispersed among the molecules. Therefore, interpretation of the bond variations and frequency shifts in B 2 H 4 could not be carried out simply.
A useful quantity which might be derived from the results of natural bond orbital analysis is NBO binding energy (E 2 ). The second-order perturbation energy can be taken as an index to judge the strength of the intermolecular bonds. Table 5, lists the quantity of charge transfer from the donor to the acceptor qCT and the second-order perturbation energy due to the interaction of donor and acceptor orbitals. E (2) allow us to quantitatively evaluate the charge transfer involving the formation of the B 2 H 4 complexes. According to results, the E (2) value of B 2 H 4 -CH 3 OH was greater than B 2 H 4 -H 2 O, confirming the order obtained for the interaction energies of these complexes. Whereas, for the amine complexes some contraversies were seen between the order obtained for their E (2) and the interaction energies.