Density Functional Theory and Perturbation Calculations on Some

Both these trends are in complete agreement with our calculations. Furthermore, it is gratifying to notice the very close agreement also between the a...
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J. Phys. Chem. 1996, 100, 15079-15082

15079

Density Functional Theory and Perturbation Calculations on Some Lewis Acid-Base Complexes. A Systematic Study of Substitution Effects Anne Skancke* and P. N. Skancke Department of Chemistry (IMR), UniVersity of Tromsø, N-9037 Tromsø, Norway ReceiVed: March 29, 1996; In Final Form: June 14, 1996X

Density functional theory and MP2 calculations have been performed on the Lewis acid-base complexes HnF3-nN f BH3 and H3N f BHnF3-n where n ) 0-3. Predicted equilibrium structures, binding energies, and charge transfers have been correlated to the degree of substitution on the base and on the acid separately. Calculations on the symmetrically substituted complexes H2FN f BH2F and F3N f BF3 have also been included. It is found that successive fluorine substitutions on nitrogen reduce the complex binding energies. The same trend is found for successive substitutions on boron. The findings are interpreted in terms of rehybridizations of the nitrogen lone-pair orbital, changes in the HOMO-LUMO gap, and back-donation to the pπ orbital on boron.

The acid-base concept is central in chemistry. Several underlying definitions of acids and bases are available, and the one by Lewis1,2 providing the basis for electron-pair donoracceptor complexes offers a versatile model for their reactions. Within the framework of this model the concepts of hard and soft acids and bases (the HSAB theory) were suggested by Pearson.3 A comprehensive discussion of the different acidbase models is given in the text by Finston and Rychtman.4 Within the Lewis theory the nucleophiles are divided into two classes: hard and soft bases. The hydroxide ion exemplifies the former, while the large iodide ion belongs to the latter category. Substances that bind strongly to hard bases are classified as hard acids. They are characterized by small size, high charge, low oxidation potential and lack of valence electrons that can be easily distorted or removed. Their soft counterparts are characterized by being large, having little or no positive charge and containing easily distorted or removed electrons (often in d subshells). In other words, they are characterized by high polarizability. One important ramification of the HSAB theory is that hard acids prefer to react with hard bases, and weak acids prefer to react with weak bases. The term “prefer” may imply two different interpretations: the product side of the reaction may be thermodynamically stabilized, leading to acid-base complexes having a large dissociation energy, or the acid-base reactivity may be high. It should be emphasized that the general HSAB theory does not have a well-defined physical basis and that physical properties attributed to hardness and softness do not always correlate well with experimental results or theoretical predictions. Nevertheless, the concept has proved to be a useful one. A fundamental approach to the concept of chemical hardness of an atom has been developed by Parr and co-workers.5-7 It is based on the chemical potential as formulated within the density functional theory (DFT). Recent evaluations of chemical potentials8 and of acid and base hardnesses based on group electronegativities have been published.9 In the present work we focus our attention on some Lewis acid-base interactions that result in dative bonds between boron and nitrogen. In particular, we have looked at the series HnF3-nN f BH3 and H3N f BHnF3-n where n ) 0-3. We have also included the symmetrically substituted complexes H2FN f BH2F and F3N f BF3. The primary purpose of our study X

Abstract published in AdVance ACS Abstracts, August 1, 1996.

