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A Short Yet Very Weak Dative Bond: Structure, Bonding, and Energetic Properties of N2-BH3 Elizabeth L. Smith,† Daniel Sadowsky,‡ James A. Phillips,*,† Christopher J. Cramer,‡ and David J. Giesen§ Department of Chemistry, UniVersity of Wisconsin - Eau Claire, 105 Garfield AVe., Eau Claire, WI 54702, Department of Chemistry and Supercomputing Institute, UniVersity of Minnesota, 207 Pleasant Street SE., Minneapolis, MN 55455, and Eastman Kodak Company, Building 83, Floor 2, RL, MC02216 Rochester, NY 14650-2216 ReceiVed: September 19, 2009; ReVised Manuscript ReceiVed: January 8, 2010
The structure, bonding, and energetic properties of the N2-BH3 complex are reported as characterized by density functional theory (DFT) and post-Hartree-Fock (HF) calculations. The equilibrium structure of the complex exhibits a short B-N distance near 1.6 Å, comparable to that of a strong acid-base complex like H3N-BH3. However, the binding energy is only 5.7 kcal/mol at the CCSD(T)/6-311+G(2df,2dp) level of theory, which is reminiscent of a weak, nonbonded complex. Natural bond orbital (NBO) and atoms in molecules (AIM) analyses of the electron density from both DFT and post-HF calculations do indicate that the extent of charge transfer and covalent character in the B-N dative bond is only somewhat less than in comparable systems with fairly large binding energies (e.g., H3N-BH3 and OC-BH3). Energy decomposition analysis indicates key differences between the N2, CO, and NH3 complexes, primarily associated with the natures of the lone pairs involved (sp vs sp3) and the donor/acceptor characteristics of the relevant occupied and virtual orbitals, both sigma and pi. Also, CCSD/6-311+G(2df,2dp) calculations indicate that the B-N distance potential is rather anharmonic and exhibits a flat, shelf-like region ranging from 2.1 to 2.5 Å that lies about 1.5 kcal/mol above the minimum at 1.67 Å. However, this region is more sloped and lies about 2.5 kcal/mol above the equilibrium region according to the CCSD(T)/6-311+G(2df,2dp)//CCSD/6-311+G(2df,2dp) potential. A 1D analysis of the vibrational motion along the B-N stretching coordinate in the CCSD/6311+G(2df,2dp) potential indicates that the average B-N distance in the ground vibrational state is 1.71 Å, about 0.04 Å longer than the equilibrium distance. Furthermore, the vibrationally averaged distance obtained via an analysis of the CCSD(T)/6-311+G(2df,2dp)//CCSD/6-311+G(2df,2dp) potential was found to be 0.03 Å longer than the CCSD(T)/6-311+G(2df,2dp) minimum. Introduction Much of our recent work has been concerned with condensedphase effects on the structural properties of nitrile-BF3 complexes1-7 as well as CH3CN-SO2.8 We have since extended these studies to nitrile-BH3 complexes,9 and two key observations led us to examine N2-BH3. First, the nitrile-BH3 complexes we examined were all quite strong, with binding energies of about 20 kcal/mol and short B-N distances of less than 1.6 Å, even with weak nitrile donors like CF3CN-BH3. Furthermore, because we rely upon accurate calculated gasphase vibrational frequencies to assess condensed-phase effects on structure via IR spectroscopy,1,2,4-6,8 we sought a density functional that would adequately reproduce the measured frequencies of BH3.10 However, we were initially unable to find a method that provided satisfactory agreement with experimental data (rms errors exceed 100 cm-1), in spite of the fact that we had previously identified several DFT methods that accurately predict BF3 frequencies (with rms error of about 7 cm-1).3 At this point, we have partially remedied this situation via anharmonic corrections to the frequencies,9 but prior to this, * Author to whom correspondence should be addressed. E-mail:
[email protected]. † University of Wisconsin - Eau Claire. ‡ University of Minnesota. § Eastman Kodak Company.
