Non-convertional hydrogen bonding interaction of BH3NH3 complexes: a comparative theoretical study

Journal of Molecular Structure: THEOCHEM 713 (2005) 135–144 www.elsevier.com/locate/theochem

Non-convertional hydrogen bonding interaction of BH3NH3 complexes: a comparative theoretical study Yun Menga,b, Zhengyu Zhouc,*, Chunsheng Duanb, Ben Wangd, Qin Zhonga a

School of Chemical Engineering, Nanjing University of Science and Technology, Jiangsu, Nanjing 430094, People’s Republic of China b Chemistry Department of Normal College, Qingdao University, Shandong, Qingdao 266071, People’s Republic of China c Department of Chemistry, Qufu Normal University, Shandong, Qufu 273165, People’s Republic of China d School of Chemical Engineering, Qingdao University of Science and Technology, Shandong, Qingdao 266042, People’s Republic of China Accepted 1 March 2004

Abstract A new type of hydrogen bond, called a dihydrogen bond, has recently been introduced. In this bond hydrogen is donated to (hydridic) hydrogen. In this paper, ab initio HF, MP2 and DFT(B3LYP) levels of theory with different basis sets in combination with counterpoise procedure for basis set superposition error correction have been applied to BH3NH3 dimer and BH3NH3 complexes of methane, hydrogen cyanide, ammonia, water, methanol and hydrogen fluoride to understand the features of dihydrogen bond. The optimized geometric parameters and interaction energies for various isomers at different levels are estimated. The structures obtained at different computational levels are in agreement with each other. Dihydrogen bond does not occur in both BH3NH3/CH4 and BH3NH3/NH3 complexes. Apart from the B–H/H–N dihydrogen bond found in the BH3NH3 crystal and dimmer, the B–H/H–X (XaC, O, F) dihydrogen bonds have been observed in the BH3NH3/HCN, BH3NH3/H2O, BH3NH3/CH3OH and BH3NH3/HF complexes, while the classic H bonds also exist in the last three complexes. As for the complexes in which only dihydrogen bonds appear the strength of dihydrogen bonds ranges from 17.9 to 18.9 kJ molK1 at B3LYP/6-311CCg(d,p) level. Binding energies obtained from the MP2 and B3LYP optimized structures are more sensitive to basis sets than those from the HF method. Larger basis functions generally tend to produce slightly longer intermolecular distances, and the B3LYP and MP2 methods generate shorter intermolecular distances though they usually produce longer bond lengths compared with those at the HF level. The infrared spectrum frequencies, IR intensities and the vibrational frequency shifts are reported. Finally the solution phase studies on BH3NH3/HF complex are also carried out using the Onsager reaction field model with a range of dielectric constants from 2 to 80 at B3LYP/6-311CCg(d,p) level. q 2004 Elsevier B.V. All rights reserved. Keywords: Ab initio; DFT; Dihydrogen bond; BH3NH3 complexes

1. Introduction Hydrogen bonds (HBs) are the most important ‘weak’ interactions encountered in solid, liquid and gas phases. They define the crystal packing of many organic and organometallic molecules, the 3D structure of molecules, as well as modulate the reactivity of different groups within a molecule. The HB can be defined as an attractive interaction between two molecular moieties in which at least one of

* Corresponding author. Tel.: C86-537-445-6765; fax: C86-537-4456305. E-mail address: [email protected] (Z. Zhou). 0166-1280/$ - see front matter q 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2004.03.049

them contains hydrogen atom that plays a fundamental role. Classical HBs correspond to those formed by two heteroatoms, A and B, with a hydrogen atom bonded to one of them and located approximately in between (A–H/B). Hibbert and Emsley [1] defined three kinds of HBs depending on the interaction energy values obtained. HBs with energies between K2.4 and K12 kcal molK1 (1 calZ4.184 J) are defined as weak HBs, those with energies between K12 and K24 kcal molK1 are defined as strong HBs and those with energies more negative than K24 kcal molK1 are considered very strong HBs. Very recently the new term dihydrogen bond was coined to describe an interaction of the type D–H/H–E, where D is a typical hydrogen donor such as N or O, Transition