S0022-3654(96)00944-6 CCC: $12.00

is to elucidate in a systematic way the changes introduced in the properties of the acid-base complexes by successive fluorine substitutions on the acid and on the base separately and also to evaluate the effects of symmetrical substitutions. This will also give a possibility to map interactions of the type hard-hard, hard-soft, soft-hard, and soft-soft and the properties of the resulting complexes. An additional aim of our investigation is to compare predictions made by second-order perturbation calculations with the ones obtained by a density functional approach encompassing a larger part of the electron correlation energy. To our knowledge DFT calculations have previously not been applied to studies of the complexes investigated here. The parent H3N f BH3 and H3N f BF3 and several other complexes have recently been extensively investigated by Frenking and co-workers10 using MP2 calculations. They studied the dative bond in some detail by the NBO partitioning scheme introduced by Weinhold and co-workers11 and also by the topological analysis developed by Bader.12 Computations In the DFT calculations we used the correlation functional of Lee, Yang, and Parr13 combined with the exchange functional of Becke14 (henceforth abbreviated BLYP). Perturbation calculations of the Møller-Plesset15 type were carried out to second order. In all calculations we used a 6-31G* basis set as implemented in Gaussian 94.16 This program was used throughout the calculations. All molecules were completely optimized, and analytical vibrational frequencies were calculated in all stationary points. This also gave us zero-point vibrational energies (ZPE). Geometries Completely optimized geometries for all species are given in Table 1 where valence angles have been omitted. For the complexes having nonequivalent bond distances of the same kind, average values are quoted in the table. The table shows that very small changes in the B-H and B-F bond distances are predicted as a result of fluorine substitution in BH3. Microwave studies17-19 of BH2F, BHF2, and BF3 give B-F bond distances in 1.321, 1.311, and 1.307 Å, respectively. Thus, the trend predicted is in agreement with the experimental results, although the absolute values are systematically longer than the experimental ones by roughly 0.01 Å. Our calculated B-F © 1996 American Chemical Society

15080 J. Phys. Chem., Vol. 100, No. 37, 1996

Skancke and Skancke

TABLE 1: Optimized Bond Distances R(X-Y) (in Å) and Net Charge q on N and Ba molecule NH3 NH2F NHF2

R(N-H) 1.017 1.030 1.024 1.037 1.028 1.043

NF3

R(N-F)

R(B-H)

BH2F BHF2 BF3

H2FN-BH3 (2) HF2N-BH3 (3) F3N-BH3 (4) H3N-BH2F (5) H3N-BHF2 (6) H3N-BF3 (7) H2FN-BH2F (8) F3N-BF3 (9) a

1.020 1.029 1.022 1.030 1.020 1.029 1.027 1.034

1.417 1.478 1.389 1.437 1.368 1.410

1.415 1.432 1.378 1.413

q(N)

q(B)

-1.117 -1.095 -0.405 -0.452 0.230 0.106 0.799 0.604 1.192 1.200 1.192 1.203 1.186 1.196

1.020 1.029 1.024 1.032 1.027 1.034

R(N-B)

1.434 1.462 1.407 1.437 1.384 1.420

BH3

H3N-BH3 (1)

R(B-F)

1.210 1.217 1.210 1.233 1.203 1.213 1.200 1.210 1.212 1.221 1.207 1.218 1.205 1.213

1.332 1.334 1.327 1.331 1.324 1.324

1.402 1.390 1.388 1.378 1.380 1.415 1.416 1.326 1.331

1.664 1.683 1.612 1.589 1.598 1.567 1.630 1.595 1.681 1.722 1.691 1.751 1.681 1.745 1.678 1.704 2.582 2.709

-0.975 -0.936 -0.299 -0.370 0.302 0.156 0.841 0.632 -1.016 -0.981 -1.043 -1.010 -1.060 -1.031 -0.334 -0.368 0.766 0.582

0.385 0.292 0.886 0.700 1.301 1.055 1.664 1.372 -0.042 -0.171 -0.081 -0.192 -0.102 -0.213 -0.085 -0.202 0.616 0.451 1.124 0.919 1.543 1.303 0.598 0.436 1.661 1.372

The first line for each compound gives results from MP2/6-31G* and the second one from BLYP/6-31G* calculations.