we became suspect of a fair degree of inconsistency among frequency measurements in the earlier literature,10a which included measurements in nitrogen matrices. Given the apparent strength of nitrile complexes, we were led to consider whether there was a particularly strong interaction between N2 and BH3 that was causing some of the inconsistency in the measured frequency data. This no longer appears to be the case, but in the process of investigating this, we found that N2-BH3 did exhibit some rather novel structural and energetic properties, and we report these herein. When we first calculated the structure of N2-BH3 via B3PW91/aug-cc-pVTZ, which has provided accurate results for weaker nitrile-BF3 systems,3,5 we were struck by the short B-N distance (vide infra), that was actually shorter than that for H3N-BH3,11 which seemed to imply the formation of a strong dative bond to molecular nitrogen. For reference, we note that the gas-phase proton affinity of N2 is 494 kJ/mol, about 350 kJ/mol less than the corresponding value for NH3 (854 kJ/mol).12 We then found that earlier studies on this complex had produced mixed results. A structure with 1.52 Å B-N distance was obtained from a CNDO calculation,13 but an HF/4-31G calculation predicted a distance of 2.644 Å,14 more typical of a van der Waals complex like N2-BF3.15 More recently, two studies involving N2-BH3 have appeared in the literature. By using B3LYP and BP86 with the 6-311+G** basis set, Li and Shu16
10.1021/jp909059n 2010 American Chemical Society Published on Web 02/02/2010
Structure, Bonding, and Energetic Properties of N2-BH3 obtained a structure with a B-N distance of 1.52 Å, and furthermore, an NBO analysis17 of the DFT density indicated that the boron atom was nearly sp3-hybridized and had a significant negative charge due to σ-donation from N2. Khaliullin et. al18 examined N2-BH3 as part of a larger effort focused on deconvoluting the interaction energies of a wide variety of complexes. They too found a short B-N distance for N2-BH3 (1.56 Å) via B3LYP/6-31++G(d,p) and a calculated binding energy of 7.2 kcal/mol, and their analysis indicated that N2 acts as a relatively weak, yet balanced σ-donor and π-acceptor in this system. Surprisingly, neither of these studies commented on the marked difference between these recent DFT results and the previously reported HF structure, which depict two very different types of complexes. Here, we report results obtained from a few additional DFT methods with larger basis sets up to aug-cc-pV5Z, MP2 results with basis sets up to aug-cc-pVTZ, as well as the results of high-level post-Hartree-Fock (HF) methods, including MP4 and coupled cluster with basis sets up to 6-311+G(2df,2pd).19 To some extent, these higher-level methods reconfirm the DFT structural results, but post-HF methods do predict a B-N distance that is somewhat longer than that obtained via DFT. Moreover, they also predict a much smaller binding energy, which is quite surprising given the short B-N distance. In an attempt to better understand the bonding in this system, we conducted natural bond orbital (NBO)17 and atoms in molecules (AIM)20 analyses of the densities obtained via B3PW91, MP2, and MP4(SDQ) and drew comparisons among related systems, including OC-BH3, an iso-electronic complex in which the dative bond is quite strong and has a significant degree of covalent character.21 We additionally conducted energy decomposition analyses (EDA) of the bonding in N2-BH3 as well as OC-BH3 and H3N-BH3, which provide additional insight into factors that affect the bonds in these complexes. Finally, we undertook a thorough analysis of the B-N distance potential in order to highlight the mechanical properties of this peculiar B-N bond and explore the degree to which anharmonicity leads to a genuine difference between the equilibrium and vibrationally averaged distances. Computational Methods Most of the electronic structure calculations were carried out directly by using Gaussian03 (revision E).22 The majority of these were performed on a recently constructed, 8-node, 56CPU computational cluster at UW-Eau Claire. The main exceptions were the CCSD(T) optimization and the M06 calculations, which were performed on machines at the Minnesota Supercomputing Institute (MSI), and the latter were executed via the Minnesota Gaussian Functional Module (MNGFM),23 which calls Gaussian03. All equilibrium geometries were obtained by using the “opt ) tight” option, and an ultrafine grid was used for all DFT calculations. NBO17 and AIM20 analyses were also carried out directly in Gaussian. The EDAs were carried out using the Amsterdam Density Functional (ADF), version 2008.01,24-26 by using the method of Morokuma.27 For these calculations, the TZ2P basis set28 was used on hydrogen atoms, the ATZ2P basis set28 was used on all heavy atoms, and no use of the frozen-core approximation was made. We used the hybrid mPW1PW (i.e., mPW1PW91)19 functional, with geometries optimized with the generalized gradient approximation (GGA) mPW (i.e., mPWPW91),19 for the EDA results discussed in detail below, because this approach was the most comparable with the structural and energetic results obtained via Gaussian. An additional set of results was obtained