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metals (such as Ir or Re) and boron are typical elements (E) that can accommodate this hydridic hydrogen. These bonds were first generalized to the system B–H/H–N [2]. What makes this hydrogen bond so unusual is that the acceptor atom is hydrogen atom. For this bond to be intuitively acceptable, one correctly infers that the accepting hydrogen atom must be negatively charged. These bonds are of the type ‘proton-hydride’, i.e. between a D–HdC and a E–HdK. As the recent CSD investigation [3,4], the main characteristics of the D–H/H–E systems are: the d(H/H) distances ˚ , significantly less for such systems are typically 1.7–2.2 A than the sum of the van der Waals radii for two hydrogen ˚ ; interaction energies in the range of atoms, 2.4 A weak conventional HBs (3–7 kcal molK1); large couplings ð1 JHH 0 Z 2K 4Þ between the AH (AZO) and the MH (MZ Ir) protons. These interactions seem to play a role in proton transfer, fluxional processes and other reactions [5,6]. Since the discovery of DH bonds, several experimental and theoretical studies have been reported [7–15]. Wil et al. [7] studied the B–H/H–N dihydrogen bond including the crystal structure of BH3NH3 by neutron diffraction. Glenn et al. [8] measured the deuterium quadrupolar coupling constants and investigated the molecular reorientation of the BD3 and ND3 in solid by deuterium nuclear magnetic resonance (NMR) powder spectra and spin-lattice relaxation times. The interaction of proton donors with Bu4NBH4 and BH3NEt3 in hexane and dichloromethane was studied by IR and NMR spectroscopy and it was found the protonaccepting center of interaction of charged and neutral borohydrides with proton donors in solution is the hydrogen atom [9]. To improve the understanding of dihydrogen bonds (DHBs), Thomas et al. [10] carried out an ab initio theoretical study on the [H3BNH3]2 dimer, by the PCIB3LYP method. Popilier [11] characterized a dihydrogen bond by means of AIM quantities. Although not computing the binding energy, Poplier discussed the characteristics of the B–H/H–N H bond on the basis of electron density. Liu and Hoffmann [12] studied the nature of the intramolecular hydrogen–hydrogen interaction in iridium complexes using the extende Hu¨ckel method and the FH/LiH complex at the RHF/6-31G* level. The systems studied by Alkorta, K Elguero et al. [13,14] are BHK 4 /HCN, BH4 /CH4, LiH/ C NH4 , LiH/HCN, LiH/HCCN, BeH2/NHC 4 , BeH2/ HCN and CH4/NHC , and Jinshan et al. [15] investigated a 4 series of BH3NH3 complexes using the Moller–Plesset second-order prturbation theory (MP2) and the 6-31CCg (d,p) basis set. Recently, density functional theory (DFT) has been accepted by the ab initio quantum chemistry community as a cost-effective approach for the computation of molecular structure, vibrational frequencies, and energies of chemical reactions. Many studies have shown that molecular structures and vibrational frequencies calculated by DFT methods are more reliable than MP2 methods [16–18]. While there is sufficient evidence that DFT provides

an accurate description of the electronic and structural properties of solids, interfaces and small molecules, relatively little is known about the systematic performance of DFT applications to molecular associates. B3LYP is a hybrid method, which includes a mixture of the HF exchange with DFT exchange-correlation. This functional described as Becke3 (B3) is the three-parameter exchange functional containing Slater exchange functional, HF and Beche’s 1988 gradient correction and LYP (Lee–Young– Parr) correlation functional. In this paper we focus on BH3NH3 (borane monoammoniate)-containing complexes: BH3NH3 dimer and BH3NH3 complexes of methane, hydrogen cyanide, ammonia, water, methanol, and hydrogen fluoride. To further access the reliability of DFT methods applied to this field of chemistry in this paper, we discuss the structure and bonding of the BH3NH3 complexes as obtained by high level ab initio calculations. We thus report geometry optimization and calculate bonding energies between BH3NH3 complexes for a variety of theoretical models and basis sets. The influence of basis sets on the BSSE, intermolecular distance and correlating interaction energy is also discussed in detail. The similarity and difference of ab initio and DFT results are analyzed. In addition, the vibrational frequencies of the monomer and the stationary complexes are calculated; the intramolecular frequencies and their shifts due to the complex formation are analyzed. Finally, as compared to the isolated gas phase results, we pay some attention to the influence of solvent effects in both structure and stability of BH3NH3/HF complex.

2. Computational methods It is well known in the SCF model, the electrostatic, exchange and some induction-polarization effects are included. In more recent years, it has been learnt that the induced-induced dispersion interaction may be of great importance [19,20], it is therefore necessary to go beyond the SCF model and include some of the correlation effects. So in the present paper, a variety of theoretical methods have been used in the research, including the Hartree–Fock (SCF), the Second-Order Moller–Plesset theory (MP2) as well as the hybrid density functional methods B3LYP in order to test the reliability of these methods to the hydrogen bonding systems. For hydrogen bonding, it is expected that both diffuse and polarization functions may be necessary in the basis sets, we thus analyze the separate influence of the diffuse and polarization functions. The different geometries of monomers and complexes, BH3NH3/CH4, BH3NH3/HCN, BH3NH3/BH3NH3, BH3NH3/NH3, BH3NH3/H2O, BH3NH3/CH3OH and BH3NH3/HF, have been carried out using SCF, MP2 and B3LYP correlation methods with the 6-31g, 6-31g(d), 6-31Cg(d), 6-311CC

Y. Meng et al. / Journal of Molecular Structure: THEOCHEM 713 (2005) 135–144

g(d,p) and 6-311CCg(2d,2p) basis set along with analytic vibrational frequency calculations. Interaction energies are calculated for the BH3NH3 complexes hydrogen bond by taking the energy difference between the monomers and the complex. Eint Z EðBH3 NH3 Þ C EðXÞ K EðBH3 NH3 XÞ

(1)

Where EðBH3 NH3 Þ , E(X) and EðBH3 NH3KXÞ are the electronic energies of BH3NH3, X (XaCH4, HCN, NH3, BH3NH3, H2O, CH3OH, HF) and complex system, respectively. To correct the basis set superposition error (BSSE), the counterpoise (CP) method [21] is employed. In this case, the corrected Eint is given by EintðcpÞ Z EðBH3 NH3 Þcp C EðXÞcp K EðBH3 NH3 XÞ

(2)

Where EðBH3 NH3 Þcp and E(X)cp are computed with the basis set of the BH3NH3 complex. Moreover, the zero-point vibrational energy (ZPVE) corrections are also applied in the present case. All quantum chemical calculations were performed with the GAUSSIAN 98 suit of programs [22].