distance in BF3 is also in good agreement with results obtained by other recent theoretical calculations.20 The predicted changes induced in the amines by successive fluorination may be compared with available experimental information. Spectroscopically obtained structures21-23 for the series, NH2F, NHF2, and NF3 give the following sequence of N-F bond distances 1.433, 1.400, and 1.371 Å. For the NF3 molecule there is also an experimental24 value of 1.365 Å. The experimental results thus indicate that there is a drastic shortening of the N-F distance with increasing number of fluorine atoms. In the same sequence of molecules there is also observed a small but systematic lengthening of the N-H bond by successive fluorination. Both these trends are in complete agreement with our calculations. Furthermore, it is gratifying to notice the very close agreement also between the absolute N-F bond lengths measured and our predicted ones using the MP2 approximation, particularly for the species NH2F and NHF2. For this series of molecules the DFT approximation gives systematically longer bond distances than the MP2 calculations. The difference is around 0.03 Å for the N-F distance and a little smaller for the N-H distance. It has been suggested21 that the bond length changes discussed above are primarily due to a reversion of polar effects as the partial charge on the nitrogen atom changes from being negative in ammonia to positive in trifluoramine. With reference to our NBO analysis (Vide infra), it may be claimed that rehybridization on nitrogen as a result of increased fluorination also plays an important role in this context. For the acid-base complexes the data in Table 1 show that the predicted changes in the B-N bond length induced by fluorine substitution have the same trend using the two different

methods, although the absolute values are dependent on the calculational method applied. For the complexes 1, 2, and 3 (see Table 1) there is a successive decrease in the N-B distance whereas in 4 the distance is longer than in 3. The predicted changes are substantially larger using the DFT method. For the complexes with fluorine on B the effect on the N-B distance is smaller, although both methods predict an elongation of this distance by successive substitutions. The molecular structures of the complexes 1 and 7 have been determined experimentally both in the solid state and in the gas phase. For complex 1 the N-B bond distance has been determined to 1.564 Å25 in the solid state and 1.57 Å26 in the gas phase. For complex 7 the corresponding experimental values are 1.6027 and 1.673 Å,28 respectively. These values confirm the general observation that donor-acceptor complexes normally have shorter bonds in the crystalline state than in the gas phase.29 The experimental gas phase values for 1 and 7 are in fair agreement with our calculated equilibrium distances of 1.664 and 1.681 Å, respectively, obtained by the MP2 calculations. Our results are also in agreement with values obtained by recent SCF, Møller-Plesset, and CI calculations.30 The experimental information available indicates that for donor-acceptor complexes the BLYP3 approximation within the density functional theory gives too long donor-acceptor bonds in the acid-base complexes. This is consistent with the prediction of correspondingly lower binding energies and vibrational stretching frequencies as compared to the MP2 calculations. See Table 3. The NBO analysis reveals a change in the hybridization on the N atom by fluorine substitution. In NH3 the lone pair orbital on N has a composition that may be expressed as sp2.51. The

Lewis Acid-Base Complexes

J. Phys. Chem., Vol. 100, No. 37, 1996 15081

TABLE 2: Total Energies (in au), Frontier Orbital (HOMO and LUMO) Energies (in au), HOMO-LUMO Gap (in au), and ZPE (in kcal/mol)a molecule

Etot

HOMO

LUMO

gap

ZPE

NH3

-56.354 42 -56.518 60 -155.292 87 -156.677 79 -254.252 92 -254.860 38 -353.226 78 -354.057 93 -26.464 24 -26.578 85 -125.568 31 -125.892 40 -224.678 63 -225.208 72 -323.778 66 -324.513 52 -82.873 29 -83.148 11 -181.806 40 -182.306 47 -280.755 24 -281.479 14 -379.712 23 -380.658 56 -181.962 03 -182.443 26 -281.067 17 -281.752 32 -380.175 42 -381.062 73 -280.890 75 -281.594 11 -677.011 16 -678.574 14

-0.422 -0.197 -0.464 -0.214 -0.506 -0.243 -0.555 -0.295 -0.496 -0.300 -0.486 -0.272 -0.556 -0.317 -0.651 -0.339 -0.408 -0.218 -0.431 -0.244 -0.453 -0.267 -0.472 -0.281 -0.408 -0.199 -0.451 -0.228 -0.547 -0.264 -0.430 -0.211 -0.573 -0.308

0.219 0.051 0.207 -0.011 0.206 -0.030 0.238 -0.050 0.089 -0.092 0.119 -0.060 0.154 -0.027 0.196 0.005 0.168 0.001 0.162 -0.075 0.161 -0.081 0.195 -0.094 0.170 0.003 0.170 0.004 0.162 -0.002 0.165 -0.067 0.213 -0.062