J. Phys. Chem. A, Vol. 114, No. 7, 2010 2629 by using the GGA BLYP19 functional, and these data are included below as well. Equilibrium geometries were optimized until Cartesian gradients with a maximum matrix element of 1.0 × 10-7 hartree/Å were reached, with the grid points being held fixed for the final cycles of the optimization procedure. In a few instances, a decomposed mapping of the donor-acceptor bond potential was also obtained by conducting the EDA analysis with the donor-acceptor distance frozen at the values noted below. All other degrees of freedom were optimized in this process, with a convergence criterion for the constrained gradient analogous to the one noted above but loosened to a value of 5.0 × 10-5 hartree/Å. The B-N potential was mapped in a stepwise manner, with 0.05 Å steps along the inner wall and near the equilibrium distance (from 1.35 to 1.75 Å) and with 0.1 Å steps from 1.8 to 3.0 Å. The vibrational motion along the B-N stretching coordinate was examined by using the FGHEVEN program,29 which provides vibrational wave functions and energy levels for a 1D system with an arbitrary potential function. The potential function was obtained by fitting the CCSD/6311+G(2df,2dp) and CCSD(T)/6-311+G(2df,2pd)//CCSD/6311+G(2df,2dp) potentials to two sixth-order polynomials: one for the inner wall out to 1.7 Å and one for the 1.65-3.0 Å range (i.e., with two common points among these ranges). The rms difference between the CCSD and CCSD(T) potentials and the fitted curves were 7 × 10-5 and 5 x10-5 hartree, respectively. The largest residual on the CCSD curve was 1.8 x10-4 hartree, and that on the CCSD(T) curve was 1.4 x10-4 hartree (both about 5% of the total energy at those points). The integration grid for the simulations consisted of 160 points spaced at 0.02bohr intervals, ranging from 2.3 to 5.5 bohr. Results and Discussion A. Equilibrium Structure and Binding Energy. We obtained our initial structural results by using the B3PW91 density functional with the aug-cc-pVTZ basis set, because this method and basis set had produced very favorable results for equilibrium geometries of weaker nitrile-BF3 complexes in our previous work.3,5 This structure is displayed in Figure 1. Initially, we had assumed the C3V-symmetric structure with the N2 subunit coordinating in an end-on manner. However, we did attempt a few additional optimizations that were initiated with the N2 subunit oriented in an approximate T-shape manner, but these also optimized to the end-on structure. Regardless, we were immediately struck by the incredibly short B-N distance of 1.540 Å, which is even shorter than that in the analogous ammonia complex by any measure. The experimental B-N distance for H3N-BH3 is 1.6576(19) Å,11 whereas that calculated in this work via B3PW91/aug-cc-pVTZ is 1.646 Å. Previously published MP2 results are quite consistent with this and range from 1.648 to 1.664 Å,21,25 whereas a recent B3LYP/ 6-31++G(d,p) result is 1.67 Å.18 At the MP2/aug-cc-pVTZ level, we subsequently found the B-N distance of N2-BH3 to be 1.623 Å, almost 0.1 Å longer than the DFT result, but still a bit shorter than that for the ammonia complex. Furthermore, the MP2 binding energy was a mere 7.1 kcal/mol, nearly 4 kcal/ mol less than that obtained via B3PW91. For reference, we note that previous results for the binding energy of H3N-BH3 range from 28.1 to 35.1 kcal/mol.18,21,25 We subsequently explored the structure with a few higherlevel post-HF methods with fairly large triple-ζ basis sets, with a few additional DFT methods with the aug-cc-pVTZ basis set, and with B3PW91 up to the aug-cc-pV5Z basis set. The complete set of structure and binding-energy results obtained
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Figure 1. Structure parameters and atomic charges for N2-BH3 from a few select computational methods (as indicated). Atomic charges were obtained from natural population analyses of the electron density at the level indicated.
TABLE 1: Computed Structural Properties and Binding Energies for N2-BH3a
a
method
basis set
R(B-N)
R(N-N)
R(B-H)