3. Results and discussion 3.1. Structure of BH3NH3, CH4, HCN, H2O, NH3 and HF monomers The structures of the super molecule will depend on the structures calculated for the BH3NH3, CH4, HCN, NH3, H2O, CH3OH and HF monomers. The calculated structures of these monomers using DFT method at 6-311CCg(d,p) basis set are presented in Table 1. For comparison, results of MP2 at 6-31Cg(d), HF at 6-311CCg(d,p) level are also given in Table 1. For simplicity, the result with 6-31 g, 6-31g(d), 6-31Cg(d) and 6-311CCg(2d,2p) are not listed. A general observation from comparing the calculated structural parameters is that all HF bond distance are shorter than the MP2 and B3LYP results. This may be due to the result of the neglect of the electron correlation by HF theory. Considering all geometric parameters obtained with different theoretical model at varied basis sets, as expected, the 6-31g predicted the bond length in relatively poorly agreement with the experimental values. When polarization and diffuse functions are added, the results are improved. MP2 and B3LYP at 6-311CCg(d,p) basis set level reproduce the experimental values most satisfactorily for the monomers. The HF bond distances are slightly shorter than the experimental ones. When the basis sets are enlarged to 6-311CCg(2d,2p), the difference between the B3LYP calculated and experimental results may be negligible. There have been numerous theoretical investigations of the molecular structure and physical properties of BH3NH3, including geometry, dipole moment, electric fields, electric field gradients, diamagnetic shielding and susceptibility,

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Table 1 ˚ and degree) for BH3NH3, CH4, HCN, Selected geometrical parameters (A H2O, NH3 and HF monomers Parameters BH3NH3 B–N B–H N–H H–B–N B–N–H H–B–H H–N–H CH4 C–H H–CH H2 O H–O H–O–H HF H–F CH3OH O–C O–H C–H H–C–H H–C–H 0 O–C–H C–O–H NH3 N–H H–N–H HCN C–N C–H H–C–N

B3LYP

HF

MP2

1.666 1.208 1.071 104.8 111.1 113.7 107.8

1.679 1.210 1.002 104.6 110.8 113.8 108.2

1.664 1.211 1.021 104.7 111.2 113.8 107.7

1.091 109.5

1.084 109.5

1.091 109.5

0.962 105.1

0.941 106.3

0.971 105.5

0.922

0.897

0.941

1.424 0.961 1.097 108.4 109.0 106.7 109.0

1.400 0.940 1.082 108.5 108.9 111.8 110.0

1.431 0.972 1.089 109.4 109.0 111.7 108.7

1.015 108.0

1.000 108.4

1.013 107.3

1.149 1.067 180.0

1.149 1.067 180.0

1.178 1.071 180.0

B–N bond dissociation energy, torsional barrier and vibrational frequencies [23–27]. In this work, for BH3NH3 monomers, it is clear that the effect of correlation is negligible, the most pronounced difference being a shorter B–N bond. 3.2. Geometry of the BH3NH3 complex and interaction energies The following question is how the monomer’s geometry changes when bound in the BH3NH3 complexes. To improve our understanding of this system, we carried out DFT (B3LYP) theoretical studies on BH3NH3 dimer and BH3NH3 complexes firstly. The numbering schemes for the optimized structures of BH3NH3 dimer and BH3NH3 complexes at B3LYP/6-311CCg(d,p) level are given in Fig. 1, and details of their geometries can be found in Table 2. Previous ab initio calculations [10] using a different level of theory on the dimer reported five different optimized structures, one of which turned out to be a transition state. Jinshan Li et al. [15] proposed several possible structure for the BH3NH3/CH4, BH3NH3/HCF, BH3NH3/NH3 and BH3NH3/HF complexes, and some

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Fig. 1. Schematic representations of the B3LYP/6-311CCg(d,p) optimized structures of the BH3NH3 complexes in this study. All open symbols stand for hydrogen atoms.

of the structures have one or two imaginary frequency. Since the purpose of this paper is to systematically explore the interaction and changes of the geometry and vibrational spectroscopy between the complexes of BH3NH3 and monomers, for every complex, we concentrate on one particular minimum. Structure S1 belongs to the optimized structures of the BH3NH3/CH4 complex. For S1 the H/H distance (rH/H) ˚ and longer than 2.4 A ˚ (the sum in the B–H/H–C is 2.929 A of the van der Waals radii for two hydrogen atoms), The B3LYP/6-311CCg(d,p) calculated interaction energy for S1 is 2.0 kJ molK1 (see Table 4), so the interaction between BH3NH3 and CH4 is very weak. The B–N bond length ˚ ) upon formation of changes very slightly (0.003 A BH3NH3/CH4 complex. For S2, the optimized structure of BH3NH3/HCN ˚ . The complex, the rH/H in the B–H/H–C is 2.211 A B3LYP/6-311CCg(d,p) calculated interaction energy for S2 is 18.9 kJ molK1 and falls within the range of binding energy (3–7 kcal molK1) of the DH bond. Thereby, relatively strong B–H/H–C bond exists in S2. Compared ˚, to the monomers, the B–N bond is decreased by 0.012 A