0.641 0.248 0.671 0.203 0.712 0.213 0.793 0.245 0.585 0.208 0.605 0.212 0.710 0.290 0.847 0.344 0.576 0.219 0.593 0.169 0.614 0.186 0.667 0.187 0.578 0.202 0.621 0.232 0.709 0.262 0.595 0.144 0.786 0.246

22.15 20.99 17.68 16.55 12.52 11.49 6.60 5.82 17.06 16.28 14.73 14.04 11.61 11.11 7.92 7.62 45.08 42.88 39.85 37.42 34.21 31.79 28.10 25.94 41.55 39.41 37.73 35.70 33.68 31.90 36.31 34.18 15.12 13.86

NH2F NHF2 NF3 BH3 BH2F BHF2 BF3 1 2 3 4 5 6 7 8 9

a First line for each molecule is MP2 value, and the second one is DFT value. Basis set is 6-31G* in all calculations. The numbering of the different complexes is given in Table 1.

corresponding hybrides in H2FN, HF2N, and NF3 as sp1.33, sp0.77, and sp0.42, respectively. Thus, there is a substantial increase in s character of this orbital by successive fluorine substitutions. When these molecules enter into a complex with the Lewis acid BH3, the donating orbital on N undergoes a similar change in composition, i.e., from sp1.78 to sp0.83 in the series H3N f BH3 to F3N f BH3. This change alone would imply a shortening of the N-B bond distance due to increased s character in the lone pair on N. The predicted shortening of the N-B bond in the series ending with HF2N f BH3 is in accordance with this. However, the elongation of the bond by going further to F3N f BH3 indicates that other factors also contribute to the determination of the equilibrium distance. Electronic Structures Table 2 gives the total energies and the ZPE for the different building blocks and complexes together with the predicted energies of their frontier orbitals (HOMO and LUMO). In NH3 the HOMO is the lone pair on N, and the LUMO is a σ orbital that is antibonding in the N-H regions. By successive fluorine substitutions, the HOMO-LUMO gap increases at the MP2 level but remains roughly constant, and much smaller, in the DFT calculations. It is worth mentioning that in NHF2 and NF3 the net charge on N is found to be positive using both approximations, indicating an electrophilic character of these species. However, the HOMO in each of these molecules is still located strictly on the N atom, making the molecules able to behave as a nucleophile. In both calculational approximations

TABLE 3: Binding Energies De (in kcal/mol), Nitrogen-Boron Bond Distances R(N-B) (in Å), Stretching Vibrational Frequencies ν(N-B) (in cm-1), Net Charges q(N) and q(B), and Transfer of Charge from Base to Acid q(s,b)a molecule

De

1

34.4 (28.5) 31.8 (27.1) 30.9 (25.8) 31.3 (26.7) 23.9 (19.3) 25.0 (21.0) 13.3 (8.9) 13.7 (9.9) 24.8 (20.1) 20.2 (15.8) 21.5 (17.5) 15.7 (12.1) 26.7 (23.1) 19.2 (15.9) 18.6 (14.7) 15.0 (11.4) 3.6 (3.0) 1.7 (1.3)

2 3 4 5 6 7 8 9

R(N-B) ν(N-B) 1.664 1.683 1.612 1.589 1.598 1.568 1.630 1.595 1.681 1.722 1.691 1.751 1.681 1.745 1.678 1.704 2.582 2.709

673 608 666 659 638 655 694 630 600 508 584 490 690 633 686 617 76 62

q(N)

q(B)

q(s,b)

-0.97 -0.94 -0.30 -0.37 0.30 0.16 0.84 0.63 -1.01 -0.98 -1.04 -1.01 -1.06 -1.03 -0.33 -0.37 0.77 0.58

-0.04 -0.17 -0.08 -0.19 -0.10 -0.21 -0.08 -0.21 0.62 0.45 1.12 0.92 1.54 1.03 0.60 0.44 1.66 1.37

