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J. Phys. Chem. B 2007, 111, 1408-1415
B-N Distance Potential of CH3CN-BF3 Revisited: Resolving the Experiment-Theory Structure Discrepancy and Modeling the Effects of Low-Dielectric Environments James A. Phillips*,† and Christopher J. Cramer‡ Department of Chemistry, UniVersity of WisconsinsEau Claire, 105 Garfield AVenue, Eau Claire, Wisconsin 54701, and Department of Chemistry and Supercomputing Institute, UniVersity of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455 ReceiVed: August 24, 2006; In Final Form: NoVember 5, 2006
We have re-examined the B-N distance potential of CH3CN-BF3 using MP2, DFT, and high-accuracy multicoefficient methods (MCG3 and MC-QCISD). In addition, we have solved a 1-D Schro¨dinger equation for nuclear motion along the B-N stretching coordinate, thereby obtaining vibrational energy levels, wave functions, and vibrationally averaged B-N distances. For the gas-phase, MCG3//MP2/aug-cc-pVTZ potential, we find an average B-N distance of 1.95 Å, which is 0.13 Å longer than the corresponding equilibrium value. In turn, this provides solid evidence that the long-standing discrepancy between the experimental (R(BN) ) 2.01 Å) and theoretical (R(B-N) ) 1.8 Å or R(B-N) ) 2.2-2.3 Å) distances may be genuine, stemming from large amplitude vibrational motion in the B-N stretching coordinate. Furthermore, we have examined the effects of low-dielectric media ( ) 1.1-5.0) on the structure of CH3CN-BF3 by calculating solvation free energies (PCM/B97-2/aug-cc-pVTZ) and adding them to the gas-phase, MCG3 potential. These calculations demonstrate that the inner region of the potential is stabilized to a greater extent by these media, and correspondingly, the equilibrium and average B-N distances decrease with increasing dielectric constant. We find that the crystallographic structural result (R(B-N) ) 1.63 Å) is nearly reproduced with a dielectric constant of only 5.0, and also predict significant structural changes for values of 1.1-1.5, consistent with results from matrix-isolation-IR experiments.
Introduction Due to its remarkable structural properties, the donoracceptor complex formed from CH3CN and BF3 has been studied extensively.1-17 Significant results include a gas-phase structure4 that depicts an intermediate dative bond, lying between the van der Waals and covalent limits, and furthermore, this structure differs markedly from the crystallographic result,5 illustrating that the B-N bond contracts by nearly 0.4 Å upon crystallization.3 Matrix-isolation-IR studies6-9 indicate that even very inert, bulk condensed-phase environments significantly alter the structure of the complex, to the extent that such a conclusion can be drawn from IR frequency shifts. To a great extent, the frequencies of the C-N stretching and BF3-localized vibrational modes shift systematically across a range of environments,9 including the solid state,10 and seem to reflect the degree to which these various media compress the dative bond relative to the gas phase. Naturally, CH3CN-BF3 also attracted the attention of theoreticians,11-17 but ab initio results differed markedly from the experimental structure, which has a B-N distance of 2.01 Å.4 Three studies conducted in the mid-1990s12-14 obtained structures with B-N distances between 2.2 and 2.3 Å, and in a more recent study,15 a structure with a B-N distance of 1.80 Å was obtained. Indeed, this situation is rather unusual, given the size of the system and that these studies utilized MP2 calculations with double-ζ basis sets, an approach that has * To whom correspondence should be addressed. E-mail: phillija@ uwec.edu. Phone: 715-836-5399. Fax: 715-836-4979. † University of WisconsinsEau Claire. ‡ University of Minnesota.