implying that the interaction between BH3NH3 and HCN can strengthen the B–N bond. This is understandable form the fact that the proton in HCN is attached to SP hybridized carbon and more acidic compared with the proton in methane. With respect to S3, the optimized structures of the BH3NH3/NH3 complex, the rH/H in the B–H/H–N ˚ and beyond the range of distance of DH bond is 2.662 A ˚ ,) mentioned in the introduction. In the paper of (1.7–2.2 A Jinshan Li et al. [15], they confirmed that there is no charge transfer the BH3NH3/NH3 complex, so it is concluded that there is no DH bond in the BH3NH3/NH3 complex. There exists only classic H bond in this complex. Compared to ˚. the monomers, the B–N bond is decreased by 0.019 A The B3LYP/6-311CCg(d,p) calculated interaction energy for S3 is 38.3 kJ molK1. Structure S4 is the optimized structures of the BH3NH3 dimer. Compared to the monomers, the B–N bond is ˚ . All B–H and N–H bonds involved in decreased by 0.026 A the DHBs elongate the B–H bonds more than the N–H bonds. All bonds not directly participating in the B–H/H– N bond shrink slightly. The bond angles all remain stable

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Table 2 ˚ and degree) of BH3NH3 dimer and BH3NH3 complexes at B3LYP/6-311CCg(d,p) level Selected intermolecular geometrical parameters (A S1 B1–N5 B1–H2,H4 B1–H3 N5–H6 N5–H7,H8 H3–B1–N5 S2 B1–N5 B1–H2,H3 B1–H4 N5–H6,H7,H8 S3 B1–N5 B1–H2,H3 B1–H4 N5–H6,H7 N5–H8 S4 B1–N5 B1–H2 B1–H3,H4 N5–H6 N5–H7,H8 H2–B1–N5 H3,H4–B1–N5 B1–N5–H6,H7 B1–N5–H8 S5 B1–N5 B1–H2 B1–H3 B1–H4 N5–H7,H8 S6 B1–N5 B1–H2 B1–H3 B1–H4 N5–H6,H7 N5–H8 H2–B1–N5 S7 B1–N5 B1–H2,H4 B1–H3 N5–H7 N5–H8