(0.32 (0.34 (0.31 (0.26 (0.28 (0.21 (0.24 (0.18 (0.29 (0.29 (0.27 (0.27 (0.26 (0.26 (0.27 (0.26 (0.01 (0.02

a

De values in parentheses are corrected for ZPE. The first line for each species is MP2/6-31G* value; the second one is BLYP/6-31G* value. The numbering of the different complexes is given in Table 1.

the energy of the HOMO is lowered from -0.42 to -0.56 au using MP2 and from -0.20 to -0.30 au using DFT in going from NH3 to NF3. This indicates that NH3 is a soft base and NF3 is hard one. Referring to the concept of like prefers like, our calculated dissociation energies are systematically reduced from H3N f BH3 to F3N f BH3, as BH3 is classified as a soft acid. Arguing along the same line for the fluorine-substituted BH3 species, we find, using both approximations, that the LUMO energies are elevated by successive F substitutions. This is consistent with a corresponding increase in the hardness of the acid as the LUMO in all cases is the virtually empty p orbital on B. Referring to the reasoning above, we would expect a decrease in binding energy from H3N f BH3 to H3N f BF3, in agreement with our findings. This conclusion is furthermore supported by the NBO analysis which shows that the backdonation from fluorine to the pπ orbital on boron increases from 0.11 to BH2F to 0.25 in BF3 using the MP2 method. The corresponding values obtained by the DFT calculations are 0.18 and 0.40. Thus, the population of the pπ orbital which is vacant in BH3 reduces the ability of this orbital to accept the lone pair from NH3 in the complex formation. Binding Energies Calculated binding energies De, shown in Table 3, are taken as the energy difference between the complex and the dissociation products (i.e., the Lewis acids and bases). The general trend comparing complexes 1 to 4, i.e., those with successive fluorination of the nitrogen atom, is a decrease in binding energy. This applies to both calculational approaches. A simple interpretation is that attachment of the electronegative fluorine atom to nitrogen diminishes the ability of the latter to donate electrons from its lone pair orbital to boron. This is in agreement with the total charge transfer obtained by the NBO analysis as shown in Table 3. The transfer is reduced from 0.32 to 0.24 electron using the MP2 approximation and from 0.34 to 0.18 electron using DFT calculations. However, in the language of the HSAB theory, one could say that the soft acid BH3 “prefers” the soft base NH3 to any of the harder fluorinated species. Within the same series of molecules, other trends are harder to explain. For instance, why is inclusion of more

15082 J. Phys. Chem., Vol. 100, No. 37, 1996 correlation energy (from the DFT method) more important for the less fluorinated species within this group? This point has been addressed by Finston and Rychtman,4 who have pointed out that van der Waals or London dispersion forces induce mutual polarizations in soft-soft adducts; hence, correlation plays a more prominent role in these cases. The predicted dissociation energies follow a trend that is in agreement with this assumption. At the MP2 level this energy is reduced from 28.5 to 8.9 kcal/mol by going from NH3 to NF3 in the complex. The corresponding change is from 27.1 to 9.9 kcal/mol using the DFT approximation. In the series with fluorinated boron (complexes 1 and 5-7) there is also a general trend of decreasing binding energies upon fluorination, but in this case the trend is broken as NH3 f BF3 has a larger binding energy than its congener NH3 f BHF2. Other indicators such as equilibrium N-B distances and N-B bond stretching frequencies, also quoted in Table 3, show the same variation. Thus, it appears that the interaction between the soft base NH3 and the hard acid BF3 is energetically more favorable than the one with the less fluorinated BHF2 involved. We suggest that in 7 electrostatic forces dominate due to a very high positive charge on boron which may overcompensate the opposite effec of back-donation from fluorine. It should be pointed out, however, that all complexes in the series 5-7 are predicted to be more weakly bound than the parent complex 1 and that the variations within the series 5-7 are very small. The symmetrically substituted complexes 8 and 9 have predicted properties that conform to the trends discussed above. In both of these complexes fluorine substitution on nitrogen reduces the electron population of its lone-pair orbital, and the substitution on boron populates its pπ orbital by back-donation from fluorine lone pairs. This reduces simultaneously the donating power of N and the accepting ability of B. This tendency is brought to an extreme, virtually nonbinding, situation in complex 9, where the calculated binding energy is 1-3 kcal/ mol depending on calculational method and where the charge transfer is virtually zero. The electrostatic attraction invoked in the case of 7 does not apply in 9 due to a large positive charge also on nitrogen. Acknowledgment. We thank The Norwegian Research Council for granting CPU time on CRAY at the SINTEF Supercomputing Center, Trondheim, Norway.