reproduced experimental structural results for many similar complexes.14 In previous computational work,17 one of us found that the B-N distance potential of CH3CN-BF3 was remarkably flat and exhibited two nearly isoenergetic minima at 1.919 and 2.315 Å (at the B3LYP/aug-cc-pVQZ level of theory). Which minimum was global (and in turn which equilibrium structure was obtained) was found to be quite sensitive to the presence of diffuse functions in the basis set (for both MP2 and B3LYP results). In most cases, including diffuse functions (signified by “+” or “aug”) favored the shorter-minimum structures (1.81.9 Å) and excluding them favored the longer (2.2-2.3 Å) structures. Indeed, this effect underlies the discrepancy among the previous computational structures.12-15 Ultimately, the flat, anharmonic potential led us to suspect that the discrepancy between the experimental and theoretical structures was genuine, the result of large amplitude vibrational motion along the B-N stretching coordinate. The results presented herein further solidify this notion. We have re-examined the gas-phase potential using several DFT methods, MP2, as well as high-accuracy, multicoefficient Gaussian-3 (MCG3)18 and multicoefficient quadratic configuration interaction (MC-QCISD)19 calculations. Furthermore, we have solved a 1-D vibrational Schro¨dinger equation for nuclear motion along the B-N stretching coordinate, thereby obtaining wave functions, vibrational energies, and average B-N distances. These simulations do predict a significant difference between the equilibrium and vibrationally averaged B-N bond lengths. We have also examined the effects of low-dielectric media by calculating the free energy of solvation with the polarized continuum model (PCM) and adding (the electrostatic component of) this quantity to the gas-phase potential. Average
10.1021/jp065485d CCC: $37.00 © 2007 American Chemical Society Published on Web 01/25/2007
B-N Distance Potential of CH3CN-BF3
J. Phys. Chem. B, Vol. 111, No. 6, 2007 1409
bond lengths obtained from these curves are quite consistent with structural changes that occur in inert condensed-phase media, as implied by matrix-IR frequency shifts.9 Computational Methods HF, MP2, and DFT20 calculations were performed using Gaussian 03,21 version b.0.1, for all methods except O3LYP, for which version c.0.3 was used. For optimizations, all geometries were constrained to C3V symmetry (in the eclipsed conformation) and convergence criteria were set using the “opt ) tight” option, which sets the maximum and root-mean-square (rms) forces to 1.5 × 10-5 and 1.0 × 10-5 hartrees/bohr, respectively, and the maximum and rms displacements to 6.0 × 10-5 and 4.0 × 10-5 bohr, respectively. An ultrafine grid was employed for all DFT calculations. The aug-cc-pVTZ basis set20 was used almost exclusively, but for equilibrium geometry calculations, we also used the cc-pVTZ basis set to assess the effect of diffuse functions. Also, for a few methods, the augcc-pVQZ basis set was used to assess convergence behavior and explore the extent of basis set superposition error (BSSE). Previously, we noted (for B3LYP) that while the results were approaching convergence at the aug-cc-pVTZ level,17 they were still not completely converged at the aug-cc-pVQZ level. Nonetheless, we chose the aug-cc-pVTZ basis set as the best compromise between size and efficiency. MCG318 and MCQCISD19 energies were obtained using MULTILEVEL version 4.0.22 The B-N potential was constructed via a series of pointwise calculations at fixed distances. For the gas-phase potential via DFT and MP2, the B-N distance was varied from 1.55 to 3.60 Å in 0.05 Å steps, and all other degrees of freedom were optimized (using opt ) tight) at every point. For the MCG3 and MC-QCISD potentials, the energy was calculated for the MP2/aug-cc-pVTZ geometries, at distances ranging from 1.6 to 3.0 Å, in 0.1 Å steps. The effects of dielectric media, with values ranging from 1.1 to 5.0, were examined using the polarized continuum model (PCM),23 with the B97-2 density functional and the aug-cc-pVTZ basis set. The range of distances in these calculations was shifted inward slightly (from 1.40 to 1.85 Å in 0.05 Å steps and from 1.9 to 3.0 Å in 0.1 Å steps), due to changes in the shape of the potential. The electrostatic component of the solvation free energy (i.e., 〈Ψ(f)|H + V(f)/ 2|Ψ(f)〉 - 〈Ψ(g)|H|Ψ(g)〉, where (g) implies optimization in the gas phase, (f) implies optimization in the condensed phase, H is the gas-phase Hamiltonian operator, V is the reaction-field operator, and Ψ is the relevant Hartree-Fock or Kohn-Sham wave function) was added to the gas-phase, MCG3 potential (with frozen geometries), yielding hybrid curves representing the B-N potential in dielectric media. To gauge the structural changes induced by dielectric media, and to assess the performance of a purely DFT-based approach, another set of curves was obtained using the B97-2 functional and allowing the other degrees of freedom (i.e., aside from the B-N distance) to relax at each point. We chose to include only the electrostatic component of the solvation free energy because we are not attempting to make specific predictions for individual solvents but rather are examining the magnitude of the sensitivity of the solute electronic structure to the polarity of the surrounding medium. In a real solvent (as opposed to a dielectric continuum), there would also be cavitation, dispersion, and Pauli repulsion influences on the bonding potential, but variations in bond length associated with varying electrostatics are not so large that we would expect nonelectrostatic components to vary by particularly large margins.