1.663 1.208 1.209 1.018 1.017 104.9

H2,H4–B1–N5 B1–5N–H6,H7,H8 C10–H9 C10–H11,H12 C10–H13 H11–C10–H9

105.0 111.1 1.093 1.091 1.092 109.8

H11–C10–H12 H11–C10–H13 H12–C10–H9 H12–C10–H13 H13–C10–H9 H13–H3

109.2 109.6 108.7 109.0 110.5 2.929

H13–H6 B1–H3–H13 H3–H13–C10

2.467 108.3 153.5

1.654 1.210 1.205 1.018

H2,H3–B1–N5 H4–B1–N5 B1–N5–H6,H7 B1–N5–H8

105.2 105.7 111.0 111.6

C9–H11 C9–N10 H11–C9–N10 H3–H11

1.074 1.150 179.3 2.211

B1–H3–H11 H3–H11–C9

95.2 151.6

1.647 1.213 1.209 1.017 1.034

H2–B1–N5 H3–B1–N5 H4–B1–N5 B1–N5–H6,H7 B1–N5–H8

105.4 105.3 106.9 111.5 108.9

N9–H10 N9–H11,H12 H10–N9–H11,H12 H11–N9–H12 H8–N9

1.018 1.016 107.5 107.3 1.987

H3–H10 B1–H3–H10 H3–H10–N9

2.662 89.5 120.2

1.640 1.205 1.214 1.027 1.017 107.3 105.8 111.3 111.1

B9–N10 B9–H11 B9–H12 B9–H13 N10–H14 N10–H15,H16 H11–B9–N10 H12–B9–N10 H13–B9–N10

1.640 1.205 1.217 1.211 1.027 1.017 107.3 105.7 106.0

B9–N10–H14 B9–N10–H15 B9–N10–H16 H6–H12 H6–H13 H14–H3 H14–H4 B1–H3–H14 B1–H4–H14

111.2 111.0 111.4 1.898 2.238 2.126 1.965 85.7 93.2

B9–H12–H6 B9–H13–H6 H3–H14–N10 H4–H14–N10 H12–H6–N5 H13–H6–N5

97.8 81.9 144.6 147.4 157.7 135.4

1.649 1.218 1.206 1.209 1.017

N5–H9 H2–B1–N5 H3–B1–N5 H4–B1–N5 B1–N5–H7

1.025 105.2 106.9 105.6 111.3

B1–N5–H8 B1–N5–H9 O6–H10 O6–H11 H10–O6–H11

111.6 109.3 0.971 0.962 106.1

H9–O6 H2–H10 B1–H2–H10 H2–H10–O6

2.009 1.929 104.9 141.9

1.648 1.217 1.207 1.209 1.017 1.027 105.2

H3–B1–N5 H4–B1–N5 B1–N5–H6 B1–N5–H7 B1–N5–H8 C9–O10 C9–H11

107.0 105.6 111.4 111.6 109.0 1.426 1.090

C9–H12 C9–H13 O10–H14 H11–C9–O10 H12–C9–O10 H13–C9–O10 C9–O10–H14

1.096 1.095 0.969 107.1 117.1 111.4 109.6

H11–C9–H12 H11–C9–H13 H12–C9–H13 H2–H14 H8–O10 B1–H2–H14 H2–H14–O10

108.9 108.5 109.2 1.956 1.978 104.0 141.2

1.647 1.203 1.225 1.021 1.017

N5–H9 H2–B1–N5 H3–B1–N5 H4–B1–N5 B1–N5–H7

1.018 106.9 105.8 106.1 110.6

B1–N5–H8 B1–N5–H9 H10–F6 F6–H7 H10–H3

110.7 111.7 0.949 2.184 1.503

B1–H3–H10 H3–H1–F6

109.0 159.9

within 28. Finally when considering the newly formed bond distances and angles, there contains four B–H/H–N bond in the BH3NH3 dimer, the distances of H/H bonds are 2.238, 1.898, 1.965 and 2.126, respectively, the B–H/H bond angles are 81.8, 97.8, 93.2 and 85.7, respectively, the N–H/H bond angles are 135.4, 157.7, 147.4 and 144.6 respectively. For the B–H/H angles the experimental ranges have also been proposed from 90 to 1718 and for the N–H/H bond angle from 117 to 1718. So all computed DHBs fall in their respective range, the average of the B–H/H bond angles and the N–H/H bond angle coinciding with the experimental values. All of the H/H

˚) contact distances shrink considerably (by almost 0.2 A under the influence of correlation and the discrepancy for N–H/H and the B–H/H bond angles can amount to 58. For S4 the B3LYP/6-311CCg(d,p) calculated interaction energy is 53.8 kJ molK1 at B3LYP/6-311CCg(d,p) level, 17.9 kJ molK1 per H-bond if we assign one-quarter of the total energy to each H-bond, this is well within the range of binding energy of the DH bond, and shows that the BH bond is a surprisingly effective base. So combined with the optimized structure S4 we can conclude that there contains four DH bonds in the BH3NH3 dimer practically. This result is different from the previous studies by Thomas et al. [10]

1.572 1.627 1.520 1.503 1.514 1.848 1.681 1.825 1.936 1.977 1.978 2.007 2.091 1.973 1.915 1.920 1.980 1.956 1.937 2.329 2.047 1.830 1.889 1.948 1.929 1.915 2.352 2.033 1.848 1.971 2.007 2.009 2.041 2.089 2.007 2.068 2.072 2.095 2.238 2.074 2.228 2.097 1.998 2.009 2.039 1.898 2.012 2.203 2.054 2.061 2.073 2.082 1.965 2.068 2.230 2.097 2.004 2.010 2.049 2.126 2.017 2.204 2.053 2.508 2.575 2.672 2.662 2.652 2.904 2.606 1.822 1.912 1.974 1.987 2.003 2.151 2.002 2.192 2.187 2.213 2.211 2.208 2.365 2.204 2.297 2.350 2.531 2.467 2.444 2.797 2.413 2.679 2.655 3.783 2.929 3.075 3.440 2.802 B3LYP/6-31 g B3LYP/6-31g(d) B3LYP/6-31Cg(d) B3LYP/6-311CCg(d,p) B3LYP/6-311CCg(2d,2p) HF/6-311CCg(d,p) MP2/6-31Cg*

S7

r3/10 r8/10

S6

r2/14 r2/10

S5

r6/9 r6/13 r6/12 r4/14

S4

r3/14 r3/10 r8/9

S3 S2

r3/11 r6/13 r3/13

S1 Method

Table 3 ˚ ) obtained at different levels Intermolecular distances (A

1.908 1.945 2.184 2.184 2.171 2.327 2.212

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r6/7

140

and Popelier [11]. Using the PCI-80/B3LYP method, Thomas et al. [10] concluded that there contains two B–H/H–N DHBs of structure very similar to the bent ones ˚ . In found in the crystallographic study, with rH/H is 1.82 A the study of Popelier [11], there are three DHBs in BH3NH3 dimer, two of which are identical due to the presence of a mirror plane (Cs symmetry). Structure S5, S6, S7 belong to the optimized structures of the BH3NH3/H2O, BH3NH3/CH3OH and BH3NH3/HF complexes. From the three structures it can be seen that the ˚ H/H contact distance (rH/H) are 1.929, 1.956 and 1. 503 A in all the B–H/H–X (XaO, F) bonds, respectively, which all fall within the contact distance of DH bond. The B–H/H bond angles are 104.9, 104.0 and 109.08, respectively, and the X–H/H bond angles are 141.9, 141.2 and 159.98, respectively. All the B–H/H bond angles tends to be bent. The X/H distance between the three kinds ˚, of BH3NH3 complexes are 2.009, 1.978 and 2.184 A ˚ respectively, and all shorter than 2.4 A, the B3LYP/ 6-311CCg(d,p) calculated interaction energies are 34.4, 33.9 and 52.8 kJ molK1, respectively, so both DH bond and N–H/X H bond exist in these three complexes. Compared to the isolated molecule, the B–N bond decreases by 0.017, ˚ , respectively, implying the hydrogen 0.018 and 0.019 A bonding formed between BH3NH3 and H2O, CH3OH, HF can strengthen the B–N bonds. In summary, among the B–H/H–X (XaC, N, O, F) DHBs we discussed, the B–H/H bond angles vary between 81.9 and 109.08, the X–H/H bond angles vary between 135.4 and 159.98, which corroborate the conclusion that the B–H/H–X bond is strongly bent at both ends. The strong bending of the B–H/H–X bond angle is a notable feature of DH bonds. This is rationalized by the boron is very negative and is at the negative end of the B–H dipole, so that a collinear X–H/H–B arrangement would lead to an unfavorable (KC)–(CK) arrangement of the two dipoles. It is therefore understandable that the H–B dipole should rotate so as to become more favorably aligned, resulting in a side-on structure. The H/H contact distances in the DHBs ˚ , which are agreement with vary between 1.503 and 2.238 A the CSD investigation mentioned in the introduction ˚ . In proposed the range of H/H distances to be 1.7–2.2 A summary we may conclude that our computed DHBs share the purely geometrical characteristics previously determined [10]. At the same time, with respect to corresponding values of isolated molecules, the B-H and X-H bonds involved in the DHBs all are elongated. The optimized intermolecular distances and the binding energy for the same interacting structure are different at different computational levels. To analyze in more detail the role of basis set size effects on the optimized intermolecular distances and binding energy of the BH3NH3 dimer and BH3NH3 complexes, the Tables 3 and 4 give a detailed analysis of the intermolecular distances and binding energy obtained with several different theoretical models.