Skancke and Skancke References and Notes (1) Lewis, G. N. Valence and the Structure of Atoms and Molecules; Chemical Catalog Co.: New York, 1923. (2) Lewis, G. N. J. Franklin Inst. 1938, 226, 293. (3) Pearson, R. G. J. Am. Chem. Soc. 1963, 85, 3533. (4) Finston, H. L.; Rychtman, A. C. A New View of Current AcidBase Theories; John Wiley & Sons: New York, 1982. (5) Parr, R. G.; Donnelly, R. A.; Levy, M.; Palke, W. E. J. Chem. Phys. 1978, 68, 3801. (6) Donnelly, R. A.; Parr, R. G. J. Chem. Phys. 1978, 69, 4431. (7) Parr, R. G.; Yang, W. Density-Functional Theory of Atoms and Molecules; Oxford University Press: New York, 1989. (8) Ohwada, K. J. Phys. Chem. 1993, 97, 1832. (9) Shea, J.; Whitehead, M. A. Philos. Mag. B 1994, 69, 807. (10) Volker, J.; Frenking, G.; Reetz, M. T. J. Am. Chem. Soc. 1994, 116, 8741. (11) Reed, A. E.; Curtiss, L. A.; Weinhold, F. Chem. ReV. 1988, 88, 899. (12) Bader, R. F. W. Acc. Chem. Res. 1985, 18, 9. (13) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785. (14) Becke, A. D. Phys. ReV. A 1988, 38, 3098. (15) Møller, C.; Plesset, M. S. Phys. ReV. 1934, 46, 618. (16) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheseman, J. R.; Keith, T.; Peterson, G. A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.; Peng, C. Y.; Ayala, P. Y.; Chen, W.; Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; HeadGordon, M.; Gonzalez, C.; Pople, J. A. Gaussian 94, Revision B.1; Gaussian, Inc., Pittsburg, PA, 1995. (17) Takeo, H.; Sugie, M.; Matsumura, C. J. Mol. Spectrosc. 1993, 158, 201. (18) Kasuya, T.; Lafferty, W. J.; Lide, Jr., D. R. J. Chem. Phys. 1968, 48, 1. (19) Yamamoto, S.; Kuwabara, R.; Takami, M.; Kuchitsu, K. J. Mol. Spectrosc. 1986, 115, 333. (20) Brinck, T.; Murray, J. S.; Politzer, P. Inorg. Chem. 1993, 32, 2622. (21) Christen, D.; Minkwitz, R.; Nass, R. J. Am. Chem. Soc. 1987, 109, 7020. (22) Lide, D. R. J. Chem. Phys. 1963, 38, 456. (23) Sheridan, J.; Gordy, W. Phys. ReV. 1950, 79, 513. (24) Otake, M.; Matsumura, C.; Morino, Y. J. Mol. Spectrosc. 1968, 28, 316. (25) Bu¨hl, M.; Steinke, T.; Schleyer, P.v.R. Angew. Chem., Int. Ed. Engl. 1991, 30, 1160. (26) Thorne, L. R.; Suenram, R. D.; Lovas, F. J. J. Chem. Phys. 1983, 78, 167. (27) Hoard, J. L.; Geller, S.; Cashin, W. M. Acta Crystallogr. 1951, 4, 396. (28) Fujiang, D.; Fowler, P. W.; Legon, A. C. J. Chem. Soc., Chem. Commun. 1995, 113. (29) Dvorak, M. A.; Ford, R. S.; Suenram, R. D.; Lovas, F. J.; Leopold, K. R. J. Am. Chem. Soc. 1992, 114, 108. (30) Volker, J.; Frenking, G. J. Chem. Soc., Chem. Commun. 1994, 1489.

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