Figure 1. Structural parameters for CH3CN-BF3 (eclipsed, C3V).
Vibrational wave functions, energy levels, and average B-N distances were obtained using the FGHEVEN program24 which utilizes the Fourier grid Hamiltonian method25 to solve a onedimensional Schro¨dinger equation for an arbitrary potential. To obtain the potential functions needed for FHGEVEN, we fit each gas-phase curve to a pair of fifth-order polynomial functions, one for the inner region (R(B-N) < 4.15 bohr for the gas phase, R < 3.40 bohr for the condensed phase) and one for the outer region (R(B-N) > 4.15 bohr for the gas phase, R(B-N) > 3.40 bohr for the condensed phase). For the gas-phase curves, these functions reproduced the calculated energies along the curves to within a maximum of 1 × 10-5 hartree for the MP2 and DFT curves (average residual ) 2 × 10-6 hartree) and to within a maximum of 4 × 10-5 hartree for the MCG3//MP2 curve (average residual 2 × 10-5 hartree). In general, the maximum residuals for fits to the condensed-phase curves were approximately 10-fold higher (maximum residuals of 2 × 10-4 hartree or less) and average residuals ranging from 1 × 10-5 to 3 × 10-5 hartree. The integration grid consisted of 200 points ranging from 2.6 to 6.6 bohr for gas-phase curves and 170 points ranging from 2.6 to 6.0 bohr for condensed-phase curves. As in our previous study of HCN-BF3,26 we considered different options for the reduced mass value. Treating the system as a pseudo-diatomic molecule, in which the individual atoms of the BF3 and CH3CN subunits move coherently with one another throughout a vibrational period of the B-N stretching mode, one might estimate the reduced mass by simply taking the product of the CH3CN and 11BF3 masses and dividing by their sum. Doing so results in a value of 25.59 amu. We compared this to the value used by Gaussian for the B-N stretching mode in the B98/aug-cc-pVTZ frequency calculation (the potential obtained using this method compared most favorably to MCG3, vide infra) and found these latter to be much lower (8.206 amu for the 11B isotopomer). The difference derives from a coupling of the BF3 umbrella mode and the B-N stretch (see ref 24). In the end, we ran FGHEVEN with mass values of 25.59, 8.206, and 6.161 amu (the latter is the value obtained directly from 11B and N atomic masses) and obtained vibrationally averaged B-N bond lengths of 1.89, 1.95, and 1.97 Å, respectively. This indicates that the choice of reduced mass does have a significant effect on the results. Nonetheless, given the coupling between the umbrella mode and B-N stretch (the z-amplitudes of the displacement vectors for the F atoms are 45% of those for the B atom), the value obtained from the Gaussian B98/aug-ccpVTZ frequency calculation seemed most reasonable, and we set the reduced mass to 8.206 amu for the remainder of this work. Results and Discussion Equilibrium Structure. Structural parameters for CH3CNBF3 (C3V, eclipsed) are displayed in Figure 1, and equilibrium values obtained using HF, MP2, and various DFT methods (and the aug-cc-pVTZ basis set) are included as Supporting Information (Table S1). Table 1 lists B-N distances and N-B-F angles
1410 J. Phys. Chem. B, Vol. 111, No. 6, 2007
Phillips and Cramer
TABLE 1: B-N Distances and N-B-F Angles for Equilibrium Geometries Obtained Using HF, MP2, and DFT Methods with the auc-cc-pVTZ and cc-pVTZ Basis Sets method HF MP2
B3LYP MPW1K B98 B97-2 O3LYP B3PW91 mPW1PW91
BPW91 HCTH mPWPW91 BLYP OLYP a
basis set
R(B-N)a