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141

Table 4 Interaction energies of BH3NH3–X (XaBH3NH3, CH4, HCN, H2O, NH3, HF) complexes (kJ molK1) Methods

S1

S2

S3

S4

S5

S6

S7

B3LYP/6-31g ZPVE corrected B3LYP/6-31g(d) ZPVE corrected B3LYP/6-31Cg(d) ZPVE corrected B3LYP/6-311CCg(d,p) ZPVE corrected B3LYP/6-311CCg(2d,2p) ZPVE corrected HF/6-311CCg(d,p) ZPVE corrected MP2/6-31Cg* ZPVE corrected

4.7 (2.4) 1.6 3.9(2.1) 1.3 2.4(1.6) 0.3 2.0 (1.8) 0.5 1.8 (1.8) 0.0 1.3(0.7) 0.3 5.5(2.9) 2.9

22.1 (21.6) 18.1 22.1(20.7) 17.9 20.0(19.4) 16.0 18.9 (18.6) 15.2 18.6(18.6) 15.2 17.1(17.1) 14.2 22.6(18.9) 17.6

60.0 (57.0) 49.4 50.1(45.7) 41.5 41.0(38.1) 33.1 38.3 (37.3) 30.5 34.7(34.9) 27.3 30.0(28.9) 22.3 30.0(27.0) 22.1

65.4 (61.2) 58.0 62.0(58.3) 55.1 55.4(54.3) 48.8 53.8 (53.3) 47.0 52.8(52.8) 46.2 42.0(42.0) 34.9 60.9(53.6) 53.0

60.6(50.7) 49.6 49.1(39.6) 39.4 38.1(36.2) 28.9 31.5 (31.4) 27.6 33.9(33.6) 24.4 29.1(28.1) 21.0 42.3(35.2) 33.1

58.5 (45.7) 50.7 48.3(38.9) 41.0 37.8(37.0) 31.2 36.8 (36.3) 29.9 34.4(33.9) 27.6 29.4 (28.6) 23.4 44.6(39.4) 37.5

68.3 (57.0) 57.0 60.1(51.2) 49.6 41.5(41.5) 32.0 40.7 (39.8) 31.0 40.2(40.2) 30.2 28.4(26.3) 19.7 40.4(34.7) 31.0

*Values in parenthesis are results with correction for basis set superposition.

Larger basis functions generally tend to produce longer intermolecular distance, since larger basis sets increase the electronic repulsion. From Table 3 it can be seen that some of the HF values for H/H distance do not fall in the range of DH distance, most of others fall in this range. B3LYP or MP2 method, which incorporate the electron correlation, generate longer bond lengths and produce shorter intermolecular distances compared with those of HF method. The contact distances at the B3LYP/6-311CCg(d,p) and MP2/6-31CG* are very similar. In Table 4, the numbers shown in parenthesis are corrected for BSSE using the CP method of Boys and Bernadi [21]. As expected, basis set sensitivity exists. The interaction energy computed with B3LYP using the minimal basis set 6-31 g is much higher. As the basis set enlarged, the computed values decreases and converge smoothly. The general importance of including BSSE corrections in calculated binding energies has been well documented in the literature. From Table 4 it can be seen that the magnitude of BSSE are decreasing with the basis set enlarged, when the diffusion and polarization functions are considered, especially for the 6-311CCg(d,p) and 6311CCg(2d,2p) basis set using B3LYP method, the inclusion of BSSE correction has minor importance to the binding energy. It was also true for SCF/6-311CCg(d,p) level. On the other hand, the ZPE corrections for the binding energies are much less than those of BSSE. 3.3. Vibrational frequencies and their shifts The vibrational spectroscopy is one of the most useful experimental tools for the study of H bond clusters, so the information on calculated harmonic vibrational frequencies can be useful. For BH3NH3 dimer and BH3NH3 complexes there are few studies on the vibrational spectra. Table 5 lists the frequencies, intensities of monomer BH3NH3, BH3NH3 dimer and BH3NH3 complexes for

the B–N, B–H and N–H stretch modes at B3LYP/6-311CC g(d,p)level. Table 6 gives the B3LYP/6-311CCg(d,p) values for both vibrational frequencies and IR intensities of the methane, hydrogen cyanide, ammonia, water, methanol, and hydrogen fluoride monomers and BH3NH3 complexes. On the basis of optimized geometry, the vibrational modes and frequencies of the BH3NH3 complexes and monomers have been assigned. Since the frequency shifts are relatively stable with respect to theoretical methods, one can estimate the IR spectrum for the complex by combining the observed fundamental vibrational frequency of its moieties and the frequency shift in Tables 5 and 6. With respect to IR intensities, most of them are IR-active. For the isolated BH3NH3 molecule, the asymmetric and symmetric N–H stretches appear at 3560.2 and 3560.3 cmK1, the asymmetric B–H stretches appear at 2484.2, 2485.0 cmK1, and symmetric B–H stretches appear at 2436.3, while the N–B stretch is at 631 cmK1. The B–N stretching frequency is found to increase for all structures considered here. Form S1 to S7, the frequency shifts are 5.5, 30.1, 47.1, 42.1, 43.3, 51.6 and 65 cmK1, respectively. This is in consistent with the bond distance change discussed above, implying that the formation of BH3NH3 complexes can strengthen the B–N bond. From Table 5 it is obtained the symmetric stretching mode of B–H is red shifted during the formation of BH3NH3 complexes. And with strengthen of interaction between subsystems, the frequency shifts and IR intensities tend to increase. For instance, the interaction between subsystems for S1 is very weak, and the change of vBH is slightly (within 4 cmK1) compared with the corresponding vBH in isolated BH3NH3 molecule, whose IR intensity decreases. While for S5 to S7 in which both classic H bond and DH bond occur, the changes of vBH (44.7, 43.0, 93.8 cmK1) and IR intensity (125.1, 116.8, 262.8 km molK1) are dramatically, the change of IR intensity for S7 is 5.2 times. With respect to asymmetric stretching modes of B–H, both red shifts

13.2 325.4 151.4 200.2 1.3 112.7 59.6 682.6 2342.5 2489.2 2532.4 3436.6 3524.9 3545.0 674.3 2393.3 2454.2 2488.4 3356.8 3513.2 3564.3 11.6 187.7 197.8 257.4 137.8 58.0 29.0 673.1 2391.6 2457.9 2492.3 3379.6 3515.7 3563.8 2.0 179.0 93.4 523.5 25.6 76.8 19.4 16.6 62.6 69.3 268.9 2.4 30.9 30.8 631.0 2436.3 2484.2 2485.0 3460.3 3560.2 3560.3

N–B stretch H–B sym stretch H–B anti stretch H–B anti stretch H–N sym stretch H–N anti stretch H–N stretch

9.6 106.9 223.0 249.3 4.0 36.5 37.8 661.1 2432.7 2471.8 2503.8 3458.3 3555.0 3556.6 15.9 59.5 274.8 266.1 5.4 53.9 30.9 636.5 2434.7 2480.3 2483.6 3458.0 3555.0 3560.4

678.1 2412.1 2441.6 2468.1 3225.1 3504.2 3562.7

11.1 82.5 285.3 295.4 490.3 39.3 21.2

696.0 2409.9 2434.7 2493.3 3340.7 3506.1 3559.2

v

S6

I S5

v I v

S4

v

I S3

v

I S2

I v

S1

Assignment I v

BH3NH3

Table 5 The selected frequencies and IR intensities (cmK1 and km molK1) of BH3NH3 monomer, dimmer and complexes at B3LYP/6-311CCg(d,p) level

11.3 179.4 194.3 270.5 206.9 60.3 28.2

I

v

I

Table 6 The frequencies and IR intensities (cmK1 and km molK1) of CH4, HCN, NH3, H2O, CH3OH, HF monomers and complexes at B3LYP/6-311CCg (d,p) level

v

Y. Meng et al. / Journal of Molecular Structure: THEOCHEM 713 (2005) 135–144

S7

142

CH4 1339.5 1339.6 1339.7 1557.5 1557.6 3026.2 3131.3 3131.4 3131.7 HCN 766.4 766.4 2195.6 3452.5 NH3 1003.6 1668.3 1669.2 3481.3 3607.0 3608.5 H2 O 1601.3 3818.9 3925.2 CH3OH 297.7 1041.7 1070.4 1167.4 1356.2 1479.6 1493.3 1505.2 2989.6 3036.8 3113.4 3846.9 HF 4096.0

I

Assignment 18.1 18.0 18.1 0.0 0.0 0.0 26.0 26.2 26.0

C–H bend out of plane C–H bend out of plane C–H bend out of plane C–H rock out of plane C–H rock out of plane C–H sym stretch C–H anti stretch C–H anti stretch C–H stretch

42.4 42.4 1.9 67.2

C–H rock C–H rock N–C–H anti stretch C–H stretch

1.2 1.1 1.1 1.9 3.6 3.7 67.1 9.3 56.6 134.7 128.1 1.2 0.2 20.9 5.1 3.3 5.0 68.3 63.7 27.2 30.0 130.1

N–H rock out of plane N–H rock N–H bend in plane N–H sym stretch N–H anti stretch N–H stretch O–H bend in plane O–H stretch O–H anti stretch O–H rock C–O stretch O–H rock H–Crock O–H rock C–H rock out of plane C–H bend C–H scissoring C–H sym stretch C–H anti stretch C–H stretch O–H stretch

V S1 1335.7 1339.7 1354.1 1560.4 1561.9 3017.5 3115.8 3127.1 3131.1 S2 810.8 842.2 2185.7 3361.2 S3 1114.3 1654.9 1670.9 3463.2 3575.2 3593.9 S5 1615.6 3702.1 3892.5 S6 547.9 1048.2 1073.9 1170.5 1394.4 1477.9 1495.9 1509.1 3004.2 3058.4 3112.9 3717.0 S7 3545.0

I 31.4 29.3 3.8 0.6 1.0 2.4 26.1 14.1 19.0 26.7 33.4 30.1 290.4 106.8 14.8 14.4 7.5 22.4 9.6 64.6 169.7 100.2 135.6 173.4 37.4 0.5 66.3 4.9 4.1 4.4 69.4 46.2 29.9 221.0 808.3

and blue shifts occur during the formation of BH3NH3 complexes. For S2 and S4, in which only DH bond exists, the X–H (XaC, N) stretching mode is red shifted, especially for S2, whose IR intensity increases dramatically from 67.2 to 290.4 km molK1, (see Table 6). N–C–H anti stretching for S2 is also red shifted, while two degenerate C–H rock mode are blue shifted. For S3, in which only N–H/N H bond appears, all N–H symmetric and asymmetric stretching are red-shifted, and IR intensities are increased. It is worth mentioning that the shift of vNH symmetric stretching for S3 is 235.2 cmK1, whose IR intensity changes from 2.4 to 490.3 km molK1.

Y. Meng et al. / Journal of Molecular Structure: THEOCHEM 713 (2005) 135–144

Fig. 2. The optimized structure of BH3NH3/HF complex in solution phase. All open symbols stand for hydrogen atoms.

For S5, S6 and S7, in which both classic H bond and DH bond occur, the X–H(XaO, F) stretching appear is red shifted, whose IR intensity is increased largely. 3.4. Solution phase results Finally, the interaction of BH3NH3 with HF monomers has been studied in solution phase using DFT. All calculations for the solution phase work have been carried out at the B3LYP/6-311CCg(d,p) level of theory. The Onsager reaction field model has been used to treat solvent effects. In this work, we obtain results using water, DMSO and cyclohaxane as the solvents with dielectric constants of 78.39, 46.7 and 2.023, respectively. The optimized structures of BH3NH3/HF complex in cyclohaxane, DMSO and water are presented in Fig. 2. Structure F1 belongs to the optimized structure of BH3NH3/HF complex in cyclohaxane. When using DMSO and water as solvents, the structures are optimized fully and all converged on structure F2 with an imaginary frequency, this implies that it is not a true minima, but a transition state. From the calculation it can conclude that the geometry of BH3NH3/HF complex is slightly modified by solvent cyclohaxane. The optimized geometry in solution can be compared to previous geometry gas phase calculations at the ˚ for the R. In same level. The B–N bond shrinks by 0.003 A ˚ , while in the B–H/H–F bond, the rH/H shrinks by 0.02 A ˚ the classic H bond, the rH/F elongates by 0.1 A. The bond angle B1H3H10 changes from 109.0 to 107.88, while H3H10F6 changes from 159.9 to 162.38. For F2, when compared to the gas phase, the contact ˚ in solution. All the distance of B–N bond shrinks by 0.026 A B–H bonds lengthen while the N–H bonds remains stable. In ˚ . From Fig. 2 the B–H/H–F bond, rH/H decreases by 0.018 A it can conclude that there is only DH bond in the transition state. The bond angle B1H3H10 changes from 109.0 to 112.78, while H3H10F6 changes from 159.9 to 171.08

4. Conclusions BH3NH3 dimer and BH3NH3 complexes of methane, hydrogen cyanide, ammonia, water, methanol, and

143

hydrogen fluoride have been studied by ab initio, MP2 and B3LYP method employing different basis set levels to understand the features of dihydrogen bond. For the complexes investigated at the B3LYP/6-311CCg(d,p), DH bond does not occur in the optimized structures of both BH3NH3/CH4 and BH3NH3/NH3 complexes. Apart from the B–H/H–N dihydrogen bond found in the BH3NH3 crystal and dimmer, the B–H/H–X (XaC, O, F) DHBs have been observed in the BH3NH3/HCN, BH3NH3/H2O, BH3NH3/CH3OH and BH3NH3/HF complexes, while the classic H bonds also exist in the last three complexes. As for the complexes in which only DHBs appear the strength of DHBs ranges from 17.9 to 18.9 kJ molK1 at B3LYP/6-311CCg(d,p) level. Upon formation of BH3NH3 complexes, the weakest B–N bond contracts. The infrared spectrum frequencies, IR intensities and the vibrational frequency shifts are reported. The frequencies of the complexes are all IR-active and most of them have larger intensities, so one can estimate the IR spectrum for the complex by combining the observed fundamental vibrational frequency of its moieties and the frequency shift. Finally, the study of the solvent effect on the potential energy surface of BH3NH3/HF complex has been performed. In the description of solvent we have employed the Onsager reaction field model. The calculations are performed at B3LYP/6-31Cg(d,p) level. We found that the geometry and the stability of the system is appreciable modified by the solvent. We have also investigated the effect of varying the dielectric constant on the energies and geometries of the BH3NH3/HF interaction. The results show the polarity of the solvents has great effect on the complex.

Acknowledgements This work was supported by the Natural Science Foundation of Shandong Province (Z2002F01), the State Key Laboratory Foundation of Crystal Material, the National Natural Science Foundation of China (29673025) and the Qingdao University Research Fund for Financial Support (Project No. 2002[7]).

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